EBS Radionuclide Transport Abstraction REV 01, ICN 00

ANL-WIS-PA-000001

November 2004 


1. PURPOSE 
The purpose of this analysis model report is to develop and analyze the engineered barrier 
system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II 
model validation, as identified in Technical Work Plan for: Near-Field Environment and 
Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report 
Integration (BSC 2004 [DIRS 170775]). The EBS radionuclide transport abstraction (or EBS RT 
Abstraction) is the conceptual model used in the total system performance assessment for the 
license application (TSPA-LA) to determine the rate of radionuclide releases from the EBS to the 
unsaturated zone (UZ). 
The EBS RT Abstraction conceptual model consists of two main componentsa flow model and 
a transport model. Both models are developed mathematically from first principles in order to 
show explicitly what assumptions, simplifications, and approximations are incorporated into the 
models used in the TSPA-LA. 
The flow model defines the pathways for water flow in the EBS and specifies how the flow rate 
is computed in each pathway. The input to this model is the seepage flux into a drift. The 
seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by 
the drip shield and some passing through breaches in the drip shield that might result from 
corrosion or seismic damage. The flux through drip shield breaches is potentially split by the 
waste package, with some (or all) of the flux being diverted by the waste package and some 
passing through waste package breaches that might result from corrosion or seismic damage. 
The flow model is validated in an independent model validation technical review. The drip 
shield and waste package flux splitting algorithms are developed and validated using 
experimental data. 
The transport model considers advective transport and diffusive transport from a breached waste 
package. Advective transport occurs when radionuclides that are dissolved or sorbed onto 
colloids or both are carried from the waste package by the portion of the seepage flux that passes 
through waste package breaches. Diffusive transport occurs as a result of a gradient in 
radionuclide concentration and may take place while advective transport is also occurring, as 
well as when no advective transport is occurring. Diffusive transport is addressed in detail 
because it is the sole means of transport when there is no flow through a waste package, which is 
postulated to predominate during the regulatory compliance period in the nominal and seismic 
cases. The advective transport rate, when it occurs, is generally greater than the diffusive 
transport rate. Colloid-facilitated advective and diffusive transport is also modeled and is 
presented in detail in Appendix B of this model report. 
Additional submodels and model parameters developed in this model report include: 
 Diffusion inside a waste packageThe time-dependent quantity of corrosion products 
inside a breached waste package is estimated; this enables the surface area available for 
adsorption of water to be approximated, which in turn gives the water saturation through 
which diffusion of radionuclides may occur. 
 Sorption onto stationary corrosion products in a breached waste package. 

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 Diffusion in the invert, accounting for the dependence of diffusion on porosity, 
saturation, and temperature. 
 Sorption in the invert. 
 EBS-UZ interface submodelimplementation in the TSPA-LA includes this submodel to 
provide a realistic concentration boundary condition. 
Parameter uncertainty associated with each model and submodel is discussed. The transport 
model and the EBS-UZ interface submodel are validated using corroborative data and models as 
well as an independent model validation technical review. 
Alternative conceptual models considered include: 
 A bathtub flow model in which water must fill a breached waste package before any 
can flow out, as opposed to the flow-through model that is used. 
 Models that show the effect of limitations on diffusion of water vapor and oxygen into a 
breached waste package and consequential delays in releases of radionuclides. 
 A dual-continuum invert flow and transport submodel. 
 Alternative invert diffusion coefficient submodels. 
Output from the EBS RT Abstraction includes: 
 The flow modelthe algorithms for computing the flow in each flow path within the 
EBS, with parameter values or sources for those parameters used in the model. 
 The transport modela model for advective and diffusive transport, specifying the 
computational procedure for both commercial spent nuclear fuel (CSNF) and codisposal 
waste packages in both seep and no-seep environments, with parameter values or sources 
for those parameters used in the model. 
 Ranges and distributions for parameters that are uncertain and are sampled in the 
TSPA-LA implementation of the EBS RT Abstraction. 
The scope of this abstraction and report is limited to flow and transport processes. Specifically, 
this report provides the algorithms that are implemented in TSPA-LA for transporting 
radionuclides using the flow geometry and radionuclide concentrations determined by other 
elements of the TSPA-LA model. The EBS RT Abstraction also identifies the important 
processes that are evaluated with process-level or component-level using analytical or numerical 
solutions. 
This model report was prepared to comply with the U.S. Nuclear Regulatory Commission (NRC) 
rule for high-level radioactive waste (HLW), 10 CFR Part 63 [DIRS 158535], which requires the 
U.S. Department of Energy (DOE) to conduct a performance assessment to demonstrate 
compliance with postclosure performance objectives. The results from this conceptual model 
allow Bechtel SAIC Company LLC (BSC) to address portions of the acceptance criteria 
presented in Yucca Mountain Review Plan, Final Report (NRC 2003 [DIRS 163274]). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 1-3 November 2004 
The following reports provide input to the EBS RT Abstraction: 
 Probability Analysis of Corrosion Rates for Waste Package Materials 
 Multiscale Thermohydrologic Model 
 Unsaturated Zone and Saturated Zone Transport Properties (U0100) 
 Thermal Conductivity of the Potential Repository Horizon 
 Calibrated Properties Model 
 UZ Flow Models and Submodels 
 Radionuclide Transport Models Under Ambient Conditions 
 Analysis of Hydrologic Properties Data 
 Drift-Scale Radionuclide Transport. 
The following documents use output from the EBS RT Abstraction as direct input: 
 In-Package Chemistry Abstraction 
 Total System Performance Assessment (TSPA) Model/Analysis for the License 
Application. 

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EBS Radionuclide Transport Abstraction 
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2. QUALITY ASSURANCE 
Development of this model report and the supporting analyses have been determined to be 
subject to the Office of Civilian Radioactive Waste Management quality assurance program 
(BSC 2004 [DIRS 170775], Section 8). Approved quality assurance procedures identified in 
Section 4 of the technical work plan have been used to conduct and document the activities 
described in this model report. Section 8 of the technical work plan also identifies the methods 
used to control the electronic management of data during the analysis and documentation 
activities. 
This model report provides models for evaluating the performance of the engineered barrier 
system, including the drip shields, waste packages, and invert, which are classified in the Q-List 
(BSC 2004 [DIRS 168361]) as Safety Category because they are important to waste isolation, as 
defined in AP-2.22Q, Classification Analyses and Maintenance of the Q-List. The results of this 
report are important to the demonstration of compliance with the postclosure performance 
objectives prescribed in 10 CFR Part 63 [DIRS 158535]. The report contributes to the analysis 
data used to support performance assessment; the conclusions do not directly impact engineered 
features important to safety, as defined in AP-2.22Q. This report was prepared in accordance 
with AP-SIII.10Q, Models. 

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EBS Radionuclide Transport Abstraction 
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3. USE OF SOFTWARE 
3.1 MICROSOFT EXCEL 
Microsoft Excel 2002 Add Trendline capability was used to perform a statistical analysis of 
diffusion coefficient values reported in Section 6.3.4.1.1. Microsoft Excel 2002 was also used to 
analyze experimental data used to develop and validate the drip shield and waste package flux 
splitting submodels (Sections 6.5.1.1.2.4, 6.5.1.1.3, and 7.1.1). A calculation of the potential 
mass of corrosion products in fully degraded waste packages, summarized in Table 6.3-4, is 
described in Appendix A. A sample calculation to demonstrate the solution procedure used in 
the colloid transport model, described in Appendix B, was also carried out using Microsoft 
Excel 2002. A complete description of the formulas, inputs, and outputs used in the Microsoft 
Excel analysis of the drip shield experimental data is provided in Appendices C (the drip shield 
flux splitting submodel), D (the waste package flux splitting submodel), and E (validation of the 
flux splitting submodels). The formulas, inputs, and outputs used in Microsoft Excel to perform 
the sample colloid transport calculation are presented in Appendix F, and the invert diffusion 
properties model analysis is described in Appendix G. 
3.2 GOLDSIM 
GoldSim V8.01 Service Pack 1 (STN: 10344-8.01 SP1-00) (Golder Associates 2003 
[DIRS 166572]) is run on Microsoft Windows 2000 on Dell workstation with Intel Xeon 
processor and was developed to perform dynamic, probabilistic simulations. GoldSim V8.01 
was used in accordance with LP-SI.11Q-BSC, Software Management. GoldSim calculations 
were done in support of validation of models developed in the EBS RT Abstraction (see 
Section 7.3.1). GoldSim calculations were also run to verify an alternative model 
implementation in Section 6.6.4.4. GoldSim V8.01 is used in these validation calculations 
because it is used in the TSPA-LA model. This software was used within the range of validation 
and was obtained from Configuration Management. 

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EBS Radionuclide Transport Abstraction 
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4. INPUTS 
4.1 DIRECT INPUT 
4.1.1 Data 
Inputs in this section are used as direct input data for the models and analyses presented in 
Section 6. Tables 4.1-1 through 4.1-6 and Figure 4.1-1 summarize the relevant input data and 
the sources for these values. Data in this section are presented as found in the source documents; 
unit conversions and manipulation of data are not done in this section, but are performed as 
needed in Section 6. 
Data uncertainty is addressed in Section 6. In particular, corrosion rates of carbon and stainless 
steels are listed in Table 6.5-13 as model input with ranges and distributions determined from the 
data in Table 4.1-1. The breached drip shield experimental test data in Tables 4.1-2 
through 4.1-6 and Figure 4.1-1 are evaluated in Section 6.5.1, resulting in uncertain model input 
parameters listed in Table 6.5-13. 
Table 4.1-1. Input Data for EBS RT Abstraction 
Value 
Model Input Rate (m yr-1) ECDF Source 
Rate of corrosion of A 516 and A 27 carbon 
steels in simulated dilute well J-13 water at 
60C, long term (= 1 yr); ECDF 
65.77 
66.75 
69.84 
70.00 
71.25 
72.21 
72.64 
72.87 
72.89 
73.47 
74.29 
74.51 
74.60 
75.41 
77.31 
79.29 
80.00 
80.87 
83.26 
83.66 
83.74 
85.68 
90.97 
106.93 
0.042 
0.083 
0.125 
0.167 
0.208 
0.250 
0.292 
0.333 
0.375 
0.417 
0.458 
0.500 
0.542 
0.583 
0.625 
0.667 
0.708 
0.750 
0.792 
0.833 
0.875 
0.917 
0.958 
1.000 
DTN: MO0409SPAACRWP.000 
[DIRS 172059]; Spreadsheet 
ECDF_metals2.xls; Worksheet 
A516-Carbon Steel, Columns 
B & C, Rows 530 

EBS Radionuclide Transport Abstraction 
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Table 4.1-1. Input Data for EBS RT Abstraction (Continued) 
Value 
Model Input Rate (m yr-1) ECDF Source 
Rate of corrosion of 316L stainless steel in 
fresh water at 50100C; ECDF 
0.037 
0.1016 
0.109 
0.1524 
0.154 
0.1778 
0.2032 
0.2286 
0.254 
0.2794 
0.51 
0.063 
0.125 
0.188 
0.250 
0.313 
0.375 
0.438 
0.563 
0.750 
0.813 
1.000 
DTN: 
MO0409SPAACRWP.000 
[DIRS 172059]; Spreadsheet 
ECDF_metals2.xls; 
Worksheet 316 ss, 
Columns L & M, Rows 515 
ECDF= empirical cumulative distribution function 
Table 4.1-2. Atlas Breached Drip Shield Experiments on Smooth Drip Shield Surface  Dripping on 
Crown  Flow into Breaches 
Water Input Mass (g) Water Collection Mass (g) 
Drip Location Tare Final 
Breach 
Where 
Water Was 
Collected Initial Final 
Single Patch Q(film) Tests (DTN: MO0207EBSATBWP.023 [DIRS 163402]) 
8 cm right of Patch 4 centerline -50.32 -228.52 B4 107.60 129.62 
Patch 5 centerline -12.66 -176.40 B5 109.40 130.52 
4 cm left of Patch 5 centerline -210.48 -344.27 B5 109.18 118.28 
Patch 4 centerline 52.77 -135.86 B4 107.57 129.82 
Multiple Patch Tests (DTN: MO0207EBSATBWP.024 [DIRS 163401]) 
27 cm right of drip shield center -0.51 -276.65 B5 109.10 113.59 
27 cm left of drip shield center 710.10 433.27 B4 107.77 110.40 
81 cm left of drip shield center 755.52 529.3 B4 107.18 110.63 
81 cm right of drip shield center 768.79 547.67 B5 107.99 111.53 
Bounding Flow Rate Tests (DTN: MO0207EBSATBWP.025 [DIRS 163403]) 
54 cm left of drip shield center 853.83 516.11 B4 107.35 153.76 
54 cm left of drip shield center 769.21 680.32 B4 107.73 115.61 
27 cm left of drip shield center 857.57 524.88 B4 107.22 110.57 
27 cm left of drip shield center 872.20 771.25 B4 107.00 107.65 
27 cm right of drip shield center 907.84 529.11 B5 109.81 112.26 
27 cm right of drip shield center* 782.29 644.57 B5 109.55 114.00 
*Drip location shown incorrectly as 7 cm in DTN: MO0207EBSATBWP.025 [DIRS 163403]; correct value of 27 cm 
obtained from Howard 2002 [DIRS 161522], p. 33. 
ECDF= empirical cumulative distribution function 

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Table 4.1-3. Atlas Breached Drip Shield Experiments on Smooth Drip Shield Surface  Dripping on 
Crown  Rivulet Spread Data  33 from Crown 
Drip Location Left (cm) Right (cm) 
Relevant 
Patch 
Single Patch Q(film) Tests (DTN: MO0207EBSATBWP.023 [DIRS 163402]) 
8 cm right of Patch 4 centerline 15.0 28.5 4 
Patch 5 centerline 28.0 0 5 
4 cm left of Patch 5 centerline Not recorded 21 5 
Patch 4 centerline 11.0 26.5 4 
Multiple Patch Tests (DTN: MO0207EBSATBWP.024 [DIRS 163401]) 
27 cm right of drip shield center 13.0 29.0 5 
27 cm left of drip shield center 21.0 21.5 4 
81 cm left of drip shield center 17.0 23.5 4 
81 cm right of drip shield center 20.0 18.0 5 
Bounding Flow Rate Tests (DTN: MO0207EBSATBWP.025 [DIRS 163403]) 
54 cm left of drip shield center (High Flow Rate) 22.0 32.0 4 
54 cm left of drip shield center (Low Flow Rate) 10.5 30.0 4 
27 cm left of drip shield center (High Flow Rate) 24 19 4 
27 cm left of drip shield center (Low Flow Rate) 10.0 8.0 4 
27 cm right of drip shield center (High Flow Rate) 24.0 16.5 5 
27 cm right of drip shield center (Low Flow Rate)* 20.0 13.5 5 
*Drip location shown incorrectly as 7 cm in DTN: MO0207EBSATBWP.025 [DIRS 163403]; correct value of 27 cm 
obtained from Howard 2002 [DIRS 161522], p. 33. 
Table 4.1-4. Atlas Breached Drip Shield Experiments on Smooth Drip Shield Surface  Dripping on 
Crown  Splash Radius Tests 
No. Drips Splash Radius (cm) Comments 
Left Right 
Splash Radius Test #1 (DTN: MO0207EBSATBWP.022 [DIRS 163400]) 
1 1.6 1.6 Measured at outer fringe 
2 26.5 18.4 Measured outer fringe 
5 37.5 18.4 Measured outer fringe 
13 37.5 27.8 Measured outer fringe 
21 37.5 31.5 Measured outer fringe 
27 52.8 35.0 Measured outer fringe 
38 59.9 54.2 Measured outer fringe 
49 25.0 29.0 Measured inner cluster 
49 72.0 63.2 Measured outer fringe 
60 40.0 40.0 Measured inner cluster 
60 72.5 54.2 Measured outer fringe 
90 48.0 43.0 Measured inner cluster 
Single Patch Q(film) Tests (DTN: MO0207EBSATBWP.023 [DIRS 163402]) 
  54.5 Patch 5, center, crown 
  82 Patch 4, center, crown 
  86 Patch 4, 8 cm right of center, crown 
NOTE:  indicates no measurements were made. 

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Table 4.1-5. Atlas Breached Drip Shield Experiments on Smooth Drip Shield Surface  Dripping at 
Off-Crown Locations  Flow into Breaches 
Water Input Mass (g) Water Collection Mass (g) 
Drip Location Tare Final 
Breach 
Where Water 
Was 
Collected Initial Final 
Single Patch Q(splash) Tests (DTN: MO0207EBSATBWP.023 [DIRS 163402]) 
P5, 17.5 cm left of center, 33 529.45 439.68 B5 108.57 108.86 
P4, center, 33 685.41 548.20 B4 106.86 216.70 
P4, 17.5 cm right of center, 33 670.30 538.88 B4 106.75 115.71 
P4, 17.5 cm right of center, 16.5 667.12 516.36 B4 106.80 108.59 
P4, centerline, 16.5 669.72 529.82 B4 106.98 191.33 
P5, 17.5 cm left of center, 16.5 661.50 474.00 B5 109.13 111.79 
P6, 35.5 cm left of center, 16.5 661.82 519.54 B4 107.31 108.90 
P5, centerline, 16.5 676.13 551.39 B5 108.60 199.16 
P6, 36.5 cm left of center, between 
crown and 16.5 660.40 531.13 B4 107.60 113.69 
Single Patch Q(film) Tests (DTN: MO0207EBSATBWP.023 [DIRS 163402]) 
P4, 8 cm right of center, 16.5 -0.90 -173.28 B4 107.16 199.69 
P2, 15 cm right of center, 16.5 36.10 -141.12 B5 109.40 109.79 
P5, 4 cm left of center, 16.5 -37.20 -210.37 B5 117.40 301.94 
P4, 8 cm right of center, 33 53.74 -83.70 B4 114.89 222.27 
Bounding Flow Rate Tests (DTN: MO0207EBSATBWP.025 [DIRS 163403]) 
54 cm left of drip shield center, 16.5 850.06 496.63 B4 107.44 277.21 
54 cm left of drip shield center, 16.5 822.71 715.70 B4 107.71 192.26 
27 cm left of drip shield center, 16.5 768.00 646.24 B5 109.21 109.79 
27 cm left of drip shield center, 16.5 868.59 498.18 B4 107.27 110.65 
27 cm right of drip shield center, 16.5 862.08 522.34 B5 109.33 113.57 
27 cm right of drip shield center, 16.5 808.93 713.52 B5 109.30 110.41 
27 cm left of drip shield center, 33 907.89 540.78 B4 107.17 108.13 
27 cm right of drip shield center, 33 835.68 518.08 B5 109.94 113.52 
54 cm left of drip shield center, 33 890.39 561.54 B4 107.28 294.13 
54 cm left of drip shield center, 33 685.39 584.26 B4 107.32 190.42 
27 cm left of drip shield center, 33 -1.99 -98.20 B4 109.88 111.06 
27 cm right of drip shield center, 33 -121.69 -217.44 B5 110.83 110.96 

EBS Radionuclide Transport Abstraction 
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Table 4.1-6. Atlas Breached Drip Shield Experiments on Smooth Drip Shield Surface  Dripping off 
Crown  Rivulet Spread Data  33 from Crown and at Transition 
At 33 At Transition 
Drop Location Right (cm) Left (cm) Right (cm) Left (cm) 
Q(film) Single Patch Tests (DTN: MO0207EBSATBWP.023 [DIRS 163402]) 
P4, 8 cm right of center, 16.5 5.5 3.5 13.5 N/A 
P2, center, 16.5 7.5 4.5 19.5 22.0 
P2, 15 cm right of center, 16.5 11.5 9.0 18.0 15.0 
P5, 4 cm left of center, 16.5 8.5 8.5 N/A N/A 
Bounding Flow Rate Tests (DTN: MO0207EBSATBWP.025 [DIRS 163403]) 
54 cm left of drip shield center, 16.5 31.0 46.0 35.0 46.0 
54 cm left of drip shield center, 16.5 8.5 10.0 19.0 27.0 
27 cm left of drip shield center, 16.5 6.0 8.0 17.0 16.0 
27 cm left of drip shield center, 16.5 18.0 24.0 22.0 19.0 
27 cm right of drip shield center, 16.5 13.0 27.0 14.0 23.0 
27 cm right of drip shield center, 16.5 12.0 17.0 16.0 19.0 
27 cm left of drip shield center, 33 N/A N/A 11.0 17.0 
27 cm right of drip shield center, 33 N/A N/A 15.0 17.0 
54 cm left of drip shield center, 33 N/A N/A 17.0 17.0 
27 cm left of drip shield center, 33 N/A N/A 9.0 9.5 
27 cm right of drip shield center, 33 N/A N/A 8.5 10.0 
NOTE: N/A indicates that rivulet spread measurements at drop location are not applicable to this analysis. 
Source: Howard 2002 [DIRS 161516], p. 14. 
NOTE: Figure modified from reference by labeling patches (16). 
Figure 4.1-1. Dimensions of Drip Shield Mock-Up Used in Breached Drip Shield Experiments on Smooth 
Drip Shield Surface 

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4.1.2 Parameters and Other Technical Information 
Parameters in Tables 4.1-7 through 4.1-14 are used as inputs for the analyses in Section 6. 
Uncertainty in certain parameters is discussed in Section 6. Specifically, sorption distribution 
coefficients (Kd values) in Tables 4.1-11 and 4.1-12 are evaluated in Section 6.3.4.2 in 
determining ranges and distributions for use in modeling retardation in the waste package; 
Tables 6.3-6 and 6.5-13 list the Kd values and their associated uncertainty. 
Parameters in Table 4.1-7 are from American Society for Testing and Materials (ASTM) codes 
and from various editions of the CRC Handbook of Chemistry and Physics (Weast 1985 
[DIRS 111561]). Input parameters in Table 4.1-8 were developed on the Yucca Mountain 
Project (YMP). Input parameters in Table 4.1-9 are from various outside sources, such as 
journals and text books. A description of each parameter is given following Table 4.1-9, 
together with the justification for its use. These inputs thus are considered qualified for their 
intended use within this report. 
Table 4.1-7. Parameters for EBS RT Abstraction (Established Fact) 
Model Input Value Source 
Avogadros number, NA 6.0221419947  1023 mol-1 Lide 2002 [DIRS 160832], p. 1-7 
Water density: at 25C 
at 50C 
997.0449 kg m-3 
988.0363 kg m-3 
Weast 1985 [DIRS 111561], p. F-5 
Water viscosity at 25C 0.890 mPa-s Lide 2000 [DIRS 162229], p. 6-180 
Density of hematite ( a-Fe2O3) 5240 kg m-3 Weast 1985 [DIRS 111561], p. B-104 
Density of A 516 carbon steel 7850 kg m-3 ASTM A 20/A20M-99a 
[DIRS 147578] 
Density of 6061 aluminum 2700 kg m-3 ASTM G 1-90 [DIRS 103515], p. 7, 
Table X1 
Molecular weight of water (H2O) 0.01801528 kg mol-1 Lide 2002 [DIRS 160832], p. 6-4 
Molecular weight of hematite (Fe2O3) 0.15969 kg mol-1 Weast 1985 [DIRS 111561], p. B-104 
Atomic weight of iron (Fe) 0.055847 kg mol-1 Weast 1985 [DIRS 111561], p. B-102 
Atomic weight of molybdenum (Mo) 0.09594 kg mol-1 Weast 1985 [DIRS 111561], p. B-116 
Atomic weight of chromium (Cr) 0.051996 kg mol-1 Weast 1985 [DIRS 111561], p. B-88 
Atomic weight of nickel (Ni) 0.05869 kg mol-1 Weast 1985 [DIRS 111561], p. B-118 
Atomic weight of aluminum (Al) 0.02698154 kg mol-1 Weast 1985 [DIRS 111561], p. B-68 
NOTE: Dependence of viscosity on temperature, T (C), 20C = T = 100C, reference temperature = 20C 
(Weast and Astle 1981 [DIRS 100833], p. F-42): 
( ) ( ) 
105 
20 001053 . 0 20 3272 . 1 log 
2 
20 
10 + 
- - - 
= . .. 
. 
. .. 
. 
T 
T T T 
.
. . 

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Table 4.1-8. Parameters for EBS RT Abstraction (Project Sources) 
Model Input Value Source 
Density of Stainless Steel Type 
316 
8000 kg m-3 DTN: MO0003RIB00076.000 [DIRS 
153044] 
Modulus of elasticity for Alloy 22 
at 204C 
196 Gpa DTN: MO0107TC239753.000 [DIRS 
169973] 
Size of patches in Breached Drip 
Shield Experiments drip shield 
mockup 
0.27 m  0.27 m Howard 2002 [DIRS 161516], p. 13 
Outer lid surface hoop stress 385.0522 MPa BSC 2004 [DIRS 172203], Table 6-9 
Porosity of TSw35 tuff rock 
matrix 
0.131 m3 pore vol. 
m-3 bulk vol. 
DTN: LB0207REVUZPRP.002 [DIRS 
159672]; Spreadsheet 
Matrix_Props.xls, Row 20, Column C 
Porosity of crushed tuff invert 
ballast 
0.45 m3 pore vol. 
m-3 bulk vol. 
BSC 2004 [DIRS 169565], Appendix X 
Unsaturated zone fracture 
frequency for TSw35 
Mean = 3.16 m-1 
Std Dev = 2.63 m-1 
Log-normal 
BSC 2004 [DIRS 170040], Appendix A, 
Table A-1 
Unsaturated zone fracture 
porosity for TSw35 
Range: 0  1 
Distribution: Beta 
Mean = 9.6  10-3 
Std Dev = 2.82  10-3 
BSC 2004 [DIRS 170040], Appendix D, 
Table D-1 
Unsaturated zone matrix porosity 
for TSw35 
Range: 0  1 
Distribution: Beta 
Mean = 0.131 
Std Dev = 0.031 
BSC 2004 [DIRS 170040], Appendix D, 
Table D-1 
Unsaturated zone fracture 
saturation 
Uniform sampling from 433 
locations for each infiltration case 
DTN: LB0307FMRADTRN.001 [DIRS 
165451], Folder U0230_excel_files.zip, 
Spreadsheet Flow and Saturation Data 
from UZ Flow Model.xls, Column D 
Unsaturated zone fracture 
residual saturation 
Uniform sampling from 433 
locations 
DTN: LB0307FMRADTRN.001 [DIRS 
165451], Folder U0230_excel_files.zip, 
Spreadsheet Fracture Residual 
Saturation.xls, Column E 
Unsaturated zone fracture 
percolation flux 
Uniform sampling from 433 
locations for each infiltration case 
DTN: LB0307FMRADTRN.001 [DIRS 
165451], Folder U0230_excel_files.zip, 
Spreadsheet Flow and Saturation Data 
from UZ Flow Model.xls, Column C 
Unsaturated zone fracture 
interface area 
9.68 m2 m-3 DTN: LB0205REVUZPRP.001 [DIRS 
159525]; Spreadsheet 
FRACTURE_PROPERTY.xls, Row 
20, Column R 
Unsaturated zone active fracture 
parameter for TSw35 for all three 
infiltration cases 
Low = 0.476 
Mean = 0.569 
High = 0.570 
DTN: LB03013DSSCP3I.001 [DIRS 
162379]; (BSC 2004 [DIRS 169861], 
Table A-1, A-2, and A-3) 
Unsaturated zone fracture 
aperture 
1.5  10-4 m DTN: LB0205REVUZPRP.001 [DIRS 
159525]; Spreadsheet 
FRACTURE_PROPERTY.xls, Row 
20, Column L 
Unsaturated zone fracture 
diffusion coefficient 
Function of matrix water content 
and effective permeability; same as 
matrix diffusion coefficient 
BSC 2004 [DIRS 170040], 
Equation 6-52 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-8 November 2004 
Table 4.1-8. Parameters for EBS RT Abstraction (Project Sources) (Continued) 
Model Input Value Source 
Unsaturated zone matrix 
saturation 
Uniform sampling from 433 
locations for each infiltration case 
DTN: LB0307FMRADTRN.001 [DIRS 
165451], Folder U0230_excel_files.zip, 
Spreadsheet Flow and Saturation Data 
from UZ Flow Model.xls, Column G 
Unsaturated zone matrix 
percolation flux 
Uniform sampling from 433 
locations for each infiltration case 
DTN: LB0307FMRADTRN.001 [DIRS 
165451], Folder U0230_excel_files.zip, 
Spreadsheet Flow and Saturation Data 
from UZ Flow Model.xls, Column F 
Unsaturated zone matrix 
diffusion coefficient 
Function of matrix water content 
and effective permeability 
BSC 2004 [DIRS 170040], 
Equation 6-52 
Unsaturated zone matrix 
effective permeability 
Function of matrix permeability and 
relative permeability 
BSC 2004 [DIRS 170040], 
Equation 6-57 
Unsaturated zone matrix 
permeability for TSw35 for all 
three infiltration cases 
Low = 2.33  10-18 m2 
Mean = 4.48  10-18 m2 
High = 8.55  10-18 m2 
DTNs: LB0208UZDSCPLI.002 [DIRS 
161788]; LB0208UZDSCPMI.002 
[DIRS 161243]; and 
LB0302UZDSCPUI.002 [DIRS 161787]; 
BSC 2004 [DIRS 170040], Table 4-6 
Unsaturated zone matrix relative 
permeability 
Uniform sampling from 433 
locations for each infiltration case 
DTN: LB0307FMRADTRN.001 [DIRS 
165451], Folder U0230_excel_files.zip, 
Spreadsheet Flow and Saturation Data 
from UZ Flow Model.xls, Column H 
Unsaturated zone dry matrix 
density for TSw35 (stratigraphic 
unit Tptpll) 
1.9793 g cm-3 DTN: SN0404T0503102.011 [DIRS 
169129], File ReadMe.doc, Table 7-10 
Unsaturated zone fracture 
percolation flow-focusing factor 
Uniform sampling from 433 
locations for each infiltration case 
DTN: LB0307FMRADTRN.001 [DIRS 
165451], Folder U0230_excel_files.zip, 
Spreadsheet Fracture Flux and Water 
Content with Flow Focusing r1.xls, 
Column D 
UZ = unsaturated zone 
Table 4.1-9. Parameters for EBS RT Abstraction (Various Sources) 
Model Input Value Source 
Self-diffusion coefficient of water at 25C 2.299  10-9 m2 s-1 Mills 1973 [DIRS 133392], Table III 
Parameter k in FHH water vapor 
adsorption isotherm for Fe2O3 
1.1 (dimensionless) Jurinak 1964 [DIRS 154381], p. 486 
Parameter s in FHH water vapor 
adsorption isotherm for Fe2O3 
2.45 (dimensionless) Jurinak 1964 [DIRS 154381], p. 486 
Water molecule cross-sectional area, Aw 10.6 2 McCafferty and Zettlemoyer 1970 [DIRS 
154382], p. 454 
Cementation factor (exponent on porosity 
in Archies law) 
1.3 (dimensionless) Bear 1988 [DIRS 101379], p. 116 
Saturation exponent in Archies law 2 (dimensionless) Bear 1988 [DIRS 101379], p. 116 
Specific surface area of natural hematite 
(Fe2O3) 
1.8 m2 g-1 Langmuir 1997 [DIRS 100051], Table 10.2 
(natural hematite) 
Specific surface area of hematite (Fe2O3) 21.4 m2 g-1 Briand et al. 2001 [DIRS 161617], Table 4 
Density of Neutronit A 978 steel 7760 kg m-3 Kgler 1996 [DIRS 107760], p. 17 
Fuel rod outside diameter (WE 17  17) 0.374 in. DOE 1992 [DIRS 102588], Volume 1, p. 2A- 
30 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-9 November 2004 
Table 4.1-9. Parameters for EBS RT Abstraction (Various Sources) (Continued) 
Model Input Value Source 
Fuel rod length (WE 17  17) 151.560 in. DOE 1992 [DIRS 102588], Volume 1, p. 2A-30 
Fuel rods per assembly (WE 17  17) 264 DOE 1992 [DIRS 102588], Volume 1, p. 2A-30 
FHH = Frenkel-Halsey-Hill adsorption isotherm equation; WE = Westinghouse Electric; DOE = U.S. Department of 
Energy 
Fuel rod dimensionsThe fuel rod dimensions for assembly Westinghouse Electric 
(WE) 17  17 are given in Characteristics of Potential Repository Wastes (DOE 1992 
[DIRS 102588]). This four-volume report is the definitive compilation of the characteristics of 
potential repository wastes. The concerns raised by Deficiency Report VAMO-98-D-132 (DOE 
1998 [DIRS 123628] regarding inconsistencies between data reported in Characteristics of 
Potential Repository Wastes (DOE 1992 [DIRS 102588] and its data sources do not impact the 
data used in this analysis with regard to the WE 17  17 fuel rods; thus, these data are considered 
reliable and are justified as suitable for intended use in this analysis. The WE 17  17 fuel 
assembly is used as the representative fuel assembly because; (1) Westinghouse fuel assemblies 
comprise a large fraction (about 21 percent) of all fuel assemblies, (2) the 17  17 configuration 
comprises about 34 percent of discharged fuel assemblies (Faruque 1993 [DIRS 170706]), and 
(3) 21-pressurized water reactor (PWR) waste packages that will contain the WE 17  17 fuel 
assemblies are the most common type of waste package, nominally comprising 4299 of the 
11,184 waste packages planned for the repository (BSC 2004 [DIRS 169472], Table 11). 
The fuel rod length is reported in Characteristics of Potential Repository Wastes (DOE 1992 
[DIRS 102588], Volume 1, p. 2A-30) as ranging from 151.560 in. to 151.635 in. Because no 
distribution for length is given in the reference (which would give some guidance on selecting a 
single representative value for length) and because the range is small (less than 0.05 percent 
variation from minimum to maximum), the minimum length is used as representative of the 
range. 
Water molecule cross-sectional areaThe cross-sectional area of the water molecule is taken 
from the paper Adsorption of Water Vapour on Alpha-Fe2O3 (McCafferty and Zettlemoyer 
1970 [DIRS 154382]). The paper was published in Discussions of the Faraday Society, a 
publication started in 1947 and continuing to this day as the Faraday Discussions under the 
sponsorship of the Royal Society of Chemistry. The Royal Society of Chemistry is the largest 
organization in Europe for advancing the chemical sciences and is supported by a network of 
45,000 members worldwide. The McCafferty and Zettlemoyer paper is directly relevant to the 
Yucca Mountain repository because hematite (Fe2O3) will be the predominant form of iron oxide 
in a degrading waste package, and hematite will comprise the bulk of the corrosion products in 
the waste package. 
The value of 10.6 2 per molecule reported by McCafferty and Zettlemoyer (1970 
[DIRS 154382], p. 454) is corroborated by Holmes et al. (1974 [DIRS 154379], p. 368), who 
also use a value of 10.6 2 for the cross-sectional area of a water molecule. Jurinak (1964 
[DIRS 154381]) assumes a cross-sectional area of 10.8 2 for a water molecule. Gregg and Sing 
(1982 [DIRS 153010], p. 188) state that a close-packed monolayer of water corresponds to a 
figure of 10.5 2 for the cross-sectional area of a water molecule. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-10 November 2004 
Self-diffusion coefficient of water at 25CThe value for the self-diffusion coefficient of water 
at 25C is 2.299  10-9 m2 s-1 and comes from the paper Self-diffusion in Normal and Heavy 
Water in the Range 1-45 (Mills 1973 [DIRS 133392]) in the Journal of Physical Chemistry. 
The Journal of Physical Chemistry has been published since 1896. Articles are reviewed by 
experts in the field, so this coefficient can be considered reliable. 
Parameter k in Frenkel-Halsey-Hill adsorption isotherm equation (FHH) water vapor 
adsorption isotherm for Fe2O3The value of the parameter k in the FHH water vapor 
adsorption isotherm for Fe2O3 is 1.1 and comes from the paper, Interaction of Water with Iron 
and Titanium Oxide Surfaces: Goethite, Hematite, and Anatase (Jurinak 1964 [DIRS 154381]) 
in the Journal of Colloid Science. The Journal of Colloid Science, now the Journal of Colloid 
and Interface Science, has been published since 1947 and is a refereed journal; therefore, the 
data in the articles can be considered reliable. 
Parameter s in FHH water vapor adsorption isotherm for Fe2O3The value of the parameter 
s in the FHH water vapor adsorption isotherm for Fe2O3 is 2.45 and comes from the paper 
Interaction of Water with Iron and Titanium Oxide Surfaces: Goethite, Hematite, and Anatase 
(Jurinak 1964 [DIRS 154381]) in the Journal of Colloid Science. The Journal of Colloid 
Science, now the Journal of Colloid and Interface Science, has been published since 1947 and is 
a refereed journal; therefore, the data in the paper can be considered reliable. 
Cementation factor (exponent on porosity in Archies law)The value of 1.3 for the porosity 
exponent in Archies law for unconsolidated sand is taken from the book Dynamics of Fluids in 
Porous Media (Bear 1988 [DIRS 101379], p. 116). The value 1.3 is corroborated by the 
Handbook of Well Log Analysis for Oil and Gas Formation Evaluation (Pirson 1963 
[DIRS 111477]). 
Saturation exponent in Archies lawThe value 2.0 for the saturation exponent in Archies law 
for unconsolidated sand is taken from the book Dynamics of Fluids in Porous Media (Bear 1988 
[DIRS 101379], p. 116). The value 2.0 is corroborated by Electrical Methods in Geophysical 
Prospecting, Volume 10 of International Series in Electromagnetic Waves (Keller and 
Frischknecht 1966 [DIRS 111470]). 
Density of Neutronit A 978 steelThe density of Neutronit A 978 steel is 7,760 kg m-3 (at 20oC) 
from Bhler Bleche GmbH (Kgler 1996 [DIRS 107760]). Bhler Bleche is producer of plate 
steel products and is an outgrowth of the steel company Schoeller-Bleckmann AG founded in 
1924. The company is a world-wide exporter of steel products and has a state-of-the-art research 
and development program to improve the material properties of steels. The companys expertise 
with steels makes the density value for Neutronit A 978 steel reliable. 
Specific surface area of hematiteThe specific surface area (surface area per unit mass) of 
hematite depends on several factors, including the source of the sample (whether natural or 
artificial), preparation of the sample, and the measurement technique. Because in the EBS RT 
Abstraction the specific surface area of hematite represents that of corrosion products, which will 
form under a wide range of conditions, this is a sample parameter in TSPA-LA. The values of 
specific surface area of hematite in Table 4.1-9 establish lower and upper bounds of the range to 
be sampled. The lower bound value, for natural hematite, is provided by Langmuir (1997 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-11 November 2004 
[DIRS 100051]), a widely used textbook on aqueous geochemistry by a reputable, extensively 
published author and environmental chemistry researcher. The upper bound value is provided by 
a study of catalytic behavior of metal oxides (Briand et al. 2001 [DIRS 161617]) published in the 
Journal of Catalysis, a reputable refereed journal. Further discussion and corroboration of the 
range of specific surface area of hematite is provided in Section 6.5.1.2.1.3. 
Table 4.1-10. Elemental Composition (Weight Percent) of Waste Package Materials 
Element 316 Stainless Steela A 516 Carbon Steelb Neutronit A 978c Aluminum 6061d 
Fe Balance Balance Balance 0.7 
Mo 3.00  2.2  
Cr 18.00  18.5 0.35 
Ni 14.00  13.0  
Al    Remainder 
Co   0.20  
W     
Mn 2.00 1.30  0.15 
C 0.08 0.26 0.04  
P 0.045 0.035   
S 0.030 0.035   
Si 0.75   0.8 
N 0.16    
Cu    0.4 
Mg    1.2 
Zn    0.25 
Ti    0.15 
V     
Residuals    0.15 
NOTES:  indicates that the alloy chemical composition specification does not include this element. 
Compositions listed are the maximum specified for each element in the data source. Balance and 
Remainder are specified in the data source for the principal component of the alloy. 
aDTN: MO0003RIB00076.000 [DIRS 153044]. 
bDTN: MO0107TC240032.000 [DIRS 169970]. 
cKgler 1991 [DIRS 155761], p. 15 (vendor-supplied data). 
dASM 1979 [DIRS 154085], p. 115. 
The data in Table 4.1-11, from DTN: LA0003AM831341.001 ([DIRS 148751], SEP table 
S00191_002), were developed in the analysis report Unsaturated Zone and Saturated Zone 
Transport Properties (U0100) (BSC 2001 [DIRS 160828], Section 6.4.2). This document has 
been cancelled because some of the output data, specifically, the transport properties of tuff, 
have been revised and updated in more recent YMP reports. However, the ranges and 
distributions of sorption distribution coefficients on iron oxide have not been revised, and they 
demonstrate the properties of interest for the analysis of sorption parameters for the waste 
package corrosion products, as discussed in Section 6.3.4.2.3. Corroborating data are available, 
and the values in Table 4.1-11 are compared with these data in Section 6.3.4.2.3 and Table 6.3-6. 
Accordingly, these factors justify these product output of the cancelled document as qualified 
input data suitable for application to modeling retardation in iron corrosion products in the EBS 
RT Abstraction. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-12 November 2004 
Table 4.1-11 includes ranges and distributions of Kd values from DTN: LA0003AM831341.001 
([DIRS 148751], SEP table S00191_002) for 10 radionuclides for sorption onto iron oxide, 
which is the Rock type specified in the reference, for unsaturated zone units. 
In DTN: LA0003AM831341.001 [DIRS 148751], the Kd value for iodine and technetium is 
listed as zero for all rock types for unsaturated zone units; Kd values for sorption onto iron 
oxide are not listed. In DTN: LA0003AM831341.001 ([DIRS 148751] SEP table 
S00191_001), the Kd value for iodine in saturated zone units is listed as ranging from 0.32 to 
0.63 ml g-1 with a uniform distribution for rock type alluvium. reporting the same SEP table, 
the Kd value for technetium in saturated zone units is listed as ranging from 0.27 to 0.62 ml g-1 
with a uniform distribution for rock type alluvium. The data for iodine and technetium in 
saturated zone units for rock type alluvium are suitable for modeling retardation in corrosion 
products because they provide evidence that some small degree of sorption of these elements is 
possible onto unspecified mineral assemblages, yet the uncertainty is small because the 
maximum Kd values are small. 
Input values for sorption distribution coefficient (Kd) ranges on devitrified tuff for unsaturated 
zone units are listed in Table 4.1-12. These data are used for calculating retardation in the invert. 
The data are appropriate for this use because the crushed tuff to be used in the invert is the same 
material that is mined from the drifts when the repository is constructed. The repository will be 
located primarily in the TSw35 horizon in which the host rock is devitrified tuff. These sorption 
distribution coefficient data are correlated using the correlation matrix in Table 4.1-13. 
Diffusion coefficient data for granular materials are listed in Table 4.1-14. These data are used 
to develop an effective diffusion coefficient for the invert in Section 6.3.4.1.1. The data are 
qualified for use in this report in Appendix H. 
Table 4.1-11. Sorption Distribution Coefficient (Kd) Ranges on Iron Oxide in Unsaturated Zone Units; All 
Distributions Are Uniform Except as Noted 
Element Minimum Kd (ml g-1) Maximum Kd (ml g-1) 
Actinium 1,000 5,000 
Americium 1,000 5,000 
Carbon 10 100 
Cesium a 0 300 
Neptunium 500 1,000 
Plutonium 1,000 5,000 
Protactinium 500 1,000 
Radium a 0 500 
Strontium b 0 20 
Thorium 1,000 5,000 
Uranium 100 1,000 
Source: DTN: LA0003AM831341.001 ([DIRS 148751] SEP table 
S00191_002). 
NOTES: E(x) = expected value of the distribution; COV = coefficient of 
variance = s(x)/E(x); s(x) = standard deviation of the distribution. 
a Distribution type: Beta; E(x) = 30; COV = 1.0. 
b Distribution type: Beta; E(x) = 10; COV = 0.25. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-13 November 2004 
Table 4.1-12. Sorption Distribution Coefficient (Kd) Ranges on Devitrified Tuff for Unsaturated Zone Units 
Speciesa Distribution Type Coefficients Describing Distributionb 
U Cumulative (0, 0) (0.2, 0.5) (4., 1.0) 
Np Cumulative (0, 0) (0.5, 0.5) (6., 1.0) 
Pu Cumulative (10., 0) (70., 0.5) (200., 1.0) 
Am Truncated Normal 
Range = 1,000  10,000 ml g-1 
Mean = 5,500 ml g-1 
Std. Dev. = 1500 ml g-1 
Pa Truncated Normal 
Range = 1,000  10,000 ml g-1 
Mean = 5,500 ml g-1 
Std. Dev. = 1,500 ml g-1 
Cs Uniform 1  15 ml g-1 
Sr Uniform 10  70 ml g-1 
Ra Uniform 100  1,000 ml g-1 
Th Uniform 1,000  10,000 ml g-1 
a DTN: LA0408AM831341.001 [DIRS 171584]. 
b For cumulative distribution: (Kd value, ml g-1; probability) and for uniform distribution: Kd range. 
Table 4.1-13. Correlations for Sampling Sorption Distribution Coefficient (Kd) Probability 
Distributions for Devitrified Tuff 
Element Am Cs Np Pa Pu Ra Sr Th U 
Am 100         
Cs 0 100        
Np 25 0 100       
Pa 75 0 0 100      
Pu 10 0 10 0 100     
Ra 0 100 0 0 0 100    
Sr 0 25 50 0 0 25 100   
Th 0 0 50 0 0 0 75 100  
U 0 0 0 0 0 0 0 0 100 
DTN: LA0311AM831341.001 [DIRS 167015] . 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-14 November 2004 
Table 4.1-14. Diffusion Coefficient for Granular Materials for Volumetric Moisture Content Between 
1.5 Percent and 66.3 Percent 
Sample 
Volumetric Moisture Content 
(%) 
Diffusion Coefficient 
(cm2 s-1) 
1 1.50 1.39  10-8 
2 1.70 6.60  10-9 
3 1.90 8.60  10-9 
4 2.17 2.77  10-8 
5 2.20 3.63  10-8 
6 2.29 1.09  10-8 
7 2.50 2.50  10-8 
8 3.10 3.30  10-8 
9 3.14 3.06  10-8 
10 3.20 1.35  10-8 
11 3.27 2.79  10-8 
12 3.33 6.35  10-8 
13 3.34 2.60  10-8 
14 3.57 3.37  10-8 
15 3.70 3.70  10-8 
16 3.70 6.60  10-8 
17 4.00 5.22  10-8 
18 4.20 5.94  10-8 
19 4.60 6.21  10-8 
20 4.90 7.20  10-8 
21 5.10 1.32  10-7 
22 5.30 2.40  10-8 
23 5.40 7.60  10-8 
24 5.51 7.68  10-8 
25 5.83 1.23  10-7 
26 5.90 9.30  10-8 
27 6.00 8.92  10-8 
28 6.30 1.06  10-7 
29 6.90 6.00  10-8 
30 6.93 1.50  10-7 
31 7.30 1.60  10-7 
32 7.40 2.50  10-7 
33 7.60 2.60  10-7 
34 7.60 1.10  10-7 
35 7.60 2.69  10-7 
36 7.70 1.10  10-7 
37 8.00 1.98  10-7 
38 8.10 1.70  10-7 
39 8.32 4.10  10-7 
40 8.35 2.15  10-7 
41 8.60 3.20  10-7 
42 8.80 2.30  10-7 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-15 November 2004 
Table 4.1-14. Diffusion Coefficient for Granular Materials for Volumetric Moisture Content Between 
1.5 Percent and 66.3 Percent (Continued) 
Sample 
Volumetric Moisture Content 
(%) 
Diffusion Coefficient 
(cm2 s-1) 
43 9.24 2.55  10-7 
44 9.24 2.55  10-7 
45 9.56 3.00  10-7 
46 9.64 3.07  10-7 
47 9.75 3.20  10-7 
48 10.1 3.51  10-7 
49 10.1 3.62  10-7 
50 10.2 3.54  10-7 
51 10.2 3.30  10-7 
52 10.3 3.34  10-7 
53 10.3 2.10  10-7 
54 10.4 3.40  10-7 
55 10.9 3.62  10-7 
56 11.1 3.72  10-7 
57 11.1 4.22  10-7 
58 11.1 4.27  10-7 
59 11.2 4.19  10-7 
60 11.2 5.48  10-7 
61 11.4 4.27  10-7 
62 11.4 4.12  10-7 
63 11.6 5.40  10-7 
64 11.7 2.60  10-7 
65 11.8 4.80  10-7 
66 12.0 2.40  10-7 
67 12.0 4.47  10-7 
68 12.2 4.09  10-7 
69 12.3 5.05  10-7 
70 12.3 4.40  10-7 
71 12.3 3.60  10-7 
72 12.3 4.50  10-7 
73 12.5 2.90  10-7 
74 12.7 4.37  10-7 
75 12.7 4.90  10-7 
76 12.7 5.32  10-7 
77 13.1 4.77  10-7 
78 13.9 5.39  10-7 
79 13.9 7.80  10-7 
80 14.1 5.12  10-7 
81 14.2 5.52  10-7 
82 14.4 4.50  10-7 
83 14.4 5.20  10-7 
84 14.4 4.50  10-7 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-16 November 2004 
Table 4.1-14. Diffusion Coefficient for Granular Materials for Volumetric Moisture Content Between 
1.5 Percent and 66.3 Percent (Continued) 
Sample 
Volumetric Moisture Content 
(%) 
Diffusion Coefficient 
(cm2 s-1) 
85 14.6 6.82  10-7 
86 14.7 9.00  10-7 
87 14.8 6.54  10-7 
88 16.0 1.47  10-6 
89 16.1 6.82  10-7 
90 16.5 5.45  10-7 
91 16.7 6.60  10-7 
92 17.0 1.20  10-6 
93 17.1 8.20  10-7 
94 17.3 1.76  10-6 
95 17.5 1.10  10-6 
96 18.8 1.60  10-6 
97 18.9 8.19  10-7 
98 19.4 9.89  10-7 
99* 20.4 4.19  10-6 
100 20.8 3.58  10-6 
101 21.0 2.34  10-6 
102 21.5 1.23  10-6 
103 21.6 1.29  10-6 
104 23.1 2.40  10-6 
105 23.1 1.90  10-6 
106 24.0 2.90  10-6 
107* 25.3 5.82  10-6 
108 25.4 2.50  10-6 
109* 25.7 9.26  10-6 
110 28.2 3.50  10-6 
111 28.5 1.00  10-6 
112 30.9 1.51  10-6 
113* 31.7 1.23  10-5 
114 32.3 4.60  10-6 
115* 33.8 1.34  10-5 
116* 35.8 1.57  10-5 
117 38.5 4.33  10-6 
118* 39.3 1.36  10-5 
119* 39.5 1.13  10-5 
120 40.0 6.90  10-6 
121 42.0 5.80  10-6 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-17 November 2004 
Table 4.1-14. Diffusion Coefficient for Granular Materials for Volumetric Moisture Content Between 
1.5 Percent and 66.3 Percent (Continued) 
Sample 
Volumetric Moisture Content 
(%) 
Diffusion Coefficient 
(cm2 s-1) 
122 42.5 3.22  10-6 
123* 43.4 1.02  10-5 
124 49.0 6.09  10-6 
125 66.3 1.83  10-5 
NOTE: All values are from Conca and Wright 1992 [DIRS 100436], Figure 2, 
except for those indicated by an asterisk, which are from Conca et al. 
1993 [DIRS 170709], Figure 2. 
4.1.3 Design Information 
Some of the information necessary for the model presented in this document consists of 
parameters and other descriptions based on the license application (LA) conceptual design of the 
repository. Included are dimensions, material amounts and properties, and physical 
configuration of the drifts and their contents, listed in Tables 4.1-15 through 4.1-17. For 
TSPA-LA analyses, this information was obtained from information exchange drawings (IEDs) 
and design drawings cited on IEDs. 
In Table 4.1-17, the component materials in a 21-PWR waste package are obtained from Design 
and Engineering, 21-PWR Waste Package Configuration (BSC 2004 [DIRS 167394]), which is 
the design version preceding the current version (BSC 2004 [DIRS 170710]). Justification for 
using the previous design data and the impact on TSPA-LA calculations is provided in Section 
6.3.4.2.3, where the impact is shown to be negligible. 
In Table 4.1-17, the masses and numbers of components in a 5 DHLW/DOE - Short waste 
package are obtained from Revision 00B of D&E/PA/C IED Typical Waste Package 
Components Assembly (BSC 2004 [DIRS 167207]), which is the version of the information 
exchange drawing (IED) preceding Revision 00C (BSC 2004 [DIRS 169472]), used for the 
21-PWR waste packages. Minor changes in component masses were made in the 
5 DHLW/DOE - Short waste package from Revision 00B to Revision 00C, whereas no changes 
were made for the other waste package types. The impacts of the changes in component masses 
in the 5 DHLW/DOE - Short waste package are analyzed in Section 6.3.4.2.3 and are shown to 
be negligible. 
Table 4.1-15. Design Information for EBS Components 
Model Input Value Source 
Diameter of the drift 5.5 m BSC 2004 [DIRS 169503] 
Length of drip shield 5805 mm BSC 2004 [DIRS 169220], Table 1 
Maximum depth of invert 2 ft 10 in BSC 2004 [DIRS 169503] 
21-PWR (Absorber Plate) Waste Package Characteristics 
Outer barrier outside diameter 1637 mm BSC 2004 [DIRS 166953], Section B-B 
Maximum outside diameter around trunnion collars 1718.3 mm BSC 2004 [DIRS 166953] 
Outer barrier inside diameter 1597 mm BSC 2004 [DIRS 166953], Section B-B 
Inner vessel inside diameter 1485.9 mm BSC 2004 [DIRS 166953], Section B-B 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-18 November 2004 
Table 4.1-15. Design Information for EBS Components (Continued) 
Model Input Value Source 
Total outside length 5024.4mm BSC 2004 [DIRS 166953], Section A-A 
Inner vessel cavity length 4584.7 mm BSC 2004 [DIRS 166953], Section A-A 
Outer barrier thickness 20 mm BSC 2004 [DIRS 169472], Table 1 
Middle lid thickness 12.7 mm BSC 2004 [DIRS 167394], Detail A 
Middle lid to outer lid gap 30.16 mm BSC 2004 [DIRS 169472], Detail A 
Outer lid thickness 25.4 mm BSC 2004 [DIRS 169472], Details A and B 
Inner vessel bottom lid thickness 50.8 mm BSC 2004 [DIRS 169472], Detail B 
Inner vessel top lid thickness 50.8 mm BSC 2004 [DIRS 169472], Detail A 
Top lid lifting device thickness 25.4 mm BSC 2004 [DIRS 169472], Detail C 
Bottom skirt length 101.6 mm BSC 2004 [DIRS 169472], Detail B 
5 DHLW/DOE SNF - Short Waste Package Characteristics 
Nominal diameter 2126.0 mm BSC 2004 [DIRS 169472], Table 1 
Nominal length 3452.8 mm BSC 2004 [DIRS 169472], Table 1 
Outer barrier thickness 25.4 mm BSC 2004 [DIRS 169472], Table 1 
Outer barrier outside diameter 2044.7 mm BSC 2004 [DIRS 166946], Section B-B 
Outer barrier inside diameter 1993.9 mm BSC 2004 [DIRS 166946], Section B-B 
Total length 3452.8 mm BSC 2004 [DIRS 166946], Section A-A 
DHLW=defense high-level (radioactive) waste, SNF=spent nuclear fuel 
Table 4.1-16. Component Dimensions in a 21-PWR (Absorber Plate) Waste Package 
Component Dimensions 
Basket Side Guide 3/8 in. thickness 
Basket Side Guide Stiffener 3/8 in. thickness 
Basket End Side Guide 3/8 in. thickness 
Basket End Guide Stiffener 3/8 in. thickness 
Basket Corner Guide 3/8 in. thickness 
Basket Corner Guide Stiffener 3/8 in. thickness 
Fuel Basket A-Plate 7 mm thickness 
Fuel Basket B-Plate 7 mm thickness 
Fuel Basket C-Plate 7 mm thickness 
Fuel Basket D-Plate  in. thickness 
Fuel Basket E-Plate  in. thickness 
Basket Tube 180 in. length; 
9.12 in. interior dimension; 
3/16 in. thickness 
Sources: Thickness: BSC 2004 [DIRS 169472], Table 2. 
Basket Tube Length: BSC 2004 [DIRS 166953], Section A-A. 
Basket Tube Interior Dimension: BSC 2004 [DIRS 166953], 
Section B-B. 

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ANL-WIS-PA-000001 REV 01 4-19 November 2004 
Table 4.1-17. Masses and Numbers of Components in Waste Packages 
21-PWR (Absorber Plate) 
(BSC 2004 [DIRS 167394], material table; BSC 2004 [DIRS 169472], Table 2) 
Material Component Mass (kg) Number 
Basket  Side Guide 24.9 16 
Basket  Side Guide Stiffener 0.615 32 
Basket  End Side Guide 32.7 32 
Basket End Side Guide Stiffener 1.38 64 
Basket Corner Guide 40.1 16 
Basket Corner Guide Stiffener 2.07 32 
Carbon Steel Type A 
516 
Fuel Basket Tube 159 21 
Fuel Basket A - Plate 86.8 8 
Fuel Basket B - Plate 86.8 8 
Neutronit A 978 
Fuel Basket C - Plate 45.8 16 
Fuel Basket D - Plate 27.4 8 Al 6061 
Fuel Basket E - Plate 27.4 8 
Inner Vessel w/o Guides 9,920 1 
Inner Lid w/ LLF 739 1 
Interface Ring 35.6 1 
Spread Ring 25.3 1 
Stainless Steel Type 316 
Total 316 Welds 81.0  
OCB with trunnion sleeves 5,730 1 
Middle Lid w/ LLF 226 1 
Outer Lid w/ LLF 445 1 
Alloy 22 
Total Alloy 22 Welds 51.8  
5 DHLW/DOE  Short 
(BSC 2004 [DIRS 166947], material table; BSC 2004 [DIRS 167207], Table 5) 
Material Component Mass (kg) Number 
Carbon Steel Type 
A 516 
Divider Plate Assembly 3,720 1 
Inner Vessel 8,860 1 
Inner Lid w/ LLF 1,170 1 
Interface Ring 44.6 1 
Spread Ring 31.9 1 
Stainless Steel Type 316 
Total 316 Welds 102  
OCB with trunnion sleeves 6,540 1 
Middle Lid w/ LLF 350 1 
Outer Lid w/ LLF 693 1 
Alloy 22 
Total Alloy 22 Welds 64.2  
NOTE:  indicates number of welds is not specified in source IED. 
BWR = boiling water reactor, DHLW = defense high-level (radioactive) waste, IED = information exchange 
drawing, LLF = lid lifting feature, PWR = pressurized water reactor; DOE = U.S. Department of Energy 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-20 November 2004 
4.2 CRITERIA 
This report was prepared to comply with 10 CFR Part 63 [DIRS 158535]. Relevant requirements 
for performance assessment from Section 114 of that document are: Any performance 
assessment used to demonstrate compliance with Sec. 113(b) shall: (a) Include data related to 
the geology, hydrology, and geochemistry  used to define parameters and conceptual models 
used in the assessment. (b) Account for uncertainties and variabilities in parameter values and 
provide the technical basis for parameter ranges, probability distributions, or bounding values 
used in the performance assessment. ... (g) Provide the technical basis for models used in the 
performance assessment such as comparisons made with outputs of detailed process-level 
models . 
Programmatic requirements for this document are listed in Technical Work Plan for: Near-Field 
Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction 
Model Report Integration (BSC 2004 [DIRS 170775]). This technical work plan (TWP) 
specifies that this document and all analyses described herein must adhere to the requirements of 
AP-SIII.10Q, Models, and to the requirements mentioned in the Project Requirements Document 
(Canori and Leitner 2003 [DIRS 166275]). This TWP also specifies that Yucca Mountain 
Review Plan, Final Report (NRC 2003 [DIRS 163274]) acceptance criteria must be addressed. 
4.2.1 Yucca Mountain Review Plan Criteria 
The acceptance criteria that concern flow and transport related to the EBS are presented in 
Section 2.2.1.3 of the Yucca Mountain Review Plan, Final Report (NRC 2003 [DIRS 163274]). 
Of the 14 model abstraction sections in the review plan, Sections 2.2.1.3.3 and 2.2.1.3.4 are 
applicable to this abstraction. The pertinent acceptance criteria from those two sections are listed 
in Sections 4.2.1.1 and 4.2.1.2, respectively. 
4.2.1.1 Applicable Acceptance Criteria from Section 2.2.1.3.3, Quantity and Chemistry 
of Water Contacting Engineered Barriers and Waste Forms 
The following acceptance criteria, listed in Section 2.2.1.3.3.3 of Yucca Mountain Review Plan, 
Final Report (NRC 2003 [DIRS 163274]), apply to this abstraction. These acceptance criteria 
are based on meeting the requirements of 10 CFR 63.114(a)(c) and (e)(g) [DIRS 158535], 
relating to the quantity and chemistry of water contacting engineered barriers and waste forms 
model abstraction. 
Acceptance Criterion 1System Description and Model Integration Are Adequate. 
(1) Total system performance assessment adequately incorporates important design 
features, physical phenomena, and couplings, and uses consistent and appropriate 
assumptions throughout the quantity and chemistry of water contacting engineered 
barriers and waste forms abstraction process. 
(2) The abstraction of the quantity and chemistry of water contacting engineered barriers 
and waste forms uses assumptions, technical bases, data, and models, that are 
appropriate and consistent with other related U.S. Department of Energy abstractions. 
For example, the assumptions used for the quantity and chemistry of water contacting 

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ANL-WIS-PA-000001 REV 01 4-21 November 2004 
engineered barriers and waste forms are consistent with the abstractions of 
Degradation of Engineered Barriers (NRC 2003 [DIRS 163274], Section 2.2.1.3.1); 
Mechanical Disruption of Engineered Barriers (NRC 2003 [DIRS 163274], 
Section 2.2.1.3.2); Radionuclide Release Rates and Solubility Limits 
(Section 2.2.1.3.4); Climate and Infiltration (NRC 2003 [DIRS 163274], 
Section 2.2.1.3.5); and Flow Paths in the Unsaturated Zone (NRC 2003 
[DIRS 163274], Section 2.2.1.3.6). The descriptions and technical bases provide 
transparent and traceable support for the abstraction of quantity and chemistry of water 
contacting engineered barriers and waste forms. 
(3) Important design features, such as waste package design and material selection, 
backfill, drip shield, ground support, thermal loading strategy, and degradation 
processes, are adequate to determine the initial and boundary conditions for 
calculations of the quantity and chemistry of water contacting engineered barriers and 
waste forms. 
(4) Spatial and temporal abstractions appropriately address physical couplings 
(thermal-hydrologic-mechanical-chemical). For example, the U.S. Department of 
Energy evaluates the potential for focusing of water flow into drifts, caused by 
coupled thermal-hydrologic-mechanical-chemical processes. 
(5) Sufficient technical bases and justification are provided for total system performance 
assessment assumptions and approximations for modeling coupled thermal-hydrologic 
mechanical-chemical effects on seepage and flow, the waste package chemical 
environment, and the chemical environment for radionuclide release. The effects of 
distribution of flow on the amount of water contacting the engineered barriers and 
waste forms are consistently addressed, in all relevant abstractions. 
(6) The expected ranges of environmental conditions within the waste package 
emplacement drifts, inside of breached waste packages, and contacting the waste 
forms and their evolution with time, are identified. These ranges may be developed to 
include: (i) the effects of the drip shield and backfill on the quantity and chemistry of 
water (e.g., the potential for condensate formation and dripping from the underside of 
the shield); (ii) conditions that promote corrosion of engineered barriers and 
degradation of waste forms; (iii) irregular wet and dry cycles; (iv) gamma-radiolysis; 
and (v) size and distribution of penetrations of engineered barriers. 
(7) The model abstraction for quantity and chemistry of water contacting engineered 
barriers and waste forms is consistent with the detailed information on engineered 
barrier design and other engineered features. For example, consistency is 
demonstrated for: (i) dimensionality of the abstractions; (ii) various design features 
and site characteristics; and (iii) alternative conceptual approaches. Analyses are 
adequate to demonstrate that no deleterious effects are caused by design or site 
features that the U.S. Department of Energy does not take into account in this 
abstraction. 

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(8) Adequate technical bases are provided, including activities such as independent 
modeling, laboratory or field data, or sensitivity studies, for inclusion of any 
thermal-hydrologic-mechanical-chemical couplings and features, events, and 
processes. 
(9) Performance-affecting processes that have been observed in thermal-hydrologic tests 
and experiments are included into the performance assessment. For example, the 
U.S. Department of Energy either demonstrates that liquid water will not reflux into 
the underground facility or incorporates refluxing water into the performance 
assessment calculation, and bounds the potential adverse effects of alteration of the 
hydraulic pathway that result from refluxing water. 
Acceptance Criterion 2Data Are Sufficient for Model Justification. 
(1) Geological, hydrological, and geochemical values used in the license application are 
adequately justified. Adequate description of how the data were used, interpreted, and 
appropriately synthesized into the parameters is provided. 
(2) Sufficient data were collected on the characteristics of the natural system and 
engineered materials to establish initial and boundary conditions for conceptual 
models of thermal-hydrologic-mechanical-chemical coupled processes, that affect 
seepage and flow and the engineered barrier chemical environment. 
(4) Sufficient information to formulate the conceptual approach(es) for analyzing water 
contact with the drip shield, engineered barriers, and waste forms is provided. 
Acceptance Criterion 3Data Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
(1) Models use parameter values, assumed ranges, probability distributions, and bounding 
assumptions that are technically defensible, reasonably account for uncertainties and 
variabilities, and do not result in an under representation of the risk estimate. 
(2) Parameter values, assumed ranges, probability distributions, and bounding 
assumptions used in the total system performance assessment calculations of quantity 
and chemistry of water contacting engineered barriers and waste forms are technically 
defensible and reasonable, based on data from the Yucca Mountain region (e.g., results 
from large block and drift-scale heater and niche tests), and a combination of 
techniques that may include laboratory experiments, field measurements, natural 
analog research, and process-level modeling studies. 
(3) Input values used in the total system performance assessment calculations of quantity 
and chemistry of water contacting engineered barriers (e.g., drip shield and waste 
package) are consistent with the initial and boundary conditions and the assumptions 
of the conceptual models and design concepts for the Yucca Mountain site. 
Correlations between input values are appropriately established in the 
U.S. Department of Energy total system performance assessment. Parameters used to 
define initial conditions, boundary conditions, and computational domain in sensitivity 

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analyses involving coupled thermal-hydrologic-mechanical-chemical effects on 
seepage and flow, the waste package chemical environment, and the chemical 
environment for radionuclide release, are consistent with available data. Reasonable 
or conservative ranges of parameters or functional relations are established. 
(4) Adequate representation of uncertainties in the characteristics of the natural system 
and engineered materials is provided in parameter development for conceptual models, 
process-level models, and alternative conceptual models. The U.S. Department of 
Energy may constrain these uncertainties using sensitivity analyses or conservative 
limits. For example, the U.S. Department of Energy demonstrates how parameters 
used to describe flow through the engineered barrier system bound the effects of 
backfill and excavation-induced changes. 
Acceptance Criterion 4Model Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
(1) Alternative modeling approaches of features, events, and processes are considered and 
are consistent with available data and current scientific understanding, and the results 
and limitations are appropriately considered in the abstraction. 
(2) Alternative modeling approaches are considered and the selected modeling approach is 
consistent with available data and current scientific understanding. A description that 
includes a discussion of alternative modeling approaches not considered in the final 
analysis and the limitations and uncertainties of the chosen model is provided. 
(3) Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog 
information and process-level modeling studies; and the treatment of conceptual 
model uncertainty does not result in an under-representation of the risk estimate. 
(4) Adequate consideration is given to effects of thermal-hydrologic-mechanical-chemical 
coupled processes in the assessment of alternative conceptual models. These effects 
may include: (i) thermal-hydrologic effects on gas, water, and mineral chemistry; 
(ii) effects of microbial processes on the engineered barrier chemical environment and 
the chemical environment for radionuclide release; (iii) changes in water chemistry 
that may result from the release of corrosion products from the engineered barriers and 
interactions between engineered materials and ground water; and (iv) changes in 
boundary conditions (e.g., drift shape and size) and hydrologic properties, relating to 
the response of the geomechanical system to thermal loading. 

EBS Radionuclide Transport Abstraction 
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Acceptance Criterion 5Model Abstraction Output Is Supported by Objective 
Comparisons. 
(1) The models implemented in this total system performance assessment abstraction 
provide results consistent with output from detailed process-level models and/or 
empirical observations (laboratory and field testings and/or natural analogs). 
(2) Abstracted models for coupled thermal-hydrologic-mechanical-chemical effects on 
seepage and flow and the engineered barrier chemical environment, as well as on the 
chemical environment for radionuclide release, are based on the same assumptions and 
approximations demonstrated to be appropriate for process-level models or closely 
analogous natural or experimental systems. For example, abstractions of processes, 
such as thermally induced changes in hydrological properties, or estimated diversion 
of percolation away from the drifts, are adequately justified by comparison to results 
of process-level modeling, that are consistent with direct observations and field 
studies. 
(3) Accepted and well-documented procedures are used to construct and test the numerical 
models that simulate coupled thermal-hydrologic-mechanical-chemical effects on 
seepage and flow, engineered barrier chemical environment, and the chemical 
environment for radionuclide release. Analytical and numerical models are 
appropriately supported. Abstracted model results are compared with different 
mathematical models, to judge robustness of results. 
4.2.1.2 Applicable Acceptance Criteria from Section 2.2.1.3.4, Radionuclide Release 
Rates and Solubility Limits 
The following acceptance criteria, listed in Section 2.2.1.3.4.3 of Yucca Mountain Review Plan, 
Final Report (NRC 2003 [DIRS 163274]), apply to this abstraction. These acceptance criteria 
are based on meeting the relevant requirements of 10 CFR 63.114(a)(c) and (e)(g) 
[DIRS 158535], as they relate to the radionuclide release rates and solubility limits model 
abstraction. 
Acceptance Criterion 1System Description and Model Integration Are Adequate. 
(1) Total system performance assessment adequately incorporates important design 
features, physical phenomena, and couplings, and uses consistent and appropriate 
assumptions throughout the radionuclide release rates and solubility limits abstraction 
process. 
(2) The abstraction of radionuclide release rates uses assumptions, technical bases, data, 
and models that are appropriate and consistent with other related U.S. Department of 
Energy abstractions. For example, the assumptions used for this model abstraction are 
consistent with the abstractions of Degradation of Engineered Barriers (NRC 2003 
[DIRS 163274], Section 2.2.1.3.1); Mechanical Disruption of Engineered Barriers 
(NRC 2003 [DIRS 163274], Section 2.2.1.3.2); Quantity and Chemistry of Water 
Contacting Engineered Barriers and Waste Forms (NRC 2003 [DIRS 163274], 
Section 2.2.1.3.3); Climate and Infiltration (NRC 2003 [DIRS 163274], 

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ANL-WIS-PA-000001 REV 01 4-25 November 2004 
Section 2.2.1.3.5); and Flow Paths in the Unsaturated Zone (NRC 2003 
[DIRS 163274], Section 2.2.1.3.6). The descriptions and technical bases provide 
transparent and traceable support for the abstraction of radionuclide release rates. 
(3) The abstraction of radionuclide release rates provides sufficient, consistent design 
information on waste packages and engineered barrier systems. For example, 
inventory calculations and selected radionuclides are based on the detailed information 
provided on the distribution (both spatially and by compositional phase) of the 
radionuclide inventory, within the various types of high-level radioactive waste. 
(4) The U.S. Department of Energy reasonably accounts for the range of environmental 
conditions expected inside breached waste packages and in the engineered barrier 
environment surrounding the waste package. For example, the U.S. Department of 
Energy should provide a description and sufficient technical bases for its abstraction of 
changes in hydrologic properties in the near field, caused by coupled 
thermal-hydrologic-mechanical-chemical processes. 
(5) The description of process-level conceptual and mathematical models is sufficiently 
complete, with respect to thermal-hydrologic processes affecting radionuclide release 
from the emplacement drifts. For example, if the U.S. Department of Energy 
uncouples coupled processes, the demonstration that uncoupled model results bound 
predictions of fully coupled results is adequate. 
(6) Technical bases for inclusion of any thermal-hydrologic-mechanical-chemical 
couplings and features, events, and processes in the radionuclide release rates and 
solubility Review Plan for Safety Analysis Report limits model abstraction are 
adequate. For example, technical bases may include activities, such as independent 
modeling, laboratory or field data, or sensitivity studies. 
Acceptance Criterion 2Data Are Sufficient for Model Justification. 
(1) Geological, hydrological, and geochemical values used in the license application are 
adequately justified. Adequate description of how the data were used, interpreted, and 
appropriately synthesized into the parameters is provided. 
(2) Sufficient data have been collected on the characteristics of the natural system and 
engineered materials to establish initial and boundary conditions for conceptual 
models and simulations of thermal-hydrologic-chemical coupled processes. For 
example, sufficient data should be provided on design features, such as the type, 
quantity, and reactivity of materials, that may affect radionuclide release for this 
abstraction. 
(4) The corrosion and radionuclide release testing program for high-level radioactive 
waste forms intended for disposal provides consistent, sufficient, and suitable data for 
the in-package and in-drift chemistry used in the abstraction of radionuclide release 
rates and solubility limits. For expected environmental conditions, the 
U.S. Department of Energy provides sufficient justification for the use of test results, 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 4-26 November 2004 
not specifically collected from the Yucca Mountain site, for engineered barrier 
components, such as high-level radioactive waste forms, drip shield, and backfill. 
Acceptance Criterion 3Data Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
(1) Models use parameter values, assumed ranges, probability distributions, and bounding 
assumptions that are technically defensible, reasonably account for uncertainties and 
variabilities, and do not result in an under representation of the risk estimate. 
(2) Parameter values, assumed ranges, probability distributions, and bounding 
assumptions used in the abstractions of radionuclide release rates and solubility limits 
in the total system performance assessment are technically defensible and reasonable 
based on data from the Yucca Mountain region, laboratory tests, and natural analogs. 
For example, parameter values, assumed ranges, probability distributions, and 
bounding assumptions adequately reflect the range of environmental conditions 
expected inside breached waste packages. 
(3) DOE uses reasonable or conservative ranges of parameters or functional relations to 
determine effects of coupled thermal-hydrologic-chemical processes on radionuclide 
release. These values are consistent with the initial and boundary conditions and the 
assumptions for the conceptual models and design concepts for natural and engineered 
barriers at the Yucca Mountain site. If any correlations between the input values exist, 
they are adequately established in the total system performance assessment. For 
example, estimations are based on a thermal loading and ventilation strategy; 
engineered barrier system design (including drift liner, backfill, and drip-shield); and 
natural system masses and fluxes that are consistent with those used in other 
abstractions. 
(4) Uncertainty is adequately represented in parameter development for conceptual 
models, process models, and alternative conceptual models considered in developing 
the abstraction of radionuclide release rates and solubility limits, either through 
sensitivity analyses or use of bounding analyses. 
(5) Parameters used to describe flow through and out of the engineered barrier, 
sufficiently bound the effects of backfill, excavation-induced changes, and thermally 
induced mechanical changes that affect flow. 
(8) DOE adequately considers the uncertainties, in the characteristics of the natural system 
and engineered materials, such as the type, quantity, and reactivity of material, in 
establishing initial and boundary conditions for conceptual models and simulations of 
thermal-hydrologic-chemical coupled processes that affect radionuclide release. 

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Acceptance Criterion 4Model Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
(1) Alternative modeling approaches of features, events, and processes are considered and 
are consistent with available data and current scientific understanding, and the results 
and limitations are appropriately considered in the abstraction. 
(2) In considering alternative conceptual models for radionuclide release rates and 
solubility limits, DOE uses appropriate models, tests, and analyses that are sensitive to 
the processes modeled for both natural and engineering systems. Conceptual model 
uncertainties are adequately defined and documented, and effects on conclusions 
regarding performance are properly assessed. For example, in modeling flow and 
radionuclide release from the drifts, DOE represents significant discrete features, such 
as fault zones, separately, or demonstrates that their inclusion in the equivalent 
continuum model produces a conservative effect on calculated performance. 
(3) Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog 
information and process-level modeling studies; and the treatment of conceptual 
model uncertainty does not result in an under-representation of the risk estimate. 
(4) The effects of thermal-hydrologic-chemical coupled processes that may occur in the 
natural setting, or from interactions with engineered materials, or their alteration 
products, on radionuclide release, are appropriately considered. 
Acceptance Criterion 5Model Abstraction Output Is Supported by Objective 
Comparisons. 
(1) The models implemented in this total system performance assessment abstraction 
provide results consistent with output from detailed process-level models and/or 
empirical observations (laboratory and field testings and/or natural analogs); 
(3) DOE adopts well-documented procedures that have been accepted by the scientific 
community to construct and test the numerical models, used to simulate coupled 
thermal-hydrologic-chemical effects on radionuclide release. For example, DOE 
demonstrates that the numerical models used for high-level radioactive waste 
degradation and dissolution, and radionuclide release from the engineered barrier 
system, are adequate representations; include consideration of uncertainties; and are 
not likely to underestimate radiological exposures to the reasonably maximally 
exposed individual and releases of radionuclides into the accessible environment; and 

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4.3 CODES, STANDARDS, AND REGULATIONS 
The relevant codes, standards, and regulations for the development of the EBS RT Abstraction 
are listed in Section 9.2. 

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ANL-WIS-PA-000001 REV 01 5-1 November 2004 
5. ASSUMPTIONS 
5.1 ALL SEEPAGE FALLS ONTO DRIP SHIELD/WASTE PACKAGE 
Assumption: It is assumed that the locations of seeps in the emplacement drifts are random with 
respect to waste package locations, but that once a seep occurs, its location does not change over 
time. It is also assumed that fragments of the drip shield that may rest on the waste package, or 
fallen rock that may rest on the drip shield or waste package, do not divert any seepage flux. In 
addition, it is assumed that all seepage into the drift falls on the crown of the drip shield, and in 
the absence of a drip shield, all seepage falls on the crown of the waste package. In the event of a 
breach in the drip shield, all the seepage that penetrates the drip shield contacts the waste 
package. 
Basis: Once seepage occurs during cooldown, the fracture characteristics that control the 
location of seepage are not expected to change. If such changes occur, they are likely to be 
limited in extent, or to occur in a random manner for many waste packages such that there is no 
overall, significant effect on the interaction of seepage water with waste forms. The mean 
seepage for the degraded drift is greater than for the non-degraded case, but the factors 
controlling seep locations are still likely to occur in a random manner for many waste packages. 
Confirmation Status: This assumption does not require confirmation because it maximizes the 
duration of seepage contact with drip shields and waste packages as represented in TSPA-LA. It 
also maximizes the flux of dripping water available to flow through breaches in the drip shield or 
waste package, once such flow is initiated as represented in the TSPA-LA. 
Use in the Model: This assumption is used throughout Sections 6 and 7. 
5.2 EVAPORATION FROM A DRIP SHIELD DOES NOT OCCUR 
Assumption: It is assumed that there is no evaporation of seepage water from the surface of the 
drip shield. 
Basis: The heat output from the waste package will cause the drip shield generally to be hotter 
than the drift wall from which seepage water is dripping. Some seepage water that drips onto the 
drip shield may be evaporated, thereby reducing the flux of water through the drip shield. A 
reduction in the quantity of water flux through the drip shield reduces the potential for advective 
transfer and subsequent release and transport of radionuclides from the waste packages. Ignoring 
the process of evaporation in this analysis therefore bounds (maximizes) the impacts of the 
seepage flux on waste packages. 
Although some splashing or splattering can occur as water droplets impinge on the drip shield, 
the splash distance would be limited, and the water would effectively be redistributed over the 
top of the drip shield. If water droplets were to fall near the edge of the top plate, some splashes 
could fall onto the invert or lower walls of the drift and drain directly into the invert. This 
situation would minimize the degrading effects of water dripping on the drip shield and therefore 
is eliminated from consideration in order to bound the impacts of the seepage flux on waste 
packages. 

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Confirmation Status: This assumption does not require confirmation because it provides for a 
reasonable upper bound on the flux available to interact with the drip shield and waste package, 
and bounds (maximizes) the potential degrading effects of seepage water on the drift 
environment. 
Use in the Model: This assumption is used in Sections 6.3.2.4, 6.5.1.1, and 7.2.1. 
5.3 EVAPORATION FROM A WASTE PACKAGE DOES NOT OCCUR 
Assumption: It is assumed that evaporation of water from the surface or interior of a waste 
package does not occur. 
Basis: Although heat released by spent nuclear fuel (SNF) will evaporate seepage water that 
drips onto the surface of or flows into breaches in a waste package, this process is not included in 
the analysis. Advective transport within the EBS is not possible if evaporation eliminates liquid 
fluxes. Therefore, evaporative processes are eliminated from this analysis to maximize the 
potential for advective transport of radionuclides. In addition to maximizing the advective flux 
of radionuclides from a waste package, this assumption also allows the water saturation inside a 
failed waste package to be set at 100 percent (fully saturated) in a codisposal waste package or in 
the degraded waste rind inside a failed fuel rod in a CSNF waste package, thereby maximizing 
the amount of water available for dissolving radionuclides. This assumption comes into play 
only after the thermal peak period of roughly 1,000 years (BSC 2004 [DIRS 169565], 
Figure 6.3-67), since dripping onto a waste package will not occur until the drift has cooled 
sufficiently for liquid water to be present. Because the relative humidity in the drift is low 
during the thermal peak period, condensation on cooler waste packages is unlikely, precluding 
evaporation from those surfaces. 
Confirmation Status: This assumption does not require confirmation because it is used to ensure 
the maximum potential for advective transport of radionuclides. 
Use in the Model: This assumption is used in Sections 6.3.3, 6.5.1.1.3, and 7.2.2. 
5.4 PRODUCTION OR CONSUMPTION OF WATER BY CHEMICAL REACTIONS 
DOES NOT OCCUR 
Assumption: It is assumed that chemical reactions in the EBS neither produce nor consume 
water and therefore do not effect on the water mass balance in the EBS. 
Basis: Chemical processes in the EBS could produce or consume water. This is generally a 
small effect. Although unlikely, water could possibly be produced by the decomposition of 
hydrated salts or minerals. However, this phenomenon would only occur at elevated 
temperatures where liquid water would not be present; this would result in the release of water 
vapor rather than liquid water, and therefore would not directly affect liquid water fluxes. Water 
absorption by hygroscopic salts deposited on the drip shield and waste package surfaces as dust 
or as precipitates from earlier drift seepage may lead to the formation of aqueous solutions when 
the relative humidity reaches the deliquescence point of the salts (BSC 2004 [DIRS 169863], 
Sections 6.3 and 6.6). While this phenomenon may have important implications for corrosion 
processes, the quantity of liquid potentially produced by deliquescence is minimal and thus 

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assumed to be negligible, limited by the amount of salts that can be deposited on the waste 
package and drip shield surfaces. It is therefore reasonable to neglect the formation of aqueous 
solutions due to water absorption by hygroscopic salts as a source of water for advective 
transport. 
However, consumption of water, particularly by corrosion reactions, is likely to occur. Anoxic 
corrosion of iron inside a waste package is a prime example of a water-consuming process that 
can consume enough water to impact flow through a waste package. Formation of hydrated 
corrosion products may also consume negligibly small amounts of water. Water absorption by 
hygroscopic salts deposited on the drip shield and waste package surfaces as dust or as 
precipitates would consume water as long as the relative humidity remains below the 
deliquescence point of the salts, although the quantity of water consumed is likely to be 
negligible. Neglecting consumption of water in the EBS radionuclide transport analysis is a 
bounding assumption, providing more water for dissolution and transport of radionuclides, and 
potentially greater releases, than would otherwise occur. 
Confirmation Status: This assumption does not require confirmation because it bounds 
(maximizes) the amount of water potentially available for advective transport and release of 
radionuclides. 
Use in the Model: This assumption is used throughout Sections 6 and 7. 
5.5 THIN WATER FILMS ALWAYS EXIST BELOW 100C 
Assumption: A thin film of adsorbed water is assumed always to exist on the surfaces of internal 
waste package components and corrosion products in a breached waste package. This water film 
is assumed to be continuous and to behave as bulk liquid insofar as allowing radionuclides to 
dissolve in and diffuse through it. At and above 100C, the thin film is assumed to evaporate, 
and no transport of radionuclides takes place. 
Basis: All surfaces exposed to water vapor will adsorb water. The amount of adsorbed water 
vapor depends principally on the nature of the sorbing material and the ambient relative 
humidity. 
The first layers of adsorbed water often do not contain ions from the sorbing solid (Lee 1994 
[DIRS 154380], p. 73). This indicates that multiple water layers are needed in order for solid 
species (such as radionuclides) to dissolve and diffuse. Thus, to assume that radionuclides will 
dissolve in and diffuse through the adsorbed water film regardless of its thickness will 
overestimate releases of radionuclides. It is also necessary to assume that the water film is 
continuous, i.e., there are no gaps in the film from one particle or surface to the next, so that 
radionuclides can diffuse throughout the waste package interior and through corrosion products. 
Above the boiling point of water, the thin films are assumed to evaporate. Due to the lack of a 
continuous water film, transport cannot take place. The boiling point is nominally 100C, but 
may vary due to the elevation of the repository or to dissolved salts in the water film. 
Temperatures above the boiling point will exist at least through the thermal peak period of 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 5-4 November 2004 
roughly 1,000 years (BSC 2004 [DIRS 169565], Figure 6.3-67), and may continue to exist on 
certain waste packages well beyond that time. 
Confirmation Status: This assumption does not require confirmation because it allows for 
radionuclide transport due to the presence of a continuous thin film of water on the surfaces of 
internal waste package components and corrosion products. 
Use in the Model: This assumption is used in Sections 6.3.4. 
5.6 ALL CORROSION PRODUCTS ARE HEMATITE (Fe2O3) 
Assumption: It is assumed that the products of the corrosion of all internal waste package 
components except for fuel rods and spent nuclear fuel (SNF) are Fe2O3 (hematite). 
Basis: This is a necessary assumption for the purpose of calculating corrosion product surface 
area and the resulting potential adsorption of water. Establishing the mineralogical type of iron 
oxide corrosion product enables the amount of water adsorbed onto surfaces to be estimated. 
This assumption also allows for reasonable estimates of the void volume of the waste package 
under conditions when the waste package internal components are fully corroded. 
The bulk of the mass of materials in a CSNF waste package, excluding the SNF and the outer 
corrosion barrier, consists of various types of steel. The iron content of these steels (Table 6.3-4) 
ranges from 61.935 weight percent (Type 316, used in the inner vessel; 
DTN: MO0003RIB00076.000 [DIRS 153044]) to 98.37 weight percent (A 516 carbon steel, 
used in the basket components; DTN: MO0107TC240032.000 [DIRS 169970]). It is thus 
reasonable to treat all corrosion products as iron oxide. 
Geochemical analyses of the basket degradation process (YMP 1998 [DIRS 104441], p. C-23) 
have demonstrated that the iron oxide produced from corrosion of carbon steel and borated 
stainless steels will remain in the waste package as insoluble hematite. In addition to hematite, 
goethite (FeOOH) is expected to form. The water vapor adsorption isotherm (expressed as water 
layer thickness) for goethite is similar to that of hematite (Jurinak 1964 [DIRS 154381], p. 486), 
although at a given relative humidity, more water is adsorbed onto hematite than onto goethite. 
The specific surface area of goethite is generally greater than hematite (Langmuir 1997 
[DIRS 100051], Table 10.2), meaning that the water content is greater and the potential for 
radionuclide sorption is greater for goethite than for hematite. However, measurements of rust 
on ancient iron artifacts indicate that the specific surface area of goethite and other iron oxides 
ranges from 6 to 15 m2 g-1 (Dillmann et al. 2004 [DIRS 171480], p. 1421 and Table 7), 
comparable to that of hematite. Thus, insofar as affecting the mobility of radionuclides in 
corrosion products, the higher specific surface area of goethite is offset by the greater water 
adsorption on hematite and the indications that the minerals comprising corrosion products have 
a much lower specific surface area than pure goethite. Hematite sorption behavior has been 
studied more thoroughly than goethite sorption behavior, which provides greater confidence that 
its behavior is represented accurately; therefore, corrosion products are assumed to be hematite. 
Confirmation Status: This assumption does not require confirmation because it is a reasonable 
approach in the absence of detailed compositional data, corrosion process information, and 
adsorption isotherms for the numerous other potential steel corrosion products. 

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Use in the Model: This assumption is used in Sections 6.3.4. 
5.7 NO CORROSION PRODUCTS EXIST IN THE INVERT 
Assumption: It is assumed that no corrosion products exist in the invert. 
Basis: Neglecting the corrosion products in the invert is an assumption that maximizes the 
potential transport of radionuclides through the invert. The invert consists of a carbon steel 
structural frame supported on the lower drift walls, and of crushed tuff ballast placed below and 
between the steel frame members. The invert steel structure consists of transverse beams 
anchored at each end on the drift wall, and of three longitudinal beams which directly support the 
waste package pallet. When the invert steel beams corrode, most of the iron oxide corrosion 
products will end up in the crushed tuff component of the invert. In addition, communication 
cables will eventually corrode, leaving copper oxide corrosion products in the invert. The 
crushed tuff has little radionuclide sorptive capacity compared to the metal oxide corrosion 
products, which are capable of sorbing large amounts of radionuclides, potentially enhancing the 
barrier capability of the invert. However, the corrosion products in the invert will tend to be 
localized and widely separated. For example, the transverse support beams in the invert are 
spaced 1.524 m (5 ft 0 in.) apart (BSC 2004 [DIRS 169503]). Thus, the corrosion products of 
the support beams will reside in a strip a few centimeters wide separated by 1.524 m of crushed 
tuff containing little or no corrosion products. Compared with the length of a waste package 
[3.45 m (5 DHLW/DOE SNF - Short) to 5.84 m (Naval long) (BSC 2004 [DIRS 169472], 
Table 1)], the width of regions within the invert that would potentially contain corrosion 
products is small. Therefore, the chance of radionuclides being released from the waste package 
and passing through corrosion products in the invert is proportionately small. Although the 
invert will contain steel corrosion products, it is bounding in terms of radionuclide releases to 
neglect their presence. 
Confirmation Status: This assumption does not require confirmation because it is a bounding 
assumption that reduces the potential effectiveness of the invert as a transport barrier; i.e., the 
potential for radionuclide sorption by steel corrosion products is ignored. 
Use in the Model: This assumption is used in Sections 6.3.4.2. 

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INTENTIONALLY LEFT BLANK 

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6. MODEL DISCUSSION 
6.1 MODELING OBJECTIVE 
The objective of the EBS RT Abstraction is to provide the conceptual model used to determine 
the time-dependent flux of radionuclides from the EBS to the unsaturated zone in the TSPA-LA. 
In particular, this model is used to quantify such releases from a failed waste package and the 
subsequent transport of those radionuclides through the EBS to the emplacement drift 
wall/unsaturated zone interface. The basic time-dependent inputs to the EBS RT Abstraction in 
TSPA-LA calculations consist of the drift seepage influx, the environmental conditions in the 
drift (temperature, relative humidity, and water chemistry), and the degradation state of the EBS 
components. Outputs consist of the rates of radionuclide fluxes to the unsaturated zone as a 
result of advective and diffusive transport, radionuclide solubility, retardation, the degree of 
liquid saturation of the waste form and invert materials, and the impact of colloids on potential 
radionuclide transport. The EBS RT Abstraction is implemented directly into the TSPA-LA 
GoldSim model to compute the release rates; details of the implementation are provided in 
Section 6.5.3. 
6.1.1 Engineered Barrier System Components 
The EBS consists of the drip shield, the waste package on an emplacement pallet, and an invert 
constructed with steel supports and filled between the steel framework with crushed tuff. Each 
of the components of the EBS is designed to act as a barrier to prevent or delay the mobilization 
and release of radionuclides into the geologic environment (see Section 6.7 for a summary of 
barrier capabilities). For example, the drip shield is designed to redirect any seepage that flows 
into the drift away from the waste package. The invert supports the waste package and 
emplacement pallet. It acts as a barrier to diffusive transport of radionuclides in liquids if the 
liquid saturation in the crushed tuff is low. Figure 6.1-1 presents a typical cross-section of an 
emplacement drift and the major components of the EBS. 
The drip shield is fabricated from titanium, a corrosion-resistant material to provide long-term 
effectiveness. The waste package outer corrosion barrier is comprised of Alloy 22. The major 
corrosive processes are stress corrosion cracking in the closure lid welds of the waste package, 
localized corrosion in the waste package outer corrosion barrier, and general corrosion for both 
the drip shield and waste package. 
Once the drip shield fails (i.e., is initially breached), a portion of the total dripping flux can drip 
onto the waste package. It is possible for breaches to occur at the gap between adjacent waste 
packages, because the overlap between adjacent drip shields is located over the gap, and this 
overlap is a potential leakage pathway. If breaches in the drip shield occur at the gap between 
two drip shield segments, the dripping flux would fall directly to the invert, avoiding the waste 
package. The possibility that breaches in the drip shield can occur over a gap, allowing liquid to 
bypass the waste package, is not considered in the EBS RT Abstraction. 

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Figure 6.1-1. Schematic Diagram of a Typical Emplacement Drift and the Major Components of the EBS 
After the waste package fails (breached by corrosion, seismic damage, or early failure 
mechanisms), a portion of the water that flows through the drip shield can enter the waste 
package, mobilizing radionuclides in any degraded waste form, and transporting these 
radionuclides into the unsaturated zone. Diffusion is the primary transport mechanism when the 
flux into the waste package is small or zero, or if stress corrosion cracks are the only penetrations 
through the waste package. Advective transport is important when the dripping flux occurs. In 
this case, advective fluxes can pass through the breaches in the drip shield and waste package. 
6.1.2 Scenario Classes for TSPA-LA 
A scenario is a well-defined, connected sequence of features, events, and processes (FEPs) that 
can be thought of as an outline of a possible future condition in the repository system. Scenarios 
can be designated as undisturbed, in which case the performance would be the expected or 
nominal performance of the system. Or, scenarios can be designated as disturbed, if altered by 
disruptive events, such as human intrusion, or by natural phenomena, such as volcanism or 
nuclear criticality. A scenario class is a set of related scenarios that share sufficient similarities 
to aggregate them usefully for the purposes of screening or analysis. The scenario classes 

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ANL-WIS-PA-000001 REV 01 6-3 November 2004 
included in TSPA-LA are the nominal scenario class, igneous scenario class, and seismic 
scenario class. 
Nominal Scenario ClassThe nominal scenario class for TSPA-LA encompasses all of the FEPs 
that are screened in, except for those FEPs related to igneous or seismic activity. This scenario 
class therefore incorporates the important effects and system perturbations caused by climate 
change and repository heating that are projected to occur over the 10,000-year 
regulatory-compliance period. In addition, the nominal scenario class considers that the waste 
packages and drip shields will be subject to EBS environments and will degrade with time until 
they are breached and expose the waste forms to percolating groundwater. Then the waste forms 
will degrade, releasing and mobilizing radionuclides that subsequently will be transported out of 
the repository. Radionuclides released from the repository then will be transported to the 
saturated zone by the groundwater percolating through the unsaturated zone below the 
repository, and then transported to the accessible environment by water flowing in the saturated 
zone. 
The nominal scenario class is represented by two modeling cases. The first is for those waste 
packages that degrade by corrosion (general corrosion, stress-corrosion cracking, and localized 
corrosion) under expected repository conditions. The second is for those waste packages that fail 
early due to manufacturing and material defects and pre-emplacement operations including 
improper heat treatment. 
Igneous Scenario ClassThe igneous scenario class describes performance of the repository 
system in the event of igneous activity that disrupts the repository and is represented by two 
modeling cases: (1) igneous intrusion into the repository emplacement drifts that results in 
release of radionuclides to the groundwater and (2) volcanic eruption through the repository 
resulting in release of radionuclides to the atmosphere. Both modeling cases assume that the 
igneous event consists of a magmatic penetration of the repository at some time after permanent 
closure. 
The igneous intrusion modeling case assumes that an igneous dike intersects drifts of the 
repository and destroys drip shields and waste packages in those drifts intruded by magma, 
exposing the waste forms to percolating water and mobilizing radionuclides. The released 
radionuclides can then be transported out of the repository, and flow down through the 
unsaturated zone to the saturated zone, and then be transported through the saturated zone flow 
and transport system to the accessible environment. Radionuclide releases occur only as a result 
of igneous interactions with EBS components and not as a result of drip shield or waste package 
corrosion processes or early waste package failure. 
The volcanic eruption modeling case assumes that the magma flow associated with a dike 
intersects the repository and destroys a limited number of waste packages, transports waste from 
the destroyed waste packages to the land surface through one or more eruptive conduits, and then 
discharges tephra and entrained waste into the atmosphere and transports it downwind. 
Seismic Scenario ClassThe seismic scenario class describes performance of the repository 
system in the event of low probability seismic activity capable of disrupting repository 
emplacement drifts and the engineered components of the EBS. This scenario class includes 

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ANL-WIS-PA-000001 REV 01 6-4 November 2004 
potential damage to drip shields, waste packages, and CSNF cladding as a function of the 
magnitude of the event in addition to localized corrosion processes on the waste package outer 
corrosion barrier. Radionuclides are dissolved and mobilized and transported out of the 
repository, transported to the water table by the groundwater percolating through the unsaturated 
zone, and then transported to the accessible environment by water flowing in the saturated zone. 
Localized corrosion processes on the waste package outer corrosion barrier are included in the 
seismic scenario class because synergistic interactions between localized corrosion and ground 
motion damage to EBS components may be important. 
The seismic scenario class is represented by two modeling cases. The first is for those waste 
packages that fail solely due to mechanical damage associated with the seismic event 
(i.e., vibratory ground motion or fault displacement). The second is for waste package localized 
corrosion initiated prior to and following the seismic event. This modeling case includes any 
mechanical damage, general corrosion and microbially influenced corrosion that also occurs 
along with the localized corrosion. 
6.2 FEATURES, EVENTS, AND PROCESSES INCLUDED IN THE MODEL 
The development of a comprehensive list of FEPs potentially relevant to postclosure 
performance of the Yucca Mountain repository is an ongoing, iterative process based on 
site-specific information, design, and regulations. The approach for developing an initial list of 
FEPs, in support of TSPA-Site Recommendation (SR) (CRWMS M&O 2000 [DIRS 153246]), 
was documented in The Development of Information Catalogued in REV00 of the YMP FEP 
Database (Freeze et al. 2001 [DIRS 154365]). The initial features, events and processes (FEP) 
list contained 328 FEPs, of which 176 were included in TSPA-SR models (CRWMS M&O 2000 
[DIRS 153246], Tables B-9 through B-17). To support TSPA-LA, the FEP list was re-evaluated 
in accordance with The Enhanced Plan for Features, Events, and Processes (FEPs) at Yucca 
Mountain (BSC 2002 [DIRS 158966], Section 3.2), resulting in the LA FEP list 
(DTN: MO0407SEPFEPLA.000 [DIRS 170760]). Table 6.2-1 provides a list of FEPs that are 
included in TSPA-LA models described in this model document, summarizes the details of their 
implementation in TSPA-LA, and provides specific references to sections within this document. 
Screening arguments for both included and excluded FEPs are summarized in Engineered 
Barrier System Features, Events, and Processes (BSC 2004 [DIRS 169898]). 
Table 6.2-1. Included FEPs for This Report 
FEP No. FEP Name/FEP Description Section Where Disposition Is Described 
2.1.06.06.0A Effects of drip shield on flow 6.3.2.4 
6.5.1.1 
2.1.08.04.0A Condensation forms on roofs of drifts (driftscale 
cold traps) 
6.3 
2.1.08.05.0A Flow through invert 6.3 
6.5 
2.1.08.06.0A Capillary effects (wicking) in EBS 6.3 
6.5 

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ANL-WIS-PA-000001 REV 01 6-5 November 2004 
Table 6.2-1. Included FEPs for This Report (Continued) 
FEP No. FEP Name/FEP Description Section Where Disposition Is Described 
2.1.08.07.0A Unsaturated flow in the EBS 6.3 
6.5 
2.1.09.05.0A Sorption of dissolved radionuclides in EBS 6.3.4.2 
6.5.1.2 
6.5.3 
2.1.09.08.0A Diffusion of dissolved radionuclides in EBS 6.3.1.2 
6.3.4.1 
6.5.1.2 
6.5.3.1 
2.1.09.08.0B Advection of dissolved radionuclides in EBS 6.3.1.2 
2.1.09.19.0B Advection of colloids in EBS 6.3.4.4 
6.5.1.2 
6.5.3 
2.1.09.24.0A Diffusion of colloids in EBS 6.3.4.4 
6.5.1.2 
6.5.3 
2.1.11.09.0A Thermal effects on flow in the EBS 6.3.1.1 
2.2.07.06.0A Episodic/pulse release from repository 6 
2.2.07.06.0B Long-term release of radionuclides from the 
repository 
6 
6.3 BASE CASE CONCEPTUAL MODEL 
6.3.1 Introduction and Overview 
6.3.1.1 EBS Flow Abstraction 
The primary source of inflow to the EBS is the seepage flux that drips from the crown (roof) of 
the drift. This flux is driven by downward infiltration through the existing fracture system at 
Yucca Mountain. The seepage flux is conceptualized to flow from discrete fractures above the 
roof of the drift, falling vertically downward. The seepage flux is represented in the TSPA-LA 
model through Abstraction of Drift Seepage (BSC 2004 [DIRS 169131]). A secondary source of 
inflow to the EBS is imbibition into the invert crushed tuff particles from the surrounding UZ 
rock matrix. The inflow from these sources can flow through the EBS along eight pathways, as 
shown in Figure 6.3-1. 
The eight pathways are (with the volumetric water flux through pathway j designated by Fj): 
1. Seepage flux (F1)This is the seepage inflow (dripping flux) from the crown (roof) of 
the drift. Any condensation that may occur on the walls of the drift above the drift 
shield is included in this seepage flux. 

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ANL-WIS-PA-000001 REV 01 6-6 November 2004 
Figure 6.3-1. Schematic of the Potential Flow Pathways in the EBS 
2. Flux through the drip shield (F2)The flux through the drip shield is based on the 
presence of patches due to general corrosion; localized corrosion and stress corrosion 
cracking on the drip shield are not expected to occur within the regulatory time period 
for repository performance (10,000 years) and are ignored (BSC 2004 [DIRS 169996], 
Section 7.2). The liquid flux through corrosion patches is proportional to the ratio of 
the axial length of the penetration(s) in the drip shield to the total axial length of a drip 
shield section (see Section 6.3.2.4). This flux splitting submodel for the drip shield 
should only be applied when there is a time-varying failure of the drip shield. 
3. Diversion around the drip shield (F3)The portion of the flux that does not flow 
through the drip shield is assumed to flow directly into the invert. 
4. Flux through the waste package (F4)The flux through the waste package is based 
on the presence of patches due to general corrosion and localized corrosion in the 

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ANL-WIS-PA-000001 REV 01 6-7 November 2004 
waste package outer barrier. The number of patches in the waste package is calculated 
independently of the EBS RT Abstraction by the WAPDEG code (BSC 2004 
[DIRS 169996]). The flux through waste package corrosion patches is proportional to 
the ratio of the axial length of the penetration(s) in the waste package to the total axial 
length of a waste package (see Section 6.3.3.2). 
5. Diversion around the waste package (F5)The portion of the flux that does not flow 
into the waste package bypasses the waste form and flows directly into the invert. 
6. Flux into the Invert (F6)All water flux from the waste package is modeled as 
flowing directly into the invert, independent of patch location on the waste package. 
In addition, the fluxes that were diverted around the waste package (F5) and around the 
drip shield (F3) flow into the invert. Only a portion of the total flux to the invert (the 
flux through the waste package, F4) will contain radionuclides. 
7. Imbibition Flux to the Invert (F7)Water can be imbibed from the host rock matrix 
into the invert. 
8. Flux from the Invert to the Unsaturated Zone (F8)A portion of the advective flux 
from the invert equal to the total dripping flux (F1) flows directly into the unsaturated 
zone (UZ) fractures. The portion of the advective flux from the invert equal to the 
imbibition flux to the invert (F7) flows into the UZ matrix. 
These pathways are time dependent, in the sense that total dripping flux, drip shield gaps, drip 
shield penetrations, and waste package penetrations will vary with time and local conditions in 
the repository. 
The conceptual model for flow through the EBS includes three domains: the waste form 
(e.g., fuel rods or HLW glass), waste package corrosion products, and the invert. The first two 
domains are conceptualized to have concentric cylindrical geometry for volume calculations, 
with one-dimensional radial flow. The first domain (waste form) is part of the waste package 
that contains fuel rods or glass logs, which undergo alteration to form a rind. The thickness of 
the rind can be as much as the diameter of the fuel rod or glass log. The second domain 
(corrosion products from degradation of steel internal components) fills the inside of a waste 
package within the Alloy 22 outer corrosion barrier, so its thickness is uncertain and can be as 
much as the radius of the waste package. The third domain (invert) is in intimate contact with 
the waste package and has a thickness of 0.597 m (see Section 6.5.3). This is the average 
thickness of the invert directly beneath the waste package. This value is appropriate because 
flow out of the waste package is primarily vertically downward, and, ignoring splashing, it will 
not drip onto the surface of the invert beyond the edges of the waste package. Because the 
presence of the emplacement pallet is ignored, water and radionuclides pass directly from the 
waste package to the invert. 
The waste form domain represents the source term for the TSPA-LA. Source term abstractions 
are defined in other model reports or design documents for radionuclide solubility (BSC 2004 
[DIRS 169425]), HLW glass dissolution rate (BSC 2004 [DIRS 169988]), cladding response 
(BSC 2004 [DIRS 170023]), and inventory by waste package type (BSC 2004 [DIRS 169472], 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-8 November 2004 
Table 11). The source term represents input data or boundary conditions for the EBS RT 
Abstraction and is not discussed in this document. 
The final output from the EBS RT Abstraction is the mass flux of radionuclides (kg yr-1) from the 
EBS into the unsaturated zone. The parameters and formulas for calculating the water fluxes in 
the various pathways are summarized in Table 6.3-1. 
Table 6.3-1. Summary of Parameters for EBS Flow Pathways 
Flow Pathway, Pathway Flux Fj Flow Parameters Data Sources & Notes 
1. Total dripping flux, F1 Total dripping flux is a function of 
fracture properties, rock properties, 
and the percolation flux. 
Abstraction of Drift Seepage (BSC 
2004 [DIRS 169131]) provides timeand 
location-dependent values of total 
dripping flux. 
2. Flux through the drip shield, 
F2 
LDS_Patch is the axial half-length of 
each patch due to general corrosion 
of Ti. 
LDS is the axial length of the drip 
shield. 
NbDS is the number of corrosion 
patches of length LDS_Patch in the drip 
shield. 
f 'DS is sampled uncertain parameter, 
Flux_Split_DS_Uncert. 
F2 = min[F1NbDSLDS_Patchf 'DS/LDS, F1] 
This flux splitting submodel for the drip 
shield should only be applied when 
there is a time-varying failure of the 
drip shield. 
3. Diversion around drip 
shield, F3 
F3 = F1 - F2. Continuity of liquid flux. 
4. Flux into the WP, F4 LWP_Patch is the axial half-length of 
each patch due to general corrosion 
of Alloy 22. 
LWP is the axial length of the WP. 
NbWP is the number of corrosion 
patches in the waste package. 
f 'WP is sampled uncertain parameter, 
Flux_Split_WP_Uncert. 
F4 = min[F2NbWPLWP_Patchf 'WP/LWP, F2] 
WAPDEG (BSC 2004 [DIRS 169996]) 
provides the number of patches and 
stress corrosion cracks on the WP. 
No flow through stress corrosion 
cracks due to plugging (BSC 2004 
[DIRS 172203], Section 6.3.7). 
Steady state flow through WP (outflow 
= inflow in steady state; this is 
bounding for release). 
5. Diversion around the WP, F5 F5 = F2 - F4 Continuity of liquid flux. 
6. Flux to the invert, F6 F6 = F5 + F4 + F3 
= F1 
All advective flux enters the invert. 
Only F4 can transport radionuclides 
into the invert. 
7. Imbibition flux from the host 
rock matrix into the invert, F7 
F7 is an input to the EBS flow model. Imbibition flux is provided by 
Multiscale Thermohydrologic Model 
calculations (BSC 2004 
[DIRS 169565]). 
8. Flux from the invert into to the 
unsaturated zone, F8 
F8 = F6 + F7 
= F1 + F7 
Total dripping flux portion (F1) of 
advective flux from the invert flows into 
the UZ fractures, imbibition flux (F7) 
flows into the UZ matrix. 
WP=waste package; UZ=unsaturated zone 

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6.3.1.2 EBS Transport Abstraction 
The waste form is the source of all radionuclides considered for the EBS. Radionuclides can be 
transported downward, through the invert and into the unsaturated zone. Transport can occur 
through advection when there is a liquid flux through the waste package and invert, via pathways 
6 and 8 in Figure 6.3-1. Transport can also occur by diffusion in the waste form, in stress 
corrosion cracks in the lid of the waste package, and in the invert, even in the absence of a liquid 
flux, because it is assumed (Assumption 5.5) that there is a continuous liquid pathway via thin 
films. Diffusive transport may occur via flow pathways 6 and 8 even when no advection occurs 
on those pathways in the EBS flow model. 
A detailed mathematical description of transport in the EBS is presented in Section 6.5.1.2. 
Retardation of radionuclides occurs in the waste package. Transport occurs by diffusion and by 
advection. Table 6.3-2 summarizes the modes and parameters for the transport pathways in the 
EBS. 
Lateral and longitudinal dispersion are neglected in modeling radionuclide transport in the EBS. 
Because the EBS radionuclide transport model is a one-dimensional model, the lateral dispersion 
effects cannot be considered. This also maximizes the concentration in a given domain for 
greater mass flux. Longitudinal dispersion could potentially be considered in the invert, where 
advection is expected to occur due to imbibition flux, even when there is no drift seepage flux. 
However, the longitudinal dispersivity is uncertain, being dependent on the scale of transport 
(Anderson and Woessner 1992 [DIRS 123665], p. 326) and on porous media characteristics that 
are not well-defined. Since the thickness of the invert is less than one meter, longitudinal 
dispersion is expected to be small and to have negligible effect on the breakthrough times 
through the invert compared to the simulated time-steps considered in TSPA (tens of years). In 
addition, as shown in Section 6.3.4.1, the uncertainty in the invert diffusion coefficient ranges 
over a factor of 20 and essentially encompasses the variable breakthrough times that could occur 
from including the longitudinal dispersion. The dispersivity of the waste form and waste 
package corrosion product domains is also difficult to characterize; however, because the scale 
of these domains is comparable to that of the invert, and because the diffusion coefficients in 
these domains are similar (or larger) than those in the invert, it is reasonable to neglect 
dispersivity in these domains as well as in the invert. 
There is no upward transport of radionuclides because there is no solid medium with a liquid 
pathway above the drip shield. After the drip shield is breached, upward diffusion is negligible 
in comparison to the downward advective flux through the drip shield. 
Colloid-facilitated transport of radionuclides is included in the EBS RT Abstraction. 
Radionuclide transport from the waste package occurs in a liquid containing colloids and 
dissolved radionuclides. There are three types of colloids in the EBS: (a) waste form colloids 
from degradation of HLW glass, (b) iron oxyhydroxide colloids due to products from the 
corrosion of steel waste packages, and (c) groundwater or seepage water colloids. All three 
types of colloids may have reversibly sorbed radionuclides. The waste form colloids may have 
irreversibly attached (embedded) radionuclides and the corrosion products colloids may have 
reversibly attached (sorbed) radionuclides. However, some radionuclides, such as Pu and Am, 
can be so strongly sorbed onto iron oxyhydroxide that for modeling purposes they can be 

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considered to be irreversibly sorbed. Colloids may be transported by diffusion as well as by 
advection. The diffusion coefficient for colloids is less than that of dissolved species, but 
colloids are not excluded from diffusion due to size. 
Table 6.3-2. Summary of Transport Modes and Parameters for the EBS Transport Pathways 
Transport Pathway Transport Modes Transport Parameters and Data Sources 
1. Waste form and 
corrosion products 
domains 
Diffusion through stress 
corrosion cracks (no 
advective transport through 
stress corrosion cracks). 
Diffusion and advection 
through patches. 
No lateral or forward dispersion. 
Colloidal particles will transport radionuclides. 
Diffusive area for each stress corrosion crack is 
7.7  10-6 m2 (see Section 6.3.3.1.2.1). 
Diffusive area for each patch is provided by WAPDEG 
(BSC 2004 [DIRS 169996]). 
Diffusion coefficient (all radionuclides): 
 2.299  10-5 cm2 s-1 at 25C (Mills 1973 
[DIRS 133392], Table III) 
 Modified for porosity and saturation (see 
Section 6.5.1.2.1.4) 
 Reduced by a factor of 100 if radionuclide is 
bound to a colloid (Section 6.3.4.4) 
The flow cross-sectional area is given by the interface 
between the waste package corrosion products 
domain and the invert domain. 
See Section 6.5.3 for further details. 
2. Invert Diffusion and advection 
(F6) from corrosion 
products domain into the 
invert. 
Liquid flux for advection = F6 = F5 (diverted by WP) + 
F4 (flux through WP) + F3 (diverted by drip shield). 
Diffusion coefficient (all radionuclides): 
 2.299  10-5 cm2 s-1 at 25C (Mills 1973 
[DIRS 133392], Table III) 
 Modified for porosity and saturation (see 
Section 6.3.4.1) 
 Temperature modification defined in 
Section 6.3.4.1.2; invert temperature is 
provided by Multiscale Thermohydrologic 
Model calculations (BSC 2004 [DIRS 
169565]) 
 Reduced by a factor of 100 if radionuclide is 
bound to a colloid (Section 6.3.4.4) 
The flow cross-sectional area is the surface area 
between the invert and the drift wall contacting the 
invert. 
See Section 6.5.3 for further details. 
3. Invert-UZ interface Advection from the invert 
to UZ fractures (F6) and UZ 
matrix (F7); total flux is F8. 
Diffusion from the invert to 
UZ fractures and matrix. 
The invert diffusion calculation uses radionuclide 
concentrations in the WP corrosion products domain 
as the boundary condition at the top of the invert and a 
series of unsaturated zone computational cells below 
the invert that provide a gradient to a zero radionuclide 
concentration at some distance from the bottom of the 
invert (Section 6.5.3.6). 
WP=waste package; UZ=unsaturated zone 

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The diffusion coefficient in the invert is based on the self-diffusion coefficient of water at 25C 
as a bounding value for all radionuclides. The effects of variable porosity, liquid saturation, 
temperature, and uncertainty in the affect of these parameters are also included in calculating the 
diffusion coefficient. 
The corrosion products from the waste package and SNFs have the potential to be strong sorbers 
for the actinides. Including sorption in the waste package and invert is beneficial to performance 
because this process can retain radionuclides in the EBS and delay release to the unsaturated 
zone. Because the waste package corrosion products are in intimate contact with or directly in 
the flow or diffusion path of the radionuclide source inside the waste package, retardation by 
corrosion products inside the waste package will occur. However, because corrosion products in 
the invert are more localized and not necessarily in any flow path from the waste package, 
sorption onto corrosion products in the invert is ignored (Assumption 5.7). 
6.3.2 Water Flux through the Drip Shield (F2) 
6.3.2.1 Water Movement into and through a Drift (F1 and F3) 
Water movement from the land surface and down through the unsaturated zone at Yucca 
Mountain is conceptualized to occur through a system of fractures (Liu et al. 1998 
[DIRS 105729]). Simulations of water movement through the mountain yield estimates of 
percolation fluxes in the vicinity of the emplacement drifts that are a function of drift location, 
the geologic unit in which the drift resides, and the climate, which varies over time (BSC 2004 
[DIRS 167652]). Consideration of the interactions between water moving through the mountain 
and the EBS form the basis of this abstraction for performance assessment. 
The basic EBS design concept is shown in Figure 6.1-1 (Canori and Leitner 2003 
[DIRS 166275], Figure 7-14). The drifts are 5.5 m in diameter. The bottom of the drift, 
commonly referred to as the invert, is filled with a ballast material of crushed tuff. The waste 
packages are to be placed on emplacement pallets that hold them in place above the invert. A 
titanium drip shield surrounds the waste packages. The space between the waste package and the 
drip shield, which is referred to as the axial space, is designed to remain air filled. The current 
repository design does not include an engineered backfill material (Canori and Leitner 2003 
[DIRS 166275]); all of the analyses in this report reflect the no-backfill design. 
At early times, any water that enters the drift is vaporized and expelled due to the heat output 
from the waste packages. According to modeling of water movement through the EBS using 
Multiscale Thermohydrologic Model (BSC 2004 [DIRS 169565]), much of the water that enters 
the drift remains as liquid once thermal output has subsided after approximately 2,000 years. 
Water that does seep into the drift can drip onto the drip shield and is diverted around the waste 
package, into the invert. 
Water enters the drift by seepage from the roof of the drift. In this section, this mechanism is 
considered, followed by a discussion of water diversion around the drip shield. 

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6.3.2.1.1 Seepage Flux (F1) 
Seepage Model for PA Including Drift Collapse (BSC 2004 [DIRS 167652]) presents results of 
drift-scale UZ flow modeling of the interaction between host rock containing a fracture 
continuum and a drift for a variety of percolation flux rates and several sets of representative host 
rock hydraulic parameters. The seepage flux was found to be related to the percolation flux. 
However, the air-filled space beneath the roof of the drift acts as a capillary barrier that diverts 
water around the drift and limits seepage. These findings are consistent with the theory for 
seepage exclusion around cylindrical cavities introduced by Philip et al. (1989 [DIRS 105743]). 
Philip et al. showed that for given capillary properties of the host rock and a given drift diameter, 
there exists a critical percolation flux beneath which water will not enter the drift. The 
drift-scale unsaturated zone flow modeling results show a propensity for flow to diverge around 
the drifts. 
Abstraction of Drift Seepage (BSC 2004 [DIRS 169131]) provides the rationale for calculating 
the seepage flux into the repository, accounting for thermal effects and spatial variability. The 
fraction of drifts that allow water seepage as a function of infiltration are given as a function of 
percolation rate. Across the range of percolation fluxes expected, a large majority of the drifts 
remain dry. 
6.3.2.1.2 Diversion around the Drip Shield (F3) 
The drip shield has been designed to divert liquid water that may enter the drift away from the 
waste package. If the drip shield works as designed (this issue is discussed in detail below), it 
then acts as a no flow boundary. Any seepage that enters the drift moves downward under the 
force of gravity. As water migrates downward around the drip shield, it encounters the invert. 
The diversion around the drip shield occurs as droplets or rivulets, and any flow that enters the 
invert is concentrated at the sides of the drip shield while the drip shield is intact. 
Once in the invert, water migrates quickly through into the unsaturated zone host rock at the 
bottom of the drift. 
The algorithm for calculating the flux diversion around a breached drip shield is discussed in 
Section 6.3.2.4. 
6.3.2.2 Drip Shield Effectiveness 
Design drawings for the drip shield are given in D&E / PA/C IED Interlocking Drip Shield and 
Emplacement Pallet (BSC 2004 [DIRS 169220]) with details in drawings 000-M00-SSE0- 
00102-000-00B (BSC 2004 [DIRS 168067]), 000-M00-SSE0-02001-000-00A (BSC 2004 
[DIRS 168326]), and other drawings cited on the information exchange drawing (IED). The drip 
shield has roughly the shape of the top of a mailbox with vertical sides and a top section that is 
curved for strength and to shed water. On one end, a drip shield connector guide is attached to 
the top of the curved section. The connector guide is a square rib, 50 mm wide (BSC 2004 
[DIRS 168326]), that is attached to and extends across the curved top section. This connector 
guide provides extra stiffness to the end of the drip shield and can deflect seepage down the sides 
of the drip shield. On the other end of the drip shield, a connector plate is attached. The 
connector plate is 15 mm thick (BSC 2004 [DIRS 169220], Table 5) and also has a 50-mm-wide 

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square connector guide (BSC 2004 [DIRS 168326]) that is attached to the underside of the 
connector plate. 
Adjacent drip shields are interlocked with one another. This is accomplished during installation 
by lowering the connector plate of one drip shield over the upward extending connector guide of 
the previously emplaced drip shield. The minimum overlap is the width of two connector 
guides, 100 mm (BSC 2004 [DIRS 168067]), and the maximum overlap between adjacent drip 
shields is 320 mm (BSC 2004 [DIRS 168067], Section A-A). 
The gaps that exist between drip shields in this interlocking design can, potentially, provide a 
pathway for water to penetrate the drip shield system. The potential for such leakage under 
design conditions is considered here, followed by consideration of the ways in which the 
integrity of the drip shield might become compromised. This discussion is limited to considering 
the top of the drip shield because any water entering the contact between drip shields from the 
side would simply flow down the vertical sides of the drip shields, never contacting the waste. 
Consider a system where the titanium walls of the drip shield form a barrier to flow. Water flux 
through the drip shield will now be limited to the gap where adjacent drip shields interlock. If 
high seepage flux conditions exist, then the flow can be driven into this gap. First, the water 
must travel laterally up to 320 mm to get beyond the overlap between the drip shields. As this 
water travels, it must remain precisely along the crown of this gap between the drip shields. If 
there is any deviation, the sloping sides of the drip shield impose gravity forces that will cause 
the water to flow down the sides and into the invert. Second, the upward extending drip shield 
connector guide provides a barrier to flow along the crown. Sufficient water pressure must be 
provided to push water up and over this barrier. Furthermore, the connector guides provide 
surfaces of contact with the drip shield and the connector plate. These contact surfaces maintain 
continuity down along the sloping sides of the top portion of the drip shield. These contacting 
surfaces will act akin to fractures in the sense that they impart capillarity and are able to transmit 
water. Any water reaching this point would run down the contact between the drip shields. Note 
also that the air-filled voids (having no capillarity) in between and beyond the connector guides 
provide an additional barrier to flow. 
6.3.2.3 Drip Shield Breaching 
The advective flow of water into the EBS has been shown to be effectively segregated from the 
waste packages as long as the integrity of the drip shield is maintained. Once corrosion patches 
form in the drip shield or adjacent drip shields separate, seepage can drip through the drip shield 
onto the waste package. The consequence of such drip shield failure is that a portion of the 
seepage water flux now migrates through the drip shield and comes into contact with the waste 
package. The thermal and mechanical response of the drip shield may produce gaps between 
adjacent sections of drip shield. These breaching mechanisms are screened out in Engineered 
Barrier System Features, Events, and Processes (BSC 2004 [DIRS 169898], Section 6.2.27, FEP 
2.1.11.07.0A; Section 6.2.27, FEP 2.1.06.07.0B). 

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6.3.2.4 Water Flux through and around a Breached Drip Shield (F2 and F3) 
Once the drip shield has been breached, a portion of the water flux (F2) will pass through the drip 
shield and have access to the waste package. In this section, a flux splitting algorithm is 
developed to determine the fraction of the seepage flux that can pass through a degraded drip 
shield. A similar algorithm is developed in a later section to determine the fraction of the liquid 
flux through the drip shield that can enter a waste package. The flux splitting algorithm is 
important to TSPA-LA because the liquid flux into the waste package determines in part the 
transport of radionuclides by advection, an important release mechanism from the waste package 
and from the repository. 
Once the flux through the drip shield is known, the flux diverted around the drip shield, 3 F , is 
calculated using a quasi-static continuity of flow approach: 
2 1 3 F F F - = . (Eq. 6.3.2.4-1) 
Key features of the drip shield flux splitting algorithm include: (1) the seepage flux into the drift 
falls as droplets from the top of the drift onto the crown of the drip shield (Assumption 5.1); 
(2) droplets fall randomly along the length of the drip shield; (3) only flow through general 
corrosion patches is considered; (4) evaporation from the drip shield is neglected 
(Assumption 5.2); all of the seepage flux either flows through corrosion patches or drains down 
the sides of the drip shield; and (5) all water that flows through breaches in the drip shield flows 
onto or into the waste package. 
Some aspects of the flux splitting algorithm have been defined or clarified by experiments. The 
breached drip shield experiments (BSC 2003 [DIRS 163406]) were performed to validate the 
drip shield flux splitting algorithm and to examine in more detail the real behavior of seepage 
water impinging on and flowing over a drip shield. The tests were conducted by dripping water 
onto a mock-up portion of a full-scale drip shield made of stainless steel. The mockup section 
included slightly more than half of the shield from the top/center down the curvature to the side. 
The side was shortened along the longitudinal and vertical axes. Simulated corrosion 
patches-square holes 27 cm wide, the size of nodes in an earlier version of the WAPDEG 
corrosion model (CRWMS M&O 2000 [DIRS 151566], p. 36)were cut into the drip shield at 
various locations to enable measurements of flow through breaches in the drip shield. Tests were 
performed with both smooth (machined stainless steel) and rough (silica anti-slip coating) 
surfaces. Data from the tests on the smooth surface were used to develop parameter values for 
the flux splitting submodel, whereas the rough surface test data were used to validate the 
submodel. Tests were conducted in a test chamber in an environment that would minimize 
evaporation (i.e., relative humidity of at least 80 percent). Water was dripped at various rates 
intended to cover the expected range of seepage rates within the repository. The dripping 
distance was the full-scale distance from the top of the drift to the crown of the drip shield, 
2.17 m (BSC 2003 [DIRS 163406], Figure 10), based on repository design. 
The tests that were conducted included (BSC 2003 [DIRS 163406]): (1) splash radius tests to 
determine the distance from the point of impact and a rough distribution of splattered water when 
drops impinge on the surface of the drip shield; (2) spread factor tests to determine the lateral 
rivulet spread distance from the drip impact point; (3) single patch splash tests to determine the 

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amount of water that enters targeted breaches as a result of splashing; (4) single patch flow tests 
to determine the amount of water that flows down the surface of the drip shield and into patches; 
(5) multiple patch tests to collect both splashed water and rivulet flows that entered all affected 
patches; and (6) bounding flow rate tests to provide data for extreme drift seepage conditions to 
compare with the nominal seepage rate. 
Observations during the breached drip shield tests revealed that the primary mechanism for water 
to enter breaches is via rivulet flow that originates from an area around the point of drip impact. 
Following droplet impact at the crown, water splatters within some distance from the point of 
impact. The splattered water coalesces, forming beads that increase in size around the center of 
impact with each successive drop. After a time, the beads closest to the downhill curvature reach 
a critical mass and roll down the face of the drip shield in the form of a rivulet. The rivulet flow 
area spreads out in a delta formation (i.e., the maximum spread is located on the vertical section 
of the drip shield and the minimum spread is located at the point of impact). No film flow was 
observed during tests on the smooth or the rough drip shield surfaces. 
Evaporation could occur in two forms during the testfrom a freely falling drop and from a flow 
surface on the drip shield. The loss from a falling droplet is negligible; however, losses from the 
drip shield surface can be large. Experimental measurements included determination of 
evaporative losses. Although these data could be used to develop or validate a drip shield 
evaporation model, evaporation is not considered, which maximizes the potential for flow 
through breaches (Assumption 5.2). 
For a given drip location onto the crown of the drip shield (see Assumption 5.1), the spreading of 
the rivulet flow is defined by a half-angle, a, formed with the vertical plane through the impact 
point (Figure 6.3-2). The lateral spread of the rivulet flow is given by a tan 2x , where x is the 
arc length from the crown of the drip shield down to a location of interest (e.g., a corrosion 
patch). For b N breaches in the drip shield of length DS L , with each patch having a width of l 2 
(m), the flux through the drip shield is given by: 
DS 
DS 
b f 
L
N F F .. 
. 
.. . + = 
2 
tan 1 1 2 
a l . (Eq. 6.3.2.4-2) 
For details of the mathematical development of this expression, see Section 6.5.1.1.2.4. 

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Spreading = 2xtan a 
Crown of Drip Shield 
a 
Droplet 
Impact 
x 
Figure 6.3-2. Illustration of Spreading for Rivulet Flow on the Drip Shield (Curvature not Shown) 
The factor accounts for the uncertainty in the submodel and is a sampled parameter in 
TSPA-LA simulations. Sources of uncertainty include: 
1. Drip location with respect to the crown of the drip shieldDrops that fall to either 
side of the crown will not divide exactly in half, as assumed by this submodel. 
2. Patch locationPatches located on the crown will allow the entire dripping flux to 
pass through, whereas Equation 6.3.2.4-2 considers all patches to be located off the 
crown. For a given value of DS f , Equation 6.3.2.4-2 underestimates the flux into 
crown patches because 1 < DS f , so 1 2 F F < , i.e., not all of the total dripping flux can 
flow through breaches. Since most of the randomly-located breaches occurring will 
not be located on the drip shield crown, this is a reasonable approximation, but not a 
bounding estimate of flow through drip shield breaches. 
3. Splattering distributionAlthough splattering of drops when they impinge on the 
drip shield is a random process, preferential directions or distributions could develop, 
for example, due to surface alteration as a result of corrosion or drift degradation 
(rockfall). 
4. Rivulet spreadThe breached drip shield experiments showed that a range of rivulet 
spread factors or spread angles can occur even on smooth surfaces. Surface roughness 
also affects the rivulet spread angle. Precipitation of salts or accumulation of dust on 
the drip shield surface could also affect rivulet flow. 
5. Interference among multiple patchesImplicit in this submodel is that the patches do 
not interfere with each other, i.e., that no patch is lower on the drip shield surface than 
another patch. Patches located below another patch will see reduced or zero flux 
through the patch. By ignoring patch interference, water flux through the drip shield 
will be overestimated. 
6. Patches outside the footprint of the waste packageFlux through these patches will 
pass directly to the invert. Since the conceptual model requires that all flow through 
DS f

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the drip shield goes onto or into the waste package, Equation 6.3.2.4-2 will 
overestimate that flow. 
7. Evaporation from the surface of the drip shieldEvaporation is neglected 
(Assumption 5.2); if it occurs, the flux through the drip shield is less than predicted by 
Equation 6.3.2.4-2. 
8. Size of corrosion patchesThe WAPDEG model assumes a fixed size and shape for 
all corrosion patches. In reality, the patches will vary widely in size and shape 
randomly as well as over time. 
Bounds and a distribution for DS f must be established for use in TSPA-LA calculations. 
Because, under some of these uncertain conditions, the flux through the drip shield may be zero 
even when breaches exist, an appropriate lower bound on DS f is zero. Under some other 
circumstances mentioned above, the entire seepage flux could flow through the drip shield. 
Thus, an upper bound on DS f cannot be specified a priori, but should be given by: 
.. 
. 
.. 
. + 
= 
2 
tan 1
1 
a 
DS 
b 
DS 
L
N 
f 
l 
, (Eq. 6.3.2.4-3) 
which makes 1 2 F F = . Since the number of patches, b N , varies over time, DS f should be a 
function of time, with a starting value of zero and potentially reaching a value equal to the total 
number of nodes in the WAPDEG corrosion model of the drip shield (BSC 2004 
[DIRS 169996]). A uniform distribution is appropriate given that the uncertainty is difficult to 
quantify. To ensure that the flux through the drip shield is not greater than the seepage flux, the 
flux through the drip shield is computed as: 
.. 
. 
.. 
. 
.. 
. 
.. . + = 1 1 2 , 
2 
tan 1 min F f 
L
N F F DS 
DS 
b a l . (Eq. 6.3.2.4-4) 
The uncertainty in spread angle a can be lumped in with DS f since both would otherwise be 
sampled independently. A lumped uncertainty factor DS f ' is defined as 
DS DS f f .. 
. 
.. 
. + = ' 
2 
tan 1 
a 
, (Eq. 6.3.2.4-5) 
with the flux through the drip shield to be computed as: 
.. 
. 
.. 
. 
' = 1 1 2 , min F f 
L
N F F DS 
DS 
bl . (Eq. 6.3.2.4-6) 

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In Section 6.5.1.1.2.4, an upper bound on DS f ' is developed based on results of the breached drip 
shield experiments, and is used in the TSPA-LA model. 
6.3.3 Water Flux through the Waste Package (F4) 
The conceptual model for the TSPA-LA is based on the assumed presence of continuous flow 
paths through the patches that penetrate the waste package. More specifically, in the TSPA-LA 
conceptual model, vertical flow of seepage into the waste package, through the waste form, and 
out of the waste package is not impeded by the location of patches on the surface of the waste 
package. In other words, there is no long-term build-up and retention of liquid within the waste 
package for flow and transport. (An alternative conceptual model in which water fills the waste 
package before any water flows outthe bathtub modelis evaluated in Section 6.4.1). There is 
also no resistance to the flow through the waste form. The TSPA-LA approach attempts to 
maximize the immediate release and mobilization of radionuclides, while retaining as much 
realism as justified by the data and understanding of the physical and chemical processes that 
take place. 
Radionuclides cannot be released from the waste package if there is insufficient water or if there 
are no openings through either the wall or lid of the waste package. Section 6.3.3.1 describes the 
types of openings that can form, how and where they form, the timing of their formation, and the 
flow through these openings. The dimensions of these openings have implications for whether 
water is able to flow into and through the waste package or whether transport out of the waste 
package is by advection and/or diffusion. Section 6.3.3.2 describes the flux of liquid around or 
through the waste package. Section 6.3.3.3 describes the alternative pathway for liquid to reach 
the waste package; namely, evaporation from the invert and condensation on the inside of the 
drip shield can provide a source of liquid to the exterior of the waste package even when there 
are no openings in the drip shield. Section 6.3.3.4 describes the flux of liquid through the invert. 
6.3.3.1 Breaching of the Waste Package 
6.3.3.1.1 Waste Package Design 
Ten waste package configurations are planned for the waste to be emplaced in the repository, 
where the nominal quantity for LA is shown in parentheses (BSC 2004 [DIRS 169472], Tables 1 
and 11): 
1. 21-PWR with absorber plates (4,299) 
2. 21-PWR with control rods (95) 
3. 12-PWR (163) 
4. 44-BWR (2,831) 
5. 24-BWR (84) 
6. 5 DHLW/DOE SNF  Long (1,406) 
7. 5 DHLW/DOE SNF  Short (1,147) 
8. 2-MCO/2-DHLW (149) 
9. Naval Short (144) 
10. Naval Long (156). 

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Waste packages are broadly categorized as CSNF waste packages (21-PWR and 44-BWR are the 
most common), codisposal waste packages (5 DHLW/DOE SNFShort and Long), and Naval 
Short and Long waste packages. Although waste packages vary depending on the waste form 
they contain, the majority of designs have features in common. These commonalties are 
described here. The waste package consists of a cylindrical inner stainless steel vessel, which is 
sealed with a stainless steel lid. The inner vessel is placed into an Alloy 22 outer corrosion 
barrier, which is sealed with a middle and outer lid. The inner vessel has 5-cm-thick walls and 
lid that provide structural integrity for the waste package. The Alloy 22 outer corrosion barrier 
has a wall approximately 2 cm thick, a middle lid approximately 13 mm thick, and a 
2.5-cm-thick outer lid, that provide resistance to corrosion. Design information for waste 
packages is provided on IED, D&E / PA/C IED Typical Waste Package Components Assembly 
(BSC 2004 [DIRS 169472]), which identifies detailed design drawings, including drawings of 
the 21-PWR, 44-BWR, the 5 DHLW/DOE SNF - Short, and the Naval Short and Long waste 
packages, among others. 
The stainless steel inner vessel of the waste package is modeled as having no resistance to 
corrosion as reflected in WAPDEG Analysis of Waste Package and Drip Shield Degradation, 
(BSC 2004 [DIRS 169996] Section 6.3), forming an immediate flow pathway once the outer 
(Alloy 22) corrosion barrier has been breached. Similarly, as modeled, the closure weld on the 
inner stainless steel lid, as part of the stainless steel inner vessel, has no resistance to corrosion, 
and the inner lid fails once the outer lids have failed. 
6.3.3.1.2 Types of Openings 
Three general types of openings can exist in the waste package due to corrosion. These are 
(1) radial stress corrosion cracks that penetrate the welds of the lids, (2) patches resulting from 
general corrosion, and (3) localized corrosion. Stress corrosion cracks and general corrosion 
patches are discussed in turn below. The opening area from localized corrosion is described in 
the General Corrosion and Localized Corrosion of Waste Package Outer Barrier (BSC 2004 
[DIRS 169984], Section 8.3.1). 
6.3.3.1.2.1 Radial Stress Corrosion Cracks in Lid Welds 
Stress corrosion cracks can appear because of the residual tensile stresses generated during the 
process of welding the lids in place. It is not possible to anneal the final closure welds, although 
laser peening has been proposed as a means to mitigate residual stress in waste package closure 
lid welds (BSC 2004 [DIRS 172203], Section 6.4.4). Stress corrosion cracks will typically form 
along two orientations. Radial stresses can generate circumferential cracks while hoop stresses 
can generate radial cracks. Only radial stress corrosion cracks are considered in the EBS RT 
Abstraction because the formation of circumferential cracks that penetrate the thickness of the 
lids is unlikely. Cracks require the presence of tensile stress for initiation and propagation. 
Detailed finite-element analyses of the welding process demonstrate that only compressive radial 
stresses exist at the inner surface (BSC 2004 [DIRS 172203], Figure 6-11, Cross-Section 1-1). 
In this condition, circumferential cracks cannot propagate through the thicknesses of the lid 
welds and are therefore not considered in the EBS RT Abstraction. 

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ANL-WIS-PA-000001 REV 01 6-20 November 2004 
Radial cracks are transverse to the weld and cannot be much longer than the weld width. A 
radial crack opening has an elliptical shape with length 2a and a gap width d (BSC 2004 
[DIRS 172203], Section 6.5.2). The equation given by Tada et al. (1973 [DIRS 118706], p. B.5) 
can be used to calculate the gap width, d (m), for a crack with length 2a in an infinite sheet under 
plane stress load: 
, 4 
E 
a a s 
d= (Eq. 6.3.3.1-1) 
where E is the modulus of elasticity (Pa), 2a is the crack length (m), and a s is the applied stress 
(Pa). Values for E for Alloy 22 are given in DTN: MO0107TC239753.000 [DIRS 169973]. 
The residual hoop stress in the as-welded waste package outer lid is higher on the outside surface 
than on the inside surface (BSC 2004 [DIRS 172203], Table 6-9). The resulting shape of the 
crack is then an ellipsoidal cone where 2a is the length of the long axis, and short axis lengths o d 
and i d are the gap widths for the outside and inside surfaces, respectively. The depth d of the 
crack is taken to be the lid thickness. Figure 6.3-3 is a schematic diagram of the geometry of the 
ellipsoidal cone crack. 
d 
2a 
do 
di 
Figure 6.3-3. Schematic of the Dimensions for an Ellipsoidal Crack 
A range of values of a s , the residual stress, and the maximum length 2a of a radial crack can be 
estimated. The region of high residual stress is identified from finite-element simulations 
(BSC 2004 [DIRS 172203], Section 6.4). The expected maximum length of a radial crack is 
approximately two times the lid thickness (BSC 2004 [DIRS 172203], Section 6.5.1). For an 
outer lid thickness of 25.4 mm (BSC 2004 [DIRS 167394]), the maximum crack length is 
approximately 50 mm. Table 6.3-3 gives the calculated gap width, based on Equation 6.3.3.1-1 
and typical residual stresses at the inner and outer surface of the lid for a 21-PWR waste package 
(BSC 2004 [DIRS 172203], Table 6-9). 
The cross-sectional area of the stress corrosion crack is important for transport by diffusion. The 
bounding (largest) cross-sectional area is defined by conditions at the outer surface of the 
5-cm-long crack. The area of this ellipse is ab p , where 2a is 5 cm and b is one-half of the larger 
gap width on the outer surface (in Table 6.3-3). The cross-sectional area of a single stress 
corrosion crack is then p(0.025 m)(9.82  10-5 m) or 7.7  10-6 m2. 
An updated analysis of stress corrosion cracking is given in Stress Corrosion Cracking of the 
Drip Shield, the Waste Package Outer Barrier, and the Stainless Steel Structural Material 
(BSC 2004 [DIRS 172203]). For the base conceptual model (BSC 2004 [DIRS 172203], 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-21 November 2004 
Appendix B, Table B-2), the estimated crack opening is smaller than the crack opening of 
7.7  10-6 m2 obtained in this section. Therefore, use of this value in TSPA-LA calculations 
when stress corrosion cracking occurs will overestimate the rate of release of radionuclides 
compared with the updated values in (BSC 2004 [DIRS 172203]). 
Table 6.3-3. Calculated Gap Width for a Range of Residual Stresses at 400F (Approximately 200C) in 
a 21-PWR Container 
Parameter Inner Surface Outer Surface 
Hoop stress, sa (BSC 2004 [DIRS 172203], Table 6-9) 231.1380 MPa 385.0522 Mpa 
Gap width for crack length 2a = 50 mm 118 m 196 m 
Dripping water is capable of contacting a stress corrosion crack only if the waste package is 
tilted upward. A possible mechanism for tilting is emplacement pallet collapse due to corrosion 
that causes one end of the waste package to fall off its emplacement pallet. This maximum angle 
of tilt occurs when the lid end of the waste package is elevated to the height of the inside of the 
drip shield while the other end rests against the invert. 
Advective flow of water through stress corrosion cracks can be neglected. This is bounding for 
several reasons. First, a film that completely spans the opening of a stress corrosion crack 
creates a differential in capillary forces that will prevent any further ingress of flowing water into 
the waste package. Second, the presence of corrosion products in the small stress corrosion 
crack may provide a capillary barrier for advective flux into the waste package. Third, in 
addition to a capillary barrier, corrosion products filling the corrosion cracks will provide 
resistance to flow, requiring a large head or pressure gradient that is unlikely to exist. Fourth, 
because corrosion patches are orders of magnitude larger in cross section and may appear in the 
same time frame, flow through corrosion cracks is negligibly small compared to flow through 
patches. 
The potential for atmospheric pumping, hygroscopic salts in the waste package, and the 
uncertainty about film thickness make it difficult unequivocally to exclude liquid flow into the 
waste package. In any case, the more important question is how much liquid flows out of the 
waste package, advectively transporting radionuclides. Given the resistance to flow into the 
waste package through stress corrosion cracks, flow out is even less likely. The uncertainty in 
flow through corrosion cracks is compensated for at least in part by the assumption that a 
continuous water film is always present in corrosion cracks through which diffusion can occur 
(see Assumption 5.5) and by no restrictions on water vapor diffusing through the cracks, which 
provides a mechanism for water to enter a waste package once stress corrosion cracks exist. 
6.3.3.1.2.2 Patches from General Corrosion 
The waste package design consists of an inner stainless steel vessel placed inside an Alloy 22 
outer corrosion barrier. No credit is taken for resistance to corrosion by the inner stainless steel 
vessel. The main corrosion mechanisms for the outer corrosion barrier are general corrosion and 
localized corrosion. The size and timing of patches resulting from general corrosion are 
predicted by the WAPDEG model (BSC 2004 [DIRS 169996]). 

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ANL-WIS-PA-000001 REV 01 6-22 November 2004 
6.3.3.1.3 Impact of Heat Generation Inside Waste Package 
Heat generated by the waste form has the potential to evaporate water within the waste package. 
In this situation, water cannot collect inside the waste package and cannot support advective 
transport of radionuclides. Preliminary estimates using Multiscale Thermohydrologic Model 
(BSC 2004 [DIRS 169565], Section 6.3) indicate that the available heat can evaporate incoming 
water for several thousand years. However, although evaporation is expected to occur, 
complexities in the internal geometry of the waste packages (particularly the response of any 
water pooled at the bottom of the package and the presence of small conduits for water vapor to 
escape through stress corrosion cracks) make it difficult to say definitively that all incoming 
water is evaporated. As a simplification, no transport is assumed to occur when the temperature 
in the waste package is above 100C (Assumption 5.5), when a continuous film of water needed 
for transport is no longer expected to exist. 
The expected evaporation in the waste package is ignored in the TSPA-LA. This approach is 
bounding because evaporation might eliminate advection as a transport mechanism. In addition, 
by ignoring evaporation from a waste package, it becomes possible to specify a water saturation 
of 1.0 (fully saturated) inside a failed waste package whenever dripping occurs. If evaporation 
were accounted for, the water saturation inside a waste package would generally be less than 
one, which would reduce the amount of radionuclides that could dissolve in the water and be 
advectively transported from the waste package. Lower water saturations would also reduce 
estimates of diffusive releases, since both the diffusion coefficient and the cross-sectional area 
for diffusion would be less. Thus, without these simplifying assumptions, the amount of 
radionuclides transported from a waste package would be expected to be much less. 
6.3.3.2 Water Flux through and around the Breached Waste Package (F4 and F5) 
The flux through (into and out of) the waste package, 4 F , is conceptualized to be the flux 
through patches, which includes the flux thorough the drip shield ( 2 F ). Advective flux of water 
through stress corrosion cracks is unlikely and therefore is neglected (Section 6.3.3.1.2.1). A 
quasi-steady state approach is used. The presence of a gap between adjacent waste packages is 
neglected in the TSPA-LA model. Dripping onto the waste package from condensation on the 
underside of the drip shield is screened out (BSC 2004 [DIRS 169898], Section 6.2.43). 
A flux splitting algorithm analogous to the drip shield flux splitting algorithm (Section 6.3.2.4) is 
developed here. The analogy is appropriate based on similarities in geometry and assumptions 
regarding the source of liquid flux falling onto the waste package. The surface of the waste 
package is a horizontal cylinder, as is the top of the drip shield, the primary difference that 
impacts liquid flow on the curved surface being that the radius of curvature of the waste package 
is smaller than that of the drip shield. Thus, flow behavior on the surface of the waste package 
should be similar to that on the drip shield. In particular, if any water is available, it is expected 
to flow over the surface of the waste package in rivulets rather than as film flow, based on 
findings of the breached drip shield experiments (BSC 2003 [DIRS 163406]). 
Whereas drip locations on the drip shield could reasonably be confined to the crown of the drip 
shield (because the drift seepage flux will most likely originate from the crown of the drift), the 
drip locations may be more widely dispersed on the waste package. This is the case for drips 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-23 November 2004 
that fall from breaches in the drip shield, which are randomly located on the drip shield. Since 
breaches (mainly general corrosion patches) in the waste package are also randomly located, the 
fraction of dripping flux falling on the waste package that flows into the waste package might be 
expected to be proportional to the total area of waste package patches. However, since drips that 
fall onto an intact waste package surface will drain down the surface, the flux of water, if any, 
entering a waste package is proportional to the total length of patches. Again, the analogy to the 
drip shield applies. Rivulets flowing down the surface of the waste package are intercepted in 
proportion to the lengths of the patches (ignoring interference by multiple patches). 
Two other considerations reinforce the comparison with the drip shield. First, any condensation 
on the underside of the drip shield that falls onto the waste package will fall from the crown of 
the drip shield. Thus, for condensation at least, the geometry is completely analogous to that of 
the drip shield inside the drift. Second, due to uncertainty in the corrosion rate of the drip shield, 
the drip shield is modeled as a single entity and all drip shields in the repository fail by general 
corrosion at the same time for a given realization (BSC 2004 [DIRS 169996], Section 6.3). Once 
the drip shield is gone, the seepage flux will now fall directly from the drift crown onto the waste 
package crown, again completing the analogy with the drip shield under the drift crown. Since 
the corrosion rate of the titanium drip shield is higher than that of the Alloy 22 waste package 
outer corrosion barrier, the situation where a breached waste package lies unprotected under 
seepage from the drift crown should be more likely than a breached waste package underneath a 
breached but still partially effective drip shield. Therefore, within the uncertainty of the model, 
it is an appropriate simplification to assume that the flux impinging on the waste package falls 
entirely on the crown of the waste package. One implication of this assumption is that, as with 
the drip shield, half of this flux flows down each side of the waste package. 
Based on these arguments, a flux splitting algorithm for the waste package can be given that is 
completely analogous to the drip shield flux splitting algorithm: 
.. 
. 
.. 
. 
.. 
. 
.. 
. + . .. 
. 
. .. 
. 
= 2 2 4 , 
2 
tan 1 min F f 
L 
N F F WP 
WP 
WP bWP a l , (Eq. 6.3.3.2-1) 
where 4 F is the flux through the waste package, 2 F is the flux through the drip shield, and WP L 
is the total axial length of the waste package. bWP N patches each of length WP l 2 comprise the 
breaches in the waste package. Flow through stress corrosion cracks is neglected as being 
unlikely to occur (see Section 6.3.3.1.2.1). 
The factor WP f accounts for the uncertainty in this algorithm. As with the corresponding factor 
DS f for the drip shield, bounds can be established for WP f based on the dimensions of the 
patches and the waste package and the uncertain rivulet spread angle. A lower bound of zero is 
necessary to account for the possibility that seepage through the drip shield is completely 
diverted by an intact portion of the waste package outer corrosion barrier. 
For an upper bound on WP f , the drip shield experiments (BSC 2003 [DIRS 163406]) provide 
some guidance. Since the radius of curvature of the waste packages is smaller than that of the 
drip shield, the rivulet spread angle on the waste packages would be expected to differ from, and 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-24 November 2004 
probably be smaller than, the spread angle on the drip shield. In some experiments, the drip 
location on the drip shield mockup was well away from the crown on more steeply inclined 
regions of the drip shield. Rivulets flowing from those drip locations may simulate more closely 
the behavior on a surface having a smaller radius, such as a waste package. Because the waste 
package has a smaller radius and more curvature than the drip shield surface, more of the surface 
is sloped to such a degree that water will readily flow down it by gravity. Only a larger 
cylindrical surface (the drip shield mockup) was available on which to observe gravity flow 
behavior. Observations away from the crown, where the slope is steep enough to initiate flow as 
readily as on a more highly curved surface, are appropriate analogs to measurements on an actual 
smaller cylinder. An analysis of drip shield experimental data for off-crown drip locations 
(Section 6.5.1.1.3) gives a mean spread angle of 13.7 and a range from 5.5 to 22.0. In 
analogy to DS f , an upper bound on WP f can be obtained using the minimum rivulet spread angle 
a of 5.5 and the known values for bWP N (BSC 2004 [DIRS 169996]), WP l 2 , and WP L : 
.. 
. 
.. 
. + 
= 
2 
tan 1 
1 
a 
WP 
WP bWP 
WP 
L 
N 
f 
l 
. (Eq. 6.3.3.2-2) 
As with the drip shield, the term .. 
. 
.. 
. + 
2 
tan 1 
a 
, which is uncertain itself, can be factored in with 
WP f to simplify the model, resulting in: 
.. 
. 
.. 
. 
' .. 
. 
.. 
. + . .. 
. 
. .. 
. 
= 2 2 4 , 
2 
tan 1 min F f 
L 
N F F WP 
WP 
WP bWP a l , (Eq. 6.3.3.2-3) 
where 
WP WP f f .. 
. 
.. 
. + = ' 
2 
tan 1 
a 
(Eq. 6.3.3.2-4) 
is assigned a uniform distribution. In Section 6.5.1.1.3, an upper bound on WP f ' is developed 
based on results of the breached drip shield experiments. The range for WP f ' based entirely on 
experimental results is used in TSPA-LA. 
Finally, the flux that is diverted around the waste package, 5 F , is calculated using continuity of 
the quasi-static flow around and into the waste package: 
4 2 5 F F F - = . (Eq. 6.3.3.2-5) 

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ANL-WIS-PA-000001 REV 01 6-25 November 2004 
6.3.3.3 Condensation on the Drip Shield 
Condensation of water on the underside of the drip shield is excluded due to low consequence 
(BSC 2004 [DIRS 169898], Section 6.2.43, FEP Number 2.1.08.14.0A). A review of the 
temperature profiles calculated using the results described in In-Drift Natural Convection and 
Condensation Model (BSC 2004 [DIRS 164327], Section 6.3) indicates that the radial 
temperatures of the drip shield are highest at the crown of this component and slightly cooler on 
the sides. This temperature profile would support condensation of any water vapor convected 
upward from the invert along the sides of the drip shield. The condensate will be a weak 
carbonic acid solution (pH approximately 5) (BSC 2004 [DIRS 169860]), with condensation 
occurring when the drip shield temperatures drop below about 96C. These conditions do not 
initiate corrosion of Alloy 22 (BSC 2004 [DIRS 169984]). Therefore, the presence of any 
condensate on the underside of the drip shield does not impact the barrier capability of the drip 
shield. 
Condensate waters present on the underside of the drip shield have a small potential to drip onto 
exposed waste packages. Analysis of advective flux through stress corrosion cracks (BSC 2004 
[DIRS 172203], Section 6.3.7), an analogous situation that similarly accounts for water on the 
underside of the drip shield, excludes this process on the basis of low consequence. 
6.3.3.4 Flux into and through the Invert (F6 and F7) 
The flux leaving the waste package is equal to the flux entering the waste package, 4 F , by the 
quasi-steady-state flow assumption (the net effect of Assumptions 5.1 through 5.4 and 5.7). The 
total flux entering the invert is equal to the sum of the diversion around the waste package, F5, 
and the flux leaving the waste package (equal to 4 F ), the diversion around the drip shield, 3 F . 
The liquid flux leaving the invert, F8, is equal to the total flux entering the invert plus the 
imbibition flux from the UZ matrix into the invert. That is, 
3 4 5 6 F F F F + + = , (Eq. 6.3.3.4-1) 
and 
7 6 8 F F F + = . (Eq. 6.3.3.4-2) 
Only the flux leaving the waste package, 4 F , can transport radionuclides to the invert. 
The Multiscale Thermohydrologic Model (BSC 2004 [DIRS 169565]) determines the imbibition 
flux from the host rock matrix into the invert, 7 F , as well as the water saturation in the invert. 
The advective flux through the invert exits the invert, flowing into the UZ fractures. 
6.3.4 Transport through the EBS 
The conceptual model for transport through the EBS consists of transport through three separate 
domains: (1) waste form, (2) waste package corrosion products, and (3) the invert. Transport 
through each of these domains occurs by advection and diffusion. Radionuclides travel in 

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ANL-WIS-PA-000001 REV 01 6-26 November 2004 
sequence through each of these domains. In other words, all radionuclides entering the corrosion 
products domain come from the waste form domain, and all radionuclides exiting the corrosion 
products domain enter the invert domain. Advection in each domain is modeled as steady state 
flow; i.e., the flow rate may vary over time, but no accumulation occurs. Diffusion through each 
domain is considered to be transient. 
The rate of diffusive transport through each domain is dependent upon the following parameters: 
the effective diffusion coefficient, the cross-sectional area available for diffusive transport, and 
the diffusion path length across which a concentration gradient exists. The effective diffusion 
coefficient for assumed transport through thin water films adsorbed to materials is taken as a 
bounding value to be the free-water diffusion coefficient, modified to account for porosity, 
saturation, and, in the case of the invert, temperature, and the uncertainty associated with the 
dependence on these parameters. The cross-sectional area for transport in each domain is 
dependent upon the geometry of the domain, the relative humidity, and the specific surface area 
and adsorption isotherm for the given material. A range of diffusion path lengths is determined 
from the geometry of the domain. 
The waste form is the source of all radionuclides in the repository system. If sufficient water is 
available, radionuclides mobilized from the waste form can be transported out of the waste 
package, downward through the invert, and into the UZ, as shown in Figure 6.3-1. Transport out 
of the waste package can occur by advection, when there is a liquid flux through the waste 
package, and by diffusion through assumed continuous liquid pathways in the waste package, 
including thin films of adsorbed water. These two transport processes (diffusion and advection) 
are each a function of the type of penetrations through the drip shield and waste package and the 
local seepage conditions. Diffusion can occur through stress corrosion cracks or through general 
corrosion patches in the waste package both with and without liquid flux through the waste 
package. Advection is not considered through stress-corrosion cracks or through corrosion 
patches in the absence of liquid flux. 
The diffusion coefficient for radionuclide transport is based on the self-diffusion coefficient of 
liquid water at 25C. This is a bounding value for all radionuclides. The effects of porosity, 
liquid saturation, and uncertainty on the diffusion coefficient are incorporated using the 
formulation in Section 6.3.4.1.1. The effects of temperature on this bounding value are modified 
using the formulation in Section 6.3.4.1.2. 
Advective transport is straightforward in the EBS RT Abstraction. In particular, mobilized 
radionuclides are transported with the local liquid flux from the waste package ( 4 F ) through the 
invert (F6) to the unsaturated zone ( 8 F ). There are no modifications for dispersive effects (see 
Section 6.3.1.2); because the flow is modeled as one-dimensional vertically downward, lateral 
dispersion is not considered in the EBS RT Abstraction. 
Diffusive transport depends on concentration gradients. The concentrations of radionuclides in 
the waste form domain are determined from the degree of waste form degradation and the 
solubility limit for each radionuclide. The concentrations in the waste package corrosion 
products domain take into account radionuclide solubility limits, sorption of radionuclides onto 
the corrosion products, sorption and desorption onto colloids, and colloid stability. The 
concentrations in the invert domain depend on the radionuclide solubility limits, colloid stability 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-27 November 2004 
in the invert, the transfer of radionuclides between the corrosion products domain and the invert, 
and the boundary concentrations at the invert-unsaturated zone interface. The boundary 
condition at the unsaturated zone interface is implemented by defining multiple grid cells in the 
unsaturated zone that provide a diffusive path length that is sufficiently long such that the 
concentration at the outlet of the farthest cell from the drift wall can realistically be assigned a 
value of zero (Section 6.5.3.6). 
The emphasis in this EBS RT Abstraction is on transport of radionuclides through the EBS after 
the radionuclides are mobilized. This abstraction does not define elements of the TSPA-LA, 
such as corrosion processes, radionuclide solubility limits, waste form dissolution rates and 
concentrations of colloidal particles, that are generally represented as boundary conditions or 
input parameters for the EBS RT Abstraction. This abstraction provides the algorithms for 
determining radionuclide transport in the EBS using the flow and radionuclide concentrations 
determined by other elements of the TSPA-LA. 
6.3.4.1 Invert Diffusion Submodel 
The TSPA-LA model requires an abstraction for the effective diffusion coefficient in granular 
materials as a function of radionuclide, porosity, saturation, temperature, and concentration. 
This submodel is intended specifically to apply to the invert. The abstraction is as follows: 
 Use the free water diffusion coefficient for self-diffusion of water, 2.299  10-5 cm2 s-1 
(Mills 1973 [DIRS 133392], Table III), as a bounding value for all radionuclides at 
25C. 
 Modify the free water diffusion coefficient for the porosity and liquid saturation of the 
invert. The modification for porosity and saturation is based on Archies law and 
experimental data for granular media, and is presented in Section 6.3.4.1.1. 
 Further modify the diffusion coefficient for variation of the invert temperature using the 
formulation in Section 6.3.4.1.2. The invert temperature is provided by the Multiscale 
Thermohydrologic Model (BSC 2004 [DIRS 169565]). 
 Ignore the increase in the diffusion coefficient with increasing ionic strength of 
concentrated solutions (see Section 6.3.4.1.2). The maximum modification for a highly 
concentrated solution of potassium iodide is a factor of 1.27. This factor is almost 
within the bounding approximation inherent in using the self-diffusion coefficient for all 
radionuclides. It is neglected for the TSPA-LA. 
6.3.4.1.1 Modification of Diffusion Coefficient for Porosity and Saturation of the Invert 
The modified diffusion coefficient for a partly saturated porous medium can be estimated from 
Archies law and the relationship between electrical conductance and diffusivity in a liquid. 
Archies law is an empirical function relating the electrical resistivity and porosity of a porous 
medium (Keller and Frischknecht 1966 [DIRS 111470], p. 21): 
m ew
s a - = f . . , (Eq. 6.3.4.1.1-1) 

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ANL-WIS-PA-000001 REV 01 6-28 November 2004 
where s . is the bulk resistivity (or specific resistance) of the fully water-saturated porous 
medium (. m), ew . is the resistivity of liquid water (. m), f is the porosity (m3 pore volume 
m-3 total volume), m is a cementation factor (dimensionless), and a is an empirical parameter 
(dimensionless) that, to a first approximation, may be assumed to have a value of 1 (Keller and 
Frischknecht 1966 [DIRS 111470], p. 21). 
For a partially saturated porous medium, the resistivity is given by (Bear 1988 [DIRS 101379], 
p. 116; Keller and Frischknecht 1966 [DIRS 111470], p. 28; Pirson 1963 [DIRS 111477], p. 24): 
n 
w s t S - = . . , (Eq. 6.3.4.1.1-2) 
where t . is the bulk resistivity (or specific resistance) of the partially saturated porous medium 
(. m), w S is the water saturation (m3 water m-3 pore volume), and n is a saturation exponent 
(dimensionless). 
The cementation factor m is somewhat larger than 2 for cemented and well-sorted granular 
rocks and somewhat less than 2 for poorly sorted and poorly cemented granular rocks 
(Keller and Frischknecht 1966 [DIRS 111470], p. 21). For unconsolidated sand, a value of 1.3 
has been reported for the cementation factor (Bear 1988 [DIRS 101379], p. 116; Pirson 1963 
[DIRS 111477], p. 24). The invert, being composed of well-graded crushed tuff (BSC 2004 
[DIRS 170559]), should have cementation characteristics similar to unconsolidated sand and 
poorly cemented granular rock, with a cementation factor of 1.3 or slightly higher, but less 
than 2. 
For unconsolidated sand, a value of 2 is accepted for the saturation exponent n (Bear 1988 
[DIRS 101379], p. 116; Keller and Frischknecht 1966 [DIRS 111470], p. 28; Pirson 1963 
[DIRS 111477], p. 24). 
Combining and simplifying Equations 6.3.4.1.1-1 and 6.3.4.1.1-2 results in an Archies law 
formulation that gives the bulk resistivity of a partially saturated porous medium: 
n 
w 
m ew
t S - - = f . . . (Eq. 6.3.4.1.1-3) 
The resistance of a porous medium of length L and cross-sectional area A is given by: 
A L R t t / . = . (Eq. 6.3.4.1.1-4) 
Since the electrical conductance, G (S = .-1), is defined as the reciprocal of resistance 
(Atkins 1990 [DIRS 111464], p. 750), Archies law can be written for a partially saturated 
porous medium in terms of the conductance of the bulk porous medium, t G (S) and the 
conductance of water, w G (S): 
nw 
m 
w t S G G f = . (Eq. 6.3.4.1.1-5) 

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ANL-WIS-PA-000001 REV 01 6-29 November 2004 
The last step is to rewrite Archies law in terms of diffusion coefficients. The diffusion 
coefficient of an ion in solution is related to the conductance through the Nernst-Haskell 
equation (Perry and Chilton 1973 [DIRS 104946], p. 3-235) for diffusion in a binary electrolyte 
mixture at infinite dilution: 
. .. 
. 
. .. 
. + 
. .. 
. 
. .. 
. 
. 
= 
- + 
- + - + 
z z 
z z l l 
F
RT D 
0
0 0 
2 . (Eq. 6.3.4.1.1-6) 
where: 
D = diffusion coefficient (m2 s-1) 
R = molar gas constant = 8.314472 J mol-1 K-1 (Lide 2002 [DIRS 160832], p. 1-8) 
T = temperature (K) 
F = Faraday constant = 96485.3415 C mol-1 (Lide 2002 [DIRS 160832], p. 1-7) 
0 0 , - + l l = cationic and anionic conductance, respectively, at infinite dilution 
(S cm2 equivalent-1) 
0 . = equivalent electrolyte conductance at infinite dilution (S cm2 equivalent-1) 
- + z z , = valence of cation and anion, respectively; magnitude onlyno sign 
(dimensionless). 
This equation can be simplified by making use of the average ionic conductance at infinite 
dilution, l , where 
2 2 
0 0 
0 - + + 
= 
. 
= l l l . (Eq. 6.3.4.1.1-7) 
Since the ionic conductances 0 
+ l and 0 
- l are non-negative numbers, ( )( ) 0 0 2 
- + = l l l , which can be 
seen as follows: 
( ) ( )( ) ( ) 
( ) ( ) ( )( ) 
( ) ( ) ( )( ) ( )( ) ( )( ) 
( ) ( ) ( )( ) ( )( ) 
( ) ( )( ) 
( )( ). 
4
1 
2 4 
2 2 2 4 
2 4 
4 
2 
2
0 0 
0 0 2 0 0 
0 0 
0 0 2 0 2 0 
0 0 0 0 0 0 2 0 2 0 
0 0 2 0 2 0 
2 0 0 0 2 0 
2 0 0 
2 
- + 
- + - + 
- + 
- + - + 
- + - + - + - + 
- + - + 
- - + + 
- + 
= 
+ - = 
+ - 
+ 
= 
- + + 
+ 
= 
+ 
+ 
= 
+ + 
= 
. .. 
. 
. .. 
. + 
= 
l l 
l l l l 
l l l l l l 
l l l l l l l l 
l l l l 
l l l l 
l l l 
(Eq. 6.3.4.1.1-8) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-30 November 2004 
Thus, the square of the average ionic conductance can be substituted for the product of the 
individual conductances. This substitution will generally overestimate the diffusion coefficient 
given by Equation 6.3.4.1.1-6. At the same time, the valence of the ions + z and - z are given a 
value one, because this, too, maximizes the diffusion coefficient. With these substitutions, 
Equation 6.3.4.1.1-5 simplifies to give the maximum diffusivity in a binary electrolyte mixture at 
infinite dilution: 
( ) 
. 
2 
2 
2 
2
0 
2 
2 
2
F 
RT 
F 
l RT 
l 
l 
F
RT D 
. 
=
= 
. .. 
. 
. .. 
. 
= 
(Eq. 6.3.4.1.1-9) 
This shows that the diffusion coefficient for ions in an infinitely dilute binary mixture is 
proportional to the conductance of the electrolyte. For multicomponent solutions at other than 
infinite dilution, this equation represents an approximation with an associated uncertainty that 
can be estimated by comparison with experimental data, which is discussed later. 
Using the conductance t G for 0 . in the bulk porous medium and w G for 0 . corresponding to 
the free water diffusivity 0 D (corresponding to the value of D when porosity and saturation are 
both 1.0), Archies law (Equation 6.3.4.1.1-5) can be written in terms of the diffusivities of the 
bulk porous medium and the free water diffusivity: 
nw 
mS D D f 0 = . (Eq. 6.3.4.1.1-10) 
This is the form of Archies law that is generally applied for determination of the diffusion 
coefficient, D, as a function of porosity and saturation in a partly saturated, granular medium. 
Note that the diffusion coefficient, D, as introduced here and used throughout this section, is an 
effective value that implicitly includes the effects of porosity, saturation, and tortuosity. As 
such, it is defined differently from the coefficient Dmi defined in Section 6.5.1.2, which applies to 
a bulk liquid phase without modification for porosity, saturation, or tortuosity. With values of 
the cementation factor, m, of 1.3 and the saturation exponent, n, of 2 for unconsolidated sand, 
Archies law becomes as: 
. 2 3 . 1 
0 w S D D f = (Eq. 6.3.4.1.1-11) 
Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 [DIRS 170709]) measured the 
diffusion coefficient of unsaturated soil, gravel, bentonite, rock, and crushed tuff from Yucca 
Mountain over a broad range of water contents. These measured data are qualified in 
Appendix H and have been used to analyze the dependence of the diffusion coefficient on 
volumetric moisture content for a variety of granular materials. Figure 6.3-4 presents a summary 
of the diffusivity data for various granular media at volumetric moisture contents ranging 
between 1.5 percent and 66.3 percent. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-31 November 2004 
Because these diffusion coefficients were measured as a function of volumetric water content, 
they have been analyzed using an alternative form of Archies law in which the cementation 
factor and saturation exponent are equal (i.e., n = m). In effect, the diffusion coefficient is then a 
function of ., the percent volumetric moisture content, defined as w S f . 100 = : 
. 
100 0
0 
n 
nw 
n 
D 
S D D 
.. 
. 
.. 
. =
= 
. 
f 
(Eq. 6.3.4.1.1-12) 
A statistical analysis using Microsoft Excel (Appendix G) produces an excellent fit to the 
diffusivity data (Conca and Wright 1992 [DIRS 100436], Figure 2; Conca et al. 1993 
[DIRS 170709], Figure 2; listed in Table 4.1-14) using Equation 6.3.4.1.1-12 for moisture 
content in the range of 1.5 percent to 66.3 percent. The statistical fit to the diffusion 
coefficient, D, is based on a linearizing transformation to the variables X and Y, defined as: 
( ) 
, 2 log 
/ log
10 
0 10 
- =
= 
. X 
D D Y 
(Eq. 6.3.4.1.1-13) 
where 
D = the diffusion coefficient (m2 s-1) 
0 D = free water diffusivity (m2 s-1) 
. = volumetric moisture content (percent). 
The slope of the X-Y relationship is found to be 1.863, leading to the following linear equation 
for Y as a function of X: 
), 2 (log 863 . 1 log 
863 . 1 
10 
0 
10 - = . .. 
. 
. .. 
. 
= 
. 
D
D 
X Y 
(Eq. 6.3.4.1.1-14) 
or 
. 
100 
863 . 1 
0 
863 . 1 863 . 1 
0 
.. 
. 
.. 
. =
= 
. 
f 
D 
S D D w 
(Eq. 6.3.4.1.1-15) 
The statistical fit for the diffusion coefficient has uncertainty, which is represented by the scatter 
of data points around the fit in Figure 6.3-4. This uncertainty is approximated by a normal 
distribution for the residuals (datamodel) in log-log space. This normal distribution of residuals 
has a mean value of 0.033 and a standard deviation of 0.218. The uncertainty can be 
incorporated into the statistical fit as an additional factor on the full statistical fit. 
( ), 10 218 . 0 , 033 . 0 863 . 1 863 . 1 
0 
= = = s  f ND 
w S D D (Eq. 6.3.4.1.1-16) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-32 November 2004 
where ND represents a normal distribution with a mean, , of 0.033 and a standard deviation, 
s, of 0.218. ND is in the exponent because the residuals are calculated in the log-log space of 
the statistical fit. This statistical fit is the submodel for the invert diffusion coefficient to be used 
for TSPA-LA. Since the normal distribution is theoretically unbounded, unrealistic values for 
the diffusion coefficient could potentially be obtained. To avoid this potential problem, the 
implementation in TSPA-LA will use a truncated normal distribution, limited to plus or minus 
three standard deviations from the mean. 
Figure 6.3-4 presents the statistical fit (solid line) and the upper and lower bounds (dashed lines) 
at three standard deviations above and below the fit. The dashed lines encompass almost all the 
data points, because  3 standard deviations includes 99.7 percent of the area under a normal 
distribution. Equation 6.3.4.1.1-16, therefore, accurately represents the uncertainty in the 
diffusivity data for the TSPA-LA calculations. 
Because the saturation exponent (1.863) is less than the generally accepted value (2), the fit to 
the data provides less of a bounding estimate for the diffusion coefficient than if the accepted 
value were used. However, the estimate using Equation 6.3.4.1.1-16 is realistic instead of simply 
bounding the diffusion coefficient because it is developed from measured data rather than using 
the general behavior of unconsolidated sand as its basis. Furthermore, being based on a large 
number of measured data, the uncertainty in diffusion coefficient using Equation 6.3.4.1.1-16 is 
quantified, which provides additional support for use of this equation instead of a more bounding 
approach using the accepted value for saturation exponent. 
One element of the uncertainty in the diffusion coefficient is the uncertainty in the porosity of the 
invert. The bulk porosity of the invert crushed tuff is expected to vary between 0.27 and 0.39, 
with an average of 0.31 (BSC 2004 [DIRS 168138], Table 5). From Equation 6.3.4.1.1-16, the 
diffusion coefficient would vary due to variations in porosity by a factor of: 
98 . 1 
27 . 0 
39 . 0 863 . 1 
863 . 1 
863 . 1 
= .. . 
.. 
. = = 
min 
max 
min 
max 
D
D 
f
f 
. (Eq. 6.3.4.1.1-17) 
The range about the mean diffusion coefficient, D , would be: 
77 . 0 
31 . 0 
27 . 0 863 . 1 
= .. 
. 
.. 
. = 
D 
Dmin (Eq. 6.3.4.1.1-18) 
to 
53 . 1 
31 . 0 
39 . 0 863 . 1 
= .. 
. 
.. 
. = 
D 
Dmax . (Eq. 6.3.4.1.1-19) 
This range of uncertainty resulting from variation in the invert porosity is well within the range 
of the uncertain factor in Equation 6.3.4.1.1-16, which ranges from: 
24 . 0 10 ) 218 . 0 ( 3 033 . 0 = - (Eq. 6.3.4.1.1-20) 
to 
86. 4 10 ) 218 . 0 ( 3 033 . 0 = + . (Eq. 6.3.4.1.1-21) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-33 November 2004 
The uncertainty associated with the porosity of the invert is subsumed by the greater uncertainty 
associated with the measurements of the diffusion coefficient; thus the porosity uncertainty can 
be considered to be accounted for in the diffusion coefficient. The same conclusion is reached if 
the nominal value of intergranular porosity (0.45 as given in Tables 4.1-8, 6.6-2, and 8.2-4) is 
substituted for the mean, with the same spread for the uncertainty range. 
y = 1.863x 
R2 = 0.915 
-4.5 
-4.0 
-3.5 
-3.0 
-2.5 
-2.0 
-1.5 
-1.0 
-0.5 
0.0 
0.5 
1.0
-2.0 -1.5 -1.0 -0.5 0.0 
log10 . - 2 
log10(D/D0) 
Source: Conca And Wright 1992 [DIRS 100436], Figure 2; Conca et al. 1993 [DIRS 170709], Figure 2. 
NOTE: The dashed lines correspond to three standard deviations above and below the statistical fit to the data. 
Figure 6.3-4. Uncertainty in the Statistical Fit for the Diffusion Coefficient 
For each realization of the TSPA-LA calculations, the normal distribution is sampled, thereby 
incorporating the uncertainty of the experimental data into the diffusivity. 
6.3.4.1.2 Modification for Temperature 
The diffusivity T D is proportional to absolute temperature and inversely proportional to 
viscosity T .; i.e., T T T D . / . (Cussler 1997 [DIRS 111468], p. 114). It follows that if the 
diffusivity is known at some temperature 0 T , the diffusivity at temperature T can be found by: 
0 
0 
0 
T
T T
T T
T 
D
D 
.
. 
= , (Eq. 6.3.4.1.2-1) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-34 November 2004 
where T D is the diffusion coefficient (m2 s-1) at temperature T (K), 0 T D is the diffusion 
coefficient (m2 s-1) at temperature 0 T (K), T . is the viscosity of water (Pa s) at temperature T 
(K), and 0 T . is the viscosity of water (Pa s) at temperature 0 T . The dependence of viscosity on 
temperature T (K) (293.15 K = T = 373.15 K) is given by (Weast and Astle 1981 [DIRS 100833], 
p. F-42): 
, 
15 . 168 
) 15 . 293 ( 001053 . 0 ) 15 . 293 ( 3272 . 1 log 
2 
20 
10 - 
- - - 
= . .. 
. 
. .. 
. 
T 
T T T 
.
. 
(Eq. 6.3.4.1.2-2) 
where 20 . is the viscosity of water at 20C (293.15 K). Then 
( ) ( ) 
( ) ( ) 
. .. 
. 
. .. 
. 
- 
- - - 
. .. 
. 
. .. 
. 
- 
- - - 
= 
15 . 168 
15 . 293 001053 . 0 15 . 293 3272 . 1 
15 . 168 
15 . 293 001053 . 0 15 . 293 3272 . 1 
0 
2 
0 0 
2 
0 10 
10 
T 
T T
T 
T T 
T
T 
.
. 
, (Eq. 6.3.4.1.2-3) 
and the diffusion coefficient at temperature T is given by: 
( ) ( ) ( ) ( ) 
. 10 15 . 168 
15 . 293 001053 . 0 15 . 293 3272 . 1 
15 . 168 
15 . 293 001053 . 0 15 . 293 3272 . 1 
0
0 
2 
0 
2 
0 0 
0 
0 
0 
. .. 
. 
. .. 
. 
- 
- - - 
- 
. .. 
. 
. .. 
. 
- 
- - - 
=
= 
T 
T T 
T 
T T 
T 
T 
T 
T T 
T
T D 
T
T D D 
.
. 
(Eq. 6.3.4.1.2-4) 
This equation is not valid above 100C (373.15 K), where it is assumed that no transport occurs 
(Assumption 5.5). The invert temperature is provided by the Multiscale Thermohydrologic 
Model (BSC 2004 [DIRS 169565]). 
6.3.4.1.3 Modification for Concentrated Aqueous Solutions 
Data in American Institute of Physics Handbook (Gray 1972 [DIRS 138541], Table 2p-2) show 
that the majority of the diffusion coefficients increase with increasing solution strength. For 
example, the diffusion coefficient of sodium iodide increases from 1.616 in a dilute solution to 
1.992 for a 3 M solution and the coefficient for potassium iodide increases from 2.00 in a dilute 
solution to 2.533 at 3.5 M. The percent increase for potassium iodide, 26.7 percent, is the 
greatest of any in Grays Table 2p-2, (Gray 1972 [DIRS 138541]) excluding HCl. HCl has been 
excluded from consideration because, being volatile, it is not representative of the type of 
radionuclides released from the waste package. 
Although the diffusion coefficients of aqueous solutions increase with increasing ionic strength, 
the self-diffusion coefficient of water is still higher. Therefore, using the self-diffusion 
coefficient for water is a bounding value for all radionuclides. The modification for concentrated 
aqueous solutions is therefore neglected in the TSPA-LA. 

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ANL-WIS-PA-000001 REV 01 6-35 November 2004 
6.3.4.2 Retardation in the Engineered Barrier System 
In this section, parameters are developed to enable the impact of sorption processes on 
radionuclide transport through the EBS to be quantified. Transport through the EBS is affected 
by the adsorption and desorption of radionuclides on the materials in the waste package and 
invert. Adsorption describes the uptake of a radionuclide by a solid surface when in contact with 
a radionuclide-laden aqueous solution. This uptake typically occurs when a bond is formed by 
surface sites that have a chemical affinity for the radionuclide. Progressive inflow of fluids with 
low radionuclide concentrations would thermodynamically favor desorption of the original 
population of sorbed radionuclides back into solution. The fully reversible sorption and 
desorption of radionuclides is often described by a linear isotherm, using a sorption distribution 
coefficient (Kd). 
Irreversible sorption refers to the tendency in natural systems for desorption to be incomplete. In 
other words, the amount of sorbed contaminant available for desorption in natural systems is 
typically less than the total sorbed mass due to chemical and physical processes occurring at or 
beneath the mineral surface. Sorption processes are referred to as adsorption if the process 
occurs on the surface or absorption if the process occurs beneath the surface. 
This section defines a conceptual model and parameters for transport through the degraded EBS, 
including appropriate ranges of Kd values for actinium, americium, carbon, cesium, iodine, 
neptunium, plutonium, protactinium, radium, strontium, technetium, thorium, and uranium, and 
the defensibility of irreversible sorption for these radionuclides. 
The TSPA-SR transport model for the EBS assumed no sorption or retardation of dissolved 
species of radionuclides (CRWMS M&O 2000 [DIRS 153246], p. 3-134). This assumption was 
bounding for several reasons: 
 A large mass of iron oxyhydroxides, including species such as hematite, is generated 
through corrosion of mild steel and stainless steels within the waste package and invert. 
The iron oxyhydroxides are known to be excellent sorbers (as indicated by their high Kd 
values) of many radionuclide species (Table 4.1-11). 
 Some sorbed radionuclides, such as plutonium, appear not to desorb in many geologic 
environments (Brady et al. 1999 [DIRS 154421], Appendix VI). In effect, the sorption 
process appears partly irreversible, and a large percentage of sorbed radionuclides would 
appear to be permanently attached to the corrosion products in the EBS. But it is 
difficult to quantify irreversibility because the time scale for laboratory experiments or 
field observations is much shorter than repository time scales. In this situation, the 
short-term data may provide misleading information about long-term irreversibility. The 
net effect of irreversible sorption on EBS transport will depend on two competing 
effects: (1) irreversible sorption on the in-drift materials will decrease releases from the 
EBS, and (2) irreversible sorption to stable colloidal particles will increase transport 
through the EBS. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-36 November 2004 
 Copper is present along the top of the invert as an electrical conductor. Two corrosion 
products produced by the alteration of elemental copper (copper oxide and copper 
sulfide) can strongly sorb iodine and technetium species (Balsley et al. 1998 
[DIRS 154439], Tables 1 and 2), an important feature for decreasing releases of two 
elements that generally have minimal sorption in oxidizing environments. 
Sorption distribution coefficients are typically measured for groundwaters and substrates at 
ambient or near ambient temperatures. There is little or no experimental data for sorption 
distribution coefficients at the elevated temperatures that may occur in the EBS with either the 
repository design and operating mode described in Yucca Mountain Science and Engineering 
Report (DOE 2001 [DIRS 153849]) or an alternative thermal operating mode. In this situation, 
the available data for sorption distribution coefficients have been used to define the ranges of Kd 
values for TSPA-LA analyses, but it is not possible to distinguish alternative thermal operating 
modes. The effect of temperature on sorption coefficients was reviewed by Meijer (1990 
[DIRS 100780], p. 17). Measured sorption coefficients onto tuffs were higher at elevated 
temperature for all elements studied: Am, Ba, Ce, Cs, Eu, Pu, Sr, and U. The conclusion was 
drawn that sorption coefficients measured at ambient temperatures should be applicable and 
generally bounding when applied to describing aqueous transport from a hot repository. This 
conclusion must be tempered by the possibility that high temperatures could result in changes in 
the near-field mineralogy and water chemistry that are not predictable by short-term laboratory 
and field experiments. 
6.3.4.2.1 Conceptual Model for the In-Drift Environment 
The mild steel and stainless steel in the waste package and invert are expected to degrade to iron 
oxyhydroxides more rapidly than the corrosion-resistant materials in the EBS (e.g., Alloy 22 and 
titanium). The time sequence for corrosion of iron-based components in the EBS is: 
 Mild steel in the invert (e.g., support beams, cap plate, and gantry rails) will begin to 
degrade after closure of the repository because the invert is directly exposed to the 
relative humidity and temperature environment within the drifts. Corrosion begins when 
the relative humidity becomes great enough to produce aqueous conditions on the 
surface, although the presence of deliquescent salts can result in aqueous conditions if 
the in-drift humidity is higher than the minimum deliquescent point of the salts 
(Campbell and Smith 1951 [DIRS 163817], p. 237). 
The steel and copper are in the top portion of the invert. More specifically, the 
longitudinal and transverse support beams are in the top half of the invert (BSC 2004 
[DIRS 169776], Section A). The transverse support beams are spaced at 
1.524-m intervals (BSC 2004 [DIRS 169503]), so the corrosion products from the beam 
will not always be directly beneath the emplacement pallet or stress corrosion cracks. 
Below and on either side of these beams, the invert is filled to depth with a granular 
ballast that does not contain any steel. 
 Stainless steel rods in the emplacement pallet will corrode more slowly than mild steel 
(for mild carbon steel and stainless steel corrosion rates see 
DTN: MO0409SPAACRWP.000 [DIRS 172059]). Again, the rods are directly exposed 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-37 November 2004 
to the in-drift temperature and relative humidity after closure. The rods in the 
emplacement pallet are located directly beneath the waste package, in the anticipated 
flow path from the waste package. 
 Mild steel (i.e., carbon steel Type A 516) inside the waste package can begin to degrade 
after stress corrosion cracks or general corrosion patches form in the waste package. 
Water vapor can enter the waste package once a crack forms, and this vapor will be 
adsorbed on the steel surfaces, providing an environment for corrosion within the waste 
package. 
 Stainless steel inside the waste package can also corrode, albeit more slowly than mild 
steel, after a stress corrosion crack forms in the waste package lid weld or general 
corrosion patches form in the waste package. 
Aluminum thermal shunts in 21-PWR and 44-BWR waste packages comprise less than 
two percent of the total mass of the waste package. Because the amount of aluminum is 
negligible, it is ignored in the EBS RT Abstraction. The Ni-Gd Alloy absorber plates in the 
CSNF waste package design are modeled as being composed of Neutronit, as in the waste 
package previous design; Neutronit is treated as having the same corrosion rate as stainless steel, 
resulting in corrosion products containing Fe2O3 in proportion to its iron content (see 
Section 6.3.4.2.3). 
Because the corrosion rate of the carbon steel used for invert components is greater than that of 
the Alloy 22 waste package outer corrosion barrier, all mild steel components in the invert will 
degrade to iron oxyhydroxides by the time the first stress corrosion cracks or general corrosion 
patches form. In other words, iron oxyhydroxides will be present in the invert before any 
radionuclides are transported from the waste package. After stress corrosion cracks form, the 
mild steel internal components in the waste package will also degrade rapidly, adding iron 
oxyhydroxides to the in-package environment. Most iron-based in-package materials will 
degrade to corrosion products by 205,000 years, based on a thickness of the inner vessel of 
stainless steel of 50.8 mm (BSC 2004 [DIRS 169472]; BSC 2004 [DIRS 166953], Section B-B) 
and a mean corrosion rate of 0.248 m yr-1 (DTN: MO0409SPAACRWP.000 [DIRS 172059]), 
early in the waste package lifetime. 
The degradation products in the waste package will include hydrous metal oxides from corrosion 
of steel and aluminum materials (YMP 1998 [DIRS 104441], p. C-23) and clays from 
degradation of HLW glass (BSC 2004 [DIRS 169988], Section 6.5.3.3). These corrosion 
products may form a residue that is similar to a highly iron-rich soil or sediment in terms of its 
bulk chemical properties for determining appropriate ranges of Kd. Because of their strong 
sorptive characteristics, the iron oxyhydroxides will dominate the sorptive properties of the 
corrosion products, although the aluminum oxides and manganese oxides are also highly 
sorptive. 
The degradation products in the invert will include iron oxyhydroxides and other hydrous metal 
oxides from the corrosion of steels and copper-based materials, and minerals from the granular 
invert backfill. The invert corrosion products occur in the top portion of the invert because all 
steel and copper is located in the top half of the invert (BSC 2001 [DIRS 154441]). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-38 November 2004 
The in-package degradation products are envisioned to be composed of unconsolidated 
particulates and larger agglomerations of clays, iron oxyhydroxides, and other mineral 
assemblages that slump to the bottom of the waste package. The invert degradation products are 
initially located near the top of the invert, but may move into the mass of granular invert backfill 
during thermal changes or seismic events. Any seepage through the waste package is expected 
to flow through this sludge at the bottom of the waste package. 
The sludge of corrosion products is represented as a single porosity medium, a reasonable 
approach given the granularity of the corrosion products and the randomness of the slumping 
process. Channelized flow paths with no sorption, as in the discrete fractures of a dual porosity 
medium, are not anticipated to occur in this unconsolidated sludge. One conceptual model is for 
the radionuclides to have access to the mass of corrosion products in the waste package. An 
alternative conceptual model, with corrosion products that form a contiguous mass that has a low 
permeability and tight pore structure, would limit access to the full sorptive capacity of the 
corrosion products. The uncertainty in which the conceptual model is most representative can be 
implicitly acknowledged in the selection of broad distributions with small minimum values for 
the sorption distribution coefficients. 
Descriptions of sorption based on a Kd are approximate because this approach is empirical, with 
little if any information about underlying mechanisms, and is therefore not easily extendable to 
different chemical environments and physical substrates (sorptive media). The use of a linear 
isotherm is also approximate because it does not predict saturation of the sorption sites with 
sorbed species that may include natural components of the groundwater. The mass of iron 
oxyhydroxides from waste package corrosion is large (Table 6.3-4), so each waste package 
provides many sites for sorption. For these reasons, the Kd approach is at best an order of 
magnitude measure of contaminant uptake in geologic environments (Davis and Kent 1990 
[DIRS 143280]). 
The use of the linear isotherm (Kd) approach to represent the subsequent release of radionuclides 
into fresh recharge (i.e., the desorption process) is often inconsistent with observations in 
geologic media. Typically, contaminants become more closely attached to a mineral surface 
after sorption, either adsorbed at high energy sites on the surface or absorbed through 
overcoating and buried due to other mineral surface reactions. The net result is that only a 
fraction of the original sorbed population remains available at the surface and able to react with 
adjacent solutions or be accessed by microorganisms. A linear isotherm (Kd) approach, on the 
other hand, assumes that all sorbed radionuclides are freely able to desorb from the substrate. 
As an example, recent reviews of field and laboratory measurements indicate that the fraction of 
sorbed plutonium that is available for desorption rarely exceeds 1 percent (Brady et al. 1999 
[DIRS 154421]; Davis and Kent 1990 [DIRS 143280]). Recognition of the strong role of 
irreversible sorption is implicit in models for watershed transport (Graf 1994 [DIRS 154419]) 
that focus solely on particulate transport. In these cases, desorption is ignored because it is rarely 
seen to occur with plutonium. However, as noted previously, the time scales for these 
observations are much shorter than the regulatory time period for repository performance 
(10,000 years), so the fraction of plutonium that is irreversibly sorbed in TSPA-LA calculations 
has a large uncertainty. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-39 November 2004 
Table 6.3-4. Estimated Masses of Steels and Iron Content in Waste Packages and Equivalent Masses 
(kg) of Iron Corrosion Products (Fe2O3) for Use in Modeling Retardation in the Waste 
Package 
21-PWR 44-BWR 
5-DHLW/DOE 
SNF - Short Naval Long 
Material 
Fe 
Content a 
(%) 
Total 
Mass b 
(kg) 
Fe 
Mass 
(kg) 
Total 
Mass c 
(kg) 
Fe 
Mass 
(kg) 
Total 
Mass d 
(kg) 
Fe 
Mass 
(kg) 
Total 
Mass e 
(kg) 
Fe 
Mass 
(kg) 
Stainless Steel 
Type 316 61.935 10,800 6,690 11,120 6,890 10,160 6,300 14,420 8,930 
A 516 Carbon 
Steel 98.37 5,600 5,510 6,800 6,690 3,720 3,660   
Neutronit 
A 978 66.06 2,120 1,400 2,990 1,970     
Total  18,520 13,600 20,910 15,550 13,880 9,960 14,420 8,930 
Percentage of 
Total as iron   73.4  74.4  71.7  61.9 
Equivalent 
Fe2O3 mass f   19,440  22,240  14,230  12,770 
NOTE: Microsoft Excel calculation of equivalent Fe2O3 mass is described in Appendix A. 
a Calculated Balance from Table 4.1-10 compositions: 100  (sum of non-Fe constituents); see Appendix A. 
b Total Mass in 21-PWR for each material in Table 4.1-17: sum of (mass  number) of each component (BSC 2004 
[DIRS 169472], Table 2; Material Table in Design and Engineering, 21-PWR Waste Package Configuration (BSC 
2004 [DIRS 167394]); see Appendix A. 
c Total Mass in 44-BWR for each material: sum of (mass  number) of each component (BSC 2004 
[DIRS 169472], Table 3; Material Table in Design and Engineering, 44-BWR Waste Package Configuration 
(BSC 2004 [DIRS 167555]); see Appendix A. 
d Total Mass in 5-DHLW/DOE SNF  Short for each material in Table 4.1-17: sum of (mass  number) of each 
component (BSC 2004 [DIRS 167207], Table 5; Material Table in Design & Engineering, 5 DHLW/DOE SNF - 
Short Waste Package Configuration (BSC 2004 [DIRS 166947]). Interface Ring mass of 1 kg erroneously used 
(Figure A-2); correct mass is 44.6 kg (BSC 2004 [DIRS 167207], Table 5); see Appendix A. 
e Total Mass in Naval Long for each material: sum of (mass  number) of each component (BSC 2004 
[DIRS 169472], Table 4; Material Table in Design and Engineering, Naval Long Waste Package Configuration 
(BSC 2003 [DIRS 165159]); see Appendix A. 
f Fe2O3 mass = (Fe mass, kg)  (molecular weight Fe2O3)  (1 mol Fe2O3/2 mol Fe) / (atomic weight Fe) 
= (Fe mass, kg)  (0.15969 kg Fe2O3/mol)  (1 mol Fe2O3/2 mol Fe) / (0.055847 kg Fe/mol) 
= 1.4297  Fe mass. 
BWR = boiling water reactor, DHLW = defense high-level (radioactive) waste, SNF = spent nuclear fuel; 
DOE = U.S. Department of Energy 
6.3.4.2.2 Sorption Parameters for the Invert 
Various conceptual models can be devised to quantify the uncertainty in retardation in the invert. 
Invert corrosion products will tend to be localized and widely spaced, with the possibility being 
that seepage from the waste package could completely miss corrosion products in the invert. In 
this case, even Kd values that would normally be considered to be small for corrosion products 
could overestimate the amount of retardation of radionuclides in the invert. At the same time, 
invert corrosion products will have a smaller sorptive capacity than waste package corrosion 
products simply because the masses of sorptive corrosion products in the invert are much less 
than in the waste packages. As a bounding treatment, sorption of radionuclides on corrosion 
products in the invert is ignored (Assumption 5.7). 

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ANL-WIS-PA-000001 REV 01 6-40 November 2004 
Sorption onto the crushed tuff is included in the EBS transport abstraction. Kd values and 
distributions for 11 selected radionuclides are presented in Table 4.1-12 
(DTN: LA0408AM831341.001 [DIRS 171584]); Kd values for sorption of carbon, iodine and 
technetium on tuff are zero. The ranges of Kd values for sorption onto devitrified tuff are used 
because the crushed tuff in the invert will be the same tuff that is removed when the drifts are 
bored; most of the repository will be developed in the TSw35 horizon, which is composed of 
devitrified tuff. The Kd values selected are summarized in Table 6.5-13. Correlations of Kd 
values among various radionuclides for sorption on tuff are given by a correlation matrix 
presented in Table 4.1-13. Invert Kd values are implemented in TSPA-LA by first computing 
unsaturated zone Kd values for devitrified tuff and then assigning those values to the invert. 
Actinium and americium have similar chemistry in aqueous solution and sorption reactions 
(BSC 2001 [DIRS 160828], p. 64). Therefore, Kd values reported for americium in Table 4.1-12 
are used for actinium in the invert. 
6.3.4.2.3 Sorption Parameters for the Waste Package 
This section presents and analyzes appropriate sorption parameters for the EBS. First, the mass 
of corrosion products (sorbers) is calculated for the repository design. Second, the available 
values for Kd are used to estimate the distributions of sorption distribution coefficients for the 
oxidizing in-drift environment in the waste package. Third, the available data on irreversible 
sorption of metals that are relevant to EBS transport are presented. 
The mass of sorbing material in the waste package has been estimated using compositional 
information from Table 4.1-10 and numbers and masses of components listed in design 
drawings. The mass of sorbing material in the waste package is based on the iron contents of 
Stainless Steel Type 304L, Stainless Steel Type 316L, Stainless Steel Type 316 (these three 
types of stainless steel have similar iron contents), Carbon Steel Type A 516, Neutronit A 978, 
and the masses of these alloys in the four most common waste package types. The estimated 
masses of corrosion products are shown in Table 6.3-4 and described in Appendix A. The 
corrosion products are assumed to be Fe2O3 (Assumption 5.6), and, the mass of corrosion 
products is calculated based on the ratio of molecular weight of Fe2O3 to the atomic weight of 
Fe, accounting for stoichiometry (footnote f in Table 6.3-4). The results shown in Table 6.3-4 
are based on an earlier version of the waste package design (IED 
800-IED-WIS0-00202-000-00B, BSC 2004 [DIRS 167207]). Due to minor design changes for 
the 5 DHLW/DOE Short waste package (see Section 4.1.3, following Table 4.1-17), the mass of 
iron in that waste package is larger using the current design (IED 
800-IED-WIS0-00202-000-00C, BSC 2004 [DIRS 169472], Table 5) than for the earlier design 
version (BSC 2004 [DIRS 167207], Table 5). In addition, in the calculation of the corrosion 
product mass (see Figure A-2), a mass of 1 kg for the Interface Ring for the 5 DHLW/DOE Short 
waste package is erroneously used; the correct value is 44.6 kg. Using the updated 
5 DHLW/DOE Short waste package design data and correcting the Interface Ring mass result in 
an increase in the estimated mass of corrosion products, from 14,230 kg (Table 6.3-4) to 
14,320 kg (updated, corrected value). The difference (0.6 percent) is negligible, so the earlier 
estimate of 14,230 kg shown in Table 6.3-4 is suitable for TSPA-LA calculations. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-41 November 2004 
In a revision to the 21-PWR and 44-BWR waste package design (Anderson 2004 
[DIRS 171637], BSC 2004 [DIRS 170710], BSC 2004 [DIRS 170838]), the Neutronit used for 
the absorber plates is replaced with a nickel-chromium-molybdenum-gadolinium alloy, N06464 
(ASTM B 932-04 [DIRS 168403]), denoted as Ni-Gd Alloy. The mass of Neutronit in a 
21-PWR waste package (2,120 kg; see Table 6.3-4) is replaced by 2400 kg of Ni-Gd Alloy. The 
mass of Neutronit in a 44-BWR waste package (2,990 kg; see Table 6.3-4) is replaced by 
3,380 kg of Ni-Gd Alloy. Whereas Neutronit contains 66.06 percent iron (Kgler 1991 
[DIRS 155761], p. 15), N06464 contains a maximum of 1.0 percent iron (ASTM B 932-04 
[DIRS 168403]). In the analysis summarized in Table 6.3-4, only the iron in the waste package 
components contributes to the corrosion product mass that is used in water adsorption 
calculations in the in-package diffusion submodel, Section 6.5.1.2.1. This corrosion product 
mass also is used in the radionuclide sorption calculations. Using N06464 instead of Neutronit 
in a 21-PWR waste package would reduce the total iron mass from 13,600 kg to 12,220 kg; the 
equivalent mass of Fe2O3 would be reduced from 19,440 kg to 17,470 kg, a reduction of 
10.1 percent. Using N06464 instead of Neutronit in a 44-BWR waste package would reduce the 
total iron mass from 15,550 kg to 13,610 kg; the equivalent mass of Fe2O3 would be reduced 
from 22,240 kg to 19,460 kg, a reduction of 12.5 percent. 
For purposes of TSPA-LA calculations, iron and corrosion product mass estimates are based on 
the earlier waste package design. For a 21-PWR waste package, the calculations use Revision 
00C of Design and Engineering, 21-PWR Waste Package Configuration (BSC 2004 
[DIRS 167394]) rather than Revision 00D (BSC 2004 [DIRS 170710]). For a 5 DHLW/DOE 
Short waste package, the calculations use Revision 00B of D&E/PA/C IED Typical Waste 
Package Components Assembly (BSC 2004 [DIRS 167207], Table 5), instead of Revision 00C 
(BSC 2004 [DIRS 169472], Table 5). The estimated masses of corrosion products in 44-BWR 
and Naval Long waste packages shown in Table 6.3-4 are not used directly in TSPA-LA 
calculations. 
This reduction in Fe2O3 mass compared with the previous waste package design has two 
competing effects on predicted releases of radionuclides from a breached waste package. First, 
the mass of sorbant of radionuclides is reduced, which could potentially increase predicted 
releases; however, as shown in Appendix B (p. B-25), the sorption capacity of a 21-PWR waste 
package is more than double the available radionuclide inventory of a waste package, so using 
the previous design with a 10-to-12 percent higher sorption capacity is inconsequential. Second, 
using the larger mass of Fe2O3 in the previous design results in a higher water saturation in a 
no-seep case (as given by the in-package diffusion submodel, Section 6.5.1.2.1), which will 
overestimate diffusive releases of radionuclides. 
As discussed previously, the use of a linear isotherm is an empirical, order-of-magnitude 
description of mineral surface processes because it is not based on underlying physical or 
chemical mechanisms. In essence, a Kd value is valid only for the specific substrate and 
chemical conditions under which it is measured. More defensible models of contaminant uptake 
by mineral surfaces require a more comprehensive mechanistic understanding of the chemical 
reactions involved (Davis et al. 1998 [DIRS 154436]). In lieu of a more involved mechanistic 
treatment based on surface complexation that includes a provision for irreversible sorption, Kd 
values can provide a first-order picture of the sorption process, using generic ranges based on 
soils and iron oxyhydroxides. The rationale for this approach is described below. 

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Based on previous TSPA calculations, the pH of waste package fluids (CRWMS M&O 2000 
[DIRS 153246], Tables 3.3-7 through 3.3-9) is expected to fall within the range observed in soils 
and groundwaters (pH values between 4 and 10). Although the composition of in-package fluids 
will vary with time due to degradation of the waste package components (primarily steels, 
Zircaloy cladding, SNF, and waste glass), major element characteristics (such as alkalinity and 
system redox state) will be controlled by equilibrium with atmospheric carbon dioxide and free 
oxygen. The primary reactive components in the degraded waste package environment are iron 
hydroxides, the same mineral phases that tend to dominate trace element sorption in soils. The 
only major element species that will be present in waste package fluids, but that tend to be 
scarcer in natural soils and groundwaters, are those containing uranium. 
The trace element composition of waste package fluids will differ due to the presence of metal 
components and various radiogenic isotopes. On the other hand, the waste package environment 
is expected to contain greater volumes of iron hydroxides than all but the most iron-rich soils. 
Consequently, sorption calculations using ranges of Kd values measured on iron-containing soils 
or iron hydroxides provide a reasonable measure of sorption inside the waste package. 
Sorption distribution coefficients often vary by at least an order of magnitude. Each range of Kd 
represents the compilation of many experimental measurements with wide variations in sorbant 
composition and characteristics, contaminant level, solution composition and temperature, and 
method of measurement. 
Sorption distribution coefficient values for a linear, reversible isotherm can be interpreted 
physically (Stumm 1992 [DIRS 141778], Section 4.12) in terms of retarding the movement of a 
contaminant relative to the velocity of the water carrying it. If the average water velocity is . 
(m s-1) and the front of the contaminant concentration profile has an average velocity c v , the 
retardation of the front relative to the bulk mass of water is described by the relation: 
d 
b 
c 
f K 
v
v R 
f 
. 
+ = = 1 , (Eq. 6.3.4.2.3-1) 
where f R is the retardation factor (dimensionless ratio of water velocity to the concentration 
front velocity), b . is the bulk density of the rock (kg m-3) having a porosity f (fraction). For 
example, a contaminant with a Kd of 1,000 ml g-1 will move at one ten-thousandth the rate of the 
carrier water for a rock porosity of 20 percent and a rock density of 2,000 kg m-3. A contaminant 
with a Kd of 1 ml g-1 will move at one-eleventh the velocity of the carrier water, and a 
contaminant with a Kd of 0 moves at the velocity of the water, both for the same values of rock 
porosity and rock density. These effective transport velocities provide an estimate of the delay 
for first breakthrough of the contaminant; after the sorption sites are completely saturated, 
changes in mass flow rate will be delayed only by the water transport time through the system. 
The corrosion product assemblage is predicted by the in-package chemistry model reaction path 
calculations to be made up primarily of iron oxyhydroxides (e.g., goethite, hematite, ferrihydrite) 
and aluminum oxides. Lesser amounts of manganese oxides, metal phosphates and clay minerals 
are anticipated. The integrated sorptive properties of the assemblage might therefore be 
approximated as being that of iron oxyhydroxides with some aluminum oxides. The latter 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-43 November 2004 
possess high specific surface areas and a strong chemical affinity for many radionuclides. 
Cesium primarily exchanges onto clay minerals. Strontium and radium tend to exchange onto 
clay lattices in soils, although strontium does sorb onto iron oxyhydroxides, particularly above 
pH 7. The fact that strontium and radium behave similarly in soils indicates that limited radium 
uptake by iron oxyhydroxides can be expected as well. Under oxidizing conditions technetium 
and iodide sorb negligibly to most soil components. However, reduction of technetium on solid 
surfaces containing reduced elements (e.g., iron metal) can cause strong retardation. 
Table 6.3-5 summarizes the observations above by listing the components of soils that tend to 
control sorption. Iron oxyhydroxides are an important sorbing component of soils for all 
radioelements except iodine and technetium. 
Table 6.3-5. Influences Over Radionuclide Sorption in Soils 
Element 
Important Solid Phase and Aqueous-Phase Parameters 
Influencing Contaminant Sorption* 
Americium [Clay Minerals], [Iron/Aluminum Oxide Minerals], pH 
Cesium [Aluminum/Iron Oxide Minerals], [Ammonium], Cation Exchange Capacity, [Clay Mineral], 
[Mica-like Clays], pH, [Potassium] 
Iodine [Dissolved Halides], [Organic Matter], Redox, Volatilization, pH 
Neptunium [Clay Minerals], [Iron/Aluminum Oxide Minerals], pH 
Radium BaSO4 Coprecipitation, [Dissolved Alkaline Earth Elements], Cation Exchange Capacity, 
[Clay Minerals], Ionic Strength, [Iron-/Aluminum-Oxide Minerals], [Organic Matter], pH 
Technetium [Organic Matter], Redox 
Plutonium [Aluminum/Iron Oxide Minerals], [Carbonate, Fluoride, Sulfate, Phosphate], [Clay Mineral], 
[Organic Matter], pH, Redox 
Strontium Cation Exchange Capacity, [Calcium], [Carbonate], pH, [Stable Strontium] 
Thorium [Aluminum/Iron Oxide Minerals], [Carbonate], [Organic Matter], pH 
Uranium [Aluminum/Iron-Oxide Minerals], [Carbonate, Fluoride, Sulfate, Phosphate], [Clay Mineral], 
[Organic Matter], pH, Redox, [U] 
Source: EPA (2004 [DIRS 172215]), Table 5.35. 
EPA (1999 [DIRS 170376]), Table 5.20. 
*Parameters listed in alphabetical order. Square brackets represent concentration. 
Corrosion product Kd ranges have been compiled by Electric Power Research Institute (EPRI) 
(2000 [DIRS 154149], Table 6-9) from a literature review of iron oxyhydroxides sorption 
measurements. Ranges and distributions of Kd values for sorption of radionuclides onto iron 
oxide are also evaluated and compiled in DTN: LA0003AM831341.001 ([DIRS 148751] SEP 
table S00191_002); these are listed in Table 4.1-11. The U.S. Environmental Protection Agency 
(EPA) has compiled Kd values for soils for many of the same radionuclides (EPA 1999 
[DIRS 170376]; EPA 2004 [DIRS 172215]). The large role of iron and aluminum 
oxyhydroxides minerals in controlling overall soil Kd values is explicitly recognized in the EPA 
documents. For this reason, one would expect EPA soil Kd values and EPRI iron oxyhydroxides 
Kd values to be similar and both to provide a reasonable approximation of retardation in the 
waste package corrosion products. There are some caveats, however, the most important one 
being that Kd values for a given material and radionuclide are approximate values that can vary 
widely depending on the specifics of the measurement (solid/solution ratio, radionuclide level, 
time allowed for equilibration). General coherence in an order-of-magnitude sense is the best 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-44 November 2004 
that can be expected as the Kd approach does a poor job of reproducing actual transport profiles; 
see, for example, Bethke and Brady (2000 [DIRS 154437]) and Reardon (1981 [DIRS 154434). 
Table 6.3-6 gives Kd ranges describing retardation in the waste package corrosion products for 
the 12 radionuclides that are tracked in TSPA-LA, with the minimum Kd and maximum Kd being 
the ranges used in TSPA-LA. For all but iodine and technetium, the maximum Kd values are 
from DTN: LA0003AM831341.001 ([DIRS 148751] SEP table S00191_002). The maximum 
Kd value for iodine and technetium is chosen to be 0.6 ml g-1, which is the approximate 
maximum Kd value for iodine and technetium specified for alluvium in saturated zone units in 
DTN: LA0003AM831341.001 ([DIRS 148751] SEP table S00191_001). The minimum Kd 
values for carbon, cesium, iodine, radium, strontium, and technetium are the minimum Kd values 
specified in DTN: LA0003AM831341.001 ([DIRS 148751] SEP table S00191_002). In order to 
provide a more bounding estimate of releases of radionuclides that have a large impact on dose, 
the minimum Kd values for actinium, americium, plutonium, and thorium are reduced by a factor 
of 10 from the minimum Kd values specified in DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002). For the same reason, the minimum Kd value for protactinium is reduced 
by a factor of 5 from the minimum Kd value of 500 ml g-1 specified in 
DTN: LA0003AM831341.001 ([DIRS 148751] SEP table S00191_002); this minimum value is 
corroborated by Evaluation of the Candidate High-Level Radioactive Waste Repository at Yucca 
Mountain Using Total System Performance Assessment, Phase 5 (EPRI 2000 [DIRS 154149], 
Table 6-9). The minimum Kd value for uranium is reduced by a factor of 100 from the minimum 
Kd value of 100 ml g-1 specified in DTN: LA0003AM831341.001 ([DIRS 148751] SEP table 
S00191_002); this minimum value is corroborated by Review of Geochemistry and Available Kd 
Values for Cadmium, Cesium, Chromium, Lead, Plutonium, Radon, Strontium, Thorium, Tritium 
(3H), and Uranium. Volume II of Understanding Variation in Partition Coefficient, Kd, Values 
(EPA 1999 [DIRS 170376], Table 5.17). The minimum Kd value for neptunium is reduced by a 
factor of 500 from the minimum Kd value of 500 ml g-1 specified in 
DTN: LA0003AM831341.001 ([DIRS 148751] SEP table S00191_002); this minimum value is 
corroborated by Evaluation of the Candidate High-Level Radioactive Waste Repository at Yucca 
Mountain Using Total System Performance Assessment, Phase 5 (EPRI 2000 [DIRS 154149], 
Table 6-9) and Review of Geochemistry and Available Kd Values for Cadmium, Cesium, 
Chromium, Lead, Plutonium, Radon, Strontium, Thorium, Tritium (3H), and Uranium. Volume II 
of Understanding Variation in Partition Coefficient, Kd, Values (EPA 1999 [DIRS 170376], 
Table 5.17). 
For cesium, radium, and strontium, a beta distribution as specified in 
DTN: LA0003AM831341.001 ([DIRS 148751] SEP table S00191_002), is used in TSPA-LA. 
For carbon, iodine, protactinium, and technetium, a uniform distribution as specified in 
DTN: LA0003AM831341.001 ([DIRS 148751] SEP table S00191_001) is used in TSPA-LA. 
Whereas DTN: LA0003AM831341.001 ([DIRS 148751] SEP table S00191_002) specified a 
uniform distribution for americium, neptunium, plutonium, thorium, and uranium, a log-uniform 
distribution is used in TSPA-LA, all of which have Kd values that range over more than an order 
of magnitude. A log-uniform distribution is specified to avoid the high-end bias that results from 
sampling from a uniform distribution that has a large range. 
Table 6.3-6 also gives corroborating ranges and data source(s) described in recent literature. To 
capture the secondary role of iron oxyhydroxides in soil sorption of strontium, radium and 

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ANL-WIS-PA-000001 REV 01 6-45 November 2004 
cesium, clay-poor soil Kd values from the EPA compilation are used in the comparison. In all 
cases the corroborating Kd ranges overlap the ranges used in TSPA-LA. Moreover, in most cases 
the TSPA-LA Kd values tend to be on the low end of the Kd range considered in aggregate. 
Table 6.3-6. Summary of Partition Coefficient (Kd) Ranges and Distributions for Retardation in the Waste 
Package Corrosion Products 
Element 
Minimum 
Kd (ml g-1) 
Maximum 
Kd (ml g-1) 
Distribution 
Type 
Corroborating Kd 
Range (ml g-1) Corroborating Kd Range Source 
Ac 100 5,000 Log-Uniform 1,00020,000 EPRI 2000 [DIRS 154149], Table 6-9 
Am 100 5,000 Log-Uniform 1,000>100,000 
1,00020,000 
EPA 2004 [DIRS 172215], 
Section 5.2.5.1; 
EPRI 2000 [DIRS 154149], Table 6-9 
C 10 100 Uniform 0100 EPRI 2000 DIRS 154149], Table 6-9 
Cs 0 300 Beta 
E(x)=30 
s(x)=30 
103,500 
1200 
EPA 1999 [DIRS 170376], 
Table D.10 (low clay soils); 
EPRI 2000 [DIRS 154149], Table 6-9 
I 0 0.6 Uniform 01 EPRI 2000 [DIRS 154149], Table 6-9 
Np 1 1,000 Log-Uniform 0.16929 
101,000 
(0.11,000) 
EPA 2004 [DIRS 172215], 
Section 5.6.5.4; 
EPRI 2000 [DIRS 154149], Table 6-9 
(reduced by factor of 100 for U site 
saturation) 
Pa 100 1,000 Uniform 10010,000 EPRI 2000 [DIRS 154149], Table 6-9 
Pu 100 5,000 Log-Uniform 6015,000 
1,00020,000 
EPA 1999 [DIRS 170376], p. G-4 
EPRI 2000 [DIRS 154149], Table 6-9 
Ra 0 500 Beta 
E(x)=30 
s(x)=30 
1120 
501,000 
EPA 2004 [DIRS 172215] 
(Section 5.7.5.1: use Sr values) 
EPRI 2000 [DIRS 154149], Table 6-9 
Sr 0 20 Beta 
E(x)=10 
s(x)=2.5 
1120 
10100 
EPA 1999 [DIRS 170376], Table 5.13 
EPRI 2000 [DIRS 154149], Table 6-9 
Tc 0 0.6 Uniform 01,000 EPRI 2000 [DIRS 154149], Table 6-9 
Th 100 5,000 Log-Uniform 20300,000 
1,00020,000 
EPA 1999 [DIRS 170376], Table 5.15 
EPRI 2000 [DIRS 154149], Table 6-9 
U 1 1,000 Log-Uniform 0630,000 
5010,000 
EPA 1999 [DIRS 170376], Table 5.17 
EPRI 2000 [DIRS 154149], Table 6-9 
EPA = Environmental Protection Agency 
Irreversible uptake can be the dominant control over contaminant transport in soils. Evidence for 
soil sequestering of bomb-pulse plutonium and americium and of uranium, iodine, technetium, 
cesium, and strontium from ore processing and reactor operations has been extensively 
documented in the literature (Coughtrey et al. 1983 [DIRS 132164]). 
Estimates of the mean fraction of irreversible sorption for various radionuclides on soil are 
derived in Site Screening and Technical Guidance for Monitored Natural Attenuation at DOE 
Sites (Brady et al. 1999 [DIRS 154421], Appendix VI). The value of the irreversible fraction for 
the EBS will differ from that for soils and will depend on the material that the specific 
radionuclide encounters, the speciation of the radionuclide, and other factors in the material and 

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ANL-WIS-PA-000001 REV 01 6-46 November 2004 
chemical environment. Irreversible sorption is an important process for many radionuclides that 
potentially contribute to dose. For the TSPA-LA model, irreversible sorption of Pu and Am is 
included, with appropriate fractions of the total mass adsorbed being based on field observations. 
Details of the radionuclide sorption component of the EBS transport model are described in 
Sections 6.5.1.1.1 and 6.5.3. 
6.3.4.2.4 Sorption Parameters for Corrosion Products in the Invert 
To compare with the mass of sorbing material in the waste packages, the mass of sorbing 
material in the invert has been estimated using the data from Repository Subsurface 
Emplacement Drifts Steel Invert Structure Sect. & Committed Materials (BSC 2004 
[DIRS 169776], Committed Materials table). The iron content of the steel invert support beams, 
stiffeners, base plates, gantry runway beams, runway beam cap plates, stub columns and top 
plates, miscellaneous stiffener plates, and the gantry rails is included in this calculation. The iron 
in the steel set ground support, the rock bolts, and the welded wire fabric steel has been ignored, 
even though the corrosion products from these components may fall on the invert. The mass of 
corrosion products is again estimated by assuming that iron converts to Fe2O3 during the 
corrosion process. The mass of A 588 carbon steel per unit length of drift in the invert is 
893 kg m-1 (BSC 2004 [DIRS 169776], Committed Materials table), having an iron content of 
859 kg m-1 (using an iron content of 96.16 percent for the composition of A 588 steel; 
ASTM A 588/A 588M-01 [DIRS 162724], Table 1). The mass of A 759 steel in the gantry rails 
is 134 kg m-1 (BSC 2004 [DIRS 169776], Committed Materials table), which has an iron content 
of 97.47 percent (ASTM A 759-00 [DIRS 159971]), or 131 kg m-1. The total iron content of the 
invert is then 990 kg m-1, which converts to 1,415 kg m-1 of Fe2O3. As a comparison, the 
average mass of Fe2O3 in the invert under a 21-PWR or 44-BWR waste package, having a 
nominal length of 5.02 m (BSC 2004 [DIRS 169472], Table 1), would be 6,820 kg, or 
approximately one-third the amount of iron corrosion products inside a waste package (Table 
6.3-4). While not negligible, the sorptive capacity of the invert is small compared to that of the 
waste packages, so, not considering retardation by corrosion products in the invert (Assumption 
5.7) will overestimate radionuclide transport. 
The impact of copper in the invert on retarding iodine and technetium is discussed here to 
complete the analysis of neglecting retardation by corrosion products in the invert and thus 
overestimating radionuclide transport. The amount of elemental copper in the drift is given by 
the nominal weight of the solid copper conductor bar rail, 4.0 kg m-1 (BSC 2001 [DIRS 154441], 
Section 3.1.7), plus the copper in the communication cable, which is 50 percent by weight of the 
total cable weight of 2.00 kg m-1 (BSC 2001 [DIRS 154441], Sections 3.1.9 and 3.2.1.3). The 
total weight of elemental copper per meter of drift is then [4.0 + (0.5)(2.00)] or a total of 
5.0 kg m-1. These values are based on the nominal mass of elemental copper, rather than the 
upper bound values, to provide a bounding estimate. The mass of elemental copper is not 
explicitly represented in the TSPA-LA model, but its presence when oxidized is noted because of 
its role as a potential sorber for iodine and technetium. 
The mass of copper is large relative to the mass of iodine and technetium. Using a waste 
package length of 5.024 m for the CSNF waste package (BSC 2004 [DIRS 169472], Table 1), 
there is 25.1 kg of elemental copper in the invert per CSNF waste package. This value (25.1 kg) 
can be compared to approximately 7.64 kg of technetium-99 and 1.75 kg of iodine-129 per 

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ANL-WIS-PA-000001 REV 01 6-47 November 2004 
CSNF waste package (DTN: SN0310T0505503.004 [DIRS 168761]). Thus, there is more 
elemental copper than iodine or technetium using a mass or molar basis. Similarly, the 
5 DHLW/DOE SNF - Short codisposal waste package has a length of 3.45 m (BSC 2004 
[DIRS 169472], Table 3), implying that there is 17.3 kg of elemental copper per 
5 DHLW/DOE SNF - Short waste package in the invert. This mass is greater than the 
approximately 0.156 kg of technetium-99 or the 0.0351 kg of iodine-129 in the codisposal waste 
packages (DTN: SN0310T0505503.004 [DIRS 168761]). Based simply on a gross comparison 
of masses, there is ample quantity of copper in the invert to adsorb all iodine and technetium that 
might be released from the waste packages. Nevertheless, because the presence of copper is 
highly localized, the probability of iodine or technetium released from the waste package 
actually contacting the copper is low. Therefore, iodine and technetium are assumed not to sorb 
onto corrosion products in the invert. 
To summarize, no credit is taken for radionuclide sorption onto corrosion products of iron or 
copper contained in the invert (Assumption 5.7), through which radionuclides must be 
transported to reach the accessible environment. By ignoring sorption in the invert, there is 
added confidence that the radionuclide inventory actually transported is less than the calculated 
value used in assessing dose to the individual. 
6.3.4.3 In-Package Diffusion Submodel for Commercial Spent Nuclear Fuel Waste 
Packages 
This submodel provides a way to quantify the uncertainty in diffusive releases from CSNF waste 
packages when no seepage occurs, when the only water present is water vapor. The object of the 
submodel is to compute the effective diffusion coefficient, cross sectional area for diffusion, and 
the diffusion path length for diffusion of radionuclides by Ficks law. From these output 
parameters, the rate of diffusion of radionuclides from the waste package to the invert can be 
determined. 
One way to picture a breached and degraded waste package is for the radionuclide inventory to 
be located just inside the thickness of the waste package outer corrosion barrier or lids from the 
invert, with a fully saturated porous medium separating the interior of the waste package from 
the invert. This scenario provides essentially no resistance to diffusion from the waste package 
and thus grossly overestimates diffusive releases of radionuclides. Compared to this picture, the 
present base submodel with in-package diffusion can potentially delay and reduce computed 
diffusive releases by providing a much more realistic estimate of the resistance to diffusion that 
occurs when little water is present. This is especially important if, as expected, much of the 
repository has no seepage into drifts. 
The fundamental basis of this submodel is that the only liquid water present is the thin film of 
adsorbed water that covers all surfaces exposed to humid air (Assumption 5.5). In this 
submodel, all dissolution and diffusion of radionuclides occur in this thin film. 
As the steel internal components corrode, the interior of the waste package becomes filled with a 
mass of porous corrosion products. Diffusion will occur on the thin films coating the surfaces of 
particles of corrosion products. The extent of corrosion will determine the amount of corrosion 
products and, in turn, the amount of adsorbed water that is present, from which the water 

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saturation is computed. Together with estimates of the porosity, the effective diffusion 
coefficient is calculated using Archies law. A bulk cross sectional area for diffusion is 
estimated, and the length of the diffusion path is a sampled parameter for each leg of the path 
from the waste form domain to the corrosion products domain to the invert domain. 
The extent of corrosion is taken to vary linearly over the lifetime of the waste package steels. 
The amount of water adsorbed is a function of the relative humidity. Consequently, the rate of 
diffusive releases varies over time. All internal steel components are considered to be iron that 
corrodes to form Fe2O3. 
A number of uncertain parameters are associated with this submodel. The lengths of the various 
diffusive pathways are also uncertain because the location of the failed fuel rods and therefore 
the distance from the points of failure to the openings in the waste package outer corrosion 
barrier cannot be known. In addition, the surface area available for adsorption of water is 
uncertain because the condition of the corrosion products cannot be determinedthey may be 
finely powdered with a high specific surface, or agglomerate into an impermeable mass with low 
specific surface area, all depending on unpredictable circumstances and material behaviors. 
Details of the in-package diffusion submodel for CSNF waste packages are presented in 
Section 6.5.1.2.1. 
6.3.4.4 Colloidal Transport 
Radionuclide transport from the waste package occurs as dissolved species at the appropriate 
solubility or dissolution rate limit and as colloidal particles. Three types of colloids are 
anticipated to exist in the EBS (BSC 2004 [DIRS 170025]): (a) waste form colloids from 
degradation of HLW glass, (b) iron oxyhydroxide colloids due to products from the corrosion of 
steel waste packages, and (c) groundwater or seepage water colloids. All three types of colloids 
may have reversibly sorbed radionuclides. The waste form colloids may have irreversibly 
attached (embedded) or reversibly attached (sorbed) radionuclides. The corrosion products 
colloids may have irreversibly attached (strongly sorbed) or reversibly attached (weakly sorbed) 
radionuclides. The stability and mass concentrations of colloids are functions of the ionic 
strength and pH of the groundwater or local liquid chemistry in the waste package and invert. 
Both groundwater and waste form colloids are stipulated to be smectite, and therefore Kd values 
associated with radionuclide sorption onto smectite colloids are used in the TSPA-LA model 
(BSC 2004 [DIRS 170025], Table 6-6). 
The potential mass of radionuclides irreversibly attached (embedded) to the waste form colloids 
(BSC 2004 [DIRS 170025], Section 6.3.3.3) is determined from reactions within the waste 
package. The mass of radionuclides reversibly attached to all three types of colloids is 
determined primarily by three parameters: 
 Mass concentration of dissolved (aqueous) radionuclide in the liquid 
 Mass concentration of colloid material in the liquid 
 Radionuclide distribution coefficient (Kd) of a specific radionuclide on a specific colloid 
mineralogical type. 

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The potential concentrations of colloids in the drifts and EBS have also been assessed 
(BSC 2004 [DIRS 170025]). In a DOE-funded research project at the University of Nevada at 
Las Vegas to evaluate the corrosion of scaled-down miniature waste packages, the data indicate a 
preponderance of amorphous corrosion products released as colloids, including magnetite 
(Fe3O4), lepidocrocite (FeOOH), and goethite (FeOOH) (DTN: MO0302UCC034JC.003 
[DIRS 162871]; BSC 2004 [DIRS 170025], Section 6.3.1.3). 
Colloidal transport of radionuclides occurs by advective and diffusive processes. Advective 
transport moves colloids (and the associated radionuclides) at approximately the same velocity as 
the liquid flux through the EBS. Longitudinal dispersion, which could potentially enable 
colloids to travel faster than the bulk average liquid velocity, is ignored because of the short 
travel distance through the EBS (see Section 6.3.1.2). Diffusive transport moves colloids due to 
the concentration gradient and the medium diffusive properties. In the absence of a rigorous 
theory of solute diffusion in liquids, order of magnitude estimates may be made on the basis of 
hydrodynamic theory. Based on the Stokes-Einstein equation (Bird et al. 1960 [DIRS 103524], 
p. 514, Equation 16.5-4), the diffusivity of a solute in a liquid is inversely proportional to the 
radius of the diffusing particles. 
Rates of diffusion of colloidal particles can be estimated by scaling those experimentally 
determined free water diffusion coefficients for dissolved actinides to dissolved colloidal 
materials on the basis of size (Stokes-Einstein relationship) as follows: 
, . .. 
. 
. .. 
. 
= 
coll 
ion 
ion coll r
r D D (Eq. 6.3.4.4-1) 
where 
coll D = diffusion constant for a colloidal actinide of radius coll r 
ion D = diffusion constant for a dissolved actinide of radius ion r 
coll r = radius of the colloidal actinide 
ion r = radius of the dissolved actinide. 
For example, given an ionic radius = ion r 1  (0.1 nm) and a colloidal particle radius 
= coll r 10 nm, the free water diffusion coefficient for the colloidal particle would be that of the 
dissolved actinide reduced by a factor of 100 ( [ ] 100 / nm nm/10 1 . 0 ion ion coll D D D = = , from 
Equation 6.3.4.4-1). This approach is consistent with discussions in Principles of Colloid and 
Surface Chemistry (Hiemenz 1986 [DIRS 117358], p. 81). 
Radionuclides may sorb onto stationary corrosion products from the degradation of waste 
package internal components (Section 6.5.3) as well as onto mobile colloids. This sorption 
process will compete with sorption onto colloids. A portion of plutonium and americium sorb 
irreversibly onto mobile colloids as well as onto stationary corrosion products in the waste 
package. In order to model both reversible and irreversible sorption of plutonium and americium 
onto iron oxyhydroxide colloids, the TSPA model reduces the upper bounds for the Kd values in 
Table 6.3-7 for plutonium and americium by a factor of 100 (BSC 2004 [DIRS 170025], 

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Section 6.3.3.2), which constrains the Kd values to the lower bound. This allows for more of the 
plutonium and americium to desorb from the iron oxyhydroxide colloids, thereby simulating 
reversible sorption. 
The sorption distribution coefficients (Kd values) for colloids used in the TSPA-LA calculations 
are presented in Table 6.3-7. The ranges of Kd values used for colloids are different from those 
used for stationary corrosion products (Table 6.3-5) and are higher for all radionuclides that are 
considered. The rationale for this difference is that the specific surface area of colloids is 
generally greater than that of stationary corrosion products, largely because colloid particles are 
smaller. The specific surface area used for corrosion products ranges from about 0.4 to 
22.4 m2 g-1 (Section 6.5.1.2.1.3.1). In contrast, the specific surface area of iron oxyhydroxide 
colloids ranges from 1.8 to 720 m2 g-1 with a log-uniform distribution 
(DTN: SN0309T0504103.010 [DIRS 165540]; BSC 2004 [DIRS 170025], Section 6.3.3.2). 
Another reason for the disparities between stationary corrosion products Kd values and colloid Kd 
values is an intentional bias toward lower Kd values in each model so as to overestimate releases 
of radionuclides. In the case of stationary corrosion products, lower Kd values will tend to 
release more radionuclides from the waste packages. For colloids, predicted releases of 
radionuclides sorbed onto colloids are higher using higher Kd values, since the radionuclides then 
remain sorbed longer and are transported farther. 
6.3.4.5 Transport through Stress Corrosion Cracks 
Transport through stress corrosion cracks in the waste package is limited to diffusion. Once 
stress corrosion cracks form in the lid of the waste package, all surfaces inside the waste package 
are assumed to be coated with a thin film of water (per Assumption 5.5). This thin film provides 
the medium for diffusion from the waste form, through the stress corrosion crack, and out of the 
waste package. The diffusive area is calculated as the product of the area and number of cracks. 
The area of each crack is estimated from the data in Table 6.3-3. The maximum cross-sectional 
area of each crack for diffusive transport is calculated to be 7.7  10-6 m2 (Section 6.3.3.1.2.1). 
Table 6.3-7. Sorption Distribution Coefficient (Kd) Values and Interval Probabilities Used for Reversible 
Radionuclide Sorption on Colloids in TSPA-LA Calculations 
Radionuclide Colloid 
Kd Value Range 
(ml g-1) 
Kd Value Intervals 
(ml g-1) 
Kd Value Interval 
Probabilities 
Iron Oxyhydroxide 104 to 106 <1  104 
1  104 to 5  104 
5  104 to 1  105 
1  105 to 5  105 
5  105 to 1  106 
> 1  106 
0 
0.15 
0.2 
0.5 
0.15 
0 
Pu 
Smectite 103 to 106 < 1  103 
1  103 to 5  103 
5  103 to 1  104 
1  104 to 5  104 
5  104 to 1  105 
1  105 to 5  105 
5  105 to 1  106 
> 1  106 
0 
0.04 
0.08 
0.25 
0.2 
0.35 
0.08 
0 

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Table 6.3-7. Sorption Distribution Coefficient (Kd) Values and Interval Probabilities Used for 
Reversible Radionuclide Sorption on Colloids in TSPA-LA Calculations (Continued) 
Radionuclide Colloid 
Kd Value Range 
(ml g-1) 
Kd Value Intervals 
(ml g-1) 
Kd Value Interval 
Probabilities 
Am, Th, Pa Iron Oxyhydroxide 105 to 107 < 1  105 
1  105 to 5  105 
5  105 to 1  106 
1  106 to 5  106 
5  106 to 1  107 
> 1  107 
0 
0.15 
0.2 
0.55 
0.1 
0 
Smectite 104 to 107 < 1  104 
1  104 to 5  104 
5  104 to 1  105 
1  105 to 5  105 
5  105 to 1  106 
1  106 to 5  106 
5  106 to 1  107 
> 1  107 
0 
0.07 
0.1 
0.23 
0.2 
0.32 
0.08 
0 
Cs Iron Oxyhydroxide 101 to 103 < 1  101 
1  101 to 5  101 
5  101 to 1  102 
1  102 to 5  102 
5  102 to 1  103 
> 1  103 
0 
0.13 
0.22 
0.55 
0.1 
0 
Smectite 102 to 104 < 1  102 
1  102 to 5  102 
5  102 to 1  103 
1  103 to 5  103 
5  103 to 1  104 
> 1  104 
0 
0.2 
0.25 
0.5 
0.05 
0 
DTN: SN0306T0504103.006 [DIRS 164131], Table 1. 
NOTE: In engineered barrier system calculations, upper bound of Kd ranges for plutonium (Pu) and 
americium (Am) on iron oxyhydroxide reduced by a factor of 100 to be compatible with mechanistic 
sorption model described in Waste Form and In-Drift Colloids-Associated Radionuclide 
Concentrations: Abstraction and Summary (BSC 2004 [DIRS 170025], Section 6.3.3.2). 
6.4 CONSIDERATION OF ALTERNATIVE CONCEPTUAL MODELS 
Alternative conceptual models considered in the EBS radionuclide transport abstraction are 
discussed in this section. A summary of models that are analyzed is presented in Table 6.4-1. 
Table 6.4-1. Alternative Conceptual Models Considered 
Alternative 
Conceptual 
Models Key Assumptions Screening Assessment and Basis 
Bathtub flow 
model (alternative 
to flow-through 
model) 
Seepage water flowing into breached waste 
package accumulates until void volume is filled 
before water containing dissolved radionuclides 
flows out. Various cases, such as changing inflow 
rates and effect of solubility and dissolution rate 
limits, are evaluated. 
Screened out in analysis in Section 6.6.1. 
For several of the most pertinent cases, 
the flow-through model is bounding with 
respect to releases of radionuclides. 

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Table 6.4-1. Alternative Conceptual Models Considered (Continued) 
Alternative 
Conceptual 
Models Key Assumptions Screening Assessment and Basis 
Water vapor 
diffusion limitations 
through stress 
corrosion cracks 
(alternative to 
unlimited access 
to water vapor) 
If the rate of corrosion of steel components inside 
waste package is greater than the rate of diffusion 
of water vapor into waste package, a film of 
adsorbed water cannot form, which delays diffusive 
releases until all steel is fully corroded. 
Water vapor concentration inside waste package is 
assumed to be zero to maximize concentration 
gradient. 
Alternative cases consider stress corrosion cracks 
that are assumed to be (1) fully open and (2) filled 
with corrosion products but still permeable. 
Alternative corrosion stoichiometry is considered for 
formation of (1) Fe2O3 and (2) Fe(OH)2. 
Alternative corrosion rates are considered 
assuming (1) only carbon steel corrodes, (2) all 
internal components corrode at carbon steel rate 
and at stainless steel rate, with mass of iron 
computed as in the in-package diffusion submodel. 
Screened out. 
Potentially delays releases for hundreds 
to thousands of years, which requires 
unattainable reduction in model 
uncertainties. 
The assumption that no water is 
physically adsorbed until all steel is 
corroded is questionable, since 
adsorption is typically a fast process. On 
the other hand, if water consumption by 
corrosion keeps the relative humidity 
inside the waste package low, the 
effective water saturation, as computed in 
the in-package diffusion submodel, will be 
so low that bulk liquid phase behavior 
allowing dissolution and diffusion of 
dissolved radionuclides will not exist until 
corrosion is complete. 
Oxygen diffusion 
limitations through 
stress corrosion 
cracks (alternative 
to unlimited 
access to oxygen) 
Same as for water vapor diffusion limitation model, 
but less restrictive in that oxygen as well as water 
vapor can corrode steels, potentially reducing time 
needed for complete corrosion of internal 
components. 
Assumes that oxic corrosion occurs at the same 
rate as anoxic corrosion with water. 
Assumes oxygen and water vapor can diffuse 
independently of each other without interfering. 
Oxygen concentration inside waste package is 
assumed to be zero to maximize concentration 
gradient. 
Screened out. 
Potentially delays releases, which is not 
justifiable in view of large model 
uncertainties. 
Comparative rates of oxic and anoxic 
corrosion should be considered. 
Competing diffusion with water vapor 
should also be addressed. 
Dual-continuum 
invert model 
Crushed tuff invert ballast is modeled as a dualcontinuum 
material consisting of intergranular pore 
space and intragranular pore space. 
All seepage flow into the drift flows through the 
intergranular pore space and into the UZ fractures. 
Imbibition from UZ host rock into the invert flows 
through the intragranular pore space. 
Diffusion of radionuclides also occurs in both the 
intergranular and intragranular pore spaces, from 
the waste package corrosion products into UZ 
fractures and matrix, as well as between the two 
invert continua. 
Screened out. 
Insufficient data to validate diffusion 
coefficients in individual continua. 
Insufficient data to confirm whether this is 
a bounding approach with respect to 
chemical behavior in the invert. 
Invert diffusion 
coefficient model 
with lower limit on 
water content 
As the water content of the crushed tuff ballast 
decreases, the water films that connect pore 
spaces become disconnected, and the effective 
diffusion coefficient drops more rapidly than 
predicted by Archies law. Below some critical 
water content, the diffusion coefficient becomes 
zero. Based on models of diffusion in soils. 
Screened out. 
Insufficient data to validate diffusive 
behavior at very low water contents. 
Does not provide upper bounds on 
diffusion coefficients. 

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6.4.1 Bathtub Model for the Waste Package 
The bathtub model is an alternative conceptual EBS flow model in which seepage collects within 
the waste package before being released to the EBS. This is an alternative to the flow-through 
geometry, and is analyzed in Section 6.6.1. It is concluded that, with respect to releases of 
radionuclides, the flow-through model increases releases relative to the bathtub model and is 
therefore bounding for the following cases: 
1. Primary case, in which the water inflow rate is constant, the rate of radionuclide 
dissolution is limited, and the radionuclide concentration is solubility-limited. Unlike 
the bathtub model, there is no delay in release of radionuclides in the flow-through 
model. 
2. Secondary case 1, in which the inflow rate undergoes a step change. The response of 
the bathtub model is identical to the flow-through model for solubility-limited 
radionuclides. For dissolution-rate-limited radionuclides, the flow-through model 
overestimates releases of radionuclides for the case of decreasing inflow, or increasing 
concentration, which is of primary interest from a performance or regulatory 
standpoint. 
3. Secondary case 2, a step change in groundwater chemistry. The flow-through model 
overestimates releases of radionuclides relative to the bathtub model when the 
solubility or dissolution rate increases because it has an instantaneous change to the 
higher equilibrium value, whereas the bathtub geometry delays the change. For 
decreasing solubility or dissolution rate, the bathtub overestimates releases of 
radionuclides, but this case is of no interest from a performance or regulatory point of 
view. 
4. Secondary case 3, wherein a second corrosion patch opens instantaneously beneath the 
water level in the waste package in the bathtub model. The impact of this alternative 
flow path was screened out because of the potential mitigation from sorption and 
diffusion and because the variability of corrosion rates provides large uncertainty in 
radionuclide release rates from the waste package. 
As a result of this analysis, the bathtub model has been screened out as an alternative conceptual 
model in order to overestimate radionuclide transport. 
6.4.2 Limited Water Vapor Diffusion Rate into Waste Package 
This alternative conceptual model accounts for the resistance to diffusion of water vapor into a 
waste package through stress corrosion cracks. In the base model, there is no limit to the amount 
of water vapor available to adsorb onto surfaces within a waste package, which creates a 
pathway for diffusive transport of radionuclides out of the waste package (This applies to the 
in-package diffusion submodel, Section 6.5.1.2.1.1.). However, the base model currently used 
for the TSPA to calculate dose overestimates releases of radionuclides, particularly at early times 
when the only breaches in a waste package are small stress corrosion cracks. If the diffusion rate 
is limited, the rate of steel corrosion is limited by the rate of diffusion of water vapor. The result 
is that no water is available to adsorb and form a thin liquid film on corrosion products, and no 

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water would be available for radionuclide transport. This is because all water is consumed by 
the corrosion process as quickly as it diffuses into the waste package. This prevents formation of 
a diffusive path until all of the internal steel components are fully corroded, which in turn delays 
diffusive releases until that time. Since this may take hundreds to thousands of years, the delay 
in releases of radionuclides from breached waste packages could be extensive. During this 
delay, radioactive decay will decrease the quantity of radionuclides in the waste package, 
ultimately reducing releases to the environment. 
A mathematical description of this model is presented in Section 6.6.2. 
6.4.3 Limited Oxygen Diffusion Rate into Waste Package 
This alternative conceptual model is similar to the alternative conceptual model dealing with 
limited water vapor diffusion into a waste package through stress corrosion cracks described in 
Section 6.4.2. In both models, the rate of steel corrosion is limited by the rate of diffusion of 
reactive gases. They also imply that no adsorbed water film can form until all of the steel is 
corroded, as long as the rate of water consumption by corrosion is greater than the rate of 
diffusion of reactants into the waste package. The difference in this model is that oxygen in the 
waste package is also diffusion limited, yet oxygen also reacts readily with the steel internal 
components. Depending on how oxygen competes with water vapor in diffusing through stress 
corrosion cracks and reacting with steel, the time required for all internal components to react 
and stop consuming water would be shortened. Then diffusive releases through the film of 
adsorbed water (given by the in-package diffusion submodel, Section 6.5.1.2.1) can begin earlier 
than predicted by the water vapor limited diffusion model alone. 
A mathematical description of this model is presented in Section 6.6.3. 
6.4.4 Dual-Continuum Invert 
This alternative conceptual model treats the crushed tuff in the invert as a dual continuum 
comprised of two pore spaces  intragranular pore space (tuff particle matrix) and intergranular 
pore space. Although radionuclide transport by both advection and diffusion can occur in both 
pore spaces, the dominant flow and transport processes in each of these two pore spaces is 
generally different. In order to simulate flow and transport through the invert accurately, the 
invert is conceptualized in this alternative conceptual model as overlapping dual continua using a 
dual-permeability approach, wherein flow and transport occur in both pore spaces, and mass 
transfer takes place between the two pore spaces. 
A mathematical description of this model is presented in Section 6.6.4. 
6.4.5 Alternative Invert Diffusion Coefficient Models 
The following two alternative models for determining the diffusion coefficient in the invert are 
assessed: the single-continuum invert diffusion coefficient model and the dual-continuum invert 
diffusion coefficient model. In the single-continuum invert diffusion coefficient model, an 
alternative to the Archies law approach for determination of the diffusion coefficient for the 
single-continuum crushed tuff invert ballast (Section 6.3.4.1) is modeled using an approach that 
has been applied to diffusion in soils. In the dual-continuum invert diffusion coefficient model, 

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the bulk diffusion coefficient is dominated by the intergranular diffusion coefficient above the 
critical bulk moisture content, while below this critical value, the intragranular diffusion 
coefficient dominates. 
Mathematical descriptions of these models are presented in Section 6.6.5. 
6.5 MODEL FORMULATION FOR BASE CASE MODEL 
6.5.1 Mathematical Description of Base Case Conceptual Model 
A solute transport model typically consists of two component models: a model to solve the flow 
equation and another to solve the transport equation (Anderson and Woessner 1992 
[DIRS 123665], p. 327). The solution of the flow equation yields the flow velocities or flow 
rates. These flow rates are input to the transport model, which predicts the concentration 
distribution in time and space. Development of the EBS flow model and the EBS transport 
model are discussed separately in the next two subsections. 
6.5.1.1 EBS Flow Model 
The EBS flow model is essentially a mass balance on water in the EBS. Because the 
microscopic details of processes that occur in the EBS are not important on a drift or waste 
package scale, an appropriate starting point for developing the EBS flow model is a general 
macroscopic balance on water within a drift (Bird et al. 1960 [DIRS 103524], p. 686): 
. w 
m
w w 
w r w w 
dt 
dm + + . - = 
. (Eq. 6.5.1.1-1) 
Here, w m (kg) is the instantaneous total mass of water within the walls of a drift, which 
encompass the EBS. This equation states that the rate of change of water mass in the EBS is 
equal to the difference between the mass rate of flow into and out of the EBS ( w w . [kg s-1]), 
plus m
w w (kg s-1), the net mass flow rate of water across bounding surfaces by mass transfer 
(e.g., condensation or evaporation transfer water across a liquid surface, which is a boundary 
between gas-phase flow and transport and liquid-phase flow and transport), plus the rate of 
production of water by chemical reactions, w r (kg s-1). Per Assumption 5.4, production or 
consumption of water by chemical reactions is assumed to be zero, resulting in: 
m
w w 
w w w 
dt 
dm + . - = . (Eq. 6.5.1.1-2) 
At steady state or when the mass of water in the EBS changes slowly, the time derivative can be 
set to zero: 
0= + . - m
w w w w . (Eq. 6.5.1.1-3) 
The alternative bathtub conceptual model, using Equation 6.5.1.1-2 for the waste package, is 
screened out as an alternative conceptual model in Section 6.6.1. By neglecting changes in the 
density of the water within a drift as it passes through the EBS, Equation 6.5.1.1-3 can be 

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divided by the density of water, w . (kg m-3), to transform it into a volume balance involving 
volumetric flow rates: 
0= + . - m 
w w F F , (Eq. 6.5.1.1-4) 
where w w w w F . / = is the volumetric flow rate (m3 s-1), and the superscript m still refers to mass 
transfer processes. Since both w F . - and m 
w F represent a net inflow minus outflow, 
Equation 6.5.1.1-4 simply states that outflow is equal to inflow. This is the general form of the 
water mass balance that is used for individual flow paths in the EBS in the EBS RT Abstraction. 
It is applicable to the EBS as a whole as well as to individual components of the EBS. In 
particular, the terms w w . and m
w w can be broken down into the separate and distinct flow paths 
listed in Section 6.3.1.1. 
The volumetric flow rate of water into the top of the EBS is referred to as the total dripping flux, 
designated 1 F in Table 6.3-1, and is comprised of seepage flux into the top of the drift and 
condensation on walls of the drift. The seepage flux is computed in the GoldSim TSPA model 
using Abstraction of Drift Seepage (BSC 2004 [DIRS 169131]); this is an input or source of 
inflow into the EBS flow model. 
Over the entire EBS, Equation 6.5.1.1-4 becomes 
8 7 1 F F F = + , (Eq. 6.5.1.1-5) 
where 1 F is the total dripping flux into the top of the drift and 7 F is the imbibition flux into the 
invert; see Figure 6.3-1. 8 F is the flow rate of water leaving the invert and entering the 
unsaturated zone. 
For the drip shield, the flux through corrosion breaches in the drip shield is 2 F , and the flux of 
water diverted by the drip shield is 3 F , so the water balance on the drip shield is: 
3 2 1 F F F + = . (Eq. 6.5.1.1-6) 
For the waste package, the water mass balance is: 
5 4 2 F F F + = . (Eq. 6.5.1.1-7) 
As modeled, there is no water storage in the waste package. Therefore, the flow rate of water 
from the waste package to the invert is equal to the flow into the waste package, 4 F . The water 
balance over the invert includes this influx of water that has flowed through the waste package as 
well as water diverted around the waste package and water diverted around the drip shield. The 
total flow into the invert that originates from seepage flux ( 1 F ), is: 
. 1 
5 4 3 6 
F 
F F F F 
= 
+ + = 
(Eq. 6.5.1.1-8) 

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A water mass balance over the invert indicates that the sum of the seepage flux (F1) and 
imbibition flux ( 7 F ) flows out of the invert (Equation 6.5.1.1-5): 
. 7 1 
7 6 8 
F F 
F F F 
+ = 
+ = 
(Eq. 6.5.1.1-9) 
6.5.1.1.1 Water Flux through a Breached Drip Shield 
Key features of the drip shield flux splitting algorithm include: (1) the seepage flux into the drift 
falls as droplets from the top of the drift onto the crown of the drip shield (Assumption 5.1), 
(2) droplets fall randomly along the length of the drip shield, (3) only flow through general 
corrosion patches is considered, (4) evaporation from the drip shield is neglected 
(Assumption 5.2); all of the seepage flux either flows through corrosion patches or drains down 
the sides of the drip shield, (5) all water that flows through breaches in the drip shield flows onto 
the waste package. 
In the conceptual model of the breached drip shield corrosion patches are represented by square 
holes, with dimensions specified in an earlier version of the WAPDEG corrosion model as 
approximately 27 cm in width (CRWMS M&O 2000 [DIRS 151566], p. 36, where the patch area 
is specified to be 7.214  104 mm2). The breached drip shield experiments (BSC 2003 
[DIRS 163406]) were designed using holes of this size. 
Consider first some simple cases with idealized behavior, in which drops falling onto the drip 
shield either fall straight through corrosion patches or, after impacting the drip shield surface, 
flow straight down the sides of the drip shield. These will provide bounding cases for 
comparison as more realism is added to the flux splitting submodel. Let l 2 be the width (m) of a 
square corrosion patch, DS L the axial length (m) of the drip shield, and b N the number of 
patches on the drip shield, assumed to not overlap each other. 
In the simplest case, b N patches are located on the crown of the drip shield, none off the crown. 
Since all of the seepage flux 1 F falls on the crown of the drip shield, the amount that passes 
straight through breaches in the drip shield (F2) is simply the ratio of the total length of the b N 
patches to the total length of the drip shield multiplied by the seepage flux: 
DS
b 
L
N F F l 2 
1 2 = . (Eq. 6.5.1.1.1-1) 
Next, suppose a single patch exists, randomly located on the top of the drip shield, but fully off 
the crown so that none of the seepage flux falls directly through the patch, but instead lands on 
the drip shield crown and then flows straight down the surface. Ideally, exactly half of the 
seepage flux drains down one side of the drip shield, and half down the other side. The reality is 
not far removed from the ideal: when drops strike the drip shield, they splatter in a random 
pattern; the region where splattered droplets fall is roughly circular. After a large number of 
drops have fallen, on average half of the droplets will have landed on each of the two sides of the 
drip shield. Since only half of the seepage flux drains down one side of the drip shield, a single 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-58 November 2004 
patch can only capture DS L / 2l of the flow down one side ) 2 / ( 1 F , so the flux through a single 
patch in the drip shield is: 
DS L 
F F l 
1 2 = . (Eq. 6.5.1.1.1-2) 
If two patches exist, with one patch on each side of the drip shield, the total flux will clearly be 
twice what flows through a single patch: 
DS L 
F F l 2 
1 2 = . (Eq. 6.5.1.1.1-3) 
If two patches are located on one side of the drip shield, away from the crown, and located 
randomly except that they do not interfere with each other (i.e., one patch is not upstream from 
another where it would intercept flow that would be captured by a lower patch), then a fraction 
DS L / 2l of the flow down one side ) 2 / ( 1 F will enter each patch. The total flux through the drip 
shield in this case is: 
DS DS L 
F 
L 
F F l l 2 2 
2 
2 1 
1 
2 = .. 
. 
.. 
. = . (Eq. 6.5.1.1.1-4) 
In the general case where b N patches are randomly distributed on the drip shield, off the crown 
and not interfering with each other, Equation 6.5.1.1.1-4 becomes: 
DS 
b 
L
N F F l 
1 2 = . (Eq. 6.5.1.1.1-5) 
Different behavior is clearly seen depending on whether the patch is located directly on the 
crown such that drops fall straight through it, or whether the seepage is split by falling on the 
drip shield first, causing half of the dripping flux to flow down each side of the drip shield. If 
c N patches are located on the crown ( b c N N = ), the most general form of the flux splitting 
algorithm for this idealization is: 
[ ] 
. ) ( 
) ( 2 
1
1 2 
DS 
c b 
c b c 
DS 
L 
N N F 
N N N 
L 
F F 
l 
l 
+ 
= 
- + = 
(Eq. 6.5.1.1.1-6) 
Although this equation is general, it requires a distinction between patches on the crown and off 
the crown. However, the location of patches is completely random, so the location cannot be 
specified a priori. To account for the different flux through crown patches, note that crown 
patches occur within a distance l 2  from the crown, or over an area DS L l 4 . The total surface 
area of a drip shield is DS DS L W , where DS W is the total unfolded width of the drip shield (m) as 

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ANL-WIS-PA-000001 REV 01 6-59 November 2004 
measured from the bottom edge of one side, over the top, and down to the bottom of the other 
side. Then the probability of a patch occurring on the crown is: 
DS DS DS 
DS 
W L W 
L l l 4 4 = . (Eq. 6.5.1.1.1-7) 
Equation 6.5.1.1.1-6 can be rewritten to account for the probability of seepage flux falling into a 
crown patch or onto intact drip shield, and for the flux through a single crown patch being twice 
the flux through an off-crown patch for a given seepage flux: 
( ) 
. 1 4 
4 
4 1 4 2 
1
1 
1 1 2 
. .. 
. 
. .. 
. 
+ = 
+ = 
. .. 
. 
. .. 
. 
- . .. 
. 
. .. 
. 
+ . .. 
. 
. .. 
. 
. .. 
. 
. .. 
. 
= 
DS DS 
b 
DS 
DS DS 
b 
DS DS 
b 
DS DS
b 
W L
N F 
W 
W L 
N F 
W L
N F 
W L
N F F 
l l 
l 
l 
l l l l 
(Eq. 6.5.1.1.1-8) 
For a patch size of cm 27 2 = l and a total drip shield width of m 94 . 6 = DS W , the term 
078 . 0 / 4 = DS W l . Then, to provide a good approximation, the term DS W / 4l can be assumed to 
be zero, yielding: 
DS 
b 
L
N F F l 
1 2 = , (Eq. 6.5.1.1.1-9) 
which is identical to Equation 6.5.1.1.1-5. This result indicates that, although the flux is higher 
through crown patches, the probability of patches occurring on the crown is small ( DS W / 2l , or 
3.9 percent) and may be ignored in light of the uncertainties discussed in Section 6.3.2.4. 
The simple model presented thus far assumes ideal drops that do no splatter and that run down 
the drip shield in straight, nondiverging paths. Next, realism is added to the flux splitting 
submodel by taking into account observations and data from breached drip shield experiments, 
which account for drop splattering and the nature of rivulet flow along the surface of the drip 
shield. 
6.5.1.1.2 Breached Drip Shield Experiments 
The breached drip shield experiments (BSC 2003 [DIRS 163406]) are described in 
Section 6.3.2.4. The tests were performed at three different drip rates, which represent the range 
of expected liquid water influx rates over a single drip shield. The bulk of the tests were 
performed at a drip rate of 2 m3 yr-1. Additional bounding flow rate tests were performed at a 
lower rate of 0.2 m3 yr-1 and a higher rate of 20 m3 yr-1. The tests were performed by dripping 
water at specified drip locations, one location at a time for a period that allowed a measurable 
amount of liquid to be collected through breaches in the drip shield (typically 30-60 min at 
2 m3 yr-1, 10 min at 20 m3 yr-1, and 5-5 hr at 0.2 m3 yr-1). 

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Four basic types of tests were performed: (1) q(splash) test, in which the splash distance was 
measured when a drop falls onto the drip shield surface; (2) q(film) tests, where the primary 
goals were to measure rivulet spread and the amount of flow into a single breach in the drip 
shield; (3) multiple breach tests, which were similar to the q(film) tests, except that multiple 
breaches existed in the drip shield mockup; and (4) bounding flow rate tests, which repeated the 
q(film) and multiple breach tests using different drip rates. Most of the tests were performed on 
both a smooth drip shield and a rough drip shield. 
The dripping distance was based on design parameters and carried out at full scale. Thus the 
dripping distance used for dripping onto the crown of the drip shield was 2.173 m (BSC 2003 
[DIRS 163406]). The splash radius on the drip shield was measured for both the smooth surface 
(DTN: MO0207EBSATBWP.022 [DIRS 163400]) and the rough surface 
(DTN: MO0207EBSATBWP.021 [DIRS 163399]). The maximum lateral splash radius 
observed in Splash Radius Test #1 on the smooth surface was 72.5 cm after 60 drops; in Test #2, 
the maximum splash radius was 53.0 cm after 66 drops. On the rough surface, the maximum 
lateral splash radius in the five tests that were conducted was 106.5 cm after 203 drops. In 
addition to the splash radius tests, splash distances were recorded for some of the single patch 
q(film) rivulet flow tests; a maximum splash distance of 86 cm (DTN: M0207EBSATBWP.023 
[DIRS 163402]) was observed for drip location Patch 4, 8 cm right of center, onto the crown of 
the drip shield. The distribution of droplet formation on the surface as a function of distance 
from the impact location was not measured, although an approximate determination was made to 
distinguish an inner cluster of droplets from an outer fringe, where the droplets were 
noticeably smaller (Table 4.1-4). It was observed that the outer splashes on the fringe tended to 
be smaller and less frequent on the rough surface than on the smooth surface. 
Observations during the breached drip shield tests revealed that the primary mechanism for water 
to enter breaches is via rivulet flow that originates from an area around the point of drip impact. 
Following droplet impact at the crown, beads formed and increased in size around the center of 
impact with each successive drop. After a time, the beads closest to the downhill curvature 
would reach a critical mass and roll down the face of the drip shield in the form of a rivulet. The 
rivulet flow area spreads out in a delta formation (i.e., the maximum spread was located on the 
vertical section of the drip shield and the minimum spread was located at the point of impact). 
No film flow was observed during tests on the smooth or the rough drip shield surfaces. 
For a given drip location onto the crown of the drip shield (Assumption 5.1), the spreading of the 
rivulet flow is defined by a half-angle, a, formed with the vertical plane through the impact 
point. The lateral spread of the rivulet flow is given by a tan 2x , where x is the arc length from 
the crown of the drip shield down to a location of interest. These definitions are illustrated in 
Figure 6.3-2. The curvature/shape of the drip shield is not shown in Figure 6.3-2 for simplicity 
and clarity. 
The spread of rivulets from drips onto the crown of the experimental drip shield is reported in 
DTNs: MO0207EBSATBWP.023 [DIRS 163402], MO0207EBSATBWP.024 [DIRS 163401], 
and MO0207EBSATBWP.025 [DIRS 163403] and summarized in Table 4.1-6. The data are 
analyzed in Microsoft Excel spreadsheet: Flux Split Drip Shield Model, Worksheet: Spread 
angles, which is documented in Appendix C. The average spread at 33 from the crown in 
26 measurements was 20.1 cm, corresponding to an average spread angle of about 13.2. The 

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range of spread angles, from one standard deviation smaller and greater than the mean, was 
about 8.9 to 17.3. The distribution for spread angle is not clearly defined by the experimental 
data, and therefore a uniform distribution is considered appropriate. 
The initial simple model wherein drips flow straight down the curved top of the drip shield is 
made more realistic by incorporating the random spread of rivulets over an angle a as they flow 
down the drip shield surface. The spreading of rivulets increases the probability that they will 
flow into a breach (corrosion patch). Three cases are considered, two for a centrally located 
breach at different distances from the crown such that different proportions of the rivulet spread 
will encounter a breach, and one for a breach at the end of the drip shield. 
6.5.1.1.2.1 Drip Shield Flux for a Centrally Located Breach, Case 1 
Consider a breach that is centrally located on the drip shield. The breach is centrally located if 
Points A and B (defined below) are located on the same segment of the drip shield as the breach 
itself. In other words, the ends of the drip shield lie beyond Point A and Point B. Figure 6.5-1 
illustrates the location and geometry for potential rivulet flows into a breach with length l 2 and 
whose top edge is located a distance of x from the crown. For simplicity in evaluating 
coordinates, the zero point of the y-axis is coincident with the center of the breach. 
In Case 1, a tan x > l ; in other words, the breach is wider than the rivulet spread at the top of the 
breach. 
Points A and B are defined as follows: 
 Point A corresponds to the leftmost point from which the edge of the fan from the rivulet 
can enter the left side of the breach. 
 Point B corresponds to the leftmost point from which all rivulets will enter the top edge 
of the breach. Point B lies between l - (left side of the breach) and the origin, 0 = y . 
 Point C corresponds to the rightmost point from which all rivulets will enter the top edge 
of the breach. Point C lies between the origin and l + (right side of the breach). 
 Point D corresponds to the rightmost point at which the edge of the fan from the rivulet 
can enter the right side of the breach. 
Rivulets originating between Point A and Point l - can flow into the left side or the top of the 
breach. Symmetrically, rivulets originating between Point l + and Point D can flow into the 
right side or the top of the breach. All rivulets originating between Point l - and l + flow only 
into the top of the breach, not into the sides. The y-coordinates of Points A through D are: 
( ) 
( ) . tan 2 
tan 
tan 
tan 2 
a 
a
a 
a 
l l
l 
l 
l l 
+ + = 
- = 
+ - = 
+ - - = 
x y 
x y 
x y 
x y
D
C
B
A 
(Eq. 6.5.1.1.2-1) 

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Figure 6.5-1. Geometry and Nomenclature for a Centrally Located Breach with l > x tan a 
The fraction f of the random rivulet flow that enters the breach depends on the origin y of the 
rivulet: 
 For . 0 , = = - A A f y y 
 For , l - = < y yA 
a 
a 
tan ) 2 ( 2 
tan ) 2 ( 
l 
l l 
l + 
+ + + 
= 
x 
x y f A (Eq. 6.5.1.1.2-2) 
 For , B y y < < - l 
a 
a 
tan 2 
tan 
x 
x y f B 
+ + 
= l 
l (Eq. 6.5.1.1.2-3) 
 For , C B y y y = = 
10 = f (Eq. 6.5.1.1.2-4) 
 For , l < < y yC 
a 
a 
tan 2 
tan 
x 
x y fC 
+ + - 
= l 
l (Eq. 6.5.1.1.2-5) 
 For , D y y < = l 
a 
a 
tan ) 2 ( 2 
tan ) 2 ( 
l 
l l 
l + 
+ + + - 
= 
x 
x y f D (Eq. 6.5.1.1.2-6) 
 For . 0 , = = + D D f y y 

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In this context, f is essentially a probability distribution function (i.e., the probability that a 
rivulet will intersect the square corrosion patch). Integrating f over the full length of the drip 
shield (from 2 / DS L - to 2 / DS L + ) gives the total water flux through a breach of width l 2 . 
Then the fraction F ) / ( 1 2 F F = of seepage flux passing through the breach is: 
.- 
= 2 / 
2 / 
) ( 
2 
1 DS 
DS 
L
L 
DS 
dy y f 
L 
F (Eq. 6.5.1.1.2-7) 
.. .
.. .
+ + + + = . . . . . - + 
+ - B D 
C 
C 
B A 
y y
D y C 
y 
y B y A 
DS 
dy y f dy y f dy f dy y f dy y f 
L l ll 
l 
l l 
l 
l ) ( ) ( ) ( ) ( 
2 
1 0 (Eq. 6.5.1.1.2-8) 
. 
2
tan
DS DS L L 
a l l + = (Eq. 6.5.1.1.2-9) 
The factor of 2 in the denominator starting in Equation 6.5.1.1.2-7 accounts for the seepage flux 
being split in two when it drips onto the crown of the drip shield, and half of the flux flows down 
each side. 
The result is independent of x, the distance from the crown. The amount of seepage flux that 
flows into a breach is, however, dependent on the rivulet spread angle a. This is reasonable 
because a wider spread angle allows rivulets from a wider span of the crown to access the 
breach. In effect, the width of the drip shield crown from which rivulets can flow into a breach 
is expanded from l 2 to a tan 2 l l + . Flow into the sides of the breach contributes only a small 
amount to the total if the spread angle is small. If, for example, = a 13.2 (the mean spread 
angle from the drip shield experiments), the total flow into a breach, from Equation 6.5.1.1.2-9, 
is ( )( ) 117 . 0 1 / + DS L l , so only about 0.117/1.117  1/10 of the total breach flow enters through 
the sides of the breach. 
As a check on this result, consider the case where the rivulets do not spread out over an angle a, 
but instead flow straight down (i.e., a a tan 0 = = ). Then Equation 6.5.1.1.2-9 becomes: 
DS L 
F l = , (Eq. 6.5.1.1.2-10) 
or 
DS L 
F F l 
1 2 = . (Eq. 6.5.1.1.2-11) 
Equation 6.5.1.1.2-11 is identical to Equation 6.5.1.1.1-2, which was obtained from simple logic 
arguments. 
As a further check on the validity of Equation 6.5.1.1.2-9, consider a single patch located 
adjacent to the crown, just far enough away from the crown that the dripping seepage flux can 
impinge on the crown and flow down both sides (i.e., 0  x , about the width of a drop). Water 

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ANL-WIS-PA-000001 REV 01 6-64 November 2004 
flowing from the crown toward the patch will immediately enter the patch, since the spread over 
the angle a is negligible. Seepage flux dripping onto the drip shield crown to the left and right 
of the patch will flow down the drip shield in rivulets, fanning out over the angle a. In this 
case, a tan 2l l - - = A y ; similarly, a tan 2l l + = B y . The fractions of the rivulet flow down one 
side of the drip shield into the patch are: 
 For . 0 , = = - A A f y y 
 For , l - < < y yA 
a 
a 
tan 4 
tan 2 
l 
l l 
l 
+ + 
= y f A (Eq. 6.5.1.1.2-12) 
 For , l l = = - y 
10 = f (Eq. 6.5.1.1.2-13) 
 For , B y y < < l 
a 
a 
tan 4 
tan 2 
l 
l l 
l 
+ + - 
= y f B (Eq. 6.5.1.1.2-14) 
 For . 0 , = = + B B f y y 
Moving right from A y y = , where 0 = f , f increases linearly until - - = l y (on the left side of 
l - ), where 2 / 1 = f ; because half of the rivulet fan is directed away from the patch at that point, 
at most half of the rivulet will enter the patch. Between l l + - and , all of the rivulets flow 
directly into the patch, so 1 = f . As on the left side of the patch, to the right of the patch, from 
a tan 2 to l l l + = = = B y y y , f decreases linearly from  to 0. Performing the same integration 
as in Equations 6.5.1.1.2-7 and 6.5.1.1.2-8 results in: 
DS DS L L 
F 
2
tan a l l + = , (Eq. 6.5.1.1.2-15) 
which is again identical to Equation 6.5.1.1.2-9. Since, as seen earlier, the flow into the top edge 
of the patch is DS L / l , the term ) 2 /( tan DS L a l accounts for rivulet flow into the sides of the 
patch. 
Multiple patches increase the flow into patches in direct proportion to the number of patches, 
assuming that patches do not interfere: 
.. 
. 
.. 
. 
+ = 
DS DS 
b L L 
N F 
2
tan a l l , (Eq. 6.5.1.1.2-16) 

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ANL-WIS-PA-000001 REV 01 6-65 November 2004 
or 
.. 
. 
.. 
. 
+ = 
DS DS 
b L L 
N F F 
2
tan 
1 2 
a l l . (Eq. 6.5.1.1.2-17) 
If patches are located below other patches, the rivulets are intercepted by the higher patches, and 
none or less flows into lower patches. In that case, the flux through the drips shield, 2 F , is less 
than predicted by Equation 6.5.1.1.2-17. However, to neglect interference among multiple 
patches and use Equation 6.5.1.1.2-17 overestimates releases of radionuclides. 
6.5.1.1.2.2 Drip Shield Flux for a Centrally Located Breach, Case 2 
In Case 2, a tan x < l ; in other words, the breach is narrower than the rivulet spread at the top of 
the breach (see Figure 6.5-2). In Case 1, over some range of y centered at 0 = y , all of the 
rivulet flow enters the top edge of the breach ( ) 1 0 = f . In contrast, in Case 2, the rivulet spread is 
too wide for all of the rivulet flow to enter the breach at any point ( ) 1 0 < f . 
Points A and B are defined as follows: 
 Point A corresponds to the leftmost point from which the edge of the fan from the rivulet 
can enter the left side and top of the breach. 
 Point B corresponds to the leftmost point from which rivulets will enter only the top 
edge of the breach. Point B lies between l - (left side of the breach) and the origin, 
0 = y . Rivulets originating between l - and Point B enter only a portion of the top 
edge of the breach. 
 Point C corresponds to the rightmost point from which all rivulets will enter the top edge 
of the breach. Point C lies between the origin and l + (right side of the breach). 
Rivulets originating between Point C and l + enter only a portion of the top edge of the 
breach. Rivulets originating between Point B and Point C can enter the entire top edge 
of the breach. 
 Point D corresponds to the rightmost point at which the edge of the fan from the rivulet 
can enter the right side and top of the breach. 

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Figure 6.5-2. Geometry and Nomenclature for a Centrally Located Breach with l < x tan a 
As in Case 1, rivulets originating between Point A and Point l - can flow into the left side or the 
top of the breach. Symmetrically, rivulets originating between Point l + and Point D can flow 
into the right side or the top of the breach. All rivulets originating between Point l - and l + 
flow only into the top of the breach, not into the sides. The y-coordinates of Points A through D 
are: 
( ) 
( ) . tan 2 
tan 
tan 
tan 2 
a 
a 
a 
a 
l l 
l 
l 
l l 
+ + = 
+ - = 
- = 
+ - - = 
x y 
x y 
x y 
x y
D
C
B
A 
(Eq. 6.5.1.1.2-18) 
The central region boundaries, C B y y and , are different for Case 2 than for Case 1. 
The fraction f of the random rivulet flow that enters the breach depends on the origin y of the 
rivulet. These fractions are identical for corresponding regions to those in Case 1 except for the 
region C B y y y = = , where now 1 0 < f instead of 1 0 = f . 
 For . 0 , = = - A A f y y 
 For , l - = < y yA 
a 
a 
tan ) 2 ( 2 
tan ) 2 ( 
l 
l l 
l + 
+ + + 
= 
x 
x y f A (Eq. 6.5.1.1.2-19) 
 For , B y y < < - l 
a 
a 
tan 2 
tan 
x 
x y f B 
+ + 
= l 
l (Eq. 6.5.1.1.2-20) 

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ANL-WIS-PA-000001 REV 01 6-67 November 2004 
 For , C B y y y = = 
a tan 2 
2 
0 x 
f l = (Eq. 6.5.1.1.2-21) 
 For , l < < y yC 
a 
a 
tan 2 
tan 
x 
x y fC 
+ + - 
= l 
l (Eq. 6.5.1.1.2-22) 
 For , D y y < = l 
a 
a 
tan ) 2 ( 2 
tan ) 2 ( 
l 
l l 
l + 
+ + + - 
= 
x 
x y f D (Eq. 6.5.1.1.2-23) 
 For . 0 , = = + D D f y y 
Integrating f over the full length of the drip shield (from 2 / DS L - to 2 / DS L + ), as in Case 1, 
gives the total water flux through a breach of width l 2 . The fraction F ) / ( 1 2 F F = of seepage 
flux passing through the breach is: 
.- 
= 2 / 
2 / 
) ( 
2 
1 DS 
DS 
L
L 
DS 
dy y f 
L 
F (Eq. 6.5.1.1.2-24) 
.. .
.. .
+ + + + = . . . . . - + 
+ - B D 
C 
C 
B A 
y y
D y C 
y 
y B y A 
DS 
dy y f dy y f dy f dy y f dy y f 
L l ll 
l 
l l 
l 
l ) ( ) ( ) ( ) ( 
2 
1 0 (Eq. 6.5.1.1.2-25) 
. 
2
tan
DS DS L L 
a l l + = (Eq. 6.5.1.1.2-26) 
For Case 2, the seepage flux passing through the breach is identical to Case 1 
(Equation 6.5.1.1.2-9). This is reasonable considering that F is independent of x. In other 
words, the breach can be located at any distance from the crown, and the same fraction of 
seepage flux will flow into it. The two cases are really a single case where the breach in Case 2 
is simply located further from the crown than in Case 1. 
6.5.1.1.2.3 Drip Shield Flux for an End-Located Patch 
The drip shield design (BSC 2004 [DIRS 168275], Sheet 1) includes a connector guide at one 
end and a connector plate at the other end that, being thicker than the plates comprising the top 
and sides of the drip shield, should survive intact longer than the plates. These components will 
prevent any rivulets from flowing off the ends of the drip shield. This will alter the fraction of 
rivulet flow that enters patches that are located at the ends of the drip shield. If the patch is 
located a short distance from the end, the space between the patch and the connector guide will 
allow water diverted by the guide to flow down the drip shield instead of into the patch. This 
distance is unknown, but for simplicity is chosen to be zero (i.e., if the patch is not coincident 
with the connector guide, it behaves as a centrally located patch). 

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Consider a breach that is located at one end of the drip shield. Figure 6.5-3 illustrates the 
location and geometry for potential rivulet flows into a breach with length l 2 and whose top 
edge is located a distance of x from the crown. For simplicity in evaluating coordinates, the zero 
point of the y-axis is again coincident with the center of the patch, and the end of the patch as 
well as the drip shield are at l - = y . 
Figure 6.5-3. Geometry and Nomenclature for an End-Located Breach with l > x tan a 
The Points A through D are defined as above for Case 1, except that A y is beyond the end of the 
drip shield. Distinguishing Point B is unimportant, because all rivulets originating to the left of 
Point C flow completely into the breach. 
( ) . tan 2 
tan 
tan 
a 
a
a 
l l
l 
l 
+ + = 
- = 
+ - = 
x y 
x y 
x y
D
C
B 
(Eq. 6.5.1.1.2-27) 
Consider first the case where a tan x > l , corresponding to Case 1 above. It is shown that the 
result is independent of x, as seen above for the centrally located breach. Therefore, a second 
analysis corresponding to Case 2 above is not necessary. The fraction f of rivulet flow into the 
patch over ranges of y are: 
 For .0 , 2 / = - = - = f L y DS l 
 For , C y y = = - l 
10 = f (Eq. 6.5.1.1.2-28) 
 For , l < < y yC 
a 
a 
tan 2 
tan 
x 
x y fC 
+ + - 
= l 
l (Eq. 6.5.1.1.2-29) 

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ANL-WIS-PA-000001 REV 01 6-69 November 2004 
 For , D y y < = l 
a 
a 
tan ) 2 ( 2 
tan ) 2 ( 
l 
l l 
l + 
+ + + - 
= 
x 
x y f D (Eq. 6.5.1.1.2-30) 
 For . 0 , = = + D D f y y 
Integrating f over the full length of the drip shield (from 2 / DS L - to 2 / DS L + ) gives the total 
water flux through a breach of width l 2 . The fraction F ) / ( 1 2 F F = of seepage flux passing 
through the breach is: 
.- 
= 2 / 
2 / 
) ( 
2 
1 DS 
DS 
L
L 
DS 
dy y f 
L 
F (Eq. 6.5.1.1.2-31) 
.. .
.. .
+ + = . . . + 
+ 
- 
D 
C 
C y 
D y C 
y 
DS 
dy y f dy y f dy f 
L l l 
l 
l l 
) ( ) ( 
2 
1 0 (Eq. 6.5.1.1.2-32) 
. 
4
tan
DS DS L L 
a l l + = (Eq. 6.5.1.1.2-33) 
Thus, the seepage flux fraction F for breaches at the end of the drip shield is independent of the 
distance x from the crown. The only difference from centrally located breaches is the term that 
accounts for flow into the side of a breach )] 4 /( tan [ DS L a l . Since only one side of the breach is 
accessible to rivulet flow, the flow through the one side of the breach at the end of the drip shield 
is just half of the flow through two sides in a centrally located breach. 
As seen above, for a small rivulet spread angle, the portion of the flow into a breach that enters 
through the side is small. For an end breach, that fraction is even smaller. In the example given 
in Section 6.5.1.1.2.1, for a mean spread angle of = a 13.2, flow through the sides of the breach 
accounts for only about 1/10 of the total. For an end breach, based on Equation 6.5.1.1.2-31, 
side flow will account for only 6 percent in this example. In Section 6.5.1.1.2, experimental 
results are discussed that show the spread angle is approximately 13.2 and that the amount of 
seepage flux that actually enters a breach varies widely. Differences of 6 percent are negligible. 
Since the end-located breach model (Equation 6.5.1.1.2-31) applies only to breaches that are 
exactly at the ends of the drip shield, which will be an infrequent occurrence, it is reasonable to 
ignore the distinction between end breaches and centrally located breaches. 
Then the flux through one patch in the drip shield is: 
.. 
. 
.. 
. + = 
2 
tan 1 1 2 
a 
DS L 
F F l . (Eq. 6.5.1.1.2-34) 

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ANL-WIS-PA-000001 REV 01 6-70 November 2004 
6.5.1.1.2.4 Analysis of Breached Drip Shield Experiments 
The breached drip shield experiments (BSC 2002 [DIRS 158193]; BSC 2003 [DIRS 163406]) 
provide estimates of the rivulet spread factor from which the spread angle acan be determined 
(DTN: MO0207EBSATBWP.022 [DIRS 163400]), the splash radius from drops falling from the 
roof of the drift to the crown of the drip shield (DTN: MO0207EBSATBWP.022 
[DIRS 163400]), and the flow into breaches from a number of discrete drip locations 
(DTN: MO0207EBSATBWP.023 [DIRS 163402]). In addition, the tests characterized the flow 
behavior on the drip shield surface, determining that flow occurs as rivulets rather than as film 
flow. 
In Splash Radius Test #1 (DTN: MO0207EBSATBWP.022 [DIRS 163400]), water was dripped 
onto the drip shield crown, and the distance that the water splattered was measured. In 
12 separate sets of measurements (Table 4.1-4), using from 1 to 90 drips, splash distances to the 
right ranged from 1.6 cm (single drip) to 63.2 cm (49 drips); splash distances to the left ranged 
from 1.6 cm (single drip) to 72.5 cm (60 drips). Tests using larger numbers of drips tended to 
result in larger maximum splash distances. Outer fringe measurements using more than 
20 drips ranged from 31.5 cm to 72.5 cm, whereas inner cluster measurements using more than 
20 drips ranged from 25.0 cm to 48.0 cm. The definition of the grouping as outer fringe and 
inner cluster was not specified, but the results indicate a distribution of splashed water heavily 
weighted to a median radius of about 40 cm. 
The splash radius is useful for providing a distribution of rivulet origins based on limited 
experimental data. In the flow tests, water was dripped onto the drip shield in only a few discrete 
locations. In order to make greater use of the data to determine the uncertainty in applying the 
drip shield flux splitting submodel (Equation 6.5.1.1.2-34), the distribution of splattered water 
can be treated as multiple drip locations in comparing Equation 6.5.1.1.2-34 to the experimental 
data. 
Rivulet spread was measured in single patch q(film) tests (DTN: MO0207EBSATBWP.023 
[DIRS 163402]), multiple patch tests (DTN: MO0207EBSATBWP.024 [DIRS 163401]), and in 
bounding flow rate tests (DTN: MO0207EBSATBWP.025 [DIRS 163403]). Table 4.1-3 
summarizes the maximum rivulet spread to the left and right of a straight line down the drip 
shield from the drip impact point. The rivulet spread data are analyzed in Microsoft Excel 
spreadsheet: Flux Split Drip Shield Model, Worksheet: Spread angles, which is documented in 
Appendix C. The resultsthe mean and range of spread anglesare reported in Section 6.5.1.1.2. 
Rivulet spread measurements at the top edge of patches in the drip shield mockup are used. The 
distance x from the drip location on the crown of the drip shield to the point of measurement is 
determined from the drawing of the drip shield mockup shown in Figure 4.1-1, which is 
reproduced from Howard (2002 [DIRS 161516], p. 14). Various dimensions used in the 
Microsoft Excel spreadsheet analysis of the data are listed in Table 6.5-1. Because the drip 
shield top surface is a circular arc (Figure 4.1-1), the 16.5 line is at half the distance from the 
crown to the 33 line, or 0.43 m from the crown. 

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ANL-WIS-PA-000001 REV 01 6-71 November 2004 
Table 6.5-1. Dimensions Used in the Analysis of Breached Drip Shield Experiments, Based on 
Dimensions Shown in Figure 4.1-1 
Dimension Calculation Distance (m) 
Crown to 33 line 2.44 m  0.94 m  0.64 m 0.86 
Crown to 16.5 line  distance from Crown to 33 line 0.43 
Crown to top edge of Patch 4 2.44 m  0.94 m  0.135 m 1.365 
Crown to top edge of Patch 5 2.44 m  0.94 m  0.64 m 0.86 
Crown to transition line 2.44 m  0.94 m 1.50 
16.5 line to transition line 0.43 m (Crown to 16.5 line)+ 0.64 m 1.07 
16.5 line to 33 line  distance from Crown to 33 line 0.43 
16.5 line to Patch 4 0.43 m (Crown to 16.5 line)+ 0.64 m  0.135 m 0.935 
16.5 line to Patch 5  distance from Crown to 33 line 0.43 
33 line to Patch 4 0.64 m  0.135 m 0.505 
33 line to transition line 0.64 m 0.64 
 distance between Crown and 16.5 
line to Patch 4 
(0.43 m [Crown to 16.5 line]) + 0.43 m (Crown to 
16.5 line) + 0.64 m -0.135 m 1.15 
Source: Howard 2002 [DIRS 161516], p. 14. 
Since the experiments involved dripping at a few discrete locations, it is not possible to calculate 
the flux through the drip shield as given by Equation 6.5.1.1.2-34 using experimental data. 
Instead, the fraction f of dripping flux at an individual drip location that flows into a given breach 
can be computed for the tests and compared with the fraction expected using one of the 
Equations 6.5.1.1.2-1 to 6.5.1.1.2-6 (Case 1) or 6.5.1.1.2-19 to 6.5.1.1.2-23 (Case 2). The 
appropriate equation to be used depends on the drip location relative to the breach. The 
variability in the experimental values ( expt f ) and comparisons with calculated values ( calc f ) show 
the range of uncertainty in the drip shield flux ratio 1 2 / F F F = . The values of expt f and calc f 
are calculated in Microsoft Excel spreadsheet: Flux Split Drip Shield Model, 
Worksheet: f calculations, which is documented in Appendix C. 
Experimental data from two breaches are pertinent to this analysisBreach 4 and Breach 5. 
Breach 4 straddled the transition line between the top of the drip shield and the vertical side, with 
the top edge 136.5 cm from the crown. Breach 5 was located on the top of the drip shield, about 
half way between the crown and the transition line, with the top edge 86 cm from the crown. 
Table 6.5-2 shows the fraction of the total dripping flux that entered a breach in each of 14 tests. 
The data sources are single patch q(film) test results (DTN: MO0207EBSATBWP.023 
[DIRS 163402]), multiple patch test results (DTN: MO0207EBSATBWP.024 [DIRS 163401]), 
and bounding flow rate test results (DTN: MO0207EBSATBWP.025 [DIRS 163403]), and are 
given in Table 4.1-2. The results are compared with calculated fractions for the mean spread 
angle as well as for the spread angles corresponding to plus or minus one standard deviation 
from the mean rivulet spread angle. The experimentally observed fractions, expt f , were 
calculated assuming that the water that flowed down the side of the drip shield where the 
breaches were located was half of the total dripping flux. This is necessary for expt f to be 
consistent with the fractions in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2, which are the fractions of 
flow down one side of the drip shield that enters a breach. 

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ANL-WIS-PA-000001 REV 01 6-72 November 2004 
Table 6.5-2. Comparison of Experimental Breach Inflow Fractions with Model Calculations from 
Appendix C 
fcalc 
Drip Location 
(Test Description) 
Breach 
No. 
y, Drip 
Location 
Relative to 
Breach Center 
(cm) 
x, Vertical 
Distance from 
Crown (drip) 
to Top of 
Breach (cm) fexpt a=8.9 a=13.2 a=17.3 
8 cm right of Patch 4 
centerline (Q[film] Test) 4 8 136.5 0.247 0.629 0.423 0.318 
Patch 5 centerline (Q[film] 
Test) 5 0 86.0 0.258 1.000 0.672 0.504 
4 cm left of Patch 5 
centerline (Q[film] Test) 5 -4 86.0 0.136 0.854 0.680 0.504 
Patch 4 centerline (Q[film] 
Test) 4 0 136.5 0.236 0.634 0.423 0.318 
27 cm right of drip shield 
center (Multiple Patch 
Test) 
5 -27 86.0 0.033 0.117 0.244 0.504 
27 cm left of drip shield 
center (Multiple patch test) 4 27 136.5 0.019 0.236 0.323 0.318 
81 cm left of drip shield 
center (Multiple Patch 
Test) 
4 -27 136.5 0.031 0.236 0.323 0.318 
81 cm right of drip shield 
center (Multiple Patch 
Test) 
5 27 86.0 0.032 0.117 0.244 0.504 
54 cm left of drip shield 
center (High Flow Rate 
Test) 
4 0 136.5 0.275 0.634 0.423 0.318 
54 cm left of drip shield 
center (Low Flow Rate 
Test) 
4 0 136.5 0.177 0.634 0.423 0.318 
27 cm left of drip shield 
center (High Flow Rate 
Test) 
4 27 136.5 0.020 0.236 0.323 0.318 
27 cm left of drip shield 
center (Low Flow Rate 
Test) 
4 27 136.5 0.013 0.236 0.323 0.318 
27 cm right of drip shield 
center (High Flow Rate 
Test) 
5 -27 86.0 0.013 0.117 0.244 0.504 
27 cm right of drip shield 
center (Low Flow Rate 
Test) 
5 -27 86.0 0.065 0.117 0.244 0.504 
Mean 0.111 0.414 0.380 0.398 
Std. Dev. 0.106 0.305 0.144 0.096 
Median 0.049 0.236 0.323 0.318 
Minimum 0.013 0.117 0.244 0.318 
Maximum 0.275 1.000 0.680 0.504 
DTNs: MO0207EBSATBWP.023 [DIRS 163402]; MO0207EBSATBWP.024 [DIRS 163401]; 
MO0207EBSATBWP.025 [DIRS 163403]. 

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ANL-WIS-PA-000001 REV 01 6-73 November 2004 
The experimentally observed fraction of drip seepage flowing into a breach varies widely. This 
variability is primarily due to the drip locationwhen the drip location is centered over the 
breach, much of the flow enters the breach, and when the drip is far off to the side of a breach, 
little of it enters the breach. However, the variability also includes differences in drip rate, the 
distance from the crown to the breach, evaporation from the drip shield surface, and random 
variability in drop splashing and rivulet flow behavior. 
The fraction of drip seepage flowing into a breach calculated from the model is found always to 
be higher than observed experimentally, particularly when the drip location is far from the 
breach. When the drip location is well away from the patch center, and little water flows into the 
breaches ( expt f less than about 0.1), the model overestimates the experimental fraction 
increasingly as the estimated spread angle increases (see Table 6.5-3). In contrast, the model 
predicts that ever-increasing amounts of water flow into a breach as the spread angle increases. 
This can be seen in Equation 6.5.1.1.2-34, which shows that the flow into breaches is 
proportional to (1 +  tan a), so as the spread angle a increases, so does the flow into breaches. 
Evaporation also plays a part. The model assumes no evaporative losses (Assumption 5.2), 
whereas evaporation from the drip shield occurred in the experiments because the relative 
humidity was less than 100 percent. Using a larger spread angle in the model results in increased 
predicted flow into a breach, whereas evaporation consistently reduces the experimentally 
measured inflow. Thus, ignoring the observed occurrence of evaporation in the development of 
the drip shield flux splitting submodel will overestimate the transport of radionuclides. 
When the drip location is directly above the breach, the model agrees more closely with 
experiments as the spread angle increases. Again, the model generally overestimates the flow 
into breaches. In this case, as the estimated spread angle increases, less flow into breaches is 
predicted, so the model agrees more closely with experiments. 
A major reason for the differences between the flux splitting submodel calculations and the 
experimental results is that splashing of the drops when they impinged on the drip shield resulted 
in a dispersed source of rivulets. In contrast, the model supposes that the entire dripping flux 
flows down the drip shield from the point of impact. Splattering spreads the dripping flux over a 
wide span of the drip shield crown. The splash radius tests recorded splashes that extended up to 
72.5 cm from the drip location, with an inner cluster radius of 25 to 48 cm 
(DTN: MO0207EBSATBWP.022 [DIRS 163400]). In three of the q(film) rivulet flow tests, 
lateral splash distances ranging from 54.5 cm to 86 cm from the drip point on the crown were 
observed (DTN: MO0207EBSATBWP.023 [DIRS 163402], Drip Location: Patch 5, center, 
crown; Patch 4, center, crown; and Patch 4, 8 cm right of center, crown). Since a large portion of 
the dripping flux in the tests splattered beyond the range of rivulet flow into individual breaches, 
the flow into breaches was much less than predicted by the model. Thus, ignoring the observed 
occurrence of splattering in the development of the drip shield flux splitting submodel will 
overestimate the transport of radionuclides. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-74 November 2004 
Table 6.5-3. Additional Comparisons of Experimental Breach Inflow Fractions with Model Calculations 
from Appendix C 
fcalc - fexpt fcalc / fexpt Drip Location 
(Test Description) fexpt a =8.9 a =13.2 a =17.3 a =8.9 a =13.2 a =17.3 
8 cm right of Patch 4 centerline 
(Q[film] Test) 0.247 0.382 0.176 0.071 2.545 1.713 1.286 
Patch 5 centerline 
(Q[film] Test) 0.258 0.742 0.414 0.246 3.876 2.604 1.955 
4 cm left of Patch 5 centerline 
(Q[film] Test) 0.136 0.718 0.544 0.368 6.277 4.998 3.707 
Patch 4 centerline (Q[film] 
Test) 0.236 0.398 0.187 0.082 2.686 1.794 1.347 
27 cm right of drip shield 
center (Multiple Patch Test) 0.033 0.085 0.212 0.472 3.606 7.515 15.507 
27 cm left of drip shield center 
(Multiple patch test) 0.019 0.217 0.304 0.299 12.393 17.016 16.722 
81 cm left of drip shield center 
(Multiple Patch Test) 0.031 0.205 0.293 0.287 7.720 10.600 10.417 
81 cm right of drip shield 
center (Multiple Patch Test) 0.032 0.085 0.212 0.472 3.662 7.632 15.750 
54 cm left of drip shield center 
(High Flow Rate Test) 0.275 0.359 0.148 0.043 2.306 1.540 1.156 
54 cm left of drip shield center 
(Low Flow Rate Test) 0.177 0.456 0.246 0.140 3.574 2.387 1.792 
27 cm left of drip shield center 
(High Flow Rate Test) 0.020 0.215 0.303 0.298 11.693 16.055 15.777 
27 cm left of drip shield center 
(Low Flow Rate Test) 0.013 0.223 0.310 0.305 18.286 25.108 24.673 
27 cm right of drip shield 
center (High Flow Rate Test) 0.013 0.104 0.231 0.491 9.064 18.888 38.978 
27 cm right of drip shield 
center (Low Flow Rate Test) 0.065 0.053 0.180 0.440 1.815 3.781 7.804 
Mean 0.111 0.303 0.269 0.287 6.393 8.688 11.205 
Std. Dev. 0.106 0.221 0.107 0.155 4.885 7.672 11.033 
Median 0.049 0.220 0.239 0.298 3.769 6.256 9.110 
Minimum 0.013 0.053 0.1484 0.043 1.8145 1.540 1.156 
Maximum 0.275 0.742 0.5439 0.491 18.286 25.108 38.978 

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ANL-WIS-PA-000001 REV 01 6-75 November 2004 
Table 6.5-4. Water Collected in Drip Shield Experiment Q(film); Drip Location: Patch 4, 8 cm Right of 
Center, Crown 
Collection Station Initial Mass (g) Final Mass (g) Net Water Mass (g) 
Water Collected in 
Each Group of 
Collection Stations (g) 
Input Water -50.32 -228.52 -178.20 178.20 
Gutter 1-1 7.652 16.434 8.782 
Gutter 3-1 7.611 8.677 1.066 
Gutter 3-2 7.600 23.213 15.613 
Gutter 3-3 7.612 8.899 1.287 
Gutter 3-4 7.521 17.124 9.603 
36.351 
Breach 2 107.02 109.00 1.98 
Breach 4 107.60 129.62 22.02 
24.00 
Drip Shield OUT 1 7.634 8.738 1.104 
Drip Shield OUT 2 7.578 19.681 12.103 
Drip Shield OUT 3 7.574 34.446 26.872 
Drip Shield OUT 4 7.702 40.308 32.606 
72.685 
DTN: MO0207EBSATBWP.023 [DIRS 163402]. 
One other cause for the discrepancies between experimental and predicted flow fractions is that, 
in the model, all dripping flux flows down the drip shield surface. In the experiments, a large 
amount of water remained on the drip shield as splattered drops that had not yet grown large 
enough to flow down the surface. For example, Table 6.5-4 shows the amount of water collected 
in the first experiment listed in Table 6.5-2. Of the 178.2 g of water that was dripped onto the 
surface, only 60.35 g was collected from the breaches or drainage gutters, whereas 72.685 g, or 
41 percent, that remained on the surface (Drip Shield OUT entries). This is a source of 
uncertainty in the experimental results that could be reduced by increasing the duration of the 
experiment far beyond the one-hour length of the test, but is inherent in the experiment and 
cannot be eliminated. The result is that less of the dripping flux actually flowed down the drip 
shield surface than is predicted by the model. This also causes the model to overestimate the 
fraction that flows into breaches, and, therefore, overestimates the transport of radionuclides. 
Results presented in Table 6.5-2 and Table 6.5-3 show a large uncertainty in the fraction of 
rivulet flow that enters breaches. The integrated fraction of flow into breaches, which is the 
desired result, is not readily discerned from the uncertainty in the inflow fractions, even though 
the flows obtained experimentally are more clearly quantified. 
Another approach, which is used to develop an uncertainty factor for use in TSPA-LA, is to 
apply the integrated flow fraction approach to a drip shield whose length is about as wide as the 
splash diameter. If the rivulet source is dispersed along the crown, the integrated flow into a 
breach, Equation 6.5.1.1.2-34, can be applied. However, instead of the full drip shield length, 
the splash diameter is used for DS L . Thus, for the breached drip shield experiments, DS L has a 
range that is double the measured range for inner cluster splash radius (25 to 48 cm, as 
discussed at the beginning of this section, Section 6.5.1.1.2.4), or 50 to 96 cm. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-76 November 2004 
The uncertainty in the effective drip shield length and in the spread angle is accounted for in a 
parameter DS f , and the fraction of seepage flux that enters a breach 1 2 / F F , is written as in 
Equation 6.3.2.4-2: 
DS 
DS 
b f 
L
N F F .. 
. 
.. 
. + = 
2 
tan 1 / 1 2 
a l . (Eq. 6.5.1.1.2-35) 
In this approach, the uncertainty factor DS f is obtained by replacing 1 2 / F F with expt f , the 
experimental fraction of drip flow that enters a breach: 
. 
2 
tan 1 
2 
tan 1 
/ 1 2 
.. 
. 
.. 
. + 
= 
.. 
. 
.. 
. + 
= 
a
a 
DS 
expt 
DS 
DS 
L 
f 
L 
F F f 
l
l 
(Eq. 6.5.1.1.2-36) 
The range of values for DS f is obtained by evaluating it with the appropriate minimum and 
maximum values of DS L and a so as to minimize and maximize DS f . The minimum value of 
DS f , using = DS L 50 cm and = a 17.3, is 356 . 0 205 . 3 = = expt DS f f using the mean value of 
0.111 for expt f . The maximum value of DS f , using = DS L 96 cm and = a 8.9, is 
732 . 0 5947 . 6 = = expt DS f f using the mean value of 0.111 for expt f . Because zero must be the low 
end of the range of DS f , these estimates are regarded as a range for the maximum value of DS f . 
By treating the experimental drip shield as a segment whose length is the splash diameter, a 
maximum value of 0.36 to 0.73 for the flux splitting uncertainty factor DS f is obtained. 
It is also reasonable to use the median value for expt f (0.0486) instead of the mean to define the 
range for DS f . In this case, DS f would range from 0.16 to 0.32, a factor of 2.3 lower than when 
the mean is used, which gives some indication of the degree of uncertainty in the experimental 
measurements and the resulting flux splitting submodel. 
The drip shield flux splitting submodel, Equation 6.3.2.4-4, includes the rivulet spread angle, a. 
As discussed in Section 6.3.2.4, this equation can be simplified by lumping the uncertainty in 
awith the range in DS f . In Section 6.5.1.1.2, a was found based on experiments to range from 
about 8.9 to 17.3. The uncertainty in a appears as a factor ( ) 2 / tan 1 a + , ranging from 1.08 to 
1.16, which multiplies DS f , resulting in a range for the product ( ) DS DS f f 2 / tan 1 a + = ' . The 
maximum for DS f ' based on experimental results is (1.16)(0.73) = 0.85 (using the maximum 
spread angle of 17.3 in the factor ( ) 2 / tan 1 a + and the minimum spread angle of 8.9 to define 
DS f ). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-77 November 2004 
The sampled parameter is then DS f ' , and the drip shield flux splitting algorithm is: 
.. 
. 
.. 
. 
' = 1 1 2 , min F f 
L
N 
F F DS 
DS 
b l , (Eq. 6.5.1.1.2-37) 
which is identical to Equation 6.3.2.4-6. Using the higher value of maximum for DS f ' of 0.85 is 
both more reliable, being based on experimental data, and overestimates releases of 
radionuclides by predicting a higher water flow rate through the drip shield. The range for DS f ' 
to be used in TSPA-LA is 0 to 0.85. A uniform distribution is appropriate for DS f ' because 
insufficient data are available to define any other distribution. 
6.5.1.1.3 Water Flux through a Breached Waste Package 
The submodel for flow through a breached waste package is conceptually identical to the 
submodel for flow through a breached drip shield. Key features listed at the start of 
Section 6.5.1.1.1 apply to both the drip shield and waste package cases. The waste package and 
drip shield flow submodels differ in two important respects: (1) the radius of curvature of the 
waste package is less than that of the drip shield; and (2) the nominal corrosion patch size as 
modeled by WAPDEG (BSC 2004 [DIRS 169996]) is smaller for a waste package than for the 
drip shield. These differences have no affect on the formulation of the waste package flow 
model. However, they have an affect on the values of uncertainty parameters that are part of the 
model. Because experiments were performed on a breached drip shield but not on a breached 
waste package, application of drip shield data to the waste package flow model introduces 
additional uncertainty in development of the model; however, these uncertainties cannot be 
quantified. 
The water flux through a breached waste package, 4 F , as developed in Section 6.3.3.2, is given 
by: 
.. 
. 
.. 
. 
' = 2 2 4 , min F f 
L 
N F F WP 
WP 
WP bWPl , (Eq. 6.5.1.1.3-1) 
where 2 F is the flux through the breached drip shield. This is a simplification of a slightly more 
rigorous expression: 
.. 
. 
.. 
. 
.. 
. 
.. 
. + = 2 2 4 , 
2 
tan 1 min F f 
L 
N F F WP 
WP 
WP bWP a l , (Eq. 6.5.1.1.3-2) 
which explicitly accounts for the rivulet spread angle a. Because a is an uncertainty parameter 
itself, it can be lumped in with the parameter WP f to give WP f ' . Equation 6.5.1.1.3-2 is 
considered first in order to examine the dependence on a. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-78 November 2004 
As with the drip shield model, the primary mechanism for water to enter breaches is via rivulet 
flow that originates from an area around the point of drip impact. The rivulets spread out in a 
delta formation from the point of impact defined by a half-angle, a, and the lateral spread of the 
rivulet flow is given by a tan 2x , where x is the distance from the crown to the top edge of the 
breach. The smaller radius of curvature of the waste package would be expected to result in a 
smaller spread angle, although the difference may be lost in the variability and uncertainty of 
rivulet flow. The radius of curvature of the drip shield is 1.40 m, whereas waste package radii 
range from 0.859 m for a 21-PWR (BSC 2004 [DIRS 169472], Table 1) to 1.063 m for a 
5 DHLW/DOE SNF - Short (BSC 2004 [DIRS 169472], Table 1). 
Rivulet spread measurements at the 16.5 line, at the 33 line, and at the transition line between 
the curved top surface and the vertical side of the drip shield are used. The distance x from the 
drip location to the point of measurement is determined from the drawing of the drip shield 
mockup shown in Figure 4.1-1, which is reproduced from Howard (2002 [DIRS 161516], p. 14); 
various dimensions used in analyzing the data are listed in Table 6.5-1. The rivulet spread angle 
data are analyzed in Microsoft Excel spreadsheet: Flux Split Waste Package Model, Worksheet: 
Spread angles, which is documented in Appendix D. 
To capture some of the effect of the smaller radius, namely the steeper incline closer to the 
crown, the data from drip locations that are off the crown of the smooth drip shield surface 
experiments are used to develop parameters for the waste package model. The results varied 
widely. In 20 measurements at the 33 line with drips at the 16.5 line, the mean spread angle 
was 17.0 (11.2 = one standard deviation). In 17 measurements at the transition line with drips 
at the 16.5 line, the mean spread angle was 11.1 (4.1). In 10 measurements at the transition 
line with drips at the 33 line, the mean spread angle was 11.5 (3.3). For all 47 measurements 
the mean spread angle was 13.7 (8.2), which is just slightly larger than the spread angle 
measured for drips on the crown of the drip shield, although the variability is greater (standard 
deviation of 8.2, compared with 4.1 for drips from the crown). Utilizing all of the data 
available, the spread angle for rivulet flow on the waste package can be assigned a mean value of 
about 13.7 and a range ( one standard deviation) from 5.5 to 22.0. 
The splash distance is uncertain for drip locations off the crown. In four of the q(film) rivulet 
flow tests, maximum lateral splash distances ranging from 56 cm to 122 cm from the drip point 
were observed (DTN: MO0207EBSATBWP.023 [DIRS 163402], pp. 14, 16, 18, and 20) for 
drip locations at the 16.5 line. However, no further observations indicated any change in the 
inner cluster splash distance range of 50 cm to 96 cm from Splash Radius Test #1 
(DTN: MO0207EBSATBWP.022 [DIRS 163400]). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-79 November 2004 
An uncertainty factor WP f that can be obtained by replacing the fraction 2 4 / F F with expt f : 
. 
2 
tan 1 
2 
tan 1 
/ 2 4 
.. 
. 
.. 
. + 
= 
.. 
. 
.. 
. + 
= 
a
a 
WP 
expt 
WP 
WP 
L 
f 
L 
F F f 
l
l 
(Eq. 6.5.1.1.3-3) 
The range of values for WP f is obtained by evaluating it with the appropriate minimum and 
maximum values of WP L and a so as to minimize and maximize WP f . The half-width of the 
patch used in the experiments ( = l 13.5 cm) is used to evaluate WP f . The minimum value of 
WP f , using = WP L 50 cm and = a 22.0, is 909 . 0 081 . 3 = = expt WP f f using the mean value of 
0.295 for expt f . The maximum value of WP f , using = WP L 96 cm and = a 5.5, is 
001 . 2 784 . 6 = = expt WP f f using the mean value of 0.295 for expt f . 
A much lower range could also be justified by using the median inflow fraction of 0.014 instead 
of the mean (0.295) to define WP f . In this case, WP f would range from 0.043 to 0.095, which 
demonstrates the large degree of uncertainty in the experimental measurements and the resulting 
flux splitting submodel. The values for WP f discussed in this section actually represent a range 
for the maximum value of WP f , since the minimum must be zero. 
If the factor (1 +  tan a) that accounts for the rivulet spread angle is lumped in with WP f , the 
sampled uncertain factor WP f ' has an upper bound (using the maximum rivulet spread angle, 
= a 22) of 2.41. The range for WP f ' to be used in TSPA-LA is 0 to 2.41. WP f ' is assigned a 
uniform distribution. 
6.5.1.2 EBS Transport Model 
The EBS transport model consists of mass balances on radionuclides. The transport model is 
more complex than the flow model for two basic reasons. First, the transport model is 
necessarily transient because the mass of each radionuclide at any particular location is 
dependent on its history (i.e., how far it has traveled, the quantity remaining at the source, and 
the extent of radioactive decay or ingrowth). Second, several complex interacting processes 
occur in transport, including dissolution and precipitation, sorption, advective transport, 
diffusion, and colloid-facilitated transport. The term colloid-facilitated transport includes 
numerous phenomena, including adsorption and desorption of radionuclides onto mobile and 
immobile colloids, capture of colloids by solid surfaces and the air-water interface, filtering, 
dispersion, and diffusion. Transport can take place at any degree of water saturation greater than 
zero, so the model has to account for water saturation. Dissolution and precipitation may occur 
at finite rates or sufficiently fast to reach equilibrium. Solubility limits that determine whether, 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-80 November 2004 
or to what extent, these processes occur are dependent on the chemical environment of the EBS. 
The EBS transport model applies to the waste package, the invert, and the invert/UZ interface. 
Mass Balance for Dissolved and Reversibly and Irreversibly Sorbed Radionuclides in the 
Aqueous Phase 
As with the flow model, the details of pore structure within the EBS are not important, and 
macroscopic mass balances using phenomenological rate expressions are appropriate. The 
starting point is the equation of continuity, or mass balance equation, for each dissolved 
radionuclide species i (Bird et al. 1960 [DIRS 103524], p. 561): 
i 
m
i i 
i r Q 
t 
+ +  -. = 
. 
. 
J 
. 
. (Eq. 6.5.1.2-1) 
Here, i . is the mass concentration of dissolved radionuclide species i (kg i m-3 bulk volume), i J 
is the mass flux vector (or mass specific discharge) (kg m-2 s-1) of dissolved radionuclide species 
i in the mobile water phase and accounts for advection, hydrodynamic dispersion, and diffusion 
of the dissolved radionuclide species i. The term m
i Q is the net rate on a bulk volume basis 
(kg m-3 s-1) of the various mass transfer processes, including reversible and irreversible sorption 
onto solid stationary materials in the EBS, dissolution and precipitation, and the various colloidfacilitated 
transport processes. The reaction term, i r , accounts for radioactive decay and 
ingrowth on a bulk volume basis (i.e., production by decay of the parent of i) (kg m-3 s-1). Each 
of these terms is expanded and described in more detail below, then simplified as appropriate for 
application in the TSPA-LA model. 
It is convenient to develop the transport model following the approach normally taken in the 
literature (Corapcioglu and Jiang 1993 [DIRS 105761], pp. 2217 to 2219; Choi and 
Corapcioglu 1997 [DIRS 161621], p. 306), with an emphasis on colloid-facilitated transport, 
since the complexity of those processes tends to dominate the analysis. First, Equation 6.5.1.2-1 
is rewritten in terms of concentrations of radionuclides in an unsaturated porous medium. The 
density, or mass concentration, of dissolved radionuclide species i is given by: 
w i i S C f . = , (Eq. 6.5.1.2-2) 
where i C is the concentration on a water volume basis of radionuclide species i (kg m-3), f is 
the porosity (m3 void m-3 EBS) of a representative elemental volume of EBS, and w S is the 
water saturation (m3 water m-3 void). The expression for i . is inserted into Equation 6.5.1.2-1, 
resulting in 
( ) 
i 
m
i i 
i w r Q 
t
C S + +  -. = 
. 
. 
J 
f 
. (Eq. 6.5.1.2-3) 
The concentration i C is constrained by the solubility limit, si C , which is defined in Dissolved 
Concentration Limits of Radioactive Elements (BSC 2004 [DIRS 169425], Table 8-3) for each of 
14 elements (U, Np, Pu, Am, Ac, Th, Tc, C, I, Ra, Pa, Pb, Cs, and Sr). The solubility limits for 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-81 November 2004 
U, Np, Pu, Th, Am, Ac, and Pa are given as functions of pH, CO2 fugacity, and fluoride 
concentration. 
The mass flux vector is expressed as 
i w i i w i C C D S q J + . - = f , (Eq. 6.5.1.2-4) 
where i D is the hydrodynamic dispersion coefficient of species i (m2 s-1), and w q is the specific 
discharge vector, or Darcy velocity, of water (m s-1). The specific discharge vector is related to 
the water flow rates j F (m3 s-1) in each pathway j of the EBS flow model (Section 6.5.1.1) by: 
i qw A 
Fj = , (Eq. 6.5.1.2-5) 
where A is the spatially dependent cross sectional flow area within the pathway j (m2), and i is a 
unit vector in the direction of the flow path. Because of the complex flow geometry in the EBS, 
assigning a value to A is not always straightforward; for example, for pathway 4 
(Section 6.5.1.1), flow through the waste package, A can be the cross sectional area of corrosion 
patches or some fraction of the cross sectional area of a waste package. 
The hydrodynamic dispersion coefficient, i D , can be expressed in terms of two components 
(Freeze and Cherry 1979 [DIRS 101173], pp. 389 to 390): 
mi D v + a , (Eq. 6.5.1.2-6) 
where a is the dispersivity (m), v is the average interstitial water velocity (m s-1), and mi D is 
the effective molecular diffusion coefficient (m2 s-1). The dispersivity can be further broken 
down into lateral and longitudinal dispersivities. However, the dispersivity in the EBS is ignored 
(see Section 6.3.1.2). Consequently, the hydrodynamic dispersion is accounted for solely by 
molecular diffusion. The free water diffusion coefficient for self-diffusion of water, 0 D , is used 
as a bounding value of the molecular diffusion coefficient for all radionuclides in the EBS. 
Modifications to the diffusion coefficient Dmi for the porosity, saturation, temperature and 
uncertainty within the invert are described in Section 6.3.4.1. Modifications to the diffusion 
coefficient for the porosity and saturation within the waste package are described in 
Section 6.5.1.2.1. The effects of concentrated solutions are ignored. Throughout the 
mathematical description of the radionuclide transport, i D represents the effective diffusion 
coefficient for species i. 
The term m
i Q (kg m-3 s-1) in Equation 6.5.1.2-3 is expanded to account for individual 
contributions of different processes to radionuclide transport: 
embed 
icm imt 
int 
icc icc 
irrev 
icm 
rev 
icm 
irrev 
is 
rev 
is iprecip id 
m
i Q Q Q Q Q Q Q Q Q Q Q -  - - - - - - - = . (Eq. 6.5.1.2-7) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-82 November 2004 
The first term is the source term, id Q , accounting for the rate of dissolution of species i, and 
iprecip Q is the rate of precipitation of species i. If the concentration of species i is below the 
solubility limit, then 0 = iprecip Q ; otherwise, the precipitation rate is determined from the mass 
balance so as to honor the solubility limit. 
The next six terms in Equation 6.5.1.2-7 account for sorption-related processes. rev 
is Q is the net 
rate of reversible sorption of radionuclide species i onto the stationary solid matrix (internal 
waste package corrosion products and invert matrix). irrev 
is Q is the net rate of irreversible 
sorption of radionuclide species i onto the stationary solid matrix (internal waste package 
corrosion products). rev 
icm Q is the net rate of reversible sorption of radionuclide species i onto 
mobile colloid surfaces. Development of this term requires assumptions regarding the 
reversibility of radionuclide sorption onto colloids and is discussed below. irrev 
icm Q is the net rate 
of irreversible sorption of radionuclide species i onto mobile colloid surfaces. 
icc Q and int 
icc Q are the net rates of sorption of radionuclide species i onto immobile colloid 
surfaces captured by the stationary solid matrix and by the air-water interface, respectively. Wan 
and Wilson (1994 [DIRS 124994]) found that particle transport was tremendously retarded by 
the air-water interface acting as a strong sorption phase (Choi and Corapcioglu 1997 
[DIRS 161621], p. 301). However, as a bounding assumption (BSC 2004 [DIRS 170025], 
Assumption 5.4), sorption by the air-water interface is assumed not to occur ) 0 ( = int 
icc Q . 
Distribution coefficients for sorption onto the stationary solid matrix and onto immobile colloid 
surfaces will generally be different. However, it is difficult to distinguish among various types 
of matrixes and immobile colloids. Therefore, no distinction is made, and the term icc Q (sorption 
onto immobile colloids) is lumped in with rev 
is Q or irrev 
is Q (sorption onto the stationary solid 
matrix). Sorption and retardation in the waste package is discussed in more detail in 
Section 6.3.4.2. 
imt Q is the net rate of interface transfer of dissolved mass between the continua in a dual 
continuum. The sign of this transfer term is determined by the sign of the concentration 
difference between the media and which medium is associated with the mass balance equation. 
This term is included even though it is zero in the single-continuum domains that represent the 
EBS in the EBS RT Abstraction in order to keep the mass balance equations as generally 
applicable as possible. In particular, the equations apply in the dual-continuum invert model 
presented as an alternative conceptual model in Section 6.6.4. 
embed 
icm Q is the rate of mass conversion from dissolved state to embedded state onto waste form 
colloids for radionuclide species i. Radionuclides become embedded only in waste form 
colloids, not in iron oxyhydroxide or groundwater colloids. The conversion rate to embedded 
species is represented by a first order conversion of the species in solution: 
i 
embed 
i 
embed 
icm C Q . = , (Eq. 6.5.1.2-8) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-83 November 2004 
where is the embed 
i . is the first order rate constant (s-1) for mass conversion from the dissolved 
state to the embedded state onto waste form colloids for radionuclide species i. 
Decay and ingrowth are expressed as: 
i w i ip w 
M 
ip ip i C S C S r r f . f . - = . (Eq. 6.5.1.2-9) 
Radionuclide species i is produced by the decay of its parent species at a rate proportional to the 
concentration of the parent, ip C (kg m-3), and the parent species decay constant, ip . (s-1). The 
decay constant is related to the half-life, ip t , 2 / 1 (s), of the radionuclide by: 
ip 
ip t , 2 / 1 
) 2 ln( = . . (Eq. 6.5.1.2-10) 
Similarly, species i is lost by decay at a rate i iC . (kg m-3 s-1), where i . is the decay constant for 
species i (s-1), defined analogously to ip . . The term M 
ip r in the production rate is the 
dimensionless ratio of the mass (kg) of species i produced by decay of the parent species to the 
mass (kg) of the parent species lost by decay. This is equal to the ratio of the atomic weight of 
species i to that of its parent for species that have just one parent. In TSPA-LA, each 
radionuclide is modeled as having at most one parent, which is implied in Equation 6.5.1.2-9. 
Transport of dissolved and reversibly sorbed radionuclide species i in the aqueous phase is then 
given by: 
( ) ( ) 
( ), 
i i ip 
M 
ip ip w 
embed 
icm imt 
irrev 
icm 
rev 
icm 
irrev 
is 
rev 
is iprecip id 
i w i i w 
i w 
C C r S Q Q 
Q Q Q Q Q Q 
C C D S 
t
C S 
. . f 
f 
f 
- + -  
- - - - - + 
 . - .  . = 
. 
. q 
(Eq. 6.5.1.2-11) 
which is essentially identical to Equations 19 and 20 by Choi and Corapcioglu (1997 
[DIRS 161621], p. 306), with the addition of decay and ingrowth terms and a dissolution source 
term, idp Q . A further modification of the equations by Choi and Corapcioglu involves the 
diffusive term, ( ) i i w C D S .  . f , which Choi and Corapcioglu write as ( ) [ ] i w i C S D f .  . . This 
form of the term incorrectly allows diffusion to occur in the absence of a concentration gradient 
as long as the water content, w S f , varies. 
The source term for radionuclide species i reversibly sorbed onto the stationary solid matrix 
(corrosion products or invert matrix) is given by: 
( ) ( ) i dis i ip dips 
M 
ip ip b 
i dis b rev 
is C K C K r 
t 
C K Q . . . 
. 
- - 
. 
. 
= , (Eq. 6.5.1.2-12) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-84 November 2004 
where b . is the dry bulk density of the stationary solid matrix (kg m-3 bulk volume). A linear 
adsorption isotherm is used for the relationship between the aqueous and solid phase equilibrium 
concentration, expressed in terms of a sorption distribution or distribution coefficient of the 
dissolved species i, dis K (m3 water kg-1 solid [more typically reported in units of ml g-1]). dis K 
depends both on the radionuclide species i being sorbed and on the solid substrate, either 
stationary iron oxyhydroxide corrosion products or invert material or both, in this case. 
The source term for radionuclide species i irreversibly sorbed onto the stationary solid iron 
oxyhydroxide corrosion products is given by: 
, i i CP b 
irrev 
is C k s Q . = (Eq. 6.5.1.2-13) 
where CP s is the specific surface area of iron oxyhydroxide corrosion products [m2 CP kg-1 CP], 
and i k is the irreversible forward rate constant (m3 water m-2 CP s-1). The reaction is modeled as 
first order in the solution concentration. 
The source term for radionuclide species i reversibly sorbed onto the mobile colloids is given by: 
( ) [ ] 
( ) 
( ) ( ) [ ], 
icGW icFeOx icWF i ipcGW ipcFeOx ipcWF 
M 
ip ip w 
icGW icFeOx icWF 
i cGW dicGW cFeOx dicFeOx cWF dicWF w rev 
icm 
C C C C C C r S 
t 
C C K C K C K S Q 
+ + - + + - 
+ +  . + 
. 
+ + . 
= 
. . f
f 
J J J (Eq. 6.5.1.2-14) 
where icWF C , icFeOx C , and icGW C are the concentrations on a water volume basis of radionuclide 
species i reversibly sorbed onto the mobile waste form, iron oxyhydroxide (FeOx), and 
groundwater (GW) colloids, respectively (kg i m-3 water). The subscript ip refers to the parent of 
radionuclide species i. The terms cWF C , cFeOx C , and cGW C are the concentrations on a water 
volume basis of mobile waste form, iron oxyhydroxide, and groundwater colloids, respectively 
(kg colloid m-3 water). The Kd values of radionuclide species i for the respective colloids are 
dicGW dicFeOx dicWF K K K and , , (typical units: ml g-1). 
The vectors for mass fluxes of colloids, icGW icFeOx icWF J J J and , , , are: 
( ) i cWF dicWF w i cWF dicWF c w icWF C C K C C K D S q J + . - = f (Eq. 6.5.1.2-15) 
( ) i cFeOx dicFeOx w i cFeOx dicFeOx c w icFeOx C C K C C K D S q J + . - = f (Eq. 6.5.1.2-16) 
( ) . i cGW dicGW w i cGW dicGW c w icGW C C K C C K D S q J + . - = f (Eq. 6.5.1.2-17) 
The source term for radionuclide species i irreversibly sorbed onto the mobile iron oxyhydroxide 
corrosion products colloids is given by: 
, i i c cFeOx w 
irrev 
icm C k s C S Q f = (Eq. 6.5.1.2-18) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-85 November 2004 
where c s is the specific surface area of mobile corrosion products colloids (m2 colloids kg-1 
colloids), and i k is the forward rate constant for irreversible sorption (m3 water m-2 FeOx 
colloids s-1). i k for mobile iron oxyhydroxide corrosion products colloids is the same as for 
stationary iron oxyhydroxide corrosion products. The reaction is modeled as first order in the 
solution concentration. Irreversible sorption onto mobile colloids occurs only onto mobile iron 
oxyhydroxide corrosion products colloids, not onto mobile waste form or mobile groundwater 
colloids. As discussed earlier, radionuclides may become embedded in waste form colloids, 
which has a similar net effect as irreversible sorption but is modeled as a distinctly separate 
process. 
The term imt Q is the net rate of interface transfer of dissolved and reversibly sorbed mass 
between the continua in a dual continuum material (as in the dual continuum invert alternative 
conceptual model; see Section 6.6.4) on a bulk volume basis (kg m-3 s-1]). It is given by 
(Corapcioglu and Wang 1999 [DIRS 167464], p. 3265; Gerke and van Genuchten 1996 
[DIRS 167466], p. 345): 
( ) ( ) [ ] 
( ) ( ) [(
) ( ) ( ) ( ) ]. 
inter icGW intra icGW inter icFeOx intra icFeOx 
inter icWF intra icWF c 
inter i intra i d imt 
C C C C 
C C 
C C Q 
- + - + 
- + 
- = 
. 
. 
(Eq. 6.5.1.2-19) 
In a single-continuum material, 0 = imt Q . The dissolved and colloid mass transfer coefficients, 
d . and c . , respectively, depend on which continuum the mass balance represents. For the 
dissolved mass transfer term: 
intra w intra d S _ af . = , for the intragranular mass balance, (Eq. 6.5.1.2-20) 
. .. 
. 
. .. 
. - 
= 
inter 
inter 
intra w intra d w
w S 1 
_ af . , for the intergranular mass balance, (Eq. 6.5.1.2-21) 
where a is the first-order mass transfer coefficient of the form: 
ie D 
d 2 
 
a= , (Eq. 6.5.1.2-22) 
 is a dimensionless geometry-dependent coefficient, d is a characteristic length (m) of the 
matrix structure (e.g., half the aggregate width or half the fracture spacing), and ie D is an 
effective diffusion coefficient (cm2 s-1) that represents the diffusion properties of the interface 
between the two continua for radionuclide species i. Because the intergranular continuum is 
open pore space, diffusion is expected to be controlled by the diffusive properties of the 
intragranular continuum. Thus, ie D is taken to be the effective diffusion coefficient in the 
intragranular continuum. The colloid coefficient c . is evaluated similarly to the dissolved 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-86 November 2004 
coefficient, but uses an effective colloid diffusion coefficient to evaluate a in 
Equation 6.5.1.2-22. The mass transfer function between the two invert continua is described in 
Section 6.6.4.1. 
In a dual-continuum material, the intergranular porosity inter f and intragranular porosity intra f are 
defined as follows. Let p V be the total volume of pore space in the bulk material, which has a 
total volume of t V . The intergranular pore space has a total volume designated by t_inter V and a 
pore volume of inter p V _ . Similarly, the intragranular pore space has a total volume designated by 
t_intra V and a pore volume of intra p V _ . inter p intra p p V V V _ _ + = and inter t intra t t V V V _ _ + = . The 
porosities are defined as: 
t
inter p 
inter V 
V _ = f (Eq. 6.5.1.2-23) 
and 
t
intra p 
intra V 
V _ = f . (Eq. 6.5.1.2-24) 
The total bulk porosity of the material is: 
intra inter 
t
p 
I V
V 
f f f + = = . (Eq. 6.5.1.2-25) 
The parameter inter w is the ratio of the intergranular continuum volume to the total bulk volume: 
t 
inter t 
inter V 
V 
w _ = . (Eq. 6.5.1.2-26) 
Then . .. 
. 
. .. 
. - 
inter 
inter 
w
w 1 is the ratio of intragranular continuum volume to intergranular continuum 
volume: 
inter t 
intra t 
inter t 
inter t t 
t 
inter t 
t 
inter t 
inter 
inter 
V
V 
V 
V V 
V 
V 
V 
V 
w
w 
_
_ 
_ 
_ 
_ 
_ 1 
1 = 
- 
= 
- 
= 
- 
. (Eq. 6.5.1.2-27) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-87 November 2004 
Mass Balance for Irreversibly Adsorbed Radionuclides on Iron Oxyhydroxide Corrosion 
Products and Colloids 
The mass balance for irreversibly adsorbed radionuclides on mobile iron oxyhydroxide colloids, 
which originate in the corrosion products, accounts for advection, diffusion, and decay and is 
given by: 
( ) ( ) 
( ) irrev 
icFeOx i 
irrev 
ipcFeOx 
M 
ip ip w 
irrev 
imt 
irrev 
icm 
irrev 
irrev 
icFeOx w 
C C r S 
Q Q 
t 
C S 
. . f 
f 
- + 
 +  -. = 
. 
. 
icFeOx J 
, (Eq. 6.5.1.2-28) 
where 
( ) ( ) [ ], inter 
irrev 
icFeOx intra 
irrev 
icFeOx c 
irrev 
imt C C Q - = . 
(Eq. 6.5.1.2-29) 
( ) . irrev 
icFeOx w 
irrev 
icFeOx c w 
irrev C C D S q JicFeOx + . - = f (Eq. 6.5.1.2-30) 
irrev 
icFeOx C is the concentration of radionuclide species i irreversibly adsorbed onto iron 
oxyhydroxide colloids on a water volume basis (kg i m-3 water). The source term for 
radionuclide species i irreversibly sorbed onto the mobile corrosion products colloids, irrev 
icm Q , is 
given by Equation 6.5.1.2-18. 
The mass balance for irreversibly adsorbed radionuclides on stationary iron oxyhydroxide 
corrosion products accounts for decay and is given by: 
( ) ( ) irrev 
iCPFeOx i 
irrev 
ipCPFeOx 
M 
ip ip w 
irrev 
is 
irrev 
iCPFeOx w C C r S Q 
t 
C S . . f 
f 
- + = 
. 
. 
, (Eq. 6.5.1.2-31) 
where irrev 
iCPFeOx C is the concentration of radionuclide species i irreversibly adsorbed onto iron 
oxyhydroxide corrosion products on a water volume basis (kg i m-3). The source term for 
radionuclide species i irreversibly sorbed onto the solid stationary iron oxyhydroxide corrosion 
products, irrev 
is Q , is given by Equation 6.5.1.2-13. 
Mass Balance for Waste Form Colloid Particles 
The waste form colloids are generated in the waste form domain and are transported in 
accordance with an advective/diffusive mass balance. The waste form colloid concentration is 
subject to stability constraints based on the local domain chemistry. The iron oxyhydroxide and 
ground water colloids both exist in the corrosion products and invert domains, and their 
concentrations are dependent on the local domain chemistry (BSC 2004 [DIRS 170025]). 
Hence, no transport mass balance equations are required for iron oxyhydroxide and ground water 
colloids. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-88 November 2004 
The mass balance for waste form colloidal particles suspended in the aqueous phase can be 
expressed as (Choi and Corapcioglu 1997 [DIRS 161621], p. 302): 
( ) 
cWFmt cWFs cWFfg 
int 
cWF cWF cWF 
cWF w Q Q Q Q Q 
t
C S  + - - -  -. = 
. 
. 
J 
f 
. (Eq. 6.5.1.2-32) 
cWF C is the concentration of suspended waste form colloids in the aqueous phase (kg waste form 
colloids m-3 water), and cWF J is the mass flux vector of waste form colloids (kg m-2 s-1). cWF Q 
(kg m-3 s-1) is the net rate of waste form colloid capture on the solid surface, with int 
cWF Q 
(kg m-3 s-1) representing capture at the air-water interface. As mentioned earlier, the latter is 
neglected. The term cWFfg Q is the net rate of waste form colloid removal from suspension 
(kg m-3 s-1) by means of physical filtering (pore clogging, sieving, and straining) and by 
gravitational settling. Both of these processes are neglected as bounding assumptions (BSC 2004 
[DIRS 170025], Section 6.3.1). Although colloid capture is akin to sorption and a different 
process from physical filtration, the net effect is indistinguishable from physical filtration, and it 
is also, too, is neglected ( 0 = cWF Q ). 
With these assumptions, Equation 6.5.1.2-32 simplifies to: 
( ) 
cWFmt cWFs cWF 
cWF w Q Q 
t
C S  +  -. = 
. 
. 
J 
f 
. (Eq. 6.5.1.2-33) 
The source term, cWFs Q (kg m-3 s-1), in Equation 6.5.1.2-33 represents the formation or 
degradation of waste form colloids. Colloid formation may be rate limited, or it may be 
instantaneous, with equilibrium between the colloids and their dissolved components. In either 
case, colloid stability is strongly dependent on the chemical environment, specifically on the pH 
and ionic strength of the aqueous phase. The colloid source term is the subject of Waste Form 
and In-Drift Colloids-Associated Radionuclide Concentrations: Abstraction and Summary 
(BSC 2004 [DIRS 170025]), and is discussed further below. 
cWFmt Q is the net rate of interface transfer of waste form colloidal mass between the intergranular 
and intragranular continua in a dual continuum model, such as the dual continuum invert 
alternative conceptual model (Section 6.6.4). For a single continuum, 0 = cWFmt Q . The sign of 
this transfer term is determined by the sign of the waste form colloid concentration difference 
between the media and which medium is associated with the mass balance equation. This is just 
the colloid transfer term in Equation 6.5.1.2-32: 
( ) ( ) [ ]. inter cWF intra cWF c cWFmt C C Q - = . (Eq. 6.5.1.2-34) 
Since Equation 6.5.1.2-34 is for the waste form colloid particles themselves, as opposed to 
radionuclides sorbed onto the particles, there are no decay or ingrowth terms. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-89 November 2004 
The mass flux vector for waste form colloids is expressed as (Choi and Corapcioglu 1997 
[DIRS 161621], p. 303, Equation 4): 
, cWF w cWF c w 
cWF w cWF MD w cWF B w 
cWF w cMD cB cWF 
C C D S 
C C D S C D S 
C
q 
q 
q J J J 
+ . - = 
+ . - . - = 
+ + = 
f 
f f (Eq. 6.5.1.2-35) 
where subscript B refers to Brownian diffusion, and MD refers to mechanical dispersion. The 
mechanical dispersion and Brownian diffusion terms can be lumped together in a colloid 
hydrodynamic dispersion term with a colloid dispersion or diffusion coefficient c D (m2 s-1). The 
diffusion coefficient of colloids is estimated to be a factor of 100 less than that of the free water 
diffusivity (Section 6.3.4.4) (i.e., 100 / 0 D Dc = ). The mass balance on waste form colloid 
particles, Equation 6.5.1.2-33, then becomes: 
( ) ( ) ( ) 
( ) ( ) [ ]. inter cWF intra cWF c 
cWFs cWF w cWF c w 
cWF w 
C C 
Q C C D S 
t
C S 
-  
+  . - .  . = 
. 
. 
. 
f 
f q 
(Eq. 6.5.1.2-36) 
Mass Balance for Embedded Mass on Waste Form Colloids 
The mass balance for the radionuclide species i embedded on waste form colloids is: 
( ) ( ) ( ) 
( ) , embed 
icm w 
embed 
i i 
embed 
ip 
M 
ip ip w 
embed 
i w 
embed 
i c w 
embed 
i w 
Q S C C r S 
C q C D S 
t 
C S 
f . . f
f 
f 
+ - + 
 . - .  . = 
. 
. 
(Eq. 6.5.1.2-37) 
where embed 
i C and embed 
ip C are the concentrations of species i and the parent of species i, 
respectively, embedded on waste form colloids. 
Inserting the source terms into Equation 6.5.1.2-11 gives the equation for the transport of 
radionuclides dissolved in the aqueous phase and reversibly sorbed: 
[ ] ( )
( ) [ ] { } 
( ) [ ] 
( ) 
( ) ( ) [ ] 
( ) ( ) [ ] 
[ ], 
1 
i fi i ip fip 
M 
ip ip w 
inter icGW icFeOx icWF intra icGW icFeOx icWF c 
inter i intra i d 
i 
embed 
i i i c cFeOx w CP b iprecip id 
i cGW dicGW cFeOx dicFeOx cWF dicWF w 
i cGW dicGW cFeOx dicFeOx cWF dicWF c w 
i i w i fi w 
C R C R r S 
C C C C C C 
C C 
C C k s C S s Q Q 
C C K C K C K 
C C K C K C K D S 
C D S C R S 
t 
. . f
.
. 
. f . 
f 
f f 
- + 
+ + - + +  
-  
- + - - + 
+ + +  . - 
+ + .  . + 
.  . = 
.
. 
q (Eq. 6.5.1.2-38) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-90 November 2004 
where 
cGW dicGW cFeOx dicFeOx cWF dicWF 
w
dis b 
fi C K C K C K 
S
K R + + + + = 
f 
. 
1 , (Eq. 6.5.1.2-39) 
and fip R is the corresponding factor for the parent species ip of radionuclide species i: 
cGW dipcGW cFeOx dipcFeOx cWF dipcWF 
w
dips b 
fip C K C K C K 
S
K 
R + + + + = 
f 
. 
1 . (Eq. 6.5.1.2-40) 
In Equation 6.5.1.2-38, the left side of the equation represents the accumulation of dissolved and 
reversibly sorbed radionuclide species i. The term in brackets is the mass of species i present in 
a unit bulk volume of EBS, so the equation units are mass of species i per unit bulk volume of 
EBS per time. The first term on the right side represents the rate of diffusion of dissolved 
species i in the aqueous phase. The second term accounts for diffusion of mobile colloids on 
which species i is adsorbed. The third term is the rate at which species i dissolved mass and 
mass reversibly sorbed to mobile colloids is transported by advection. The fourth and fifth terms 
represent the net rate of dissolution and precipitation of species i, respectively. The sixth term is 
the conversion rate due to irreversible sorption on both iron oxyhydroxide corrosion products 
and colloids. The seventh term is the rate of irreversible capture of species i by embedding in 
waste form colloids. The eighth and ninth terms represent respectively the mass flux of 
dissolved and reversibly sorbed species i between the continua in a dual-continuum material; for 
a single-continuum material, these terms are omitted. The last (tenth) term accounts for 
ingrowth, or production of species i by decay of the parent of i, and decay of species i, as 
dissolved species and as sorbed onto colloids and immobile matrix. 
Inserting the source terms into Equation 6.5.1.2-28, the mass balance for irreversibly adsorbed 
radionuclides on iron oxyhydroxide corrosion product colloids becomes: 
( ) ( ) [ ] ( ) 
( ) ( ) [ ] 
( ). 
irrev 
icFeOx i 
irrev 
ipcFeOx 
M 
ip ip w 
inter 
irrev 
icFeOx intra 
irrev 
icFeOx c i i c cFeOx w 
irrev 
icFeOx w 
irrev 
icFeOx c w 
irrev 
icFeOx w 
C C r S 
C C C k s C S 
C C D S 
t 
C S 
. . f 
. f 
f 
f 
- + 
-  + 
 . - .  . = 
. 
. q 
(Eq. 6.5.1.2-41) 
The source term in Equation 6.5.1.2-41, i i c cFeOx w C k s C S f , couples this equation to 
Equation 6.5.1.2-38. 
The mass balance for irreversibly adsorbed radionuclides on iron oxyhydroxide corrosion 
products accounts for decay and is given by: 
( ) ( ) irrev 
iCPFeOx i 
irrev 
ipCPFeOx 
M 
ip ip w i i CP b 
irrev 
iCPFeOx w C C r S C k s 
t 
C S . . f . 
f 
- + = 
. 
. 
. (Eq. 6.5.1.2-42) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-91 November 2004 
The source term in Equation 6.5.1.2-42, i i CP b C k s . , couples this equation to Equation 6.5.1.2-38. 
For a single continuum medium with no colloids or corrosion products present, 
Equation 6.5.1.2-38 reduces to the conventional advection/diffusion transport equation (with 
source and sink terms): 
( ) ( ) ( ) 
( ), fi i i fip ip 
M 
ip ip w 
iprecip id i w i i w 
i fi w 
R C R C r S 
Q Q C C D S 
t 
C R S 
. . f 
f 
f 
- + 
- +  . - .  . = 
. 
. 
q 
(Eq. 6.5.1.2-43) 
with the conventional retardation factors for radionuclide species i and parent species ip, 
respectively: 
w
dis b 
fi S
K R 
f 
. 
+ =1 (Eq. 6.5.1.2-44) 
and 
w
dips b 
fip S
K 
R 
f 
. 
+ =1 . (Eq. 6.5.1.2-45) 
Equations 6.5.1.2-38 (mass balance for dissolved and reversibly sorbed radionuclide species i), 
6.5.1.2-41 (mass balance for radionuclide species i irreversibly sorbed to iron oxyhydroxide 
colloids) and 6.5.1.2-42 (mass balance radionuclide species i irreversibly sorbed to iron 
oxyhydroxide corrosion products) are solved simultaneously for all radionuclides to obtain the 
dependent variables, i C , irrev 
icFeOx C , and irrev 
iCPFeOx C , the concentration of dissolved radionuclide species 
i, the concentration of species i irreversibly sorbed to iron oxyhydroxide colloids, and species i 
irreversibly sorbed to iron oxyhydroxide corrosion products, respectively. 
The initial conditions are 0 = = = irrev 
iCPFeOx 
irrev 
icFeOx i C C C for all i. Upstream of the waste form 
domain, all radionuclide concentrations are zero. Consequently, the upstream boundary 
maintains a zero flux condition. Radionuclide concentrations will remain zero until a waste 
package failure occurs. A treatment of the zero concentration boundary within the UZ is 
provided in Section 6.5.3.6. The radionuclides are released or mobilized within the waste form 
domain. Flow is expected to be predominately downward. Then the resulting transport will be 
in a downward direction from the waste form to the corrosion products, which will accumulate in 
the bottom of the waste container. From the corrosion products, the radionuclide will migrate 
down to the invert, and from there it will enter the UZ. The representation for the radionuclide 
transport is consequently a one-dimensional mass balance equation for radionuclide species. For 
the one-dimensional EBS radionuclide transport model (in the downward +z-direction), the 
specific discharge (Darcy velocity) vector, w q , is in the downward +z-direction only and is 
denoted by i q wz w q = , where i is a unit vector in the z-direction, and wz q is the scalar specific 
discharge in the z-direction (zero in the other two directions). In one dimension, the mass 
balance equations can be written as scalar equations and are summarized as follows. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-92 November 2004 
The one-dimensional mass balance equation describing transport of dissolved and reversibly 
sorbed radionuclide species i in (from Equation 6.5.1.2-38) is: 
[ ] 
( ) [ ] 
( ) [ ] 
( ) 
( ) ( ) [ ] 
( ) ( ) [ ] 
[ ]. 
1 
i fi i ip fip 
M 
ip ip w 
inter icGW icFeOx icWF intra icGW icFeOx icWF c 
inter i intra i d 
i 
embed 
i i i c cFeOx w CP b iprecip id 
i cGW dicGW cFeOx dicFeOx cWF dicWF wz 
i cGW dicGW cFeOx dicFeOx cWF dicWF c w 
i 
i w i fi w 
C R C R r S 
C C C C C C 
C C 
C C k s C S s Q Q 
C C K C K C K q 
z 
C C K C K C K 
z 
D S 
z 
z 
C D S 
z 
C R S 
t 
. . f
.
. 
. f . 
f 
f f 
- + 
+ + - + +  
-  
- + - - + 
+ + + 
.
. 
- 
.. 
. 
.. 
. + + 
.
. 
.
. 
+ 
.. 
. 
.. 
. 
. 
. 
.
. 
= 
.
. 
(Eq. 6.5.1.2-46) 
Similarly, the one-dimensional mass balance equation for irreversibly sorbed radionuclide 
species i on iron oxyhydroxide colloids (from Equation 6.5.1.2-41) is: 
( ) ( ) ( ) 
( ) ( ) [ ] 
( ). 
irrev 
icFeOx i 
irrev 
ipcFeOx 
M 
ip ip w 
inter 
irrev 
icFeOx intra 
irrev 
icFeOx c i i c cFeOx w 
irrev 
icFeOx wz 
irrev 
icFeOx c w 
irrev 
icFeOx w 
C C r S 
C C C k s C S 
C q 
z 
C 
z 
D S 
z t 
C S 
. . f 
. f 
f 
f 
- + 
-  + 
.
. 
- .. 
. 
.. 
. 
.
. 
.
. 
= 
. 
. 
(Eq. 6.5.1.2-47) 
The one-dimensional mass balance equation for irreversibly sorbed radionuclide species i on iron 
oxyhydroxide corrosion products is the same as Equation 6.5.1.2-42, since there is no advection 
or diffusion of corrosion products: 
( ) ( ) irrev 
iCPFeOx i 
irrev 
ipCPFeOx 
M 
ip ip w i i CP b 
irrev 
iCPFeOx w C C r S C k s 
t 
C S . . f . 
f 
- + = 
. 
. 
. (Eq. 6.5.1.2-48) 
The one-dimensional mass balance equation for waste form colloid transport (from 
Equation 6.5.1.2-36) is: 
( ) ( ) 
( ) ( ) [ ]. inter cWF intra cWF c cWFs 
cWF w cWF c w 
cWF w 
C C Q 
C 
z 
C 
z 
D S 
z t
C S 
-  + 
.
. 
- .. 
. 
.. 
. 
.
. 
.
. 
= 
. 
. 
. 
f 
f q 
(Eq. 6.5.1.2-49) 
Within the waste package, the media supporting transport are represented as single continua. In 
the UZ, however, the bulk medium is conceptualized as a dual continuum, characterized by two 
sets of local-scale properties unique to each continuum. Transport in the dual continuum media 
is represented by a mass balance equation for each continuum. The single invert continuum 
interfaces a dual continuum (fracture/matrix) UZ medium. Advective transport from the invert 
enters both the UZ fracture and matrix continua. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-93 November 2004 
The diffusive fluxes to the dual UZ continua are determined from the flux continuity at the 
interface. This requirement states that the diffusive flux exiting the invert domain is equal to the 
sum of the diffusive fluxes entering the two UZ continua. The diffusive flux split will depend on 
the diffusive properties in the invert domain and both UZ continua together with the 
concentration gradients across the interface. 
For discussion of the diffusive flux treatment at the invert/UZ interface consider a diffusive flux 
term, either aqueous or colloid flux, within the transport mass balance equation. Let interface z 
denote the spatial location of the invert/UZ interface. Then for interface z z < , the diffusive flux for 
radionuclide species i at a location within the invert domain is: 
z 
C D S iI 
iI wI I . 
. 
f , (Eq. 6.5.1.2-50) 
where I f is the porosity of the single-continuum invert domain. 
For interface z z > , the diffusive fluxes within the UZ matrix and UZ fracture media are, 
respectively, 
z 
C D S im 
im wm m . 
. 
f , (Eq. 6.5.1.2-51) 
z 
C 
D S if 
if wf f . 
. 
f . (Eq. 6.5.1.2-52) 
For the case with no advection, the mass transport via diffusion across this interface is coupled 
by the flux continuity condition at the interface: 
+ + - . 
. 
+ 
. 
. 
= 
. 
. 
z
C 
D S 
z 
C D S 
z
C D S if 
if wf f 
im 
im wm m 
iI 
iI wI I f f f , (Eq. 6.5.1.2-53) 
where 
- .
.
z 
and + .
.
z 
are the derivative from the left and the derivative from the right, respectively, at the interface. 
The waste form colloids are generated in the waste form domain and are transported in 
accordance with an advective/diffusive mass balance. The waste form colloid concentration is 
subject to stability constraints based on the local domain chemistry. The waste form colloids 
transport both reversibly sorbed radionuclide mass and embedded (irreversibly sorbed) 
radionuclide mass. The iron oxyhydroxide colloids exist in the corrosion products and invert 
domains, and their concentrations are dependent on the local domain chemistry. The iron 
oxyhydroxide colloids transport both reversibly sorbed and irreversibly sorbed radionuclide 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-94 November 2004 
mass; the irreversibly sorbed radionuclides are sorbed onto the surface of these colloids, rather 
than being embedded within the colloid matrix, as are the radionuclides associated with the 
waste form colloids. The ground water colloids exist in the corrosion products and invert 
domains, and their concentrations are dependent on the local domain chemistry. The ground 
water colloids transport only reversibly sorbed radionuclide mass. The iron oxyhydroxide 
corrosion products are immobile and found only in the corrosion products domain. These 
corrosion products support both reversibly sorbed and irreversibly sorbed radionuclide mass. 
Since corrosion products are immobile, all radionuclide mass sorbed to corrosion products is not 
transported but is retarded. 
All of the features of the EBS radionuclide transport abstraction are accounted for in 
Equations 6.5.1.2-38, 6.5.1.2-36, 6.5.1.2-41, and 6.5.1.2-42 (or the one-dimensional versions of 
these equations, Equations 6.5.1.2-46, 6.5.1.2-49, 6.5.1.2-47, and 6.5.1.2-48, respectively), 
including invert diffusion, retardation in the waste package, in-package diffusion, and transport 
facilitated by reversible and irreversible colloids. Implementation of these equations into 
TSPA-LA involves additional simplifications and restrictions that are discussed in Section 6.5.3. 
6.5.1.2.1 Mathematical Description of In-Package Diffusion Submodel for Commercial 
Spent Nuclear Fuel Waste Packages 
The objective of the in-package diffusion submodel is to quantify the uncertainty in the effective 
diffusion coefficient for diffusion of radionuclides through a breached waste package. Transport 
within the waste package can occur through advective or diffusive mechanisms. Advective 
transport occurs when a radionuclide, either as a dissolved species in an aqueous solution or 
attached to a colloidal particle, moves with a flowing fluid. Diffusive transport occurs when a 
radionuclide, either as a dissolved species in aqueous solution or attached to a colloidal particle, 
moves from a region of high concentration to a region of lower concentration in water that may 
be stagnant or flowing. Both advective and diffusive transport occur for those waste packages 
exposed to a seep environment in the repository. Only diffusive transport is anticipated to occur 
in those waste packages in the dry (no-seep) regions of the repository. In-package diffusion is an 
important process for release of radionuclides from the waste package, especially if no seepage 
occurs in large portions of the repository. This section provides a model to enable the impact of 
in-package diffusion on repository performance to be quantified. 
The focus in this submodel is on diffusive releases from CSNF waste packages in no-seep 
regions of the repository. In a no-seep environment, the water saturation inside the CSNF waste 
package is computed as a function of relative humidity. In a seep environment, the water 
saturation in a CSNF waste package is set to 1.0, and is not dependent on the relative humidity in 
the waste package. For HLW packages, the water saturation is set to 1.0 in both seep and 
no-seep environments independently of the relative humidity in the waste package. HLW 
packages are treated differently from CSNF waste packages because the hygroscopic nature of 
HLW glass will result in a comparatively high water saturation at lower relative humidities than 
for CSNF. 
In the EBS transport base model, the waste package is considered to be adjacent to the invert for 
purposes of calculating diffusive releases. This eliminates any resistance to diffusion between 
the waste package and the invert and maximizes estimated releases. If the first breaches are 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-95 November 2004 
stress corrosion cracks in the lid welds, the earliest diffusive path is through these cracks. The 
length of the diffusive path is taken to be the distance through the multiple lids on the waste 
package. This implies that the entire radionuclide inventory of the waste package is modeled as 
lying at the inside surface of the lid, which provides the maximum concentration gradient over a 
short distance, thereby maximizing calculated diffusive releases. 
In reality, the internal components of the waste package will degrade slowly over thousands of 
years, keeping much of the radionuclides suspended within a crumbling framework, but 
nevertheless well dispersed throughout much of the interior of the canister. Even in its fully 
degraded state, when all internal components are completely corroded, the interior will consist of 
a large mass of porous corrosion products slumped in the bottom of the breached waste package, 
with radionuclides dispersed throughout. This dispersion inside a waste package is simply the 
result of the steel baskets, side guides, and inner vessel corroding at a faster rate than the 
Zircaloy fuel rods and assemblies. Thus, the actual diffusive path length can be greater than just 
the thickness of the lids, which reduces the rate of diffusive releases in comparison to the model 
where the radionuclide source is modeled as being adjacent to the interior surface of the waste 
package. 
In a no-seep environment, the interior of a breached waste package will generally not be fully 
saturated with water. In this case, the only water present may be a thin film of adsorbed water 
that offers only a small diffusive area, which further hinders diffusive releases from the waste 
package. 
These two conditionsa longer diffusive path length and a much smaller cross sectional area for 
diffusioncan delay or reduce the rate of predicted diffusive releases of radionuclides from the 
waste packages, relative to the EBS transport base model. 
6.5.1.2.1.1 Conceptual Model for the Commercial Spent Nuclear Fuel In-Package 
Environment 
Fuel rods are expected to be robust because the Zircaloy cladding around the fuel pellets is 
corrosion-resistant; at 100C, the cladding remains intact for at least 100,000 years (CRWMS 
M&O 2000 [DIRS 136058], p. 48) barring damage from rockfalls. However, some fuel rods 
may be damaged while in use or during handling and shipping to the repository. A number of 
mechanisms cause fuel rod failure inside a reactor core, including damage from debris striking 
the rods, manufacturing defects, radiation-enhanced corrosion resulting in splitting of the rods, 
localized corrosion, and chafing where the rods contact the assembly spacer grids. Fuel rod 
cladding that has not failed (i.e., become perforated) is predicted to remain intact for the 
regulatory period (BSC 2004 [DIRS 170023], Section 1). Cladding that has failed is assumed to 
undergo instantaneous axial splitting after a waste package is breached (BSC 2004 
[DIRS 170023], Assumption 5.3), exposing the fuel to the environment. These failed rods 
release radionuclides through diffusion once a waste package is breached, when a continuous 
film of liquid water is assumed (Assumption 5.5) to cover all the internal components of the 
waste package. 
Baskets and guides support fuel rod assemblies inside a waste package for CSNF. These support 
components are fabricated from carbon steel and will begin to corrode once the waste package is 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-96 November 2004 
breached. Corrosion begins when the relative humidity is sufficient to produce aqueous 
conditions on the surface. The presence of deliquescent salts can result in aqueous conditions if 
the in-drift humidity is higher than the minimum deliquescent point of the salts (Campbell and 
Smith 1951 [DIRS 163817], p. 237). As the support components become thinner due to 
corrosion, they will weaken and eventually allow fuel rod assemblies to fall to the bottom of the 
waste package. 
Corrosion of the internal support components will increase the surface area for adsorption of 
water and increase the area for diffusive transport, resulting in greater diffusive releases from the 
waste package. The fuel rods could also be bent if sections of the support components fail 
sooner than other parts. This could result in enhanced rod failure rates, with a greater mass of 
radionuclides available to diffuse out of a waste package. 
The waste package inner vessel, made of Stainless Steel Type 316, has a long lifetime as 
computed from known general corrosion rates. However, the potential performance credit of the 
stainless steel inner vessel is not included in the nominal TSPA-LA analysis. As with the 
baskets and other waste form components (except for the fuel rods), the degradation of the inner 
vessel will provide additional surface area for adsorption of water and additional cross-sectional 
area for diffusion of radionuclides through the water film. 
6.5.1.2.1.2 Adsorption of Water Vapor in Commercial Spent Nuclear Fuel Waste 
Packages 
All surfaces exposed to water vapor will adsorb water. The amount of adsorbed water vapor 
depends principally on the nature of the material and the relative humidity. In many cases, the 
first layer of water adsorbed is chemically bound to the surface (McCafferty and 
Zettlemoyer 1971 [DIRS 154378], p. 239) and is difficult to remove except at high temperatures, 
higher than will exist in the repository. Subsequent layers are less tightly bound, being attracted 
simply by van der Waals forces to lower water layers. The first few layers of water often form 
an ice-like structure with little mobility. As the relative humidity approaches 100 percent, the 
outer layers of water begin to behave more like bulk liquid; at 100 percent relative humidity, 
bulk condensation of water occurs, forming a liquid phase. 
Except for inert metals such as gold and platinum, most metals form a passivating oxide surface 
layer when exposed to oxygen or water. Oxygen diffuses slowly through the oxide layer; the 
resistance to oxygen diffusion protects the metal underneath. In the case of Alloy 22, stainless 
steel, Zircaloy, and aluminummetals found in the waste package or waste formthe surface 
oxide layer is passivating. Thus, all metals in a waste package contain a surface oxide layer on 
which water adsorption takes place. 
Adsorption isotherms define the amount of water adsorbed as a function of relative humidity or 
relative pressure, provided sufficient time is allowed for equilibrium to be achieved. Extensive 
measurements have been made for a few substances, such as iron oxide and titanium oxide, but 
adsorption isotherms are only available for a few materials. Isotherms for metal oxides found in 
waste packages have been measured for NiO, Fe2O3, and ZrO2. Isotherms for other major 
components of stainless steel, such as Cr2O3 and Mo2O3, are not readily available. However, the 
oxides of iron, nickel, and zirconium make up the bulk of oxides in a package and are 
representative of in-package materials. Figure 6.5-4 presents the adsorption isotherms for Fe2O3, 
NiO, and ZrO2. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-97 November 2004 
Sources: Jurinak 1964 [DIRS 154381]; Lee 1994 [DIRS 154380]; Holmes et al. 1974 [DIRS 154379]. 
Figure 6.5-4. Comparison of Adsorption Isotherms for Water Vapor on Fe2O3, NiO, and ZrO2 
6.5.1.2.1.2.1 Iron Oxide Isotherm 
The isotherm for adsorption of water onto a-Fe2O3, a form of hematite, has been extensively 
measured and reported in the literature (McCafferty and Zettlemoyer 1970 [DIRS 154382]; 
Jurinak 1964 [DIRS 154381]). These measurements are directly relevant to the repository 
because (1) hematite will be the predominant form of iron oxide in a degrading waste package 
(YMP 1998 [DIRS 104441], p. C-23), and (2) hematite will comprise the bulk of the corrosion 
products in the waste package, because iron is the largest constituent of waste package internal 
components, as shown in Table 6.5-9 for the three major types of steel used in the 21-PWR 
waste package components. The contents of Table 6.5-9 are derived from compositional data 
presented in Table 4.1-10. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-98 November 2004 
Jurinak (1964 [DIRS 154381], p. 486) provides a functional relationship for the coverage 
(i.e., number of monolayers of water adsorbed) as a function of relative humidity based on the 
Frenkel-Halsey-Hill (FHH) equation for multilayer adsorption: 
( ) ( ) , 
/ 
/ log o 
10 s 
m 
w w V V 
k p p - = (Eq. 6.5.1.2.1-1) 
where 
w p = partial pressure of water (Pa) 
ow 
p = vapor pressure of water (Pa) 
k = FHH adsorption isotherm fitting parameter (dimensionless) 
s = FHH adsorption isotherm fitting parameter (dimensionless) 
V = volume of water vapor adsorbed at reference conditions (m3 H2O kg-1 Fe2O3) 
m V = volume of adsorbed water vapor that provides a one-monolayer coverage on the 
surface (m3 H2O kg-1 Fe2O3). 
The ratio of water vapor partial pressure to vapor pressure is the relative humidity (RH). The 
ratio of V to m V is the number of monolayers of water (i.e., the number of layers of individual 
water molecules) adsorbed on the surface, assuming complete and uniform coverage. Letting 
m a V V / = . and o / w w p p RH = , and making use of the relationship to convert base 10 logarithms 
to natural logarithms ( e RH e RH RH 
10 
ln 
10 10 log ln log log = = ), Jurinaks correlation may be 
written in general terms with parameters k and s: 
( ) , 
log 
ln 
10 e 
k RH s 
a . 
- = (Eq. 6.5.1.2.1-2) 
or ( ) [ ] . ln 
log 
/ 1 
1 
10 
s 
s 
a RH 
e 
k - - . .. . 
. .. 
. 
= . 
. 
(Eq. 6.5.1.2.1-3) 
For Fe2O3, k = 1.1 and s = 2.45 (Jurinak 1964 [DIRS 154381], p. 486): 
( ) 45 . 2 5328 . 2 ln - - = a RH . (Eq. 6.5.1.2.1-4) 
or 
( ) [ ] 40816 . 0 ln 461296 . 1 - - = RH a . . (Eq. 6.5.1.2.1-5) 
This isotherm is plotted in Figure 6.5-4. 
The average thickness of a monolayer of water can be computed from the cross-sectional area of 
a water molecule. Holmes et al. (1974 [DIRS 154379], p. 368) use a value of 10.6 2 for the 
cross-sectional area of a water molecule. Jurinak (1964 [DIRS 154381]) assumes a 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-99 November 2004 
cross-sectional area of 10.8 2 for a water molecule. McCafferty and Zettlemoyer (1970 
[DIRS 154382], p. 453) report a single value of 10 m2 g-1 for nominal argon surface area and 
assume a cross-sectional area of the water molecule of 10.6 2. Gregg and Sing (1982 
[DIRS 153010], p. 188) state that a close-packed monolayer of water corresponds to a figure 
of 10.5 2 for the cross-sectional area of a water molecule. In this report, a value for the 
cross-sectional area of a water molecule of = w A 10.6 2 per molecule (McCafferty and 
Zettlemoyer 1970 [DIRS 154382], p. 454) is used. Using a water density at 25C of 
= w . 997.0449 kg m-3 (Weast 1985 [DIRS 111561], p. F-5), the thickness of a water 
monolayer, , f t is: 
m, 10 83 . 2 
mol 
molec 10 02214199 . 6 
m
kg 0449 . 997 
molec 
m 10 6 . 10 
mol 
kg 10 01528 . 18 
10 
23 
3 
2 
20 
3 
- 
- 
- 
 = 
.. 
. 
.. 
.  .. 
. 
.. 
. 
. .. 
. 
. .. 
. 
 
 
=
= 
A w w 
w 
f N A 
M t 
. 
(Eq. 6.5.1.2.1-6) 
where A N is Avogadros number (Lide 2002 [DIRS 160832], p. 1-7), and w M is the molecular 
weight of water (kg mol-1). 
At 50C, the density of water is 988.0363 kg m-3 (Weast 1985 [DIRS 111561], p. F-5) and the 
adsorbed water monolayer thickness is 2.85  10-10 m, which shows that the monolayer thickness 
sensitivity to temperature is small. 
The adsorption isotherm for water vapor on ZrO2 at 25C (Holmes et al. 1974 [DIRS 154379], 
p. 367, Figure 3) is shown in Figure 6.5-4 as monolayers of water adsorbed; Table 6.5-5 lists the 
same data, taken from Figure 3 of Holmes et al. and given in units of mg water adsorbed 
g-1 ZrO2. The conversion from mg g-1 to monolayers adsorbed is made using 14.5 m2 g-1 for 
specific surface area (Holmes et al. 1974 [DIRS 154379], p. 368; average of 2 values): 
/monolayer 
ZrO g 
O H mg 092 . 4 
mol 
molecule 10 0221419947 . 6 
molecule 
m 10 10.6 
mol
O H mg 10 01528 . 18 
ZrO g 
m 5 . 14 
2 
2 
23 
2 
20 - 
2 3 
2 
2 
= 
.. 
. 
.. .  . .. . 
. .. 
. 
 
.. 
. 
.. 
.  . .. 
. 
. .. 
. 
. 
(Eq. 6.5.1.2.1-7) 

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ANL-WIS-PA-000001 REV 01 6-100 November 2004 
Table 6.5-5. Adsorption of Water on ZrO2 at 25C, Outgassed at 500C 
RH Water Adsorbed on ZrO2 (mg g-1) 
0.010 5.54 
0.050 6.92 
0.100 7.76 
0.150 8.53 
0.200 9.12 
0.300 10.4 
0.400 11.52 
0.500 12.80 
0.600 14.56 
0.658 16.00 
0.700 17.81 
0.784 24.00 
0.840 32.00 
0.880 40.00 
0.917 48.00 
0.947 56.00 
Source: Holmes et al. 1974 [DIRS 154379], p. 367; taken from Adsorption 
curve on Figure 3. 
6.5.1.2.1.2.2 Behavior of Thin Water Films 
In this section, the behavior of thin films of water is described. It is assumed in the EBS RT 
Abstraction that continuous thin films of adsorbed water will cover all surfaces inside a breached 
waste package and that these films behave the same as bulk liquid (Assumption 5.5). In order to 
understand the bounding nature of this assumption and how it leads to overestimating releases of 
radionuclides from the EBS, it is necessary to understand the actual behavior of thin films. 
Water at solid surfaces varies in nature from a highly structured form on hydrophilic substrates 
to a loose, entropic form on more hydrophobic substrates possessing hydrophilic sites (Lee 1994 
[DIRS 154380], p. 74). The adsorption of water on solids depends on the capacity of the surface 
to orient the water dipoles, usually with the proton outward. Near polar surfaces of solids such 
as metal and oxides, the cause of the orientation of water molecules at the interface could be 
either hydrogen bonding or dipole-dipole interactions, depending on the chemical nature of the 
solid. Depending on the dissimilarity between the ordered (dipole-dipole), induced structure 
near the interface and the bulk structure, various thicknesses of the ordered layers are possible 
(Lee 1994 [DIRS 154380], p. 75). 
The structure of liquid water is considered to consist of unbonded molecules and of molecules 
hydrogen-bonded in clusters that have a mean size of about 90 molecules at 0C (Lee 1994 
[DIRS 154380], p. 79). At hydrophilic surfaces, such as oxides, the structure of water resembles 
that of ice (McCafferty and Zettlemoyer 1971 [DIRS 154378], p. 239). This behavior is 
attributed to the existence of a monolayer in which the adsorbed water is held rigidly to the solid 
surface at fixed sites. The first layer is localized by double hydrogen bonding of a single water 
molecule to two surface hydroxyls. This highly constrained first layer relaxes in the next layers, 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-101 November 2004 
where the water molecules start to possess a rotational degree of freedom, being singly 
hydrogen-bonded. The second layer becomes more ordered when hydrogen bonds to a third 
layer, and so on, until the ordering effect of the surface is overcome and bulk liquid layers form 
farther from the surface. On a hydrophobic surface, such as silica, different behavior is 
observed. When half of the surface hydroxyls on silica are occupied by water, the water starts to 
agglomerate into clusters instead of adsorbing uniformly over the surface. 
Layers of water adsorbed on an oxide surface can promote lateral ion movement, which sets up 
localized electrochemical cells due to inhomogeneities in the underlying metal (Lee 1994, 
[DIRS 154380] p. 141). Such cells promote localized corrosion. Surface water dipoles may act 
to shield oxygen ions from an internal field that promotes ion movement. On the other hand, the 
gel-like structure of a metal oxyhydroxide may not support the charge separation that normally 
accounts for the field-driven process. Instead, ion movement may take place under the influence 
of a concentration gradient. The first layers of adsorbed water often do not contain ions from the 
solid (Lee 1994 [DIRS 154380], p. 73). This says that multiple water layers are needed in order 
for solid species (such as radionuclides) to dissolve and diffuse. 
6.5.1.2.1.3 Specific Surface Areas of Component Materials 
6.5.1.2.1.3.1 Specific Surface Area for Metal Oxides 
Most studies of the nature of adsorbed water at solid surfaces have been done with solid powders 
whose specific surface area is at least 5 m2 g-1. Such high interfacial areas are required for 
sufficient sensitivity in the measurements of adsorbed mass using routine gravimetric techniques. 
However, the use of surface areas of 10 to 20 m2 g-1 typical of the samples used in adsorption 
studies for Fe2O3 and ZrO2 results in predicted quantities of adsorbed water being larger than 
might be realistically expected for materials with lower specific surface area such as hematite 
corrosion products, resulting in an overestimation of the amount of radionuclides released by 
purely diffusive mechanisms. 
Values for the specific surface area of a-Fe2O3 (hematite) shown in Table 6.5-6 range from 
1.8 to 21.4 m2 g-1. At the low end is natural hematite, with a specific surface area of 1.8 m2 g-1 
(Langmuir 1997 [DIRS 100051], Table 10.2). At the high end is a sample of Fe2O3 used in an 
analysis of its catalytic activity (Briand et al. 2001 [DIRS 161617], Table 4). Morimoto et al. 
(1969 [DIRS 162877], Table I) and Tamura et al. (1999 [DIRS 161625], Table 1) each report 
two values for Fe2O3 samples prepared by different methods that differ by factors of 1.5 and 2.8, 
respectively. These results illustrate how the method of preparation can have a large effect on 
the specific surface area of a material. Gregg and Sing (1982 [DIRS 153010], p. 188) report 
surface area measurements of a material identified only as iron oxide by mercury porosimetry 
and by nitrogen adsorption. 
Jurinak (1964 [DIRS 154381], p. 480) measured surface area of Fe2O3 by nitrogen adsorption 
ranging from 9.60 to 9.70 m2 g-1, whereas water adsorption surface areas ranged from 6.52 to 
9.10 m2 g-1. It was concluded that about one-third of the Fe2O3 is covered with chemisorbed 
water that, unless removed by activation (i.e., heating to at least 425C), blocks water adsorption 
sites on the surface. The latter value (9.10 m2 g-1) is used in sample calculations in the EBS RT 
Abstraction, because it is consistent with the water adsorption isotherm of Jurinak that is used. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-102 November 2004 
The value of 10.0 m2 g-1 reported by McCafferty and Zettlemoyer (1970 [DIRS 154382], p. 453) 
is close to that of Jurinak and is consistent with their water adsorption isotherm, which is used in 
Section 7.2.1 to corroborate the isotherm of Jurinak (1964 [DIRS 154381]). 
The specific surface area of Fe2O3 plays an important role in the EBS radionuclide transport 
abstraction because all corrosion products are assumed to be hematite (Assumption 5.6). It is 
appropriate to account for the uncertainty in the measured values of the specific surface area by 
sampling the value. A range from 1.0 m2 g-1 to 22 m2 g-1 covers the range of observed values. A 
uniform distribution is assigned to this parameter in order to achieve an unbiased sampling of the 
full range of variability. 
In example calculations in Section 6.5.1.2.1 (e.g., Tables 37 and 38), a value of 9.1 m2 g-1 
obtained by Jurinak (1964 [DIRS 154381], p. 480) is generally used in order to be consistent 
with the water vapor adsorption isotherm of Jurinak that is used in the in-package diffusion 
submodel. However, it is appropriate in the in-package diffusion submodel to use any value of 
specific surface area for Fe2O3 within the range specified for this uncertain parameter. 
Table 6.5-6. Specific Surface Area of Fe2O3 
Specific Surface Area (m2 g-1) Source 
9.1 Jurinak 1964 [DIRS 154381], p. 480 
10 McCafferty and Zettlemoyer 1970 [DIRS 154382], p. 453 
13.3  14.3 Gregg and Sing 1982 [DIRS 153010], Table 3.17 
21.4 Briand et al. 2001 [DIRS 161617], Table 4 
14.5 Morimoto et al. 1969 [DIRS 162877], Table I (treated at 250C; from 
calcinations of FeSO4.7H2O) 
21.2 Morimoto et al. 1969 [DIRS 162877], Table I (treated at 250C; from 
calcinations of a-FeOOH) 
15.9 Tamura et al. 1999 [DIRS 161625], Table 1 (NaOH method) 
5.60 Tamura et al. 1999 [DIRS 161625], Table 1 (Grignard method) 
1.8 Langmuir 1997 [DIRS 100051], Table 10.2 (natural hematite) 
3.1 Langmuir 1997 [DIRS 100051], Table 10.2 (synthetic hematite) 
For ZrO2, Holmes et al. (1974 [DIRS 154379], pp. 367 to 368) measured specific surface areas 
by nitrogen adsorption and by argon adsorption; the average value was 14.5 m2 g-1. 
The products of the corrosion of all internal waste package components except for fuel rods and 
SNF are assumed to be Fe2O3 (hematite) (Assumption 5.6). The bulk of the mass of materials in 
a CSNF waste package, excluding the SNF itself and the outer corrosion barrier of the waste 
package, consists of various types of steel. The iron content of these steels (see Table 6.5-9 
below) ranges from 61.935 weight percent (Type 316, used in the inner vessel; 
DTN: MO0003RIB00076.000 [DIRS 153044]) to 98.37 weight percent (A 516 carbon steel, 
used in the basket components; DTN: MO0107TC240032.000 [DIRS 169970]). It is thus 
reasonable to treat all corrosion products as iron oxide, specifically Fe2O3 (hematite), for which 
specific surface area and adsorption data are readily available. The specific surface areas of 
some other waste package component corrosion products are shown in Table 6.5-7, which 
demonstrates that the bulk of corrosion products exhibit similar adsorption characteristics. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-103 November 2004 
Table 6.5-7. Specific Surface Area of Various Waste Package Corrosion Products 
Corrosion 
Product 
Specific Surface 
Area (m2 g-1) Source 
3.0 Briand et al. 2001 [DIRS 161617], Table 4 
1.09 Tamura et al. 1999 [DIRS 161625], Table 1 
Cr2O3 
12.0 Nagao et al. 1995 [DIRS 162878], p. 222 
1.1 Briand et al. 2001 [DIRS 161617], Table 4 NiO 
22.4 Matsuda et al. 1992 [DIRS 154383], p. 1839 
[for NiO(II)] 
CoO 0.4 Briand et al. 2001 [DIRS 161617], Table 4 
MoO3 5.0 Briand et al. 2001 [DIRS 161617], Table 4 
UO2 
(SNF) 
0.4 BSC 2004 [DIRS 167618], Table 6-9 (Group 
8b) 
TiO2 9.94 Morimoto et al. 1969 [DIRS 162877], Table I 
14.5 Holmes et al. 1974 [DIRS 154379], p. 368; 
average of 2 values 
ZrO2 
39.0 Briand et al. 2001 [DIRS 161617], Table 4 
6.5.1.2.1.3.2 Interior Surface Area for Commercial Spent Nuclear Fuel Waste 
Package 
The internal surface area of an as-emplaced waste package (i.e., in an undegraded state) 
containing CSNF can be approximated if the dimensions and numbers of fuel rods, baskets, side 
guides, and other support components are known. Since the surface area will increase by orders 
of magnitudes as the waste package components degrade, the initial surface area is useful only as 
a limiting value, but one that can be estimated accurately (unlike the surface area of corrosion 
products). Typical measurements for a 21-PWR waste package are used (BSC 2004 
[DIRS 169472], Table 1). The surface areas of fuel assembly spacer grids and end connections 
are ignored. The total internal surface area of a 21-PWR waste package as emplaced is 
approximately 1061 m2. The surface area of basket components is computed as shown in 
Table 6.5-8 (footnote h) by dividing the total mass of each component by the density of the 
material (which gives the volume of material), then dividing by the thickness of the component. 
This results in the area of component material as though it were a plate, ignoring the area of 
edges. To account for both sides of the component being exposed to air and able to adsorb 
water, the area is multiplied by two. 
The calculation of pore volume for a CSNF waste package is also summarized in Table 6.5-8. 
From these results, the initial porosity of an average 21-PWR waste package is determined to be 
5.63/9.62 = 0.58. 

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Table 6.5-8. Characteristics of a 21-PWR Waste Package 
Component Dimensionsa 
Qty. in 
WPb 
Massb 
(kg) 
Density 
(kg m-3) 
Total 
Surface 
Area (m2) 
Total 
Volumej 
(m3) 
Fuel Rods 0.94996 cm ODc; 
384.962 cm lengthc 5,544   636.93 1.513 
Basket Side Guide 9.525 mm thickness 16 24.9 7,850d 10.66h 0.051 
Basket Side Guide Stiffener 9.525 mm thickness 32 0.615 7,850d 0.53h 0.003 
Basket End Side Guide 9.525 mm thickness 32 32.7 7,850d 27.99h 0.133 
Basket End Guide Stiffener 9.525 mm thickness 64 1.38 7,850d 2.36h 0.011 
Basket Corner Guide 9.525 mm thickness 16 40.1 7,850d 17.16h 0.082 
Basket Corner Guide Stiffener 9.525 mm thickness 32 2.07 7,850d 1.77h 0.008 
Fuel Basket A-Plate 7 mm thickness 8 86.8 7,760e 25.57h 0.089 
Fuel Basket B-Plate 7 mm thickness 8 86.8 7,760e 25.57h 0.089 
Fuel Basket C-Plate 7 mm thickness 16 45.8 7,760e 26.98h 0.094 
Fuel Basket D-Plate 6.35 mm thickness 8 27.4 2,700f 25.57h 0.081 
Fuel Basket E-Plate 6.35 mm thickness 8 27.4 2,700f 25.57h 0.081 
Basket Tube 4,572 mm lengthl; 
231.648 mm interior 
dimensionk; 
241.173 mm exterior 
dimensionm 
21 159 7,850d 181.59 0.425 
Inner Vessel 1.4859 m IDk; 
1.5875 m ODk; 
4.5847 m cavity lengthl 
1 9,920 8,000g 49.10 1.240 
Inner Lid 1.4859 m vessel IDk 
0.0508 m thicknessn 1 739 8,000g 3.37 0.088 
Total Surface Area 1,061  
Total Volumei  9.62 
Total Solids Volume  3.99 
Total Void Volume  5.63 
a Thicknesses from BSC 2004 [DIRS 169472], Table 2. 
b Quantity (number) and mass of components in a 21-PWR waste package from BSC 2004 [DIRS 169472], Table 2. 
c DOE 1992 [DIRS 102588], Volume 1, p. 2A-30. 264 rods/assembly. W1717WL chosen as average assembly. 
d ASTM A 20/A20M-99a [DIRS 147578] (A 516 carbon steel). 
e Kgler 1996 [DIRS 107760], p. 17 (Neutronit A 978). 
f ASTM G 1-90 [DIRS 103515], p. 7, Table X1 (Al 6061). 
g DTN: MO0003RIB00076.000 [DIRS 153044] (316 stainless steel). 
h Surface Area = 2mN/(..x); m = mass (kg); N = quantity; . = density (kg m-3); .x = thickness (m); 2 accounts for 
2 sides of a plate; edges ignored. 
I Volume enclosed by Alloy 22 outer corrosion barrier having an inside diameter of 1.597 m (BSC 2004 
[DIRS 166953], Section B-B) and inside length of 4.80374 m = 5,024.4 mm (total length, BSC 2004 
[DIRS 166953], Section A-A)  25.4 mm (lid lifting device thickness, BSC 2004 [DIRS 167394], Detail C)  
101.6 mm (bottom skirt, BSC 2004 [DIRS 167394], Detail B)  25.4 mm (top outer lid thickness, BSC 2004 
[DIRS 167394], Detail A)  25.4 m (bottom outer lid thickness, BSC 2004 [DIRS 167394], Detail B)  30.16 mm 
(middle lid to outer lid gap, BSC 2004 [DIRS 167394], Detail A)  12.7 mm (middle lid, BSC 2004 [DIRS 167394], 
Detail A). 
j Except for fuel rod volume, Volume = mN/.. See footnote h for nomenclature. 
k BSC 2004 [DIRS 166953], Section B-B. 
l BSC 2004 [DIRS 166953], Section A-A. 
m Outside dimension = inside dimension + 2  thickness = 9.12 in. (BSC 2004 [DIRS 166953], Section B-B) + 
2  3/16 in(BSC 2004 [DIRS 169472], Table 2) = 231.648 mm + 2 (4.7625 mm) = 241.173 mm. 
n BSC 2004 [DIRS 167394], Details A and B. 
ID = inside diameter; OD = outside diameter; WP = waste package 

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ANL-WIS-PA-000001 REV 01 6-105 November 2004 
An estimate of the waste package porosity in a fully degraded state can be obtained using the 
total potential equivalent mass of Fe2O3 in a 21-PWR from the corrosion of non-SNF 
components as shown in Table 6.3-4. The 19,440 kg equivalent mass of corrosion products from 
the iron comprising the steel internal components has a volume of (density of Fe2O3 from Weast 
(1985 [DIRS 111561], p. B-104): 
3 2 
3 
3 2 
3 
3 2 
3 2 O Fe m 710 . 3 
O Fe m 
O Fe kg 
5240 
O Fe kg 19440 = . (Eq. 6.5.1.2.1-7a) 
The internal volume of a 21-PWR waste package outer corrosion barrier, with an inside diameter 
of 1.597 m and length of 4.8038 m, is 9.62 m3 (from Table 6.5-8). The 5,544 fuel rods have a 
total volume of 1.513 m3. Then the void volume that can be occupied by corrosion products 
is 8.110 m3. If the corrosion products are uniformly dispersed throughout that volume, their 
porosity is: 1 - (3.710/8.110) = 0.54. 
Lamination and flaking of corrosion products is expected to redistribute this material within the 
waste package pore space (Knight 1982 [DIRS 106733], p. 50), rather than leave it uniformly 
distributed throughout the waste package void volume. If the oxide settles to the bottom of a 
waste package, the physical geometry of the granular iron oxide that has settled can be 
represented by that of tightly packed sand, which has a solid content of 58 percent (Brown and 
Richards 1970 [DIRS 131479], Table 2.2), or a porosity of 0.42 (CRWMS M&O 1997 
[DIRS 102824], p. 29). This value (0.42) for corrosion products porosity within a waste package 
has been used in criticality studies (CRWMS M&O 1997 [DIRS 102824], p. 29) and in an 
independent performance assessment of the Yucca Mountain repository (EPRI 2000 
[DIRS 154149], p. 6-21 to 6-22). A porosity of 0.4 has been used in other criticality studies 
(YMP 1998 [DIRS 104441], p. C-23 to C-25) and in a model of diffusive releases from breached 
waste packages (Lee et al. 1996 [DIRS 100913], p. 5-67). A value of 0.4 is used for porosity of 
corrosion products in TSPA-LA. 
In the calculation shown in Table 6.5-8, all the fuel rods are intact. The surface area of intact 
fuel rods accounts for about 62 percent of the total initial surface area. SNF pellets are generally 
highly fractured and can contribute to the surface area available for adsorption when a waste 
package is first breached. However, water adsorbed on the fuel itself constitutes the rind water 
(i.e., water in the conceptual waste form domain). It does not directly affect diffusion to the 
exterior of the waste package because the fuel is the source, rather than part of the corrosion 
products that comprise the diffusive path to the exterior. 
Over time, the surface area of steel corrosion products would be expected to increase relative to 
the surface area of ZrO2, since the cladding is predicted to degrade and fail at a slower rate than 
iron-based materials. In principle, the surface area inside a waste package can be computed as a 
function of time, if the degradation rates of the basket components and the stainless steel inner 
vessel and the failure rate of fuel rods are known. The calculation is complicated by the different 
compositions of each component of the waste package. Spatial variability in degradation rates 
due to variations in accessibility to water vapor further complicate the picture. For example, the 
fuel rod assemblies in 44-BWR waste packages are enclosed in flow tubes that provide added 

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ANL-WIS-PA-000001 REV 01 6-106 November 2004 
protection from corrosion over 21-PWR fuel rod assemblies. However, an average corrosion 
rate for a 21-PWR waste package provides a reasonable approximation from which surface areas 
and quantities of adsorbed water can be computed. 
The complete degradation of a 21-PWR waste package gives an estimated upper bound on the 
surface area available for adsorption. For this bounding estimate, the assumption is made that all 
corrodible material inside a 21-PWR waste package completely oxidizes to Fe2O3. The mass of 
each major component for four types of waste package is listed in Table 6.3-4. The amounts and 
composition of each waste package component are converted to total moles of material in 
Table 6.5-9. 
The masses of materials differ little between the two types of waste packages for commercial 
SNF (21-PWR and 44-BWR), and all other types of packages comprise a much smaller fraction 
of the total waste in the repository. Therefore, the calculation is performed for the 21-PWR 
waste package as representative of all packages in the repository. Suppose that the stainless steel 
inner vessel fully corrodes, but that the Alloy 22 outer corrosion barrier remains intact (except 
for breaches, the sizes of which are neglected). Also suppose that the Zircaloy fuel claddings 
and assembly grid spacers do not degrade because the Zircaloy will remain uncorroded for tens 
of thousands of years after the steel has fully corroded. 
Based on the elemental composition of each material shown in Table 6.5-9, the mass of each 
material listed in Table 6.5-8 is converted to moles by element. The moles of material, now 
considered to be iron, are summed, and the stoichiometrically equivalent amount of Fe2O3 in the 
waste package is determined. Using the measured surface area of Fe2O3, the total surface area 
for adsorption is calculated for the basket materials and inner vessel. This value provides an 
upper bound estimate for the surface area for adsorption in a completely degraded waste 
package. 
The total amount of material in a 21-PWR waste package (treated as though it were iron) is 
346,330 mol (see lower right-hand entry in Table 6.5-9). This iron will oxidize to 27,700 kg 
Fe2O3. Using a specific surface area of 9.1 m2 g-1 for the oxide (Jurinak 1964 [DIRS 154381], 
p. 480), the estimated upper bound for total surface area for adsorption in a 21-PWR waste 
package is 2.5  108 m2/package. 
This approach differs from that used to estimate retardation in the waste package in that the latter 
used only the actual iron content of waste package components to determine the adsorptive 
capacity of corrosion products. Both approaches are bounding for their intended purposes. For 
the retardation calculation, the mass of sorbant in the waste package is underestimated, which in 
turn underestimates the amount of retardation that occurs in the waste package, maximizing the 
releases of radionuclides. For in-package diffusion, the surface area for adsorption of water is 
overestimated, resulting in an overestimation of diffusive releases. The higher estimate of total 
corrosion products mass is used in this section to analyze the relationship between corrosion 
products mass and waste package water saturation. However, for consistency, the mass 
developed for modeling in-package retardation (19,440 kg; see Table 6.3-4) is used in the EBS 
transport abstraction. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-107 November 2004 
The surface area of the interior of a waste package at any particular time is estimated by 
interpolating between the surface area when the waste package is initially breached and the area 
at the time when the internal components are fully corroded. The latter is the estimated lifetime 
of each component that is determined by dividing the thickness of each component by the 
corrosion rate of the material that makes up the component under some given conditions. 
For simplicity, the components are considered to be composed of either stainless steel or carbon 
steel. The maximum thickness of stainless steel in the interior of a waste package is 5 cm, which 
is the thickness of the inner vessel (BSC 2004 [DIRS 169472], Table 1; BSC 2004 
[DIRS 166953], Section B-B). The maximum thickness of any carbon steel component is 
10 mm (BSC 2004 [DIRS 169472], Table 1). 
The corrosion rates for the two types of steel are known with some uncertainty, as shown by the 
data presented in Table 4.1-1 for carbon steel and for stainless steel 
(DTN: MO0409SPAACRWP.000 [DIRS 172059]). The data set used is for corrosion rates at 
60C in simulated dilute well J-13 water. The average corrosion rate for carbon steel is 
77.43 m yr-1, with a standard deviation of 8.83 m yr-1 (DTN: MO0409SPAACRWP.000 
[DIRS 172059]). An empirical cumulative distribution function developed in 
DTN: MO0409SPAACRWP.000 [DIRS 172059] is used for parameter CS_Corrosion_Rate to 
be sampled in TSPA-LA. The TSPA-LA implementation in GoldSim requires that the 
cumulative distribution functions (CDFs) cover the entire range of probabilities of 0.0 to 1.0. To 
accommodate this, another row for the zeroth percentile is added using a corrosion rate that is 
slightly lower than the minimum in the empirical cumulative distribution function (ECDF); this 
row is 65.76 m yr-1 and zero probability. 
The mean corrosion rate for Stainless Steel Type 316L is 0.248 m yr-1, with a standard 
deviation of 0.146 m yr-1 (DTN: MO0409SPAACRWP.000 [DIRS 172059]). The data set used 
is for corrosion rates in fresh water for the temperature range of 50C to 100C. An ECDF 
developed in DTN: MO0409SPAACRWP.000 [DIRS 172059] is used for parameter 
SS_Corrosion_Rate to be sampled in TSPA-LA. As with carbon steel, the TSPA-LA 
implementation in GoldSim requires that the CDFs cover the entire range of probabilities of 
0.0 to 1.0. To accommodate this, another row for the zeroth percentile is added using a corrosion 
rate that is slightly lower than the minimum in the ECDF; this row is 0.03699 m yr-1 and zero 
probability. 
From these rates and the thicknesses of the steel components, the lifetime of each type of steel is 
computed. From Table 6.3-4 above, carbon steel comprises about one-third of the total mass of 
steel in a CSNF waste package (30 percent in a 21-PWR; 33 percent in a 44-BWR). Based on 
this fraction, the surface area is interpolated over time. More details of the implementation of 
this interpolation scheme are presented in Section 6.5.3.2. 
Although this interpolation provides a reasonable means for approximating the surface area of 
the interior of a waste package over time as it degrades, there is still uncertainty as to the actual 
surface area. The corrosion rates themselves are uncertain. In addition, many factors affect the 
surface area of the corrosion products. The chemical and physical conditions under which 
corrosion takes place impacts the morphology of the corrosion products. Seismic occurrences 
and collapse of the internal components as they degrade will affect the surface area. The 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-108 November 2004 
hematite samples used in adsorption isotherm measurements are typically finely ground and 
highly purified, and have a higher specific surface area than typical corrosion products. At the 
same time, the morphology of corrosion products inside a waste package over the course of 
thousands of years is so uncertain that specific surface areas higher than purified hematite are 
possible. 
Therefore, when the surface area of the corrosion products is computed, it is justifiable to factor 
in this uncertainty by using a sample specific surface area for corrosion products, ranging from 
1.0 m2 g-1 to 22 m2 g-1. This range is large enough to reflect the uncertainty in the condition of 
the corrosion products. It reflects the uncertainty observed in measurements of the specific 
surface area of hematite (Table 6.5-6), as well as the fact that iron oxides do not adhere to the 
metal surface and may slough off in a finely divided state. Swelling as oxygen is incorporated 
into the crystal structure may provide a mechanism for breaking up the corrosion products more 
finely. Under certain conditions, iron oxyhydroxide colloid particles (0.001 to 1 m) having a 
potentially enormous surface area may form in the waste package (BSC 2004 [DIRS 170025], 
Section 6.3.1.3). At the same time, in such a static environment as an enclosed waste package, 
where, as is the case here, no water is flowing through the waste package to stir up or erode the 
corrosion products, it is unlikely that such finely divided materials will form. The range attempts 
to account for the absence mechanisms that actively break up the mass of corrosion products, the 
lack of water with which to suspend and move particles apart, and the possibility that swelling 
against enclosures may agglomerate particles into low-surface-area masses. 
Table 6.5-9. Elemental Composition of Each Waste Package Material in a 21-PWR 
Stainless Steel 
Type 316 A 516 Steel Neutronit A 978 Aluminum 6061 Total 
Material 
Mass 10,800 kg 5,600 kg 2,120 kg 440 kg 
wt% a mol wt% b Mol wt% c mol wt% d mol mol 
Fe 61.935 119,780 98.37 98,630 66.06 25,100 0.7 60 243,570 
Mo 3.00 3,380 0 0 2.2 490 0 0 3,860 
Cr 18.00 37,390 0 0 18.5 7,550 0.35 30 44,970 
Ni 14.00 25,760 0 0 13.0 4,700 0 0 30,460 
Al 0 0 0 0 0 0 95.85 15,570 15,570 
Other 3.065 5,930 1.63 1,630 0.24 90 3.1 240 7,900 
Total 100 192,240 100 100,260 100 37,930 100 15,900 346,330 
Source: Material mass: Table 6.3-4. 
NOTE: Other is treated as iron. 
aComposition: DTN: MO0003RIB00076.000 [DIRS 153044]. 
bComposition: DTN: MO0107TC240032.000 [DIRS 169970]. 
cComposition: Kgler 1991 [DIRS 155761], p. 15. 
dComposition: ASM 1979 [DIRS 154085], p. 115. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-109 November 2004 
6.5.1.2.1.4 Cross-Sectional Areas, Diffusion Path Lengths, and Effective Diffusivity 
6.5.1.2.1.4.1 Diffusion Coefficient in the Waste Package 
The rate of diffusion of radionuclide species i, i q (kg i s-1), from a waste package to the exterior 
is given by: 
, 
x 
C A D 
x 
C A D q 
i 
s 
i 
s i 
. 
. 
-  
. 
. 
- = 
(Eq. 6.5.1.2.1-8) 
where 
s D = the effective diffusion coefficient (m2 s-1) 
A = the cross-sectional area of the diffusive pathway (m2) 
i C = the concentration of the radionuclide (kg m-3) 
x = the length of the path (m). 
Note that the effective diffusion coefficient, Ds, as defined and used in this section, implicitly 
includes the effects of porosity, saturation, and tortuosity. The amount of water vapor that 
adsorbs on a surface is determined from the iron oxide adsorption isotherm discussed in 
Section 6.5.1.2.1.2.1. This provides the thickness of the water film. To calculate the 
cross-sectional area of the pathway, the width of the water film is also needed. Because of the 
difficulty in characterizing the waste, both initially and after it degrades, calculation of this width 
(and consequently, the cross-sectional area) is complex. The length of the diffusive path is also 
variable because the radionuclide sources may develop at random locations within a waste 
package and the path length will depend on the geometry of the film connecting the source to a 
breach. Finally, the effective diffusion coefficient itself depends on the complex interactions of 
source term composition, water chemistry, porosity, water saturation, and temperature, none of 
which can be characterized in a deterministic fashion. Thus, each term in the above equation 
s D , A, and .xneeds to be sampled, and a reasonable range and distribution for each has to be 
determined. All three terms are interrelated through the geometry used for the waste package 
interior, and all are effectively a function of relative humidity and time. 
Cross-Sectional Area of the Diffusive Pathway 
This section describes alternative methods for computing the cross-sectional area of the diffusive 
pathway. The area used for TSPA-LA calculations is presented in Section 6.5.3.1. 
In the simplest model, a single fuel rod fails in one location, a point source, and an adsorbed 
water film covers the fuel rod and provides direct connection to a breach. In this case, the 
cross-sectional area for diffusion, f A , is that of the film uniformly covering the cylindrical fuel 
rod. The thickness of the film is obtained from the adsorption isotherm of water vapor adsorbed 
on ZrO2 at the known relative humidity. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-110 November 2004 
Thus, 
( ) [ ] 
( ), 
2 
4 
0 
2 
0 
2 
0 
f f 
f f 
t d t 
d t d A 
+ = 
- + = 
p
p 
(Eq. 6.5.1.2.1-9) 
where 0 d is the outer diameter of the fuel rod (m) and f t is the adsorbed water film thickness 
(m). In this simple case, the minimum path length, .x, would be the shortest distance along a 
solid surface from a fuel rod to the exterior of a waste package. This minimum length is 7 cm, 
which is the combined thickness of the waste package outer corrosion barrier and inner vessel. 
The maximum value for .x would be the length of a fuel rod (151.560 in = 3.85 m; DOE 1992 
[DIRS 102588], Volume 1, p. 2A-30) plus the maximum distance from a fuel rod to the exterior 
(approximately the inside diameter of a waste package outer corrosion barrier, 1.597 m; 
BSC 2004 [DIRS 166953], Section B-B), for a total of 3.85 m + 1.597 m = 5.45 m. 
The adsorbed water film on ZrO2, as shown in Figure 6.5-4, is 10 monolayers thick at about 
88 percent relative humidity, the highest humidity value shown in Figure 6.5-4 for ZrO2. From 
Equation 6.5.1.2.1-6, the thickness of a water monolayer is f t = 2.83  10-10 m, so the water 
layer thickness at 88 percent relative humidity is 2.83  10-9 m, and the cross-sectional area on a 
0.94996-cm diameter fuel rod is: 
( )[ ] 
. mm 10 44 . 8 
m 10 44 . 8 
m 10 83 . 2 m 10 4966 . 9 m 10 83 . 2 
2 5 
2 11 
9 3 9 
-
- 
- - - 
 = 
 = 
 +   = p A 
(Eq. 6.5.1.2.1-10) 
This is a small area through which radionuclides can diffuse, and releases from a single failed 
rod would be negligible on the basis of this area alone. Even if the average 2.2 rods per 
assembly (EPRI 2001 [DIRS 100444], p. 4-1), or 46.2 rods per 21-PWR waste package, have 
failed prior to emplacement, the total cross-sectional area of adsorbed water films on fuel rods 
for a waste package is only 3.9  10-3 mm2. While this is small, it shows that a reasonable 
quantitative estimate of diffusive releases from a breached waste package can be obtained. 
Another approach to determining the cross-sectional area is to ignore the dispersion of water 
over all surfaces within a waste package. Suppose that all the water adsorbed on surfaces is 
collected into a tube, connecting the source to the exterior surface. As shown in Table 6.5-8 
above, the total initial surface area in a waste package is 1,061 m2. Most of the surfaces are 
oxidized steel, so it is appropriate to use the Fe2O3 adsorption isotherm. From 
Equation 6.5.1.2.1-5, at an example 95 percent relative humidity, the amount of water adsorbed 
is 4.91 monolayers. Using a monolayer thickness of 2.83  10-10 m, the water film is 
1.39  10-9 m thick. The total volume of adsorbed water is then 1.47  10-6 m3. If the length of 
the diffusion pathway is the total outside length of a waste package (4.8974 m, see in 
Table 6.5-11, Note e), then the cross-sectional area for diffusion is 3.00  10-7 m2 = 0.30 mm2, 
equivalent to a square about 0.55 mm on a side. This is a large area for diffusion, considering 
that diffusion will take place for thousands of years. Porosity, saturation, and tortuosity are 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-111 November 2004 
factors that would retard radionuclide transport, and these factors have been neglected in this 
approach. This is therefore a bounding estimate for cross-sectional area. 
At the other extreme in time and waste package condition, consider the cross-sectional area 
available when the interior of a waste package is fully degraded, at least to the extent that all 
iron-containing basket and inner vessel components have completely corroded. The Alloy 22 
outer corrosion barrier should still be largely intact at this point; a number of general corrosion 
patches will have penetrated the waste package, but it will still provide some overall structural 
support. By this time, a large number of fuel rods will have failed by localized corrosion or axial 
splitting, but the Zircaloy spacer grids will provide enough support to hold assemblies together 
and support assemblies collapsed on top of them. Interspersed throughout the assemblies are 
porous corrosion products. Under this condition, the source is dispersed throughout the waste 
package interior. Diffusion will occur through the porous medium in which all surfaces are 
coated with the thin film of adsorbed water. 
The cross-sectional area can be estimated for this degraded state. The fully degraded surface 
area is determined in Section 6.5.1.2.1.3.2 to be 2.5  108 m2. At an example 95 percent relative 
humidity, the film thickness is 1.39  10-9 m, so the diffusion area over a path the length of a 
waste package is 0.071 m2, equivalent to a square about 0.27 m on a side. This provides an 
upper bound on the cross-sectional area for diffusion in the waste package. 
A more realistic estimate must take into account the saturation and porosity of the corrosion 
products. For porous media such as soils, the diffusion coefficient is reduced by a tortuosity 
factor (a function of porosity and saturation) to account for the increased path length and 
decreased cross-sectional area of the diffusing solute in an unsaturated porous medium. In the 
absence of an advective flux and negligible vapor phase transport, one-dimensional transient 
diffusion is given by Ficks second law of diffusion (Bird et al. 1960 [DIRS 103524], p. 558): 
, 2 
2
x
C D 
t 
C 
s . 
. 
= 
. 
. 
(Eq. 6.5.1.2.1-11) 
where C is the concentration of a solute (kg m-3), and s D is the effective diffusion coefficient 
(m2 s-1). 
Archies Law 
Archies law, discussed in Section 6.3.4.1.1, gives the diffusion coefficient as a function of 
porosity and saturation in a partly saturated, granular medium as: 
, 2 3 . 1 
0 w s S D D f = (Eq. 6.5.1.2.1-12) 
where f is the porosity, and w S is the liquid saturation of the porous medium, and 0 D is the free 
water diffusion coefficient. Diffusion coefficient Ds is an effective value that implicitly includes 
the effect of porosity, saturation, and tortuosity in a porous medium. As such, it is defined 
differently from the coefficient Dmi defined in Section 6.5.1.2, which applies to a bulk liquid 
phase without modification for porosity, saturation, or tortuosity. The exponents in Archies law 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-112 November 2004 
are typical values, and will vary for different materials (Bear 1988 [DIRS 101379], p. 116). 
Whereas exponents of 1.863 are used for invert materials, based on experimental measurements 
of diffusion coefficients for crushed rock, the typical values (1.3 and 2) are used throughout this 
section to estimate in-package diffusion coefficients for corrosion products. 
Effective Water Saturation 
The effective water saturation, we S , is obtained from adsorption isotherms as a function of 
relative humidity. Per Assumption 5.6, all corrosion products are assumed to be Fe2O3. The 
water saturation is given by: 
, 2 
WP
N 
WP 
w 
we V
s
s V 
S 
. .
.
. 
. .
.
. 
= (Eq. 6.5.1.2.1-13) 
where 
w V = the volume of water adsorbed (m3 H2O kg-1 Fe2O3) 
WP V = the pore volume of a waste package (m3 pore volume) 
WP s = the surface area of a waste package (m2) 
2 N s = the specific surface area of the porous degraded waste form (m2 kg-1 Fe2O3). 
Since w V is normalized to the mass of Fe2O3, it must be multiplied by ( ) 2 / N WP s s to obtain the 
volume of water in an entire waste package. 2 / N w s V is the volume of water adsorbed per unit 
surface area, which is multiplied by the total surface area of the waste package to get the volume 
of water adsorbed in the entire waste package; it is divided by the pore volume of the waste 
package to obtain the saturation. 2 / N w s V is obtained from an FHH multilayer adsorption 
isotherm model (Jurinak 1964 [DIRS 154381], p. 486), shown in Section 6.5.1.2.1.2.1, that gives 
the fractional surface coverage, or number of monolayers a . covering a surface 
(Equation 6.5.1.2.1-1 with terms rearranged): 
, 
log 
1 . 1 45 . 2
1 
10 
. .. 
. 
. .. 
. - 
= = = 
RH m
m 
V
V 
m
a 
m
w 
a . (Eq. 6.5.1.2.1-14) 
where 
Vm = the volume of adsorbed water vapor that provides a one monolayer coverage on 
the surface (m3 H2O kg-1 Fe2O3) 
a m = the mass adsorbed per unit mass of adsorbent (kg H2O kg-1 Fe2O3) 
m m = the specific mass of one monolayer of adsorbate per unit mass of adsorbent (kg 
H2O kg-1 Fe2O3). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-113 November 2004 
The specific mass of a monolayer adsorbate on Fe2O3 is: 
. 
O Fe g 
O H mg 
57 . 2 
mol 
molecule 10 022 . 6 
molecule 
m 10 6 . 10 
g 1000 
kg 1 
mol
O H kg 
10 01528 . 18 
O Fe kg 
m 9100 
3 2 
2 
23 
2 
20 
2 3 
3 2 
2 
2 
= 
.. 
. 
.. 
.  . .. 
. 
. .. 
. 
 
. .. 
. 
. .. 
. 
.. 
. 
.. 
.  . .. 
. 
. .. 
. 
=
= 
- 
- 
A w 
w N 
m N A 
M s 
m 
(Eq. 6.5.1.2.1-15) 
Suppose that bulk liquid properties apply to the adsorbed water, in particular that the density of 
adsorbed water is equal to that of liquid water. Then 
w w a V m . = (Eq. 6.5.1.2.1-16) 
and 
m w m V m . = . (Eq. 6.5.1.2.1-17) 
Combining these expressions with the definition of a . , 
. 
2 
w w 
a 
A w 
w N 
a m a 
V
N A 
M s
m m 
. 
. 
. 
=
=
= 
(Eq. 6.5.1.2.1-18) 
Then the quantity ( ) 2 / N w s V needed for the saturation is: 
. 
log 
1 . 1 45 . 2
1 
10 
2 
. .. 
. 
. .. 
. - 
=
= 
RH N A
M 
N A
M 
s
V 
A w w 
w 
a 
A w w 
w 
N
w 
. 
. 
. 
(Eq. 6.5.1.2.1-19) 

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ANL-WIS-PA-000001 REV 01 6-114 November 2004 
Inserting this expression into we S gives the effective water saturation of the entire waste 
package: 
. 
log 
1 . 1 45 . 2
1 
10 
2 
. .. 
. 
. .. 
. - 
=
= 
RH N A
M 
V
s 
V
s 
s
V S 
A w w 
w 
WP 
WP 
WP 
WP 
N
w 
we 
. 
(Eq. 6.5.1.2.1-20) 
The parameters used in this expression include the surface area and void volume of the waste 
package. The surface area can vary over five orders of magnitude, from an initial value of 
1,061 m2 to a fully degraded state value of 2.5  108 m2. The initial void volume, as shown in 
Table 6.5-8, is 5.63 m3. This void volume will decrease and the surface area will increase as 
corrosion products form, since the oxides occupy greater volume and have a greater surface area 
than the metals from which they are formed. However, the change depends on time and extent 
of corrosion, so for simplicity the initial void volume is used for all times. To give some idea of 
the effect of water saturation on surface area, some values of saturation are listed in Table 6.5-10 
for various relative humidity values. The value used for the density of water is 988.0363 kg m-3 
at 50C. It is clear that the saturation can change enormously between the initial condition when 
the surface area is on the order of 1,000 m2 to the time when the steel components are fully 
degraded. 
Effective Diffusion Coefficient 
Inserting we S for w S in the expression for the diffusion coefficient, Equation 6.5.1.2.1-12, and 
using water density at 50C and the initial waste package porosity of 0.58 (Section 6.5.1.2.1.3.2, 
0 
2 
2 
3 . 1 
0 
2 3 . 1 
D 
N A
M 
V
s 
D S D 
a 
A w w 
w 
WP 
WP 
we s 
. 
. 
f
f 
. .. 
. 
. .. 
. 
=
= 
(Eq. 6.5.1.2.1-21) 
( ) . log 10 39 . 1 
log 
1 . 1 10 29 . 1 
0 
816 . 0 
10 
2 21 
0 
45 . 2
2 
10 
2 21 
D RH s 
D 
RH 
s D 
WP 
WP s 
- -
- 
-  = 
. .. 
. 
. .. 
. - 
 = (Eq. 6.5.1.2.1-22) 
For consistency with other uses of adsorption models, natural logarithms are used instead of base 
10 logarithms, using the relation: 
( ) e RH e RH RH 
10 
ln 
10 10 log ln log log - = - = - . (Eq. 6.5.1.2.1-23) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-115 November 2004 
Then the final expression for the diffusion coefficient is: 
( ) 0 
816 . 0 2 21 ln 10 75 . 2 D RH s D WP s 
- - -  = . (Eq. 6.5.1.2.1-24) 
Table 6.5-10 lists some values of 0 / D Ds using Equation 6.5.1.2.1-24 for initial and fully 
degraded state surface areas over a range of relative humidity values, showing the range of 
factors that impact the diffusion coefficient. Thus, initially, due to the low surface area available 
for water adsorption, the diffusion rate is negligibly small, whereas when the internal 
components of the waste package are fully corroded, the water saturation is sufficiently high that 
diffusive releases can be large. 
Table 6.5-10. Values of Effective Water Saturation and Diffusion Coefficient Normalized to the Diffusion 
Coefficient in Water for Waste Package Surface Areas and Relative Humidities (RH) 
Using Equation 6.5.1.2.1-24 
sWP = 1,061 m2 sWP = 2.5108 m2 
RH Swe Ds/D0 Swe Ds/D0 
0.1 5.6  10-8 1.6  10-15 0.013 8.7  10-5 
0.2 6.4  10-8 2.1  10-15 0.015 1.2  10-4 
0.3 7.2  10-8 2.6  10-15 0.017 1.5  10-4 
0.4 8.1  10-8 3.3  10-15 0.019 1.8  10-4 
0.5 9.1  10-8 4.1  10-15 0.021 2.3  10-4 
0.6 1.0  10-7 5.3  10-15 0.024 3.0  10-4 
0.7 1.2  10-7 7.1  10-15 0.028 4.0  10-4 
0.8 1.4  10-7 1.0  10-14 0.034 5.8  10-4 
0.9 2.0  10-7 1.9  10-14 0.046 1.1  10-3 
0.95 2.6  10-7 3.5  10-14 0.062 1.9  10-3 
0.99 5.1  10-7 1.3  10-13 0.12 7.3 10-3 
6.5.1.2.1.4.2 Diffusion Coefficient in General Corrosion Patches and Corrosion Products 
If radionuclide sources (i.e., failed fuel rods) are distributed uniformly throughout a waste 
package, then the source can be thought of as residing at the inside surface of the waste package, 
particularly if the inside of the package is largely degraded. In this case, the diffusive path is 
short: the distance through the breach in the outer corrosion barrier. The cross-sectional area for 
diffusion is the area of the water film covering the material that fills the corrosion patch. If the 
corrosion patch is mostly empty space, then diffusion must occur through a much smaller area 
around the perimeter of the breach. This situation will occur if the corroded Alloy 22 falls away, 
leaving a gaping hole where the breach occurs. In any event, the size of the breach, rather than 
the diffusive path area inside the waste package, is the limiting factor for diffusion out of a waste 
package. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-116 November 2004 
The nominal area of a single general corrosion patch is fixed in the current waste package 
degradation model, WAPDEG (BSC 2004 [DIRS 169996]). The diffusive area of the corrosion 
products domain is the total area of all waste package breaches, including corrosion patches and 
stress corrosion cracks and is determined differently for each scenario class, as discussed in 
Section 6.5.3.1.1. 
The diffusion coefficient in the corrosion products is given by Archies law, Equation 
6.5.1.2.1-12, as a function of porosity and saturation. The water saturation within the corrosion 
products, CP we S , , can be obtained as a function of RH using Equation 6.5.1.2.1-20, replacing the 
waste package pore volume, WP V , with CP V , the pore volume of the corrosion products, and 
replacing the waste package surface area, WP s , with CP s , the surface area of the corrosion 
products (m2 Fe2O3), given by: 
. 1 
. .. 
. 
. .. 
. - 
=
= 
CP
CP 
CP CP FeOx
CP CP CP 
s V 
s m s 
f
f 
. 
(Eq. 6.5.1.2.1-25) 
In this equation, CP m is the mass of corrosion products (kg Fe2O3). The ratio of surface area to 
pore volume of the corrosion products can be expressed as: 
. .. 
. 
. .. 
. - 
= 
CP
CP 
CP FeOx 
CP 
CP s 
V
s 
f
f 
. 1 . (Eq. 6.5.1.2.1-26) 
Using a solid density for Fe2O3 of = FeOx . 5,240 kg m-3 (Weast 1985 [DIRS 111561], p. B-104), 
the density of water at 50C, the specific surface area of corrosion products ( CP s ) in units of 
m2 kg-1, and a porosity for corrosion products, CP f , of 0.4 (Section 6.5.1.2.1.3.2), the effective 
saturation of the corrosion products is given by: 
( ) . ln 10 28 . 3 
log 
1 . 1 1 
45 . 2 / 1 6 
45 . 2
1 
10 
, 
- - -  = 
. .. 
. 
. .. 
. - 
. .. 
. 
. .. 
. - 
=
= 
RH s 
RH N A 
M s 
N A
M 
V
s S 
CP 
CP
CP 
A w w 
w CP FeOx 
a 
A w w 
w 
CP 
CP 
CP we 
f
f 
. 
. 
. 
. 
(Eq. 6.5.1.2.1-27) 
The equivalent of Equation 6.5.1.2.1-24, which gives the effective diffusion coefficient based on 
Archies law, can similarly be obtained for the corrosion products: 
( ) ( ) [ ] 
( ) . ln 10 27 . 3 
ln 10 28 . 3 4 . 0 
0 
816 . 0 2 12 
0 
2 45 . 2 / 1 6 3 . 1 
0 
2 
, 
3 . 1 
D RH s 
D RH s 
D S D 
CP 
CP 
CP we CP s 
- - 
- - 
-  = 
-  =
= f 
(Eq. 6.5.1.2.1-28) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-117 November 2004 
Using RH = 0.95 and = CP s 9.1  103 m2 kg-1 as an example, and with the self-diffusion 
coefficient for water (Section 6.3.4.1) of -1 2 9 
0 s m 10 299 . 2 -  = D , the effective diffusion 
coefficient for the corrosion products using Archies law (Equation 6.5.1.2.1-28) is 
s D = 7.03  10-12 m2 s-1, or 0 / D Ds = 3.06  10-3, for comparison with earlier estimates 
(Table 6.5-10). For the range of porosities of geologic media, 0.25 to 0.7 (Freeze and 
Cherry 1979 [DIRS 101173], p. 37), s D ranges from 1.53  10-11 m2 s-1 to 1.19  10-12 m2 s-1. 
6.5.1.2.1.4.3 Diffusion Coefficient in Stress Corrosion Cracks 
When stress corrosion cracks first appear and are the only breaches in the package, the steel 
components will be largely intact. The surface area and diffusional cross-sectional areas of 
internal components will be small compared to the diffusional cross sectional area of stress 
corrosion cracks, resulting in a small diffusion coefficient. Since at this time this portion of the 
diffusion pathway will have both a smaller diffusion coefficient and a smaller cross sectional 
area, this pathway will control diffusive releases. Consider an example where 25 stress corrosion 
cracks per waste package appear (BSC 2004 [DIRS 169996], Figure 26), which is an upper 
bound estimate that occurs at approximately 300,000 years. With a cross sectional area of 
7.7  10-6 m2 for each crack (Section 6.3.3.1.2.1), the total area of stress corrosion crack 
openings in this example calculation is 1.93 cm2. Since even the bounding estimate of initial 
cross-sectional area for diffusion within a package is 3.00  10-7 m2 = 3.00  10-3 cm2, it is the 
adsorbed water film inside the package that controls diffusive releases because the diffusional 
cross-sectional area inside the waste package is much less than that of the stress corrosion cracks. 
This conclusion is appropriate when corrosion products fill the stress corrosion cracks, as they 
eventually will, and radionuclides diffuse through these products. 
If the stress corrosion crack is not filled with corrosion products, diffusion can still occur through 
an adsorbed water film on the sides of the stress corrosion cracks. In this case, the 
cross-sectional area through the stress corrosion cracks is computed from the perimeter of the 
stress corrosion crack and the film thickness. The maximum length of a crack is about 5 cm 
(Section 6.3.3.1.2.1). Although a stress corrosion crack is theoretically ellipsoidal in shape, it is 
so narrow that the perimeter is approximately twice the length, or 10 cm. Using the example 
above with 25 stress corrosion cracks/package, the total width of the diffusive path is 250 cm. 
The water film thickness, assuming adsorption on Fe2O3 at RH = 95 percent, as an example, is 
1.39  10-9 m (4.91 monolayers of thickness f t = 2.8310-10 m), so the cross-sectional area for 
diffusion on the sides of stress corrosion cracks is 3.5  10-5 cm2, or a factor of 100 less than the 
high estimate for cross-sectional area inside the waste package (3.0010-3 cm2). While it is not 
unreasonable for the actual diffusive area inside the waste package to be at least two orders of 
magnitude less than the high estimate, the area for diffusion along the walls of the stress 
corrosion cracks is at least as small as the diffusive area in the interior of the waste package, and 
may in fact be the controlling dimension. If the stress corrosion cracks are filled with corrosion 
products, then the cross-sectional area inside the waste package is more likely to be controlling, 
as discussed in the preceding paragraph. 
Expressions for the effective saturation and diffusion coefficient based on Archies law in a 
stress corrosion crack are identical to those obtained above for general corrosion patches, as long 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-118 November 2004 
as the same porous material properties are used. In Equation 6.5.1.2.1-27 (effective saturation), 
the ratio of the surface area to the pore volume of patches, CP CP V s / , is independent of the 
dimensions of the penetration, since, from Equation 6.5.1.2.1-26, 
( ) CP CP FeOx CP CP CP s V s f f . / 1 / - = , where CP s is the sampled specific surface area of Fe2O3 
(m2 kg-1), whose density is FeOx . (kg m-3), and porosity is CP f . Hence, the effective saturation 
and diffusion coefficient for a stress corrosion crack are identical to those for general corrosion 
patches if the same porous material properties are valid. 
6.5.1.2.1.5 Diffusive Path Length 
For stress corrosion cracks, the diffusion path length may be as long as the waste package or 
longer, depending on the tortuosity. It may also be only a few centimeters, the shortest distance 
from a fuel rod through a stress corrosion crack to the exterior of a waste package. The distance 
for corrosion patches is generally shorter, since by the time the general corrosion patches occur, 
the waste package should be filled with porous corrosion products through which a more direct 
path will exist from failed fuel rods to the exterior. 
When a package is first breached and the interior components have not yet degraded (except for 
the few initially failed fuel rods), a range of path lengths can be estimated with some certainty. 
As the steel components inside a package corrode, the diffusion path will become more tortuous 
on a microscopic scale, but more direct on a larger scale. The uncertainty in cross-sectional area 
for diffusion increases, whereas the range and uncertainty in porosity, saturation, and path length 
remain small in comparison. 
6.5.1.2.1.6 Comparison of Diffusive Release Estimates 
In Table 6.5-11, the cross-sectional diffusion areas are summarized for the conditions described 
above. In addition, the quantity i i s C q x A D . - = . / / is computed to provide a consistent 
comparison among the different states and conditions for a waste package. Based on these 
results, the highest releases are predicted to occur when all the adsorbed water is consolidated 
into a single bulk water pathway in a package with fully degraded internal components. 
However, this result is based on the most extreme degradation state and on the bounding 
approach to calculating diffusive releases from a waste package. More realistic estimates for this 
quantity range from 10-15 to 10-11 m3 s-1. 

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ANL-WIS-PA-000001 REV 01 6-119 November 2004 
Table 6.5-11. Summary and Comparison of Cross-Sectional Areas for Diffusion for Various 
Configurations at a Relative Humidity of 95 Percent 
Component/ 
Configuration Diffusive Path 
Path 
Length e 
(m) 
Cross-Sect. 
Area (mm2) 
Diffusion 
Coefficient a 
(m2 s-1) 
DsA 
.x 
(m3 s-1) 
Initial WP surface 
consolidated 
Axially through full 
length of WP 
4.90 0.297 2.29910-9 1.410-16 
Initial WP surface 
consolidated; 46.2 failed 
fuel rods 
Axially through full 
length of WP 
4.90 0.405 2.29910-9 1.910-16 
Initial WP surface 
consolidated; no 
cladding 
Axially through full 
length of WP 
4.90 14.0 2.29910-9 6.610-15 
Initial WP surface as 
porous medium 
Axially through  length 
of WP 
2.45 1.73106 c 8.0010-23 d 5.710-23 
Stress corrosion cracks 
(filled with porous 
corrosion products) 
Axially through stress 
corrosion cracks in lids 
0.068 b 193 7.0310-12 2.010-14 
Fully degraded WP 
surface consolidated 
Axially through  length 
of WP 
2.45 7.5104 2.29910-9 7.010-11 
Fully degraded WP; 
porous medium 
Axially through  length 
of WP 
2.45 1.73106 c 4.4610-12 3.210-12 
Corrosion patch (1) Radially outward 
through 1 patch in Alloy 
22 
0.02 2.346104 7.0310-12 8.210-12 
Corrosion patches (10) Radially outward 
through 10 patches in 
Alloy 22 outer corrosion 
barrier 
0.02 2.346105 7.0310-12 8.210-11 
a Self-diffusion coefficient of water (Mills 1973 [DIRS 133392], Table III) is used except for porous media in waste 
packages and in corrosion patches, which use effective diffusion coefficients. 
b For 21-PWR; thickness of closure end lids plus the air gap between lids: 
Middle lid thickness: 12.7 mm (BSC 2004 [DIRS 167394], Detail A). 
Middle lid to outer lid gap: 30.16 mm (BSC 2004 [DIRS 167394], Detail A). 
Outer lid thickness: 25.4 mm. 
Total top lids thickness: 68.26 mm (BSC 2004 [DIRS 167394], Detail A). 
c WP cross section; inner diameter = 1.4859 m (BSC 2004 [DIRS 169472]; BSC 2004 [DIRS 166953], Section B). 
dDs/D0 = 3.0810-14 (Equation 6.5.1.2.1-24, using initial surface area sWP = 1,061 m2/waste package). 
e21-PWR outside waste package length is the distance from the outside of the top lid to the outside of the bottom 
lid, and is given by the overall length minus the length of the skirt around the bottom minus the thickness of the 
lifting device on the top lid: 
Total length: 5,024.4 mm (BSC 2004 [DIRS 166953], Section A-A). 
Bottom skirt length: 101.6 mm (BSC 2004 [DIRS 167394], Detail B). 
Top lid lifting device thickness: 25.4 mm. 
Total waste package length: 4,897.4 mm (BSC 2004 [DIRS 167394], Detail C). 
WP = waste package 

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ANL-WIS-PA-000001 REV 01 6-120 November 2004 
6.5.1.3 Nomenclature 
Symbols used in Sections 6, 7, and 8 are summarized in Table 6.5-12. 
Table 6.5-12. Nomenclature 
Variable Definition Units Where First Used 
A Cross sectional area of diffusive or flow pathway m2 Eq. 6.5.1.2-5 
f A Cross sectional area for diffusion on exterior of an 
intact fuel rod m2 Eq. 6.5.1.2.1-9 
f A Diffusive area of UZ fracture cell m2 Eq. 6.5.3.5-21 
g A 
Surface area of crushed tuff granule m2 Section 6.6.4.1 
I A Invert cross sectional area (circle segment) m2 Eq. 6.5.3.3-2 
I A Diffusive area of invert cell m2 Eq. 6.5.3.5-21 
Is A 
Intercepted flow area of a drift over the length of 
one waste package m2 Eq. 6.5.3.3-12 
UZ I A / Diffusive area between invert and UZ cells m2 Eq. 6.5.3.3-4 
m A Diffusive area of UZ matrix cell m2 Eq. 6.5.3.5-21 
scc A Cross sectional area of stress corrosion crack cm2 Eq. 6.6.2-8 
eff scc A , Effective cross sectional area of stress corrosion 
crack cm2 Section 6.6.2 
UZ A 
Projected area of UZ normal to vertical flux m2 Eq. 6.5.3.6-1 
w A Cross sectional area of water molecule m2 Table 4.1-9; 
Eq. 6.5.1.2.1-6 
a One-half the length of a stress corrosion crack m Eq. 6.3.3.1-1 
a 
Constant in equation for binary diffusion 
coefficient dimensionless Eq. 6.6.2-6 
a Empirical parameter in Archies law dimensionless Eq. 6.3.4.1.1-1 
g a 
Effective length of tuff granule matrix pore system m Section 6.6.4.1 
b One-half the stress corrosion crack gap width m Section 6.3.3.1.2.1 
b 
Exponent in equation for binary diffusion 
coefficient dimensionless Eq. 6.6.2-6 
b Slope of the ln . versus ln . curve dimensionless Eq. 6.6.5.1-2 
cFeOx C Concentration of mobile iron oxyhydroxide (FeOx) 
colloids kg m-3 Eq. 6.5.1.2-14 
cGW C Concentration of mobile groundwater (GW) 
colloids kg m-3 Eq. 6.5.1.2-14 
cWF C Concentration of mobile waste form colloids kg m-3 Eq. 6.5.1.2-14 
i C Concentration of radionuclide species i kg m-3 Eq. 6.5.1.2-2 
embed 
i C 
Concentration of radionuclide species i embedded 
on waste form colloids kg m-3 Eq. 6.5.1.2-37 
iI C Concentration of radionuclide species i in the 
invert cell kg m-3 Eq. 6.5.3.5-11 
UZ iI C / Concentration of radionuclide species i at the 
interface between the invert and UZ cells 
kg m-3 Eq. 6.5.3.5-11 

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ANL-WIS-PA-000001 REV 01 6-121 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
if C Concentration of radionuclide species i in the UZ 
fracture cell 
kg m-3 Eq. 6.5.3.5-12 
im C Concentration of radionuclide species i in the UZ 
matrix cell 
kg m-3 Eq. 6.5.3.5-13 
new i C , New input concentration of radionuclide species 
i kg m-3 Eq. 6.6.1.2.1-1 
old i C , Old input concentration of radionuclide species i kg m-3 Eq. 6.6.1.2.1-1 
embed 
ip C 
Concentration of parent ip of radionuclide species 
i embedded on waste form colloids kg m-3 Eq. 6.5.1.2-37 
icFeOx C Concentration of radionuclide species i sorbed 
onto mobile iron oxyhydroxide (FeOx) colloids kg m-3 Eq. 6.5.1.2-14 
irrev 
icFeOx C 
Concentration of radionuclide species i 
irreversibly adsorbed onto iron oxyhydroxide 
(FeOx) colloids 
kg m-3 Eq. 6.5.1.2-28 
icGW C Concentration of radionuclide species i sorbed 
onto mobile GW colloids kg m-3 Eq. 6.5.1.2-14 
iCP C Concentration of dissolved radionuclide species i 
in corrosion products domain or cell kg m-3 Eq. 6.5.1.2-50 
irrev 
iCPFeOx C 
Concentration of radionuclide species i 
irreversibly adsorbed onto iron oxyhydroxide 
corrosion products 
kg m-3 Eq. 6.5.1.2-31 
invint iCP C / 
Concentration of radionuclide species i at the 
interface between the corrosion products and 
invert cells 
kg m-3 Eq. 6.5.3.5-7 
icWF C Concentration of radionuclide species i sorbed 
onto mobile waste form colloids kg m-3 Eq. 6.5.1.2-14 
iinter C Concentration of dissolved radionuclide species i 
in invert intergranular continuum kg m-3 Eq. 6.5.1.2-51 
iintra C Concentration of dissolved radionuclide species i 
in invert intragranular continuum kg m-3 Eq. 6.5.1.2-52 
ip C Concentration of parent ip of radionuclide 
species i kg m-3 Eq. 6.5.1.2-9 
ipcFeOx C 
Concentration of parent ip of radionuclide species 
i sorbed onto mobile iron oxyhydroxide (FeOx) 
colloids 
kg m-3 Eq. 6.5.1.2-14 
irrev 
ipcFeOx C 
Concentration of parent ip of radionuclide species 
i irreversibly adsorbed onto iron oxyhydroxide 
(FeOx) colloids 
kg m-3 Eq. 6.5.1.2-28 
ipcGW C Concentration of parent ip of radionuclide species 
i sorbed onto mobile (GW) colloids kg m-3 Eq. 6.5.1.2-14 
irrev 
ipCPFeOx C 
Concentration of parent ip of radionuclide species 
i irreversibly adsorbed onto iron oxyhydroxide 
corrosion products 
kg m-3 Eq. 6.5.1.2-31 
ipcWF C Concentration of parent ip of radionuclide species 
i sorbed onto mobile waste form colloids kg m-3 Eq. 6.5.1.2-14 
si C Maximum concentration (solubility limit) of 
radionuclide species i kg m-3 Eq. 6.6.1.1.2-1 
new si C , Maximum concentration (solubility limit) of 
radionuclide species i in new chemistry kg m-3 Eq. 6.6.1.2.2-9 
old si C , Maximum concentration (solubility limit) of 
radionuclide species i in old chemistry kg m-3 Eq. 6.6.1.2.2-9 
COV Coefficient of variance [= s(x)/E(x)] dimensionless Table 4.1-11 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-122 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
2 O C 
Molar concentration of oxygen in air mol cm-3 Eq. 6.6.3-2 
wv C Molar concentration of water vapor in air mol cm-3 Eq. 6.6.2-5 
AB D Binary diffusion coefficient cm2 s-1 Eq. 6.6.2-6 
B D 
Diffusion coefficient for Brownian motion cm2 s-1 Eq. 6.5.1.2-35 
c D Colloid dispersion or diffusion coefficient m2 s-1 Eq. 6.5.1.2-35 
B A c D / _ Interface diffusive conductance between cell A 
and cell B cm3 s-1 Eq. 6.5.3.5-6 
C B c D / _ Interface diffusive conductance between cell B 
and cell C cm3 s-1 Eq. 6.5.3.5-8 
coll D Colloid diffusion coefficient m2 s-1 Eq. 6.3.4.4-1 
i D Hydrodynamic dispersion coefficient, or effective 
diffusion coefficient, of radionuclide species i m2 s-1 Eq. 6.5.1.2-4 
CP D Diffusion coefficient in corrosion products domain cm2 s-1 Eq. 6.6.4-1 
CP D 
Diffusive conductance in corrosion products cell cm3 s-1 Eq. 6.6.4.2-1 
int CP CP D - /  
Diffusive conductance between corrosion 
products cell and corrosion products interface cell cm3 s-1 Eq. 6.6.4.2-15 
inter int CP D /  - 
Diffusive conductance between corrosion 
products interface cell and invert intergranular cell cm3 s-1 Eq. 6.6.4.2-16 
intra int CP D /  - 
Diffusive conductance between corrosion 
products interface cell and invert intragranular cell cm3 s-1 Eq. 6.6.4.2-17 
inter CP D /  
Effective diffusive conductance between corrosion 
products cell and invert intergranular cell cm3 s-1 Eq. 6.6.4.2-8 
intra CP D /  
Effective diffusive conductance between corrosion 
products cell and invert intragranular cell cm3 s-1 Eq. 6.6.4.2-9 
inter intra D /  
Effective diffusive conductance between 
intragranular and invert intergranular cells cm3 s-1 Eq. 6.6.4.2-10 
e D Effective diffusion coefficient cm2 s-1 Eq. 6.5.1.2-22 
f D Effective diffusion coefficient within the UZ 
fracture cell cm2 s-1 Eq. 6.5.3.5-12 
I D Effective diffusion coefficient within the invert cell cm2 s-1 Eq. 6.5.3.5-11 
If D 
Effective diffusive conductance between invert 
cell and UZ fracture cell cm3 s-1 Eq. 6.5.3.5-18 
Im D 
Effective diffusive conductance between invert 
cell and UZ matrix cell cm3 s-1 Eq. 6.5.3.5-19 
int I I D - /  Diffusive conductance between the invert cell and 
the invert interface cell cm3 s-1 Eq. 6.5.3.5-25 
f int I D /  - Diffusive conductance between the invert 
interface cell and the UZ fracture cell cm3 s-1 Eq. 6.5.3.5-26 
m int I D /  - Diffusive conductance between the invert 
interface cell and the UZ matrix cell cm3 s-1 Eq. 6.5.3.5-27 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-123 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
inter D 
Diffusion coefficient for invert intergranular 
continuum cm2 s-1 Eq. 6.6.4-2 
inter D 
Diffusive conductance in invert intergranular cell cm3 s-1 Eq. 6.6.4.2-2 
int inter inter D - /  
Diffusive conductance between the invert 
intergranular cell and the invert intergranular 
interface cell 
cm3 s-1 Eq. 6.6.4.2-19 
UZm int intra D /  - 
Diffusive conductance between the invert 
intergranular cell and the invert intragranular 
interface cell 
cm3 s-1 Eq. 6.6.4.2-23 
UZf int intra D /  - 
Diffusive conductance between the invert 
intergranular cell and the UZ fracture cell cm3 s-1 Eq. 6.6.4.2-24 
intra D 
Diffusion coefficient for invert intragranular 
continuum cm2 s-1 Eq. 6.6.4-3 
intra D 
Diffusive conductance in invert intragranular cell cm3 s-1 Eq. 6.6.4.2-3 
int intra intra D - /  
Diffusive conductance between the invert 
intragranular cell and the UZ matrix cell cm3 s-1 Eq. 6.6.4.2-21 
UZm int inter D /  - 
Diffusive conductance between the invert 
intragranular cell and the invert intragranular 
interface cell 
cm3 s-1 Eq. 6.6.4.2-20 
UZf int inter D /  - 
Diffusive conductance between the invert 
intragranular cell and the UZ fracture cell cm3 s-1 Eq. 6.6.4.2-22 
m D 
Effective diffusion coefficient within the UZ matrix 
cell cm2 s-1 Eq. 6.5.3.5-13 
mf D 
Effective diffusive conductance between UZ 
fracture and matrix cells cm3 s-1 Eq. 6.5.3.5-20 
ion D Ion diffusion coefficient m2 s-1 Eq. 6.3.4.4-1 
limit D Diffusion coefficient measurement limit cm2 s-1 Eq. 6.6.5.2-5 
MD D 
Mechanical dispersion coefficient cm2 s-1 Eq. 6.5.1.2-35 
mi D Molecular diffusion coefficient of species i m2 s-1 Eq. 6.5.1.2-6 
ms D Diffusion coefficient for saturated tuff matrix cm2 s-1 Eq. 6.5.3.6-2 
s D Effective diffusion coefficient m2 s-1 Eq. 6.5.1.2.1-8 
T D Diffusion coefficient at temperature T m2 s-1 Eq. 6.3.4.1.2-1 
0 T D Diffusion coefficient at temperature T0 m2 s-1 Eq. 6.3.4.1.2-1 
WF D Diffusion coefficient in waste form domain cm2 s-1 Table 8.2-1 
0 D Free water diffusion coefficient m2 s-1 Eq. 6.3.4.1.1-10 
* D Molecular diffusion coefficient cm2 s-1 Table 7.2-1, footnote a 
d Depth of stress corrosion crack m Figure 6.3-3 
d Characteristic length of the tuff matrix structure m Eq. 6.5.1.2-22 
D d Diameter of drift m Eq. 6.5.3.6-1 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-124 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
g d Geometric particle diameter mm Eq. 6.6.5.1-3 
0 d Diameter of fuel rod m Eq. 6.5.1.2.1-9 
E Modulus of elasticity Pa Eq. 6.3.3.1-1 
) (x E Expected value of the Kd distribution ml g-1 Table 4.1-11 
e Elementary charge C Table 7.2-1, footnote a 
e Natural logarithm base dimensionless Eq. 6.5.1.2.1-2 
F Faraday constant C mol-1 Eq. 6.3.4.1.1.-6 
F 
Fraction of seepage flux onto drip shield or waste 
package that flows into a breach dimensionless Eq. 6.5.1.1.2-7 
alt F Radionuclide release rate from waste package in 
alternative patch geometry model kg s-1 Eq. 6.6.1.2.3-2 
iCP F 
Diffusive flux of radionuclide species i in corrosion 
products cell kg s-1 Eq. 6.6.4.2-1 
if F 
Diffusive fluxes of radionuclide species i within the 
UZ fracture cell kg s-1 Eq. 6.5.3.5-12 
iI F 
Diffusive fluxes of radionuclide species i within the 
invert cell kg s-1 Eq. 6.5.3.5-11 
iinter F 
Diffusive flux of radionuclide species i in invert 
intergranular cell kg s-1 Eq. 6.6.4.2-2 
iintra F 
Diffusive flux of radionuclide species i in invert 
intragranular cell kg s-1 Eq. 6.6.4.2-3 
im F 
Diffusive fluxes of radionuclide species i within the 
UZ matrix cell kg s-1 Eq. 6.5.3.5-13 
j F 
Volumetric flow rate or flux of water in flow path j 
(j = 1 to 8) m3 s-1 Table 6.3-1; Eq. 6.5.1.1-5 
pri F 
Radionuclide release rate from waste package in 
primary patch geometry model kg s Eq. 6.6.1.2.3-1 
w F Volumetric flow rate of water m3 s-1 Eq. 6.5.1.1-4 
l A f 
Theoretical fraction of dripping flux falling at Point 
y<yA that flows into a drip shield breach dimensionless Eq. 6.5.1.1.2-2 
- A f 
Theoretical fraction of dripping flux falling between 
Points l and B that flows into a drip shield breach dimensionless Eq. 6.5.1.1.2-2 
+ B f 
Theoretical fraction of dripping flux falling at Point 
y>yB that flows into a drip shield breach dimensionless Eq. 6.5.1.1.2-14 
l C f 
Theoretical fraction of dripping flux falling between 
Points C and +l that flows into a drip shield breach dimensionless Eq. 6.5.1.1.2-5 
calc f Calculated fraction of dripping flux that flows into 
a drip shield breach dimensionless Section 6.5.1.1.2.4 
DS f Uncertain drip shield flux splitting factor dimensionless Eq. 6.3.2.4-2 
DS f ' Sampled drip shield flux splitting factor that 
accounts for rivulet spread angle uncertainty dimensionless Eq. 6.3.2.4-5 
+ D f 
Theoretical fraction of dripping flux falling at Point 
y>yD that flows into a drip shield breach dimensionless Eq. 6.5.1.1.2-6 
expt f 
Experimentally measured fraction of dripping flux 
that flows into a drip shield breach dimensionless Section 6.5.1.1.2.4 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-125 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
B fl 
Theoretical fraction of dripping flux falling between 
Points l and B that flows into a drip shield breach dimensionless Eq. 6.5.1.1.2-3 
D fl 
Theoretical fraction of dripping flux falling between 
Points l and D that flows into a drip shield breach dimensionless Eq. 6.5.1.1.2-6 
VD f 
Model validation uncertain drip shield flux splitting 
factor dimensionless Eq. 7.1.1.1-1 
VD f ' 
Model validation sampled drip shield flux splitting 
factor that accounts for rivulet spread angle 
uncertainty 
dimensionless Eq. 7.1.1.1-3 
VW f 
Model validation uncertain waste package flux 
splitting factor dimensionless Eq. 7.1.1.2-1 
VW f ' 
Model validation sampled waste package flux 
splitting factor that accounts for rivulet spread 
angle uncertainty 
dimensionless Eq. 7.1.1.2-3 
WP f Uncertain waste package flux splitting factor dimensionless Eq. 6.3.3.2-1 
WP f ' 
Sampled waste package flux splitting factor dimensionless Eq. 6.3.3.2-3 
0 f 
Theoretical fraction of dripping flux falling between 
Points B and C that flows into a drip shield breach dimensionless Eq. 6.5.1.1.2-4 
t G Conductance of bulk porous medium S Eq. 6.3.4.1.1-5 
w G Conductance of water S Eq. 6.3.4.1.1-5 
m H Absolute humidity of air kg kg-1 Eq. 6.6.2-3 
mol H Molal humidity of air mol mol-1 Eq. 6.6.2-4 
s I Hydraulic head gradient in the invert m m-1 Eq. 6.5.3.3-12 
i 
Unit vector in the x-direction or the direction of 
flow dimensionless Eq. 6.5.1.2-5 
cB J 
Mass flux of waste form colloids due to Brownian 
motion kg m-2 s-1 Eq. 6.5.1.2-35 
cMD J 
Mass flux of waste form colloids due to 
mechanical dispersion kg m-2 s-1 Eq. 6.5.1.2-35 
cWF J Mass flux of waste form colloids kg m-2 s-1 Eq. 6.5.1.2-32 
i J 
Mass flux (mass specific discharge) of 
radionuclide species i kg m-2 s-1 Eq. 6.5.1.2-1 
icFeOx J 
Total mass flux of mobile iron oxyhydroxide 
(FeOx) colloids containing adsorbed radionuclide 
species i 
kg m-2 s-1 Eq. 6.5.1.2-14 
irrev JicFeOx 
Total mass flux of mobile iron oxyhydroxide 
(FeOx) colloids containing irreversibly adsorbed 
radionuclide species i 
kg m-2 s-1 Eq. 6.5.1.2-28 
icGW J Total mass flux of mobile GW colloids containing 
adsorbed radionuclide species i kg m-2 s-1 Eq. 6.5.1.2-14 
icWF J Total mass flux of mobile waste form colloids 
containing adsorbed radionuclide species i kg m-2 s-1 Eq. 6.5.1.2-14 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-126 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
d K Sorption distribution (or distribution) coefficient ml g-1 Table 4.1-11 
dicFeOx K 
Sorption distribution (or distribution) coefficient of 
iron oxyhydroxide colloids containing adsorbed 
radionuclide species i 
ml g-1 Eq. 6.5.1.2-14 
dicGW K 
Sorption distribution (or distribution) coefficient of 
groundwater colloids containing adsorbed 
radionuclide species i 
ml g-1 Eq. 6.5.1.2-14 
dicWF K 
Sorption distribution (or distribution) coefficient of 
waste form colloids containing adsorbed 
radionuclide species i 
ml g-1 Eq. 6.5.1.2-14 
dips K Sorption distribution (or distribution) coefficient of 
parent ip of radionuclide species i ml g-1 Eq. 6.5.1.2-12 
dis K Sorption distribution (or distribution) coefficient of 
radionuclide species i ml g-1 Eq. 6.5.1.2-12 
us K Unsaturated hydraulic conductivity of invert m s-1 Eq. 6.5.3.3-12 
k Boltzmann constant J K-1 Table 7.2-1, footnote a 
k Parameter in FHH adsorption isotherm dimensionless Eq. 6.5.1.2.1-2 
i k Irreversible forward rate constant m3 m-2 s-1 Eq. 6.5.1.2-13 
m k Intrinsic permeability of saturated tuff matrix m2 Eq. 6.5.3.6-3 
me k Effective permeability of tuff matrix m2 Eq. 6.5.3.6-2 
rm k Relative permeability of tuff matrix dimensionless Eq. 6.5.3.6-3 
A L 
Diffusive lengths from the cell centers to the cell 
interface within cell A m Eq. 6.5.3.5-5 
B L Diffusive lengths from the cell centers to the cell 
interface within cell B m Eq. 6.5.3.5-5 
DS L Axial length of drip shield m Table 6.3-1 
Patch DS L _ Axial half-length of each drip shield patch due to 
general corrosion m Table 6.3-1 
f L 
Diffusive length within the UZ fracture cell m Eq. 6.5.3.5-12 
I L 
Diffusive length within the invert cell m Eq. 6.5.3.5-11 
inter L 
Diffusive length within the invert intergranular cell m Eq. 6.6.4.2-2 
intra L 
Diffusive length within the invert intragranular cell m Eq. 6.6.4.2-3 
m L Diffusive length within the UZ matrix cell m Eq. 6.5.3.5-13 
WP L Length of waste package m Table 6.3-1 
Patch WP L _ 
Axial half-length of each drip waste package due 
to general corrosion m Table 6.3-1 
l Average ionic conductance at infinite dilution S cm2 equivalent-1 Eq. 6.3.4.1.1-7 
0 0 , - + l l 
Cationic and anionic conductance at infinite 
dilution S cm2 equivalent-1 Eq. 6.3.4.1.1-6 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-127 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
l One-half width of corrosion patch in drip shield m Eq. 6.3.2.4-2 
WP l 
One-half width of corrosion patch in waste 
package m Eq. 6.3.3.2-1 
B A M M , Molecular weights of components A and B g mol-1 Eq. 6.6.2-6 
a M Molecular weight of air kg mol-1 Eq. 6.6.2-3 
w M Molecular weight of water kg mol-1 Eq. 6.5.1.2.1-6 
m Exponent on porosity in Archies law dimensionless Eq. 6.3.4.1.1-1 
m Mass of waste package internal components kg Table 6.5-8, footnote h 
a m 
Mass of water adsorbed per unit mass of 
adsorbent kg kg-1 Eq. 6.5.1.2.1-14 
CP m Mass of corrosion products inside waste package; 
function of time t kg Eq. 6.5.1.2.1-25 
CPf m 
Mass of corrosion products inside waste package 
from complete corrosion of all steel internal 
components 
kg Eq. 6.5.3.2-3 
1 CP m Mass of corrosion products inside waste package 
from corrosion of carbon steel kg Eq. 6.5.3.2-3 
2 CP m Mass of corrosion products inside waste package 
from corrosion of stainless steel kg Eq. 6.5.3.2-4 
i m Mass of radionuclide species i in waste package kg Eq. 6.6.1.1.1-2 
i m& 
Rate of release of radionuclide species i into 
water in waste package kg s-1 Eq. 6.6.1.1.1-1 
m m 
Mass of one monolayer of adsorbate per unit 
mass of adsorbent kg kg-1 Eq. 6.5.1.2.1-14 
w m 
Instantaneous total mass of water within the walls 
of a drift kg Eq. 6.5.1.1-1 
N Number of waste package internal components dimensionless Table 6.5-8, footnote h 
A N Avogadros number molecules mol-1 Eq. 6.5.1.2.1-6 
b N 
Number of breaches (corrosion patches) in drip 
shield dimensionless Eq. 6.3.2.4-2 
bDS N Number of breaches (corrosion patches) in drip 
shield dimensionless Table 6.3-1 
bWP N 
Number of breaches (corrosion patches) in waste 
package dimensionless Table 6.3-1 
c N Number of breaches (corrosion patches) on crown 
of drip shield dimensionless Eq. 6.5.1.1.1-6 
ND Normal distribution dimensionless Eq. 6.3.4.1.1-16 
n 
Exponent on saturation or water content in power 
law dependence of diffusion coefficient (e.g., 
Archies law) 
dimensionless Eq. 6.3.4.1.1-2 
n Time step number dimensionless Eq. 6.5.3.5-1 
p Slope of the model function dimensionless Eq. 6.6.5.2-6 
p Total pressure atm Eq. 6.6.2-6 
cB cA p p , 
Critical pressure of components A and B atm Eq. 6.6.2-6 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-128 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
w p Partial pressure of water Pa Eq. 6.5.1.2.1-1 
ow 
p 
Vapor pressure of water Pa Eq. 6.5.1.2.1-1 
cWF Q Net rate of waste form colloid capture on the solid 
surface kg m-3 s-1 Eq. 6.5.1.2-32 
int 
cWF Q Net rate of waste form colloid capture at the airwater 
interface kg m-3 s-1 Eq. 6.5.1.2-32 
cWFfg Q 
Net rate of waste form colloid removal from 
suspension by means of physical filtering (pore 
clogging, sieving, and straining) and by 
gravitational settling 
kg m-3 s-1 Eq. 6.5.1.2-32 
cWFmt Q 
Net rate of interface transfer of waste form 
colloidal mass between the continua in the dual 
continuum invert 
kg m-3 s-1 Eq. 6.5.1.2-32 
cWFs Q Net rate of waste form colloid formation kg m-3 s-1 Eq. 6.5.1.2-32 
I Q Volumetric discharge into the invert m3 s-1 Eq. 6.5.3.3-12 
m
i Q 
Net rate of various mass transfer process 
involving radionuclide species i kg m-3 s-1 Eq. 6.5.1.2-1 
icc Q 
Net rate of sorption of radionuclide species i onto 
immobile colloid surfaces captured by the solid 
matrix 
kg m-3 s-1 Eq. 6.5.1.2-7 
int 
icc Q 
Net rate of sorption of radionuclide species i onto 
immobile colloid surfaces captured by the airwater 
interface 
kg m-3 s-1 Eq. 6.5.1.2-7 
embed 
icm Q 
Rate of mass conversion from dissolved state to 
embedded state onto waste form colloids for 
radionuclide species i 
kg m-3 s-1 Eq. 6.5.1.2-7 
irrev 
icm Q Net rate of irreversible sorption of radionuclide 
species i onto mobile colloid surfaces kg m-3 s-1 Eq. 6.5.1.2-7 
rev 
icm Q Net rate of reversible sorption of radionuclide 
species i onto mobile colloid surfaces kg m-3 s-1 Eq. 6.5.1.2-7 
id Q Net rate of dissolution of radionuclide species i kg m-3 s-1 Eq. 6.5.1.2-7 
imt Q 
Net rate of interface transfer of dissolved mass 
between the continua in the dual continuum invert kg m-3 s-1 Eq. 6.5.1.2-7 
irrev 
imt Q 
Net rate of interface transfer between the continua 
in the dual continuum invert of radionuclide 
species i irreversibly sorbed onto mobile colloids 
kg m-3 s-1 Eq. 6.5.1.2-28 
iprecip Q 
Net rate of precipitation of radionuclide species i kg m-3 s-1 Eq. 6.5.1.2-7 
irrev 
is Q Net rate of irreversible sorption of radionuclide 
species i onto the solid matrix kg m-3 s-1 Eq. 6.5.1.2-7 
rev 
is Q Net rate of reversible sorption of radionuclide 
species i onto the solid matrix kg m-3 s-1 Eq. 6.5.1.2-7 
wz Q Advective water volume flux per unit bulk volume m3 m-3 yr-1 Eq. 6.5.3.5-3 
q Rate of diffusion of water vapor through air mol s-1 Eq. 6.6.2-8 
i q Rate of diffusion of radionuclide species i kg s-1 Eq. 6.5.1.2.1-8 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-129 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
in q Rate of water flow into waste package m3 s-1 Section 6.6.1.1.1 
new in q , New rate of water flow into waste package m3 s-1 Section 6.6.1.2.1 
old in q , Old rate of water flow into waste package m3 s-1 Section 6.6.1.2.1 
out q Rate of water flow out of waste package m3 s-1 Section 6.6.1.1.1 
new out q , New rate of water flow out of waste package m3 s-1 Section 6.6.1.2.1 
wz q Scalar specific discharge (Darcy velocity) of water 
in the downward +z-direction m s-1 Eq. 6.5.1.2-46 
w q Specific discharge (Darcy velocity) of water m s-1 Eq. 6.5.1.2-4 
2 R Coefficient of determination dimensionless Figure 6.3-4 
f R Retardation factor dimensionless Eq. 6.3.4.2.2-1 
fi R Retardation factor for radionuclide species i dimensionless Eq. 6.5.1.2-38 
fip R Retardation factor for parent ip of radionuclide 
species i dimensionless Eq. 6.5.1.2-38 
RH Relative humidity kg kg-1 Eq. 6.5.1.2.1-2 
t R Resistance of a porous medium . Eq. 6.3.4.1.1-4 
coll r Colloid particle radius m Eq. 6.3.4.4-1 
corr r Steel corrosion rate mol yr-1 Table 6.6-1 
D r Drift radius m Eq. 6.5.3.3-1 
i r 
Reaction term accounting for decay and ingrowth 
of species i kg m-3s-1 Eq. 6.5.1.2-1 
ion r Ion radius m Eq. 6.3.4.4-1 
M 
ip r 
Ratio of the mass of radionuclide species i 
produced by decay of the parent species ip to the 
mass of the parent species lost by decay 
kg kg-1 Eq. 6.5.1.2-9 
s r Dissolution rate of the waste form kg s-1 Eq. 6.6.1.1.1-1 
w r Rate of production of water by chemical reactions kg s-1 Eq. 6.5.1.1-1 
1 r Sampled value for the corrosion rate of carbon 
steel m yr-1 Eq. 6.5.3.2-1 
2 r Sampled value for the corrosion rate of stainless 
steel m yr-1 Eq. 6.5.3.2-2 
ef S Effective UZ fracture saturation m3 m-3 Eq. 6.5.3.6-4 
w S Water saturation m3 m-3 Eq. 6.5.1.2-2 
we S Effective water saturation m3 m-3 Eq. 6.5.1.2.1-13 
CP we S , Effective water saturation within a corrosion patch 
or corrosion products m3 m-3 Eq. 6.5.1.2.1-27 
CP w S _ 
Water saturation in corrosion products domain m3 m-3 Eq. 6.6.4-1 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-130 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
wf S 
UZ fracture water saturation m3 m-3 Eq. 6.5.1.2-52 
wfr S 
UZ fracture residual water saturation m3 m-3 Eq. 6.5.3.6-4 
wI S 
Invert water saturation m3 m-3 Eq. 6.5.1.2-50 
inter w S _ 
Water saturation in invert intergranular continuum m3 m-3 Eq. 6.6.4-2 
intra w S _ 
Water saturation in invert intragranular continuum m3 m-3 Eq. 6.5.3.3-7 
wm S 
UZ matrix water saturation m3 m-3 Eq. 6.5.1.2-51 
s Exponent in FHH adsorption isotherm dimensionless Eq. 6.5.1.2.1-2 
CP s Surface area of corrosion products m2 Eq. 6.5.1.2.1-27 
c s Specific surface area of colloids m2 g-1 Eq. 6.5.1.2-18 
CP s 
Specific surface area of iron oxyhydroxide 
corrosion products m2 kg-1 Eq. 6.5.1.2-13 
2 N s Specific surface area of porous material obtained 
by BET nitrogen adsorption measurements m2 kg-1 Eq. 6.5.1.2.1-13 
WP s Internal surface area of waste package m2 Eq. 6.5.1.2.1-13 
T Temperature K Table 4.1-7 
cB cA T T , Critical temperatures of components A and B K Eq. 6.6.2-6 
0 T Reference temperature K Eq. 6.3.4.1.2-1 
t Time s Eq. 6.5.1.1-1 
corr t Lifetime of steel yr Table 6.6-1 
f t Thickness of a water monolayer m Eq. 6.5.1.2.1-6 
fill t 
Time for a waste package to fill with water s Section 6.6.1.1 
1 f t 
Lifetime of carbon steel yr Eq. 6.5.3.2-1 
2 f t 
Lifetime of stainless steel yr Eq. 6.5.3.2-2 
max I t , Maximum thickness of the invert m Eq. 6.5.3.3-1 
I t Average thickness of the invert m Eq. 6.5.3.5-5 
0 t Time of first breach of the waste package yr Eq. 6.5.3.2-3 
ip t , 2 / 1 
Half-life of parent ip of radionuclide species i s Eq. 6.5.1.2-10 
u Ion mobility cm2 s-1 V-1 Table 7.2-1, footnote a 
V Volume of water vapor adsorbed at reference 
conditions m3 kg-1 Eq. 6.5.1.2.1-1 
) (t V Volume of water within a waste package at time t m3 Section 6.6.1.1 
B V Volume of cell B m3 Eq. 6.5.3.5-4 
b V Bulk volume of UZ matrix cell m3 kg-1 Section 6.5.3.6 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-131 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
CP V Pore volume (water volume when fully saturated) 
of corrosion products m3 Eq. 6.5.1.2.1-25 
DSNF V Volume of degraded DSNF m3 Table 8.2-1 
g V 
Volume of crushed tuff granule m3 Section 6.6.4.1 
m V Volume of water adsorbed that provides one 
monolayer coverage on the surface m3 kg-1 Eq. 6.5.1.2.1-1 
new V Volume of new water in waste package m3 Section 6.6.1.2.2 
old V Volume of old water in waste package m3 Section 6.6.1.2.1 
p V Total volume of pore space in bulk invert m3 Eq. 6.5.1.2-23 
inter p V _ Intergranular pore space pore volume m3 Eq. 6.5.1.2-23 
intra p V _ Intragranular pore space pore volume m3 Eq. 6.5.1.2-24 
t V Bulk invert total volume m3 Eq. 6.5.1.2-23 
t_inter V Intergranular pore space total volume m3 Eq. 6.5.1.2-26 
t_intra V Intragranular pore space total volume m3 Eq. 6.5.1.2-27 
tub V Volume of water that can be retained within a 
waste package before it overflows m3 Section 6.6.1.1 
w V Volume of water adsorbed m3 kg-1 
Eq. 6.5.1.2.1-13 
wI V Volume of water in invert m3 Eq. 6.5.3.3-3 
inter w V _ Volume of water in invert intergranular pore space m3 Eq. 6.5.3.3-6 
w_intra V Volume of water in invert intragranular pore space m3 Eq. 6.5.3.3-6 
WP V Pore volume of waste package m3 Eq. 6.5.1.2.1-13 
v Average water velocity m yr-1 Eq. 6.3.4.2.2-1 
c v Average contaminant front velocity m yr-1 Eq. 6.3.4.2.2-1 
DS W Total unfolded width of drip shield m Eq. 6.5.1.1.1-7 
I w Width of top surface of invert m Eq. 6.5.3.3-1 
inter w 
Volumetric ratio of the intergranular continuum 
volume to the total bulk invert volume m3 m-3 Eq. 6.5.1.2-26 
m
w w Net mass flow rate of water across bounding 
surfaces by mass transfer kg s-1 Eq. 6.5.1.1-1 
x One-dimensional coordinate or distance m Figure 6.3-2 
y Distance along drip shield crown m Section 6.5.1.1.2.1 
A y 
Distance along drip shield crown from center of 
breach  farthest point to the left from which 
rivulets can enter breach 
m Eq. 6.5.1.1.2-1 
B y 
Distance along drip shield crown from center of 
breach  farthest point to the left from which 
rivulets can enter top of breach 
m Eq. 6.5.1.1.2-1 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-132 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
C y 
Distance along drip shield crown from center of 
breach  farthest point to the right from which 
rivulets can enter top of breach 
m Eq. 6.5.1.1.2-1 
D y 
Distance along drip shield crown from center of 
breach  farthest point to the right from which 
rivulets can enter breach 
m Eq. 6.5.1.1.2-1 
z One-dimensional coordinate or distance m Eq. 6.5.1.2-46 
z Valence of an ion dimensionless Table 7.2-1, footnote a 
interface z 
Spatial location of the corrosion products 
domain/invert interface m Section 6.5.1.2 
- + z z , Valence of cation and anion, respectively; 
magnitude only  no sign dimensionless Eq. 6.3.4.1.1-6 
i C . Concentration difference kg m-3 Section 6.5.1.2.1.6 
2 O C . Oxygen concentration difference kg m-3 Eq. 6.6.3-3 
wv C . Water vapor concentration difference kg m-3 Eq. 6.6.2-8 
w F . Difference between volumetric flow rate into and 
out of the EBS m3 s-1 Eq. 6.5.1.1-4 
t . Time to empty retained water in waste package s Eq. 6.6.1.2.3-2 
t . Time step size from the nth to the (n+1)th time s or yr Eq. 6.5.3.5-1 
w w . Difference between mass rate of flow into and out 
of the EBS kg s-1 Eq. 6.5.1.1-1 
x . Thickness or length of flow or diffusion path m Table 6.5-8, footnote h 
F Volumetric water content percent Eq. 7.2.1.2-1 
0 . Equivalent electrolyte conductance at infinite 
dilution S cm2 equivalent-1 Eq. 6.3.4.1.1-6 
. 
Colloid flux out ratio dimensionless Eq. 6.5.3.4-1 
a Drip shield or waste package rivulet spread half 
angle radian or degree Eq. 6.3.2.4-2 
a Dispersivity m Eq. 6.5.1.2-6 
a First-order mass transfer coefficient s-1 Eq. 6.5.1.2-20 
 
Geometry-dependent factor in expression for 
dual-continuum invert interface mass transfer 
coefficient 
dimensionless Eq. 6.5.1.2-22 
 Volume fraction of old water in total water 
volume of waste package m3 m-3 Eq. 6.6.1.2.1-2 
. UZ active fracture parameter dimensionless Section 6.5.3.6 
c . Colloid mass transfer coefficient s-1 Eq. 6.5.1.2-19 
d . Dissolved species mass transfer coefficient s-1 Eq. 6.5.1.2-19 
d Stress corrosion crack gap width m Eq. 6.3.3.1-1 
i d Stress corrosion crack gap width, inner surface m Figure 6.3-3 
o d Stress corrosion crack gap width, outer surface m Figure 6.3-3 
. 
Dimensionless surface-area-to-volume ratio dimensionless Section 6.6.4.1 
T . Viscosity of water at temperature T Pa s Table 4.1-7 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-133 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
0 T . Viscosity of water at temperature T0 Pa s Eq. 6.3.4.1.2-1 
20 . Viscosity of water at temperature T = 20C Pa s Table 4.1-7 
. Volumetric moisture content percent Eq. 6.3.4.1.1-12 
C . Critical volumetric moisture content percent Eq. 6.6.5.2-2 
a . Number of monolayers of adsorbed water dimensionless Eq. 6.5.1.2.1-2 
inter . 
Intergranular moisture content percent Eq. 6.6.5.1-5 
intra . 
Moisture content of invert intragranular continuum percent Eq. 6.6.5.2-5 
m . 
Moisture content of UZ matrix percent Eq. 6.5.3.6-2 
min . 
Minimum volumetric moisture content for 
diffusivity to be greater than limiting diffusivity percent Eq. 6.6.5.2-5 
s . 
Saturated moisture content percent Eq. 6.6.5.1-2 
i . Radioactive decay constant for species i s-1 or yr-1 Eq. 6.5.1.2-9 
ip . 
Radioactive decay constant for parent ip of 
species i s-1 or yr-1 Eq. 6.5.1.2-9 
embed 
i . 
First order rate constant for mass conversion from 
dissolved state to embedded state onto waste 
form colloids for radionuclide species i 
s-1 or yr-1 Eq. 6.5.1.2-8 
 Mean value dimensionless Eq. 6.3.4.1.1-16 
v Average linear interstitial water velocity m s-1 Eq. 6.3.4.2.2-1 
c v Average velocity of front of the contaminant 
concentration profile m s-1 Eq. 6.3.4.2.2-1 
p Ratio of circle circumference to diameter dimensionless Eq. 6.5.1.2.1-9 
. Density of waste package internal components kg m-3 Table 6.5-8, footnote h 
b . Dry bulk density of the solid matrix kg m-3 Eq. 6.3.4.2.2-1 
FeOx . Density of Fe2O3 kg m-3 Eq. 6.5.1.2.1-25 
i . Mass concentration of radionuclide species i kg m-3 Eq. 6.5.1.2-1 
s . Electrical resistivity of a porous medium . m Eq. 6.3.4.1.1-1 
t . Bulk resistivity of a partially saturated porous 
medium . m Eq. 6.3.4.1.1-2 
w . Density of water kg m-3 Eq. 6.5.1.1-4 
ew . Electrical resistivity of liquid water . m Eq. 6.3.4.1.1-1 
s Standard deviation dimensionless Eq. 6.3.4.1.1-16 
) (x s Standard deviation of the Kd distribution ml g-1 Table 4.1-11 
a s Applied stress Pa Eq. 6.3.3.1-1 
g s 
Standard deviation of the pore size mm Eq. 6.6.5.1-4 
s s Sample standard deviation dimensionless Section 7.3.1.2 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-134 November 2004 
Table 6.5-12. Nomenclature (Continued) 
Variable Definition Units Where First Used 
f Porosity m3 m-3 Eq. 6.3.4.2.2-1 
CP f Porosity of corrosion products m3 m-3 Eq. 6.5.1.2.1-25 
f f 
Porosity of UZ fractures m3 m-3 Eq. 6.5.1.2-52 
I f Bulk porosity of invert m3 m-3 Eq. 6.5.1.2-25 
inter f 
Porosity of invert intergranular continuum m3 m-3 Eq. 6.5.3.3-10 
intra f 
Porosity of invert intragranular continuum m3 m-3 Eq. 6.5.3.3-7 
m f 
Porosity of saturated tuff matrix m3 m-3 Eq. 6.5.1.2-51 
. 
Moisture potential J kg-1 Eq. 6.6.5.1-2 
e . 
Air-entry moisture potential J kg-1 Eq. 6.6.5.1-2 
es . 
Air-entry moisture potential at a bulk density of 
1,300 kg m-3 
J kg-1 Eq. 6.6.5.1-3 
i . Mass fraction of radionuclide species i released 
per unit mass of waste form kg kg-1 Eq. 6.6.1.1.1-1 
. 
Del operator: 
z y x .
. 
+ 
.
. 
+ 
.
. k j i , where i, j, 
and k are unit vectors in the x-, y-, and zdirections, 
respectively 
m-1 Eq. 6.5.1.2-1 
BET = Brunauer, Emmett and Teller; CP = corrosion products; COV = coefficient of variance; 
DSNF = defense spent nuclear fuel; FHH = Frenkel-Halsey-Hill adsorption isotherm equation 
6.5.2 Base Case Model Inputs 
Table 6.5-13 summarizes model inputs used in the EBS RT Abstraction that are sampled in the 
TSPA-LA model calculations. The uncertainty associated with each parameter is indicated by 
the range and distribution shown for the parameter and is discussed in this section. 

ANL-WIS-PA-000001 REV 01 6-135 November 2004 
EBS Radionuclide Transport Abstraction 
Table 6.5-13. Sampled Model Inputs Used in the EBS Radionuclide Transport Abstraction 
Input Name Input Description Input Source 
Range and 
Distribution * 
Type of 
Uncertainty 
Invert_Diff_Coeff_Uncert Invert diffusion coefficient uncertainty Developed in Section 6.3.4.1.1, based on 
Conca and Wright (1992 [DIRS 100436], Figure 
2), Conca et al. (1993 [DIRS 170709], Figure 2) 
10ND; ND = Truncated 
Normal Distribution; 
Range: 103 s 
Mean  = 0.033; 
Std. Dev. s = 0.218 
Epistemic 
Kd_Ac_FeOx_CP Kd of Ac on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
1005,000 ml g-1 
Log-uniform 
Epistemic & 
Aleatoric 
Kd_Am_FeOx_CP Kd of Am on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
1005,000 ml g-1 
Log-uniform 
Epistemic & 
Aleatoric 
Kd_C_FeOx_CP Kd of C on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
10100 ml g-1 Uniform Epistemic & 
Aleatoric 
Kd_Cs_FeOx_CP Kd of Cs on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
0300 ml g-1; Beta 
E(x) = 30; s(x) = 30 
Epistemic & 
Aleatoric 
Kd_I_FeOx_CP Kd of I on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_001) 
0.00.6 ml g-1 Uniform Epistemic & 
Aleatoric 
Kd_Np_FeOx_CP Kd of Np on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
11,000 ml g-1 
Log-uniform 
Epistemic & 
Aleatoric 
Kd_Pa_FeOx_CP Kd of Pa on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
1001,000 ml g-1 Uniform Epistemic & 
Aleatoric 
Kd_Pu_FeOx_CP Kd of Pu on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
1005,000 ml g-1 
Log uniform 
Epistemic & 
Aleatoric 
Kd_Ra_FeOx_CP Kd of Ra on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
0500 ml g-1; Beta 
E(x) = 30; s(x) = 30 
Epistemic & 
Aleatoric 
Kd_Sr_FeOx_CP Kd of Sr on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
020 ml g-1; Beta 
E(x) = 10; s(x) = 2.5 
Epistemic & 
Aleatoric 
Kd_Tc_FeOx_CP Kd of Tc on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_001) 
0.00.6 ml g-1 Uniform Epistemic & 
Aleatoric 
Kd_Th_FeOx_CP Kd of Th on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
1005,000 ml g-1 
Log-uniform 
Epistemic & 
Aleatoric 
Kd_U_FeOx_CP Kd of U on corrosion products DTN: LA0003AM831341.001 ([DIRS 148751] 
SEP table S00191_002) 
1001,000 ml g-1 
Log-uniform 
Epistemic & 
Aleatoric 
Kd_Ac_Invert Kd of Ac on crushed tuff in the invert Developed in Section 6.3.4.2.2 Range = 1,00010,000 
ml g-1; 
Mean = 5,500 ml g-1; 
Std. Dev. = 1,500 ml g-1 
Epistemic & 
Aleatoric 
Kd_Am_Invert Kd of Am on crushed tuff in the invert DTN: LA0408AM831341.001 [DIRS 171584] Range = 1,00010,000 
ml g-1; 
Mean = 5,500 ml g-1; 
Std. Dev. = 1,500 ml g-1 
Epistemic & 
Aleatoric 

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EBS Radionuclide Transport Abstraction 
Table 6.5-13. Sampled Model Inputs Used in the EBS Radionuclide Transport Abstraction (Continued) 
Input Name Input Description Input Source 
Range and 
Distribution * 
Type of 
Uncertainty 
Kd_Cs_Invert Kd of Cs on crushed tuff in the invert DTN: LA0408AM831341.001 [DIRS 171584] 115 ml g-1; Uniform Epistemic & 
Aleatoric 
Kd_Np_Invert Kd of Np on crushed tuff in the invert DTN: LA0408AM831341.001 [DIRS 171584] (0,0) (0.5,0.5) (6.,1.0) 
Cumulative 
Epistemic & 
Aleatoric 
Kd_Pa_Invert Kd of Pa on crushed tuff in the invert DTN: LA0408AM831341.001 [DIRS 171584] Range = 1,00010,000 
ml g-1; 
Mean = 5,500 ml g-1; 
Std. Dev. = 1,500 ml g-1 
Epistemic & 
Aleatoric 
Kd_Pu_Invert Kd of Pu on crushed tuff in the invert DTN: LA0408AM831341.001 [DIRS 171584] (10.,0) (70.,0.5) (200.,1.0) 
Cumulative 
Epistemic & 
Aleatoric 
Kd_Ra_Invert Kd of Ra on crushed tuff in the invert DTN: LA0408AM831341.001 [DIRS 171584] 1001,000 ml g-1; Uniform Epistemic & 
Aleatoric 
Kd_Sr_Invert Kd of Sr on crushed tuff in the invert DTN: LA0408AM831341.001 [DIRS 171584] 1070 ml g-1; Uniform Epistemic & 
Aleatoric 
Kd_Th_Invert Kd of Th on crushed tuff in the invert DTN: LA0408AM831341.001 [DIRS 171584] 1,00010,000 ml g-1 
Uniform 
Epistemic & 
Aleatoric 
Kd_U_Invert Kd of U on corrosion products DTN: LA0408AM831341.001 [DIRS 171584] (0,0) (0.2,0.5) (4.,1.0) 
Cumulative 
Epistemic & 
Aleatoric 
SS_Corrosion_Rate Stainless steel corrosion rate DTN: MO0409SPAACRWP.000 [DIRS 172059]; 
Spreadsheet ECDF_metals2.xls; Worksheet 
316 ss, Columns L & M, 
Rows 515 
Empirical cumulative distribution function 
Rate 
(m yr-1) 
0.03699 
0.037 
0.1016 
0.109 
0.1524 
0.154 
0.1778 
0.2032 
0.2286 
0.254 
0.2794 
0.51 
ECDF 
0.000 
0.063 
0.125 
0.188 
0.250 
0.313 
0.375 
0.438 
0.563 
0.750 
0.813 
1.000 
Epistemic & 
Aleatoric 

ANL-WIS-PA-000001 REV 01 6-137 November 2004 
EBS Radionuclide Transport Abstraction 
Table 6.5-13. Sampled Model Inputs Used in the EBS Radionuclide Transport Abstraction (Continued) 
Input Name Input Description Input Source 
Range and 
Distribution * 
Type of 
Uncertainty 
CS_Corrosion_Rate Carbon steel corrosion rate DTN: MO0409SPAACRWP.000 
[DIRS 172059]; Spreadsheet 
ECDF_metals2.xls; Worksheet 
A516-Carbon Steel, Columns 
B & C, Rows 530 
Empirical cumulative distribution 
function 
Rate 
(m yr-1) 
65.76 
65.77 
66.75 
69.84 
70.00 
71.25 
72.21 
72.64 
72.87 
72.89 
73.47 
74.29 
74.51 
74.60 
75.41 
77.31 
79.29 
80.00 
80.87 
83.26 
83.66 
83.74 
85.68 
90.97 
106.93 
ECDF 
0.000 
0.042 
0.083 
0.125 
0.167 
0.208 
0.250 
0.292 
0.333 
0.375 
0.417 
0.458 
0.500 
0.542 
0.583 
0.625 
0.667 
0.708 
0.750 
0.792 
0.833 
0.875 
0.917 
0.958 
1.000 
Epistemic & 
Aleatoric 
Diff_Path_Length_CP_CSNF Diffusive path length through corrosion products domain 
for CSNF packages 
Developed in Section 6.5.3.1.1 0.020.859 m; Uniform Epistemic & 
Aleatoric 
Diff_Path_Length_CP_CDSP Diffusive path length through corrosion products domain 
for codisposal waste packages 
Developed in Section 6.5.3.1.1 0.0251.063 m; Uniform Epistemic & 
Aleatoric 
Surface_Area_CP Specific surface area of Fe2O3 corrosion products Developed in Section 6.5.1.2.1.3.1 1.022 m2 g-1; Uniform Epistemic & 
Aleatoric 

ANL-WIS-PA-000001 REV 01 6-138 November 2004 
EBS Radionuclide Transport Abstraction 
Table 6.5-13. Sampled Model Inputs Used in the EBS Radionuclide Transport Abstraction (Continued) 
Input Name Input Description Input Source 
Range and 
Distribution * 
Type of 
Uncertainty 
Flux_Split_DS_Uncert DS flux splitting uncertainty factor Developed in Section 6.5.1.1.2.4 00.85 
(dimensionless); 
Uniform 
Epistemic & 
Aleatoric 
Flux_Split_WP_Uncert WP flux splitting uncertainty factor Developed in Section 6.5.1.1.3 02.41 
(dimensionless); 
Uniform 
Epistemic & 
Aleatoric 
Fracture_Frequency UZ fracture frequency BSC 2004 [DIRS 170040], 
Appendix A, Table A-1 
Mean = 3.16 m-1 
Std. Dev. = 2.63 m-1 
Log-normal 
Epistemic 
UZ_Fracture_Fraction UZ fracture porosity BSC 2004 [DIRS 170040], 
Appendix D, Table D-1 
01 (fraction); Beta 
E(x)=9.6  10-3; 
s(x)=2.82  10-3 
Epistemic 
UZ_Matrix_Porosity UZ matrix porosity BSC 2004 [DIRS 170040], 
Appendix D, Table D-1 
01 (fraction); Beta 
E(x) = 0.131; 
s(x) = 0.031 
Epistemic 
Fracture_Saturation Unsaturated zone fracture saturation 
(DTN: LB0307FMRADTRN.001 [DIRS 165451]) 
Uniform sampling from 433 
locations for each infiltration case 
Provided in source DTN Epistemic 
Fracture_Residual_Sat Unsaturated zone fracture residual saturation 
(DTN: LB0307FMRADTRN.001 [DIRS 165451]) 
Uniform sampling from 433 
locations 
Provided in source DTN Epistemic 
Fracture_Percolation_Flux Unsaturated zone fracture percolation flux 
(DTN: LB0307FMRADTRN.001 [DIRS 165451]) 
Uniform sampling from 433 
locations for each infiltration case 
Provided in source DTN Epistemic 
Flow_Focus_Factor Unsaturated zone fracture percolation flow-focusing 
factor (DTN: LB0307FMRADTRN.001 [DIRS 165451]) 
Uniform sampling from 433 
locations for each infiltration case 
Provided in source DTN Epistemic 
UZ_Matrix_Saturation Unsaturated zone matrix saturation 
(DTN: LB0307FMRADTRN.001 [DIRS 165451]) 
Uniform sampling from 433 
locations for each infiltration case 
Provided in source DTN Epistemic 
Matrix_Percolation_Flux Unsaturated zone matrix percolation flux 
(DTN: LB0307FMRADTRN.001 [DIRS 165451]) 
Uniform sampling from 433 
locations for each infiltration case 
Provided in source DTN Epistemic 
Matrix_Rel_Perm_Low, 
Matrix_Rel_Perm_Mean, 
Matrix_Rel_Perm_High 
Unsaturated zone relative permeability for all three 
infiltration cases (DTN: LB0307FMRADTRN.001 
[DIRS 165451]) 
Uniform sampling from 433 
locations for each infiltration case 
Provided in source DTN Epistemic 
*For distribution type beta, E(x) = expected value, s(x) = standard deviation. 
CP = corrosion products, CDSP = codisposal, WP = waste package, BET = Brunauer, Emmett and Teller, ECDF = empirical cumulative distribution function 

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ANL-WIS-PA-000001 REV 01 6-139 November 2004 
6.5.2.1 Invert Diffusion Coefficient 
The invert diffusion coefficient is used to calculate the rate of diffusion of radionuclides through 
the invert, after they have been released from the waste package. The uncertainty in the invert 
diffusion coefficient is epistemic. The values were derived from measured values of diffusion 
coefficients in various granular materials, including tuff. However, the data were scattered. This 
was particularly true at lower values of volumetric water content, where experimental difficulties 
are more pronounced  achieving uniform and consistent degrees of water saturation is difficult, 
resulting in uncertainties in the actual water content. The use of electrical conductivity 
measurements as an analog for diffusivity becomes more uncertain at low water content due to 
uncertainty in the electrical connectivity between electrodes and the porous material as well as 
between the particles themselves. The reported uncertainty approximates a normal distribution 
for the residuals in the statistical fit to the experimental data. Uncertainty in the porosity of the 
invert is subsumed by the greater uncertainty associated with the measurements of the diffusion 
coefficient; thus the porosity uncertainty can be considered to be accounted for in the diffusion 
coefficient. 
6.5.2.2 Sorption Distribution Coefficients for Calculating In-Package Retardation 
Sorption distribution coefficients (Kd values) are used to calculate sorption of radionuclides 
inside a breached waste package. Selection of Kd values for the 12 radionuclides listed in 
Table 6.5-13 is discussed in Section 6.3.4.2.2, where justification for the ranges is provided. 
For iodine and technetium, the ranges are narrow (low uncertainty) because these elements have 
been found to be largely nonsorbing in most media, including the iron oxyhydroxides that will 
comprise the bulk of corrosion products. There is, however, still some uncertainty associated 
with these elements because they do sorb strongly onto certain substances, such as copper oxide 
and copper sulfide (Balsley et al. 1998 [DIRS 154439], Tables 1 and 2) and in oxidizing 
conditions (Onishi et al. 1981 [DIRS 154420], Table 8.96). Although the composition of the 
internal waste package components is known, the exact composition of the corrosion products 
over time is uncertain. Furthermore, the sorptive behavior of iodine and technetium in a mixture 
of corrosion products having a wide range of compositions is uncertain. Thus, assigning at least 
a small range of uncertainty is appropriate, as is a uniform distribution. 
Kd values for the other elements (Am, C, Cs, Np, Pa, Pu, Ra, Sr, Th, and U) considered in 
calculating retardation in the EBS have been given wide ranges, reflecting the uncertainty in 
their values for sorption on corrosion products inside the breached waste package. Most of these 
elements are known to sorb strongly onto iron oxyhydroxides, as shown in Table 4.1-11. In 
particular, the ranges of values shown in Table 4.1-11 for sorption on iron oxide illustrates the 
large uncertainty in sorption distribution coefficients. One cause of this uncertainty is in the 
determination of the Kd values themselves, which are inherently inaccurate for high (and low) Kd 
values. When a great deal of sorption occurs, there can be large uncertainties associated with the 
measurement of the small amount of radioactivity left in solution after sorption (BSC 2001 
[DIRS 160828], p. 50). This results in large uncertainties in the calculated Kd. Because of these 
uncertainties, most Kd values are only reported to one significant figure (BSC 2001 
[DIRS 160828], p. 51). Distributions for sorption on iron oxide are uniform for C, I, Pa, and Tc, 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-140 November 2004 
and log-uniform for Am, Np, Pu, Th, and U. Kd values are assigned beta distributions for Cs, Ra, 
and Sr. 
The Kd values for sorption on corrosion products for all radionuclides are sampled 
independently. Although Kd values for certain groups of elements may in reality be coupled or 
correlated due to their similar sorptive behavior and chemical response, the sparseness of data 
and the inherent approximations in the linear Kd approach preclude correlating Kd values for 
sorption on corrosion products. 
Some aleatoric uncertainty exists for all of the Kd values in the uncertain chemistry of the water 
that might result from changes in seepage water conditions and thermal events and processes that 
could alter the concentration of dissolved species that affect sorption. 
6.5.2.3 Sorption Distribution Coefficients for Calculating Invert Sorption 
Sorption on crushed devitrified tuff in the invert also involves some epistemic uncertainty for 
most radionuclides. The exceptions are C, I, and Tc, which do not sorb measurably on tuff (Kd 
values are zero). As with Kd values for sorption on corrosion products, the invert Kd values also 
involve some aleatoric uncertainty due to the unpredictable chemistry of the seepage water and 
changes resulting from chemical processes that occur as EBS components degrade. Invert Kd 
values are correlated as shown in Table 4.1-13 (DTN: LA0311AM831341.001 [DIRS 167015]). 
In the implementation of sorption distribution coefficients in the invert in TSPA-LA, the 
devitrified tuff Kd values developed for the UZ submodel are assigned to the invert. 
6.5.2.4 In-Package Diffusion Submodel 
The corrosion rates for carbon steel and stainless steel are known with some uncertainty, as 
shown in the data presented in Table 4.1-1 (DTN: MO0409SPAACRWP.000 [DIRS 172059]). 
An empirical cumulative distribution function developed in DTN: MO0409SPAACRWP.000 
[DIRS 172059] is used for parameter CS_Corrosion_Rate to be sampled in TSPA-LA. An 
empirical cumulative distribution function developed in DTN: MO0409SPAACRWP.000 
[DIRS 172059] is used for parameter SS_Corrosion_Rate to be sampled in TSPA-LA. In view 
of the large range in the measured data even among multiple samples under identical conditions, 
some epistemic uncertainty exists in corrosion rates. In addition, the future physiochemical 
environment of the waste package interior will influence corrosion rates, as evidenced by the 
variability in rates under different conditions (DTN: MO0409SPAACRWP.000 [DIRS 172059]). 
Thus, aleatoric uncertainty also exists in the corrosion rates owing to the uncertain future waste 
package environment. 
The parameters Diff_Path_Length_CP_CSNF and Diff_Path_Length_CP_CDSP are developed 
in Sections 6.5.3.1.1 and 6.5.3.1.2. These are the diffusion path lengths from the internal waste 
package corrosion products domain to the invert domain of the EBS transport abstraction for 
CSNF (e.g., 21-PWR and 44_BWR) and codisposal (CDSP) (e.g., 5 DHLW/DOE SNF  Short) 
waste packages, respectively. The radionuclide source (failed fuel rods or glass logs) and the 
porous corrosion products are treated as being uniformly distributed throughout the volume of 
the breached waste package. Breached fuel rods or glass logs may lie adjacent to the interior of a 
breach in the waste package or nearby. Some aleatoric uncertainty exists in the location of the 

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ANL-WIS-PA-000001 REV 01 6-141 November 2004 
radionuclide source embedded in the corrosion products. The minimum path length is the 
thickness of the waste package outer corrosion barrier, 0.02 m for CSNF waste packages and 
0.025 m for codisposal waste packages. The maximum is the radius of a waste package, 0.859 m 
for CSNF waste packages and 1.063 m for codisposal waste packages. A uniform distribution is 
appropriate for this parameter. 
The parameter Surface_Area_CP, the specific surface area of corrosion products, is developed in 
Section 6.5.1.2.1.3.1, where uncertainties are discussed. This parameter accounts for the 
uncertainty in the computed surface area of corrosion products that is available for water 
adsorption inside a breached waste package. The calculated mass of corrosion products is 
multiplied by their specific surface area to compute the bulk surface area. The uncertainties are 
both aleatoric and epistemic. Unpredictable processes or events may occur that impact the 
morphology of corrosion products and alter their surface area, including seismic events, collapse 
of waste package internal structures, and changes in seepage rates. The nature of corrosion 
products formed under the conditions in a breached waste package in a humid environment, from 
a mixture of various types of steel, and their behavior in response to events and process that may 
occur is also uncertain. Due to the sparseness of the data for the specific surface area of 
corrosion products, only a uniform distribution can be justified for this parameter. 
6.5.2.5 EBS-UZ Boundary Condition Implementation in TSPA-LA 
The EBS-UZ boundary condition implementation, discussed in Section 6.5.3.6, is applied when 
the EBS transport abstraction is discretized and implemented in GoldSim. This model provides 
the radionuclide concentration boundary condition at the invert-UZ boundary such that the 
far-field concentration is approximately zero. To compute this boundary condition, a portion of 
the UZ is modeled, so input parameters for the UZ are used and therefore become EBS transport 
input parameters. The uncertainty in sampled parameters is discussed in this section; details 
about how UZ parameters are used are provided in Section 6.5.3.6. 
Most of the parameters used for the EBS-UZ boundary condition implementation are taken from 
the output of Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040]), in which 
specification of the ranges and distributions for the parameters is discussed. The parameters 
were developed for the discrete fracture-matrix partitioning model (BSC 2004 [DIRS 170040]). 
Although the modeling approach used in the EBS RT Abstraction is different, the parameter 
values remain unchanged. The parameter values are given in DTN: LB0307FMRADTRN.001 
([DIRS 165451], Folder: U0230_excel_files.zip). These parameters were developed for the 
lower, mean, and upper bound flow fields for the glacial transition climate and recommended for 
use in TSPA-LA for the entire duration of the simulation. The glacial transition lower, mean, 
and upper infiltration cases cover a range of conditions that encompass all of the monsoon 
climates and all but the present-day lower infiltration climate. Furthermore, most of the 
regulatory compliance period (2,000 to 10,000 years) is modeled as being under glacial transition 
climate. Because of the predominance in time and wide range of the glacial transition infiltration 
cases, these three cases are used as representative for the low, mean, and high infiltration cases 
for the entire compliance period. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-142 November 2004 
6.5.2.5.1 Matrix and Fracture Percolation Fluxes 
Similar to the approach taken in Drift-Scale Radionuclide Transport (BSC 2004 
[DIRS 170040]), in the EBS-UZ interface submodel, the parameter uncertainty is included 
through uniform sampling of the 433 different repository locations that have been assigned 
model parameters such as fracture and matrix flux and water saturation values. These values 
have been taken from the output of the UZ flow model for the repository host rock; see 
Sections 6.4.5 and 6.4.6 of Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040]) for 
additional information. The sampled parameters that are based on repository locations are 
sampled such that if a flux for a certain location is considered then the saturation for the same 
location is also used. 
6.5.2.5.2 Fracture Frequency 
The fracture frequency distribution for each UZ model layer is presented in Table A-1 of 
Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040], Appendix A, Table A-1). Since 
approximately 80 percent of the waste emplacement drift area is occupied by the TSw35 
(Topopah Spring welded tuff lower lithophysal) unit of the UZ model (Appendix H of Drift- 
Scale Radionuclide Transport, BSC 2004 [DIRS 170040]), and because of the small variation in 
fracture frequency among various units, it is sufficient to use the fracture frequency distribution 
for TSw35 as given in Table A-1 of Drift-Scale Radionuclide Transport (BSC 2004 
[DIRS 170040], Appendix A, Table A-1). 
6.5.2.5.3 Fracture Fraction 
The average fraction of the UZ that is occupied by fractures (also referred to as fracture porosity) 
is given as a distribution in Table D-1 of Drift-Scale Radionuclide Transport (BSC 2004 
[DIRS 170040], Appendix D). As with fracture frequency, the fracture porosity distribution for 
TSw35 given in Table D-1 of Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040], 
Appendix D) is sufficient for modeling purposes. 
6.5.2.5.4 Fracture Flow-Focusing Factor 
The flow focusing of fracture flux at the drift scale is included through a flow-focusing factor. 
The sampled fracture flux is adjusted by multiplying it by the sampled flow-focusing factor (see 
Drift Scale Radionuclide Transport, BSC 2004 [DIRS 170040], Equation G-3 and Appendix C). 
A separate flow focusing factor is presented for each of the 433 repository locations. 
6.5.2.5.5 Matrix Porosity 
A distribution for matrix porosity for various UZ model layers is given in Table D-1 of 
Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040], Appendix D, Table D-1). 
Matrix porosity distribution for TSw35 is used for modeling purpose. 
6.5.2.5.6 Fracture Saturation 
The physical saturation of the fracture is computed in Drift-Scale Radionuclide Transport 
(BSC 2004 [DIRS 170040], Appendix G, Equation G-6). This takes into account the effect of 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-143 November 2004 
flow focusing to account for sub-grid-block-scale heterogeneity for the mountain-scale flow 
fields in the fracture continuum. This value is calculated for the 433 repository locations for all 
three infiltration cases. 
6.5.2.5.7 Fracture Residual Saturation 
The fracture residual saturation is computed in Drift-Scale Radionuclide Transport (BSC 2004 
[DIRS 170040], Appendix G). It is developed for 433 repository locations and does not vary by 
the infiltration case. 
6.5.2.5.8 Matrix Relative Permeability 
The matrix effective permeability to water is derived from Drift-Scale Radionuclide Transport 
(BSC 2004 [DIRS 170040], Equation 6-57), by multiplying the matrix intrinsic permeability by 
the matrix relative permeability. The matrix intrinsic permeability for all four UZ model layers 
at the repository horizon (TSw33, TSw34, TSw35, and TSw36) are given in Drift-Scale 
Radionuclide Transport (BSC 2004 [DIRS 170040], Table 4-6) for each infiltration case. The 
relative permeability is sampled for 433 repository locations and varies with the infiltration case; 
it is given in Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040], Table B-1). 
6.5.3 Summary of Computational Model 
The object of the EBS radionuclide transport abstraction is to determine the rate of radionuclide 
releases from the EBS to the unsaturated zone. In the proposed EBS transport model, the EBS is 
spatially partitioned into the following domains: (1) waste form, consisting of for example, fuel 
rods or HLW glass; (2) waste package corrosion products; and (3) invert. In addition, the UZ 
immediately underlying the invert is conceptualized as a dual continuum consisting of (4) UZ 
matrix continuum and (5) UZ fracture continuum. The inclusion of a portion of the UZ is needed 
for an accurate calculation of the invert-to-UZ interface fluxes by providing a diffusive path 
length that is sufficiently long such that the concentration at the outlet of the UZ can realistically 
be assigned a value of zero. 
In the waste form domain, degradation processes occur, including breaching and axial splitting 
of fuel rods, dissolution of SNF and HLW glass, and formation of waste form colloids wherever 
applicable. Dissolved species are transported by advection and/or diffusion to the waste package 
corrosion products domain. The primary interactions in the corrosion products domain involving 
radionuclide species are reversible and irreversible sorption of dissolved species onto iron 
oxyhydroxide colloids and stationary corrosion products, and reversible sorption onto 
groundwater colloids and waste form colloids (when present). In the invert domain, 
radionuclides released from the corrosion products domain are transported by advection and 
diffusion, and interact with the crushed tuff by adsorption processes. The properties of each 
domain, including the volume, porosity, water saturation, diffusion cross sectional area, and 
diffusive path length, affect the rate of advective and diffusive transport of radionuclides through 
the domain. The invert domain interfaces with both continua of the UZ. The properties of the 
domains are defined in the following sections. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-144 November 2004 
6.5.3.1 Waste Form and Waste Package Diffusion Properties 
This section summarizes the general approach, major assumptions, main steps in the 
computational algorithm, and the stochastic parameters for the in-package diffusion submodel 
for TSPA-LA sensitivity studies. The mathematical equations for the in-package diffusion 
submodel are described in Section 6.5.1.2.1. 
The general approach for the commercial SNF (21-PWR and 44-BWR) waste packages is to 
consider two pathways for diffusion: (1) through porous waste form products inside the 
package, and (2) through porous corrosion products filling the bottom of the waste package. 
Starting from the time when a package is first breached, the extent of degradation is determined. 
This parameter is the basis for estimating the amount of corrosion products present inside a 
package, and allows the water saturation and effective diffusion coefficient to be computed. 
Implementation of the three-domain EBS abstraction requires that properties be specified for 
each domain, including the volume, diffusive area, the diffusive path length, porosity, water 
saturation, and the procedure for calculating the diffusion coefficient. These properties must be 
specified for each type of waste package (CSNF and codisposal waste packages) and for the drip 
and no-seep environment. 
6.5.3.1.1 CSNF Waste Packages Properties 
This section discusses the CSNF waste package properties in the following two domains: CSNF 
waste form and CSNF corrosion products. 
6.5.3.1.1.1 CSNF Waste Form Domain: 
In CSNF waste packages, the waste form domain consists of fuel rods. Radionuclides are 
released only from failed rods. Although fuel rods initially fail either by perforations in the 
cladding as a result of corrosion or by damage in handling or in seismic events, it is assumed that 
the fuel rod cladding instantly splits along its length when the waste package fails (BSC 2004 
[DIRS 170023], Assumption 5.3). Fuel rods split when the SNF reacts with the oxygen and 
moisture inside the waste package, forming metaschoepite. The resulting material, having a 
greater volume than SNF (mostly UO2), causes the fuel rod to split open. The configuration of 
the failed rod is a mostly intact tube with the slit along the length exposing the SNF inside. 
The reacted SNF constitutes a porous rind that is modeled as saturating quickly and completely 
with water, both in a seep and no-seep environment. The volume of the rind as a function of 
time and the rind porosity are provided by Clad Degradation  Summary and Abstraction for LA 
(BSC 2004 [DIRS 170023]). Radionuclides dissolve in the water that fully saturates the pore 
volume of the rind. 
The diffusive area of the waste form domain is the total exposed surface area of the SNF in all of 
the axially split fuel rods, i.e., the area of the slit times the number of failed fuel rods. This area 
is provided by Clad Degradation  Summary and Abstraction for LA (BSC 2004 
[DIRS 170023]). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-145 November 2004 
The diffusive path length is the thickness of the rind, which is a function of time as the SNF 
reacts to form metaschoepite. 
The diffusion coefficient is computed using Archies law (Equation 6.5.1.2.1-12), with the 
porosity of the rind and the assigned water saturation of 1.0. As discussed in Section 6.5.3.5, the 
discretized mass balance equations use a diffusive conductance, which is a harmonic average of 
diffusion coefficient terms (including diffusivity, porosity, saturation, diffusive path length, and 
cross-sectional area for diffusion; see Equation 6.5.3.5-7), in this case, for the waste form and 
corrosion products domains. Since the TSPA-LA model, GoldSim (GoldSim Technology Group 
2002 [DIRS 160579]) computes the diffusive conductance, only the diffusion coefficients need 
to be input, rather than the diffusive conductances themselves. 
6.5.3.1.1.2 CSNF Corrosion Products Domain: 
The second domain consists of the corrosion products inside the waste package. The mass of 
corrosion products ( CP m ) is given as a function of time by Equation 6.5.3.2-5 below. In 
Section 6.5.1.2.1.3.2, a porosity ( CP f ) of 0.4 for corrosion products is shown to be appropriate. 
The corrosion products are assumed to be Fe2O3. With the known density of Fe2O3 ( FeOx . ), the 
pore volume of the corrosion products domain is computed from: 
. .. 
. 
. .. 
. 
- 
= 
CP 
CP 
FeOx 
CP 
CP 
m V 
f 
f 
. 1 
. (Eq. 6.5.3.1.1-1) 
In a seep environment, the water saturation ( w S ) is assigned a value of 1.0. In a no-seep 
environment, the only water present is adsorbed water, and the saturation is the effective 
saturation of corrosion products given by Equation 6.5.1.2.1-27. Uncertainty in the water 
saturation of the corrosion products is provided for in the sampled specific surface area of the 
corrosion products. 
In a seep environment, the effective diffusion coefficient for corrosion products is given by 
Archies law (Equation 6.5.1.2.1-12), with the porosity CP f =0.4 and the assigned water 
saturation of 1.0. 
In a non-seep environment, the effective diffusion coefficient is given by Eq. 6.5.1.2.1-28. The 
diffusive area of the corrosion products domain for diffusion to the invert domain is the total area 
of all waste package breaches, including corrosion patches and stress corrosion cracks. The 
breached area is determined differently for each scenario class: 
 For the nominal scenario class: 
- Without early failure modeling cases and with no localized corrosion, the breached 
area is provided by the integrated waste package degradation model developed in 
WAPDEG Analysis of Waste Package and Drip Shield Degradation (BSC 2004 
[DIRS 169996], Section 7.1.1.1). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-146 November 2004 
- In the early failure modeling cases (no localized corrosion), the entire surface area of 
the waste package is breached (WAPDEG Analysis of Waste Package and Drip Shield 
Degradation [BSC 2004 (DIRS 169996), Section 6.3.8]). 
- In the localized corrosion case, localized corrosion results from dust deliquescence 
only (i.e., no dripping flux), and the breached area is the entire lateral surface area of 
the waste package (General Corrosion and Localized Corrosion of Waste Package 
Outer Barrier [BSC 2004 (DIRS 169984), Section 8.3.1]). Values for the breached 
areas for CSNF and CDSP waste packages are provided by WAPDEG Analysis of 
Waste Package and Drip Shield Degradation (BSC 2004 [DIRS 169996], 
Section 6.3.2). 
 For the seismic scenario class: 
- With ground motion damage only (no localized corrosion), the breached area is 
provided by the Seismic Consequence Abstraction (BSC 2004 [DIRS 169183], 
Section 6.5.3). This breached area is applied to the thickness of the waste package 
outer shell only. For the rest of the corrosion products domain, the waste package 
plan area, equal to the waste package diameter times its length, is used. 
- For the localized corrosion case, localized corrosion results from dust deliquescence 
as well as from seepage flux when seismic damage to the drip shield has occurred. 
The breached area is provided by the General Corrosion and Localized Corrosion of 
Waste Package Outer Barrier (BSC 2004 [DIRS 169984], Section 8.3.1). 
 For the igneous scenario class: 
- In the igneous intrusive scenario, the entire waste package is breached, and the waste 
package and cladding provide no further protection to the waste forms (BSC 2004 
[DIRS 168960], Section 6.7.1). 
- In the igneous eruptive scenario, the entire inventory of affected waste packages is 
made available for release to the air as ash. The EBS transport model does not apply. 
The diffusive path length is a sampled parameter (see Table 6.5-13) ranging from 0.02 m (the 
thickness of the waste package outer corrosion barrier) to 0.859 m (the outside radius of a 
21-PWR) (BSC 2004 [DIRS 169472], Table 1). 
6.5.3.1.2 Codisposal Waste Packages Properties 
Codisposal waste packages consist of five cylindrical canisters containing HLW glass (glass 
logs) surrounding a central canister of defense spent nuclear fuel (DSNF). After the 
codisposal waste package is breached, the HLW glass eventually degrades to a clay-like 
material. However, the DSNF degrades almost instantaneously (within a single TSPA-LA time 
step) to uranium oxide (BSC 2004 [DIRS 167618], Section 8.1) after the waste package is 
breached, compared to the slower degradation of the HLW glass logs. Although the steel 
support framework inside the waste package corrodes, allowing the canisters of glass to collapse 
onto each other, the general cylindrical shape of the canisters is retained. With this assumption 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-147 November 2004 
of the internal configuration of a degraded codisposal waste package, the diffusive area between 
the conceptual waste form domain and the corrosion product domain is the sum of the initial 
surface area of the five glass logs. The DSNF is treated as part of the corrosion product domain, 
rather than part of the waste form domain, because degraded DSNF is conceptualized to be 
present corroded mass of uranium oxide, just as the iron corrosion products formed from the 
degradation of steel components inside the waste package. 
The volume of the waste form domain is equal to the volume of degraded glass, which is 
determined from the degradation rate of the glass as provided by the defense HLW glass 
degradation model (BSC 2004 [DIRS 169988], Section 6.5). 
The diffusive path length from the waste form domain to the corrosion products domain is the 
thickness of the degraded glass (the rind thickness), which is a function of time. This is 
determined from the degradation rate of the glass. 
The diffusion coefficient of degraded glass is computed using Archies law 
(Equation 6.5.1.2.1-12), with the porosity of the glass degradation products provided by the 
Defense HLW Glass Degradation Model (BSC 2004 [DIRS 169988], Table 8-1) and the assigned 
water saturation of 1.0. 
The volume of corrosion products in a codisposal waste package is proportional to the mass of 
steel that has corroded. The mass of corrosion products is estimated as a function of time based 
on sampled corrosion rates for carbon and stainless steels. As shown in Table 6.3-4, the total 
mass of steel in a codisposal waste package (5 DHLW/DOE SNF  Short) is slightly less than in 
a 21-PWR. Using this mass and the porosity and density of corrosion products, the volume of 
the corrosion products domain in a codisposal waste package is computed using 
Equation 6.5.3.1.1-1. Because of the deliquescent nature of glass and glass degradation 
products, the corrosion products that surround those materials are considered to be fully saturated 
with water. 
The degraded DSNF, considered to be part of the corrosion product domain, has water associated 
with it. The initial volume of DSNF in a codisposal waste package is given as 1 m3 (BSC 2004 
[DIRS 167618], Section 8.1). Because the degraded DSNF is conceptualized to be in a 
powdered form, it can be modeled as having a porosity of 0.2. The porosity is based on the 
porosity of unconsolidated sand, which ranges from 0.25 to 0.50 (Freeze and Cherry 1979 
[DIRS 101173], Table 2.4); a value lower than this range is used to account for some 
consolidation. In addition, a smaller water volume results in higher radionuclide concentrations 
and hence overestimates releases. Just like corrosion products, the powdered DSNF can be 
considered fully saturated, yielding a water volume of 0.2 m3. The water volume associated with 
the corrosion products is expected to dominate the water volume associated with DSNF due to 
the larger mass of steel. For this reason, the water volume associated with DSNF can be 
considered as the lower bound for the water volume in the corrosion product domain. Once the 
water volume associated with corrosion products exceeds the water volume associated with 
DSNF, then the corrosion product water volume is used. 
The diffusive area between the corrosion products domain and the invert domain is the total area 
of all breaches in the Alloy 22 outer corrosion barrier of the waste package. The diffusive area is 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-148 November 2004 
dependent on the scenario class; the determination of diffusive areas as discussed in 
Section 6.5.3.1.1 for CSNF waste packages also applies to CDSP waste packages. 
The diffusive path length is uncertain since the actual source of dissolved radionuclides inside 
the waste package may be located anywhere within the waste package at any given time. Thus, 
the path length is sampled, ranging from the thickness of the outer corrosion barrier (0.02 m) to 
the nominal radius of the 5 DHLW/DOE SNF - Short codisposal waste package, 1.063 m 
(BSC 2004 [DIRS 169472], Table 1). 
The diffusion coefficient in codisposal waste package corrosion products is computed the same 
as for CSNF corrosion products using Archies law (Equation 6.5.1.2.1-12), with the porosity of 
the corrosion products ( CP f =0.4) and the assigned water saturation of 1.0. 
6.5.3.2 Calculation of Corrosion Products Mass and Saturation 
The major steps in the computational procedure are: 
 Determine the extent of degradation of the iron-based internal components of the waste 
package and the resulting surface area available for adsorption of water vapor. This is a 
two-step process. 
First StepSuppose the iron-based internal components have a lifetime equal to that of 
either the carbon steel components (maximum 10 mm thick) or the stainless steel inner 
vessel, which is 50 mm thick. Compute the lifetime by dividing the thickness by the 
corrosion rate for each type of steel. From Table 6.3-4, carbon steel comprises 
30 percent of the total mass of steel in a 21-PWR and 33 percent in a 44-BWR. As an 
approximation, one-third of the iron-based internal components in all waste packages is 
carbon steel and two-thirds is stainless steel. Each type of steel corrodes at a different 
rate, determined by sampling its rate distribution. The lifetime of carbon steel (yr) is 
then given by: 
1 
1 r 
t f 
_CS) (Max_Thick 1000 = , (Eq. 6.5.3.2-1) 
where 1 r is the sampled value for the corrosion rate of carbon steel (m yr-1), and 
Max_Thick_CS is the maximum thickness of carbon steel components (mm). From 
D&E/PA/C IED Typical Waste Package Components Assembly (BSC 2004 
[DIRS 169472], Table 2), the maximum thickness of a carbon steel waste package 
component is 3/8 in. = 9.525 mm, which is rounded to 10 mm for this parameter value. 
Similarly, the lifetime of stainless steel (yr) is given by: 
2 
2 r 
t f 
_SS) (Max_Thick 1000 = , (Eq. 6.5.3.2-2) 
where 2 r is the sampled value for the corrosion rate of stainless steel (m yr-1), and 
Max_Thick_SS is the maximum thickness of stainless steel components (mm). From 

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ANL-WIS-PA-000001 REV 01 6-149 November 2004 
Design and Engineering, 21-PWR Waste Package Configuration (BSC 2004 
[DIRS 167394], Detail A), the maximum thickness of a stainless steel in a waste 
package is the inner vessel thickness of 50.8 mm. 
Second StepOne-third of the total mass of the internal components is assigned to 
carbon steel components and two-thirds are assigned to stainless steel components, 
similar to the assumption for the first step. When these components are fully corroded, 
the same proportions hold, but the rate of formation of corrosion products depends on 
the sampled rates of the two types of steel. The total mass of corrosion products when 
internal components are fully degraded, CPf m (19,440 kg Fe2O3 in a 21-PWR; see 
Section 6.3.4.2.2), is based on data presented in Table 6.3-4. The initial mass of 
corrosion products is zero. For each type of steel, the mass of corrosion products present 
at time t (yr) is proportional to the fraction of the lifetime of each steel since the waste 
package was breached: 
Carbon steel: 
. .
.
. .
.
. 
> - 
= - . .
.
. 
. .
.
. - 
= 
, , 
3
1 
, 
3
1 
1 0 
1 0 
1 
0 
1 
f CPf 
f CPf 
f 
CP 
t t t m 
t t t m 
t 
t t 
m (Eq. 6.5.3.2-3) 
Stainless steel: 
. .
.
. .
.
. 
> - 
= - . .
.
. 
. .
.
. - 
= 
, , 
3
2 
, 
3
2 
2 0 
2 0 
2 
0 
2 
f CPf 
f CPf 
f 
CP 
t t t m 
t t t m 
t 
t t 
m (Eq. 6.5.3.2-4) 
where 0 t is the time (yr) when the first breach appears in the waste package. 
Then the total mass of corrosion products present is 2 1 ) ( CP CP CP m m t m + = . During the 
regulatory period: 
Total corrosion products: . .
.
. 
. .
.
. 
+ - = 
2 1 
0 
2 1 ) ( 
3
1 ) ( 
f f 
CPf CP t t 
t t m t m , (Eq. 6.5.3.2-5) 
The total surface area of corrosion products, CP s , is obtained using the sampled value for 
the specific surface area of corrosion products, CP s : 
Total surface area: CP CP CP m s s = . (Eq. 6.5.3.2-6) 
 Let the water saturation in the waste package corrosion products be 1.0 in the seep 
environment for both CSNF and codisposal waste packages and in the no-seep 
environment for codisposal waste packages. For CSNF waste packages in the no-seep 
environment, use the adsorption isotherm for Fe2O3 and compute the amount of water 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-150 November 2004 
vapor adsorbed (number of monolayers and film thickness) and the water saturation in 
the waste package corrosion products as follows (see Section 6.5.1.2.1.4.2): 
( ) 45 . 2 / 1 6 
, ln 10 28 . 3 - - -  = RH s S CP CP we (Eq. 6.5.3.2-7) 
 Compute the effective diffusion coefficient for steel corrosion products, s D , using 
Archies law with a fixed porosity of 0.4 (see Section 6.5.1.2.1.3.2) and the water 
saturation we S obtained from the preceding bullet (either 1.0 or Equation 6.5.3.2-7). 
6.5.3.3 Invert Domain Properties 
The volume of the invert is equal to its cross sectional area (i.e., the area of a segment of a circle) 
times the axial length. Based on the drift diameter of 5.5 m (BSC 2004 [DIRS 169503]) (or drift 
radius = D r 2.75 m) and maximum invert thickness of = max I t , 2 ft 10 in. = 0.8636 m (BSC 2004 
[DIRS 169503]), the width of the top surface of the invert is (Perry et al. 1963 [DIRS 119529], 
p. 2-6): 
( ) m 00 . 4 2 2 2 = - - = I,max D D I t r r w . (Eq. 6.5.3.3-1) 
The frontal cross sectional area of the invert is (Perry et al. 1963 [DIRS 119529], p. 2-6): 
( ) 
. m 39 . 2 
2 cos 
2 
2
, , , 
, 1 2 
= 
- - - . .. 
. 
. .. 
. - 
= - 
max I max I D max I D 
D 
max I D 
D I t t r t r 
r
t r 
r A 
(Eq. 6.5.3.3-2) 
The invert volume is this area ( I A ) multiplied by the length of interest, for example, the length 
of a waste package, WP L . The volume of water in the invert beneath a waste package of length 
WP L is: 
WP I w wI L A S V f = , (Eq. 6.5.3.3-3) 
where f is the porosity of the invert, and w S is the water saturation of the invert. 
For purposes of modeling flow and diffusion through the invert, the invert is regarded as having 
a rectangular cross section with a top surface being the actual top surface of the invert. The cross 
sectional area for flow or diffusion between the invert and the unsaturated zone is: 
. / WP I UZ I L w A = (Eq. 6.5.3.3-4) 
The average thickness of the invert is given by: 
. m 597 . 0 = = 
I
I 
I w
A t (Eq. 6.5.3.3-5) 

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ANL-WIS-PA-000001 REV 01 6-151 November 2004 
Using this value preserves the top surface area and volume of the invert. 
Sorption of radionuclides to the invert crushed tuff is modeled by applying the devitrified tuff Kd 
values from the UZ submodel to the invert. Ranges and distributions for these Kd values are 
shown in Table 4.1-12. The Kd values are correlated using the correlation matrix shown in 
Table 4.1-13. 
The bulk water content in the invert, . (fraction: m3 water m-3 bulk volume), is used to compute 
the diffusion coefficient in the invert, Equation 6.3.4.1.1-16 (in which 863 . 1 863 . 1 863 . 1 . f = w S ). The 
bulk water content in the invert is determined from the intragranular water saturation provided by 
Multiscale Thermohydrologic Model (BSC 2004 [DIRS 169565], Appendix X) and the seepage 
flux provided by the Seepage Model for PA Including Drift Collapse (BSC 2004 
[DIRS 167652]). 
The relationship between the bulk water content and the intergranular and intragranular water 
contents is based on the definitions of water content using the volumes of water, solids, and pore 
spaces: 
, 
_ _ 
t 
w_intra 
inter 
t 
w_intra 
t
inter w 
t 
w_intra inter w 
V 
V 
V 
V 
V 
V 
V 
V V 
+ = 
+ = 
+ 
= 
. 
. 
(Eq. 6.5.3.3-6) 
where inter w V _ is the volume of water in the intergranular pore space (m3), w_intra V is the volume of 
water in the intragranular (matrix) pore space (m3), t V is the total bulk invert volume (m3), and 
inter . is the intergranular water content (a fraction here: m3 water m-3 bulk volume; generally 
having units of percent throughout this report). 
The ratio of water volume to total invert bulk volume, t w_intra V V / , is related to the porosity of the 
of the intragranular (tuff matrix) pore space, intra f (m3 pore volume m-3 matrix volume): 
( ) 
t 
w_intra t_inter t intra 
t 
w_intra t_intra 
t 
w_intra 
V 
S V V 
V
S V 
V 
V - 
= = 
f 
, (Eq. 6.5.3.3-7) 
where w_intra S is the water saturation of the matrix (m3 water m-3 pore volume), t_intra V is the total 
pore volume of the matrix (m3), and t_inter V is the total pore volume of the intergranular pore 
space (m3). This expression makes use of the definition of matrix porosity, intra f , as the ratio of 
matrix pore volume to total matrix volume, where the latter is the difference between the bulk 
invert volume, t V , and the intergranular pore volume, t_inter V : 
t_inter t 
t_intra 
intra V V 
V
- 
= f , (Eq. 6.5.3.3-8) 

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ANL-WIS-PA-000001 REV 01 6-152 November 2004 
which can be rearranged to give: 
( ) t_inter t intra t_intra V V V - = f . (Eq. 6.5.3.3-9) 
Substituting the definitions of water content ( ) w_intra intra intra S f . = and porosity of the intergranular 
pore space, ( ) t t_inter inter V V / = f , the ratio t w_intra V V / in Equation 6.5.3.3-6 can be written: 
( ) inter intra 
t 
w_inter 
V 
V 
f . - = 1 . (Eq. 6.5.3.3-10) 
Inserting this into Equation 6.5.3.3-6 results in the expression for the bulk water content of the 
invert: 
( ) intra inter inter . f . . - + = 1 . (Eq. 6.5.3.3-11) 
The intragranular water content, intra . , is calculated by multiplying the intragranular water 
saturation provided by the Multiscale Thermohydrologic Model (BSC 2004 [DIRS 169565]) with 
the intragranular porosity of intra f = 0.131 (DTN: LB0207REVUZPRP.002 [DIRS 159672]; 
Spreadsheet Matrix_Props.xls, Row 20, Column C). 
The intergranular water content, inter . , is evaluated indirectly from the seepage flux into the drift. 
The volumetric discharge into the invert, I Q (m3 water s-1), which is equal to the seepage flux 
into the drift (see Equation 6.5.1.1-8, where 1 6 F F = ), is given by: 
Is s us I A I K Q = (Eq. 6.5.3.3-12) 
where us K is the unsaturated hydraulic conductivity of the invert (m s-1), s I is the hydraulic head 
gradient in the invert (m m-1), and Is A is the intercepted flow area of a drift over the length of 
one waste package, having a value of 28.05 m2 (BSC 2004 [DIRS 167652], Section 6.3.1). For 
vertical one-dimensional flow, a hydraulic head gradient of unity ( ) m/m 1 = s I is a bounding 
value for saturated rock with a free surface exposed to the open drift. Unsaturated crushed rock 
in the invert will have a lower head gradient, but by using a gradient of unity, 
Equation 6.5.3.3-12 simplifies and allows the unsaturated hydraulic conductivity of the invert to 
be evaluated given the seepage flux into the drift: 
Is 
I 
us A
Q K = . (Eq. 6.5.3.3-13) 
The unsaturated hydraulic conductivity of the invert has been evaluated as a function of moisture 
potential, . (bar), in the Multiscale Thermohydrologic Model (BSC 2004 [DIRS 169565], 
Appendix X, Table X-6) for various particle sizes. The determination of intergranular water 
content uses a particle size of 3 mm (BSC 2004 [DIRS 169565], Section 6.3.11). Interpolating in 
Table X-6 of Multiscale Thermohydrologic Model (BSC 2004 [DIRS 169565]) for the 

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ANL-WIS-PA-000001 REV 01 6-153 November 2004 
unsaturated hydraulic conductivity of the invert, us K , as given by Equation 6.5.3.3-13, results in 
a value for the moisture potential, ., which is inserted into a van Genuchten fitting function 
(BSC 2004 [DIRS 169565], Equation X.4) to give the intergranular water content: 
( ) 
( ) [ ]m n 
r s 
r inter .a
. . 
. . 
+ 
- 
+ = 
1 
, (Eq. 6.5.3.3-14) 
Parameters in Equation 6.5.3.3-14 are: 
r . = residual volumetric water content in the invert (fraction) 
= 0.050 (BSC 2004 [DIRS 169565], Appendix X, Table X-7) 
s . = saturated volumetric water content in the invert (fraction) 
= 0.450 (BSC 2004 [DIRS 169565], Appendix X, Table X-7) 
a = van Genuchten air-entry parameter (bar-1) 
= 624. bar-1 (BSC 2004 [DIRS 169565], Appendix X, Table X-7) 
n = van Genuchten n value (dimensionless) 
= 8.013 (BSC 2004 [DIRS 169565], Appendix X, Table X-7) 
m = van Genuchten m value (dimensionless) 
= 0.875 (BSC 2004 [DIRS 169565], Appendix X, Table X-7) 
With the algorithm and parameters described in this section, the bulk volumetric water content in 
the invert is obtained. 
6.5.3.4 Irreversible Sorption onto Iron Oxyhydroxide Colloids and Stationary 
Corrosion Products 
Irreversible sorption of Pu and Am onto iron oxyhydroxide colloids and stationary corrosion 
products in the corrosion product domain is considered. A linear forward rate constant is needed 
for modeling irreversible sorption. In the no-seep case or where iron oxyhydroxide colloids are 
unstable, the forward rate constant is randomly sampled from a range of 0.01 m3 m-2 yr-1 to 
0.24 m3 m-2 yr-1, with a log-uniform distribution (DTN: SN0309T0504103.010 [DIRS 165540]). 
For the seep case where colloids are stable, the forward rate constant i k describing irreversible 
sorption to iron oxyhydroxide corrosion products and colloids (Equations 6.5.1.2-12 and 
6.5.1.2-17) is computed as a fitting parameter to match a specified flux out ratio for the corrosion 
products domain (BSC 2004 [DIRS 170025], Section 6.3.3.2). The flux out ratio (.) is the ratio 
of radionuclide flux exiting the corrosion product domain that is transported by colloids to the 
total flux exiting the corrosion product domain (in dissolved state or sorbed onto colloids). The 
mass of radionuclides in the fluid exiting the corrosion products domain is expected to be 
proportioned such that the mass of radionuclide species i sorbed onto all colloids is some fraction 
of the total mass of radionuclide species i exiting the system in all formsaqueous, reversibly 
sorbed, and irreversibly sorbed. Observations in nature, such as the transport of Pu from the 

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ANL-WIS-PA-000001 REV 01 6-154 November 2004 
Benham test site (Kersting et al. 1999 [DIRS 103282]) indicate that this fraction is about 
95 percent. 
This is expressed as: 
95 . 0 
out flux mass total 
out flux mass colloid = = . . (Eq. 6.5.3.4-1) 
This flux out ratio value of 95 percent is uncertain with an uncertainty range of 0.9 to 0.99 
associated with it (BSC 2004 [DIRS 170025], Table 6-12, p. 6-72). It also may be a function of 
time, since the observation time for the Benham test is only about 50 years. In TSPA-LA, 
irreversible sorption occurs only for Pu and Am. 
The dependence of the forward rate constant on the flux out ratio is obtained from an analytical 
solution of a finite difference approximation of transport in the corrosion products domain. The 
function for evaluating the forward rate constant is given by Equation B-72 in Appendix B. 
This treatment applies in a seep environment. The calculated forward rate constant is 
constrained to be less than or equal to the maximum value of the sampled range, 0.24 m3 m-2 yr-1. 
6.5.3.5 Discretization and Development of Computational Model for TSPA-LA 
The continuum mass balance equations for EBS transport model are described and developed in 
Section 6.5.1.2. The one-dimensional mass balance equation describing transport of dissolved 
and reversibly sorbed radionuclide species i is provided by Equation 6.5.1.2-46. The 
one-dimensional mass balance equations for irreversibly sorbed radionuclide species i on iron 
oxyhydroxide colloids and corrosion products are given by Equations 6.5.1.2-47 and 6.5.1.2-48, 
respectively. The solution of these continuum-form mass balance equations is approximated for 
the purpose of numerical modeling by the solution of discrete forms of these equations using a 
finite-difference approach. This requires the discretization of the time derivative (or mass 
accumulation term) and the advective and diffusive terms for both dissolved and colloidal 
transport. All other source terms and decay terms do not require discretization in either time or 
space. 
Numerical modeling of the EBS radionuclide transport is performed using the GoldSim software 
(Golder Associates 2003 [DIRS 166572]) cell pathway capability, available in the GoldSim 
Contaminant Transport Module. The cell pathway acts as a batch reactor, where radionuclide 
mass is assumed to be instantaneously and completely mixed and partitioned among all media 
(fluid or solid) within the cell. Both advective and diffusive transport mechanisms can be 
explicitly represented using the cell pathways. When multiple cells are linked together via 
advective and diffusive mechanisms, the behavior of the cell network is mathematically 
described using a coupled system of differential equations, and is mathematically equivalent to a 
finite difference network. GoldSim numerically solves the coupled system of equations to 
compute the radionuclide mass present in each cell and the mass fluxes between cells as a 
function of time. Both initial and boundary conditions for a cell can be defined explicitly, and 
systems of varying geometry can be modeled. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-155 November 2004 
Within a computational cell network, each cell is allowed to communicate by advection and/or 
diffusion with any other cell. This concept is crucial in implementing the bifurcation of diffusive 
fluxes across an interface between a single continuum domain and a dual continuum domain, 
such as at the interface between the invert domain and the unsaturated zone. Each computational 
cell is provided with parameters describing water volumes, diffusive properties, and advective 
and diffusive flux links to other cells. Between any two cells, the diffusive flux can be 
bidirectional, depending on the concentration gradient, while the advective flux is unidirectional. 
The output of a cell is given in terms of the advective and diffusive mass fluxes for radionuclide 
species i and its concentration at the cell center. 
The number of cells in the finite-difference network and the discretization of the cells is chosen 
in such a way as to capture the unique physical and chemical properties of the EBS components 
with respect to radionuclide transport. The abstractions are in the form of logic statements and 
stochastic distributions that provide a method for linking various cells in the network. 
Implementation of the EBS flow and transport model for TSPA-LA uses the output of the drift 
seepage model (BSC 2004 [DIRS 169131]), the models for drip shield and waste package 
degradation (BSC 2004 [DIRS 169996]), the EBS physical and chemical environment model 
(BSC 2004 [DIRS 169860]), the thermal-hydrologic environment model (BSC 2004 
[DIRS 169565]), and the waste form degradation and mobilization model (BSC 2004 
[DIRS 167618]); Defense HLW Glass Degradation Model (BSC 2004 [DIRS 169988]); and 
CSNF Waste Form Degradation: Summary Abstraction (BSC 2004 [DIRS 169987]). The flow 
through various cells is based on the continuity equations and conservation of mass, as discussed 
in Section 6.3. An overview of the computational model for TSPA-LA, as implemented using 
GoldSim, is provided below. 
Radionuclide transport through the waste package is modeled by spatially discretizing the waste 
package into two domains: an upstream waste form domain and a downstream corrosion 
products domain. As implemented using GoldSim, a single waste form cell represents the entire 
volume of the waste form domain, while a single corrosion products cell represents the entire 
volume of the corrosion products domain. These are illustrated in Figure 6.5-5 below by the 
EBS portion of the cell network  waste form cell, corrosion products cell, and invert cell. 
The waste form cell receives mass from a specialized GoldSim Source cell, which models the 
waste package failure, degradation of the waste form, and release of the inventory for possible 
transport through the EBS. The Source cell provides the specified flux boundary condition for 
solving the mass transport equations. Both advective and diffusive transport can occur from the 
waste form cell to the corrosion products cell. Reversible and irreversible sorption of 
radionuclides to the corrosion products along with colloid facilitated transport of radionuclides is 
modeled as described in Appendix B. Three types of colloids, namely, waste form colloids, iron 
oxyhydroxide colloids, and groundwater colloids, are considered that can facilitate the transport 
of radionuclides by reversible and/or irreversible sorption. The waste form colloids are 
generated in the waste form cell (for the co-disposal waste package only), while the iron 
oxyhydroxide colloids and groundwater colloids are modeled in the corrosion products cell. All 
three types of colloids can transport to the downstream cells by diffusion and advection. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-156 November 2004 
The discretization of the invert domain, using GoldSim, consists of one cell. Both advective and 
diffusive flux communication exists between the corrosion products and invert cells. Advective 
flux due to imbibition from the host rock to the invert may enter the invert cell. 
Below the invert, part of the near-field UZ is modeled by an array of cells. The inclusion of the 
UZ portion in the model serves to establish a far field zero-concentration boundary and an 
accurate representation of the flux at the invert-to-UZ interface. The EBS-UZ interface 
submodel is described in more detail in Section 6.5.3.6. The dual continuum approach for 
modeling the UZ is achieved by creating UZ matrix and fracture cells. The invert cell 
communicates with the UZ matrix and fracture cells directly below it in the UZ cell array (see 
Section 6.5.3.6). 
The following description will focus on discretization of the mass balance equation for the 
dissolved and reversibly sorbed mass (Equation 6.5.1.2-46). Similar treatments apply to the 
mass balance transport equations for the irreversibly sorbed radionuclide species. In order to 
describe the time discretization, let the superscript n represent a solution at the nth time. The nth 
time step assumes the radionuclide concentrations are known at time level n, and the solution 
provides the concentrations at time level n+1. Over this time step, the accumulation term uses a 
first order backward in time discretization: 
[ ] ( ) 
1 
t 
C C R S 
C R S 
t 
n 
i 
n 
i 
n
fi w 
i fi w . 
- 
 
.
. + f 
f , (Eq. 6.5.3.5-1) 
where the adsorption retardation factor, 
cGW dicGW cFeOx dicFeOx cWF dicWF 
w
dis b 
fi C K C K C K 
S
K R + + + + = 
f 
. 
1 , (Eq. 6.5.3.5-2) 
and the cell water content are evaluated at the beginning of the time step, and t . is the time step 
size from the nth to the ( )th 1 + n time. 
The advective transport is discretized with a first order backward (with respect to the flow 
direction) difference approximation. If the mass balance is applied to cell B, and the advective 
flux is from cell A to cell B with magnitude wz q (m3 water m-2 yr-1), then 
( ) [ ] 
( ) [ ] 
( ) [ ] 
, 1 
1 
1 
1 
1 
B 
n 
i 
n 
cGW dicGW cFeOx dicFeOx cWF dicWF 
n 
wz 
A 
n 
i 
n 
cGW dicGW cFeOx dicFeOx cWF dicWF 
n 
wz 
i cGW dicGW cFeOx dicFeOx cWF dicWF wz 
C C K C K C K Q 
C C K C K C K Q 
C C K C K C K q 
z 
+ 
+ 
+ + + - 
+ + + 
 + + + 
.
. 
(Eq. 6.5.3.5-3) 
where wz Q (m3 water m-3 cell B yr-1) is the advective water volume flux per unit bulk volume. 
The advective flux and colloid concentrations are evaluated at the beginning of the time step. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-157 November 2004 
The concentration of radionuclide species i is evaluated at the end of time step. The first term in 
the difference approximation is the advective mass flux entering cell B from cell A. The second 
term is the advective mass flux exiting cell B. 
Consider the accumulation of solute mass in cell B due to diffusion. Suppose there is a diffusive 
flux link from cell A to cell B and from cell B to cell C. The dissolved mass diffusive flux 
accumulation in cell B is approximated by: 
B 
C B B A i 
w V 
F F 
x 
C D S 
x 
/ / - 
 .. 
. 
.. 
. 
. 
. 
.
. 
f , (Eq. 6.5.3.5-4) 
where B A F / is the diffusive mass flux (mass/time) across cells A and B interface. Similarly, 
C B F / is the diffusive mass flux (mass/time) across cells B and C interface. Consider the 
discretization of the diffusive flux at the A/B interface. A similar representation occurs at the 
B/C interface. 
Apply Ficks First Law and assume continuity of flux at the interface. Then the flux entering the 
A/B interface from cell A must equal the flux exiting the A/B interface to cell B. This interface 
flux continuity condition is expressed as: 
[ ] [ ] ( ) 
[ ] [ ] ( ), 1 
/ 
1 
/ 
1 1 
/ 
B 
n 
i B A 
n 
i 
B 
w 
B A 
n 
i A 
n 
i 
A 
w 
B A 
C C 
L
DA S 
C C 
L
DA S F 
+ + 
+ + 
- .. 
. 
.. 
. = 
- .. 
. 
.. 
. = 
f
f 
(Eq. 6.5.3.5-5) 
where 1 + n 
i C is the concentration at time step n+1 at the interface, as indicated by the subscript 
A/B, and D, A , and L are the cell effective diffusion coefficient, diffusive area, and diffusive 
length, respectively. If the A/B interface diffusive flux is expressed as an interface diffusive 
conductance times the concentration difference between cells A and B: 
( ) B A B A c B A C C D F - = / _ / , (Eq. 6.5.3.5-6) 
then the flux continuity condition provided by Equation 6.5.3.5-5 gives the interface diffusive 
conductance as: 
B w A w 
B A c 
DA S 
L 
DA S 
L 
D 
. .. 
. 
. .. 
. 
+ . .. 
. 
. .. 
. 
= 
f f 
1 
/ _ . (Eq. 6.5.3.5-7) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-158 November 2004 
The diffusive conductance is the harmonic average of 
L
DA Sw 
2 
f 
between the two cells. At the B/C 
interface a similar expression gives: 
C w B w 
C B c 
DA S 
L 
DA S 
L 
D 
. .. 
. 
. .. 
. 
+ . .. 
. 
. .. 
. 
= 
f f 
1 
/ _ . (Eq. 6.5.3.5-8) 
The discretization of the accumulation of solute mass in cell B due to diffusive transport is: 
[ ] [ ] ( ) [ ] [ ] ( ) 
B 
A 
n 
i B 
n 
i B A c B 
n 
i C 
n 
i C B c 
w V 
C C D C C D 
x
c D S 
x 
1 1 
/ _ 
1 1 
/ _ 
+ + + + - - - 
 .. 
. 
.. 
. 
.
. 
.
. 
f . (Eq. 6.5.3.5-9) 
The mass balance equations are discretized with the dependent concentration variable for the 
spatially dependent terms evaluated at the end of time step, 1 + n 
i C . This is stated explicitly in the 
discretization of the advective/diffusive terms. For other source terms, such as radionuclide 
decay, irreversible sorption reaction onto iron oxyhydroxide material and so forth, the 
concentration is evaluated at the end of the time step. In this sense, the mass balance equations 
are fully implicit and the discretization provides numerical stability. However, coefficient terms 
such as the moisture content are evaluated at the beginning of the time step. This formulation 
results in a linear system of equations that is solved for concentrations. If the coefficient 
dependence on concentrations were evaluated at the end of time step, then the resulting 
discretized algebraic equations would be nonlinear. The nonlinear system would require much 
more computational effort. Furthermore, the computational modeling tool (GoldSim) only 
solves linear systems. For this reason, all concentration dependent coefficient terms are 
evaluated explicitly at time level n. 
The rate constant, embed 
i ., for conversion of mass from solution to embedded mass on the waste 
form colloids, is calculated at each time step from information provided by the previous time 
step. Suppose that the solution for all radionuclide and colloid concentrations has been 
determined at time level n and the solution at time level (n+1) is required. At the known time 
level n, the concentration with respect to the water volume of the embedded radionuclide mass, 
( )n embed 
i C , and the waste form colloid mass, ( )n 
cWF C , are determined by the waste package 
chemistry as discussed in Waste Form and In-Drift Colloids-Associated Radionuclide 
Concentrations: Abstraction and Summary (BSC 2004 [DIRS 170025], Section 6.5.1.1, 
Step 1a). The ratio of the radionuclide concentration to the colloid concentration is the ratio of 
radionuclide mass to waste form colloid mass. The advective/diffusive mass rate of the waste 
form colloid mass, ( )n wfc 
diff adv Q / , is provided from the previous time step solution of the waste form 
colloid mass balance transport equation. The expression 
n 
cWF 
embed 
i wfc 
diff adv C 
C Q . .. 
. 
. .. 
. 
/ represents the 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-159 November 2004 
advective/diffusive mass flux rate of embedded mass of species i for the previous time step. The 
discrete mass balance for embedded radionuclide mass is then expressed in the form: 
( ) ( ) 
( )( ) ( ) . 
/ 
1 
1 
n 
i 
embed 
i 
n 
w 
embed 
i i 
embed 
ip 
M 
ip ip 
n 
w 
n 
cWF 
embed 
i wfc 
diff adv 
n n 
n embed 
i w 
n embed 
i w 
C S C C r S 
C 
C Q 
t t 
C S C S 
. f . . f 
f f 
+ - + 
. .. 
. 
. .. 
. 
= 
-
- 
- 
- 
(Eq. 6.5.3.5-10) 
This equation is solved for the conversion rate embed 
i .. This value, which is calculated from 
information at time level n, is then used as the conversion rate in the mass balance for the 
radionuclide concentration in solution at time level n+1. 
The above diffusive flux discussion considers the diffusive flux communication from cells within 
a single continuum. For transport from the invert domain (single continuum) to the UZ (dual 
continuum), the flux continuity condition at the interface provides the diffusive flux bifurcation 
between the single continuum and the dual continuum. 
The diffusive fluxes of radionuclide species i within the invert cell, the UZ fracture cell, and the 
UZ matrix cell are, respectively, 
( ) 
( ),  / 
/ 
/ 
UZ iI iI I 
UZ iI iI 
I 
UZ I I w 
iI 
C C D 
C C 
L 
A D S F 
- = 
- = 
f 
(Eq. 6.5.3.5-11) 
( ) 
( ),  / 
/ 
/ 
if UZ iI f 
if UZ iI 
f 
UZ I f w 
if 
C C D 
C C 
L 
A D S 
F 
- = 
- = 
f 
(Eq. 6.5.3.5-12) 
( ) 
( ),  / 
/ 
/ 
im UZ iI m 
im UZ iI 
m 
UZ I m w 
im 
C C D 
C C 
L 
A D S F 
- = 
- = 
f 
(Eq. 6.5.3.5-13) 
where 
I D = effective diffusion coefficient within the invert cell (cm2 s-1), 
f D = effective diffusion coefficient within the UZ fracture cell (cm2 s-1), 
m D = effective diffusion coefficient within the UZ matrix cell (cm2 s-1), 
UZ I A / = diffusive area between the invert and UZ cells (m2), 
I L = diffusive length within the invert cell (m), 
f L = diffusive length within the UZ fracture cell (m), 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-160 November 2004 
m L = diffusive length within the UZ matrix cell (m) = f L , 
iI C = concentration of radionuclide species i in the invert cell (kg i m-3), 
if C = concentration of radionuclide species i in the UZ fracture cell (kg i m-3), 
im C = concentration of radionuclide species i in the UZ matrix cell (kg i m-3), 
UZ iI C / = concentration of radionuclide species i at the interface between the invert 
and UZ cells (kg i m-3), 
and the 
L
DA S D w f 
=  are respective diffusive conductances (cm3 s-1). 
The flux continuity at the interface requires: 
im if iI F F F + = . (Eq. 6.5.3.5-14) 
From the flux continuity, the interface concentration of radionuclide species i is determined as a 
function of the diffusive parameters and the cell concentrations as: 
m f I 
im m if f iI I 
UZ iI D D D 
C D C D C D 
C    
   
/ + + 
+ + 
= . (Eq. 6.5.3.5-15) 
This provides the invert intergranular and intragranular diffusive fluxes of radionuclide species i, 
respectively, as: 
( ) ( ) if im 
m f I 
m f 
if iI 
m f I 
f I 
if C C 
D D D 
D D 
C C 
D D D 
D D 
F - 
+ + 
+ - 
+ + 
=    
  
   
  
(Eq. 6.5.3.5-16) 
( ) ( ) if im 
m f I 
m f 
im iI 
m f I 
m I 
im C C 
D D D 
D D 
C C 
D D D 
D D F - 
+ + 
- - 
+ + 
=    
  
   
  
. (Eq. 6.5.3.5-17) 
The expression for the diffusive flux of radionuclide species i from the invert cell to the UZ 
fracture cell can be expressed as a diffusive conductance multiplied by a concentration difference 
of radionuclide species i between the invert cell and the UZ fracture cell plus a corrective flux 
between the UZ fracture and matrix cells. Similarly, the expression for the diffusive flux from 
the invert to the UZ matrix cell is expressed as a diffusive flux between the invert and the UZ 
matrix cell minus the same corrective flux between the UZ cells. The inclusion of the corrective 
flux term is explained as follows. The flux to both UZ cells should depend on the diffusive 
properties in the invert cell and the two UZ cells, together with the concentrations in these three 
cells. Therefore, the flux to the UZ fracture cell cannot be expressed only in terms of the 
concentration drawdown between the invert cell and the UZ fracture cell. The corrective term 
includes the dependence of the UZ fracture flux on the concentration of radionuclide species i in 
the UZ matrix cell. Further, the corrective flux term is not a true flux expression between the 
two UZ cells, since the diffusive conductance coefficient is dependent on the diffusive area 
between the invert and the UZ, and the diffusive lengths are the lengths with respect to flow from 
the invert cell to the UZ cells. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-161 November 2004 
The UZ fluxes result in defining three diffusive conductances from the flux expressions: 
( ) ( ) if iI 
m f I 
f I 
if iI If C C 
D D D 
D D 
C C D - 
+ + 
= -    
  
 , (Eq. 6.5.3.5-18) 
( ) ( ) im iI 
m f I 
m I 
im iI Im C C 
D D D 
D D C C D - 
+ + 
= -    
   , (Eq. 6.5.3.5-19) 
( ) ( ) if im 
m f I 
f m 
if im mf C C 
D D D 
D D 
C C D - 
+ + 
= -    
  
 , (Eq. 6.5.3.5-20) 
where 
If D 
= effective diffusive conductance between invert cell and UZ fracture cell 
(cm3 s-1); 
Im D 
= effective diffusive conductance between invert cell and UZ matrix cell 
(cm3 s-1); 
mf D 
= effective diffusive conductance between UZ fracture and matrix cells 
(cm3 s-1). 
In order to accommodate the GoldSim representation of diffusive conductance as a two-term 
expression, the diffusive conductances of radionuclide species i are written as: 
( ) ( ) 
( ) ( ) 
( )f w 
f 
m w f w 
f w 
I w 
I 
If 
DA S 
L 
D S D S 
D S 
DA S 
L 
D 
f 
f f 
f 
f 
+ 
. .. 
. 
. .. 
. 
+ 
= 1  , (Eq. 6.5.3.5-21) 
( ) ( ) 
( ) ( ) 
( )m w 
m 
m w f w 
m w 
I w 
I 
Im 
DA S 
L 
D S D S 
D S 
DA S 
L D 
f 
f f 
f 
f 
+ 
. .. 
. 
. .. 
. 
+ 
= 1  , (Eq. 6.5.3.5-22) 
( ) ( ) 
( ) ( ) 
( )m w 
m 
I w m m w I 
m w I 
f w 
f 
mf 
DA S 
L 
D S L D S L 
D S L 
DA S 
L D 
f 
f f 
f 
f 
+ 
.. 
. 
.. 
. 
+ 
= 1  . (Eq. 6.5.3.5-23) 
Although the above approach is rigorous, it is complex and difficult to implement in the 
TSPA-LA model. A second approach that is easier to understand and simpler to implement, 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-162 November 2004 
while providing the same results as the above approach, is presented here. This approach 
requires introduction of an interface cell, located between the invert cell and the UZ cells. This 
interface cell provides an approximate interface concentration and the resulting flux split at the 
invert-to-UZ cell interface. The interface cell is conceptualized as a very thin slice of the invert 
cell. This implies the interface cell takes on the invert diffusive properties, with the exception of 
diffusive length. Let the diffusive length within the interface cell be some small fraction (a scale 
factor) of the invert diffusive length, say, Interface_Scale_Factor = 10-6: 
I int I L L 6 10- 
- = . (Eq. 6.5.3.5-24) 
The diffusive conductance between the invert cell and the invert interface cell is calculated as the 
harmonic average: 
( ) ( ) int I w 
int I 
I w 
I 
int I I 
DA S 
L 
DA S 
L D 
- 
- 
- 
+ 
= 
f f 
1  / . (Eq. 6.5.3.5-25) 
For diffusion between the interface cell and the UZ fracture and matrix cells, the diffusive 
conductances of radionuclide species i are, respectively, 
( ) ( )f w
UZ 
int I w 
int I 
f int I 
DA S
L 
DA S 
L D 
f f 
+ 
= 
- 
- 
- 
1  / , (Eq. 6.5.3.5-26) 
( ) ( )m w
UZ 
int I w 
int I 
m int I 
DA S
L 
DA S 
L D 
f f 
+ 
= 
- 
- 
- 
1  / . (Eq. 6.5.3.5-27) 
The interface cell concentration of radionuclide species i is computed as part of the cell network 
solution. Because the transport mass balance equations conserve mass, the mass flux leaving the 
interface cell must equal the sum of the mass fluxes entering the two UZ cells. The solution 
provides the flux continuity across the interface between the invert interface cell and UZ cells. 
This formulation expects the flux exiting the invert cell (or entering the interface cell) is 
approximately equal to the flux exiting the interface cell. This approximation is dependent on 
the diffusive length within the interface cell. The error in this approximate solution approaches 
zero as the diffusive length of the interface cell approaches zero. 
6.5.3.6 EBS-UZ Boundary Condition Implementation in TSPA-LA 
For TSPA-LA, a semi-infinite zero-concentration boundary condition is used for the EBS-UZ 
interface. This is approximated by applying an effective zero-concentration boundary at 
approximately three drift diameters below the invert-UZ boundary into the UZ. In an alternative 
approach, a zero-concentration boundary condition can be used at the interface between the 
invert and the UZ, which will result in an unrealistically high diffusive gradient through the 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-163 November 2004 
invert. By moving the zero-concentration boundary some distance below the invert, a more 
realistic diffusive gradient through the invert is achieved. 
In the EBS-UZ interface submodel, the near-field UZ is modeled as a dual continuum of 
overlapping UZ-matrix and UZ-fracture media. This approach is consistent with the 
dual-permeability modeling approach used by the UZ transport model, as described in Particle 
Tracking Model and Abstraction of Transport Processes (BSC 2004 [DIRS 170041]). The 
matrix and fracture continua are represented in the EBS RT Abstraction by a two-dimensional 
vertical array of cells oriented parallel to a cross section of a drift and located immediately 
beneath a drift (Figure 6.5-5). This array consists of three columns or vertical zones, with each 
zone containing both a fracture cell and a matrix cell. The invert is in direct communication with 
the second or center zone of UZ matrix/fracture cells. Each zone is four layers deep in the 
vertical direction. Thus, the array consists of twelve pairs of matrix and fracture cells within the 
UZ. Laterally, each zone is one drift diameter wide, with the middle zone centered beneath the 
drift, so that each layer of the array extends one drift diameter on either side of the drift. In the 
longitudinal direction of a drift, the length of the array is equal to the length of the waste package 
being modeled. 
The thickness of the first (top) layer of cells is 10 percent greater than the average invert 
thickness (0.597 m), or 0.6567 m. The thickness of the second layer is double that of the first 
layer, or 1.3134 m. The third and fourth layers are given an arbitrary thickness of 5 m and 10 m, 
respectively. A collector cell is placed beneath the fourth layer and is given a very large, 
numerically infinite, water volume (1010 m3) to simulate an effective zero-concentration 
boundary. This collector cell acts as a sink for all the mass flow from the invert and UZ cells. 
As depicted in Figure 6.5-5, each fracture cell interacts, via diffusive connection only, with the 
matrix cell of the same zone. The fracture cell also interacts via diffusive connection vertically 
with the fracture cell of underlying and overlying layers of the same zone. The matrix cell of 
each zone interacts via diffusive connection laterally with the matrix cells of adjacent zones and 
vertically with the matrix cell of underlying and overlying layers of the same zone. 
Radionuclides diffuse based on the concentration gradient between cells. Advection occurs 
downward only, from the fracture cell of one layer to the fracture cell of the underlying layer in 
the same zone, and from the matrix cell of one layer to the matrix cell of the underlying layer in 
the same zone; advection does not occur across zones. Each zone is spatially distinct. Each is 
one drift diameter in width. The only connection possible between adjacent zones is through the 
middle zone. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-164 November 2004 
Figure 6.5-5. Computational Grid in the EBS-UZ Interface Submodel 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-165 November 2004 
The mass flux from the invert flows into the top layer of the middle zone in the UZ. The portion 
of the advective flux from the invert that is attributable to the total dripping flux (F1) flows into 
the UZ fractures. The imbibition flux into the invert (F7) flows out of the invert into the UZ 
matrix. The diffusive flux from the invert can go into both UZ continua based on the 
concentration gradient and effective diffusion coefficient. The advective flux flowing through 
the UZ fracture cells in the middle zone is given by the greater of the advective flux out of the 
invert (F1) and the steady state UZ fracture flux. Because of the application of a flow focusing 
factor in the calculation of the total dripping flux (F1), the flux going into UZ fractures in the 
EBS-UZ interface submodel can be greater than the steady state UZ fracture flux. The advective 
flux in the two outer zones is given by the steady state UZ flow in each continuum at the 
repository horizon; the drift shadow effects are ignored. 
For the advective mass transport calculation shown in Equation 6.5.3.5-3, volumetric discharge 
for the fracture and matrix continua is needed. Since fracture and matrix percolation flux 
(described in Section 6.5.2 and provided by DTN: LB0307FMRADTRN.001 [DIRS 165451]) is 
given as specific discharge, the volumetric flux is calculated by multiplying the percolation flux 
for each continuum by the projected bulk area normal to the flux, where the projected area UZ A 
is calculated as: 
WP D UZ L d A = , (Eq. 6.5.3.6-1) 
where D d is the drift diameter (m) and WP L is the length of a waste package (m). This area is 
used for the diffusive and advective flux calculations between UZ cells. For the calculation 
between the invert and UZ, the area UZ I A / given by Equation 6.5.3.3.-4 is used. 
The bulk volume calculation for each continuum is computed by multiplying the bulk volume for 
each discretized zone in each layer (based on the geometry) by either the fracture porosity 
(fracture fraction) or matrix porosity. Similarly, the water volume is calculated by multiplying 
the bulk volume of each continuum by its respective saturation. 
For diffusive mass transport, in the calculation shown in Equation 6.5.3.5-5, the effective 
diffusion coefficient for the matrix continuum is calculated based on Equation 6-52 in 
Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040]): 
me m ms k D 10 10 log 165 . 0 0138 . 0 49 . 3 log + + - = . , (Eq. 6.5.3.6-2) 
where ms D is the effective UZ matrix diffusion coefficient (cm2 s-1), m . is the matrix water 
content (percent), and me k is the matrix effective permeability (m2) (BSC 2004 [DIRS 170040], 
Equation 6-57): 
m rm me k k k = , (Eq. 6.5.3.6-3) 
where rm k is the relative permeability of unsaturated zone tuff matrix (dimensionless), and m k is 
the intrinsic permeability of unsaturated zone tuff matrix (m2). The same value of the diffusion 
coefficient is applied to the fracture diffusion coefficient as recommended by the Drift-Scale 

EBS Radionuclide Transport Abstraction 
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Radionuclide Transport (BSC 2004 [DIRS 170040]). The sampling of the input parameters is 
described in Section 6.5.2. 
The diffusive area between the fracture and matrix continua is computed by multiplying the bulk 
volume by the fracture interface area, which provides the connection area per unit bulk volume. 
This diffusive area is further reduced by the fracture-matrix interface reduction factor, given as 
. + 1
ef S , where ef S is the effective fracture saturation, and . is the active fracture parameter (UZ 
Flow Models and Submodels, BSC 2004 [DIRS 169861]). The effective fracture saturation 
( ef S ) is computed as: 
wfr
wfr wf 
ef S
S S 
S 
-
- 
= 
1 
, (Eq. 6.5.3.6-4) 
where wf S is the fracture water saturation, and wfr S is the fracture residual saturation. The mass 
flux of radionuclides from the invert domain to the dual continuum UZ, computed at the 
boundary of the EBS-UZ interface (between the invert cell and the adjacent UZ matrix and 
fracture cells), is passed to the UZ transport model for TSPA-LA calculations as described in 
Particle Tracking Model and Abstraction of Transport Processes (BSC 2004 [DIRS 170041]). 
In addition to the total mass flux, the relative fraction of the mass going into each of the fracture 
and the matrix cells at the EBS-UZ boundary is required by the UZ transport model. This 
fracture-matrix partitioning of mass is calculated on the basis of the mass fraction going into the 
fracture continuum (compared to the matrix continuum) from the invert domain in the EBS-UZ 
interface submodel. This partitioning is time dependent and captures the temporal processes 
active in the EBS, such as varying radionuclide concentrations in the waste form, corrosion 
products, and invert domains, and the changing water flux through various subcomponents of the 
EBS. Furthermore, this partitioning is computed by solving the mass transport equations for the 
EBS and part of the UZ as a coupled system with appropriate boundary conditions and adopting 
a modeling approach consistent with the Multiscale Thermohydrologic Model dual continuum 
model for the invert (BSC 2004 [DIRS 169565]) and the dual continuum transport model for the 
UZ (BSC 2004 [DIRS 170041]). 
Sorption of radionuclides to the UZ matrix continuum is modeled by applying the devitrified tuff 
Kd values from the UZ submodel. For sorption calculations, the mass of UZ matrix continuum is 
calculated as: ( ) f b b V f . - 1 , where b V is the bulk volume of the matrix cell considered (m3), f f 
is the fracture porosity (fraction), and bm . is the dry bulk density of TSw35 matrix (kg m-3). 
All three types of colloids are transported from the invert to the UZ cells. Groundwater colloids 
are present in all four layers. The iron oxyhydroxide and waste form colloids with reversibly 
sorbed radionuclides are modeled to be present in only the first two layers of the middle column, 
making the groundwater colloid the only type of colloid available for far-field transport, 
consistent with colloid-facilitated transport modeled in the UZ is covered in Particle Tracking 
Model and Abstraction of Transport Processes (BSC 2004 [DIRS 170041]). 

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6.6 MODEL FORMULATION FOR ALTERNATIVE CONCEPTUAL MODELS 
6.6.1 Bathtub Flow Model 
The conceptual model for the TSPA-LA is based on the presence of continuous flow paths 
through the patches and stress corrosion cracks that penetrate the waste package. More 
specifically, the TSPA-LA model conceptualizes that vertical flow of seepage into the waste 
package, through the waste form and out of the waste package is not impeded by the location of 
patches and stress corrosion cracks on the surface of the waste package. There is no long-term 
build-up and retention of liquid within the waste package for flow and transport. There is also no 
resistance to the flow through the waste form. The TSPA-LA approach attempts to maximize the 
immediate release and mobilization of radionuclides into the local groundwater environment. 
This approach is referred to as the flow through geometry. 
An alternative conceptual model to the flow through geometry is the bathtub geometry 
(Mohanty et al. 1996 [DIRS 130419]). The bathtub geometry allows seepage to collect within 
the waste package before being released to the EBS. In theory, a bathtub geometry could result 
in the sudden release of a large pulse of radionuclides when a package overflows with liquid or 
when a second patch appears abruptly beneath the water line. 
The bathtub effect would be most important during the period when only a few patches or 
cracks have penetrated the drip shield and waste package. In this situation, there may be 
penetrations through the top of the waste package while the bottom surface remains intact, 
leading to retention of liquid. At later times, the presence of multiple penetrations makes a 
flow-through geometry the more likely configuration. 
The response of the bathtub geometry is evaluated for a primary case and for three secondary 
cases. The primary case includes consideration of two limiting conditions on radionuclide 
releases: dissolution rate limited and solubility limited. Tc is typical of dissolution rate limited 
radionuclides. The Tc released due to waste dissolution can always be dissolved in the available 
water because the solubility limit of Tc is high (BSC 2004 [DIRS 169425], Section 6.14). Np is 
typical of the solubility limited type of radionuclide, where all the release of Np from dissolution 
is limited by its low solubility (BSC 2004 [DIRS 169425], Section 6.6). 
The results for the primary case are based on a closed form analytic solution with constant values 
of inflow rate, dissolution rate, and solubility. The three secondary cases consider a step change 
in inflow rate, such as would occur from a climatic change, a step change in water chemistry, or 
a step change in flow geometry, as would occur if a patch suddenly appeared beneath the 
waterline. The basic geometry and flow pattern for the primary bathtub model is shown in 
Figure 6.6-1 (from Mohanty et al. 1996 [DIRS 130419], Figure 2-7) in q is identical to 4 F and in 
Section 6.3.1.1. 

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qin = F4 
q out 
Liquid Overflow Level 
Figure 6.6-1. Schematic of the Bathtub Geometry for the Waste Package 
6.6.1.1 Primary Case 
6.6.1.1.1 Dissolution-Rate-Limited Radionuclide 
In this case, the concentration of radionuclides is limited by the rate of dissolution. Consider the 
system shown in Figure 6.6-1, with a constant inflow rate, in q , and let tub V be the total volume of 
liquid that can be retained within the waste package before it overflows. The response of the 
waste package is a two step process. During Step 1, the package is filling with liquid and the 
outflow rate, out q , is zero. This condition continues until the waste package fills with liquid at a 
time, fill t , given by in tub q V / . Step 2 occurs after time fill t ; the amount of liquid inside the waste 
package remains constant, and in out q q = . This is a steady state condition, consistent with the 
assumption that in q is constant and that liquid does not continue to accumulate within the 
package. The following analysis also supposes there is complete contact between the liquid and 
the waste form within the waste package, and that the dissolution rate is constant. 
During Step 1, for time t such that , 0 fill t t < < the dissolution of a radioisotope into the water 
inside the waste package can be represented as: 
,i s i r m . = & (Eq. 6.6.1.1.1-1) 
where 
i m& = the rate of release of radionuclide into the liquid (kg s-1) 
s r = the dissolution rate of the waste form (kg s-1) 
i . = the mass fraction of radioisotope i released per unit mass of waste form 
(dimensionless); i . is less than one for a waste form with multiple radionuclides. 
During the fill period out q is zero, so the mass, ) (t mi , of radioisotope dissolved within the liquid 
in the waste package at time t is given by: 
, ) ( t r t m i s i . = (Eq. 6.6.1.1.1-2) 

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because s r and i . are constant. Similarly, the volume of liquid in the waste package at time t, 
) (t V , is given by: 
, ) ( t q t V in = (Eq. 6.6.1.1.1-3) 
so the concentration of dissolved isotope i in the waste package, ) (t Ci , is 
. 
) ( 
) ( ) ( 
in
i s 
in
i s i 
i q 
r 
t q 
t r 
t V 
t m t C 
. . 
= = = (Eq. 6.6.1.1.1-4) 
The concentration, ) (t Ci , is constant during the fill phase because the values of s r , i ., and in q 
are chosen to be constant. This condition is appropriate because the dissolved mass, i m , and the 
volume of liquid, V, are linear functions of the time (and initially both are zero), so their ratio 
remains constant. 
The result in Equation 6.6.1.1.1-4 holds for each dissolution-rate-limited radioisotope i in the 
waste form, although the numerical value of ) (t Ci differs because the mass fraction, i ., is 
different for each isotope. 
During Step 2, when fill t t > , the radioisotope mass within the waste package is a balance 
between the dissolution of radioisotope into the groundwater within the waste package and the 
loss of radioisotope due to outflow from the waste package: 
).(t C q r m i out i s i - = . & (Eq. 6.6.1.1.1-5) 
Because the water inflow rate, waste form solubility, and mass fraction of radioisotope i all 
remain constant, the concentration ) (t Ci remains constant even when the solution is removed at 
a rate out q . Therefore, at fill t t > , the net rate of radionuclide release into the water inside the 
waste package is zero (i.e., the dissolution rate is exactly offset by the outflow rate): 
0) ( = - = t C q r m i out i s i . & . (Eq. 6.6.1.1.1-6) 
For constant in q , with in out q q = , 
in 
i s 
i q 
r t C 
. 
= ) ( . (Eq. 6.6.1.1.1-7) 
The dissolved mass in the waste package is constant for fill t t > . In addition, the concentration of 
dissolved radionuclide is constant for all time 0 > t , as shown by Equations 6.6.1.1.1-4 and 
6.6.1.1.1-7. These results are reasonable because the waste package is in steady state for fill t t > . 
This means that the inflow rate equals the outflow rate and that any loss of dissolved 

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radionuclide mass in the outflow from the waste package is exactly balanced by the addition of 
dissolved radionuclide mass from dissolution of the waste form. 
The response for the comparable flow-through model has the same radionuclide concentration, 
) (t Ci , and the same release flux, given by out i q t C ) ( , as the bathtub geometry. The sole 
difference between the flow-through and bathtub models is that the flux from the flow-through 
model starts from 0 = t while the flux from the bathtub model is zero until time fill t . The 
bathtub model introduces a delay in the response but does not change the concentration in the 
package or the mass flux out of the package. 
Therefore, for the dissolution-rate-limited case, the flow-through model is bounding relative to 
the bathtub model for radionuclide releases from the waste package. This analysis considers 
advective transport with no sorption of radionuclides, whereas the current EBS transport model 
includes sorption onto stationary corrosion products (retardation in the waste package) as well as 
colloid-facilitated transport. In this analysis of alternative conceptual models, sorption onto 
stationary corrosion products inside the waste package would effectively reduce the dissolution 
rate. Since that rate is still constant and the same for both the flow-through and bathtub models, 
sorption would affect the concentrations of radionuclides in the outflow, but would have no 
impact on the conclusion that the bathtub model introduces a delay in releases compared to the 
flow-through model. Sorption onto colloids would have the opposite net effect of increasing the 
solubility and again would have no impact on the conclusions. 
6.6.1.1.2 Solubility-Limited Radionuclide 
The response for a solubility-limited radionuclide, in which the solubility limit of the 
radionuclide is instantaneous achieved, is similar to that for a dissolution-rate-limited 
radionuclide, in the sense that the bathtub model delays the release from the waste package but 
does not change the dose rate. 
During Step 1, , 0 fill t t < < the amount of radionuclide dissolved in the groundwater in the waste 
package can be represented as: 
,in si i q C m = & (Eq. 6.6.1.1.2-1) 
where si C is the solubility limit of the radionuclide. If the groundwater chemistry is constant, 
the solubility is constant and the mass, i m , of radioisotope retained in the waste package at time t 
is: 
. ) ( t q C t m in si i = (Eq. 6.6.1.1.2-2) 
The volume of liquid in the waste package at time t, ) (t V , is given by: 
, ) ( t q t V in = (Eq. 6.6.1.1.2-3) 

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so that the concentration of dissolved isotope in the waste package is: 
. 
) ( 
) ( ) ( si 
in 
in si i 
i C 
t q 
t q C 
t V 
t m t C = = = (Eq. 6.6.1.1.2-4) 
The concentration is constant during the fill phase and equal to the solubility limit, as would be 
expected. This is true for each radionuclide in the system, although the numerical values of the 
solubility limit vary. 
For fill t t > , the mass balance within the waste package is a steady state condition given by: 
0 ) ( ) ( = - = - = out 
tub 
i 
in si out i in si i q 
V 
t m q C q t C q C m& . (Eq. 6.6.1.1.2-5) 
The solution to Equation 6.6.1.1.2-5 with in out q q = is: 
, ) ( tub siV C t m = (Eq. 6.6.1.1.2-6) 
with 
.) ( si i C t C = (Eq. 6.6.1.1.2-7) 
Again the dissolved mass in the waste package is constant for fill t t > and the concentration of 
dissolved radionuclide is constant at the solubility limit for all times 0 > t . 
The comparable flow-through model has the same radionuclide concentration, si C , and the same 
release flux, given by out siq C , as the bathtub geometry. The sole difference is that the flux from 
the flow-through model starts from t = 0 while the flux from the bathtub model is zero until time 
fill t . The bathtub model introduces a delay in the response but does not change the dose rate. 
Therefore, the flow-through model is again bounding relative to the bathtub model because 
radionuclides are released with no delay time to the EBS. 
6.6.1.2 Secondary Cases 
The secondary cases evaluate the response of the bathtub model when changes occur in the 
groundwater inflow rate, in inflow chemistry, or in the flow geometry. 
6.6.1.2.1 Change in Inflow Rate 
The response of a bathtub model to a change in inflow rate differs for a solubility-limited or a 
dissolution-rate-limited radionuclide. The solubility-limited case is simpler because of chemical 
equilibrium and is discussed first. 
Consider a step change in inflow rate after the bathtub has filled for a solubility-limited 
radionuclide. Since kinetic effects are ignored, the chemical system is always at equilibrium and 

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the concentration within the waste package remains unchanged at the solubility limit. The only 
change in the system is that the radionuclide mass flux out of the waste package changes 
instantaneously from out iq C to new out iq C , . This response is exactly the same as it would be for the 
flow-through model, so the response of the bathtub model is identical to that for the flow-through 
model. 
Now consider a step change in inflow rate after the bathtub has filled for a 
dissolution-rate-limited radionuclide. In this case, the mass released per unit time remains 
constant because the dissolution rate remains constant, but the radionuclide concentration comes 
to a new equilibrium value. This new equilibrium value can be determined by 
Equation 6.6.1.1.1-7, with the product of concentration and liquid inflow remaining constant: 
, , , , i s old in old i new in new i r q C q C . = = . (Eq. 6.6.1.2.1-1) 
If the inflow rate decreases, the final concentration increases because the product of 
concentration and liquid inflow remains constant. A flow-through model has an instantaneous 
increase in concentration, whereas the bathtub model shows an exponential growth to the new 
concentration. Thus, the flow-through model is bounding for concentration released into the 
EBS because there is no delay in changing to the new increased radionuclide concentration. 
The exponential growth to the new concentration can be seen as follows. The replacement of 
old inflow with concentration old i C , with new inflow with concentration new i C , is represented 
through a parameter, , the volume fraction of old inflow to tub V , the total liquid volume in the 
bathtub. The rate of change of the volume of old inflow, old V , is given by: 
. , , new in new out 
old q q 
dt 
dV   - = - = (Eq. 6.6.1.2.1-2) 
Equation 6.6.1.2.1-2 represents the loss of old inflow through outflow, with the factor  
representing the (decreasing) volume fraction of old inflow that is lost. By definition, 
tub 
old 
V
V =  . (Eq. 6.6.1.2.1-3) 
Substituting this definition into the left-hand side of Equation 6.6.1.2.1-2 gives: 
. ,  
 
tub 
new in 
V 
q 
dt 
d - = (Eq. 6.6.1.2.1-4) 
The solution to Equation 6.6.1.2.1-4 with initial condition 1 =  at 0 = t is: 
. .. 
. 
. .. 
. 
- = t 
V 
q 
tub 
new in, exp  , (Eq. 6.6.1.2.1-5) 

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which corresponds to an exponential decay of i C from old i C , to new i C , . 
If the inflow rate were to increase, the concentration would decrease. In a flow-through model, 
the concentration would instantaneously decrease, whereas in the bathtub model, the 
concentration would exponentially relax to the new concentration. The flow-through model is 
then not bounding for concentration released into the EBS. The mass of radionuclide mobilized 
is identical, as implied by Equation 6.6.1.2.1-1, but the dissolved concentration varies with the 
amount of fluid flowing through the system. However, the TSPA-LA model passes mass to the 
unsaturated zone, rather than concentration, so the difference between the flow through model 
and the bathtub model for this case is not critical to performance. 
Finally, a change in inflow rate during the initial period, when the bathtub is filling, only affects 
the value of fill t and hence the delay until the bathtub fills, after which it behaves as described in 
Section 6.6.1.1. 
In summary, the response of the bathtub model to a change in inflow rate is identical to that of 
the flow-through model for solubility-limited radionuclides. For dissolution-rate-limited 
radionuclides, the response of the bathtub model is less bounding than the flow-through model 
when the inflow rate decreases (and concentration increases). If the inflow rate increases 
(resulting in a decrease in the outflow concentration of radionuclides), the bathtub model is more 
bounding than the flow-through model for dissolution-rate-limited radionuclides. 
6.6.1.2.2 Change in Inflow Chemistry 
Consider a step change in inflow chemistry after the bathtub has filled. Initially, there will be 
minor changes in concentration within the bathtub because the bulk of the water retains the 
original inflow composition. Eventually the old groundwater is flushed out and replaced with 
the new inflow, resulting in new concentrations within the bathtub. 
As in the preceding section where a change in inflow rate was examined, the replacement of old 
with new inflow can be represented through a parameter , representing the volume fraction of 
old inflow in tub V , the total liquid volume in the bathtub. The rates of change of the volumes of 
old and new inflow are given by: 
, out 
old q 
dt 
dV  - = (Eq. 6.6.1.2.2-1) 
and 
, ) 1 ( out in 
new q q 
dt 
dV  - - = (Eq. 6.6.1.2.2-2) 
where old V and new V represent the volumes of inflow with the old and new chemistries, 
respectively. Equation 6.6.1.2.2-1 represents the loss of old inflow through outflow, with the 
factor  representing the volume fraction of old inflow that is lost. Equation 6.6.1.2.2-2 

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represents the addition of new inflow and its partial loss through outflow. Remembering that 
in out q q = because of the steady state assumption, it follows that: 
. ; in 
new 
in 
old q 
dt 
dV 
q 
dt 
dV   + = - = (Eq. 6.6.1.2.2-3) 
By definition: 
tub 
old 
V
V =  . (Eq. 6.6.1.2.2-4) 
Substituting this definition into the left-hand equation in 6.6.1.2.2-3, it follows that: 
. 1   
 
fill tub 
in 
t V
q 
dt 
d - = - = (Eq. 6.6.1.2.2-5) 
The solution to Equation 6.6.1.2.2-5 with the initial condition 1 ) 0 ( =  is given by: 
fill t 
t 
e t 
- 
= ) (  . (Eq. 6.6.1.2.2-6) 
It follows that the old and new volumes of inflow are given by: 
fill t 
t 
tub old e V V 
- 
= (Eq. 6.6.1.2.2-7) 
and: 
. 1 . . 
.
. 
. . 
.
. 
- = 
- 
fill t 
t 
tub new e V V (Eq. 6.6.1.2.2-8) 
These equations say that the volume fraction of inflow with the old chemistry decays 
exponentially with the characteristic time fill t . Alternatively, the volume fraction of new inflow 
increases to 1.0 with a characteristic time of fill t for the exponential growth given by 
Equation 6.6.1.2.2-8. 
The impact of changing inflow chemistry on dissolution rate or solubility is much more difficult 
to predict analytically because chemical interactions are nonlinear. More specifically, the pH of 
mixtures of inflows is not proportional to  because the pH scale is proportional to the log of 
the hydrogen ion concentration and inherently nonlinear and because potential chemical 
interactions in mixtures, such as buffering, produce a nonlinear response. In addition, solubility 
and dissolution rate are often complex nonlinear functions of the pH. 

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Nonlinear response makes it particularly difficult to predict the time-dependent response for 
solubility; however, the starting state and the ending state, for fill t t >> , are well defined and can 
be approximated to first order by: 
. 1 ) ( , , . . 
.
. 
. . 
.
. 
- +  
- - 
fill fill t 
t 
new si 
t 
t 
old si si e C e C t C (Eq. 6.6.1.2.2-9) 
Consider the response when old si new si C C , , >> . This condition can easily occur for the actinides, 
where solubility increases by several orders of magnitude as pH changes from between 7 and 8 
to a value below 6 or above 10. In the limit of large new si C , , Equation 6.6.1.2.2-9 becomes: 
( old si new si C C , , >> ): . 1 ) ( , . . 
.
. 
. . 
.
. 
-  
- 
fill t 
t 
new si si e C t C (Eq. 6.6.1.2.2-10) 
In effect the initial solubility is negligible compared to new si C , , and solubility at late times 
increases to new si C , from below. Alternatively, if old si new si C C , , << , 
( old si new si C C , , << ): . ) ( , , new si 
t 
t 
old si si C e C t C fill +  
- 
(Eq. 6.6.1.2.2-11) 
Here the solubility decays towards a much smaller value in the new inflow mixture. 
While the details of the time-dependent behavior are unknown, the starting and ending states 
must be accurate and Equations 6.6.1.2.2-10 and 6.6.1.2.2-11 provide a simplified approximation 
to the transition from one chemical regime to another. The dissolution rate could replace 
solubility in Equations 6.6.1.2.2-9 through 6.6.1.2.2-11, and the same general conclusions would 
hold. 
In summary, the response of the bathtub model to a change in inflow chemistry is slower than 
that of a flow-through model, where the solubility or dissolution rate changes abruptly with a 
step change in inflow chemistry. The bathtub dampens or delays the response to a change in 
inflow chemistry over a time scale on the order of fill t to fill t 7 . The upper estimate of fill t7 
corresponds to an exponential factor of e-7 or 0.0009, at which point Equation 6.6.1.2.2-11 has 
reached an asymptote of new si C , . The analytic models cannot predict the precise time dependence 
because of the nonlinear effects of mixing on pH and of pH on solubility and dissolution rate. 
The flow-through model overestimates radionuclide releases compared to the bathtub model 
when solubility increases because the bathtub geometry delays the increase in radionuclide 
concentrations and mass fluxes from the waste package to the EBS. The case of increasing 
solubility or increasing dissolution rate is important because it will increase the peak dose rate. 
The fact that the flow-through model is not bounding when solubility or dissolution rate 

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decreases is therefore of less importance for performance assessment and is of secondary 
importance in selecting the conceptual model for flow through the waste package. 
6.6.1.2.3 Change in Patch Geometry 
The geometry for the bathtub model allows seepage to collect within the waste package before 
being released to the EBS. In the primary model (Figure 6.6-1), the patch is positioned such that 
release is governed by the condition in out q q = after the package fills with liquid. 
As an alternative to the primary patch model, consider a waste package that does not have an 
existing (outflow) patch on the side of the package, but instead has a second patch open abruptly 
beneath the water line. While the radionuclide concentration within the waste package is 
unchanged by the alternative location, failure results in the sudden release of a larger pulse of 
radionuclide mass at the time the second patch opens. Mathematically, the flux of radionuclides 
leaving the waste package in the primary model, pri F , is given by: 
, 
fill 
tub 
i in i out i pri t
V C q C q C F = = = (Eq. 6.6.1.2.3-1) 
and the flux of radionuclides leaving the waste package in the alternative model, alt F , is given 
by: 
, 
t 
V C F tub 
i alt . 
= (Eq. 6.6.1.2.3-2) 
where t . is the time to empty the retained liquid through the second patch. In theory, it is 
possible that fill t t << . , so that pri alt F F >> . 
Equations 6.6.1.2.3-1 and 6.6.1.2.3-2 have the same value for radionuclide concentration, i C , in 
the retained liquid because the chemistry of the groundwater is independent of patch location. 
Implicit in Equations 6.6.1.2.3-1 and 6.6.1.2.3-2 is that the second patch in the alternative 
conceptual model occurs when the volume of liquid is identical to the capacity of the waste 
package in the primary model. 
The flow-through model produces an average release continuously, while the bathtub model with 
the alternative flow path produces zero release initially, followed by a high pulse that soon 
returns to the same flux as the flow-through model. In other words, the flow-through model 
represents a time average of the response of the bathtub model. From this viewpoint, the 
potential difference between alt F and pri F is partly mitigated by the sorption and diffusion 
processes in the unsaturated and saturated zones. The potential difference between alt F and pri F 
is also small if the second patch appears shortly after the first penetration because there is less 
retained liquid. 
This alternative can also be thought of as being equivalent to the appearance of additional 
penetrations in the waste package. This analogy is appropriate because additional penetrations in 

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the waste package increase the inflow flux into the waste form, resulting in higher releases to the 
EBS. The main effect of the alternative patch geometry model is to generate this increase earlier. 
This is not considered a major difference because there is a wide range of variability in corrosion 
rates for the TSPA-LA model (BSC 2004 [DIRS 169996]). The effect of the alternative patch 
geometry model can then be reasonably considered to be captured within this variability. 
The results and observations in this section (6.6.1.2.3) and throughout Section 6.6.1 are 
appropriate for the general boundary conditions considered here. In other words, this 
comparison is based on the full fluid flux into the waste package having access to all 
radioisotopes in the waste. The model implemented in TSPA-LA, in which radionuclides are 
mobilized in a mass of corrosion products around the fuel pellets, partly mitigates the differences 
discussed here. This mitigation occurs because a large fluid flux will not transport radionuclides 
at the solubility limit if the mass in solution is limited by the pore volume in a mass of corrosion 
products. The situation is then similar to that mentioned at the end of Section 6.6.1.2.1, where 
mass transfer to the unsaturated zone is the dominant issue, rather than dissolved concentration. 
6.6.1.3 Summary 
The response of the bathtub geometry has been evaluated for a primary case, with constant 
boundary conditions and material properties, and for three secondary cases. Analyses for the 
three secondary cases consider a step change in inflow rate, a step change in inflow chemistry, 
and a change in flow geometry, as would occur if a patch suddenly appeared beneath the 
waterline. All cases include consideration of two types of radionuclide release mechanisms: 
dissolution-rate-limited and solubility-limited. The comparisons are based on closed form 
analytic solutions. 
The key conclusions from the evaluation follow: 
 The bathtub model introduces a time delay in the release of radionuclides from the waste 
package to the EBS in comparison to the flow-through model for the primary case. The 
flow-through model overestimates releases of radionuclides in relation to the bathtub 
geometry for the primary case because there is no delay in release of radionuclides to the 
EBS. 
 The response of the bathtub model to a step change in inflow rate (secondary case 1) is 
identical to the flow-through model for solubility-limited radionuclides. The response of 
the bathtub model for dissolution-rate-limited radionuclides is to delay the change in 
concentration and mass flux associated with the new inflow rate. The flow-through 
model overestimates releases of radionuclides with respect to the bathtub geometry for 
the case of decreasing inflow, when the concentration of radionuclide increases. The 
case of increasing radionuclide concentration is of primary interest from a performance 
or regulatory viewpoint since this case will result in greater releases. 
 The response of the bathtub model to a step change in inflow chemistry (secondary 
case 2) is to delay the change in concentration and mass flux associated with the new 
inflow chemistry. Analytical models cannot define the exact time delay, which are 
sensitive to nonlinear chemical effects when inflows mix. Limiting cases, when 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-178 November 2004 
solubility increases or decreases by several orders of magnitude, have been examined to 
define a first order approximation to the response of the chemical system. 
The flow-through model overestimates releases of radionuclides relative to the bathtub 
geometry when solubility or dissolution rate increase with changing inflow chemistry. 
The flow-through model has an instantaneous change to the higher equilibrium value 
while the bathtub geometry delays the change until the initial inflow is flushed out of the 
waste package. Increases in radionuclide concentrations and fluxes are of primary 
interest from a performance or regulatory viewpoint, so the underestimation of releases 
of radionuclides in the flow-through model for decreasing solubility or dissolution rate 
can reasonably be excluded from the TSPA-LA. 
 The response of the bathtub model when a second patch opens instantaneously beneath 
the water level in the waste package (secondary case 3) has also been analyzed. The 
impact of the instantaneous opening is to release a pulse of radionuclides in comparison 
to the flow-through model. The impact of this alternative conceptual model is mitigated 
by the time delays introduced through sorption and diffusion in the unsaturated and 
saturated zones. In addition, the higher mass flux from the alternative flow path is 
similar to the impact from additional patches opening in the waste package. There is a 
wide range of variability in corrosion rates for the TSPA-LA model, and the impact from 
the instantaneous opening is encompassed in the uncertainty in corrosion rates. 
The impact of this alternative flow model has therefore been screened out of TSPA-LA 
analyses because of the potential mitigation from sorption and diffusion and because the 
variability of corrosion rates provides large uncertainty in radionuclide release rates 
from the waste package. 
6.6.2 Limited Water Vapor Diffusion Rate into Waste Package 
In this alternative conceptual model, a film of adsorbed water cannot form on the surface of 
corrosion products if the water consumption rate is greater than the rate of diffusion of water 
vapor into the waste package. Until a film of water forms on internal corrosion products 
surfaces, diffusive releases of radionuclides through the adsorbed water cannot occur (according 
to the in-package diffusion submodel). Thus, the resistance to diffusion of water vapor through 
stress corrosion cracks delays releases until all of the corrodible materials inside a waste package 
are fully degraded. It is implicit in this alternative conceptual model that stress corrosion cracks 
appear before general corrosion patches form; this will not necessarily be the outcome of 
TSPA-LA calculations. 
The objective is to determine the length of time required to complete the corrosion of internal 
component steels, which is equivalent to the delay from the time a waste package is first 
breached by stress corrosion cracks until diffusive releases can first take place. This delay can 
potentially be important since it provides additional time for decay to reduce the concentration of 
radionuclides before they are released from a waste package. The rate of diffusion of water 
vapor through stress corrosion cracks into the waste package is estimated and compared with the 
rate of consumption of water by corrosion of steel internal components to show that diffusion 
rates are less than corrosion rates. Then, at the rate limited by diffusion, the time needed to 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-179 November 2004 
corrode the steels completely is calculated to give the delay before diffusive releases of 
radionuclides can occur. 
An example calculation is presented for a typical set of conditions in the drift and waste package 
to estimate the time lag between appearance of stress corrosion cracks and the earliest times 
when an adsorbed water film can first form through which radionuclides can diffuse. Suppose 
that the temperature of the waste package and drift air is 50C, the relative humidity in the drift 
is 95 percent, and the relative humidity is zero inside the waste package. Letting the humidity be 
zero inside the waste package maximizes the water vapor concentration gradient between the 
exterior and interior of the waste package. The diffusion distance is cm 54 . 2 = .x , the thickness 
of waste package outer lid (BSC 2004 [DIRS 169472]; BSC 2004 [DIRS 167394], Detail A). 
This is the outer closure lid, made of Alloy 22, with a circumferential weld in which stress 
corrosion cracks may develop. The average diffusive distance is greater  half the length of the 
waste package interior, or about 240 cm for a 21-PWR (Note i in Table 6.5-8)  but the cross 
sectional area is less in the stress corrosion cracks than in the waste package, or about 1.93 cm2 
in the example calculation shown in Section 6.5.1.2.1.4.3 vs. 20,030 cm2 (cross-sectional area of 
the inside of the outer corrosion barrier in a 21-PWR having a diameter of 1,597 mm; BSC 2004 
[DIRS 166953], Section B-B), so diffusion through the cracks is the limiting segment of the path. 
To calculate the diffusion rate, the concentration of water vapor in humid air is obtained from 
psychrometric data. Equations for the determination of psychrometric properties are given by 
Singh et al. (2002 [DIRS 161624]). At relative humidity RH (fraction) and temperature T (C), 
the partial pressure of water w p (Pa) is: 
,ow
w p RH p  = (Eq. 6.6.2-1) 
where ow 
p (Pa) is the vapor pressure of water at T (C), given by: 
). C 110 C (63.0 
01585 . 1 3 . 236 
269 . 17 exp 78 . 610 
) C 0 . 63 C (0 
3 . 237
269 . 17 exp 78 . 610 
o 
. .
.
. .
.
. 
< < .. 
. 
.. 
. 
+ 
< < .. 
. 
.. 
. 
+ 
= 
o o 
o o 
T 
T 
T 
T 
T 
T 
pw (Eq. 6.6.2-2) 
The absolute humidity m H (kg water kg-1 dry air) is then: 
. .. 
. 
. .. 
. 
- . .. 
. 
. .. 
. 
= 
w 
w 
a
w 
m p p 
p 
M
M H , (Eq. 6.6.2-3) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-180 November 2004 
where p is the total pressure, chosen to be one atmosphere (101325 Pa), w M is the molecular 
weight of water (0.01801528 kg mol-1), and a M is the molecular weight of air 
(0.028964 kg mol-1) (Weast 1985 [DIRS 111561], p. F-150). 
At 50C and a relative humidity in the drift of 95 percent, the vapor pressure of water, from 
Equation 6.6.2-2, is = ow 
p 12,334 Pa, so the partial pressure at RH = 0.95 is 717 , 11 = w p Pa. 
Then the absolute humidity is 0.0815 kg water kg-1 dry air. 
The molal humidity is: 
air dry mol O H mol 1308 . 0 1 - 
2 = 
- 
= = 
w 
w 
w 
a m 
mol p p 
p 
M
M H 
H , (Eq. 6.6.2-4) 
or 0.1156 mol H2O mol-1 wet air. Assuming ideal gas behavior, with an ideal gas molar volume 
of 22,414 cm3 mol-1 (at 0C and 1 atm pressure) (Weast 1985 [DIRS 111561], p. F-194), the 
concentration of water vapor in air at 50C and 95 percent relative humidity is: 
3 - 
2 
6 
3 
2 
cm O H mol 10 361 . 4 
K 15 . 273 
K 15 . 323 
mol 
cm 22414 
air mol 
O H mol 
1156 . 0 
-  = 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
.. 
. 
.. 
. 
= wv C . (Eq. 6.6.2-5) 
To calculate the binary diffusion coefficient, the following equation is used (Bird et al. 1960 
[DIRS 103524], Equation 16.3-1): 
( ) ( ) 1 
2 / 1 
12 / 5 3 / 1 1 1 - 
. .. 
. 
. .. 
. 
+ . .
.
. 
. .
.
. 
= p 
M M 
T T p p 
T T
T a D 
B A 
cB cA cB cA 
b 
cB cA 
AB , (Eq. 6.6.2-6) 
where: 
DAB = the diffusion coefficient (cm2 s-1) for water (A) in air (B) 
T = absolute temperature (K) 
p = pressure (atm) 
M = molecular weight (g mol-1) 
a = 3.640  10-4 for H2O with a nonpolar gas 
b = 2.334 for H2O with a nonpolar gas 
subscript c refers to critical properties. 

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ANL-WIS-PA-000001 REV 01 6-181 November 2004 
For water (A), = cA T 374.1C = 647.25 K, = cA p 218.3 atm (Weast 1985 [DIRS 111561], 
p. F-64), and = A M 18.01528 g mol-1; for air (B), = cB T 132 K, = cB p 36.4 atm (Bird et al. 1960 
[DIRS 103524], Table B-1), and = B M 28.964 g mol-1 (Weast 1985 [DIRS 111561], p. F-150). 
Substituting these values into the above equation, the binary diffusion coefficient for water vapor 
in air is: 
( ) 
( )( ) 
( )( ) [ ] 
( )( ) [ ] ( ) 
. s cm 3126 . 0 
0 . 1 
964 . 28
1 
01528 . 18 
1 . 132 25 . 647 
4 . 36 3 . 218 
. 132 25 . 647 
15 . 323 10 640 . 3 
1 - 2 
1 
2 / 1 
12 / 5 
3 / 1 
334 . 2 
4 
= 
.. 
. 
.. 
. + 
 . .
.
. 
. .
.
. 
 = 
- 
- 
AB D 
(Eq. 6.6.2-7) 
For diffusion of water vapor through stagnant air in the stress corrosion cracks, the rate of 
diffusion is, from Ficks first law (Bird et al. 1960 [DIRS 103524], p. 503) for a binary system 
with constant molar density: 
, s cm mol 10 363 . 1 
cm 1 
cm 
mol 10 361 . 4 
s 
cm 3126 . 0 
1 - 2 - 6 
3 
6 
2 
scc 
scc 
wv 
scc AB 
wv 
scc AB 
wv 
scc AB 
A 
A 
x 
C 
A D 
x 
C 
A D 
x 
C 
A D q 
  = 
. . . . 
.
. 
. . . . 
.
.  
. .. 
. 
. .. 
. 
= 
. 
= 
. 
. 
= 
. 
. 
= 
- 
- (Eq. 6.6.2-8) 
where scc A is the cross-sectional area (cm2) of stress corrosion cracks through which water vapor 
can diffuse. The typical cross-sectional area of a stress corrosion crack is 7.7  10-6 m2 per stress 
corrosion crack (Section 6.3.3.1.2.1). Using the example from Section 6.5.1.2.1.4.3 of 25 stress 
corrosion cracks per waste package (BSC 2004 [DIRS 169996], Figure 26), A = 1.93  10-4 m2 
= 1.93 cm2, and the rate of diffusion of water vapor is q = 2.63  10-6 mol s-1 = 83.0 mol 
H2O yr-1. Assuming a stoichiometry of 3 mol H2O/2 mol Fe (to form Fe2O3), this water diffusion 
rate allows carbon steel to corrode at a rate of 55.3 mol Fe yr-1. 
When stress corrosion cracks first appear, water vapor that diffuses through will probably be 
consumed by corrosion of the most reactive materials within a waste package, namely the 
A 516 carbon steel that makes up the baskets. These steel components have an average 
corrosion rate of 77.43 m yr-1 (DTN: MO0409SPAACRWP.000 [DIRS 172059]; Spreadsheet 
aqueous-A516.xls; Worksheet Freshwater, 1-year data at 60C) and a maximum thickness of 
3/8 in. (9.525 mm) (BSC 2004 [DIRS 169472], Table 1), for an average lifetime of about 123 yr. 
From Table 6.5-9, the total A 516 steel in a 21-PWR waste package is 100,260 mol (assumed to 
be Fe; hence, all corrosion products are Fe2O3). The rate of iron consumption over the average 

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ANL-WIS-PA-000001 REV 01 6-182 November 2004 
lifetime of this steel is about 815 mol Fe yr-1. Two simplified reaction stoichiometries are 
considered: 
2 Fe + 3 H2O = Fe2O3 + 3 H2 
Fe + 2 H2O = Fe(OH)2 + H2. 
Anoxic corrosion of iron will typically result in Fe(OH)2; however, to be consistent with the 
in-package diffusion submodel, the first reaction is also assumed to occur, producing Fe2O3 as 
the corrosion product. Assuming a stoichiometry of 3 mol H2O/2 mol Fe (to form Fe2O3), 
corrosion of 815 mol Fe yr-1 of A 516 carbon steel consumes 1,220 mol H2O yr-1, which is a 
factor of 15 greater than the rate of diffusion of water vapor through stress corrosion cracks. 
Another estimate uses the stoichiometry for the formation of Fe(OH)2 (i.e., 2 mol H2O mol-1 Fe), 
which gives a water consumption rate of 1,630 mol H2O yr-1, a factor of 20 greater than the 
diffusion rate of water vapor through stress corrosion cracks. 
If the stress corrosion cracks are filled with porous corrosion products, the cross sectional area 
for diffusion is less. For a porosity scc f of the stress corrosion crack, the effective cross sectional 
area is scc scc eff scc A A f = , . For a porosity of 0.4, ( ) 2 2 
, cm 77 . 0 cm 93 . 1 4 . 0 = = eff scc A . The corrosion 
rates given above are now higher than the diffusion rate by an additional factor of scc f /1 , or a 
factor of 37 higher than the diffusion rate for Fe2O3 formation and a factor of 49 higher for 
Fe(OH)2 formation. 
Another way to show the effect of the corrosion rate being limited by the rate of diffusion of 
water vapor is to calculate the time required to corrode all of the steel in a waste package. As 
shown above, the lifetime of the carbon steel components is 130 yr when not limited by the 
availability of water. When the corrosion rate is limited by the water vapor diffusion rate, the 
lifetime is greater than 130 years. The diffusion rate of 83.0 mol H2O yr-1 allows 55.3 mol 
Fe yr-1 to corrode to Fe2O3, thereby requiring 100,260 mol Fe/(55.3 mol Fe yr-1) = 1,810 years 
for all A 516 steel components to degrade fully once stress corrosion cracks appear. To degrade 
to Fe(OH)2, where the stoichiometry is 1 mol Fe/2 mol H2O, and the diffusion limited corrosion 
rate is 41.5 mol Fe yr-1, would require 2,420 yr. Accounting for a typical 40 percent porosity in 
the corrosion products increases these estimates to 4,530 yr and 6,040 yr, respectively. 
A further refinement of these estimates includes corrosion of the stainless steel components in 
addition to the carbon steel. Suppose that all internal components corrode, and the composition 
of the component materials is treated as in Section 6.5.1.2.1.3.2 and Table 6.5-9, in which all 
elemental components of the metals are treated as though they were iron, on a molar basis. 
Effectively 346,330 mol Fe are to be corroded at a rate limited by water diffusion through stress 
corrosion cracks. Then 6,260 yr are required to consume all of the material to Fe2O3, at the 
water vapor diffusion-limited rate of 55.3 mol Fe yr-1. At the mean stainless steel corrosion rate 
of 0.248 m yr-1 (DTN: MO0409SPAACRWP.000 [DIRS 172059]; Spreadsheet aqueous- 
316L.xls; Worksheet freshwater, 50-100C data), the 50.8-mm-thick inner vessel (BSC 2004 
[DIRS 169472]; BSC 2004 [DIRS 167394], Detail A) has a lifetime of 205,000 yr. Assuming 
that all 10,800 kg of the 316 stainless steel listed in Table 6.3-4 is part of the inner vessel or lids, 
and that this is equivalent to 192,240 mol Fe (Table 6.5-9), the mean molar corrosion rate is 
192,240 mol/205,000 yr = 0.94 mol yr-1. A stoichiometrically equivalent rate of water 

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ANL-WIS-PA-000001 REV 01 6-183 November 2004 
consumption due to stainless steel corrosion to Fe2O3 is 1.4 mol H2O yr-1, which is a factor of 59 
less than the rate of diffusion of water vapor through open stress corrosion cracks 
(83.0 mol H2O yr-1). In this case, water vapor diffusion through the stress corrosion cracks does 
not control the rate of corrosion and water consumption. If the cracks are filled with corrosion 
products to a porosity of 0.4, the rate of water vapor diffusion is less, as discussed earlier, and 
may then control the rate of corrosion. 
In Table 6.6-1, the time required to corrode all of the carbon steel or all of the stainless steel is 
shown for various assumptions and conditions (temperature, relative humidity in the drift). If no 
diffusive path can form until all of the steels are fully corroded, the time needed to corrode the 
steel is effectively the time lag between the first appearance of stress corrosion cracks and the 
first diffusive releases from the breached waste package. Depending on conditions and 
assumptions, this delay can range from 630 yr (at 70C) to more than 34,000 yr (at 30C) even at 
100 percent relative humidity in the drift. At lower relative humidities, the delay can be longer, 
for example, more than 43,000 yr at 30C and 80 percent relative humidity. In this table, the 
water vapor concentration, wv C , is obtained from Equations 6.6.2-4 and 6.6.2-5 as a function of 
relative humidity and temperature. The water vapor flux through stress corrosion cracks, q , is 
given by Equation 6.6.2-8. The corrosion rate, corr r , is the stoichiometrically equivalent rate of 
iron consumption that occurs when limited by the water vapor influx, q . The release delay is the 
time, corr t , required to corrode through 10 mm of carbon steel or 50.8 mm of stainless steel at the 
rate, corr r . 
Table 6.6-1. Summary of Release Delays Resulting from Limitations on Diffusion of Water Vapor 
Through Stress Corrosion Cracks 
Drift RH 0.8 0.9 0.95 0.99 1.00 
T = 50C, DAB = 0.313 cm2 s-1 
Cwv (mol cm-3) 3.6710-6 4.1310-6 4.3610-6 4.5410-6 4.5910-6 
q (mol H2O yr-1) 69.9 78.6 83.0 86.5 87.3 
rcorr (mol Fe yr-1) 46.6 52.4 55.3 57.6 58.2 
tcorr, Carbon steel only, Fe2O3 
stoichiometry, open stress 
corrosion cracks (yr) 
2,150 1,910 1,810 1,740 1,720 
tcorr, Carbon steel only, Fe(OH)2 
stoichiometry, open stress 
corrosion cracks (yr) 
2,870 2,550 2,420 2,320 2,300 
tcorr, Carbon steel only, Fe2O3 
stoichiometry, fscc = 0.4 (yr) 
5,380 4,780 4,530 4,350 4,310 
tcorr, Carbon steel only, Fe(OH)2 
stoichiometry, fscc = 0.4 (yr) 
7,180 6,380 6,040 5,800 5,740 
tcorr, All steel as stainless steel, 
Fe2O3 stoichiometry, open 
stress corrosion cracks (yr) 
4,130 3,670 3,480 3,340 3,300 
tcorr, All steel as stainless steel, 
Fe(OH)2 stoichiometry, open 
stress corrosion cracks (yr) 
5,500 4,890 4,630 4,450 4,400 

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ANL-WIS-PA-000001 REV 01 6-184 November 2004 
Table 6.6-1. Summary of Release Delays Resulting from Limitations on Diffusion of Water Vapor 
Through Stress Corrosion Cracks (Continued) 
Drift RH 0.8 0.9 0.95 0.99 1.00 
T = 50C, DAB = 0.313 cm2 s-1 
tcorr, All steel as stainless steel, 
Fe2O3 stoichiometry, 
fscc = 0.4 (yr) 
10,320 9,170 8,690 8,340 8,250 
tcorr, All steel as stainless steel, 
Fe(OH)2 stoichiometry, 
fscc = 0.4 (yr) 
13,760 12,230 11,590 11,120 11,010 
T = 70C, DAB = 0.360 cm2 s-1 
Cwv (mol cm-3) 8.7510-6 9.8410-6 1.0410-5 1.0810-5 1.0910-5 
q (mol H2O yr-1) 192 215 227 237 239 
rcorr (mol Fe yr-1) 128 144 152 158 160 
tcorr, Carbon steel only, Fe2O3 
stoichiometry, open stress 
corrosion cracks (yr) 
790 700 660 630 630 
tcorr, Carbon steel only, Fe(OH)2 
stoichiometry, open stress 
corrosion cracks (yr) 
1,050 930 880 850 840 
tcorr, Carbon steel only, Fe2O3 
stoichiometry, fscc = 0.4 (yr) 
1,960 1,750 1,650 1,590 1,570 
tcorr, Carbon steel only, Fe(OH)2 
stoichiometry, fscc = 0.4 (yr) 
2,620 2,330 2,200 2,120 2,090 
tcorr, All steel as stainless steel, 
Fe2O3 stoichiometry, open 
stress corrosion cracks (yr) 
1,510 1,340 1,270 1,220 1,200 
tcorr, All steel as stainless steel, 
Fe(OH)2 stoichiometry, open 
stress corrosion cracks (yr) 
2,010 1,780 1,690 1,620 1,610 
tcorr, All steel as stainless steel, 
Fe2O3 stoichiometry, 
fscc = 0.4 (yr) 
3,760 3,350 3,170 3,040 3,010 
tcorr, All steel as stainless steel, 
Fe(OH)2 stoichiometry, 
fscc = 0.4 (yr) 
5,020 4,460 4,230 4,060 4,020 
T = 30C, DAB = 0.269 cm2 s-1 
Cwv (mol cm-3) 1.3510-6 1.5110-6 1.6010-6 1.6710-6 1.6810-6 
q (mol H2O yr-1) 22.1 24.8 26.2 27.3 27.6 
rcorr (mol Fe yr-1) 14.7 16.6 17.5 18.2 18.4 
T = 30C, DAB = 0.269 cm2 s-1 
tcorr, Carbon steel only, Fe2O3 
stoichiometry, open stress 
corrosion cracks (yr) 
6,820 6,060 5,740 5,510 5,450 
tcorr, Carbon steel only, Fe(OH)2 
stoichiometry, open stress 
corrosion cracks (yr) 
9,090 8,080 7,650 7,340 7,270 
tcorr, Carbon steel only, Fe2O3 
stoichiometry, fscc = 0.4 (yr) 
17,040 15,140 14,350 13,770 13,630 
tcorr, Carbon steel only, Fe(OH)2 
stoichiometry, fscc = 0.4 (yr) 
22,720 20,190 19,130 18,360 18,170 

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ANL-WIS-PA-000001 REV 01 6-185 November 2004 
Table 6.6-1. Summary of Release Delays Resulting from Limitations on Diffusion of Water Vapor 
Through Stress Corrosion Cracks (Continued) 
Drift RH 0.8 0.9 0.95 0.99 1.00 
tcorr, All steel as stainless steel, 
Fe2O3 stoichiometry, open 
stress corrosion cracks (yr) 
13,070 11,620 11,000 10,560 10,450 
tcorr, All steel as stainless steel, 
Fe(OH)2 stoichiometry, open 
stress corrosion cracks (yr) 
17,420 15,490 14,670 14,080 13,940 
tcorr, All steel as stainless steel, 
Fe2O3 stoichiometry, 
fscc = 0.4 (yr) 
32,670 29,040 27,510 26,400 26,140 
tcorr, All steel as stainless steel, 
Fe(OH)2 stoichiometry, 
fscc = 0.4 (yr) 
43,560 38,720 36,680 35,200 34,850 
6.6.3 Limited Oxygen Diffusion Rate into Waste Package 
Dry air oxidation under atmospheric conditions can also proceed once stress corrosion cracks 
appear (CRWMS M&O 2000 [DIRS 135968], p. 14). Therefore, the rate of oxygen diffusion 
through cracks should also be considered, since oxygen diffusion may limit the corrosion rate. 
The mean corrosion rate of Stainless Steel Type 316L under atmospheric conditions, 
0.113 m yr-1 (DTN: MO0312SPAPCEML.003 [DIRS 167409], Spreadsheet: atmospheric.xls, 
Worksheet: 316) is lower than under aqueous conditions, 0.248 m yr-1 
(DTN: MO0409SPAACRWP.000 [DIRS 172059]; Spreadsheet aqueous-316L.xls; Worksheet 
freshwater, 50-100C data). To compare the corrosion rate with the oxygen diffusion rate, the 
lifetime of the waste package inner vessel is estimated, since this is the thickest component of a 
waste package and will provide the longest component lifetime. The inner vessel is 50.8 mm 
thick (BSC 2004 [DIRS 169472]; BSC 2004 [DIRS 167394], Detail A); with unlimited oxygen 
availability, its lifetime is 50.8 mm/(0.113  10-3 mm yr-1) = 4.50  105 yr. An estimate of the 
molar corrosion rate can be obtained by letting the effective Fe content of the Stainless Steel 
Type 316 listed in Table 6.5-9 be inner vessel and lid material. Then the corrosion rate is 
192240 mol/(4.5105 yr) = 0.43 mol Fe yr-1. Accounting for the stoichiometry to produce Fe2O3 
(3 mol O2/4 mol Fe): 
4 Fe + 3 O2 . 2 Fe2O3. 
This is equivalent to an oxygen consumption rate of 0.32 mol O2 yr-1. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-186 November 2004 
For nonpolar gas pairs, parameters a and b in the diffusion coefficient expression, 
Equation 5.4.2-6, are 2.74510-4 and 1.823, respectively (Bird et al. 1960 [DIRS 103524], 
Equation 16.3-1). Using the appropriate parameters for oxygen (A) diffusing in air, = cA T 154.58 
K, = cA p 5.043 MPa = 49.77 atm (Weast 1985 [DIRS 111561], p. F-62), and = A M 31.9988 
g mol-1, it follows that: 
( ) 
( )( ) 
( )( ) [ ] 
( )( ) [ ] ( ) 
. s cm 2374 . 0 
0 . 1 
964 . 28
1 
9988 . 31 
1 . 132 58 . 154 
4 . 36 7 . 49 
. 132 58 . 154 
15 . 323 10 745 . 2 
1 - 2 
1 
2 / 1 
12 / 5 
3 / 1 
823 . 1 
4 
= 
.. 
. 
.. 
. + 
. .
.
. 
. .
.
. 
 = 
- 
- 
AB D 
(Eq. 6.6.3-1) 
Let the oxygen concentration in air in a drift outside a waste package be the same as in the 
atmosphere: 20.946 volume-percent (Weast 1985 [DIRS 111561], p. F-156) or 0.20946 mol 
O2 mol-1 air. As an example, suppose the temperature is a uniform 50C. With 
22,414 cm3 mol-1, the O2 concentration is: 
. air cm O mol 10 899 . 7 
15 . 273 
15 . 323 
mol 
cm 22414 
air mol
O mol 
20946 . 0 
3 - 
2 
6
3 
2 
2 
-  = 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
.. 
. 
.. 
. 
= O C 
(Eq. 6.6.3-2) 
Inside a waste package, suppose the oxygen concentration is essentially zero. For an example 
with 25 stress corrosion cracks (Section 6.5.1.2.1.4.3) with a total cross-sectional area of 
1.93 cm2, the rate of diffusion of oxygen is: 
( ) 
. yr O mol 114 
yr 
s 10 1556926 . 3 
cm 1 
cm
O mol 
10 7.899 
cm 93 . 1 
s 
cm 2375 . 0 
1 - 
2 
7 
3 
2 6 - 
2 
2 
2 
= 
. .. 
. 
. .. 
. 
 
. . . . 
.
. 
. . . . 
.
.  
. .. 
. 
. .. 
. 
= 
. 
. 
= 
x 
C 
A D q O 
AB 
(Eq. 6.6.3-3) 
In this case, the corrosion rate is limited by the reaction kinetics, rather than the rate of diffusion 
of oxygen, since the oxygen diffusion rate is about 360 times greater than the oxygen 
consumption rate due to stainless steel corrosion under atmospheric conditions (114 mol yr-1 vs. 
0.32 mol yr-1). If corrosion products fill the stress corrosion cracks to a porosity of, say 0.4, the 
diffusion rate is still 140 times greater than the oxygen consumption rate due to stainless steel 
corrosion. 

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Accounting for the stoichiometry to produce Fe2O3 (3 mol O2/4 mol Fe), the oxygen diffusion 
rate is equivalent to an iron consumption rate of 152 mol Fe yr-1. At the same temperature 
(50C), water vapor diffusion allows, at most, 58.2 mol Fe yr-1 (Table 6.6-1, RH = 1.0) to be 
consumed, primarily because the water vapor concentration in air is much less than the oxygen 
concentration, so the gradient into the waste package is smaller. However, the reaction rate of 
iron with oxygen is lower than that of iron with water, so the steel components inside a waste 
package have a lesser affinity for oxygen than for water. 
These calculations indicate that a more accurate mass balance for water and oxygen inside a 
waste package could reduce predicted releases of radionuclides to the invert, and thus releases to 
the accessible environment. Releases could be delayed for several thousand years compared 
with current estimates as the corrosion of fuel baskets and inner vessel components scavenges 
water and oxygen that diffuse through small stress corrosion cracks (providing general corrosion 
patches do not form first). Formation of a diffusive pathway could then be delayed until 
corrosion of iron-based materials is largely completed. 
Despite the potential for delays in releases of radionuclides predicted by these models, 
uncertainty exists in the processes that are modeled. The assumption that no water is physically 
adsorbed until all steel is corroded is questionable, since adsorption is typically a fast process. 
On the other hand, if water consumption by corrosion does keep the relative humidity lower 
inside the waste package than outside, the effective water saturation could be less than when 
calculated using the humidity of the drift. If this occurs, calculated diffusion coefficients are 
simply lower than given by the in-package diffusion submodel, rather than zero, but for the time 
required for the internal components to corrode. The net effect is similar to what these 
alternative conceptual models predict. The corrosion rates that have been used are for aqueous 
conditions, which might exist on a microscopic scale. However, to be consistent with the 
assumption here that no adsorbed water film forms, rates in a low-humidity gaseous environment 
should be used. This increased realism would increase the time required for complete corrosion 
of the steel. 
6.6.4 Dual-Continuum Invert 
The LA invert design (BSC 2004 [DIRS 169503]) uses crushed tuff as the invert ballast material. 
This material is actually comprised of two pore spaces  intragranular pore space (tuff particle 
matrix) and intergranular pore space. Although radionuclide transport by both advection and 
diffusion can occur in both pore spaces, the dominant flow and transport processes in each of 
these two pore spaces is generally different. In order to simulate flow and transport through the 
invert accurately, the invert may be conceptualized as overlapping dual continua and modeled 
using a dual-permeability approach (imunek et al. 2003 [DIRS 167469], p. 22), wherein flow 
and transport occur in both pore spaces, and mass transfer takes place between the two pore 
spaces. 
Transport through the drift invert can occur either through the intergranular porosity of the invert 
ballast material or through the intragranular porosity. Advective transport depends upon the 
liquid flux through each of these porosities. Diffusive transport through each of these porosities 
depends upon the diffusive properties associated with each pathway. For this alternative 
conceptual model, the invert is modeled as overlapping dual continua in which one continuum is 

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ANL-WIS-PA-000001 REV 01 6-188 November 2004 
represented by the intergranular porosity and the other continuum is represented by the 
intragranular porosity, as shown in Figure 6.6-2. 
Whereas the single-continuum invert model, as shown in Figure 6.3-1, has a single advective 
flow path (Pathway 8) from the invert to the unsaturated zone, the dual-continuum invert has two 
potential advective flow pathways, as shown in Figure 6.6-2: 
Pathway 8 Flux from the Intragranular Invert Continuum to the Unsaturated 
Zone  Advective flux from the invert intragranular continuum flows directly 
into the UZ matrix. 
Pathway 9 Flux from the Intergranular Invert Continuum to the Unsaturated Zone  
All advective flux from the invert intergranular continuum flows directly into 
the UZ fractures. 
In this model, no advective flux occurs between the two invert continua. Thus, the flux through 
pathway 8 is identical to the imbibition flux, pathway 7: 7 8 F F = . 
Ignoring three-dimensional effects (e.g., flow along the axis of the drift), the quasi-steady state 
flux through the intergranular invert continuum is equal to the seepage flux: 1 9 F F = . 
This alternative conceptual model for flow and transport through the EBS includes five domains: 
the waste form (e.g., fuel rods or HLW glass), waste package corrosion products, the 
intergranular invert continuum, the intragranular invert continuum, and the invert/UZ interface 
domain. The first two domains are the same as in the base case model. The third domain (the 
intergranular invert continuum) is in intimate contact with the waste package and has an average 
thickness of 0.597 m (Section 6.5.3). The fourth domain (the intragranular invert continuum) is 
also in intimate contact with the waste package and has the same average thickness, 0.597 m, as 
the intergranular invert continuum. 
Table 6.6-2 summarizes the transport modes and transport parameters for the transport pathways 
in the EBS when the invert is modeled as a dual continuum. 
The diffusive fluxes to the dual invert continua are determined from the flux continuity at the 
interface between the corrosion products domain and the invert continua. This requirement 
states that the diffusive flux exiting the corrosion products domain is equal to the sum of the 
diffusive fluxes entering the two invert continua. The diffusive flux split will depend on the 
diffusive properties in the corrosion products domain and both invert continua together with the 
concentration gradients across the corrosion products domain/invert interface. 

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Figure 6.6-2. Schematic of the Potential Flow Pathways in the EBS 

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Table 6.6-2. Summary of Transport Modes and Parameters for the EBS Transport Pathways with 
Dual-Continuum Invert 
Transport Pathway Transport Modes Transport Parameters and Data Sources 
1. Waste form and 
corrosion products 
domains 
Diffusion through stress 
corrosion cracks (no 
advective transport through 
stress corrosion cracks). 
Diffusion and advection 
through patches. 
No lateral or forward dispersion. 
Colloidal particles will transport radionuclides. 
Diffusive area for each stress corrosion crack is 
7.7  10-6 m2 (see Section 6.3.3.1.2.1). 
Diffusive area for each patch is provided by WAPDEG 
(BSC 2004 [DIRS 169996]). 
Diffusion coefficient (all radionuclides): 
 2.299  10-5 cm2 s-1 at 25C (Mills 1973 
[DIRS 133392], Table III) 
 Modified for porosity and saturation (see Section 
6.5.1.2.1.4) 
 Reduced by a factor of 100 if radionuclide is 
bound to a colloid (see Section 6.3.4.4). 
The cross-sectional area ACP/invert for radionuclide 
transport is given by the interface between the waste 
package corrosion products domain and the invert 
domain. 
See Section 6.5.3 for further details. 
2. Intragranular invert 
continuum 
Diffusion from corrosion 
products domain into the 
invert intragranular 
continuum. 
No advection from corrosion products domain into 
invert intragranular continuum 
Diffusion coefficient (all radionuclides): 
 2.299  10-5 cm2 s-1 at 25C (Mills 1973 
[DIRS 133392], Table III) 
 Modified for porosity and saturation (see 
Section 6.3.4.1) 
 Temperature modification defined in 
Section 6.3.4.1.2 
 Reduced by a factor of 100 if radionuclide is 
bound to a colloid (see Section 6.3.4.4). 
Flow cross-sectional areas given by the top surface 
area of the invert, AI/UZ (Equation 6.5.3.3-4). 
3. Intergranular invert 
continuum 
Diffusion and advection (F6) 
corrosion products domain 
into the invert intergranular 
continuum. 
Liquid flux for advection = F6 = F5 (diverted by WP) + 
F4 (flux through WP) + F3 (diverted by drip shield). 
Diffusion coefficient (all radionuclides): 
 2.299  10-5 cm2 s-1 at 25C (Mills 1973 
[DIRS 133392], Table III) 
 Modified for porosity and saturation (see 
Section 6.3.4.1) 
 Temperature modification defined in 
Section 6.3.4.1.2; invert temperature is provided 
by Multiscale Thermohydrologic Model 
calculations (BSC 2004 [DIRS 169565] 
 Reduced by a factor of 100 if radionuclide is 
bound to a colloid (see Section 6.3.4.4). 
The cross-sectional area AI/UZ for radionuclide 
transport is the top surface area of the invert 
(Equation 6.5.3.3-4). 

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Table 6.6-2. Summary of Transport Modes and Parameters for the EBS Transport Pathways with 
Dual-Continuum Invert (Continued) 
Transport Pathway Transport Modes Transport Parameters and Data Sources 
4. Invert intragranular  
intergranular 
interface 
Diffusion between the invert 
intergranular continuum and 
the intragranular continuum. 
Mass transfer coefficient uses (see Section 6.6.4.1): 
 Diffusion coefficient of the intragranular continuum 
 Sampled geometry-dependent factor,  
(Invert_Geometry_Coef) 
 Diffusive path length equal to mean invert tuff 
particle radius, 5 mm. 
Parameters are dependent on discretization of the 
invert model; see Section 6.5.3.5 for discretization and 
implementation details. 
5. Invert-UZ interface Advection from the invert 
intragranular continuum to UZ 
matrix (F8). 
Advection from the invert 
intergranular continuum to UZ 
fractures (F9). 
Diffusion from the invert 
intragranular continuum to UZ 
fractures and matrix. 
Diffusion from the invert 
intergranular continuum to UZ 
fractures and matrix. 
The invert diffusion calculation uses radionuclide 
concentrations in the WP corrosion products domain 
as the boundary condition at the top of the invert and a 
series of unsaturated zone computational cells below 
the invert that provide a gradient to a zero radionuclide 
concentration at some distance from the bottom of the 
invert. See Section 6.5.3.6. 
WP = waste package 
For discussion of the diffusive flux treatment at the corrosion products domain/invert interface 
consider a diffusive flux term, either aqueous or colloid flux, within the transport mass balance 
equation. Let interface z denote the spatial location of the corrosion products domain/invert 
interface. Then for interface z z < , the diffusive flux for radionuclide species i at a location within 
the corrosion products domain is: 
z 
C D S iCP 
CP CP w CP . 
. 
_ f , (Eq. 6.6.4-1) 
where CP f is the porosity of the single-continuum corrosion products domain. 
For interface z z > , the diffusive fluxes within the intergranular invert and intragranular invert media 
are, respectively, 
z 
C D S iinter 
inter inter w inter . 
. 
_ f , (Eq. 6.6.4-2) 
z 
C D S iintra 
intra intra w intra . 
. 
_ f . (Eq. 6.6.4-3) 

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The mass transport across this interface is coupled by the flux continuity condition at the 
interface: 
, _ 
_ _ 
+ 
+ - 
. 
. 
+ 
. 
. 
= 
. 
. 
z 
C D S 
z 
C D S 
z 
C D S 
iintra 
intra intra w intra 
iinter 
inter inter w inter 
iCP 
CP CP w CP 
f 
f f 
(Eq. 6.6.4-4) 
where 
- .
.
z 
and + .
.
z 
are the derivative from the left and the derivative from the right, respectively, at the interface. 
A similar flux continuity condition for each invert continuum is applied at the invert/UZ 
interface. 
6.6.4.1 Invert Dual Continuum Interface Transfer 
If a gradient exists in the concentration of dissolved radionuclide species i or of colloids that 
contain radionuclide species i, mass will be transferred across the interface between the two 
continua. The mass transfer coefficients for dissolved species and colloids, a (given by 
Equation 6.5.1.2-22), are dependent on the geometry and diffusivity in the neighborhood of the 
interface. 
Mass will also be transferred with advective flow across the interface as a result of head or 
pressure gradients between the two continua, for example, when imbibition into the tuff matrix 
(i.e., intragranular continuum) occurs. This effect is ignored in the invert since it should be a 
short term and infrequent occurrence. 
When advective interface mass transfer is neglected, the mass transfer coefficient has the form 
(Gerke and van Genuchten 1996 [DIRS 167466], p. 345; Corapcioglu and Wang 1999 
[DIRS 167464], p. 3263; imunek et al. 2003 [DIRS 167469], pp. 28 and 30): 
e D 
d 2 
 
a= , (Eq. 6.6.4.1-1) 
where  is a dimensionless geometry-dependent coefficient, d is a characteristic length (m) of 
the matrix structure (e.g., half the aggregate width or half the fracture spacing), and e D is an 
effective diffusion coefficient (cm2 s-1) that represents the diffusion properties of dissolved 
species at the interface between the two continua for radionuclide species i. For colloids 
containing sorbed radionuclides, e D represents the diffusion properties of those colloids at the 
interface between the two continua. Since the self diffusion coefficient of water is used as a 
bounding value for all radionuclides, the subscript on the diffusion coefficient in 
Equation 6.5.1.2-22 can be dropped in Equation 6.6.4.1-1. 

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Mass transfer coefficients obtained analytically using Laplace transform comparisons derived 
values for  of 3 for rectangular slabs, 8 for solid cylinders, and 15 for spheres (Gerke and van 
Genuchten 1996 [DIRS 167466], p. 345). Values of  have also been obtained (Gerke and van 
Genuchten 1996 [DIRS 167466]) by directly matching analytical solutions of the diffusion 
models to results obtained with the first-order model such as Equation 6.5.1.2-18. Gerke and van 
Genuchten (1996 [DIRS 167466]) derived an empirical expression to estimate  for complex 
and mixed types of structural geometry. A dimensionless surface-area-to-volume ratio of a 
particle, g 
g
g a 
V
A 
= . , is defined, where g a is the effective length of the matrix pore system; for 
example, for a cylinder, g a is the radius; for a cube, g a is half the length of a side; for a sphere, 
g a is the radius. Thus, for a cylinder, 2 = . , and for a sphere and a cube, 3 = . . For values 
10 2 = < . , Gerke and van Genuchten (1996 [DIRS 167466], p. 354) give the following fitted 
empirical expression: 
2 5473 . 3 4438 . 7 4275 . 11 . .  + - = . (Eq. 6.6.4.1-2) 
For cubes and spheres, Equation 6.6.4.1-2 gives a value for  of 21.0, and for a cylinder, 
=  10.7. Since the geometry of crushed tuff invert particles is uncertain, these estimates of  
help to establish a range of values over which  can be sampled. 
The crushed tuff invert material will be produced by a tunnel boring machine that will excavate 
the drifts for the repository. The cuttings from TBMs can be characterized as generally well 
graded material containing large flat and elongated chips and moderate excess of fines (Gertsch 
et al. 1993 [DIRS 107880], p. 20). Tests done on samples of TSw2 tuff using a linear cutting 
machine produced cuttings that, in the plus inch fraction, were elongated and flat, while the finer 
particles were more cubic (Gertsch et al. 1993 [DIRS 107880], p. 42-43). The operating 
parameters expected to be utilized in the Yucca Mountain Project tunnel boring machine will 
reduce the maximum particle size and result in the particles being more cubic (Gertsch et al. 
1993 [DIRS 107880], p. 44). Particle sizes for the invert material will range from 0.075 mm 
(No. 200 sieve) to 50 mm, with 50 percent of the particles passing a 10-mm sieve (BSC 2004 
[DIRS 170559], Sheet 2). Therefore, the average diameter for invert crushed tuff particles 
(spherical or cylindrical) is 10 mm; if the particles are treated as cubes, the average length of a 
side is 10 mm. The characteristic length d (Diff_Length_Inv_Inter_Intra) is the radius or half the 
distance through a cube, or 5 mm. 
The invert material will be composed of particles that are roughly spherical or cubic, along with 
elongated particles that can be considered roughly cylindrical. For cylinders, cubes, and spheres, 
estimates of  (Invert_Geometry_Coef) range from 8 to 21. A particle shape distribution is not 
available; therefore, a uniform distribution for  is appropriate. 
The model for the mass transfer between overlapping continua is represented by the diffusion of 
solute on a macroscopic control volume scale, i.e., between two entire domains or computational 
cells, rather than on the elemental volume scale used to formulate the mass balance equations in 
Section 6.5.1.2. Consequently, the mass transfer between the two invert continua is not written 

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as a gradient of diffusive mass flux with respect to the coordinate dimensions. In the discrete 
formulation, this flux is modeled as a diffusive flux between two invert cells. For the discrete 
realization of the invert continua mass transfer, the diffusive length within the intergranular 
continuum is taken to be zero. This is a result of the water within the intergranular continuum 
consisting of a film of negligible thickness on the surface of the intragranular materials. The 
diffusive length within the intragranular continuum depends on some mean diffusive length 
within the crushed tuff material. This diffusive length is taken as a mean radius of spherical 
particles, 5 mm. The diffusive area is estimated as the surface area of all spherical particles 
necessary to fill the invert volume. Therefore, the characteristic length parameter, d, is identified 
as the diffusive length (5 mm) within the intragranular continuum. 
6.6.4.2 Discretization of Dual-Continuum Invert Alternative Computational Model 
Discretization of the continuum mass balance equations for EBS transport model is described in 
Section 6.5.3.5 for a single-continuum invert. Numerical modeling of the EBS radionuclide 
transport is performed using the GoldSim software (Golder Associates 2003 [DIRS 166572]) cell 
pathway capability. The cell pathway acts as a batch reactor, where radionuclide mass is 
assumed to be instantaneously and completely mixed and partitioned among all media (fluid or 
solid) within the cell. When multiple cells are linked together in a cell network via advective and 
diffusive mechanisms, GoldSim numerically solves the coupled system of equations to compute 
the radionuclide mass present in each cell and the mass fluxes between cells as a function of 
time. 
Within a computational cell network, each cell is allowed to communicate by advection and/or 
diffusion with any other cell. This concept is crucial in implementing the bifurcation of diffusive 
fluxes across an interface between a single continuum domain and a dual continuum domain, 
such as at the interface between the corrosion products domain and the dual continuum invert 
domains. Each computational cell is provided with parameters describing water volumes, 
diffusive properties, and advective and diffusive flux links to other cells. Between any two cells, 
the diffusive flux can be bidirectional, depending on the concentration gradient, while the 
advective flux is unidirectional. The output of a cell is given in terms of the advective and 
diffusive mass fluxes for radionuclide species i and its concentration at the cell center. 
In this alternative conceptual model, the invert is conceptualized as a dual continuum domain of 
intergranular and intragranular continua. The discretization of the invert domain, using 
GoldSim, consists of two cells  one representing the invert intergranular continuum and the 
other representing the invert intragranular continuum. 
Between the corrosion products and invert domains, an advective flux communication exists 
from the corrosion products cell to the invert intergranular cell only; none enters the 
intragranular invert cell. Any advective flux due to imbibition from the host rock to the invert 
enters the intragranular cell only. The advective exchange from the intergranular continuum to 
the intragranular continuum is excluded by capillary pressure differences. Diffusive flux 
communication exists between the single continuum corrosion products and dual continuum 
invert. It is shown subsequently in this section how the diffusive flux bifurcation at this interface 
satisfies the flux continuity condition (Equation 6.5.1.2-53). The mass balance transport 
equations for the dual continuum invert cells are coupled by the radionuclide mass transfer flux 

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(Section 6.6.4.1), which is represented within GoldSim as a diffusive flux link between the 
intergranular and intragranular invert cells. 
Below the invert, part of the near-field UZ is modeled by an array of cells, which serves to 
establish a far field zero-concentration boundary and an accurate representation of the flux at the 
invert-to-UZ interface. The EBS-UZ interface submodel is described in more detail in 
Section 6.5.3.6. The dual continuum approach for modeling the UZ is considered by creating 
UZ matrix and fracture cells. The two invert cells communicate with the UZ matrix and fracture 
cells directly below them in the UZ cell array (Section 6.5.3.6). 
For transport from the corrosion products domain (single continuum) to the invert domain (dual 
continuum), the flux continuity condition at the interface provides the diffusive flux bifurcation 
between the single continuum and the dual continuum. 
The diffusive fluxes of radionuclide species i within the corrosion products cell, the invert 
intergranular cell, and the invert intragranular cell are, respectively, 
( ) ( ) 
( ),  / 
/ 
invint iCP iCP CP 
invint iCP iCP 
CP 
CP w 
iCP 
C C D 
C C 
L
DA S 
F 
- = 
- = 
f 
(Eq. 6.6.4.2-1) 
( ) ( ) 
( ),  / 
/ 
iinter invint iCP inter 
iinter invint iCP 
inter 
inter w 
iinter 
C C D 
C C 
L
DA S 
F 
- = 
- = 
f 
(Eq. 6.6.4.2-2) 
( ) ( ) 
( ),  / 
/ 
iintra invint iCP intra 
iintra invint iCP 
intra 
intra w 
iintra 
C C D 
C C 
L
DA S 
F 
- = 
- = 
f 
(Eq. 6.6.4.2-3) 
where 
CP D = effective diffusion coefficient of radionuclide species i within the corrosion 
products cell (cm2 s-1) 
inter D = effective diffusion coefficient of radionuclide species i within the invert 
intergranular cell (cm2 s-1) 
intra D = effective diffusion coefficient of radionuclide species i within the invert 
intragranular cell (cm2 s-1) 
CP L = diffusive length within the corrosion products cell (m) 
inter L = diffusive length within the invert intergranular cell (m) 
intra L = diffusive length within the invert intragranular cell (m) 
= inter L 

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iCP C = concentration of radionuclide species i in the corrosion products cell 
(kg i m-3) 
iinter C = concentration of radionuclide species i in the invert intergranular cell 
(kg i m-3) 
iintra C = concentration of radionuclide species i in the invert intragranular cell 
(kg i m-3) 
invint iCP C / = concentration of radionuclide species i at the interface between the 
corrosion products and invert cells (kg i m-3) 
and the 
L
DA S D w f 
=  are respective diffusive conductances (cm3 s-1). 
The flux continuity at the interface requires: 
iintra iinter iCP F F F + = . (Eq. 6.6.4.2-4) 
From the flux continuity, the interface concentration of radionuclide species i is determined as a 
function of the diffusive parameters and the cell concentrations as: 
intra inter CP 
iintra intra iinter inter iCP CP 
invint iCP D D D 
C D C D C D C    
   
/ + + 
+ + 
= . (Eq. 6.6.4.2-5) 
This provides the invert intergranular and intragranular diffusive fluxes of radionuclide species i, 
respectively, as: 
( ) 
( ) iinter iintra 
intra inter CP 
intra inter 
iinter iCP 
intra inter CP 
inter CP 
iinter 
C C 
D D D 
D D 
C C 
D D D 
D D F 
- 
+ + 
+ 
- 
+ + 
= 
   
  
   
  
(Eq. 6.6.4.2-6) 
( ) 
( ).    
  
   
  
iinter iintra 
intra inter CP 
intra inter 
iintra iCP 
intra inter CP 
intra CP 
iintra 
C C 
D D D 
D D 
C C 
D D D 
D D F 
- 
+ + 
- 
- 
+ + 
= 
(Eq. 6.6.4.2-7) 
The expression for the diffusive flux of radionuclide species i from the corrosion products cell to 
the invert intergranular cell can be expressed as a diffusive conductance multiplied by a 
concentration difference of radionuclide species i between the corrosion products cell and the 
invert intergranular cell plus a corrective flux between the invert intergranular and intragranular 
cells. Similarly, the expression for the diffusive flux from the corrosion products to the invert 
intragranular cell is expressed as a diffusive flux between the corrosion products and the invert 
intragranular cell minus the same corrective flux between the invert cells. The inclusion of the 
corrective flux term is explained as follows. The flux to both invert cells should depend on the 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 6-197 November 2004 
diffusive properties in the corrosion products cell and the two invert cells, together with the 
concentrations in these three cells. Therefore, the flux to the invert intergranular cell cannot be 
expressed only in terms of the concentration drawdown between the corrosion products cell and 
the invert intergranular cell. The corrective term includes the dependence of the invert 
intergranular flux on the concentration of radionuclide species i in the invert intragranular cell. 
Further, the corrective flux term is not a true flux expression between the two invert cells, since 
the diffusive conductance coefficient is dependent on the diffusive area between the corrosion 
products and the invert, and the diffusive lengths are the lengths with respect to flow from the 
corrosion products cell to the invert cells. 
The invert fluxes result in defining three diffusive conductances from the flux expressions: 
( ) ( ) iinter iCP 
intra inter CP 
inter CP 
iinter iCP inter CP C C 
D D D 
D D C C D - 
+ + 
= -    
   / , (Eq. 6.6.4.2-8) 
( ) ( ) iintra iCP 
intra inter CP 
intra CP 
iintra iCP intra CP C C 
D D D 
D D C C D - 
+ + 
= -    
   / , (Eq. 6.6.4.2-9) 
( ) ( ) iinter iintra 
intra inter CP 
inter intra 
iinter iintra inter intra C C 
D D D 
D D C C D - 
+ + 
= -    
   / , (Eq. 6.6.4.2-10) 
where 
inter CP D / = effective diffusive conductance between corrosion products cell and invert 
intergranular cell (cm3 s-1) 
intra CP D /  = effective diffusive conductance between corrosion products cell and invert 
intragranular cell (cm3 s-1) 
inter intra D /  = effective diffusive conductance between intragranular and invert 
intergranular cells (cm3 s-1). 
In order to accommodate the GoldSim representation of diffusive conductance as a two-term 
expression, the diffusive conductances of radionuclide species i are written as: 
( ) ( ) 
( ) ( ) 
( )inter w 
inter 
intra w inter w 
inter w 
CP w 
CP 
inter CP 
DA S 
L 
DA S DA S 
DA S 
DA S 
L D 
f 
f f 
f 
f 
+ 
.. 
. 
.. . 
+ 
= 1  / , (Eq. 6.6.4.2-11) 
( ) ( ) 
( ) ( ) 
( )intra w 
intra 
intra w inter w 
intra w 
CP w 
CP 
intra CP 
DA S 
L 
DA S DA S 
DA S 
DA S 
L D 
f 
f f 
f 
f 
+ 
.. 
. 
.. 
. 
+ 
= 1  / , (Eq. 6.6.4.2-12) 

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( ) ( ) 
( ) ( ) 
( )intra w 
intra 
CP w intra intra w CP 
intra w CP 
inter w 
inter 
inter intra 
DA S 
L 
DA S L DA S L 
DA S L 
DA S 
L D 
f 
f f 
f 
f 
+ 
.. 
. 
.. 
. 
+ 
= 1  / . (Eq. 6.6.4.2-13) 
Another approach to discretizing the dual-continuum invert requires introduction of an interface 
cell, located between the corrosion products cell and the invert cells. This interface cell provides 
an approximate interface concentration and the resulting flux split at the corrosion products to 
invert cell interface. The interface cell is conceptualized as a very thin slice of the corrosion 
products cell. 
This implies the interface cell takes on the corrosion products diffusive properties, with the 
exception of diffusive length. Let the diffusive length within the interface cell be some small 
fraction (an Interface_Scale_Factor) of the corrosion products diffusive length, say, 
Interface_Scale_Factor = 10-6: 
CP int CP L L 6 10- 
- = . (Eq. 6.6.4.2-14) 
The use of a Interface_Scale_Factor of 10-6 is examined in Section 6.6.4.4. 
The diffusive conductance between the corrosion products cell and the corrosion products 
interface cell is calculated as the harmonic average: 
( ) ( )CP w 
int CP 
CP w 
CP 
int CP CP 
DA S
L 
DA S 
L D 
f f 
- 
- 
+ 
= 1  / . (Eq. 6.6.4.2-15) 
For diffusion between the interface cell and the invert intergranular and intragranular cells, the 
diffusive conductances are, respectively, 
( ) ( )inter w 
invert 
CP w 
int CP 
inter int CP 
DA S
L 
DA S
L D 
f f 
+ 
= 
- 
- 
1  / , (Eq. 6.6.4.2-16) 
( ) ( )intra w 
invert 
CP w 
int CP 
intra int CP 
DA S
L 
DA S
L D 
f f 
+ 
= 
- 
- 
1  / . (Eq. 6.6.4.2-17) 
The interface cell concentration of radionuclide species i is computed as part of the cell network 
solution. Because the transport mass balance equations conserve mass, the mass flux leaving the 
interface cell must equal the sum of the mass fluxes entering the two invert cells. The solution 
provides the flux continuity across the interface between the corrosion products interface cell and 
invert cells. This formulation expects the flux exiting the corrosion products cell (or entering the 
interface cell) is approximately equal to the flux exiting the interface cell. This approximation is 

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ANL-WIS-PA-000001 REV 01 6-199 November 2004 
dependent on the diffusive length within the interface cell. The error in this approximate 
solution will approach zero as the diffusive length of the interface cell approaches zero. 
At the invert-to-UZ interface, there is diffusive transport between both the invert cells and the 
UZ matrix and fracture cells. This implies four connections: from invert intergranular to UZ 
matrix, from invert intergranular to UZ fracture, invert intragranular to UZ matrix, and from 
invert intragranular to UZ fracture. An analysis similar to that for the diffusive conductances 
between the corrosion products cell and the dual invert cells (Equations 6.6.4.25-11 through 
6.6.4.2-13) would provide expressions for diffusive conductances for each of the four diffusive 
flux links. However, for the TSPA-LA, the approximation provided by introducing an interface 
cell when diffusing from a single to a dual continuum exits is used. An approximate solution is 
obtained by the introduction of two interface cells at the invert-UZ interface. This approach is 
identical to that used above for the interface between the corrosion products cell and the invert 
dual continuum cells. One interface cell represents a thin slice of the invert intergranular cell, 
and the other represents a thin slice of the invert intragranular cell. Let the length of both invert 
interface cells be a fraction (an Interface_Scale_Factor) of the invert diffusive length, say, 
Interface_Scale_Factor = 10-6: 
invert int invert L L 6 
_ 10- = . (Eq. 6.6.4.2-18) 
The use of an Interface_Scale_Factor of 10-6 is examined in Section 6.6.4.4. 
The diffusive conductance between the invert intergranular cell and the invert intergranular 
interface cell is: 
( ) ( )inter w 
int invert 
inter w 
invert 
int inter inter 
DA S
L 
DA S
L 
D 
f f 
_ 
/ 
1  
+ 
= - , (Eq. 6.6.4.2-19) 
while the diffusive conductance between the invert intragranular cell and the invert intragranular 
interface cell is: 
( ) ( )intra w 
int invert 
intra w 
invert 
int intra intra 
DA S
L 
DA S
L 
D 
f f 
_ 
/ 
1  
+ 
= - . (Eq. 6.6.4.2-20) 
The fluxes of radionuclide species i from the invert intergranular boundary cell to the matrixfracture 
UZ cells are computed with diffusive conductances: 
( ) ( )UZm w 
UZ 
inter w 
int invert 
UZm int inter 
DA S 
L 
DA S
L D 
f f 
+ 
= - 
_ 
/ 
1  , (Eq. 6.6.4.2-21) 

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( ) ( )UZf w 
UZ 
inter w 
int invert 
UZf int inter 
DA S 
L 
DA S
L D 
f f 
+ 
= - 
_ 
/ 
1  . (Eq. 6.6.4.2-22) 
Similarly, the fluxes of radionuclide species i from the invert intragranular boundary cell to the 
matrix-fracture UZ cells are computed with diffusive conductances: 
( ) ( )UZm w 
UZ 
intra w 
int invert 
UZm int intra 
DA S 
L 
DA S
L D 
f f 
+ 
= - 
_ 
/ 
1  , (Eq. 6.6.4.2-23) 
( ) ( )UZf w 
UZ 
intra w 
int invert 
UZf int intra 
DA S 
L 
DA S
L D 
f f 
+ 
= - 
_ 
/ 
1  . (Eq. 6.6.4.2-24) 
One last term to be discussed is the mass transfer term, imt Q , between the two invert continua 
given by Equation 6.5.1.2-19. This term appears in the mass balance for the transport of 
radionuclides dissolved in the aqueous phase and reversibly sorbed (Equation 6.5.1.2-38, or, for 
the one-dimensional case, Equation 6.5.1.2-46), and in Equation 6.5.1.2-27 (Equation 6.5.1.2-47 
in one dimension), the mass balance for irreversibly adsorbed radionuclides on iron 
oxyhydroxide colloids. In these equations, the mass transfer between overlapping continua is 
represented by the diffusion of solute on a macroscopic control volume scale. Consequently, the 
mass transfer between the two invert continua is not written as a gradient of diffusive mass flux 
with respect to the coordinate dimensions, and the treatment described above for diffusive 
conductances does not directly apply. For the discrete realization of the invert continua mass 
transfer, the diffusive length within the intergranular continuum is taken to be zero. This is a 
result of the water within the intergranular continuum consisting of a thin film on the surface of 
the intragranular materials. The diffusive length within the intragranular continuum depends on 
some mean diffusive length within the crushed tuff material. This diffusive length is taken as a 
mean radius of spherical particles. The effective diffusive area is estimated as the surface area of 
all spherical particles necessary to fill the invert volume. Therefore, the characteristic length 
parameter, d, is identified as the diffusive length within the intragranular continuum and the 
diffusive area to length ratio with transfer term included as mentioned in Equation 6.5.1.2-19 is: 
2 
_ 
d
V 
L
A intra t intra 
a inter/intr 
. 
= .. 
. 
.. 
. , (Eq. 6.6.4.2-25) 
where intra t V _ is the volume of the invert intragranular continuum, and  is the sampled 
geometry-dependent factor, Invert_Geometry_Coef. The effective diffusive conductance is: 
a inter/intr 
intra c L
A D D .. 
. 
.. 
. =  . (Eq. 6.6.4.2-26) 

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6.6.4.3 Dual-Continuum EBS-UZ Boundary Condition 
The EBS-UZ boundary condition implementation described in Section 6.5.3.6 is used to obtain a 
realistic concentration boundary condition at the invert-UZ interface. For the dual-continuum 
invert alternative model, the boundary condition implementation is modified to account for 
diffusive fluxes from each invert continuum to both UZ fractures and matrix. This 
implementation is represented in Figure 6.6-3. 
The mass flux from either invert continuum flows into the top layer of the middle zone in the 
UZ. The intergranular invert advective flux flows into the top middle UZ fracture cell, while the 
intragranular invert advective flux flows into the top middle UZ matrix cell. Transfer of water 
between the two continua is ignored. The diffusive flux from each of the invert continua can go 
into both UZ continua based on the concentration gradient and effective diffusion coefficient. 
The advective flux flowing through the UZ fracture cells in the middle zone is given by the 
greater of the advective flux out of the invert and the steady state UZ fracture flux. The 
advective flux in the two outer zones is given by the steady state UZ flow in each continuum at 
the repository horizon; the drift shadow effects are ignored. 
The mass flux from the dual continuum invert domain to the dual continuum UZ, computed at 
the boundary of the EBS-UZ interface, is passed to the UZ transport model, which is described in 
Particle Tracking Model and Abstraction of Transport Processes (BSC 2004 [DIRS 170041]). 
In addition to the total mass flux, the relative fraction of the mass going into each of the fracture 
and the matrix cells at the EBS-UZ boundary is required by the UZ transport model. This 
fracture-matrix partitioning of mass is calculated on the basis of the mass fraction going into the 
fracture continuum (compared to the matrix continuum) from the dual continuum invert domain 
in the EBS-UZ interface submodel. This partitioning is time dependent and captures the 
temporal processes active in the EBS, such as varying radionuclide concentrations in the waste 
form, corrosion products, and invert domains and changing water flux through various 
subcomponents of the EBS. 
6.6.4.4 Verification of Dual Invert/Dual UZ Diffusive Flux Bifurcation 
In this section, calculation of the diffusive flux from a single cell (corrosion products) to dual 
invert cells (intergranular invert and intragranular invert) and then to two UZ cells (UZ matrix 
and UZ fracture) is tested. These tests show that the approximations in the GoldSim 
implementation using an Interface_Scale_Factor of 1.0  10-6 are correct and that the 
implementation in GoldSim agrees with Microsoft Excel calculations. 
As modeled, there is no diffusive communication between the dual invert cells and between the 
UZ matrix/fracture cells. The corrosion products cell provides a diffusive flux to the dual invert 
cells. Each invert cell provides a diffusive flux to both the UZ matrix and fracture cells. For this 
verification, at time zero, an initial mass of one gram is released in the corrosion products cell, 
while all other cells have initial mass of zero. Parameters controlling diffusion through this test 
network were not determined strictly from TSPA-LA data, but were set so that measurable mass 
transport to all cells within the network occurs in a reasonable time frame. No parameters were 
assigned a value of one (other than the initial mass in the waste form cell), because any mistake 
in multiplication or division by a unit parameter would not be readily detectable. 

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Figure 6.6-3. Computational Grid in the EBS-UZ Interface Submodel (Dual-Continuum Invert) 

EBS Radionuclide Transport Abstraction 
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Two analytical approaches (A1 and A2) to the flux bifurcation can be taken when diffusion 
occurs from a single cell to dual cells: 
A1: The first approach computes diffusive conductances between the single cell and each 
dual continuum cell; an auxiliary conductance is required between the dual continuum cells. 
This formulation presents the appearance of a diffusive flux communication between the dual 
continuum cells, when physically there is no such flux. This approach requires a five-cell 
network and provides an exact representation of the fluxes. 
A2: The second approach incorporates an interface cell between cells where diffusion 
bifurcates from a single continuum cell to dual continuum cells. The interface cell provides 
an approximate concentration at the flux bifurcation interface. For diffusion from a single 
continuum cell to dual continuum cells, the interface cell is conceptualized as a thin slice of 
the single continuum cell. This implies that, for the proposed cell network, an interface cell 
is located between the corrosion products cell and the dual invert continuum cells. This cell 
is assigned representative properties of the corrosion products cell, with the exception of the 
diffusive length. The diffusive length for the interface cell is taken to be an 
Interface_Scale_Factor times the diffusive length of the corrosion products cell. Between the 
intergranular invert cell and the dual UZ cells, an intergranular invert interface cell is 
introduced with diffusive properties of the intergranular invert and a diffusive length of the 
Interface_Scale_Factor times the diffusive length of the invert. Similarly, between the 
intragranular invert cell and the dual UZ cells, an intragranular invert interface cell is 
introduced. This conceptualization requires an eight-cell network (five cells of A1 plus three 
interface cells) and provides an approximate solution. 
Three solutions to the diffusion problem are presented: 
S1: The first solution is an Excel calculation using A1 approach. This provides an exact 
solution for the transport network. 
S2: The second solution is an Excel calculation using A2 approach. This provides an 
approximate solution dependent on the Interface_Scale_Factor parameter. A successive 
refinement of the Interface_Scale_Factor demonstrates the convergence of the approximate 
solution (S2) to the exact solution (S1). 
S3: The third solution is a GoldSim stand-alone calculation using the A2 approach. This 
solution is compared with solution S2 to verify the GoldSim implementation of the model 
within the EBS transport abstraction. 
The convergence of the approximate solution S2 to the exact solution S1 with refinement of the 
Interface_Scale_Factor is shown in Figure 6.6-4, where the relative error of the mass in place for 
each network cell is plotted as a function of the Interface_Scale_Factor. Figure 6.6-4 shows that 
the solution S2 converges to the exact solution S1 (i.e., a relative error of zero) with first order 
convergence rate with respect to the Interface_Scale_Factor. The error in the UZ matrix cell is 
not observed in Figure 6.6-4, since it is overlain by the error in the UZ fracture cell. 
Figure 6.6-5 presents the GoldSim solution S3 and the Microsoft Excel solution S2. The 
Microsoft Excel solution S2 and GoldSim solution S3 use an Interface_Scale_Factor of 

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ANL-WIS-PA-000001 REV 01 6-204 November 2004 
1.0  10-6. Figure 6.6-5 shows the mass in place for each of the five cells and demonstrates the 
excellent agreement between the Microsoft Excel solution and GoldSim solution. After 2 years, 
the maximum relative error for the corrosion products cell and the two invert cells is 0.2 percent, 
and the maximum relative error for the two UZ cells is 1.5 percent. 
These results confirm that the bifurcation of diffusive flux from a single continuum (corrosion 
products domain) to a dual continuum (invert domain) and then to another dual continuum (UZ) 
is accurate and properly implemented in GoldSim. 
6.6.5 Alternative Invert Diffusion Coefficient Models 
The following two alternative models for determining the diffusion coefficient in the invert are 
assessed in this section: the single-continuum invert diffusion coefficient model and the 
dual-continuum invert diffusion coefficient model. 
6.6.5.1 Alternative Single-Continuum Invert Diffusion Coefficient Model 
As an alternative to the Archies law approach for determination of the diffusion coefficient for 
the single-continuum invert (Section 6.3.4.1), diffusion through the crushed tuff invert ballast is 
modeled using an approach that has been applied to diffusion in soils. Studies generally show 
that the bulk diffusion coefficients of soils at high water content decline with the moisture 
content and that a Millington-Quirk power law developed for high moisture content overpredicts 
the diffusion coefficient at low moisture content (Nye 1979 [DIRS 167377]; Olesen et al. 1999 
[DIRS 154588]). The studies also show that, below a critical moisture content, the diffusion 
coefficient for granular materials becomes negligible (So and Nye 1989 [DIRS 170588]). 
Olesen et al. (1996 [DIRS 155700]) found the best description of the bulk diffusion coefficient of 
granular soils is the following: 
, 2 . 2 , 0 
2 . 2 , 
) 2 . 2 100 ( 
) 2 . 2 ( 0045 . 0 0 
b D 
b 
b 
b D D 
< = 
= 
- 
- 
= 
.
. 
f 
. 
. 
(Eq. 6.6.5.1-1) 
where D, . , and fare the bulk diffusion coefficient (cm2 s-1), moisture content (percent), and 
bulk porosity of the soil (fraction), respectively, 0 D is the free water diffusion coefficient for 
self-diffusion of water, 2.299  10-5 cm2 s-1 at 25C (Mills 1973 [DIRS 133392], Table III), and 
the term 2.2b (percent) corresponds to the critical moisture content for these soils. In this 
expression, the parameter b corresponds to the dimensionless slope of the Campbell moisture 
retention curve on a log-log plot that varies with the pore and grain size distribution of the soil 
(Olesen et al. 1996 [DIRS 155700]). 

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1.E-09 
1.E-08 
1.E-07 
1.E-06 
1.E-05 
1.E-04 
1.E-03 
1.E-02 
1.E-01
1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 
Scale_Factor 
Relative Error 
error CP 
error inter-invert 
error intra-invert 
error UZ matrix 
error UZ fracture 
Figure 6.6-4. Relative Error of Mass-in-Place for Microsoft Excel Approximate Solution 
1.E-04 
1.E-03 
1.E-02 
1.E-01 
1.E+00 
0 20 40 60 80 100 120 140 160 180 200 
Time, yr 
Mass, g 
CP_Excel 
CP_GS 
inter_Excel 
inter_GS 
intra_Excel 
intra_GS 
UZm_Excel 
UZm_GS 
UZf_Excel 
UZf_GS 
Figure 6.6-5. Comparison of Microsoft Excel and GoldSim Flux Bifurcation Solutions 

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This behavior for granular materials is generally explained (Olesen et al. 1999 [DIRS 154588]) 
in terms of a picture in which: 
 Above the critical moisture content, the bulk diffusion coefficient of granular materials 
is dominated by diffusion coefficient in films of moisture on the grain surfaces 
 The diffusion coefficient declines as the moisture content decreases and the tortuosity 
associated with these films increases 
 Below the critical moisture content, diffusion by the surface films cannot be supported 
and the diffusion coefficient is reduced to a very low value. 
Conca and Wright (1990 [DIRS 101582]) have concluded that this picture is consistent with their 
measurements of crushed tuff. 
A moisture retention relation proposed by Campbell (1985 [DIRS 100565], pp. 45-47) is used to 
develop the moisture potential relation for the crushed tuff invert. The relationship between 
moisture potential, . (J kg-1), and volumetric moisture content, . (percent), is the soil moisture 
retention curve, described by the function (Campbell 1985 [DIRS 100565], p. 43): 
b 
s e 
- = ) / ( . . . . , (Eq. 6.6.5.1-2) 
where e . is the air-entry moisture potential (i.e., water potential at which the largest water-filled 
pore in the soil will drain) (J kg-1), .s 
is the saturated moisture content (percent), and b is the 
slope (dimensionless) of the . ln versus . ln curve. As the mean pore diameter becomes 
smaller, the air-entry moisture potential decreases (becomes more negative). The b parameter 
increases as the standard deviation g s (mm) of the pore size increases. Campbell studied the 
relationships between geometric particle diameter, g d (mm), geometric standard deviation, g s 
(mm), and air entry potential, e . (J kg-1). By fitting Equation 6.6.5.1-2 to measured data, he 
obtained the following approximate relationships for soils (Campbell 1985 [DIRS 100565], 
p. 45) having a bulk density of 1,300 kg m-3: 
2 / 1 5 . 0 - - = g es d . , (Eq. 6.6.5.1-3) 
g es b s . 2 . 0 2 + - = , (Eq. 6.6.5.1-4) 
where es . is the air-entry moisture potential (J kg-1); the subscript es refers to the bulk density of 
1,300 kg m-3. The geometric standard deviation depends on the soil texture. The geometric 
standard deviation can be estimated from a soil texture diagram as equal to 1 for coarse sand 
particles and 5 for fine-grained material (Campbell 1985 [DIRS 100565], Figure 2.1). 
The results for the Campbell retention relation for crushed tuff of 0.45 bulk porosity and grain 
sizes ranging from 0.317 mm to 20 mm (BSC 2004 [DIRS 169565], Appendix X) are shown in 
Table 6.6-3. Table 6.6-3 also shows the associated range of the critical bulk moisture content in 
Equation 6.6.5.1-1. 

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Table 6.6-3. Parameters Developed for Crushed Tuff 
Parameter 
Grain Size (mm) a 0.317 3 10 20 
Bulk Porosity b 0.45 0.45 0.45 0.45 
Standard Deviation, sg (mm) c 5 1 1 1 
Slope of the Campbell retention curve, b 2.78 0.777 0.516 0.424 
Critical bulk moisture content, 2.2b (%) 6.12 1.71 1.14 0.932 
a BSC 2004 [DIRS 169565], Appendix X, Section X.4. 
b BSC 2004 [DIRS 169565], Appendix X, Section X.3. 
c Campbell 1985 [DIRS 100565], Figure 2.1. 
Figure 6.6-6 shows the corresponding range in the diffusion coefficient evaluated according to 
Equation 6.6.5.1-1. In general, the invert will include a distribution of tuff grain sizes. 
Therefore, the determination of the critical bulk moisture content is made by sampling from a 
uniform distribution between 0.932 percent and 6.12 percent. This corresponds to the range of 
tuff grain sizes from 20 mm to 0.317 mm, as shown in Table 6.6-3; a uniform distribution is 
appropriate for covering the range for an initial analysis of an alternative conceptual model. The 
corresponding diffusion coefficient would then be evaluated for this sampled moisture content 
according to Equation 6.6.5.1-1. 
1.E-11 
1.E-10 
1.E-09 
1.E-08 
1.E-07 
1.E-06 
1.E-05 
1.E-04
0.1 1 10 100 
Bulk Moisture Content, % 
Diffusion Coefficient, cm2/s 
Conca and Wright 1992 
(6.3 - 9.5 mm) 
Conca and Wright 1992 
(2 - 4 mm) 
Hu et al. 2001 (2 - 4 
mm) 
CRWMS M&O 2000 
b=2.78 
b=0.777 
b=0.516 
b=0.424 
Eq. 6.3.4.1.1-16 
Source: Conca and Wright 1992 [DIRS 100436]; CRWMS M&O 2000 [DIRS 156680]; Hu et al. 2001 [DIRS 
161623]. 
Figure 6.6-6. Range of the Bulk Diffusion Coefficients for Crushed Tuff 

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For conditions in which advective flow does not occur in the crushed tuff, observations indicate 
that the intergranular moisture content will generally be negligible. Conca and Wright 
(1990 [DIRS 101582]) observed that tuff gravel samples allowed to stand for several hours in the 
presence of 100 percent relative humidity reached moisture contents between 0.5 and 1.5 percent 
and negligible surface moisture. The measured diffusion coefficients were found in these cases 
to be below their measurement limit of 1.03  10-11 cm2 s-1. Therefore, in the portion of the 
invert in which there is no flow, the diffusion coefficient is expected to be negligible. 
For conditions in which flow does occur in the crushed tuff, the bulk diffusion coefficient can be 
directly evaluated from Equation 6.6.5.1-1 as described above. This uncertainty is accounted for 
by expressing the threshold in terms of the critical bulk moisture content: 
, , 0 
, 
) 100 ( 
) ( 0045 . 0 0 
C
C 
C 
C 
D 
D D 
. . 
. . 
. f 
. . 
. 
< = 
= 
- 
- 
= 
(Eq. 6.6.5.1-5) 
where . is the bulk moisture content (percent), given by Equation 6.5.3.3-11, and C . is the 
critical value of the bulk moisture content, 0.022b (percent). The critical bulk moisture content 
is selected by sampling a uniform distribution between 0.932 percent and 6.12 percent, as 
discussed earlier in this section. 
Diffusion coefficients of crushed tuff have been estimated using the ultracentrifuge technique 
and measurements of electrical resistivity. Conca and Wright (1992 [DIRS 100436]) and Conca 
et al. (1993 [DIRS 170709]) measured the bulk diffusion coefficients for a variety of granular 
materials, including crushed tuff, as a function of moisture content. Figure 6.6-6 shows the 
results of their measurements of crushed tuff samples with tuff grains sizes between 6.3 mm and 
9.5 mm, and between 2 mm and 4 mm. Diffusion coefficients for crushed tuff with grain sizes 
between 2 mm and 4 mm have also been measured by Hu et al. (2001 [DIRS 161623]); these 
results are also shown in Figure 6.6-6. Finally, the diffusion coefficient measured for samples 
with a wide distribution of grain sizes (CRWMS M&O 2000 [DIRS 156680]) are also shown in 
Figure 6.6-6. Comparison of all of these measurements for crushed tuff indicates that the model 
provides a reasonable representation of the diffusion coefficient for these measured moisture 
contents (1.4 to 55 percent). 
6.6.5.2 Alternative Dual-Continuum Invert Diffusion Coefficient Model 
In general, the literature supports a dual continuum picture of the diffusive conductance by the 
invert granular material. For example, Roberts and Lin (1997 [DIRS 101710]) observed multiple 
conduction pathways in their measurements of the electrical conductance of unsaturated tuff 
samples. Their measurements indicated conduction by adsorbed water on the solid surfaces of 
the tuff samples and conduction by water within the tuff rock. These measurements support a 
dual continuum picture of the tuff samples in which the water on the surface of the samples 
corresponds to the intergranular continuum and the water within the samples corresponds to the 
intragranular continuum. 

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Other observations also support this picture. Porter et al. (1960 [DIRS 123115]) studied the way 
in which chloride ions move through soil and the effect of the moisture content of the soil on this 
movement. These characteristics were interpreted in terms of diffusion within the soil grains and 
diffusion on the solid surfaces of those grains. Nye (1979 [DIRS 167377]) concluded that, to a 
first approximation at least, diffusion can be considered to occur through two independent 
pathways in soil: through moisture between the soil grains and through the grains themselves. 
In this picture, the bulk diffusion coefficient, D, is represented by: 
( ) inter intra inter inter D D D f f - + = 1 , (Eq. 6.6.5.2-1) 
where inter D is the diffusion coefficient for the intergranular continuum determined by the 
moisture films on the surfaces of the grains, intra D is the diffusion coefficient for the 
intragranular continuum determined by the moisture within the grains, and inter f is the 
intergranular porosity of the material. 
In this picture, the bulk diffusion coefficient is dominated by the intergranular diffusion 
coefficient above the critical bulk moisture content, while below this critical value, the 
intragranular diffusion coefficient dominates. That is, Equation 6.6.5.2-1 becomes: 
, ), 1 ( 
, ) ( 
C inter intra 
C inter inter 
D D 
D D 
. . f 
. . f . 
< - = 
=  
(Eq. 6.6.5.2-2) 
where C . is the critical moisture content (percent). In this picture, the intergranular diffusion 
coefficient is represented by the model in Equation 6.6.5.1-1, divided by the intergranular 
porosity: 
. , 
, 
100 100 
45 . 0 0 
C limit inter 
C 
C I 
C 
inter 
inter 
D D 
D D 
. . 
. . 
. f 
. . 
f 
. 
< = 
= . .. 
. 
. .. 
. 
- 
- 
. .. 
. 
. .. 
. 
= 
(Eq. 6.6.5.2-3) 
limit D is the measurement limit, 10-12 cm2 s-1, I f is the bulk porosity of the invert, 
( )intra inter inter I f f f f - + = 1 (fraction), and C . corresponds to 2.2b in Equation 6.6.5.1-1. 
The intragranular diffusion coefficient is determined by the following considerations. 
Reimus et al. (2002 [DIRS 163008]) measured diffusion coefficients for saturated whole rock 
samples of tuff. The measured values for the samples ranged from 1.5  10-7 cm2 s-1 to 
2  10-5 cm2 s-1. From these measurements, Reimus et al. (2002 [DIRS 163008]) developed a 
correlation between the saturated diffusion coefficient, ms D , and the porosity, m f , and intrinsic 
permeability, m k , of the tuff rock matrix: 
m m ms k D 10 10 log 165 . 0 38 . 1 49 . 3 log + + - = f . (Eq. 6.6.5.2-4) 

EBS Radionuclide Transport Abstraction 
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The tuff samples were from Pahute Mesa, Nevada, but many of them are similar to tuff rocks at 
Yucca Mountain. To evaluate the flow characteristics of the drift invert, matrix porosity and 
intrinsic permeability for tuff from two different Topopah Spring welded tuff units, TSw35 and 
TSw36, were identified (DTN: LB0207REVUZPRP.002 [DIRS 159672]; Spreadsheet: 
Matrix_Props.xls, Row 20, Column C). These properties are summarized in Table 6.6-4. Using 
the correlation in Equation 6.6.5.2-4, the diffusion coefficient for saturated tuff whole rock with 
a saturated moisture content of 10.3 percent is 3.69  10-7 cm2 s-1, and the diffusion coefficient 
for a saturated moisture content of 13.1 percent is 6.73  10-7 cm2 s-1. 
Table 6.6-4. Tuff Matrix Properties for TSw35 and TSw36 
Parameter TSw36 TSw35 
Porosity of the rock matrix in an individual granule, fm 0.103 0.131 
Intrinsic Permeability, km (m2) 2.00  10-19 4.48  10-18 
Saturated diffusion coefficient (from Equation 6.6.5.2-4), Dms (cm2 s-1) 3.69  10-7 6.73  10-7 
DTN: LB0208UZDSCPMI.002 [DIRS 161243]; Spreadsheet drift-scale calibrated properties for mean 
infiltration2.xls, Rows 17-18, Columns B-C. 
A laser ablation microprofiling technique has been used to estimate the diffusion characteristics 
for an unsaturated whole tuff rock sample (Hu et al. 2001 [DIRS 161623]). Hu et al. 
(2001 [DIRS 161623], p. 25) found that, for a measured moisture content of the sample of 
8.9 percent, the internal diffusion coefficients were on the order of 10-12 cm2 s-1 (Hu et al. 2001 
[DIRS 161623], p. 25). This result indicates a very low intragranular diffusion coefficient for 
tuff at intragranular saturations below about 80 percent. 
The model developed for the intragranular diffusion coefficient considering this information is 
the following. For intragranular moisture content, intra . , below 8.9 percent, a value of 
10-12 cm2 s-1 is used to represent the diffusion coefficient. For saturated conditions ( intra 
intra f 
. 
= 
100 
, 
the intragranular porosity), the diffusion coefficient is set to a value corresponding to 
Equation 6.6.5.2-4. For unsaturated grains with moisture content above 8.9 percent, a power-law 
extrapolation from the saturated value is used. The overall model proposed for the intragranular 
diffusion coefficient is the following power law model: 
, , 
, 100 
min intra limit intra 
min intra 
p 
intra 
intra 
ms intra 
D D 
D D 
. . 
. . 
f
. 
< = 
= 
. . . . 
.
. 
. . . . 
.
. 
.. 
. 
.. 
. 
= 
(Eq. 6.6.5.2-5) 
where intra . is the intragranular moisture content (percent), intra f is the intragranular porosity 
(fraction), limit D is the measurement limit, 10-12 cm2 s-1, and min . is equal to 8.9 percent. 

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The exponent p is the slope of Equation 6.6.5.2-5 in a plot of ( ) intra D 10 log versus ( ) intra . 10 log . 
This plot is a straight line between points .. 
. 
.. 
. 
100 
, min 
limit D 
. 
and ( ) intra ms D f , . Thus, p is given by: 
) ( log 
100 
log 
) ( log ) ( log 
10 10 
10 10 
intra 
min 
ms limit D D p 
f 
. 
- .. 
. 
.. 
. 
- 
= . (Eq. 6.6.5.2-6) 
The dual porosity model for the invert diffusion coefficient follows by specifying values for the 
intergranular and intragranular diffusion coefficients. The intergranular diffusion coefficient is 
evaluated from Equation 6.6.5.1-5 and dividing by the intergranular porosity. The intragranular 
diffusion coefficient is evaluated from Equation 6.6.5.2-5. The effective bulk diffusion 
coefficient is determined from Equation 6.6.5.2-2. 
6.7 DESCRIPTION OF BARRIER CAPABILITY 
6.7.1 Analyses of Engineered Barrier Capability 
This section discusses the ability of barriers to prevent or delay the movement of water 
or radioactive materials and deals specifically with the engineered barriers addressed in this 
report  the drip shield, the waste package, and the invert. In assessing these barriers, a number 
of assumptions are made (see Section 5). 
The drip shield prevents groundwater seepage that enters the drift from dripping onto the waste 
package. It will be completely effective until it is breached, and it is partially effective 
thereafter. Condensation on the underside of the drip shield has been screened out due to low 
consequence (BSC 2004 [DIRS 169898], Section 6.2.41). In this case, the presence of the drip 
shield can potentially increase the amount of water that contacts the waste package, but the effect 
is negligible. This report presents an algorithm to determine the fraction of seepage entering the 
drift that passes through a breached drip shield, based on the number and size of breaches 
(Section 6.3.2.4). In the case where no groundwater seepage or dripping of drift-wall 
condensation into the drift occurs, there will be no water flux through the drip shield. The flux 
of water into the waste package is equal to the groundwater and dripping condensation flux 
passing through the drip shield, less the fraction that is diverted by intact portions of the waste 
package. In this way, the effectiveness of the drip shield as a barrier can be quantified. 
The waste package outer corrosion barrier consists of corrosion-resistant material that will 
prevent and delay water from entering the waste package. Once breaches occur, water may enter 
the waste package, dissolve radionuclides, and flow out, thereby generating advective releases of 
radionuclides. This report presents an algorithm to determine the fraction of the water flux 
impinging on the waste package (having passed through drip shield breaches) that enters the 
waste package, depending on the size and number of breaches, as well as the total water flux 
through the waste package (Section 6.3.3.2). Flow is modeled as steady state and passing 
through the waste package without accumulating. Submodels not detailed in this report provide 
the concentration of radionuclides that are dissolved in the water flowing through the waste 
package (BSC 2004 [DIRS 169425]) and the behavior of colloids (BSC 2004 [DIRS 170025]). 

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Sorption and retardation characteristics of radionuclides inside the waste package are discussed 
in this report (Section 6.3.4.2). When there is no advective transport, diffusive releases may still 
occur; a submodel for diffusion inside the waste package is presented (Section 6.5.1.2.1). With 
these models implemented in TSPA-LA, the effectiveness of the waste package as a barrier can 
be quantified. 
The invert consists of crushed tuff that can delay releases of radionuclides to the unsaturated 
zone. The invert provides a diffusive barrier. A simple model for computing the diffusion 
coefficient of the invert as a function of the porosity and water saturation is presented in this 
report (Section 6.3.4.1). This enables the effectiveness of the invert as a barrier to be quantified 
when implemented in TSPA-LA. 
6.7.2 Summary of Natural and Engineered Barrier Capability 
Table 6.7-1 summarizes the performance function of natural and engineered barriers. Only 
engineered barriers are analyzed in this report; the performance of natural barriers is outside the 
scope of this report and is included in this table for completeness. 
Table 6.7-1. Summary of Barrier and Performance Functions for a Yucca Mountain Repository 
Barrier Barrier Performance Function 
Surficial soils and topography Reduce the amount of water entering the unsaturated zone by surficial 
processes (e.g., precipitation lost to runoff, evaporation, and plant uptake). 
Unsaturated rock layers 
overlying the repository and 
host unit 
Reduce the amount of water entering emplacement drifts by natural subsurface 
processes including lateral diversion of flow, flow in fractures around 
emplacement drifts, reduction in seepage due to capillary pressure in the 
unsaturated zone, reduction in dripping onto waste packages due to film flow. 
In the repository, induced coupled thermal-hydrologic processes also reduce 
the amount of water available to contact waste packages through enhanced 
evaporation near emplacement drifts (and drainage through pillars), 
remobilization of water by boiling and condensate shedding in pillars (for higher 
temperature operating modes). 
Also, in the physical/chemical environment in the unsaturated zone at Yucca 
Mountain (mildly oxidizing, pH near neutral), the vast majority of radionuclides 
are present in thermodynamically stable forms (metal oxides or ceramics) that 
are not geochemically mobile, and therefore are unlikely to move. 
Unsaturated rock layers below 
the repository 
Delay radionuclide movement and decrease radionuclide concentrations in the 
groundwater aquifer because of water residence time (flow rates), matrix 
diffusion, precipitation, dispersion, sorption. 
Saturated zone volcanic tuff and 
alluvial deposits below the 
water table from the repository 
to a point of compliance 
approximately 18 km south 
Delay radionuclide movement to the receptor location and reduce radionuclide 
concentrations by water residence time, matrix diffusion, sorption, dispersion, 
and dilution. 
Drip shield around the waste 
packages 
Prevent water contacting the waste package and waste form by diverting water 
flow around the waste package, limiting advective transport through the invert. 
Waste package Prevent water from contacting the waste form for the effective life of the 
package. Limit advective and diffusive transport of radionuclides from failed 
waste packages by sorption onto steel internal component corrosion products. 

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Table 6.7-1. Summary of Barrier and Performance Functions for a Yucca Mountain Repository 
(Continued) 
Barrier Barrier Performance Function 
Cladding Delay and/or limit liquid water contacting SNF after waste packages have 
degraded (Note no cladding exists for High-Level Radioactive Waste.). 
Waste form (CSNF, DOE SNF, 
DOE high-level radioactive 
waste) 
Limit radionuclide release rates as a result of low degradation rates for the 
waste forms, and low radionuclide solubilities. 
Invert Limit diffusive transport of radionuclides out of the engineered barriers by 
maintaining unsaturated conditions under the waste package. Limit advective 
and diffusive transport of radionuclides by sorption onto crushed tuff. 

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7. VALIDATION 
Model validation for the EBS Radionuclide Transport Abstraction was performed in accordance 
with AP-2.27Q, Planning for Science Activities, and AP-SIII.10Q, Models, and follows the 
validation guidelines in the Technical Work Plan for: Near-Field Environment and 
Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report 
Integration (BSC 2004 [DIRS 170775]). 
AP-SIII.10Q, Models, requires that TSPA-LA model components be validated for their intended 
purpose and stated limitations, and to the level of confidence required by the relative importance 
of the component to the potential performance of the repository system. Three levels of model 
validation are defined in AP-2.27Q, Planning for Science Activities, Attachment 3, with the level 
of validation increasing with an increasing level of model importance ranging from low to 
moderate to high. Models whose variation could lead to a potentially large effect on the estimate 
of mean annual dose (e.g., a change greater than 1 mrem yr-1) should receive a high or Level III 
model validation. Models whose variation could lead to moderate effect on the estimate of mean 
annual dose (less than 1 mrem yr-1, but greater than 0.1 mrem yr-1) should receive Level II model 
validation. Level I validation is sufficient for models of less importance to the estimate of mean 
annual dose. 
The levels of confidence required for the models of the EBS RT Abstraction, as stated in 
Section 2.2.2 of the TWP, are given as follows. 
The required level of confidence for radionuclide transport from the waste package to the drift 
wall through the invert is Level I (also specified in Table 1 of AP-2.27Q, Planning for Science 
Activities). The EBS-UZ interface submodel of the EBS RT Abstraction provides input to the 
unsaturated zone radionuclide transport model as described in Particle Tracking Model and 
Abstraction of Transport Processes (BSC 2004 [DIRS 170041]). The appropriate level of 
confidence identified for unsaturated zone radionuclide transport is Level II. Therefore, Level II 
also represents appropriate level of confidence for the EBS-UZ interface submodel of the EBS 
RT Abstraction. 
Confidence Building During Model Development to Establish Scientific Basis and 
Accuracy for Intended Use 
For Level I validation, Section 2.2.3 of Technical Work Plan for: Near-Field Environment and 
Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report 
Integration (BSC 2004 [DIRS 170775]) cites Attachment 3 of AP-2.27Q as guidance for 
documenting a discussion of decisions and activities for confidence building during model 
development. Additionally, the development of the model will be documented in accordance 
with the requirements of Section 5.3.2(b) of AP-SIII.10Q. The development of the EBS RT 
Abstraction model has been conducted according to these requirements and the requisite criteria 
have been met as discussed below: 
1. Selection of input parameters and/or input data, and a discussion of how the selection 
process builds confidence in the model. [AP-SIII.10 Q 5.3.2(b) (1) and AP-2.27Q 
Attachment 3 Level I (a)] 

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The inputs to the EBS RT Abstraction have been obtained from appropriate sources as 
described in Section 4.1. All the data are qualified project data developed by or for the 
Yucca Mountain Project. Tables 4.1-1 through 4.1-17 describe the input parameters, the 
values of the parameters and the source of the information. Inputs were selected because 
they are expected to represent conditions at the repository and therefore build confidence 
in the model. Thus, this requirement can be considered satisfied. 
2. Description of calibration activities, initial boundary condition runs, run convergences, 
simulation conditions set up to span the range of intended use and avoid inconsistent 
outputs, and a discussion of how the activity or activities build confidence in the model. 
Inclusion of a discussion of impacts of any non-convergence runs [(AP-SIII.10Q 
5.3.2(b)(2) and AP-2.27Q Attachment 3 Level I (e)]. 
A detailed discussion of the computational implementation of the EBS RT Abstraction is 
described in Section 6.5.3. The discretization and development of the computational cell 
network of the sub-model domains is described in Section 6.5.3.5. Section 6.5.3.6 
provides special emphasis and discussion of the EBS-UZ boundary condition. 
Simulation conditions account for both seepage or no seepage boundary conditions and 
the flux splitting algorithm accounts for the eight key flow pathways in the engineered 
barrier system. Discussion about non-convergence runs is not relevant for this model 
report. Thus, this requirement can also be considered satisfied. 
3. Discussion of the impacts of uncertainties to the model results including how the model 
results represent the range of possible outcomes consistent with important 
uncertainties.[(AP-SIII.10 Q 5.3.2(b)(3) and AP-2.27Q Attachment 3 Level 1 (d) and 
(f)]. 
Data uncertainty is addressed in Section 6 and parameter uncertainties are summarized 
in Table 6.5-13. In particular, corrosion rates of carbon and stainless steels are listed as 
model input with ranges and distributions determined from the data in Table 4.1-1. 
Sorption coefficient distribution ranges are summarized in Tables 4.1-11 and 4.1-12 and 
sampling correlations are given in Table 4.1-13. Table 4.1-8 provides uncertainty for 
unsaturated zone parameters. The breached drip shield experimental test data in 
Tables 4.1-2 through 4.1-6 and Figure 4.1-1 are evaluated in Section 6.5.1, resulting in 
uncertain model input parameters listed in Table 6.5-13 (Flux_Split_DS_Uncert and 
Flux_Split_WP_Uncert). 
Model uncertainty is addressed through the evaluation of alternative conceptual models. 
In considering alternative conceptual models for radionuclide release rates and solubility 
limits (Sections 6.4. and 6.6), the EBS radionuclide transport abstraction uses models and 
analyses that are sensitive to the processes modeled for both natural and engineering 
systems. 
Conceptual model uncertainties are defined and documented, and effects on 
conclusions regarding performance are assessed. The fundamental relationships, 
e.g., mass balance and flow equations, upon which the EBS RT Abstraction is based, are 
well-established with a long history of use in the scientific community and as such are 
not subject to significant uncertainty. In addition, the alternative conceptual models have 

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been screened out (Section 6.4), thereby increasing confidence in the selected conceptual 
model. Other sources of uncertainty involve modeling choices (e.g., assumptions, 
geometry) that, because of their conservative nature, effectively bound uncertainty. 
Therefore this requirement can be considered satisfied. 
4. Formulation of defensible assumptions and simplifications. [AP-2.27Q Attachment 3 
Level I (b)]. 
A discussion of assumptions is provided in Section 5. The conceptual model for EBS RT 
Abstraction are documented in Section 6.3.1. and the simplifications necessary for 
implementation bases on EBS design details and failure mechanisms are presented in 
Sections 6.3.3 and 6.3.4. Thus, this requirement can also be considered satisfied. 
5. Consistency with physical principles, such as conservation of mass, energy, and 
momentum. [AP-2.27Q Attachment 3 Level I (c)] 
Consistency with physical principles is demonstrated by the development of the mass 
balance mathematical formulations in Section 6.5.1. Thus, this requirement can also be 
considered satisfied. 
Confidence Building After Model Development to Support the Scientific Basis of the Model 
Level II validation includes the above Level I criteria and a single post development model 
validation method described in Paragraph 5.3.2c of AP-SIII.10Q, Models, consistent with a 
model of moderate importance to mean annual dose. The post development model validation 
method selected for the EBS-UZ interface submodel, as delineated in the TWP, consists of: 
corroboration by comparison to an alternative mathematical model developed for a closely 
comparable description of the relevant EBS-UZ features. This validation approach is consistent 
with Paragraph 5.3.2c (2) of AP-SIII.10Q, Models, which lists corroboration of results with 
alternative mathematical models as one of the validation methods for Level II validation. The 
comparison is documented in Section 7.3.1. 
To build further confidence in the EBS RT Abstraction, an independent model validation 
technical review was conducted as specified by the TWP (BSC 2004 [DIRS 170775], 
Sections 2.2.3 and 2.2.4) for the EBS flow model, the EBS transport model, and the EBS-UZ 
interface submodel. This approach is based on requirements of AP-SIII.10Q, Section 5.3.2 c), 
where independent technical review is listed as an appropriate method for model validation. 
Validation is achieved if the review determines that the questions/criteria for this model, listed in 
Section 2.2.4 of the TWP, are met. Qualifications of and review tasks to be completed by the 
independent technical reviewer are described in Section 2.2.4 of the TWP. The model validation 
criteria are described as follows (BSC 2004 [DIRS 170775], Section 2.2.4). 

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EBS Flow Model Validation Criteria 
Criteria that the validation of the EBS flow model is met are as follows. Each shall be confirmed 
by the independent model validation technical reviewer. 
a) The approach and algorithms described in the document and provided to the TSPA 
capture all known flow pathways into and from EBS components. 
b) Modeling assumptions are clearly defined, discussed, and justified as appropriate for the 
intended use of the model. 
c) Uncertainties in parameters, processes, and assumptions are sufficiently described, and 
impacts of these uncertainties discussed. 
d) The overall technical credibility of the approach, including assumptions, parameters, 
equations, and the TSPA implementation, are sufficient for the models intended use. 
EBS Transport Model Validation Criteria 
Criteria that the validation of the EBS transport model is met are as follows. Each shall be 
confirmed by the independent model validation technical reviewer. 
a) The approach and algorithms described in the document and provided to TSPA address 
all known modes of radionuclide transport within and from the EBS components. 
b) Modeling assumptions are clearly defined, discussed, and justified as appropriate for the 
intended use of the model. 
c) Uncertainties in parameters, processes, and assumptions are sufficiently described, and 
impacts of these uncertainties discussed. 
d) The overall technical credibility of the approach, including assumptions, parameters, 
equations, and the TSPA implementation, are sufficient for the models intended use. 
EBS-UZ Interface Submodel Validation Criteria 
The criterion that the validation of the EBS-UZ interface submodel is met shall consist of 
concurrence by an independent technical reviewer that the invert fracture-matrix partitioning 
results obtained using this model compare favorably with the fracture-matrix partitioning 
cumulative distribution function obtained using a discrete fracture model described in the 
Drift-Scale Radionuclide Transport model (BSC 2004 [DIRS 170040]). Results of the 
comparison shall show qualitative agreement between the two methods. The report shall 
document equivalent trends and correlations between input parameter variation and predicted 
results, identification of differences between the model results, and a discussion of the reasons 
and potential significance of these differences, and shall also demonstrate that the EBS-UZ 
interface submodel provided to TSPA does not underestimate radionuclide transport from the 
EBS to the UZ. 

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The results of the independent model validation technical review for the flow and transport 
models demonstrate that the appropriate criteria from above have been met, and are presented in 
Section 7.2.3. The results of the EBS-UZ interface submodel review demonstrate that the 
appropriate criteria listed above have been met, and are presented in Section 7.3.2. 
The validation guidelines in the Technical Work Plan for: Near-Field Environment and 
Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report 
Integration (BSC 2004 [DIRS 170775]) also state that the Subject Matter Expert (author) may 
elect, as deemed appropriate, to provide additional validation in the form of: 
 Corroboration of model results with data previously acquired from laboratory 
experiments or other relevant observations 
 Corroboration of model results with results of alternative models. 
Additional validation of the flux splitting portion of the flow model was performed through 
corroboration of model results of experimental data. The results of that validation exercise are 
presented in Section 7.1.1. 
Additional validation of the in-package diffusion portion of the transport model was performed 
through corroboration with alternative models. The results of that validation exercise are 
presented below in Section 7.2. 
7.1 EBS FLOW MODEL 
The EBS flow is modeled as a one-dimensional, steady advective flow through the components 
of the EBS. The sources of flow to the model include a seepage flux from the roof of the drift, 
condensation on the walls of the drift above the drift shield, and an imbibition flux from the 
unsaturated zone into the crushed tuff invert. The output of the flow model includes an 
advective flux from the invert into the unsaturated zone. 
The conceptual model divides the EBS components into three domains: waste form, waste 
package corrosion products, and the invert. Flow and transport in these domains are treated 
separately. The output of the waste form domain feeds into the corrosion products domain. The 
output of the corrosion products domain in turn feeds the invert. 
The flow through the EBS may occur along eight pathways: (1) dripping flux, (2) flux through 
the drip shield, (3) diversion around the drip shield, (4) flux through the waste package, 
(5) diversion around the waste package, (6) total flux into the invert, (7) imbibition flux from the 
unsaturated zone matrix to the invert, and (8) flux from the invert to the unsaturated zone 
fractures. 
The magnitude of seepage fluid passing through the drip shield and the waste package is 
accounted for using the flux splitting submodel. This submodel determines how much water 
flows through the drip shield or waste package and how much is diverted around these 
components. Below is the validation of the submodel and validation criteria for both the drip 
shield and waste package applications. Further discussions relevant to the validation of the flow 
model can be found in Sections 5, 6.3.2, 6.3.3, 6.5.1.1.1, 6.5.1.1.2, and 6.5.1.1.3. 

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7.1.1 Flux Splitting Submodel 
The EBS flux splitting submodel, which is part of the EBS RT Abstraction flow model, 
determines the fraction of total dripping flux that will flow through the drip shield and/or waste 
package. This submodel is directly related to the waste isolation attribute (i.e., the limited 
release of radionuclides from engineered barriers). The amount of water flowing through 
engineered barriers, when combined with radionuclide solubility limits and diffusive transport, 
defines the mass flux of radionuclides that is mobilized for transport through the EBS to the 
unsaturated zone. 
Level I validation is appropriate for the flux splitting submodel, because it is part of the process 
for radionuclide transport from waste package to the drift wall through the invert (see Section 7 
above). In addition, the flux splitting submodel has the following features: 
 The submodel is not extrapolated over large distances, spaces or time. 
 The submodel has large uncertainties because of the chaotic nature of the flow of 
droplets or rivulets on corroded, roughened surfaces. 
 Sensitivity analyses in the prioritization report Risk Information to Support 
Prioritization of Performance Assessment Models (BSC 2003 [DIRS 168796], 
Sections 3.3.6 through 3.3.11) show that the flux splitting abstraction will not have a 
large impact on dose in the first 10,000 years. 
 The flux splitting submodel plays a minor role in TSPA-LA. In the nominal scenario 
class, neither the drip shield nor the waste package fails due to general corrosion within 
the 10,000-year regulatory period, and when the drip shield does fail, it is modeled as 
failing completely in a single time step (BSC 2004 [DIRS 169996], Section 6.3). In the 
igneous scenario class, neither the drip shield nor the waste package survives an igneous 
intrusion, so the flux splitting submodel is not used. Thus, the flux splitting submodel is 
actually applied only in the seismic scenario class when seismic damage occurs to the 
waste package. 
This flux splitting submodel is validated through comparison to experimental data. A work plan 
entitled Test Plan for: Atlas Breached Waste Package Test and Drip Shield Experiments 
(BSC 2002 [DIRS 158193]) defines the experiments used for validation of this flux splitting 
submodel. 
The flux splitting submodel is applied to two components of the EBSthe drip shield and the 
waste packageand is validated for each. Validation is achieved through comparison of the 
models developed in this document (based in part on the qualified experimental data) to other 
qualified data collected during associated testing. This comparison is limited because the 
validation experiments are based on flow measurements from a single fixed source for dripping, 
whereas the abstraction is based on randomly located drips relative to multiple patches on the 
drip shield. In this situation, the appropriate criterion for model validation is that the predictions 
of the abstraction bound the experimental measurements made on the rough drip shield surface. 
This criterion is appropriate because of the large spread of the experimental data. 

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The rough drip shield surface experiments replicate the smooth drip shield surface experiments 
and constitute a consistent set of data that can be compared with and serve as validation for the 
smooth drip shield surface data. The rough surface would be expected to yield results 
(specifically, the flux splitting uncertainty factors) that differ from those obtained for the smooth 
surface. However, because the only difference in the experiments is the surface texture, the 
trends in the data and the values obtained for the uncertainty factors should be similar, which 
validates the flux splitting submodel. 
Experimental data used to develop the flux splitting submodel include the splash radius, the 
rivulet spread distance or angle, and the fraction of dripping flux that flowed into breaches. For 
the drip shield and waste package flux splitting submodels, data from smooth drip shield 
experiments were used (DTNs: MO0207EBSATBWP.022 [DIRS 163400]; 
MO0207EBSATBWP.023 [DIRS 163402]; MO0207EBSATBWP.024 [DIRS 163401]; 
MO0207EBSATBWP.025 [DIRS 163403]). For validation of the models, data from the rough 
drip shield experiments are used (DTNs: MO0207EBSATBWP.021 [DIRS 163399]; 
MO0208EBSATBWP.027 [DIRS 163404]; MO0208EBSATBWP.028 [DIRS 163405]). Each of 
the types of data used is discussed below, first for the drip shield submodel validation and then 
for the waste package flux splitting submodel validation. 
7.1.1.1 Drip Shield Flux Splitting Submodel 
Splash radius data for dripping onto the crown of the rough drip shield surface are listed in 
Table 7.1-1. The data are analyzed in the Microsoft Excel spreadsheet: Flux Splitting 
Validation, Worksheet: Splash Rad vs Number, which is documented in Appendix E. As shown 
in Figure 7.1-1, the splash radius tends to increase as the number of drips increases. The inner 
cluster radius is of interest because it is used to define the effective length of the drip shield in 
developing the flux splitting submodel (see Section 6.5.1.1.2). While the data do not indicate 
that a maximum splash radius was achieved, it stands to reason that a maximum must exist, 
simply because the distance a splashed droplet can travel is finite, limited by the kinetic energy 
of a falling drop. The uncertain parameter in the drip shield flux splitting submodel, DS f ' , was 
based on the maximum splash distance observed for the inner cluster of droplets on a smooth 
drip shield, 48 cm (see Section 6.5.1.1.2.4 for a discussion of the development of DS f ' based on 
the 48-cm maximum inner cluster splash radius). For the rough drip shield tests, the maximum 
inner cluster splash radius for dripping onto the crown was again 48 cm. Another approach is to 
use the splash radius at which rivulets begin to flow from coalesced droplets. In Splash Radius 
Test #1, rivulet flow began after 143 drips; in Test #2, after 145 drips; and in Test #3, after 
133 drips (DTN: MO0207EBSATBWP.021 [DIRS 163399]), for an average of 140 drips. 
Using the Microsoft Excel Trendline application (least squares fitting routine) for the inner 
cluster data in Figure 7.1-1, the splash radius when rivulets began to flow was 31 cm. The 
minimum splash radius was about 3.5 cm for more than 20 drips (see Table 7.1-1). The range of 
uncertainty is bounded using the extreme values of splash radius (3.5  48 cm). Since the value 
of splash radius at which rivulets begin to flow (31 cm) is between those extremes, an estimate of 
uncertainty based on that value will not affect the estimated bounds on uncertainty. 
The flux splitting submodel also depends on the rivulet spread angle. These data are analyzed in 
the Microsoft Excel spreadsheet: Flux Splitting Validation, Worksheet: Rough DS, which is 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-8 November 2004 
documented in Appendix E. For the smooth drip shield, the spread angle from crown drip 
locations ranged from 8.9 to 17.3 ( one standard deviation from the mean of 13.2; see 
Section 6.5.1.1.2.4). For drip locations on the crown, the rough drip shield surface had a mean 
rivulet spread angle of 7.3, with a range of 0 to 14.4 ( one standard deviation from the 
mean). Rivulet spread data for the rough surface are shown in Table 7.1-2. In Table 7.1-4, the 
spread angle calculation results are shown. 
The amount of water dripped onto the crown and water flow into breaches on the rough drip 
shield surface are listed in Table 7.1-3. The fraction of the dripping flux that flowed into the 
pertinent breach, expt f , is shown along with the rivulet spread angle for each particular test in 
Table 7.1-4. 
Table 7.1-1. Atlas Breached Drip Shield Experiments on Rough Drip Shield Surface  Dripping on 
Crown  Splash Radius Tests 
Splash Radius (cm) 
No. Drips Left Right Comments 
Splash Radius Test #1 
10 2.0 2.0 Measured inner cluster (bulk) 
10 15.0 25.5 Measured outer fringe 
21 5.0 4.0 Measured inner cluster (bulk) 
21 15.0 42.5 Measured outer fringe 
60 18.0 22.0 Measured inner cluster (bulk) 
60 72.5 75.5 Measured outer fringe 
143 35.0 48.0 Measured inner cluster (bulk) 
143 54.0 82.5 Measured outer fringe 
203 35.0 48.0 Measured inner cluster (bulk) 
203 79.5 106.5 Measured outer fringe 
Splash Radius Test #2 
21 3.5 4.0 Measured inner cluster (bulk) 
21 37.5 7.0 Measured outer fringe 
82 10.5 19.0 Measured inner cluster (bulk) 
82 63.0 32.0 Measured outer fringe 
149 31.5 30.0 Measured inner cluster (bulk) 
207 45.0 40.0 Measured inner cluster (bulk) 
Splash Radius Test #3 
30 7.5 9.0 Measured inner cluster (bulk) 
82 19.0 17.5 Measured inner cluster (bulk) 
137 28.0 27.5 Measured inner cluster (bulk) 
205 29.0 28.0 Measured inner cluster (bulk) 
DTN: MO0207EBSATBWP.021 [DIRS 163399]. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-9 November 2004 
R2 = 0.664 
y = -6.509E-04x2 + 3.280E-01x - 1.882E+00 
R2 = 8.509E-01 
0 
20 
40 
60 
80 
100 
120 
0 50 100 150 200 250 
Number of Drips 
Splash Radius (cm) 
Inner Cluster 
Outer Fringe 
Poly. (Outer 
Fringe) 
Poly. (Inner 
Cluster) 
Figure 7.1-1. Splash Radius Dependence on Number of Drips for Rough Drip Shield Tests 
Table 7.1-2. Atlas Breached Drip Shield Experiments on Rough Drip Shield Surface  Dripping on 
Crown  Rivulet Spread Data  33 from Crown 
Drip Location Left (cm) Right (cm) 
Relevant 
Patch 
Multiple Patch Tests (DTN: MO0208EBSATBWP.027 [DIRS 163404]) 
81 cm left of drip shield center 32.5 17.5 4 
27 cm left of drip shield center 21.5 18.0 4 
27 cm right of drip shield center 10.0 10.0 5 
27 cm right of drip shield center 1.0 0 5 
81 cm right of drip shield center 17.0 34.0 5 
Bounding Flow Rate Tests (DTN: MO0208EBSATBWP.028 [DIRS 163405]) 
54 cm left of drip shield center (High Flow Rate) 2 0 4 
27 cm left of drip shield center (High Flow Rate) 15 15 4 
27 cm right of drip shield center (High Flow Rate) 6 6 5 
27 cm right of drip shield center (Low Flow Rate) 50.0 16.0 5 
27 cm right of drip shield center (Low Flow Rate)  1.0 5 
27 cm left of drip shield center (Low Flow Rate) 25.5 12.0 4 
54 cm left of drip shield center (Low Flow Rate) 0 0 4 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-10 November 2004 
Table 7.1-3. Atlas Breached Drip Shield Experiments on Rough Drip Shield Surface  Dripping on 
Crown  Flow into Breaches 
Drip Location Relative to: Water Collected in: 
Drip Location 
Breach B4 
(cm) 
Breach B5 
(cm) 
Water 
Input (g) 
Breach B4 
(g) 
Breach B5 
(g) 
Multiple Patch Tests (DTN: MO0208EBSATBWP.027 [DIRS 163404]) 
81 cm left of drip shield center -27 -135 292.35 0.27 0.00 
27 cm left of drip shield center 27 -81 288.45 5.27 0.00 
27 cm right of drip shield center 81 -27 291.62 0.00 0.08 
27 cm right of drip shield center 81 -27 294.13 0.00 0.27 
81 cm right of drip shield center 135 27 290.10 0.00 1.01 
Bounding Flow Rate Tests (DTN: MO0208EBSATBWP.028 [DIRS 163405]) 
54 cm left of drip shield center 
(High Flow Rate) 0 -108 330.74 193.87 0.00 
27 cm left of drip shield center 
(High Flow Rate) 27 -81 328.65 0.63 0.00 
27 cm right of drip shield center 
(High Flow Rate) 81 -27 306.65 0.00 0.35 
27 cm right of drip shield center 
(Low Flow Rate) 81 -27 545.14 0.00 11.11 
27 cm right of drip shield center 
(Low Flow Rate) 81 -27 70.80 0.00 0.00 
27 cm left of drip shield center 
(Low Flow Rate) 27 -81 113.32 1.36 0.00 
54 cm left of drip shield center 
(Low Flow Rate) 0 -108 118.10 0.00 0.00 
Table 7.1-4. Atlas Breached Drip Shield Experiments on Rough Drip Shield Surface  Dripping on 
Crown  Fraction of Dripping That Flowed into Breaches and Rivulet Spread Angle 
Spread Angle (degree) 
Drip Location 
Breach 
Collecting Flow fexpt Left Right 
81 cm left of drip shield center 4 0.0018 32.5 17.5 
27 cm left of drip shield center 4 0.0365 21.5 18 
27 cm right of drip shield center 5 0.0005 10 10 
27 cm right of drip shield center 5 0.0018 0 1 
81 cm right of drip shield center 5 0.0070 17 34 
54 cm left of drip shield center 
(High Flow Rate) 4 1.1723 2 0 
27 cm left of drip shield center 
(High Flow Rate) 4 0.0038 15 15 
27 cm right of drip shield center (High Flow Rate) 5 0.0023 6 6 
27 cm right of drip shield center 
(Low Flow Rate) 5 0.0408 50 16 
27 cm right of drip shield center 
(Low Flow Rate) 5 0.0110  1 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-11 November 2004 
Table 7.1-4. Atlas Breached Drip Shield Experiments on Rough Drip Shield Surface  Dripping on 
Crown  Fraction of Dripping That Flowed into Breaches and Rivulet Spread Angle 
(Continued) 
Spread Angle (degree) 
Drip Location 
Breach Collecting 
Flow fexpt Left Right 
27 cm left of drip shield center (Low Flow Rate) 4 0.0240 25.5 12 
54 cm left of drip shield center (Low Flow Rate) 4 0.0 0 0 
Mean  0.108 7.25 
Standard Deviation  0.335 7.18 
Median  0.005 6.29 
NOTES:  = no measurement. 
Mean, standard deviation, and median for spread angle are for all (left and right) measurements. 
Following the approach used in Section 6.5.1.1.2.4, the inner cluster splash diameter is used 
for the effective length of the drip shield in the validation of the flux splitting algorithm, which is 
given by Equations 6.3.2.4-4 and 6.3.2.4-6 (or 6.5.1.1.2-35). The form of the equation is: 
, 
2 
tan 1 VD 
DS 
b f 
L
N F .. 
. 
.. 
. + = 
a l (Eq. 7.1.1.1-1) 
where F is the fraction of dripping flux that flows through breaches, l is one-half the width of a 
breach or patch, DS L is the effective length of the drip shield (i.e., the length over which dripping 
or splattering occurs), a is the rivulet spread angle, and VD f is the uncertainty factor for the drip 
shield developed for validation, corresponding to the drip shield uncertainty factor, DS f . For the 
validation tests, the number of breaches, b N , is one. 
The splash diameter is used for the effective length, DS L . As shown in Table 7.1-1, the inner 
cluster splash radius on the rough drip shield surface ranged from 3.5 cm to 48 cm (for more 
than 20 drops), giving a range for DS L of 7 cm to 96 cm. The spread angle ranged (one standard 
deviation from the mean) from zero to 14.4. For a drip shield patch width of 27 cm, = l 
13.5 cm. Then, as shown in Table 7.1-5, .. 
. 
.. 
. + = 
2 
tan 1 / 
a 
DS 
b 
VD L
N f F l ranges from 0.141 to 2.17. 
Table 7.1-5. Range of Estimates for F/fVD 
Drip Shield 
F/fVD 
LDS (cm) a = 0 a = 14.4 
7 1.93 2.17 
96 0.141 0.158 
The fraction of dripping flux, expt f , that entered breaches in 12 rough drip shield experiments 
ranged from zero to 1.17, with a mean of 0.108 and a median of 0.0054. The wide range of 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-12 November 2004 
uncertainty and randomness in the experiments is demonstrated in two of the tests having the 
same drip location (54 cm to the left of the drip shield center). The high drip rate test yielded the 
highest flow into a breach with a negligible spread, which is the expected result. The low drip 
rate test at the same drip location, which had zero rivulet spread, unexpectedly resulted in no 
flow into the breach. Statistics for expt f are compared in Table 7.1-6 between the smooth drip 
shield surface experimental results (Table 6.5-2) and the rough surface results discussed in this 
section. 
Table 7.1-6. Comparison of fexpt Statistics for Smooth and Rough Drip Shield Surfaces 
Experiments Mean fexpt Minimum fexpt Maximum fexpt Median fexpt 
Drip Shield (Smooth Surface) 0.111 0.013 0.275 0.049 
Drip Shield Validation (Rough Surface) 0.108 0.0 1.17 0.0054 
The rough surface experimental results are now used to calibrate the drip shield flux splitting 
submodel that is developed for validation purposes, yielding the uncertainty factor VD f : 
.. 
. 
.. 
. + 
= 
2 
tan 1 
a 
DS 
expt 
VD 
L 
f 
f 
l 
. (Eq. 7.1.1.1-2) 
VD f is at a minimum using the minimum value for DS L (7 cm) and the maximum value for a 
(14.4), resulting in expt VD f f 46 . 0 = . The maximum for VD f is obtained using the maximum 
value for DS L (96 cm) and the minimum value for a (0), resulting in expt VD f f 1 . 7 = . Using the 
mean value for expt f (0.108) results in a range for VD f of 0.050 to 0.77. The drip shield flux 
splitting algorithm developed in Section 6.5.1.1.2.4 produced the corresponding factor DS f 
ranging from about 0.36 to 0.73. These factors ( VD f and DS f ) actually represent the estimates of 
the upper bound on the uncertainty, since a lower bound is necessarily zero (i.e., no flow through 
a breach). Using the actual measured range of expt f (0.0 to 1.17) instead of the mean increases 
the range estimated for VD f to 0.0 to (7.1)(1.17) = 8.3. The corresponding range for DS f , using 
the measured range of expt f (0.013 to 0.275) (Table 6.5-2) for the smooth surface tests instead of 
the mean (0.111), is 0.013/0.31 = 0.041 (for cm 50 = DS L , = a 17.3) to 0.275/0.152 = 1.8 (for 
cm 96 = DS L , = a 8.9). Thus, using the extreme values of expt f for estimating DS f and VD f , the 
upper bound on VD f actually spans the uncertainty in the upper bound estimate of DS f , as 
summarized in Table 7.1-7. 
Table 7.1-7. Summary of fDS and fVD Values 
Based on Mean fexpt Based on Minimum fexpt Based on Maximum fexpt 
Minimum Maximum Minimum Maximum 
fDS 0.36 0.73 0.041 1.8 
fVD 0.050 0.77 0 8.3 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-13 November 2004 
Based on mean values for the experimentally measured fraction of the dripping flux that flows 
through a breach, the rough drip shield surface factor shows that less of the dripping flux will 
flow through a breach, compared with the smooth surface results used to develop the drip shield 
flux splitting submodel. The rough surface data validate the drip shield submodel by confirming 
an estimate of the upper bound on the uncertainty of 0.77, based on mean values for expt f . The 
range on the estimate for VD f is also about 0.7, which is comparable (about a factor of 2) to the 
uncertainty in DS f . While the upper bound on the uncertainty factor is about the same for both 
the smooth and rough surfaces (0.73 vs. 0.77), the lower bound is much higher for the smooth 
surface (0.36 vs. 0.05). A random sampling from these ranges will give a mean value of about 
0.54 for the smooth surface versus about 0.42 for the rough surface. So the smooth surface range 
will, on average, overestimate the flux through the drip shield compared to the rough surface 
range. Both the smooth surface and the rough surface results include a wide range of variability 
that is incorporated in the sampled uncertainty parameter DS f for the drip shield flux splitting 
submodel. The rough drip shield surface data provide confirmation that the drip shield submodel 
will generally overestimate the flux through that barrier. 
A final comparison is made between DS f ' , which lumps the uncertainty in the rivulet spread 
angle into DS f , and a corresponding parameter for the rough drip shield surface, VD f ' , is derived, 
where 
VD VD f f .. 
. 
.. 
. + = ' 
2 
tan 1 
a 
. (Eq. 7.1.1.1-3) 
Since a ranges from 0 to 14.4, applying the maximum value for a will result in the range for 
VD f ' of 0 to 0.87, based on the mean value of expt f (0.054) that gives a range of 0.050 to 0.77 for 
VD f . For comparison, DS f ' was estimated to range from 0 to 0.85. The nearly-identical ranges 
for DS f ' and VD f ' validate the drip shield flux splitting submodel. 
7.1.1.2 Waste Package Flux Splitting Submodel 
Using off-crown drip location data for the rough drip shield surface (Table 7.1-8), the rivulet 
spread angle was found to depend strongly on the drip rate. These data are analyzed in the 
Microsoft Excel spreadsheet: Flux Splitting Validation, Worksheet: Rough off crown WP model, 
which is documented in Appendix E. The high drip rate resulted in an average spread angle of 
27.1; the nominal drip rate had a mean spread angle of 20.6; and the low drip rate had a mean 
spread angle of 3.1. However, to be consistent with the development of the spread angle for the 
waste package submodel, and to incorporate the real possibility of widely varying drip rates, all 
50 data points are combined. The mean spread angle for the rough drip shield surface with 
off-crown drip locations is therefore 9.4, with a range ( one standard deviation of 9.6) of 0 to 
19.0. 
In the off-crown splash radius tests #4 and #5 (Table 7.1-9) (Microsoft Excel spreadsheet: Flux 
Splitting Validation, Worksheet: Splash Radius, which is documented in Appendix E), the drip 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-14 November 2004 
location was 33 and 16.5 off the crown. The mean splash radius was 8.9 cm, with a measured 
range of 3.0 cm to 15.0 cm. This gives an effective waste package length of about 6 cm to 30 cm 
for the tests. 
Table 7.1-8. Atlas Breached Drip Shield Experiments on Rough Drip Shield Surface  Dripping off 
Crown  Rivulet Spread Data 
Spread at 33 Spread at Transition 
Drip Location Left (cm) Right (cm) Left (cm) Right (cm) 
Relevant 
Patch 
Multiple Patch Tests (DTN: MO0208EBSATBWP.027 [DIRS 163404]) 
81 cm right of drip shield center, 16.5  a    5 
27 cm right of drip shield center, 16.5 8 12 6 8 5 
27 cm left of drip shield center, 16.5 21 19 12 13 4 
81 cm left of drip shield center, 16.5 16 22 14 12 4 
81 cm right of drip shield center, 33   2 2 5 
27 cm right of drip shield center, 33   3 1 5 
27 cm left of drip shield center, 33   2 1 4 
81 cm left of drip shield center, 33   3 4 4 
Bounding Flow Rate Tests (DTN: MO0208EBSATBWP.028 [DIRS 163405]) 
54 cm left of drip shield center, 33 (Low Flow 
Rate)     4 
54 cm left of drip shield center, 33 (High Flow 
Rate)     4 
27 cm left of drip shield center, 33 (High Flow 
Rate) 6 b 9 b 8 14 4 
27 cm right of drip shield center, 33 (High 
Flow Rate) 5 b 3 b 12 11 5 
27 cm right of drip shield center, 33 (Low 
Flow Rate)   2.5 2.5 5 
27 cm right of drip shield center, 16.5 (High 
Flow Rate) 16 15 17 10 5 
27 cm left of drip shield center, 16.5 (High 
Flow Rate) 26 32 13 34 4 
54 cm left of drip shield center, 16.5 (High 
Flow Rate) 25 20 26 19 4 
54 cm left of drip shield center, 16.5 (Low 
Flow Rate) 3 6   4 
27 cm left of drip shield center, 16.5 (Low 
Flow Rate) 3 2 1 0 4 
27 cm right of drip shield center, 16.5 (Low 
Flow Rate) 0 0 0 0 5 
27 cm left of drip shield center, 33 (Low Flow 
Rate)   6 4.5 4 
a  = rivulet spread not measured. 
b These data are ignored due to inconsistent behavior  rivulet spread should not occur at the drip location. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-15 November 2004 
Table 7.1-9. Atlas Breached Drip Shield Experiments on Rough Drip Shield Surface  Dripping off 
Crown  Splash Radius Tests 
Splash Radius (cm) 
No. Drips Left Right Comments 
Splash Radius Test #4 (33) (DTN: MO0207EBSATBWP.021 [DIRS 163399]) 
31 3.0 3.5 Measured inner cluster (bulk) 
82 5.5 6.0 Measured inner cluster (bulk) 
158 6.5 6.5 Measured inner cluster (bulk) 
Splash Radius Test #5 (16.5) (DTN: MO0207EBSATBWP.021 [DIRS 163399]) 
22 9.0 10.0 Measured inner cluster (bulk) 
82 13.0 14.5 Measured inner cluster (bulk) 
156 14.0 15.0 Measured inner cluster (bulk) 
The experimentally measured fraction of the drip flux (Table 7.1-10) that flowed into all 
breaches ( expt f ) from off-crown drip locations had a mean of 0.12, with a standard deviation of 
0.23. The measured minimum fraction was 0.0 and the maximum was 0.621. 
Following the approach used in Section 6.5.1.1.3, the inner cluster splash diameter is used for 
the effective length of the waste package in the validation of the flux splitting algorithm, which 
is given by Equations 6.3.3.2-1 (or 6.5.1.1.3-2) and 6.3.3.2-3 (or 6.5.1.1.3-1). The form of the 
equation is: 
VW 
WP 
b f 
L
N F .. 
. 
.. 
. + = 
2 
tan 1 
a l , (Eq. 7.1.1.2-1) 
where F is the fraction of dripping flux that flows through breaches, l is one-half the width of a 
breach or patch, WP L is the effective length of the waste package (i.e., the length over which 
dripping or splattering occurs), a is the rivulet spread angle, and VW f is the uncertainty factor 
for the waste package developed for validation, corresponding to the waste package uncertainty 
factor, WP f . For the validation tests, the number of breaches, b N , is one. VW f is obtained by 
inserting expt f , the measured fraction of the dripping flux that flowed into breaches, for F in 
Equation 7.1.1.2-1: 
.. 
. 
.. 
. + 
= 
2 
tan 1 
a 
WP 
b 
expt 
VW 
L
N 
f 
f 
l 
. (Eq. 7.1.1.2-2) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-16 November 2004 
Table 7.1-10. Atlas Breached Drip Shield Experiments on Rough Drip Shield Surface  Dripping off 
Crown  Flow into Breaches 
Drip Location 
Water Input 
(g) 
Breach 4 
Inflow (g) 
Breach 4 
fexpt 
Breach 5 
Inflow (g) 
Breach 5 
fexpt 
81 cm right of drip shield center, 
16.5 282.96 0 0 0.76 0.0027 
27 cm right of drip shield center, 
16.5 316.74 0 0 0.35 0.0011 
27 cm left of drip shield center, 
16.5 309.57 0.48 0.0016 0.44 0.0014 
81 cm left of drip shield center, 
16.5 242.56 0.94 0.0039 0 0 
81 cm right of drip shield center, 
33 109.4 0 0 0.22 0.0020 
27 cm right of drip shield center, 
33 108.44 0 0 0.30 0.0028 
27 cm left of drip shield center, 33 107.33 0.33 0.0031 0 0 
81 cm left of drip shield center, 33 106.75 0.01 0.0001 0 0 
54 cm left of drip shield center, 33 
(Low Flow Rate) 123.13 53.27 0.4326 0 0 
54 cm left of drip shield center, 33 
(High Flow Rate) 330.03 204.99 0.6211 0 0 
27 cm left of drip shield center, 33 
(High Flow Rate) 339.24 0.06 0.0002 0 0 
27 cm right of drip shield center, 
33 (High Flow Rate) 330.22 0.10 0.0003 1.23 0.0037 
27 cm right of drip shield center, 
33 (Low Flow Rate) 112.36 0 0 0.80 0.0071 
27 cm right of drip shield center, 
16.5 (High Flow Rate) 313.82 0 0 1.14 0.0036 
27 cm left of drip shield center, 
16.5 (High Flow Rate) 322.07 1.34 0.0042 0.19 0.00059 
54 cm left of drip shield center, 
16.5 (High Flow Rate) 328.27 197.92 0.6029 0 0 
54 cm left of drip shield center, 
16.5 (Low Flow Rate) 94.41 57.18 0.6056 0 0 
27 cm left of drip shield center, 
16.5 (Low Flow Rate) 115.97 0.34 0.0029 0.45 0.0039 
27 cm right of drip shield center, 
16.5 (Low Flow Rate) 119.76 0 0 0.09 0.0008 
27 cm left of drip shield center, 33 
(Low Flow Rate) 115.81 0.36 0.0031 0 0 
DTNs: MO0208EBSATBWP.027 [DIRS 163404], MO0208EBSATBWP.028 [DIRS 163405]. 
NOTE: For all fexpt values in bold: mean = 0.115; standard deviation = 0.234; median = 0.0031; minimum = 
0.00014; maximum = 0.621. 
Statistics for expt f are compared in Table 7.1-11 between the smooth drip shield surface 
experimental results used for the waste package flux splitting submodel (Appendix D) and the 
rough surface results discussed in this section (Table 7.1-10). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-17 November 2004 
Table 7.1-11. Comparison of fexpt Statistics for Smooth and Rough Drip Shield Surfaces 
Experiments Mean fexpt Minimum fexpt Maximum fexpt Median fexpt 
Waste Package (Smooth Surface) 0.295 0.0 1.066 0.0142 
WP Validation (Rough Surface) 0.115 0.0001 0.621 0.0031 
WP = waste package 
With the values for the breach flow fraction ( expt f ), the effective waste package length ( WP L ), 
and the spread angle ( a) as determined above using off-crown rough drip shield surface test 
data, the range for VW f is be determined. The half-width of the patch used in the experiments 
( = l 13.5 cm) is used to evaluate VW f . The minimum for VW f is obtained using the minimum 
effective waste package length ( = WP L 6.0 cm) and the maximum spread angle ( = a 19.0), 
resulting in expt VW f f 379 . 0 = . The maximum for VW f is obtained using the maximum effective 
waste package length ( = WP L 30 cm) and the minimum spread angle ( = a 0), resulting in 
expt VW f f 22 . 2 = . Using the mean value of expt f (0.115), VW f for the waste package ranges from 
0.044 to 0.26. Over the measured range of expt f (0 to 0.621), VW f ranges from 0.0 to 
(2.22)(0.621) = 1.38. The range obtained for WP f (0.909 to 2.00), based on the mean smooth 
drip shield surface value of expt f (0.295), is higher. When the measured range of smooth surface 
expt f values (0.0 to 1.066; see Figure D-10) for the waste package flux splitting analysis is used 
instead of the mean, WP f ranges from 0.0 to 3.28. The waste package flux splitting submodel 
overestimates flow through breaches compared to the model validation estimates, which in turn 
overestimates the advective releases of radionuclides compared to the model validation 
estimates. The estimated values for WP f and VW f are summarized in Table 7.1-12. 
Table 7.1-12. Summary of fWP and fVW Values 
Based on Mean fexpt Based on Minimum fexpt Based on Maximum fexpt 
Minimum Maximum Minimum Maximum 
fWP 0.909 2.001 0.0 3.28 
fVW 0.044 0.26 0.0 1.38 
As with the drip shield submodel, a final comparison is between WP f ' , which lumps the 
uncertainty in the rivulet spread angle into WP f , and a corresponding parameter for the rough 
drip shield surface, VW f ' , where 
VW VW f f .. 
. 
.. 
. + = ' 
2 
tan 1 
a 
. (Eq. 7.1.1.2-3) 
For the rough drip shield surface, a ranges from 0 to 19.0. Applying the maximum value for 
a results in the range for VW f ' of 0 to 0.30, based on the mean value of expt f . For comparison, 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-18 November 2004 
WP f ' was estimated to range from 0 to 2.41. The wider range for WP f ' means that the drip shield 
flux splitting submodel tends to overestimate the flow through breaches in the drip shield. The 
overlapping ranges for WP f ' and VW f ' validate the waste package flux splitting submodel. 
Sections 7.1.1.1 and 7.1.1.2 have demonstrated that the drip shield and waste package flux 
splitting submodels overestimate fluxes when compared to the experimental data presented. The 
validations discussed uncertainties in relevant parameters. Based on these validation results, the 
EBS flow model is adequate for its intended use. 
7.1.2 Results of Independent Model Validation Technical Review of the EBS Flow Model 
The results of the independent model validation technical review of the EBS flow model are 
given in a memo (Jin 2004 [DIRS 170952]) presented in Section 7.2.3 that combines the 
technical reviews of the EBS flow and transport models. 
7.2 EBS TRANSPORT MODEL 
The transport of radionuclides through the EBS is modeled, using assumptions in Section 5, as a 
combination of advective and diffusive transport including retardation between a series of three 
domains: 
 Waste form domain 
 Corrosion products domain 
 Invert domain. 
Advective transport is considered when water enters the waste form domain and is able to flow 
through the EBS and enter the UZ. The EBS flow model (Section 7.1) calculates the water flux 
between each domain and a separate model provides radionuclide concentrations. 
Diffusive transport between each of the domains occurs regardless of whether water is flowing 
though the EBS. Diffusive transport between each domain is modeled in one dimension and 
therefore is dependent upon the following parameters that can vary as a function of time and 
according to the specific transport pathway: 
 Effective diffusion coefficient 
 Diffusive area 
 Diffusion length. 
The effective diffusion coefficient is calculated from Archies law and is dependent upon the free 
water diffusion coefficient, porosity, and saturation in each domain. Additionally a temperature 
correction is made for diffusion in the invert domain. Porosity is either assumed to be constant 
or is provided by a separate model (e.g., BSC 2004 [DIRS 170023]). Saturation varies with 
relative humidity. The diffusive area is calculated differently for each domain, but is either a 
function of the number of breaches in the waste package (corrosion patches or stress corrosion 
cracks) or it is calculated from the geometry of the different components of the EBS. The 
diffusive area of breaches also depends on the scenario class being modeled. The diffusion 
length is either calculated from EBS geometry or is sampled, depending upon the domain. 

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As stated in Section 7, the level of confidence required for the EBS transport model is Level I. 
Level I validation is described in Section 7. In Sections 6.3 and 6.5, a detailed explanation and 
justification is presented on the formulation of the transport model. These sections include a 
great amount of information that is relevant to Level I validation. In addition, the following 
sections include auxiliary information aimed to validate further certain components of the 
transport model. In some cases these descriptions and comparisons go beyond Level I validation 
criteria, but are included for completeness. 
Section 7.2.1 describes a comparison between the in-package diffusion submodel and two 
similar, independently developed models of transport from a waste package to the invert. The 
comparison shows that although each model uses a different set of assumptions, the assumptions 
used and the final diffusion coefficients calculated by each model generally agree and thus the 
transport model is valid for its intended purpose. 
Section 7.2.2 compares the invert diffusion coefficient of free water diffusivity for radionuclides 
at different temperatures and with other cations and anions and shows that the self-diffusion 
coefficient of water at 25C is an upper bound. 
7.2.1 In-Package Diffusion Submodel 
Diffusive transport within the waste package will limit the release of radionuclides for those 
waste packages in a no-seep environment. The in-package diffusion submodel is directly related 
to the waste isolation attribute, limited release of radionuclides from the engineered barriers, 
because the model predicts delays in the release of mass from the waste package in comparison 
to the TSPA-SR model, which immediately mobilized radionuclides at the external surface of the 
waste package. 
Level I validation is appropriate for the in-package diffusion submodel, as it is part of the 
mechanisms for radionuclide transport from waste package to the drift wall through the invert 
(see Section 7 above). In addition, the in-package diffusion submodel has the following features: 
 The in-package diffusion submodel is not extrapolated over large distances or spaces. 
There is an inherent time extrapolation in the model. 
 The in-package diffusion submodel bounds the uncertainties by considering 
two bounding states. In the first state, the waste package internal components are 
considered to be in their intact, as-emplaced condition. For the second state, the 
iron-based waste package internal components are considered to be completely degraded 
to a porous material. Although these are two bounding end states, uncertainties exist in 
the time- and spatially-dependent intermediate conditions. 
 The in-package diffusion submodel has a modest impact on dose time history in the first 
10,000 years, based on sensitivity calculations performed for the prioritization report 
Risk Information to Support Prioritization of Performance Assessment Models 
(BSC 2003 [DIRS 168796], Sections 3.3.6 through 3.3.11). Those studies indicate that 
the estimate of mean annual dose in the first 10,000 years has only a minor dependence 
on in-package conditions that impact diffusion. 

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The in-package diffusion submodel is validated by comparison to two other models: 
 Electric Power Research Institute (EPRI) Phase 5 report (EPRI 2000 [DIRS 154149]) 
 A model by Lee et al. (1996 [DIRS 100913]) for diffusive releases from waste package 
containers with multiple perforations. 
The in-package diffusion submodel is based on the one-dimensional diffusion equation, Ficks 
first law of diffusion (Bird et al. 1960 [DIRS 103524], p. 503): 
x 
C D 
A 
q i i 
. 
. 
- = . (Eq. 7.2.1-1) 
That is, the fundamental process being modeled is diffusion through a porous medium, a process 
that is well understood and fully accepted throughout the scientific and engineering community. 
Certain underlying assumptions need to be addressed. It is assumed that the bulk of the 
corrosion products inside a waste package is hematite, Fe2O3, based simply on the predominance 
of iron in the composition of internal non-waste form components. This assumption is also used 
in the EPRI report (EPRI 2000 [DIRS 154149], p. 6-22), based on cited studies (EPRI 2000 
[DIRS 154149], p. 6-31) of corrosion products of carbon steel in humid, oxidizing environments 
that indicate that in the presence of an abundant supply of oxygen, iron would be expected to 
exist as Fe2O3, or FeOOH or Fe(OH)3. 
The specific surface area of hematite has been measured by numerous investigators. The range 
of values obtained varies widely, depending on the morphology of the sample. As can be seen in 
the expressions for effective saturation and diffusion coefficient, Equations 6.5.1.2.1-27 
and 6.5.1.2.1-28, the diffusion coefficient is proportional to the square of the specific surface 
area, which from Table 6.5-6 varies by about a factor of about 12. This uncertainty is accounted 
for in the uncertain parameter, Surface_Area_CP (Table 6.5-13), which ranges from 1.0 to 
22 m2 g-1. 
The water adsorption isotherm used for the in-package diffusion submodel is compared with 
another measured isotherm (McCafferty and Zettlemoyer 1971 [DIRS 154378], Figure 3) in 
Figure 7.2-1, which shows the close agreement between independent investigators. In addition, 
Figure 6.5-4 shows that hematite over-predicts the amount of water adsorbed compared to nickel 
oxide, which is one of the other major components of stainless steel 
(DTN: MO0003RIB00076.000 [DIRS 153044]) that would comprise the products of corrosion 
of the waste package internal components. 

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Source: Jurinak curve: Jurinak 1964 [DIRS 154381]; McCafferty and Zettlemoyer curve: McCafferty and 
Zettlemoyer 1971 [DIRS 154378]. 
Figure 7.2-1. Adsorption Isotherms for Water Vapor on a- Fe2O3 
7.2.1.1 Comparison with Electric Power Research Institute 2000 
Validation of the in-package diffusion submodel is provided in part by qualitative comparison 
with a similar model developed independently by a reputable performance assessment program 
(EPRI 2000 [DIRS 154149]). 
The EPRI source-term model, COMPASS2000, implements five compartmentsWaste, 
Corrosion Products, Canister, Invert, Near-Field Rockof which two (Corrosion Products and 
Canister) are analogous to portions of the in-package diffusion submodel. The Corrosion 
Products compartment represents the porous material that is formed after the basket materials are 
corroded. The Canister compartment represents the failed metal canisters. As with the GoldSim 
TSPA-LA model, each compartment is treated as a mixing cell in which radionuclide 
concentrations are assumed to be uniform. Mass balances in each compartment account for the 
various processes that comprise the model, including transport by diffusion and advection, 
radioactive decay and ingrowth, sorption, dissolution, and precipitation. 

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In the EPRI model, EBS transport parameters are assigned fixed values. Both the Corrosion 
Products and corroded Canister compartments have a porosity of 0.42 (EPRI 2000 
[DIRS 154149], p. 6-21), less than the initial porosity of a CSNF waste package, 0.54, as 
estimated in Section 6.5.1.2.1.3. The EPRI value accounts for the volume occupied by the oxide. 
A lower value for porosity overestimates releases of radionuclides. However, in the in-package 
diffusion submodel (Equation 6.5.1.2.1-28), the higher value of porosity increases the estimated 
diffusion coefficient by only a factor of 1.5, which is small compared to other uncertainties in the 
model. 
The EPRI model assumes a fixed water saturation of 0.35 in both the Corrosion Products and 
corroded Canister compartments (EPRI 2000 [DIRS 154149], p. 6-21). This value is appropriate 
for scenarios involving advective transport, but overestimates releases of radionuclides for the 
expected large fraction of the repository that has no seepage flux, where the only water present is 
adsorbed water. The in-package diffusion submodel specifically applies to those regions and 
provides a more realistic estimate of saturation as a function of relative humidity. 
The EPRI model uses a fixed value for effective diffusion coefficient of 4.64510-4 m2 yr-1 in 
both the Corrosion Products and corroded Canister compartments (EPRI 2000 [DIRS 154149], 
p. 6-22). This converts to 1.47210-7 cm2 s-1 or to 1.47210-11 m2 s-1. For diffusion through a 
fully degraded waste package (Equation 6.5.1.2.1-27), this corresponds to a relative humidity of 
97.9 percent. Thus, when the humidity is high, the EPRI model and the in-package diffusion 
submodel agree well. In contrast, the in-package diffusion submodel provides 
humidity-dependent diffusion coefficient values. 
The EPRI model also specifies fixed diffusive lengths, which are defined as the distance from the 
center of the compartment to the interface of the two contacting compartments. For the 
Corrosion Products compartment, the diffusion length is 0.046 m; for the Canister compartment, 
the diffusion length is 0.025 m (EPRI 2000 [DIRS 154149], p. 6-22). In a well-degraded waste 
package, these are reasonable values, comparable to those used in the in-package diffusion 
submodel. However, the in-package diffusion submodel accounts for the uncertainty in diffusion 
lengths at all times, and provides special treatment at early times when large masses of corrosion 
products are not yet formed. 
For the conditions assumed in the EPRI model, namely, at later times when the waste package is 
extensively corroded, the in-package diffusion submodel agrees quite well with the EPRI model. 
The primary differences are that the in-package diffusion submodel accounts for a wider range of 
conditions, including times just after breaches first appear in the waste package. In addition, the 
in-package diffusion submodel accounts explicitly for the relative humidity, which realistically is 
the only source of water when seepage does not occur. And finally, in contrast to the EPRI 
model, the in-package diffusion submodel accounts for uncertainty in diffusive path lengths. 
Thus, there is agreement between the models, and where differences occur, it is primarily to 
increase the realism of the diffusive release calculation and to account for uncertainty. 

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7.2.1.2 Comparison with Lee et al. 1996 
Validation of the in-package diffusion submodel is provided in part by comparison with a similar 
model developed independently and published in technical literature (Lee et al. 1996 
[DIRS 100913]). 
Lee et al. (1996 [DIRS 100913]) developed a model for steady-state and quasi-transient 
diffusive releases from waste packages into the invert. In this model, perforations in the package 
are assumed to be cylindrical in shape. The diffusion path consists of the approach to the 
opening of the perforation from the waste form side; the path through the cylindrical portion of 
the perforation, which is filled with corrosion products; and the path through the exit disk 
separating the perforation from the invert. The waste is assumed to be distributed uniformly 
inside the waste container. The package is approximated by an equivalent spherical 
configuration, and the underlying invert is represented by a spherical shell surrounding the 
package. 
The model of Lee et al. (1996 [DIRS 100913]) is suitable for the late stages of package 
degradation, when the waste form has become a mass of porous corrosion products. Although 
Lee et al. (1996 [DIRS 100913]) assumed the packages failed by localized corrosion, this model 
should be equally applicable to failure by general corrosion. 
The assumption of Lee et al. (1996 [DIRS 100913]) that the waste (i.e., the radionuclide source) 
is uniformly distributed inside the waste package restricts the applicability of the model and 
comparison to the in-package diffusion submodel to the times when the waste package has 
extensively corroded. The object of the in-package diffusion submodel is to provide more 
realism at earlier and intermediate times, when the waste cannot yet be considered a uniform 
porous medium. (In the in-package diffusion submodel, the dependence of the diffusive 
properties of the waste package on the extent of degradation is computed explicitly as a function 
of time; see Sections 6.5.1.2.1.3.2 and 6.5.3.2.) On the other hand, the fundamental assumption 
that diffusive releases are controlled by diffusion through breaches that are filled with porous 
corrosion products may be valid over much of the waste package lifetime, including early times, 
when stress corrosion cracks are the first breaches to appear. Lee et al. (1996 [DIRS 100913], 
p. 5-67) assume that the porosity of the perforations is CP f = 0.4, and the volumetric water 
content is 10 = F percent (so the water saturation in the perforations is a constant 
( ) 25 . 0 100 / = F = CP w S f ). Based on data by Conca and Wright (1990 [DIRS 101582]; 1992 
[DIRS 100436]), Lee et al. compute a diffusion coefficient, D (cm2 s-1), for the porous corrosion 
products filling the perforations (Lee et al. 1996 [DIRS 100913], p. 5-67): 
F  +  - = 10 10 log ) 0464 . 0 ( 898 . 1 ) 0499 . 0 ( 255 . 8 log D , (Eq. 7.2.1.2-1) 
where the numbers in parentheses are one standard deviation. For 10 = F percent (the assumed 
volumetric water content of the perforations), D = 4.4  10-7 cm2 s-1. Lee et al. assume that the 
diffusion coefficient inside the waste package (as opposed to the perforations) is 10-5 cm2 s-1 
(Lee et al. 1996 [DIRS 100913], p. 5-67). As a comparison, the self-diffusion coefficient for 
water is 2.299  10-5 cm2 s-1 (Mills 1973 [DIRS 133392], Table III), and for many actinides the 
diffusion coefficient in water is roughly 5  10-6 cm2 s-1 (Table 7.2-11). The value for D given 

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ANL-WIS-PA-000001 REV 01 7-24 November 2004 
by Equation 7.2.1.2-1 accounts for porosity and saturation, and so is comparable to the value 
for s D given by Equation 6.5.1.2.1-28. 
Using Equation 7.2.1.2-1 to obtain D = 4.4  10-7 cm2 s-1 (for 10 = F percent) and dividing this 
value by the self-diffusion coefficient for water, 0 D (2.29910-5 cm2 s-1), gives 
0 / D D = 1.91  10-2. This is greater than the largest value in Table 6.5-10, indicating that the 
Lee et al. (1996 [DIRS 100913]) model for D represents high relative humidity and high surface 
area if adsorption is the sole mechanism for water appearing in the corrosion products. If no 
advection takes place, the assumption of a water saturation of = w S 0.25 is excessive. Using the 
lower saturations obtained from adsorption isotherms brings the diffusion coefficient from 
Equation 7.2.1.2-1 into closer agreement with the values in Table 6.5-11. For example, if 
= w S 10-5, then Equation 7.2.1.2-1 would give 0 / D D = 8.59  10-11. 
A more detailed calculation can be performed to estimate the surface area of corrosion patches, 
the amount of water adsorbed at various relative humidity values, the resulting water saturation 
of the patches, and obtain a diffusion coefficient using Equation 6.5.1.2.1-28 or 
Equation 7.2.1.2-1. Alternatively, the diffusion coefficient can be obtained using 
Equation 7.2.1.2-1, in which 
( ) 408 . 0 
, ln 194 . 1 100 - - = = F RH S CP CP we f . (Eq. 7.2.1.2-2) 
This equation uses a porosity of CP f = 0.4, but obtains the effective water saturation from 
Equation 6.5.1.2.1-27, which is based on the assumption that all water comes from adsorption of 
water vapor onto hematite having a specific surface area of 9.1 m2 g-1. Then 
( ) [ ] 
( ). RH 
RH 
D 
ln log 775 . 0 109 . 8 
ln log 408 . 0 07707 . 0 898 . 1 255 . 8 
log 898 . 1 255 . 8 log 
10 
10 
10 10 
- - - = 
- - + - = 
F + - = 
(Eq. 7.2.1.2-3) 
For example, at RH = 0.95, and using -1 2 9 
0 s m 10 299 . 2 -  = D (self-diffusion coefficient 
for water), the effective diffusion coefficient for the patch using Archies law 
(Equation 6.5.1.2.1-28) is s D = 7.03  10-12 m2 s-1, whereas using Equation 7.2.1.2-3, the 
diffusion coefficient for the corrosion patch is D = 7.77  10-12 m2 s-1. For comparison with 
Table 6.5-10, 0 / D Ds = 3.06  10-3 and 3.38  10-3 for these respective cases. 
Thus, for those cases where the release rate is controlled by diffusion through porous corrosion 
products, the in-package diffusion submodel agrees well with the model of Lee et al. (1996 
[DIRS 100913]). 
The in-package diffusion submodel provides a means for quantifying the uncertainty in diffusion 
coefficients for diffusion of radionuclides from within the waste form to the invert. Whereas 
other models consider only the times when the waste package is largely degraded, the in-package 
diffusion submodel presented here also considers earlier times, starting from the time of the 
initial waste package breach. The time period between initial breach and complete degradation 

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ANL-WIS-PA-000001 REV 01 7-25 November 2004 
of the internal components may span many thousands of years. Thus, the in-package diffusion 
submodel fills a major time gap in modeling diffusive releases from a waste package. In effect, 
it provides a rationale for interpolating between essentially a zero diffusion coefficient (due to 
the absence of water) when a waste package is first breached to a value at a time when porous 
corrosion products can be expected to fill the waste package with a degree of water saturation 
capable of transporting radionuclides. The in-package diffusion submodel is considered 
validated based on corroborating data for input parameters such as water adsorption isotherms 
and specific surface areas, and based on the agreement with two other waste package diffusion 
models in areas where these models apply. 
7.2.2 Invert Diffusion Submodel 
Level I validation is appropriate for the invert diffusion submodel, as it is part of the mechanisms 
for radionuclide transport from waste package to the drift wall through the invert (see Section 7). 
In addition, the invert diffusion submodel has the following features: 
 Diffusive release from the engineered barrier system does not result in significant 
releases from the repository system. Under expected conditions, there is a small 
probability of waste package breaching, and only limited release at all is likely. 
Therefore, the diffusion properties of the invert that might affect this release are expected 
to play a small role in the estimate of performance of the system under these conditions. 
The invert diffusion coefficient is also expected to play a small role for disruptive 
conditions under which more significant breaching of the waste package might occur. In 
this case, transport through the invert would be dominated by advection, and diffusion 
would therefore provide only a minor contribution. Therefore, the diffusion submodel is 
not expected to play a major role in the assessment of system performance. 
 In addition to the above, the invert diffusion properties submodel is not extrapolated 
beyond the conditions and distances considered in the development of the model. The 
model applies only on the scale of the EBS and is not applied to larger scales, for 
example to the unsaturated zone rock. 
The invert diffusion coefficient abstraction considers the free water diffusivity for radionuclides 
as an upper bound. The validation of each of these factors is considered in the following 
sections. 
Section 6.3.4.1.2 describes modification of the self-diffusion coefficient due to temperature. The 
modification is based on established principles of diffusion in fluids and thus no validation is 
necessary. The temperature modification is based on the relationship between diffusion and 
viscosity and temperature (Cussler 1997 [DIRS 111468], p. 114). The relationship between 
temperature and viscosity of water is available in text books. Thus, it is straightforward to 
establish a direct relationship between diffusion coefficient and temperature. 
7.2.2.1 Self-Diffusion Coefficient of Water 
The self-diffusion coefficient of water at 25C, 2.299  10-5 cm2 s-1 (Mills 1973 [DIRS 133392], 
Table III), provides an upper bound for the diffusion of ionic and neutral inorganic, and 

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ANL-WIS-PA-000001 REV 01 7-26 November 2004 
organo-metal species that may be released from a waste package. This assertion is based on the 
following points, which are discussed in the text following this list: 
1. A survey of compiled diffusion coefficients at 25C shows that simple cation and 
anion species (excluding the proton and hydroxyl species, which are not appropriate 
analogs to diffusing radionuclide species) have diffusion coefficients that are smaller 
than that of water. 
2. The self-diffusion coefficient for water at 90C is larger than compiled diffusion 
coefficients for simple inorganic species at 100C. 
3. Diffusion coefficients for simple lanthanide and actinide cations are much smaller than 
the self-diffusion coefficient of water and are expected to be even smaller for their 
hydroxyl and carbonate complexes. 
In a compilation of diffusion coefficients for 97 ionic species , only 3 species, H+, OH-, and ODhave 
diffusion coefficients at 25C that are larger than the self-diffusion of water at 25C (Mills 
and Lobo 1989 [DIRS 138725], Appendix A, Tables 1.1 to 1.6, pages 314 to 319). Of the 
33 ionic species for which Mills and Lobo list diffusion coefficients at 100C in Tables 1.1 
through Table 1.7, only 2 species, H+ and OH-, have diffusion coefficients larger than the 
self-diffusion of water (H2
18O) at 90C (Mills and Lobo 1989 [DIRS 138725]; Table 1, page 17). 
The fact that the self-diffusion of H2
18O is less than that of H2O, and that the self-diffusion of 
H2O at 90C would be greater than that of various ionic species at 100C, further supports the 
contention that the self-diffusion of water at 25C is bounding. 
The compilation below (Table 7.2-1) lists a selection of diffusion coefficients for some trivalent 
lanthanides and actinides. Table 7.2-1 also includes some anions not listed in most compilations 
but relevant and/or analogous to those expected for radionuclides released from the waste 
package. The listing shows that the diffusion coefficients for these species are all smaller than 
the self-diffusion of water, by factors ranging from 1.6 to 14.7. In the case of uranium, the 
carbonate complexes of the metal species have even smaller diffusion coefficients. Based on the 
Stokes-Einstein equation (Bird et al. 1960 [DIRS 103524], p. 514, Equation 16.5-4), the 
diffusivity of a solute in a liquid is inversely proportional to the radius of the diffusing particles. 
It is therefore expected that other carbonate and hydroxyl complexes, on the basis of the greater 
size of the complexes relative to the metal species, will also have smaller diffusion coefficients 
than the metal species listed in Table 7.2-1. 
As an alternative, four diffusion coefficients could be used. One coefficient could be used for 
each charge (mono-, di-, and tri-valent species) and one for the hydroxyl and carbonate 
complexes of the actinides and lanthanides. At 25C, the mono-, di-, and trivalent species have 
bounding values of 2.2  10-5 cm2 s-1, 1.2  10-5 cm2 s-1, 0.7  10-5 cm2 s-1, respectively, as shown 
in Figure 7.2-2. Although this alternative model is not used for TSPA-LA, it provides further 
evidence that the use of the self-diffusion coefficient of water bounds the diffusion coefficients 
of diffusing radionuclide species in the EBS. 

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Limiting diffusion coefficients for anions and 
simple (non-complexed) cations 
Ionic charge 
0 1 2 3 4 
Coefficient of diffusion, cm2/s x 105 
0
1
2 
cations 
anions 
Source: Selected from Mills and Lobo 1989 [DIRS 138725], Appendix I, Tables 1.1 to 1.6; pp. 314 to 319. 
Figure 7.2-2. Limiting Diffusion Coefficients for Anions and Simple (Non-Complexed) Cations 
Table 7.2-1. Compilation of Diffusion Coefficients for Yttrium, Technetium, Molecular Iodine, and 
Lanthanide and Actinide Species 
Species D*, cm2 s-1 Comments Reference 
Y3+ 5.70.06  10-6 25C Mills and Lobo 1989 [DIRS 138725], 
p. 220. 
TcO4
- 1.480.01  10-5 25C Mills and Lobo 1989 [DIRS 138725], 
p. 105. 
I2 1.360.04  10-5 25C; 0.075 M H2SO4 Cantrel et al. 1997 [DIRS 138551], 
Table 5. 
La3+ 
5.42  10-6 
25C; 0.1 M NaClO4; 
u = 6.33 cm2 s-1 V-1 
Rosch and Khalkin 1990 [DIRS 138739], 
calculated from mobility data reported in 
Table 1, p. 103.a 
La3+ 6.180.06  10-6 25C Mills and Lobo 1989 [DIRS 138725], 
p. 93. 
Ce(III)- 
carbonate 2.680.12  10-6 5.5 M K2CO3, pH 13, 
presumably at 25C. 
Haltier et al. 1990 [DIRS 138643], p. 111. 
Ce(IV)- 
carbonate 1.560.07  10-6 5.5 M K2CO3, pH 13, 
presumably at 25C. 
Haltier et al. 1990 [DIRS 138643], p. 111. 
Eu3+ 
4.38  10-6 
25C; 0.1 M NaClO4; 
u = 5.12 cm2 s-1 V-1 
Rosch and Khalkin 1990 [DIRS 138739]; 
calculated from mobility data reported in 
Table 1, p. 103.a 
Gd3+ 
5.24  10-6 
25C; 0.1 M NaClO4; 
u = 6.12 cm2 s-1 V-1 
Rosch and Khalkin 1990 [DIRS 138739]; 
calculated from mobility data reported in 
Table 1, p. 103.a 

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Table 7.2-1. Compilation of Diffusion Coefficients for Yttrium, Technetium, Molecular Iodine, and 
Lanthanide and Actinide Species (Continued) 
Species D*, cm2 s-1 Comments Reference 
Tb3+ 
5.01  10-6 
25C; 0.1 M NaClO4; 
u = 5.85 cm2 s-1 V-1 
Rosch and Khalkin 1990 [DIRS 138739]; 
calculated from mobility data reported in 
Table 1, p. 103.a 
Tm3+ 
5.10  10-6 
25C; 0.1 M NaClO4; 
u = 5.96 cm2 s-1 V-1 
Rosch and Khalkin 1990 [DIRS 138739], 
calculated from mobility data reported in 
Table 1; p. 103.a 
Yb3+ 
5.23  10-6 
25C; 0.1 M NaClO4; 
u = 6.11 cm2 s-1 V-1 
Rosch and Khalkin 1990 [DIRS 138739], 
calculated from mobility data reported in 
Table 1; p. 103.a 
Lu3+ 
5.01  10-6 
25C; 0.1 M NaClO4; 
u = 5.85 cm2 s-1 V-1 
Rosch and Khalkin 1990 [DIRS 138739], 
calculated from mobility data reported in 
Table 1; p. 103.a 
UO2(CO3)3
4- 3.6  10-6 1 M total carbonate, 22C Perry et al. 1988 [DIRS 138732], p. 302. 
UO2(CO3)3
4- 3.00.7  10-6 0.2 M total carbonate, pH 9.8, 
25C 
Perry et al. 1988 [DIRS 138732], p. 302. 
UO2(CO3)3
5- 3.810.26  10-6 0.75 M Na2CO3, 0.6 M NaClO4, 
pH 11.5, presumably at 25C 
Haltier et al. 1990 [DIRS 138643], p. 110. 
UO2
++ 6.8  10-6 25C Millard and Hedges 1996 [DIRS 138677], 
p. 2141. 
UO2-carbonate 
1.9  10-6 
Calculated using Stokes- 
Einstein with a radius of 
8  at 10C 
Millard and Hedges 1996 [DIRS 138677], 
p. 2141. 
Np(V)-carbonate 
7  10-6 
Calculated using Stokes- 
Einstein with a radius of 
3.4  at 25C 
Tsukamoto et al. 1994 [DIRS 138747]; p. 
469. 
Am3+ 
5.78  10-6 
25C; 0.1 M NaClO4; 
u = 6.75 cm2 s-1 V-1 
Rosch and Khalkin 1990 [DIRS 138739]; 
calculated from mobility data reported in 
Table 1; p. 103.a 
Am3+ 5.950.06  10-6 25C, in 0.0002 M Nd(ClO4)3 Mills and Lobo 1989 [DIRS 138725]; 
p. 131. 
Cf3+ 
4.39  10-6 
25C; 0.1 M NaClO4; 
u = 5.13 cm2 s-1 V-1 
Rosch and Khalkin 1990 [DIRS 138739]; 
calculated from mobility data reported in 
Table 1; p. 103.a 
Cf3+ 5.500.06  10-6 25C, in 0.0002 M Nd(ClO4)3 Mills and Lobo 1989 [DIRS 138725]; 
p. 132. 
Es3+ 5.500.06  10-6 25C, in 0.0002 M Nd(ClO4)3 Mills and Lobo 1989 [DIRS 138725]; 
p. 132. 
a Calculation of diffusion coefficients from reported ionic mobilities (Rosch and Khalkin 1990 [DIRS 138739]; 
Table 1). The mobilities (u) were measured in 0.1 M NaClO4 at various pHs (below the pH of hydrolysis) and 
were slightly larger at pHs greater than 5, and these are the data that were used for the calculation. The equation 
used to calculate the diffusion coefficient is: D* = (kT/(|z|e)) u, where k is Boltzmann constant (J K-1), T is the 
temperature (K), z is the valence of the ion, e is the elementary charge (C), and u is the mobility (cm2 s-1 V-1) 
(Atkins 1990 [DIRS 111464], Box 25.1, Einstein relation, p. 765). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-29 November 2004 
7.2.2.2 Modification for Porosity and Saturation 
Validation of the dependence of invert diffusion coefficient on porosity and saturation is 
provided by comparison with measured data obtained independently of the data used for model 
development. Data used for validation are obtained from diffusivity measurements for crushed 
tuff using electrical conductivity measurements (CRWMS M&O 2000 [DIRS 156680]) and from 
direct measurements of diffusivity between machined cubes of tuff (Hu et al. 2001 
[DIRS 161623]). 
Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 [DIRS 170709]) obtained 
diffusion coefficients from electrical conductivity measurements for various granular materials, 
including tuff, with volumetric moisture content ranging from 0.5 percent to 66.3 percent. A 
statistical fit of the data (Conca and Wright 1992 [DIRS 100436], Figure 2; Conca et al. 1993 
[DIRS 170709], Figure 2; listed in Table 4.1-14) ranging from 1.5 percent to 66.3 percent 
volumetric moisture content, based on Archies law, results in the model used in TSPA-LA 
(Section 6.3.4.1.1 and Appendix G): 
( ) 
( ), 10 
10 
218 . 0 , 033 . 0 863 . 1 
0 
218 . 0 , 033 . 0 863 . 1 863 . 1 
0 
= = 
= = 
=
= 
s  
s  
.
f 
ND 
ND 
w 
D 
S D D 
(Eq. 7.2.2.2-1) 
where w S f .= is the volumetric moisture content (fraction: m3 water m-3 rock). The object of 
this validation is to show that the diffusion coefficient given by Equation 7.2.2.2-1 obtained from 
the electrical conductivity measurements of Conca and Wright (1992 [DIRS 100436]) and Conca 
et al. (1993 [DIRS 170709]) tends to overestimate the diffusivity of invert materials. 
The diffusion coefficient has also been determined specifically for tuff, also using electrical 
conductivity measurements (CRWMS M&O 2000 [DIRS 156680], Tables A-1 and A-2). These 
data are listed in Table 7.2-2 and are plotted in Figure 7.2-3, along with the mean value and plus 
and minus three standard deviations from Equation 7.2.2.2-1. This plot shows that the fit to the 
measured diffusion coefficient data (Equation 7.2.2.2-1) overestimates the diffusion coefficient 
relative to The Determination of Diffusion Coefficient of Invert Materials (CRWMS M&O 2000 
[DIRS 156680], Tables A-1 and A-2). This plot was created using Microsoft Excel; see 
Appendix G, Worksheet: Validation, p. VII-10. 
The electrical conductivity measurements by Conca and Wright (1992 [DIRS 100436]) and 
Conca et al. (1993 [DIRS 170709]) use conductivity as an analog for diffusivity. While the 
analog is known to be valid in fully saturated media, its application to unsaturated media, 
particularly at low moisture contents, is questionable due to the difficulty in preparing samples 
and in making reliable electrical contact between the electrical leads and the samples. To avoid 
these problems, Hu et al. (2001 [DIRS 161623]) measured diffusive tracer concentrations in tuff 
cubes directly using laser ablation coupled with inductively coupled plasma-mass spectrometry 
(LA-ICP-MS), rather than relying on electrical analogs. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-30 November 2004 
1.E-11 
1.E-10 
1.E-09 
1.E-08 
1.E-07 
1.E-06 
1.E-05 
1.E-04
0.10 1.00 10.00 100.00 
Water Content (%) 
Diffusion Coefficient (cm2/s)
CRWMS M&O 2000l 
EBS RTA Model (Mean) 
(Equation 7.2.2.2-1) 
EBS RTA + 3 std dev 
EBS RTA - 3 std dev 
Source: CRWMS M&O 2000 [DIRS 156680]. 
Figure 7.2-3. Comparison of EBS Radionuclide Transport Abstraction Invert Diffusion Submodel 
(Equation 7.2.2.2-1) with Measured Diffusion Coefficients for Tuff 
Table 7.2-2. Diffusion Coefficient of Crushed Tuff Invert Materials 
Sample 
Volumetric Moisture 
Content (%) 
Diffusion Coefficient 
(cm2 s-1) 
1 32.13 2.02  10-6 
2 18.15 5.40  10-7 
3 9.26 4.05  10-8 
4 7.03 6.75  10-9 
5 6.97 7.45  10-9 
6 6.89 6.73  10-9 
7 6.75 5.42  10-9 
8 6.63 4.39  10-9 
9 6.63 3.76  10-9 
10 6.23 3.40  10-9 
11 6.00 3.43  10-9 
12 5.55 2.04  10-9 
13 5.46 2.04  10-9 
14 8.29 2.24  10-9 

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ANL-WIS-PA-000001 REV 01 7-31 November 2004 
Table 7.2-2. Diffusion Coefficient of Crushed Tuff Invert Materials (Continued) 
Sample 
Volumetric Moisture 
Content (%) 
Diffusion Coefficient 
(cm2 s-1) 
15 7.54 6.81  10-9 
16 7.36 6.21  10-9 
17 7.22 4.38  10-9 
18 6.84 2.19  10-9 
19 6.11 1.55  10-9 
20 5.41 9.97  10-10 
21 4.45 6.19  10-10 
22 3.64 5.00  10-10 
23 0.29 1.24  10-10 
24 0.20 1.25  10-10 
Source: CRWMS M&O 2000 [DIRS 156680], Tables A-1 and A-2. 
LA-ICP-MS has recently evolved as a powerful analytical tool for solid samples (Russo 
et al. 2000 [DIRS 155697]). It can simultaneously determine a large number of chemical 
elements with low detection limits. Laser ablation uses an intense burst of energy delivered by a 
short laser pulse to vaporize a minute sample (in the range of nanograms) from a small area. 
Several spot sizes can be selected (from 25 m to 200 m in diameter), allowing a choice of 
appropriate spot size for different applications. A smaller spot size will sample less solid 
material, leading to lower analytical precision, but allowing more heterogeneity to be observed. 
A single laser pulse reveals surface compositions, while multiple pulses allows compositions to 
measured at various depths below the surface, with the crater depth proportional to the number of 
laser pulses applied. For example, two pulses reach about 4 m into the tuff matrix 
(Hu et al. 2001 [DIRS 161623], p. 22), and 50 pulses ablates to a depth of about 35 m 
(Hu et al. 2001 [DIRS 161623], Figure 6). 
In the approach of Hu et al. (2001 [DIRS 161623]), a machined 1.5-cm tuff cube containing a 
tracer was placed in contact with a cube not containing the tracer, both under the same 
thermodynamic conditions. The tracer is allowed to diffuse from the tracer-containing cube to 
the other. Tracers were chosen based on their chemical similarity to radionuclides of interest. 
The source cube was vacuum-saturated with a tracer solution mixture of NaBr, NaReO4, CsBr, 
and RbBr; both Br- and perrhenate (ReO4
-) act as nonsorbing tracers. The sink cube was also 
vacuum-saturated, but had no tracers. Source and sink cubes were separately placed inside a 
humidity chamber within an incubator maintained at 22C until the cubes equilibrated to a 
constant weight (13 days). The cubes were then clamped together in the relative humidity (RH) 
chamber to start the diffusion test. After 87 days, the diffusion test was stopped by separating 
the source and sink cubes. The surface and depth distribution of the tracer was then mapped 
using LA-ICP-MS. The mapping was done on the interface, the far side face (opposite side from 
the interface), and along the side perpendicular to the interface. 
Measurements along the outside surface of the sink cube indicated that a nonsorbing tracer 
(ReO4
-) diffused along the surface at a rate similar to its aqueous diffusion rate in bulk water 
(Hu et al. 2001 [DIRS 161623], pp. 21 and 22). This result was reasonable because the tuff 
cubes were located in the high-RH chamber, with the likely presence on the outside of the cube 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-32 November 2004 
of a thick water film that behaves like bulk water. These measurements provided a bounding 
value for the diffusivity of the tracer, comparable to the diffusion coefficient of 1.4810-5 cm2 s-1 
(Table 7.2-1) for its analog, TcO4
-. In other words, in regions on the tuff samples that were 
saturated or at least had high water saturation, the direct diffusivity measurements agreed with 
theoretical predictions. 
Hu et al. also measured tracer concentrations at greater depths into the cube by using the laser 
ablation technique to probe into the surface. They found that internal diffusion coefficients, at 
depths of 60-410 m, were on the order of 10-12 cm2 s-1 (Hu et al. 2001 [DIRS 161623], p. 22). 
The measured volumetric water content of the tuff matrix was 8.9 percent (Hu et al. 2001 
[DIRS 161623], p. 25). The mean diffusion coefficient predicted by the invert diffusion 
properties submodel (Equation 7.2.2.2-1) would then be 2.6  10-7 cm2 s-1. This is a factor of 105 
larger than the measurement. Thus, the diffusion coefficient throughout most of a grain of 
crushed tuff is lower than that predicted by the invert diffusion properties submodel. This 
provides corroborating evidence that the invert diffusion properties submodel overestimates 
releases of radionuclides from the EBS. These data also show that the overestimation of 
diffusivities in the invert diffusion properties submodel may be excessive. However, insufficient 
data exist to reduce the uncertainty in this model, and, if this additional uncertainty were 
included in the invert diffusion submodel, estimated releases of radionuclides from the EBS 
would be reduced and no longer be bounding. Because the model has a low impact on repository 
performance, the degree of uncertainty in this model is acceptable for TSPA-LA. 
The study by Hu et al. (2001 [DIRS 161623]) was primarily a development of the technique for 
using LA-ICP-MS of microscale profiling of the distribution of diffusing tracers. However, in 
the process, some preliminary data were obtained that can be used to corroborate the electrical 
conductivity measurements of Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 
[DIRS 170709]). 
Sections 7.2.1 and 7.2.2 have demonstrated that the component models of the EBS transport 
model meet Level I validation. Based on the validation results, the EBS transport model is 
adequate for its intended use. 
7.2.3 Results of Independent Model Validation Technical Review of the EBS Flow and 
Transport Models 
An independent model validation technical review of the EBS flow and transport models was 
conducted, as specified in the TWP (BSC 2004 [DIRS 170775], Section 2.2.3). This model 
validation approach is justified based on requirements of AP-SIII.10Q, Section 5.3.2 c), where 
independent technical review is listed as an appropriate method for model validation. The results 
of the independent model validation technical review of the EBS flow and transport models are 
presented in a memo (Jin 2004 [DIRS 170952]), a verbatim copy of which follows. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-33 November 2004 
MEMO 
Date: July 22, 2004 
To: James Schreiber, Cliff Howard, and Kathryn Knowles, Yucca Mountain Project 
From: Minquan Jin, INTERA Inc., Austin, Texas 
RE: Independent Model Validation Technical Review of the EBS Flow and Transport Sub- 
Models of the Radionuclide Transport Abstraction Model for the Yucca Mountain 
Project 
Pursuant to your request to perform an independent model validation, a technical review is being 
conducted of three sub-models of the Engineered Barrier System (EBS) Radionuclide Transport 
Abstraction model as documented in ANL-WIS-PA-000001 Rev 01K, I have performed and 
documented the following review. This review is being conducted consistent with the 
requirements of the Technical Work Plan TWP-MGR-PA-000020 Rev 00. The three sub-models 
are the EBS flow sub-model, EBS transport sub-model, and EBS UZ interface sub-model. This 
memo describes the results of my review of the EBS flow sub-model and EBS transport submodel 
only. 
Review Qualifications 
Section 2.2.4 of the Technical Work Plan TWP-MGR-PA-000020 Rev 00 describes the 
qualifications and responsibilities of the independent model validation technical reviewer. Based 
on the evaluation of the information provided in the document, I qualify to perform the work 
described for the following reasons. (1). I have not contributed to the development of the model 
assumptions, parameters, or implementing algorithms documented in ANL-WIS-PA-000001 Rev 
01K, (2). I have a PhD degree in Petroleum and Geosystems Engineering and am a Licensed 
Professional Engineer in the State of Texas, and (3). I have more than ten years of professional 
expertise in modeling fluid flow and transport in porous media. More detailed information 
regarding my credentials can be found in the resume attached. 
Appropriateness and Adequacy of the Conceptual Model 
Document ANL-WIS-PA-000001 Rev 01K describes the conceptual model used to determine the 
rate of radionuclide release from EBS to the unsaturated zone. This model consists of two main 
componentsa flow model and a transport model. The flow model defines the pathways for 
water flow in the EBS and specifies how the flow rate is computed for each pathway. The 
transport model considers the transport of radionuclide through each pathway. Sections 6.1, 
6.3.1.1, 6.3.2, and 6.3.3 of the document provide a complete and clear description of the 
fundamental bases of the conceptual flow model. Sections 6.3.1.2 and 6.3.4 provide detailed 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-34 November 2004 
MEMO (Continued) 
description of the fundamental bases of the conceptual transport model. In addition to the 
conceptual models developed, several alternative conceptual models are also considered and 
presented in Section 6.4. These alternative models are screened out in analysis and the rationales 
are summarized in Table 27. Based on the review of these sections and other related sections of 
the document, it is my professional judgment that both the flow model and the transport model 
incorporate the important design features, physical phenomena, and the relevant mechanisms that 
have a significant effect on the flow and transport of radionuclide in EBS. 
The conceptual flow sub-model logically divides the EBS components into three domains: the 
waste form, the waste package corrosion products, and the invert. As a result, flow and transport 
in these domains is treated separately. The output of the waste form domain feeds into the 
corrosion products domain. The output of the corrosion products domain, in turn, feeds into the 
invert. Separation of domain makes it easier to identify the eight unique pathways of water flow 
through EBS. This approach and the algorithms therefore capture all known flow pathways into 
and from the EBS components and simplify a complicated problem. The magnitude of seepage 
fluid passing through the drip shield and the waste package is accounted for using the flux 
splitting sub-model. 
The transport sub-model consists of the same three domains as the flow sub-model, the waste 
form, the waste package corrosion products, and the invert. The waste form is the source of all 
radionuclides where degradation processes occur. Dissolved radionuclide species are transported 
by advection and/or diffusion to the waste package corrosion products domain. Radionuclide 
species released from the corrosion products domain are then transported to the invert domain and 
interact with the crushed tuff in the invert by adsorption processes. Advective transport is 
considered when water enters the waste form domain and is able to flow through the EBS. 
Diffusive transport between each of the domains occurs regardless of whether water is flowing 
though the EBS. The properties that affect the rate of transport of radionuclides through each 
domain include the volume, porosity, water saturation, sorption, temperature, diffusion cross 
sectional area, and diffusive path length. These properties are well defined and discussed in 
details in the document. The concentration of each radionuclide during transport is limited by the 
sum of its solubility limit and the presence of any colloidal particles that may act as reversible or 
irreversible carriers for the radionuclide. 
In general, the document sufficiently describes the uncertainties in model parameters, processes, 
and assumptions. The potential impacts of these uncertainties are discussed. In addition to the 
description of the conceptual model, the modeling assumptions are clearly defined, discussed, and 
justified as appropriate for the intended use of the two sub-models. This is done in a separate 
section (Section 5). Based on the review of the sections of the document described above, it is my 
professional judgment that the conceptual flow model and the conceptual transport model 
developed for water flow and radionuclide transport through the EBS are appropriate and adequate 
for their intended use. 
Appropriateness of the Mathematical Representation of the Conceptual Model 
Section 6.5 of the report provides a complete and clear description of the mathematic 
representation of the conceptual flow model and the conceptual transport model. As with any 
engineering mathematical model, assumptions and simplifications have been made in the 
development of the mathematical representations of the conceptual EBS flow sub-model and the 
transport sub-model. Review of the document indicates that the mathematical formulations 
developed provide justifiable representations of the technically important mechanisms identified in 
the conceptual models. Assumptions which are used to formulate models are justified and have a 
defensible technical basis (Section 5). The important parameters for the mathematical models are 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-35 November 2004 
MEMO (Continued) 
derived from experimental data and by comparison of the experimental data to model calculations 
(Sections 6.5.1.1 and 6.5.1.2). Uncertainties associated with experimental data are quantified. For 
the parameters with high uncertainty, assumptions are made such that the parameters used would 
predict a higher radionuclide release rate through the system. Based on review of this information, 
I conclude that both mathematical representations of the flow model and the transport model are 
appropriate for their intended use. 
Appropriateness of the Key Model Assumptions 
In Section 5 of the document, a number of key assumptions are identified and discussed in detail. 
The table below presents an assessment of the assumptions. 
Assumptions Comments 
1. All seepage into the drift falls on the crown 
of the drip shield, and, in the absence of a drip 
shield, all seepage falls on the crown of the 
waste package. 
I agree with the assumption and assessment 
as provided by the author. The assumption is 
reasonable and appropriate. 
2. There is no evaporation of seepage water 
from the surface of the drip shield. 
This assumption will overestimate water flow, 
since water evaporation will occur upon contact 
with a hot object. Nevertheless, this assumption 
has no adverse effect on the model results and 
only maximizes the water flux through the EBS. 
3. Evaporation of water from the surface or 
interior of a waste package does not occur. 
Same comments as item #2 above. 
4. Chemical reactions in the EBS neither 
produce nor consume water and therefore do 
not affect water mass balance in the EBS 
I concur with the author. This is a very reasonabl 
assumption. In general, the consumption or 
production of water tends to be negligible. 
5. A thin film of adsorbed water is assumed to 
always exist on the surfaces of internal waste 
package components and corrosion products 
in a breached waste package 
I agree with the assumption and assessment 
as provided by the author. The assumption 
allows radionuclides to diffuse through the 
waste package interior and through corrosion 
products under no liquid flux condition. This 
assumption maximizes the rate of radionuclide 
transport through the EBS. 
6. The products of the corrosion of all internal 
waste package components, except for the fuel 
rods and spent nuclear fuel, are Fe2O3 
(hematite). 
I concur with the author. The assumption is 
reasonable in the absence of detailed 
compositional data, corrosion process 
information, and adsorption isotherms for the 
numerous other potential steel corrosion 
products. The limited experimental data 
presented in the report also appear to support 
the validity of this assumption. 

EBS Radionuclide Transport Abstraction 
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MEMO (Continued) 
Assumptions Comments 
7. The void volume of a waste package remains 
constant as the internal components degrade. 
I agree with the assumption and assessment 
as provided by the author. Reduction of void 
volume due to corrosion is a time-dependent 
variable and difficult to quantify. Nevertheless, 
a reduction in void volume can only reduce the 
diffusive releases of radionuclides. This 
assumption therefore maximizes the rate of 
radionuclide release through the EBS. 
8. No corrosion products exist in the invert. This is a reasonable assumption. It reduces 
the potential effectiveness of the invert as a 
transport barrier, and therefore, maximizes the 
rate of radionuclide release through the EBS. 
As stated in the table above, the assumptions used for model development and application are 
appropriate. This is standard practice and is appropriate. 
Evaluation of Model Validation 
Documentation of the flow sub-model validation is presented in Section 7.1 and was performed in 
accordance with AP-2.27Q, Planning for Science Activities, and AP-SIII.10Q according to the 
author. Validation is achieved through comparison of the model calculation results to qualified 
experimental data collected during associated testing. The method of model validation by 
comparison of model calculation results to that of the experimental data is standard practice and 
therefore the model validation method used here is appropriate. Because of the large spread of the 
experimental data and the uncertainties associated with the chaotic nature of the flow of droplets 
on a corroded surface, the model validation criterion is that the predictions of the abstraction 
bound the experimental measurements. This is also standard practice and is appropriate. The 
results documented in the report demonstrate that the drip shield and waste package flux splitting 
sub-models bound the experimental data. Calculations could not be checked for accuracy because 
of their complexity. The calculations do, however, appear to be reasonable and consistent with the 
methodology. Review of the document indicates to me that the validation calculation of the flow 
sub-model is adequate and appropriate. 
Documentation of the transport sub-model validation is presented in Section 7.2. Validation is 
achieved through comparison of the model calculation results to qualified literature data. The 
method of model validation by comparison of model calculation results to that of the literature 
data is standard practice and therefore the model validation method used here is also appropriate. 
Section 7.2.1 describes a comparison of the in-package diffusion sub-model to the model reported 
by Electric Power Research Institute Phase 5 report (EPRI 2000) and a model by Lee et al. (1996). 
The comparison shows that the final diffusion coefficients calculated by each model generally 
agree. Section 7.2.2 provides a compilation of literature data to show that the use of self-diffusion 
coefficient of water at 25oC for radionuclide species in the invert diffusion sub-model as an upper 
bound is appropriate. A comparison of the mean diffusion coefficient predicted by the invert 
diffusion sub-model with experimental data reported by Conca and Wright (1992) and by Hu et al. 
(2001) indicates that the invert diffusion sub-model significantly overestimates releases of 
radionuclides from the EBS. It is recommended that further studies be conducted to reduce the 
uncertainties of this model predication. Nevertheless, this overestimation has no adverse effect on 
the model results and only maximizes the release of radionuclides through the EBS. Review of 
the document indicates to me that the model validation meets Level I validation criteria and the 
model developed is therefore adequate for its intended use. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-37 November 2004 
MEMO (Continued) 
Evaluation of Model Validation Criteria 
In Section 2.2.4 of Technical Work Plan TWP-MGR-PA-000020 Rev 00, a number of model 
validation criteria are identified. The tables below present an assessment of these criteria. 
Evaluation of Flow Sub-model Validation Criteria 
Criteria 
Criteria 
met? Response 
a) The approach and algorithms 
described in the document and provided 
to the TSPA capture all known flow 
pathways into and from EBS 
components. 
Yes Section 6.3 of the document 
provides detailed information on the 
approach and algorithms of the flow 
model and Table 21 summarizes all 
known flow pathways and related 
parameters. 
b) Modeling assumptions are clearly 
defined, discussed, and justified as 
appropriate for the intended use of the 
model. 
Yes Section 5 of the document presents 
a clear and complete description of 
the model assumptions and 
justifications. 
c) Uncertainties in parameters, 
processes, and assumptions are 
sufficiently described, and impacts of 
these uncertainties discussed. 
Yes Input parameters are documented in 
Section 4. Uncertainties are 
discussed throughout the document 
whenever the related parameters are 
used. 
d) The overall technical credibility of the 
approach, including assumptions, 
parameters, equations, and the TSPA 
implementation, are sufficient for the 
models intended use. 
Yes The conceptual model is well 
presented and documented. Some 
of the assumptions are made such 
that the model would overestimate 
flow rate and therefore the model is 
well suited for its intended use. 
Evaluation of Transport Sub-model Validation Criteria 
Criteria 
Criteria 
met? Response 
a) The approach and algorithms 
described in the document and provided 
to TSPA address all known modes of 
radionuclide transport within and from 
the EBS components. 
Yes The detailed explanation on the 
approach and algorithms of the 
transport model developed is 
presented in Sections 6.3 and 6.5 of 
the document. All known transport 
modes and related parameters are 
summarized in Table 22. 
b) Modeling assumptions are clearly 
defined, discussed, and justified as 
appropriate for the intended use of the 
model. 
Yes Section 5 of the document presents 
a clear and complete description of 
the model assumptions and 
justifications. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 7-38 November 2004 
MEMO (Continued) 
Criteria 
Criteria 
met? Response 
c) Uncertainties in parameters, 
processes, and assumptions are 
sufficiently described, and impacts of 
these uncertainties discussed. 
Yes Input parameters are documented in 
Section 4. Uncertainties are 
discussed throughout the document 
whenever the related parameters are 
used. 
d) The overall technical credibility of the 
approach, including assumptions, 
parameters, equations, and the TSPA 
implementation, are sufficient for the 
models intended use. 
Yes A great amount of information is 
given in the development, 
formulation and validation of the 
conceptual model. Review of the 
document indicates to me that EBS 
transport sub-model is adequate for 
its intended use. 
Conclusions 
The EBS flow sub-model and transport sub-model documented in report ANL-WIS-PA-000001 
Rev 01K incorporate important design features, physical phenomena, and appropriate 
assumptions. Sufficient technical bases and justifications are provided for the model development 
and mathematical representation. Assumptions are well documented and justified and some of the 
model assumptions are made such that the model would overestimate water flow rate and 
radionuclide release through the EBS. Uncertainties are adequately and realistically bounded. 
Model validations are performed either by comparison of the model calculation results to the 
experimental data or by comparison to the literature values. It is my professional judgment that 
both EBS flow sub-model and EBS transport sub-model are adequate for their intended use. 
References 
Conca, J.L. and Wright, J. 1992. Diffusion and Flow in Gravel, Soil and Whole Rock. Applied 
Hydrogeology, 1, 5-24. Hanover, Germany: Verlag Heinz Heise GmbH. TIC: 224081. 
EPRI (Electric Power Research Institute) 2000. Evaluation of the Candidate High-Level 
Radioactive Waste Repository at Yucca Mountain Using Total System Performance Assessment, 
Phase 5. 1000802. Palo Alto, California: Electric Power Research Institute. TIC: 249555. 
Hu, Q.; Kneafsey, T.; Wang, J.S.Y.; Roberts, J.; and Carlson, S. 2001. Summary Report on 
[Phase I] Feasibility Study of In-Drift Diffusion. LBNL-49063. Berkeley, California: Lawrence 
Berkeley National Laboratory. ACC: MOL.20030225.0125. 
Lee, J.H.; Chambr, P.L.; and Andrews, R.W. 1996. Mathematical Models for Diffusive Mass 
Transfer from Waste Package Container with Multiple Perforations. Proceedings of the 1996 
International Conference on Deep Geological Disposal of Radioactive Waste, September 16-19, 
1996, Winnipeg, Manitoba, Canada. Pages 5 61 - 5 72. Toronto, Ontario, Canada: Canadian 
Nuclear Society. TIC: 233923. 

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ANL-WIS-PA-000001 REV 01 7-39 November 2004 
7.3 EBS-UZ INTERFACE SUBMODEL 
The output of the invert domain feeds into the unsaturated zone through the EBS-UZ interface 
submodel. In the EBS RT Abstraction, the invert is modeled as a single-continuum porous 
medium whereas the adjacent UZ is modeled as a dual continuum fracture-matrix medium. The 
model is described in detail in Section 6.5.3.6. 
The mass flux from the invert flows into the top layer of the middle zone in the UZ. The portion 
of the advective flux from the invert that is attributable to the seepage flux (F1) flows into the UZ 
fractures. The imbibition flux into the invert (F7) flows out of the invert into the UZ matrix. The 
diffusive flux from the invert can go into both UZ continua based on the concentration gradient 
and effective diffusion coefficient. The diffusive area remains the same because they are 
overlapping continua. The advective flux flowing through the UZ fracture cells in the middle 
zone is given by the greater of the advective flux out of the invert and the steady state UZ 
fracture flux. The advective flux in the two outer zones is given by the steady state UZ flow in 
each continuum at the repository horizon; the drift shadow effects are ignored. 
For TSPA-LA, a semi-infinite zero concentration boundary condition is used for the EBS-UZ 
interface. This is approximated by applying an effective zero-concentration boundary at 
approximately three drift diameters below the invert-UZ boundary into the UZ. By moving the 
zero concentration boundary some distance below the invert, a more realistic diffusive gradient 
through the invert is achieved. 
The EBS-UZ interface submodel of the EBS RT Abstraction provides input to the unsaturated 
zone radionuclide transport model in Particle Tracking Model and Abstraction of Transport 
Processes (BSC 2004 [DIRS 170041]). The appropriate level of confidence identified for 
unsaturated zone radionuclide transport is Level II. Therefore, Level II also represents 
appropriate level of confidence for the EBS-UZ interface submodel of the EBS RT Abstraction. 
Section 7.3.1.1 describes the semi-analytical fracture-matrix partitioning model that is used to 
validate the EBS-UZ interface submodel of the EBS RT Abstraction. Section 7.3.1.2 compares 
the two interface models, and Section 7.3.1.3 provides an evaluation of differences between the 
two models and discussion of the applicability and suitability of the EBS-UZ interface submodel 
for TSPA-LA transport modeling. 
7.3.1 Validation of EBS-UZ Boundary Condition Implementation in TSPA-LA 
In this section, the predictions of the analytical fracture-matrix partitioning model developed in 
Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040]) are compared with the 
fracture-matrix partitioning at the EBS-UZ boundary predicted by the EBS RT Abstraction 
(Section 6.5.3.6). Because the two models are conceptually different, exact agreement in their 
results is not expected. The objective of the validation is to demonstrate qualitative agreement, 
i.e., that the trends and general qualitative behavior of the EBS-UZ boundary condition 
implementation in the EBS RT Abstraction are also seen in a model that has been independently 
developed and uses a completely different solution approach. 

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7.3.1.1 Description of Fracture-Matrix Partitioning Model 
The fracture-matrix partitioning model, described in Drift-Scale Radionuclide Transport 
(BSC 2004 [DIRS 170040]), is developed for the case where there is no seepage inside the drift. 
It may be used to compute the relative fraction of the radionuclide mass entering the UZ matrix 
and UZ fracture from the invert by the process of diffusion. The fracture-matrix partitioning 
model is extended to the case where there is seepage through the drift by specifying that all mass 
leaving the invert by advection enters the UZ fractures, i.e., there is no partitioning in this case. 
The fracture-matrix partitioning model considers only that part of the invert that is directly 
underneath the waste package, and effectively treats the invert as a single continuum by 
assuming zero saturation in the intergranular pores of the invert and a fully saturated 
intragranular invert continuum, in order to compute a single continuum (or bulk) water content. 
A rectangular geometry is used for the invert, with a vertical length sampled from a uniform 
distribution whose maximum is the maximum thickness of the invert directly under the package 
and whose minimum is the thickness of the invert under the projected edges of the package. The 
invert width is defined to be equal to the half-fracture spacing in the UZ, which is the reciprocal 
of the sampled value of the fracture frequency. The model assumes two-dimensional steady state 
diffusion in a homogeneous invert material. The governing mass transport equation is the 
Laplace equation: 
0) , ( 2 = . y x Ci . (Eq. 7.3.1.1-1) 
Both lateral boundaries are considered lines of symmetry and treated as no-flow boundaries 
(BSC 2004 [DIRS 170040], Section 6.4.1 and Figure 6-10). Along the top of the invert, a 
constant concentration boundary condition is imposed. At the bottom of the invert, two flux 
boundary conditions are imposed  one across the interface between the invert and the saturated 
width of the single UZ fracture (i.e., the water film thickness), and one for the interface of the 
invert with UZ matrix. The model only considers a single fracture in the UZ, located directly 
under the left boundary of the invert. The remaining width (the half fracture spacing minus the 
fracture water film thickness) interfaces with the UZ matrix. Within the single UZ fracture, only 
diffusive transport is allowed for a vertical distance below the invert that is sampled uniformly 
between zero and the fracture spacing. Beneath that point, only advective transport in the 
fracture is allowed. The imposed boundary condition is such that the diffusive flux in the 
fracture is equal to the downward advective flux in the fracture at this sampled transition point 
between diffusion and advection. For the UZ matrix, only advective transport is allowed, and the 
boundary condition is such that the diffusive flux from the invert to the UZ matrix is equal to the 
UZ matrix advective mass flux. 
The fracture-matrix partitioning first formulates the above partial differential equation for 
concentration with boundary conditions in dimensionless form, which is then solved analytically 
by infinite series expansion in cosines and hyperbolic tangent functions. The flux to the fracture 
is then determined by integration at the invert-UZ boundary of the gradient of the concentration. 
The integral over the UZ fracture portion of the UZ represents the flux to the UZ fracture, while 
integration of the concentration gradient over the UZ matrix portion of the boundary provides the 
flux to the UZ matrix. 

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7.3.1.2 Comparison of Results from Fracture-Matrix Partitioning Model with Results 
from the Modified EBS RT Abstraction 
The two models are compared for the predictions of the fraction of mass of radionuclides 
released to fractures of the unsaturated zone. The comparison is based on the results of the 
Fracture-Matrix Partitioning Model reported in Section 6.4.6 of the Drift-Scale Radionuclide 
Transport (BSC 2004 [DIRS 170040]). In that report, calculations are done for the three 
infiltration rates (lower, mean and upper) of the glacial transition climate. The calculations 
include parameter uncertainty. The EBS-UZ interface submodel is modified, as discussed 
below, to allow comparison of the two models without changing the conceptual design or 
solution algorithm. GoldSim V8.01 (Golder Associates 2003 [DIRS 166572]) is used for the 
EBS RT Abstraction calculations. 
In order to compare the EBS RT Abstraction with the fracture-matrix partitioning model, all 
sampled and time-varying parameters in the EBS and UZ in the TSPA-LA system model are 
made consistent with the parameters used in the fracture-matrix partitioning model. Additional 
modifications made to the EBS RT Abstraction are listed below: 
1. Delete the upstream waste form and corrosion products domains. 
2. Apply uniform concentration at the top of the invert domain. 
3. Set the seepage flux entering the invert domain to zero, so that the only transport 
mechanism is via diffusion. 
4. Set the water saturation of invert intragranular continuum to 1.0 (fully saturated) and 
the water saturation of the intergranular continuum to zero. For the single continuum 
representation of the invert, the bulk water content is computed. 
5. Turn off the imbibition flux entering the invert domain. 
6. Change the diffusive property of the invert domain to match Equation E-1 of 
Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040]). 
7. Change the free water diffusion coefficient ( 0 D ) to a lognormal distribution with the 
mean of 0 logD of 4.69 mm2 yr-1 (1.49  10-9 cm2 s-1) and standard deviation of 0 logD 
of 0.150 mm2 yr-1 (4.8  10-11 cm2 s-1), consistent with the approach adopted in 
Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040], p. E-2 of 
Appendix E). 
8. Change the diffusive thickness in the invert to a uniform distribution between 0.675 m 
and 0.806 m, as shown in Drift-Scale Radionuclide Transport (BSC 2004 
[DIRS 170040], Appendix G, p. G-8). 
9. Set the diffusive outflow area of the UZ matrix cells to zero, consistent with the 
boundary conditions imposed by the fracture-matrix partitioning model Drift-Scale 
Radionuclide Transport (BSC 2004 [DIRS 170040], Section 6.4.1). As a result, only 

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diffusive transport occurs from invert domain to the UZ matrix continuum, and only 
advective transport occurs in the UZ matrix continuum. 
10. The distance where the flow occurs in the UZ fracture is uniformly sampled between 
0 m and the fracture spacing (inverse of fracture frequency). For the UZ matrix, the 
flow occurs immediately under the invert. 
11. Set the diffusive mass transfer term between the UZ matrix and fracture continuum to 
zero. 
12. Ignore the transverse diffusion to the side UZ matrix and fracture cells from the UZ 
cells in the middle zone (These zones and cells in the EBS-UZ interface submodel are 
described in Section 6.5.3.6 and Figure 6.5-5). 
Figure 7.3-1 (shown below) compares the fraction of the radionuclide mass released to the 
fractures as predicted by the fracture-matrix partitioning model (labeled as F-M Partitioning 
Model in Figure 7.3-1) with the fraction predicted by the EBS-UZ boundary condition 
implementation for TSPA-LA in the modified EBS RT Abstraction (labeled as EBS RT Model 
in Figure 7.3-1). The cumulative distribution function from the EBS RT Abstraction (thick red 
and green curves) is based on 100 realizations, while that for fracture-matrix partitioning model 
is based on 24 random samples selected for each infiltration case, as discussed in Section 6.4.6 of 
Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040]). The 24 samples are the 
minimum required to ensure sampling of hydrologic parameters from each of the four host rock 
units (TSw33, TSw34, TSw35, and TSw36). Based on this sample size, it is estimated that for 
95 percent confidence limit, the sample mean is within s s 41 . 0  of the population mean, where 
s s is the sample standard deviation. Increasing the sample size narrows the estimated spread 
around the true mean and improves the accuracy of estimation. For the 100 realizations 
performed by the modified EBS RT Abstraction, the estimate of the sample mean for 95 percent 
confidence limit is within s s 2 . 0  of the population mean. The uncertain parameters for the 
100 realizations are sampled using the Latin Hypercube Sampling methodology employed by 
GoldSim. 
The results for the fracture-matrix partitioning model for the three infiltration cases have been 
combined (weighted by the probability of each infiltration case) into a single curve (thick blue 
curve  Combined Infiltration) for comparison with the EBS-UZ boundary condition 
implementation for TSPA-LA EBS RT Abstraction. The thick red curve shows the results for the 
modified EBS RT Abstraction using the single continuum representation of the invert, which is 
the base case model used in TSPA-LA. (Though not pertinent to model validation, the modified 
EBS RT Abstraction was also run using the dual continuum representation of the invert, an 
alternative conceptual model; results are shown as the thick green curve. These thick red and 
green curves virtually overlap showing little effect on the mass fraction released to fractures.) 
In general, the modified EBS RT Abstraction predicts less mass fraction released to fracture 
compared to the fracture-matrix partitioning model. The difference is due to the fact that the two 
models are conceptually different with regard to the placement of fracture and matrix medium 
underneath the invert and in computing the flux out of the invert. The fracture-matrix 

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partitioning model solves the transport equation semi-analytically, whereas the modified EBS RT 
Abstraction model uses a finite difference approach. Because of these differences, a perfect 
match between the two models is not expected. Nevertheless, the comparison shows a similar 
qualitative and quantitative behavior between the two models. 
The modified EBS RT Abstraction and the fracture-matrix partitioning model (combined 
infiltration curve) agree within a factor of three for the median and lower quantile values. At 
higher quantiles, the modified EBS RT Abstraction tends to agree more closely with the high 
infiltration case, in which releases are smaller than for lower infiltration cases because of the 
larger advective flux in the matrix (BSC 2004 [DIRS 170040], Section 6.4.6). The median 
matrix flux for the high infiltration case is more than a factor of four greater than the median 
matrix fluxes for the low and mean infiltration cases, which in turn are similar and therefore have 
similar fractions released to fractures in Figure 7.3-1 (BSC 2004 [DIRS 170040], Section 6.4.6). 
The uncertainty in the three infiltration curves, shown as error bars in Figures 6-26 and 6-28 of 
Drift-Scale Radionuclide Transport (BSC 2004 [DIRS 170040]), is bounded by the Upper Error 
margin and Lower Error margin curves in Figure 7.3-1. The thick red (or green) curve 
generally falls within the error margins of the individual infiltration case curves, indicating a 
close match between the modified EBS RT Abstraction and the fracture-matrix partitioning 
model, considering the uncertainties in the infiltration curves. 
Although conceptual differences exist between the fracture-matrix partitioning model and the 
EBS-UZ interface submodel in the EBS RT Abstraction, with appropriate modifications to bring 
them into closer conceptual alignment, the two models display similar qualitative and 
quantitative behavior. The similarity in the results gives confidence that the EBS-UZ interface 
submodel is valid for use in TSPA-LA. 
7.3.1.3 Applicability of EBS-UZ Interface Submodel in TSPA-LA in Comparison with 
Fracture-Matrix Partitioning Model 
The EBS-UZ interface submodel of the EBS RT Abstraction is more suitable for TSPA-LA 
compared to the fracture-matrix partitioning model for the following reasons: 
 The fracture-matrix partitioning model assumes steady state mass transport and is solved 
with a semi-analytic solution to the Laplace equation, assuming a constant concentration 
boundary at the top of the invert and a variable flux boundary at the bottom. This 
approach is restrictive compared to the EBS RT Abstraction, wherein the radionuclide 
concentrations will be varying with time. Thus, important transient effects related to 
fuel degradation, thermal-hydrology, in-drift chemistry, and seepage are captured in the 
EBS RT Abstraction, but may not be captured adequately in the fracture-matrix 
partitioning model. 

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Fracture-Matrix Partitioning Model: BSC 2004 [DIRS 170040], Figures 6-26b and 6-28b. 
Figure 7.3-1. Fracture-Matrix Partitioning for No Seepage Case 
 The EBS RT Abstraction is a finite difference type model that treats the EBS processes 
and the near-field UZ processes as a coupled system. The upstream boundary condition 
is provided by a specified mass flux based on the degradation rate of the waste form and 
the radionuclide solubility limits, while the downstream boundary is provided by 
assuming a zero concentration boundary at some distance (~3 drift diameters) from the 
invert in the UZ. Consequently, the mass flux of radionuclides from the waste package 
to the invert and from the invert to the UZ is based on solving the coupled system of 
differential equations with realistic boundary conditions. Since the mass flux from the 
invert to the UZ is based on the EBS-UZ boundary condition implementation for 
TSPA-LA in the EBS RT Abstraction, to be consistent, the mass flux partitioning into 
the far-field UZ transport model (FEHM) should also be based on the EBS RT 
Abstraction, rather than on the fracture-matrix partitioning model. 
 The fracture-matrix partitioning model assumes a discrete fracture network with no 
coupling between the fracture and matrix domains. In contrast, the EBS-UZ boundary 
condition implementation for TSPA-LA in the EBS RT Abstraction treats the UZ as a 
dual continuum (overlapping UZ fracture and matrix continua), with diffusive mass 
transfer capability between the two continua. This dual continuum modeling approach is 
consistent with the various process-level UZ flow and transport models created for the 
YMP. 

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 The imbibition flux from the surrounding host rock into the intragranular continuum is 
modeled in the EBS RT Abstraction, whereas its contribution in the fracture-matrix 
partitioning model is ignored. This flux could potentially carry some radionuclide mass 
into the UZ matrix that could lower the partitioning to the fracture continuum, which is 
realistic. The fracture-matrix partitioning model may overestimate the fraction released 
to the fractures where imbibition flux is significant. 
 In the regions of the repository where water seeps through the drift, the fracture-matrix 
partitioning model arbitrarily proposes putting all the mass from the invert into the UZ 
fracture. This is a bounding approach and ignores the matrix pathway, which occupies 
most of the area under the invert. The EBS-UZ boundary condition implementation for 
TSPA-LA in the EBS RT Abstraction, however, applies a more realistic approach, 
computing the fracture-matrix partitioning based on the appropriate set of boundary 
conditions in drifts with seepage and including transport in the UZ matrix, as discussed 
in item (b) above. Sections 6.5.3.5 and 6.5.3.6 discuss how the advective flux from the 
invert is apportioned between fractures and matrix in the UZ. 
The above comparisons of the results of the two models and their comparative suitability for 
TSPA-LA have demonstrated that the EBS-UZ interface submodel meets Level II validation 
criteria. Based on the validation results, the EBS-UZ interface submodel is suitable for its 
intended use. 
7.3.2 Results of Independent Model Validation Technical Review of the EBS-UZ Interface 
Submodel 
An independent model validation technical review of the EBS-UZ interface submodel was 
conducted, as specified in the TWP (BSC 2004 [DIRS 170775], Section 2.2.3). This model 
validation approach is justified based on requirements of AP-SIII.10Q, Section 5.3.2 c), where 
independent technical review is listed as an appropriate method for model validation. The results 
of the independent model validation technical review of the EBS-UZ interface submodel are 
presented in a memo (Baker and Grisak 2004 [DIRS 170953]), a verbatim copy of which 
follows. 
MEMO 
Date: July 27, 2004 
To: James Schreiber and Cliff Howard, Yucca Mountain Project 
Cc: 
From: Noreen A. Baker, Gerald E. Grisak, INTERA Inc., Austin, Texas 
RE: Independent Model Validation Technical Review of the EBS-UZ Interface Sub- 
Model of the Radionuclide Transport Abstraction Model for the Yucca Mountain 
Project 

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ANL-WIS-PA-000001 REV 01 7-46 November 2004 
MEMO (Continued) 
Pursuant to your request to perform an independent model validation technical review of three 
sub-models of the Engineered Barrier System (EBS) Radionuclide Transport Abstraction (RTA) 
model as documented in ANL-WIS-PA-000001 Rev 01K, we have performed and documented the 
review consistent with the requirements of the Technical Work Plan TWP-MGR-PA-000020 Rev 
00. We reviewed the EBS-UZ interface sub-model of the EBS RTA report, and the results of the 
review are provided in this memo. 
Review Qualifications 
Section 2.2.4 of the Technical Work Plan TWP-MGR-PA-000020 Rev 00 describes the 
qualifications and responsibilities the independent model validation technical reviewer. We are 
qualified to perform the work described for the following reasons. (1). we have not contributed to 
the development of the model assumptions, parameters, or implementing algorithms documented 
in ANL-WIS-PA-000001 Rev 01K, (2). Noreen A. Baker has a BS and MS degree in Geology 
with specialties in Engineering Geology and Hydrogeology, respectively, with more than ten years 
of professional experience modeling fluid flow and transport in geologic media (3) G. E. Grisak 
has BS (Geology) and MS (Hydrogeology) degrees, and over 30 years experience evaluating and 
modeling fluid flow and transport in geologic media, including several publications on 
fracture/matrix flow and transport, (3) Both N. A. Baker and G. E. Grisak are licensed 
Professional Geoscientists in the State of Texas. More detailed information regarding credentials 
can be found in the resumes attached. 
Appropriateness and Adequacy of the EBS-UZ Interface Sub-Model Conceptual Model 
Discussion of the EBS-UZ interface sub-model is provided in Section 6.5.3.6. Discussion of the 
EBS-UZ interface sub-model is provided in Section 6.5.3.6. In the EBS-UZ interface sub-model, 
the near-field UZ is modeled as a dual continuum of overlapping UZ-matrix and UZ-fracture 
media. This approach is consistent with current technical approaches to modeling flow and 
ransport in fractured geologic media (Liu et al., 1998; Nitao, 1991). The matrix and fracture 
continua are represented by a two dimensional vertical array of cells oriented parallel to a cross 
section of a drift and located immediately beneath a drift. The array consists of three vertical 
zones, with each zone containing both a fracture cell and a matrix cell. The vertical zones are four 
layers deep in the vertical direction. The invert is in direct communication with the center zone of 
UZ matrix/fracture cells. A semi-infinite zero concentration boundary condition at the EBS-UZ 
interface is approximated by setting a zero concentration boundary at a distance of 3 drift 
diameters below the invert-UZ boundary. 
The mass flux from the invert flows into the top layer of the middle zone in the UZ. The mass 
flux from the invert is routed to both the fracture cell and the matrix cell in the center zone beneath 
the invert, with the advective flux routed to the fracture and matrix cells in a manner that is 
consistent with physical reality. That is, the advective flux coming out of the invert, which is 
attributable to the dripping flux is routed to the fracture cell in the middle zone, while the 
imbibition flux is routed to the matrix. The diffusive flux is allowed to enter both the matrix and 
the fracture cells. The advective flux in the fractures is taken as the larger of the steady-state 
advective flux in the fractures and the advective flux out of the invert. 
The mass flux that enters the center zone cells in the UZ below the invert is then transported by 
advection and diffusion throughout the modeled area. The advective flux in the two outer zones is 
given by the steady state UZ flow in the fractures and the matrix at the repository horizon. 
Advection occurs downward only, from the fracture cell of one layer to the fracture cell of the 
underlying layer in the same zone, and from the matrix cell of one layer to the matrix cell of the 
underlying layer in the same zone. Advection does not occur across zones. The fracture and 

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MEMO (Continued) 
matrix cells of each zone interact via diffusion. The entire modeled area interacts through 
thematrix cells via diffusion, with the matrix cells of one zone interacting via diffusion with the 
matrix cells of adjacent zones, and the matrix cells of one layer in a zone interacting with adjacent 
overlying and underlying matrix cells in the same zone. 
The conceptual model of how the EBS and UZ interface is well captured by the EBS-UZ interface 
model. The conceptual model recognizes the physical reality by considering both an advective 
and diffusive flux and by treating the UZ as a dual-permeability medium with both fracture and 
matrix continua. This modeling approach is consistent with the manner in which dualpermeability 
continua are modeled (Pruess, 2003). The conceptual model is appropriate for 
describing the interconnection between the EBS and the UZ because it considers the important 
components of mass flux out of the EBS and it conserves all the mass flux from the EBS and 
transfers it to the UZ. The mass transfer to the UZ also captures temporal variations, which may 
be due to variable radionuclide concentrations in the waste, production of corrosion products, or 
varying water flux through the EBS. The mass is distributed to the fractures and the matrix in the 
EBS-UZ interface sub-model in a manner that is conceptually logical. The mass is finally 
gathered from the EBS-UZ interface sub-model into a collector cell for delivery to the UZ 
transport model. The delivery from the collector cell to the UZ transport model retains the relative 
fractions of mass in the fractures and the matrix that is determined within the EBS-UZ interface 
sub-model. 
Appropriateness of the Mathematical Representation of the EBS-UZ Interface Sub-Model 
The EBS-UZ interface sub-model represents the UZ immediately below the invert as a dual 
continuum of UZ matrix and UZ fracture media. The dual permeability modeling approach is an 
appropriate way to model transport in fractured media. Mass is tracked and accounted for in the 
model in both fracture and matrix cells and the fracture and matrix cells have physical dimensions 
which adequately approximate the physical hydrogeologic system. The mathematical formulation 
of the dual permeability modeling approach is described in Particle Tracking Model and 
Abstraction of Transport Processes (BSC 2003w). 
EBS-UZ Interface Sub-Model Assumptions and Boundary Conditions 
The EBS-UZ sub-model assumptions and comments are provided below. 
Assumptions/Boundary Condition Comments 
1. A semi-infinite zero concentration boundary 
condition is used for the EBS-UZ interface. 
The boundary condition is set at a distance of 
3 drift diameters below the invert-UZ boundary. 
We agree with the boundary condition and with 
the manner in which it is implemented. Placing 
the boundary condition at the interface would 
result in an unrealistically high diffusive flux 
from the invert to the UZ. 
2. With respect to the advective flux in the 
outer two zones of cells, drift shadow effects 
are ignored. 
We agree with the assumption. Drift shadow 
effects would increase the advective flux in the 
two outer zones and result in dilution of 
radionuclide concentrations entering the UZ 
immediately below the invert. 
Evaluation of Model Validation 
Documentation of the model validation is presented in Section 7.3.1. The EBS-UZ sub-model is 
validated by comparison with an alternative mathematical model developed for a closely 

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MEMO (Continued) 
comparable description of the EBS-UZ interface. The alternative model used for the comparison 
is the fracture-matrix partitioning model described in Drift-Scale Radionuclide Transport (BSC 
2004m). The primary validation criterion is corroboration of the model results with an alternative 
mathematical model, as described in TWP-MGR-PA-000020 Rev 00. This is a common approach 
to model validation where site specific or generic field or laboratory data or experiments do not 
adequately capture the processes involved. The EBS-UZ interface sub-model involves coupling 
the porous medium invert to the dual-permeability UZ with a numerical solution of a discretized 
model. In the fracture-matrix partitioning model, the coupling is accomplished by formulating the 
problem as a partial differential equation for concentration and deriving an analytical solution to 
the problem. In order to compare the two models, all sampled and time-varying parameters in the 
EBS-UZ interface sub-model are made consistent with the parameters used in the fracture-matrix 
partitioning model. Additionally, other changes to the EBS-UZ interface sub-model were made to 
more closely approximate conditions in the fracture-matrix partitioning model. The EBS-UZ 
interface sub-model was also run using an alternative conceptualization for the invert as a dual 
continuum. The results of the CDFs of the fraction released to fractures are then compared. This 
is a technically reasonable and appropriate approach to model validation. 
Evaluation of Model Validation Criteria 
In Section 2.2.4 of Technical Work Plan TWP-MGR-PA-000020 Rev 00, provides validation 
criteria for the EBS-UZ interface sub-model. The table below provides our assessment of these 
criteria. 
Criteria 
Criteria 
met? Response 
1. The results of the UBS-UZ interface 
sub-model shall show qualitative 
agreement with the results of the 
fracture-matrix partitioning model. 
Yes 
The two models display similar 
qualitative results, and in addition are 
reasonably similar quantitatively, in 
that the results of the EBS-UZ 
interface sub-model fall within the 
shadow of the error bars of the low, 
mean and high infiltration cases of the 
fracture-matrix partitioning model. 
2. The report shall document equivalent 
trends and correlations between input 
parameter variation and predicted results 
Yes 
Equivalent trends and correlations 
between input parameter variations 
and predicted results are visually 
obvious on the graphical comparison 
between the two methods. Either the 
single or dual continuum 
representation of the invert by the 
EBS-UZ interface sub-model is 
adequate. 
3. Identification of differences between 
model results. 
Yes 
Differences between model results 
and the reasons for the differences 
are provided in section 7.3.1.2 
4. Demonstrate that the EBS-UZ 
interface sub-model does not 
underestimate radionuclide transport 
from the EBS to the UZ. 
Yes 
The suitability and applicability of the 
EBS-UZ interface sub-model is 
discussed and justified in 
Section 7.3.1.3. The sub-model is 
suitable for its intended use. 

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MEMO (Continued) 
Conclusions 
The EBS-UZ interface sub-model documented in report ANL-WIS-PA-000001 Rev 01K 
incorporates all the significant aspects contributing to mass flux from the invert to the UZ. The 
sub-model is validated against an alternative model developed for similar purposes and the results 
are comparable. The advective flux is the primary uncertainty in the mass flux to the fractures, 
and this uncertainty has been adequately and realistically bounded by the low, mean and high 
infiltration cases used in the fracture-matrix partitioning model in the validation comparison. It is 
our professional judgment that the EBS flow sub-model is appropriate for use in the Radionuclide 
Transport Abstraction. 
References 
Liu, H.H., C. Doughty and G.S. Bodvarsson, 1998, An active fracture model for unsaturated flow 
and transport in fractured rock, Water Resources Research, vol. 34, no. 10, pages 2633-2646. 
Nitao, J.J., 1991, Theory of matrix and fracture flow regimes in unsaturated, fractured media, 
Proc., Second International High Level Radioactive Waste Management Conference, Las Vegas, 
NV, April 29-May 3, 1991. 
Pruess, K. (editor), 2003, Proceedings, TOUGH Symposium 2003, Lawrence Berkeley National 
Laboratory, CA, May 12-14. 
7.4 VALIDATION SUMMARY 
The EBS RT Abstraction has been validated by applying acceptance criteria based on an 
evaluation of the models relative importance to the potential performance of the repository 
system. All validation requirements defined in the Technical Work Plan for: Near-Field 
Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction 
Model Report Integration (BSC 2004 [DIRS 170775]), Sections 2.2.1, 2.2.2, and 2.2.3 have been 
fulfilled. Requirements for confidence building during model development have also been 
satisfied. The model development activities and post-development validation activities described 
establish the scientific bases for the EBS RT Abstraction. Based on this, the EBS RT Abstraction 
is considered to be sufficiently accurate and adequate for the intended purpose and to the level of 
confidence required by the models relative importance to the performance of the proposed 
repository system. 

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INTENTIONALLY LEFT BLANK

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8. CONCLUSIONS 
This abstraction defines the conceptual model used to determine the rate of release of 
radionuclides from the EBS to the unsaturated zone in the TSPA-LA given the assumptions 
listed in Section 5. The EBS RT Abstraction includes algorithms used in the TSPA-LA for 
computing the flow of water and the transport of radionuclides through the EBS and specifies 
how parameters used in the model are calculated or from what other models they are obtained. 
This model is reasonably bounding because it overestimates flow through the drip shield and into 
the waste package and transport out of the EBS. At the same time, wherever possible, it is 
realistic, not just bounding, within the appropriate range of uncertainty for TSPA-LA 
calculations. 
8.1 CONCEPTUAL MODEL SUMMARY 
This section summarizes the conceptual model for transport of radionuclides from the EBS as 
modeled in TSPA-LA. Radionuclide transport out of the waste form and waste package, through 
the invert, and into the unsaturated zone is dependent on a complex series of events in the 
repository. After the waste packages are emplaced, radioactive decay of the waste will heat the 
drifts and locally perturb the normal percolation of water through the mountain. As the drifts 
cool, some of the water percolating through the mountain may drip into the drifts and 
subsequently contact some of the drip shields. Over time, the drip shield, waste package, and 
other components of the EBS are expected to degrade, leading to contact between the water and 
the waste form, resulting in the mobilization and transport of radionuclides through the EBS to 
the unsaturated zone. The primary transport medium through the EBS is anticipated to be water. 
Either a thin film of water or moving water is necessary for radionuclides to be transported out of 
the waste package and through the invert to the unsaturated zone. 
A number of key factors will affect the mobilization and transport of radionuclides through the 
EBS, including barrier effectiveness and transport behavior: 
 Performance of the drip shields 
 Performance of the waste packages 
 Protection provided by cladding 
 Waste form degradation rates 
 Entry and movement of water through waste packages 
 Solubilities of radionuclides 
 Transport of radionuclides through and out of the waste packages 
 Transport of radionuclides through the invert below the waste packages 
 Colloidal transport of radionuclides. 
Once the drip shield is breached, water may contact the waste packages. Once a waste package 
is breached, water may enter the package as water vapor or as drips. If the cladding around spent 
fuel rods or the canister around a vitrified waste form is also breached, radionuclides may start to 
dissolve in the water. The concentration of each radionuclide mobilized from the waste form 
cannot exceed the radionuclide solubility limit, unless suspended colloids are included. Colloids 
are important for two reasons: they may potentially increase the release of radionuclides from 
the waste package, and they may potentially increase the transport velocity of radionuclides. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-2 November 2004 
Radionuclides mobilized in water as dissolved species or in association with colloidal species 
may then be transported by advection and/or diffusion from the waste form, through the waste 
package, and out of breaches in the waste packages. Once outside the package, the radionuclides 
may be transported through the invert predominantly by diffusion, if water is not flowing 
through the invert, or by advection, if water is flowing through the invert. 
The conceptual model for flow of water through the EBS identifies eight key flow pathways. 
These pathways and their relationships are summarized in the following list and in Table 8.1-1. 
Sections 6.3.1.1, 6.3.2, 6.3.3, and 6.5.1.1 contain detailed technical discussions of the EBS flow 
abstraction portion of the EBS RT Abstraction. 
 Seepage FluxThis is the input flux or boundary condition; it is a time- and 
location-dependent input to this model provided by Abstraction of Drift Seepage 
(BSC 2004 [DIRS 169131]). Any condensation that may occur on the walls of the drift 
above the drip shield is included in the seepage flux. 
 Through the Drip Shield to the Waste PackageFlux through the drip shield is 
proportional to the ratio of the axial lengths of breaches in the drip shield to the total 
axial length of the drip shield, multiplied by a sampled factor that accounts for 
uncertainty in the fraction of the flux that is diverted by the drip shield. This flux 
splitting submodel for the drip shield should only be applied when there is a 
time-varying failure of the drip shield. 
 Drip Shield to Invert (Diversion around the Drip Shield)Any seepage flux that does 
not go through the drip shield flows directly into the invert. 
 Through the Waste Package to the Waste FormFlux into the waste package is 
proportional to the product of the flux through the drip shield and the ratio of the lengths 
of breaches in the waste package to the total axial length of the waste package, 
multiplied by a sampled factor that accounts for uncertainty in the fraction of the flux 
that is diverted by the waste package. The number of patches in the waste package is 
calculated by the waste package degradation model, WAPDEG Analysis of Waste 
Package and Drip Shield Degradation (BSC 2004 [DIRS 169996]). 
 Waste Package to Invert (Diversion around the Waste Package)Flow that does not 
go through the waste package is diverted directly to the invert. 
 Waste Package to InvertAll of the flux from the waste package flows directly to the 
invert, independent of breach location on the waste package. The presence of the 
emplacement pallet, which maintains an air gap between the waste package and the 
invert and could potentially interfere with flow to the invert, is ignored in order to bound 
the water flow through this pathway. 
 Imbibition to InvertWater can be imbibed from the host rock matrix into the invert. 
 Invert to Unsaturated ZoneAll of the flux into the invert is released into the 
unsaturated zone. 
In the conceptual model of radionuclide transport through the EBS, the waste form is the source 
of all radionuclides in the repository system. Radionuclides can be transported downward, 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-3 November 2004 
through corrosion products in the waste package, through the invert, and into the unsaturated 
zone. Transport can occur through advection when there is a liquid flux through the waste 
package, and by diffusion through any water present in the waste package. Diffusion can occur 
in a seep environment, when advective transport also takes place, as well as in a no-seep 
environment where no advective transport occurs; thin films of water are assumed to be present 
on all surfaces. If the only breaches in a waste package are stress corrosion cracks, advective 
transport does not occur, but diffusion of radionuclides out of the waste package can still take 
place. The concentration of each radionuclide during transport is limited by the sum of its 
solubility limit and the presence of any colloidal particles that may act as reversible or 
irreversible carriers for the radionuclide. The transport pathways and transport processes 
(advection or diffusion) are summarized in Table 8.1-2. Sections 6.3.4, 6.5.1.2, and 6.5.3 
contain a detailed technical discussion of the EBS transport abstraction. 
Table 8.1-1. Summary of EBS Flow Abstraction 
Flow Pathway, Pathway Flux Flow Parameters Data Sources & Notes 
1. Total dripping flux, F1 Total dripping flux is a function of 
fracture properties, rock properties, 
and the percolation flux. 
Abstraction of Drift Seepage (BSC 
2004 [DIRS 169131]) provides timeand 
location-dependent values of total 
dripping flux. 
2. Flux through the drip shield, 
F2 
LDS_Patch is axial half-length of each 
patch due to general corrosion of Ti. 
LDS is axial length of the drip shield. 
NbDS is number of corrosion patches 
of length LDS_Patch in the drip shield. 
f 'DS is sampled uncertain parameter, 
Flux_Split_DS_Uncert. 
F2 = min[F1NbDSLDS_Patchf 'DS/LDS, F1] 
This flux splitting submodel for the drip 
shield should only be applied when 
there is a time-varying failure of the 
drip shield. For the seismic scenario, 
the opening area is computed based 
on the drip shield damage fraction 
multiplied by the area of the drip 
shield. 
3. Diversion around drip 
shield, F3 
F3 = F1  F2. Continuity of liquid flux. 
4. Flux into the WP, F4 LWP_Patch is axial half-length of each 
patch due to general corrosion of 
Alloy 22. 
LWP is axial length of the WP. 
NbWP is number of corrosion patches 
in the waste package. 
f 'WP is sampled uncertain parameter, 
Flux_Split_WP_Uncert. 
F4 = min[F2NbWPLWP_Patchf 'WP/LWP, F2] 
WAPDEG (BSC 2004 [DIRS 169996]) 
provides the number of patches and 
stress corrosion cracks on the WP. 
No flow through stress corrosion 
cracks due to plugging (BSC 2004 
[DIRS 172203], Section 6.3.7). 
Steady state flow through WP (outflow 
= inflow in steady state; this is 
bounding for release). 
5. Diversion around the WP, F5 F5 = F2 - F4 Continuity of liquid flux. 
6. Flux to the invert, F6 F6 = F5 + F4 + F3 
= F1 
All advective flux enters the invert. 
Only F4 can transport radionuclides 
into the invert. 
7. Imbibition flux from the host 
rock matrix into the invert, F7 
F7 is an input to the EBS flow model. Imbibition flux is provided by 
Multiscale Thermohydrologic Model 
calculations (BSC 2004 [DIRS 
169565]). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-4 November 2004 
Table 8.1-1. Summary of EBS Flow Abstraction (Continued) 
Flow Pathway, Pathway Flux Flow Parameters Data Sources & Notes 
8. Flux from the invert into to the 
unsaturated zone, F8 
F8 = F6 + F7 
= F1 + F7 
Total dripping flux portion (F1) of 
advective flux from the invert flows into 
the UZ fractures, imbibition flux (F7) 
flows into the UZ matrix. 
Output DTN: SN0410T0507703.018. 
WP = waste package 
In the transport abstraction, the EBS is modeled as consisting of three domains. The first domain 
is the source (i.e., SNF or HLW). The second domain consists of corrosion products from the 
degradation of steel waste package internal components. The third domain is the invert. The 
physical and chemical properties and conditions are uniform throughout each domain, as though 
the contents of the domain were thoroughly and continuously stirred. 
Parameters that define the size of the two waste package domains, specifically the volumes and 
diffusive path lengths, are summarized in Table 8.2-1. Parameter values that are provided by 
other models are identified there. The path length for diffusion through the invert is set to the 
average thickness of the invert, 0.597 m. 
The mass of corrosion products is a function of time and depends on the corrosion rates of 
carbon steel and stainless steel, which are uncertain parameters with values that are sampled in 
TSPA-LA. In a seep environment, the corrosion products are fully saturated with water. In a 
no-seep environment for CSNF, the water saturation is based on the amount of water adsorbed 
onto iron oxide surfaces, which is a function of the relative humidity. The RH is an input to the 
transport model that depends on time and location in the repository. Calculation of corrosion 
products mass and saturation is discussed in Section 6.5.3.2. 
The diffusion coefficient in the corrosion products is based on the self-diffusion coefficient of 
water at 25C as a bounding value for all radionuclides, modified for the porosity and 
time-dependent water saturation. 
The diffusion coefficient in the invert is also based on the self-diffusion coefficient of water at 
25C as a bounding value for all radionuclides. The effects of porosity and time-dependent 
saturation in the invert are incorporated, based on experimental data. The effect of temperature 
is also incorporated into the abstraction for the diffusion coefficient. The diffusion coefficient 
for colloids is assumed to be 1/100th of the diffusion coefficient for a dissolved species 
(Section 6.3.4.4). 
Sorption of radionuclides may occur on corrosion products in the waste package and on crushed 
tuff in the invert. Values for sorption distribution coefficients on corrosion products and on 
crushed tuff for all radionuclides of interest are determined in Section 6.3.4.2. Kd values for 
sorption on corrosion products are summarized in Table 8.2-2, with the uncertainty in each value 
represented by a specified range and distribution. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-5 November 2004 
Table 8.1-2. Summary of EBS Transport Abstraction 
Transport Pathway Transport Modes Transport Parameters and Data Sources 
1. Waste form and 
corrosion products 
domains 
Diffusion through stress 
corrosion cracks (no 
advective transport through 
stress corrosion cracks). 
Diffusion and advection 
through patches. 
No lateral or forward dispersion. 
Colloidal particles will transport radionuclides. 
Diffusive area for each stress corrosion crack is 
7.7  10-6 m2 (see Section 6.3.3.1.2.1). 
Diffusion coefficient (all radionuclides): 
 Free water diffusion coefficient: 2.299  10-5 
cm2 s-1 at 25C (Mills 1973 [DIRS 133392], 
Table III) 
 Modified for porosity and saturation (see 
Section 6.5.1.2.1.4) 
 Reduced by a factor of 100 if radionuclide is 
bound to a colloid (see Section 6.3.4.4). 
The cross-sectional area for radionuclide transport is 
dependent on the scenario class (see 
Sections 6.5.3.1.1 and 6.5.3.1.2). 
Transport of radionuclides is retarded by sorption onto 
corrosion products; time-dependent mass of corrosion 
products available for sorption is calculated based on 
corrosion rates of carbon and stainless steels. 
See Section 6.5.3 for further details. 
2. Invert Diffusion and advection 
(F6) from corrosion 
products domain into the 
invert. 
Liquid flux for advection = F6 = F5 (diverted by WP) + 
F4 (flux through WP) + F3 (diverted by drip shield). 
Diffusion coefficient (all radionuclides): 
 Free water diffusion coefficient: 2.299  10-5 
cm2 s-1 at 25C (Mills 1973 [DIRS 133392], Table 
III) 
 Modified for porosity and saturation (see Section 
6.3.4.1) 
 Temperature modification defined in Section 
6.3.4.1.2; invert temperature is provided by 
Multiscale Thermohydrologic Model calculations 
(BSC 2004 [DIRS 169565] 
 Reduced by a factor of 100 if radionuclide is 
bound to a colloid (see Section 6.3.4.4). 
The cross-sectional area for radionuclide transport is 
the width of the invert times the waste package length. 
Transport of radionuclides is retarded by sorption onto 
crushed tuff in invert. 
See Section 6.5.3 for further details. 
3. Invert-UZ interface Advection from the invert 
to UZ fractures (F6) and UZ 
matrix (F7); total flux is F8. 
Diffusion from the invert to 
UZ fractures and matrix. 
The invert diffusion calculation uses radionuclide 
concentrations in the WP corrosion products domain 
as the boundary condition at the top of the invert and a 
series of unsaturated zone computational cells below 
the invert that provide a gradient to a zero radionuclide 
concentration at some distance from the bottom of the 
invert. See Section 6.5.3.6. 
Output DTN: SN0410T0507703.018. 
WP = waste package 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-6 November 2004 
8.2 MODEL OUTPUTS 
Table 8.2-1 summarizes parameters that define the three-domain EBS transport abstraction, 
which is described in more detail in Section 6.5.3. These domains are comprised of: 
 The waste form. In the case of CSNF waste packages, this consists of fuel rods. In 
codisposal waste packages, the waste form is a composite of HLW glass and DSNF; 
however, only HLW is modeled in this domain, because DSNF mass is added to the 
corrosion product domain due to near-instantaneous degradation. Transport processes 
that occur in this domain are dissolution of radionuclides in the waste form and diffusion 
from the waste form domain to the corrosion products domain. 
 Corrosion products inside the waste package. These are the result of corrosion of steel 
internal waste package components such as baskets, HLW canisters, and the inner 
stainless steel vessel. The stationary iron-oxide-based corrosion products are strong 
sorbers of many radionuclides. In addition, radionuclides sorb onto colloidal materials 
released from the corrosion products and onto groundwater colloids. These sorption 
processes, both reversible and irreversible, are modeled as occurring in the corrosion 
products domain. Precipitation and dissolution can also take place in this domain. 
Diffusion transports radionuclides into this domain from the waste form domain and 
from this domain to the invert domain. In a codisposal waste package, the degraded 
DSNF is conceptualized to be in a powdered form that is commingled with steel 
corrosion products and is thus included in the corrosion product domain for purposes of 
calculating the mass of corrosion products and the volume of water in the domain. 
 Invert. Advection and diffusion transport radionuclides into this domain from the 
corrosion products domain and from this domain to the unsaturated zone. Because the 
chemical environment of the invert may be different from the corrosion products 
domain, colloid stability may be affected and dissolution or precipitation of 
radionuclides may take place. The submodel for transport through the invert is 
summarized in transport pathway 3 of the transport abstraction summary, Table 8.1-2. 
Transport is affected by the parameters that define the physicochemical environment, including 
the porosity and pore volume, water saturation, interfacial diffusive areas, diffusive path lengths, 
and diffusion coefficients. These diffusive transport parameters are discussed in Section 6.5.3. 
Output from the EBS RT Abstraction, including algorithms and parameters, is summarized in 
final output DTN: SN0410T0507703.018. In addition, two preliminary output DTNs were 
created prior to final approval of this report: DTNs: SN0403T0507703.015 and 
SN0409T0507703.017. The DTNs consist of the tables found in Sections 8.1 and 8.2 of the EBS 
RT Abstraction. Differences between the preliminary and final DTNs are described in Appendix 
I. Both of the preliminary DTNs that were developed have been superseded by the final output 
DTN SN0410T0507703.018. The two preliminary output DTNs are discussed in Appendix I 
solely to provide transparency and traceability for TSPA-LA applications that were initially 
developed based on the preliminary DTNs. These two DTNs are not intended for any other 
application. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-7 November 2004 
Table 8.2-1. Parameters for EBS Transport Abstraction 
Waste Type 
Transport 
Mode Seep Case No-Seep Case 
Waste Form Domain (Fuel Rods, HLW) 
Advection Rind and water volume 
 Provided by Clad Degradation  
Summary and Abstraction for LA 
(BSC 2004 [DIRS 170023]) 
 Same as Seep Case CSNF 
Diffusion Diffusive area of Waste Form Domain: 
 Total exposed surface area of all 
failed (axially split) fuel rods, limited 
to the total surface area of the 
waste package. 
 Provided by Clad Degradation  
Summary and Abstraction for LA 
(BSC 2004 [DIRS 170023]) 
Diffusion path length: 
 Thickness of rind; function of time. 
 Provided by Clad Degradation  
Summary and Abstraction for LA 
(BSC 2004 [DIRS 170023]) 
Diffusion coefficient in Waste Form 
Domain, DWF: 
 Archies law: DWF = f1.3Sw
2D0 
 f = porosity of rind (BSC 2004 
[DIRS 170023]) 
 Sw = water saturation in rind = 1.0 
 D0 = free water diffusion coefficient 
(Note the DWF is an effective value 
defined in the same manner as Ds in 
Equation 6.5.1.2.1-12.) 
 Same as Seep Case 
Waste Form Domain (Fuel Rods, HLW) 
Codisposal Advection Volume of rind: 
 Provided as function of time by 
Defense HLW Glass Degradation 
Model (BSC 2004 [DIRS 169988], 
Section 6.7, Eq. 56) 
 Porosity provided by Defense HLW 
Glass Degradation Model 
(BSC 2004 [DIRS 169988], 
Table 8-1) 
 Sw = water saturation = 1.0 
 Same as Seep Case 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-8 November 2004 
Table 8.2-1. Parameters for EBS Transport Abstraction (Continued) 
Waste Type 
Transport 
Mode Seep Case No-Seep Case 
Diffusion Diffusive area: 
 Total initial surface area of 5 glass 
logs 
 Provided by Defense HLW Glass 
Degradation Model (BSC 2004 
[DIRS 169988], Section 8.1) 
Diffusion path length: 
 Thickness of degraded glass layer; 
function of time. 
 Provided by Defense HLW Glass 
Degradation Model (BSC 2004 
[DIRS 169988], Section 6.7, Eq. 56) 
Diffusion coefficient in Waste Form 
Domain, DWF: 
 Archies law: DWF = f1.3Sw
2D0 
 f = porosity of degraded glass layer 
(BSC 2004 [DIRS 169988], 
Table 8-1) 
 Sw = water saturation = 1.0 
 D0 = free water diffusion coefficient 
(Note the DWF is an effective value 
defined in the same manner as Ds in 
Equation 6.5.1.2.1-12.) 
 Same as Seep Case 
Corrosion Product Domain 
Volume of corrosion products, VCP: 
 Mass of corrosion products, mCP, is 
function of time, Table 8.2-5, 
Equation 8-7 
 Porosity fCP = 0.4 
 VCP from Table 8.2-5, Equation 8-6 
 Same as Seep Case Advection 
Volume of water: 
 Sw = water saturation in CP = 1.0 
 Water volume = SwVCP 
Volume of water: 
 Swe,CP = effective water saturation in 
CP from adsorbed water 
(in-package diffusion submodel); 
Table 8.2-5, Equation 8-5 
 Swe,CP function of RH and sampled 
specific surface area of CP 
CP_Spec_Surf_Area 
 Water volume = Swe,CPVCP 
Diffusive area: 
 Total area of all waste package 
breaches 
 Same as Seep Case 
CSNF 
Diffusion 
Diffusion path length: 
 Sampled parameter 
Diff_Path_Length_CP_CSNF 
 Same as Seep Case 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-9 November 2004 
Table 8.2-1. Parameters for EBS Transport Abstraction (Continued) 
Waste Type 
Transport 
Mode Seep Case No-Seep Case 
Diffusion coefficient in corrosion 
products, DCP: 
 Archies law: DCP = fCP
1.3Sw
2D0 
 fCP = porosity of CP = 0.4 
 Sw = water saturation in CP = 1.0 
 D0 = free water diffusion coefficient 
(Note the DCP is an effective value 
defined in the same manner as Ds in 
Equation 6.5.1.2.1-12.) 
Diffusion coefficient in corrosion 
products, DCP: 
 Swe,CP = effective water saturation in 
CP from adsorbed water 
(in-package diffusion submodel); 
Table 8.2-5, Equation 8-5 
 Swe,CP function of RH and sampled 
specific surface area of CP 
CP_Spec_Surf_Area 
 fCP = porosity of CP = 0.4 
 D0 = free water diffusion coefficient 
Volume of corrosion products, VCP: 
 Same as for CSNF drip case 
 fCP = porosity of CP = 0.4 
 Sw = water saturation in CP = 1.0 
Volume of degraded DSNF, VDSNF 
 VDSNF = 1 m3 
 fDSNF = porosity of DSNF = 0.2 
 Sw = water saturation in DSNF = 1 
 Same as Seep Case Advection 
Volume of water: 
 Water volume = 
max[SwVCP, Sw fDSNFVDSNF] 
 Same as Seep Case 
Codisposal 
Diffusion Diffusive area: 
 Same as for CSNF drip case 
Diffusion path length: 
 Sampled parameter 
Diff_Path_Length_CP_CDSP 
Diffusion coefficient in corrosion 
products, DCP: 
 Archies law: DCP = fCP
1.3Sw
2D0 
 fCP = porosity of CP = 0.4 
 Sw = water saturation = 1.0 
 D0 = free water diffusion 
coefficient 
(Note the DCP is an effective value 
defined in the same manner as Ds in 
Equation 6.5.1.2.1-12.) 
 Same as Seep Case 
Output DTN: SN0410T0507703.018. 
DSNF = defense spent nuclear fuel 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-10 November 2004 
Table 8.2-2 summarizes the range and distribution of radionuclide sorption distribution 
coefficients for retardation in the waste package corrosion products. These parameter values are 
discussed in Section 6.3.4.2. 
The ranges and distributions of radionuclide sorption distribution coefficients for sorption on 
devitrified unsaturated zone tuff given in Table 4.1-12 (DTNs: LA0408AM831341.001 
[DIRS 171584]) are assigned to Kd values on crushed tuff in the invert. Correlations for 
sampling sorption distribution coefficient probability distributions for devitrified UZ tuff given 
in Table 4.1-13 (DTN: LA0311AM831341.001 [DIRS 167015]) are assigned to invert crushed 
tuff. The value for actinium sorption distribution coefficient for sorption on crushed tuff in the 
invert is set equal to the sampled americium Kd value on crushed tuff in the invert. 
Table 8.2-2. Summary of Sorption Distribution Coefficient (Kd) Ranges and Distributions for Sorption on 
Waste Package Corrosion Products 
Input Name Element 
Minimum Kd 
(ml g-1) 
Maximum Kd 
(ml g-1) Distribution Type 
Kd_Ac_FeOx_CP Actinium 100 5,000 Log-Uniform 
Kd_Am_FeOx_CP Americium 100 5,000 Log-Uniform 
Kd_C_FeOx_CP Carbon 10 100 Uniform 
Kd_Cs_FeOx_CP Cesium 0 300 Beta 
E(x)=30; s(x)=30 
Kd_I_FeOx_CP Iodine 0 0.6 Uniform 
Kd_Np_FeOx_CP Neptunium 1 1,000 Log-Uniform 
Kd_Pu_FeOx_CP Plutonium 100 5,000 Log-Uniform 
Kd_Pa_FeOx_CP Protactinium 100 1,000 Uniform 
Kd_Ra_FeOx_CP Radium 0 500 Beta 
E(x)=30; s(x)=30 
Kd_Sr_FeOx_CP Strontium 0 20 Beta 
E(x)=10; s(x)=2.5 
Kd_Tc_FeOx_CP Technetium 0 0.6 Uniform 
Kd_Th_FeOx_CP Thorium 100 5,000 Log-Uniform 
Kd_U_FeOx_CP Uranium 100 1,000 Log-Uniform 
Output DTN: SN0410T0507703.018. 
NOTES: E(x) = Expected value 
s(x) = Standard deviation 
Table 8.2-3 summarizes various sampled parameters to be used in the EBS radionuclide transport 
abstraction, with the range and distribution of each parameter provided. This table is itself a 
summary of Table 6.5-13, which, along with the rest of Section 6.5.2, gives further details about 
each parameter and the location in this document where the parameter is developed. A summary 
of fixed, single-value parameters to be used in the EBS radionuclide transport abstraction is 
given in Table 8.2-4. Equations used to compute various parameters in the EBS radionuclide 
transport abstraction are shown in Table 8.2-5. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-11 November 2004 
Table 8.2-3. Sampled Model Inputs Used in the EBS Radionuclide Transport Abstraction 
Input Name Input Description Range Distribution 
Invert_Diff_Coeff_Uncert Invert diffusion coefficient uncertainty; 
Table 8.2-5, Equation 8-1 
Range: 103 s 
(dimensionless) 
Mean:  = 0.033; 
Std. Dev. s = 0.218 
10ND 
SS_Corrosion_Rate Stainless steel corrosion rate (DTN: 
MO0409SPAACRWP.000 [DIRS 
172059]; Spreadsheet 
ECDF_metals2.xls; Worksheet 
316 ss, Columns L & M, Rows 515); 
cumulative distribution function 
Rate (m yr-1) 
0.03699 
0.037 
0.1016 
0.109 
0.1524 
0.154 
0.1778 
0.2032 
0.2286 
0.254 
0.2794 
0.51 
CDF 
0.000 
0.063 
0.125 
0.188 
0.250 
0.313 
0.375 
0.438 
0.563 
0.750 
0.813 
1.000 
CS_Corrosion_Rate Carbon steel corrosion rate (DTN: 
MO0409SPAACRWP.000 [DIRS 
172059]; Spreadsheet 
ECDF_metals2.xls; Worksheet 
A516-Carbon Steel, Columns B & C, 
Rows 5-30);cumulative distribution 
function 
Rate (m yr-1) 
65.76 
65.77 
66.75 
69.84 
70.00 
71.25 
72.21 
72.64 
72.87 
72.89 
73.47 
74.29 
74.51 
74.60 
75.41 
77.31 
79.29 
80.00 
80.87 
83.26 
83.66 
83.74 
85.68 
90.97 
106.93 
CDF 
0.000 
0.042 
0.083 
0.125 
0.167 
0.208 
0.250 
0.292 
0.333 
0.375 
0.417 
0.458 
0.500 
0.542 
0.583 
0.625 
0.667 
0.708 
0.750 
0.792 
0.833 
0.875 
0.917 
0.958 
1.000 
Diff_Path_Length_CP_CSNF Diffusive path length through corrosion 
products domain for CSNF packages 
0.02  0.859 m Uniform 
Diff_Path_Length_CP_CDSP Diffusive path length through corrosion 
products domain for codisposal 
packages 
0.025  1.063 m Uniform 
CP_Spec_Surf_Area Specific surface area of Fe2O3 
corrosion products 
1.0  22 m2 g-1 Uniform 
DS_Flux_Uncertainty Drip shield flux splitting uncertainty 
factor 
0  0.85 
(dimensionless) 
Uniform 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-12 November 2004 
Table 8.2-3. Sampled Model Inputs Used in the EBS Radionuclide Transport Abstraction (Continued) 
Input Name Input Description Range Distribution 
WP_Flux_Uncertainty Waste package flux splitting 
uncertainty factor 
0  2.41 
(dimensionless) 
Uniform 
Fracture_Frequency Unsaturated zone fracture frequency 
(BSC 2004 [DIRS 170040], 
Appendix A, Table A-1) 
Mean=3.16 m-1 
Std. Dev.=2.63 m-1 
Log-normal 
UZ_Fracture_Fraction Unsaturated zone fracture porosity 
(BSC 2004 [DIRS 170040], 
Appendix D, Table D-1) 
0  1 
(fraction); 
E(x)=9.6  10-3; 
s(x)=2.82  10-3 
Beta 
UZ_Matrix_Porosity Unsaturated zone matrix porosity 
(BSC 2004 [DIRS 170040], 
Appendix D, Table D-1) 
0  1 
(fraction); 
E(x)=0.131; 
s(x)=0.031 
Beta 
Fracture_Saturation Unsaturated zone fracture saturation 
(DTN: LB0307FMRADTRN.001 
[DIRS 165451]) 
Uniform sampling 
from 433 locations for 
each infiltration case 
Provided in 
source DTN 
Fracture_Residual_Sat Unsaturated zone fracture residual 
saturation 
(DTN: LB0307FMRADTRN.001 
[DIRS 165451]) 
Uniform sampling 
from 433 locations 
Provided in 
source DTN 
Fracture_Percolation_Flux Unsaturated zone fracture percolation 
flux (DTN: LB0307FMRADTRN.001 
[DIRS 165451]) 
Uniform sampling 
from 433 locations for 
each infiltration case 
Provided in 
source DTN 
Flow_Focus_Factor Unsaturated zone fracture percolation 
flow-focusing factor (DTN: 
LB0307FMRADTRN.001 
[DIRS 165451]) 
Uniform sampling 
from 433 locations for 
each infiltration case 
Provided in 
source DTN 
UZ_Matrix_Saturation Unsaturated zone matrix saturation 
(DTN: LB0307FMRADTRN.001 
[DIRS 165451]) 
Uniform sampling 
from 433 locations for 
each infiltration case 
Provided in 
source DTN 
Matrix_Percolation_Flux Unsaturated zone matrix percolation 
flux (DTN: LB0307FMRADTRN.001 
[DIRS 165451]) 
Uniform sampling 
from 433 locations for 
each infiltration case 
Provided in 
source DTN 
Matrix_Rel_Perm_Low, 
Matrix_Rel_Perm_Mean, 
Matrix_Rel_Perm_High 
Unsaturated zone matrix relative 
permeability for all three infiltration 
cases (DTN: LB0307FMRADTRN.001 
[DIRS 165451]) 
Uniform sampling 
from 433 locations for 
each infiltration case 
Provided in 
source DTN 
Output DTN: SN0410T0507703.018. 
NOTES: ND = Truncated normal distribution 
E(x) = Expected value 
s(x) = Standard deviation 
CDF = cumulative distribution function 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-13 November 2004 
Table 8.2-4. Fixed Model Inputs Used in the EBS Radionuclide Transport Abstraction 
Input Name Input Description 
Source, or Developed in 
EBS RT Abstraction Value 
Max_Mass_CP_CSNF Mass of corrosion products in 
CSNF waste package 
Developed: Table 6.3-4 19,440 kg 
Max_Mass_CP_HLW Mass of corrosion products in 
CDSP waste package 
Developed: Table 6.3-4 14,230 kg 
Max_Thick_CS Maximum thickness of carbon 
steel waste package internal 
components 
IED BSC 2004 
[DIRS 169472] 
10 mm 
Max_Thick_SS Maximum thickness of stainless 
steel waste package internal 
components 
IED BSC 2004 
[DIRS 167394] 
50.8 mm 
DS_Total_Length Length of drip shield IED BSC 2004 
[DIRS 169220], Table 1 
5,805 mm 
Density_CP Density of corrosion products Weast 1985 
[DIRS 111561] 
5,240 kg m-3 
Porosity_CP Porosity of corrosion products Developed: 
Section 6.5.1.2.1.3.2 
0.4 
(fraction) 
Width_Invert Width of invert Developed: 
Equation 6.5.3.3-1 
4.00 m 
Thick_Invert Average thickness of invert 
(flow and diffusive path length) 
Developed: 
Equation 6.5.3.3-5 
0.597 m 
Vert_Cross_Sect_Area_Invert Vertical cross sectional area of 
invert 
Developed: 
Equation 6.5.3.3-2 
2.39 m2 
Density_Water Water density at 25C Weast 1985 
[DIRS 111561] 
997.0449 kg m-3 
Viscosity_Water Water viscosity at 25C Lide 2000 [DIRS 162229] 0.890  10-3 Pa s 
(0.000890 kg m-1 s-1) 
Intergranular_Porosity_Invert Porosity of crushed tuff invert 
ballast 
BSC 2004 [DIRS 169565], 
Appendix X 
0.45 
(fraction) 
Invert_Viscosity_Ref_Temp Reference temperature for 
viscosity giving temperature 
dependence of invert diffusion 
coefficient 
Reference temperature for 
free water diffusion 
coefficient (25C) 
298.15 K 
Interface_Scale_Factor Scale factor used in numerical 
approximation for computing 
mass flux distribution from 
single-continuum to dualcontinuum 
medium 
Developed: 
Section 6.5.3.5 
1  10-6 
(dimensionless) 
Intragranular_Porosity_Invert Porosity of TSw35 tuff rock 
matrix (used in dual-continuum 
invert alternative conceptual 
model) 
DTN: 
LB0207REVUZPRP.002 
[DIRS 159672], 
Spreadsheet 
Matrix_Props.xls, Row 
20, Column C 
0.131 
(fraction) 
Fracture_Aperture Unsaturated zone fracture 
aperture 
DTN: 
LB0205REVUZPRP.001 
[DIRS 159525], 
Spreadsheet 
FRACTURE_PROPERTY 
.xls, Row 20, Column L 
1.5  10-4 m 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-14 November 2004 
Table 8.2-4. Fixed Model Inputs Used in the EBS Radionuclide Transport Abstraction (Continued) 
Input Name Input Description 
Source, or Developed in 
EBS RT Abstraction Value 
Fracture_Interface_Area Unsaturated zone fracture 
interface area 
DTN: 
LB0205REVUZPRP.001 
[DIRS 159525], 
Spreadsheet 
FRACTURE_PROPERTY 
.xls, Row 20, Column R 
9.68 m2 m-3 
Active_Fracture_Parameter Unsaturated zone active 
fracture parameter for TSw35 
for all three infiltration cases 
DTN: 
LB03013DSSCP3I.001 
[DIRS 162379] 
Low=0.476 
Mean=0.569 
High=0.570 
(dimensionless) 
DTNs: 
LB0208UZDSCPLI.002 
[DIRS 161788] 
Low=1.60  10-18 m2 
LB0208UZDSCPMI.002 
[DIRS 161243] 
Mean=6.57  10-18 m2 
Matrix_Perm_TSW33 Unsaturated zone matrix 
permeability for TSw33 for all 
three infiltration cases 
LB0302UZDSCPUI.002 
[DIRS 161787] 
High=2.39  10-17 m2 
DTNs: 
LB0208UZDSCPLI.002 
[DIRS 161788]; 
Low=1.38  10-19 m2 
LB0208UZDSCPMI.002 
[DIRS 161243] 
Mean=1.77  10-19 m2 
Matrix_Perm_TSW34 Unsaturated zone matrix 
permeability for TSw34 for all 
three infiltration cases 
LB0302UZDSCPUI.002 
[DIRS 161787] 
High=2.96  10-19 m2 
DTNs: 
LB0208UZDSCPLI.002 
[DIRS 161788] 
Low=2.33  10-18 m2 
LB0208UZDSCPMI.002 
[DIRS 161243] 
Mean=4.48  10-18 m2 
Matrix_Perm_TSW35 Unsaturated zone matrix 
permeability for TSw35 for all 
three infiltration cases 
LB0302UZDSCPUI.002 
[DIRS 161787] 
High=8.55  10-18 m2 
DTNs: 
LB0208UZDSCPLI.002 
[DIRS 161788] 
Low=5.58  10-19 m2 
LB0208UZDSCPMI.002 
[DIRS 161243] 
Mean=2.00  10-19 m2 
Matrix_Perm_TSW36 Unsaturated zone matrix 
permeability for TSw36 for all 
three infiltration cases 
LB0302UZDSCPUI.002 
[DIRS 161787] 
High=7.41  10-19 m2 
UZ_Matrix_Density Unsaturated zone dry matrix 
density for TSw35 
DTN: 
SN0404T0503102.011 
[DIRS 169129] 
1,980 kg m-3 
Output DTN: SN0410T0507703.018. 
IED = information exchange drawing 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-15 November 2004 
Table 8.2-5. Calculated Model Inputs Used in the EBS Radionuclide Transport Abstraction 
Input Description 
Input Equation and 
Parameter Description 
Equation 8-1 
Invert diffusion 
coefficient 
(Equation 6.3.4.1.1-16) 
) 218 . 0 , 033 . 0 ( 863 . 1 863 . 1 
0 10 = = = s  f ND 
w S D D 
D = invert diffusion coefficient (cm2 s-1) 
0 D = free water diffusion coefficient (cm2 s-1) 
f = invert bulk porosity (fraction) 
w S = invert water saturation (fraction) 
ND = truncated normal distribution (3 standard deviations from the mean) 
 = mean 
s = standard deviation 
(Note that D is an effective value that includes the effects from porosity, 
saturation, and tortuosity.) 
Equation 8-2 
Temperature 
modification for invert 
diffusion coefficient 
(Equation 6.3.4.1.2-4) 
( ) ( ) ( ) ( ) 
. .. 
. 
. .. 
. 
- 
- - - 
- 
. .. 
. 
. .. 
. 
- 
- - - 
= 15 . 168 
15 . 293 001053 . 0 15 . 293 3272 . 1 
15 . 168 
15 . 293 001053 . 0 15 . 293 3272 . 1 
0 
2 
0 
2 
0 0 
0 10 T 
T T 
T 
T T 
T T T
T D D 
T D = invert diffusion coefficient at temperature T (cm2 s-1) 
0 T D = invert diffusion coefficient at temperature T0 (cm2 s-1) 
T = temperature (K); valid range: 293.15 K = T = 373.15 K 
0 T = reference temperature (K) (Invert_Viscosity_Ref_Temp) 
Equation 8-3 
Diffusion coefficient of 
unsaturated zone matrix 
and fractures 
(Equation 6.5.3.6-2) 
me m ms k D 10 10 log 165 . 0 0138 . 0 49 . 3 log + + - = . 
ms D = diffusion coefficient of unsaturated zone matrix (cm2 s-1) 
m . = unsaturated zone matrix water content (percent) 
me k = effective permeability of unsaturated zone matrix (m2) 
(Note that Dms is an effective value that includes the effects from porosity, 
saturation, and tortuosity in the rock matrix.) 
Equation 8-4 
Effective permeability of 
unsaturated zone matrix 
(Equation 6.5.3.6-3) 
m rm me k k k = 
me k = effective permeability of unsaturated zone tuff matrix (m2) 
rm k = relative permeability of unsaturated zone tuff matrix (dimensionless) 
m k = intrinsic permeability of unsaturated zone tuff matrix (m2) 
(Matrix_Perm_TSWxx, xx = 33, 34, 35, 36) 
Equation 8-5 
Effective water 
saturation of corrosion 
products 
(Equation 6.5.1.2.1-27) 
( ) 45 . 2 / 1 6 
, ln 10 28 . 3 - - -  = RH s S CP CP we 
CP we S , = effective water saturation of corrosion products 
CP s = specific surface area of corrosion products (m2 kg-1) 
(CP_Spec_Surf_Area) 
RH = relative humidity 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-16 November 2004 
Table 8.2-5. Calculated Model Inputs Used in the EBS Radionuclide Transport Abstraction (Continued) 
Input Description 
Input Equation and 
Parameter Description 
Equation 8-6 
Pore volume of 
corrosion products 
(Equation 6.5.3.1.1-1) 
. .. 
. 
. .. 
. 
- 
= 
CP 
CP 
FeOx 
CP 
CP 
m V 
f 
f 
. 1 
CP V = pore volume of corrosion products (m3) 
CP m = mass of corrosion products (kg) 
FeOx . = density of corrosion products (kg m-3) (Density_CP) 
CP f = porosity of corrosion products (m3 void m-3 bulk volume) (Porosity_CP) 
Equation 8-7 
Mass of corrosion 
products 
(Equations 6.5.3.2-1 to 
6.5.3.2-5) 
2 1 ) ( CP CP CP m m t m + = 
CP m = mass of corrosion products (kg) 
t = time since waste package emplacement (yr) 
0 t = time when waste package breach occurs (yr) 
1 CP m = 
. .
.
. .
.
. 
> - 
= - . .
.
. 
. .
.
. - 
1 0 
1 0 
1 
0 
, 
3
1 
, 
3
1 
f CPf 
f CPf 
f 
t t t m 
t t t m 
t 
t t 
CPf m = mass of corrosion products when internal components are fully 
degraded (kg) (Max_Mass_CP_CSNF or Max_Mass_CP_HLW) 
1 f t = lifetime of carbon steel (yr) 
= 
1 r 
_CS) (Max_Thick 1000 
1 r = corrosion rate of carbon steel (m yr-1) (CS_Corrosion_Rate) 
2 CP m = 
. .
.
. .
.
. 
> - 
= - . .
.
. 
. .
.
. - 
2 0 
2 0 
2 
0 
, 
3
2 
, 
3
2 
f CPf 
f CPf 
f 
t t t m 
t t t m 
t 
t t 
2 f t = lifetime of stainless steel (yr) 
= 
2 r 
_SS) (Max_Thick 1000 
2 r = corrosion rate of stainless steel (m yr-1) (SS_Corrosion_Rate) 
Output DTN: SN0410T0507703.018. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-17 November 2004 
Input parameters for the dual-continuum invert alternative conceptual model are listed in 
Table 8.2-6. Equations for calculating the intergranular and intragranular diffusion coefficients 
are listed in Table 8.2-7. 
Table 8.2-6. Invert Diffusion Coefficient Alternative Conceptual Model Parameters 
Input Name Input Description 
Where Developed in 
EBS RT Abstraction Value 
Invert_Geometry_Coef Dimensionless geometrydependent 
coefficient for 
intergranular-intragranular mass 
transfer coefficient 
Section 6.6.4.1 8 - 21 
(dimensionless) 
Uniform 
Diff_Length_Inv_Inter_Intra Characteristic length of the 
matrix structure 
Section 6.6.4.1 5 mm 
Crit_Moisture_Content_Intra Critical moisture content of invert 
intragranular continuum 
Section 6.6.5.1 0.089 
(fraction) 
Crit_Moisture_Content_Inter Critical moisture content of invert 
intergranular continuum 
Section 6.6.5.1 0.00932  0.0612 
Uniform 
Diff_Threshold_Invert Threshold value of diffusion 
coefficient in intragranular invert 
continuum 
Section 6.6.5.2 1  10-12 cm2 s-1 
Sat_Diff_Coeff_Matrix Diffusion coefficient in saturated 
UZ matrix 
Section 6.6.5.2 9.24  10-7 cm2 s-1 
Output DTN: SN0410T0507703.018. 
Table 8.2-7. Calculated Model Inputs Used in the EBS Radionuclide Transport Abstraction Invert Diffusion 
Coefficient Alternative Conceptual Model 
Input Description 
Input Equation and 
Parameter Description 
Equation 8-8 
Invert intergranular 
continuum diffusion 
coefficient 
(Equation 6.6.5.2-3) C limit inter 
C 
C I 
C 
inter 
inter 
D D 
D D 
. . 
. . 
. f 
. . 
f 
. 
< = 
= . .. 
. 
. .. 
. 
- 
- 
. .. 
. 
. .. 
. 
= 
, 
, 
100 100 
45 . 0 0 
0 D = free water diffusion coefficient (cm2 s-1) 
inter D = invert intergranular continuum diffusion coefficient (cm2 s-1) 
I f = ( ) intra inter inter f f f - + 1 = bulk porosity of invert (fraction) 
inter f = invert intergranular continuum porosity (fraction) 
(Intergranular_Porosity_Invert) 
intra f = invert intragranular continuum porosity (fraction) 
(Intragranular_Porosity_Invert) 
. = invert bulk moisture content (percent) 
C . = invert intergranular continuum critical moisture content (percent) 
(Crit_Moisture_Content_Inter) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-18 November 2004 
Table 8.2-7. Calculated Model Inputs Used in the EBS Radionuclide Transport Abstraction Invert Diffusion 
Coefficient Alternative Conceptual Model (Continued) 
Input Description 
Input Equation and 
Parameter Description 
Equation 8-9 
Invert intragranular 
continuum diffusion 
coefficient 
(Equations 6.6.5.2-5 
and 6.6.5.2-6) 
min intra limit intra 
min intra 
p 
intra 
intra 
ms intra 
D D 
D D 
. . 
. . 
f 
. 
< = 
= . .. 
. 
. .. 
. 
= 
, 
, 
100 
intra D = invert intragranular continuum diffusion coefficient (cm2 s-1) 
ms D = tuff matrix saturated diffusion coefficient (cm2 s-1) (Sat_Diff_Coeff_Matrix) 
limit D = threshold value of diffusion coefficient in intragranular invert continuum 
(cm2 s-1) (Diff_Threshold_Invert) 
intra . = invert intragranular continuum moisture content (percent) 
intra f = invert intragranular continuum porosity (fraction) 
(Intragranular_Porosity_Invert) 
p = 
intra 
min 
ms limit D D 
f 
. 
10 10 
10 10 
log 
100 
log 
log log 
- .. 
. 
.. 
. 
- 
min . = critical moisture content of invert intragranular continuum (percent) 
(Crit_Moisture_Content_Intra) 
Output DTN: SN0410T0507703.018. 
8.3 EVALUATION OF YUCCA MOUNTAIN REVIEW PLAN CRITERIA 
This model report documents the abstraction model for flow of liquid and transport of 
radionuclides through the EBS. This section provides responses to the Yucca Mountain Review 
Plan, Final Report acceptance criteria applicable to this model report. Being conceptual in 
nature, it is not possible to evaluate quantitatively many of the Yucca Mountain Review Plan, 
Final Report (NRC 2003 [DIRS 163274]) acceptance criteria in Section 4.2.1. 
The relevance of this model report to Yucca Mountain Review Plan, Final Report (NRC 2003 
[DIRS 163274], Section 2.2.1.3.3) criteria for Quantity and Chemistry of Water Contacting 
Engineered Barriers and Waste Forms, which are based on meeting the requirements of 
10 CFR 63.114(a)(c) and (e)(g) [DIRS 158535], is as follows: 
Acceptance Criterion 1System Description and Model Integration are Adequate. 
(1) Total system performance assessment adequately incorporates important design 
features, physical phenomena, and couplings, and uses consistent and appropriate 
assumptions throughout the quantity and chemistry of water contacting engineered 
barriers and waste forms abstraction process. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-19 November 2004 
Response: The EBS radionuclide transport abstraction incorporates important design features, 
physical phenomena, and couplings, and uses consistent assumptions throughout the evaluation 
of the quantity of water contacting engineered barriers and waste forms. Sections 6.3.2 and 6.3.3 
describe the conceptual model for water flux through the EBS. Section 6.5.1 describes the 
mathematical description of the EBS flow model. These sections provide information on 
seepage, effectiveness of the EBS components and mechanisms for breach or failure of the drip 
shield and waste package. Important general technical information related to water flow through 
the EBS can also be found throughout Section 6. 
(2) The abstraction of the quantity and chemistry of water contacting engineered barriers 
and waste forms uses assumptions, technical bases, data, and models, that are 
appropriate and consistent with other related U.S. Department of Energy abstractions. 
For example, the assumptions used for the quantity and chemistry of water contacting 
engineered barriers and waste forms are consistent with the abstractions of 
Degradation of Engineered Barriers (NRC 2003 [DIRS 163274], Section 2.2.1.3.1); 
Mechanical Disruption of Engineered Barriers (NRC 2003 [DIRS 163274], 
Section 2.2.1.3.2); Radionuclide Release Rates and Solubility Limits 
(Section 2.2.1.3.4); Climate and Infiltration (NRC 2003 [DIRS 163274], 
Section 2.2.1.3.5); and Flow Paths in the Unsaturated Zone (NRC 2003 
[DIRS 163274], Section 2.2.1.3.6). The descriptions and technical bases provide 
transparent and traceable support for the abstraction of quantity and chemistry of water 
contacting engineered barriers and waste forms. 
Response: The EBS radionuclide transport abstraction uses assumptions, technical bases, data, 
and models that are consistent with other related U.S. Department of Energy abstractions. 
Sections 6.3.2, 6.3.3 and 6.5.1 of this model report provide descriptions and technical bases to 
support the quantity-related portion of the abstraction of quantity and chemistry of water 
contacting engineered barriers and waste forms. Section 5 provides assumptions that are relevant 
to the EBS flow model. 
(3) Important design features, such as waste package design and material selection, drip 
shield, ground support, thermal loading strategy, and degradation processes, are 
considered during the determination of initial and boundary conditions for calculations 
of the quantity of water contacting engineered barriers and waste forms. 
Response: Sections 6.3 and 6.5 provide the technical bases and details of model features for the 
EBS flow model. Section 6.3.2 describes drip shield design, effectiveness and breaching. 
Section 6.3.3 describes waste package design, breaching and impact of heat generation. Sections 
6.3.3 and 6.5.3 provide invert model features. 
(4) The U.S. Department of Energy reasonably accounts for the range of environmental 
conditions expected inside breached waste packages and in the engineered barrier 
environment surrounding the waste package. For example, the U.S. Department of 
Energy should provide a description and sufficient technical bases for its abstraction of 
changes in hydrologic properties in the near field, caused by coupled 
thermal-hydrologic-mechanical-chemical processes. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-20 November 2004 
Response: Spatial and temporal abstractions address physical couplings (thermal-hydrologicmechanical-
chemical). Sections 6.3 and 6.5 provide descriptions of coupled effects for the flow 
model. These effects include heat generation inside the waste package and condensation on the 
drip shield surface. The seepage and imbibition fluxes are also the product of coupled 
thermal-hydrologic-mechanical-chemical processes. 
(5) Sufficient technical bases and justification are provided for total system performance 
assessment assumptions and approximations for modeling coupled thermal-hydrologic 
mechanical-chemical effects on seepage and flow, the waste package chemical 
environment, and the chemical environment for radionuclide release. The effects of 
distribution of flow on the amount of water contacting the engineered barriers and 
waste forms are consistently addressed, in all relevant abstractions. 
Response: The technical bases and justification are provided for total system performance 
assessment assumptions and approximations for modeling coupled thermal-hydrologicmechanical-
chemical effects on flow and radionuclide release throughout Sections 5 and 6. The 
effects of distribution of flow on the amount of water contacting the engineered barriers and 
waste forms are consistently addressed in Sections 6.3 and 6.5. 
(6) The expected ranges of environmental conditions within the waste package 
emplacement drifts, inside of breached waste packages, and contacting the waste 
forms and their evolution with time are identified. 
Response: These are provided in Sections 6.3, 6.5 and 6.7. Examples include the effects of the 
drip shield on the quantity of water (Sections 6.3.2 and 6.5.1); conditions that promote corrosion 
of engineered barriers and degradation of waste forms (Sections 6.3 and 6.5); wet and dry cycles; 
and size and distribution of penetrations of engineered barriers. 
(7) The model abstraction for quantity and chemistry of water contacting engineered 
barriers and waste forms is consistent with the detailed information on engineered 
barrier design and other engineered features. For example, consistency is 
demonstrated for: (i) dimensionality of the abstractions; (ii) various design features 
and site characteristics; and (iii) alternative conceptual approaches. Analyses are 
adequate to demonstrate that no deleterious effects are caused by design or site 
features that the U.S. Department of Energy does not take into account in this 
abstraction. 
Response: The EBS radionuclide transport abstraction is consistent with detailed information on 
engineered barrier design and other engineered features. Analysis discussions in Section 6 
demonstrate that no deleterious effects are caused by design or site features that are not taken 
into account in this abstraction. Section 6.7 provides a summary discussion on the capability of 
the engineered barriers. 
(8) Adequate technical bases are provided, including activities such as independent 
modeling, laboratory or field data, or sensitivity studies, for inclusion of any 
thermal-hydrologic-mechanical-chemical couplings and features, events, and 
processes. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-21 November 2004 
Response: Technical bases are provided, including activities such as independent modeling, 
laboratory or field data, or sensitivity studies, for inclusion of any thermal-hydrologicmechanical-
chemical couplings and features, events, and processes. These are provided 
throughout Sections 6 and 7. 
(9) Performance-affecting processes that have been observed in thermal-hydrologic tests 
and experiments are included into the performance assessment. For example, the 
U.S. Department of Energy either demonstrates that liquid water will not reflux into 
the underground facility or incorporates refluxing water into the performance 
assessment calculation, and bounds the potential adverse effects of alteration of the 
hydraulic pathway that result from refluxing water. 
Response: Performance-affecting processes that have been observed in thermal-hydrologic tests 
and experiments are included primarily through the inputs (e.g., seepage values from Abstraction 
of Drift Seepage (BSC 2004 [DIRS 169131]), described in Section 6.3.2 of this model report, 
required to implement the EBS radionuclide transport abstraction. 
Acceptance Criterion 2Data are Sufficient for Model Justification. 
(1) Geological, hydrological, and geochemical values used in the license application are 
adequately justified. Adequate description of how the data were used, interpreted, and 
appropriately synthesized into the parameters is provided. 
Response: The EBS radionuclide transport abstraction provides the technical justification for 
geological, hydrological, and geochemical values used. There is also a description of how the 
data were used, interpreted, and synthesized into associated parameter values. Section 6.5.2 
provides a summary discussion on the use and interpretation of data used in the EBS flow and 
transport models. The discussion includes the range, distribution and uncertainty of model data. 
Detailed description of data and technical justification of values used are provided throughout 
Sections 6.3 and 6.5. 
(2) Sufficient data were collected on the characteristics of the natural system and 
engineered materials to establish initial and boundary conditions for conceptual 
models of thermal-hydrologic-mechanical-chemical coupled processes, that affect 
seepage and flow and the engineered barrier chemical environment. 
Response: Data and sources of data are provided in Section 4.1 on the characteristics of the 
natural system and engineered materials needed to establish initial and boundary conditions for 
conceptual models of thermal-hydrologic-mechanical-chemical coupled processes that affect 
flow. Collection of input data used in this model report was done using acceptable techniques 
under the YMP quality assurance plan; specific techniques are provided in Sections 4.1.1 to 
4.1.3. 
(4) Sufficient information to formulate the conceptual approach(es) for analyzing water 
contact with the drip shield, engineered barriers, and waste forms is provided. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 8-22 November 2004 
Response: Information required to formulate the conceptual approaches for analyzing water 
contact with the drip shield, engineered barriers, and waste forms is provided in Sections 6.3 and 
6.5. Sections 6.3.2, 6.3.3 and 6.5.1 present the conceptual models used for water flux through the 
Engineered Barrier System, together with information on drip shield effectiveness, drip shield 
and waste package breaching, seepage and imbibition flux from the unsaturated zone matrix. 
Acceptance Criterion 3Data Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
(1) Models use parameter values, assumed ranges, probability distributions, and bounding 
assumptions that are technically defensible, reasonably account for uncertainties and 
variabilities, and do not result in an under representation of the risk estimate. 
Response: The EBS radionuclide transport abstraction uses parameter values, assumed ranges, 
probability distributions, and bounding assumptions that account for uncertainties and 
variabilities, and that do not result in an under-representation of the risk estimate. Section 4.1 
lists the data and parameters used, together with their sources. Section 6.5.2 provides a summary 
of the base case model inputs together with associated uncertainties. 
(2) Parameter values, assumed ranges, probability distributions, and bounding 
assumptions used in the total system performance assessment calculations of quantity 
and chemistry of water contacting engineered barriers and waste forms are technically 
defensible and reasonable, based on data from the Yucca Mountain region (e.g., results 
from large block and drift-scale heater and niche tests), and a combination of 
techniques that may include laboratory experiments, field measurements, natural 
analog research, and process-level modeling studies. 
Response: Parameter values, assumed ranges, probability distributions, and bounding 
assumptions used in the total system performance assessment calculations of quantity of water 
contacting engineered barriers and waste forms are based on data from the Yucca Mountain 
region, laboratory experiments, field measurements, natural analog research, and process-level 
modeling studies. Section 4.1 lists the data and parameters used, together with their sources. 
Section 6.5.2 provides a summary of the base case model inputs together with associated 
uncertainties. 
(3) Input values used in the total system performance assessment calculations of quantity 
and chemistry of water contacting engineered barriers (e.g., drip shield and waste 
package) are consistent with the initial and boundary conditions and the assumptions 
of the conceptual models and design concepts for the Yucca Mountain site. 
Correlations between input values are appropriately established in the 
U.S. Department of Energy total system performance assessment. Parameters used to 
define initial conditions, boundary conditions, and computational domain in sensitivity 
analyses involving coupled thermal-hydrologic-mechanical-chemical effects on 
seepage and flow, the waste package chemical environment, and the chemical 
environment for radionuclide release, are consistent with available data. Reasonable 
or conservative ranges of parameters or functional relations are established. 

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Response: Input values used in the total system performance assessment calculations of quantity 
of water contacting engineered barriers (e.g., drip shield and waste package) are consistent with 
the initial and boundary conditions and the assumptions of the conceptual models and design 
concepts for the Yucca Mountain site. Reasonable or conservative ranges of parameters or 
functional relations have been established. Section 4.1 lists the data and parameters used, 
together with their sources. Section 6.5.2 provides a summary of the base case model inputs 
together with associated uncertainties. 
(4) Uncertainty is adequately represented in parameter development for conceptual 
models, process models, and alternative conceptual models considered in developing 
the abstraction of radionuclide release rates and solubility limits, either through 
sensitivity analyses or use of bounding analyses. 
Response: Adequate representation of uncertainties in the characteristics of the natural system 
and engineered materials is provided in parameter development for conceptual models, 
process-level models, and alternative conceptual models. In some instances, uncertainty is 
constrained using conservative limits. Parameter development for the models described in this 
model report is provided throughout Sections 6.3, 6.4, 6.5 and 6.6. 
Acceptance Criterion 4Model Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
(1) Alternative modeling approaches of features, events, and processes are considered and 
are consistent with available data and current scientific understanding, and the results 
and limitations are appropriately considered in the abstraction. 
Response: Alternative modeling approaches of features, events, and processes are considered in 
Sections 6.4 and 6.6 and are consistent with available data and current scientific understanding, 
and the results and limitations are considered. 
(2) Alternative modeling approaches are considered and the selected modeling approach is 
consistent with available data and current scientific understanding. A description that 
includes a discussion of alternative modeling approaches not considered in the final 
analysis and the limitations and uncertainties of the chosen model is provided. 
Response: Alternative modeling approaches are considered in Sections 6.4 and 6.6. The 
selected modeling approach is consistent with available data and current scientific understanding. 
A description that includes a discussion of alternative modeling approaches not considered in the 
final analysis and the limitations and uncertainties of the chosen model is provided. 
(3) Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog 
information and process-level modeling studies; and the treatment of conceptual 
model uncertainty does not result in an under-representation of the risk estimate. 

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Response: Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog information 
and process-level modeling studies. The fundamental relationships, e.g., mass balance and flow 
equations, upon which the EBS radionuclide transport abstraction is based, are well-established 
with a long history of use in the scientific community and as such are not subject to significant 
uncertainty. In addition, the alternative conceptual models have been screened out (Section 6.4), 
thereby increasing confidence in the selected conceptual model. Other sources of uncertainty 
involve modeling choices (e.g., assumptions, geometry) that, because of their conservative 
nature, effectively bound uncertainty. This treatment of conceptual model uncertainty does not 
result in an under-representation of the risk estimate. 
(4) Adequate consideration is given to effects of thermal-hydrologic-mechanical-chemical 
coupled processes in the assessment of alternative conceptual models. These effects 
may include: (i) thermal-hydrologic effects on gas, water, and mineral chemistry; 
(ii) effects of microbial processes on the engineered barrier chemical environment and 
the chemical environment for radionuclide release; (iii) changes in water chemistry 
that may result from the release of corrosion products from the engineered barriers and 
interactions between engineered materials and ground water; and (iv) changes in 
boundary conditions (e.g., drift shape and size) and hydrologic properties, relating to 
the response of the geomechanical system to thermal loading. 
Response: Consideration is given in Sections 6.4 and 6.6 to effects of thermal-hydrologicmechanical-
chemical coupled processes in the assessment of alternative conceptual models. 
Acceptance Criterion 5Model Abstraction Output Is Supported by Objective 
Comparisons. 
(1) The models implemented in this total system performance assessment abstraction 
provide results consistent with output from detailed process-level models and/or 
empirical observations (laboratory and field testings and/or natural analogs). 
Response: The models implemented in this total system performance assessment abstraction 
provide results consistent with output from detailed process-level models and/or empirical 
observations (laboratory testings). For example, Sections 6.5.1 and 7.1 provide comparison of 
the drip shield and waste package flux splitting models with breached drip shield and waste 
package experiments. 
(2) Abstracted models for coupled thermal-hydrologic-mechanical-chemical effects on 
seepage and flow and the engineered barrier chemical environment, as well as on the 
chemical environment for radionuclide release, are based on the same assumptions and 
approximations demonstrated to be appropriate for process-level models or closely 
analogous natural or experimental systems. For example, abstractions of processes, 
such as thermally induced changes in hydrological properties, or estimated diversion 
of percolation away from the drifts, are adequately justified by comparison to results 
of process-level modeling, that are consistent with direct observations and field 
studies. 

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Response: Abstracted models for coupled thermal-hydrologic-mechanical-chemical effects on 
flow and radionuclide release are based on the same assumptions and approximations 
demonstrated to be appropriate for process-level models or closely analogous natural or 
experimental systems, as demonstrated throughout Sections 5 and 6. 
(3) Accepted and well-documented procedures are used to construct and test the numerical 
models that simulate coupled thermal-hydrologic-mechanical-chemical effects on 
seepage and flow, engineered barrier chemical environment, and the chemical 
environment for radionuclide release. Analytical and numerical models are 
appropriately supported. Abstracted model results are compared with different 
mathematical models, to judge robustness of results. 
Response: The EBS radionuclide transport abstraction uses accepted and well-documented 
procedures to construct and test the numerical models that simulate coupled thermal-hydrologicmechanical-
chemical effects on flow and radionuclide release, as provided throughout Sections 6 
and 7. Technical support is presented for analytical and numerical models. 
The relevance of this model report to the Yucca Mountain Review Plan criteria for Radionuclide 
Release Rates and Solubility Limits (NRC 2003 [DIRS 163274], Section 2.2.1.3.4), which are 
based on meeting the requirements of 10 CFR 63.114(a)(c) and (e)(g) [DIRS 158535], is as 
follows: 
Acceptance Criterion 1System Description and Model Integration Are Adequate. 
(1) Total system performance assessment adequately incorporates important design 
features, physical phenomena, and couplings, and uses consistent and appropriate 
assumptions throughout the radionuclide release rates and solubility limits abstraction 
process. 
Response: Total system performance assessment adequately incorporates important design 
features, physical phenomena, and couplings, and uses consistent and appropriate assumptions 
throughout the radionuclide release rates and solubility limits abstraction process. Section 6.3.4 
describes the conceptual model for EBS transport model. Sections 6.5.1 and 6.5.3 describe the 
mathematical description of the EBS transport model components. These sections provide 
information on diffusion, retardation, transport through stress corrosion cracks and EBS-UZ 
boundary condition implementation. Important general technical information related to 
radionuclide transport through the EBS can also be found throughout Section 6. 
(2) The abstraction of radionuclide release rates uses assumptions, technical bases, data, 
and models that are appropriate and consistent with other related U.S. Department of 
Energy abstractions. For example, the assumptions used for this model abstraction are 
consistent with the abstractions of Degradation of Engineered Barriers (NRC 2003 
[DIRS 163274], Section 2.2.1.3.1); Mechanical Disruption of Engineered Barriers 
(NRC 2003 [DIRS 163274], Section 2.2.1.3.2); Quantity and Chemistry of Water 
Contacting Engineered Barriers and Waste Forms (NRC 2003 [DIRS 163274], 
Section 2.2.1.3.3); Climate and Infiltration (NRC 2003 [DIRS 163274], 
Section 2.2.1.3.5); and Flow Paths in the Unsaturated Zone (NRC 2003 

EBS Radionuclide Transport Abstraction 
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[DIRS 163274], Section 2.2.1.3.6). The descriptions and technical bases provide 
transparent and traceable support for the abstraction of radionuclide release rates. 
Response: The EBS radionuclide transport abstraction uses assumptions, technical bases, data, 
and models consistent with other related U.S. Department of Energy abstractions. The 
descriptions and technical bases described in Sections 6.3.4, 6.5.1, and 6.5.3 provide support for 
the abstraction of radionuclide release rates. Section 5 provides assumptions that are relevant to 
the EBS transport model. 
(3) The abstraction of radionuclide release rates provides sufficient, consistent design 
information on waste packages and engineered barrier systems. For example, 
inventory calculations and selected radionuclides are based on the detailed information 
provided on the distribution (both spatially and by compositional phase) of the 
radionuclide inventory, within the various types of high-level radioactive waste. 
Response: The EBS radionuclide transport abstraction provides consistent design information 
on waste packages and engineered barrier systems (Section 4.1 and throughout Section 6). 
Selected radionuclides are based on the detailed information provided on the distribution (both 
spatially and by compositional phase) of the radionuclide inventory, within the various types of 
high-level radioactive waste. Input data on radionuclides are provided in Section 4.1 and 6.5.2. 
(4) The U.S. Department of Energy reasonably accounts for the range of environmental 
conditions expected inside breached waste packages and in the engineered barrier 
environment surrounding the waste package. For example, the U.S. Department of 
Energy should provide a description and sufficient technical bases for its abstraction of 
changes in hydrologic properties in the near field, caused by coupled 
thermal-hydrologic-mechanical-chemical processes. 
Response: The EBS radionuclide transport abstraction accounts for the range of environmental 
conditions expected inside breached waste packages and in the engineered barrier environment 
surrounding the waste package. Sections 6.3 and 6.5 describe provisions for thermal, chemical, 
and hydrologic conditions inside and surrounding the waste package. 
(5) The description of process-level conceptual and mathematical models is sufficiently 
complete, with respect to thermal-hydrologic processes affecting radionuclide release 
from the emplacement drifts. For example, if the U.S. Department of Energy 
uncouples coupled processes, the demonstration that uncoupled model results bound 
predictions of fully coupled results is adequate. 
Response: The description of process-level conceptual and mathematical models, with respect 
to thermal-hydrologic processes affecting radionuclide release from the emplacement drifts is 
provided in Section 6.5. 
(6) Technical bases for inclusion of any thermal-hydrologic-mechanical-chemical 
couplings and features, events, and processes in the radionuclide release rates and 
solubility Review Plan for Safety Analysis Report limits model abstraction are 
adequate. For example, technical bases may include activities, such as independent 
modeling, laboratory or field data, or sensitivity studies. 

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Response: Technical bases for inclusion of thermal-hydrologic-mechanical-chemical couplings 
and the disposition of features, events, and processes in the EBS radionuclide transport 
abstraction are summarized in Section 6.2. 
Acceptance Criterion 2Data Are Sufficient for Model Justification. 
(1) Geological, hydrological, and geochemical values used in the license application are 
adequately justified. Adequate description of how the data were used, interpreted, and 
appropriately synthesized into the parameters is provided. 
Response: Technical justification for the geological, hydrological, and geochemical values used 
in the EBS radionuclide transport abstraction is provided. There is also a discussion of how the 
data are used, interpreted, and synthesized into associated parameters values. Section 6.5.2 
provides a summary discussion on the use and interpretation of data used in the EBS flow and 
transport models. The discussion includes the range, distribution and uncertainty of model data. 
Detailed descriptions of data and technical justification of values used are provided throughout 
Sections 6.3 and 6.5. 
(2) Sufficient data have been collected on the characteristics of the natural system and 
engineered materials to establish initial and boundary conditions for conceptual 
models and simulations of thermal-hydrologic-chemical coupled processes. For 
example, sufficient data should be provided on design features, such as the type, 
quantity, and reactivity of materials, that may affect radionuclide release for this 
abstraction. 
Response: Section 4.1 provides data on characteristics of the natural system and engineered 
materials needed to establish initial and boundary conditions for the EBS radionuclide transport 
abstraction conceptual models and simulations of thermal-hydrologic-chemical coupled 
processes. 
(4) The corrosion and radionuclide release testing program for high-level radioactive 
waste forms intended for disposal provides consistent, sufficient, and suitable data for 
the in-package and in-drift chemistry used in the abstraction of radionuclide release 
rates and solubility limits. For expected environmental conditions, the 
U.S. Department of Energy provides sufficient justification for the use of test results, 
not specifically collected from the Yucca Mountain site, for engineered barrier 
components, such as high-level radioactive waste forms, drip shield, and backfill. 
Response: The corrosion and radionuclide release testing program for HLW forms intended for 
disposal provides data for the in-package and in-drift chemistry used in the EBS radionuclide 
transport abstraction (Section 4.1). For expected environmental conditions, the EBS 
radionuclide transport abstraction provides justification for the use of test results, not specifically 
collected from the Yucca Mountain site, for engineered barrier components, such as HLW forms 
and drip shield (Sections 6.3 and 6.5). 

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Acceptance Criterion 3Data Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
(1) Models use parameter values, assumed ranges, probability distributions, and bounding 
assumptions that are technically defensible, reasonably account for uncertainties and 
variabilities, and do not result in an under representation of the risk estimate. 
Response: The EBS radionuclide transport abstraction uses parameter values, assumed ranges, 
probability distributions, and/or bounding assumptions that account for uncertainties and 
variabilities, and that do not cause an under-representation of the risk estimate. Section 4.1 lists 
the data and parameters used, together with their sources. Section 6.5.2 provides a summary of 
the base case model inputs together with associated uncertainties. 
(2) Parameter values, assumed ranges, probability distributions, and bounding 
assumptions used in the abstractions of radionuclide release rates and solubility limits 
in the total system performance assessment are technically defensible and reasonable 
based on data from the Yucca Mountain region, laboratory tests, and natural analogs. 
For example, parameter values, assumed ranges, probability distributions, and 
bounding assumptions adequately reflect the range of environmental conditions 
expected inside breached waste packages. 
Response: Parameter values, assumed ranges, probability distributions, and bounding 
assumptions used in the abstractions of radionuclide release rates and solubility limits in the total 
system performance assessment are based on data from the Yucca Mountain region, laboratory 
tests, and natural analogs. Parameter values, assumed ranges, probability distributions, and 
bounding assumptions reflect the range of environmental conditions expected inside breached 
waste packages. Section 4.1 lists the data and parameters used, together with their sources. 
Section 6.5.2 provides a summary of the base case model inputs together with associated 
uncertainties. 
(3) DOE uses reasonable or conservative ranges of parameters or functional relations to 
determine effects of coupled thermal-hydrologic-chemical processes on radionuclide 
release. These values are consistent with the initial and boundary conditions and the 
assumptions for the conceptual models and design concepts for natural and engineered 
barriers at the Yucca Mountain site. If any correlations between the input values exist, 
they are adequately established in the total system performance assessment. For 
example, estimations are based on a thermal loading and ventilation strategy; 
engineered barrier system design (including drift liner, backfill, and drip-shield); and 
natural system masses and fluxes that are consistent with those used in other 
abstractions. 

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Response: The EBS radionuclide transport abstraction uses reasonable or conservative ranges of 
parameters or functional relations to determine effects of coupled thermal-hydrologic-chemical 
processes on radionuclide release. These values are consistent with the initial and boundary 
conditions and the assumptions for the conceptual models and design concepts for natural and 
engineered barriers at the Yucca Mountain site. Section 4.1 lists the data and parameters used, 
together with their sources. Section 6.5.2 provides a summary of the base case model inputs 
together with associated uncertainties. 
(4) Uncertainty is adequately represented in parameter development for conceptual 
models, process models, and alternative conceptual models considered in developing 
the abstraction of radionuclide release rates and solubility limits, either through 
sensitivity analyses or use of bounding analyses. 
Response: Uncertainty is represented in parameter development for conceptual models, process 
models, and alternative conceptual models considered in developing the abstraction of 
radionuclide release rates and solubility limits. Parameter development for the models described 
in this model report is provided throughout Sections 6.3, 6.4, 6.5, and 6.6. 
(5) Parameters used to describe flow through and out of the engineered barrier, 
sufficiently bound the effects of backfill, excavation-induced changes, and thermally 
induced mechanical changes that affect flow. 
Response: The EBS radionuclide transport abstraction considers the uncertainties, in the 
characteristics of the natural system and engineered materials, such as the type, quantity, and 
reactivity of material, in establishing initial and boundary conditions for conceptual models and 
simulations of thermal-hydrologic-chemical coupled processes that affect radionuclide release. 
Parameter development for the models described in this model report is provided throughout 
Sections 6.3, 6.4, 6.5, and 6.6. 
(8) DOE adequately considers the uncertainties, in the characteristics of the natural system 
and engineered materials, such as the type, quantity, and reactivity of material, in 
establishing initial and boundary conditions for conceptual models and simulations of 
thermal-hydrologic-chemical coupled processes that affect radionuclide release. 
Response: Parameters used to describe flow through and out of the engineered barrier bound the 
effects of excavation-induced changes and thermally induced mechanical changes that affect 
flow. 
Acceptance Criterion 4Model Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
(1) Alternative modeling approaches of features, events, and processes are considered and 
are consistent with available data and current scientific understanding, and the results 
and limitations are appropriately considered in the abstraction. 

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Response: Alternative modeling approaches of features, events, and processes are considered in 
Section 6.4 and are consistent with available data and current scientific understanding, and the 
results and limitations are considered. 
(2) In considering alternative conceptual models for radionuclide release rates and 
solubility limits, DOE uses appropriate models, tests, and analyses that are sensitive to 
the processes modeled for both natural and engineering systems. Conceptual model 
uncertainties are adequately defined and documented, and effects on conclusions 
regarding performance are properly assessed. For example, in modeling flow and 
radionuclide release from the drifts, DOE represents significant discrete features, such 
as fault zones, separately, or demonstrates that their inclusion in the equivalent 
continuum model produces a conservative effect on calculated performance. 
Response: In considering alternative conceptual models for radionuclide release rates and 
solubility limits (Sections 6.4. and 6.6), the EBS radionuclide transport abstraction uses models 
and analyses that are sensitive to the processes modeled for both natural and engineering 
systems. Conceptual model uncertainties are defined and documented, and effects on 
conclusions regarding performance are assessed. The fundamental relationships, e.g., mass 
balance and flow equations, upon which the EBS radionuclide transport abstraction is based, are 
well-established with a long history of use in the scientific community and as such are not 
subject to significant uncertainty. In addition, the alternative conceptual models have been 
screened out (Section 6.4), thereby increasing confidence in the selected conceptual model. 
Other sources of uncertainty involve modeling choices (e.g., assumptions, geometry) that, 
because of their conservative nature, effectively bound uncertainty. 
(3) Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog 
information and process-level modeling studies; and the treatment of conceptual 
model uncertainty does not result in an under-representation of the risk estimate. 
Response: Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog information 
and process-level modeling studies; and the treatment of conceptual model uncertainty does not 
result in an under-representation of the risk estimate, as discussed throughout Section 6. Section 
6.5.2 provides discussions on parameter uncertainty. 
(4) The effects of thermal-hydrologic-chemical coupled processes that may occur in the 
natural setting, or from interactions with engineered materials, or their alteration 
products, on radionuclide release, are appropriately considered. 
Response: The effects of thermal-hydrologic-chemical coupled processes that may occur in the 
natural setting or from interactions with engineered materials or their alteration products, on 
radionuclide release, are considered in Section 6. For example, the effect of corrosion products 
on the transport of radionuclides is provided in Sections 6.3.4, 6.5.1, and 6.5.3. 

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Acceptance Criterion 5Model Abstraction Output Is Supported by Objective 
Comparisons. 
(1) The models implemented in this total system performance assessment abstraction 
provide results consistent with output from detailed process-level models and/or 
empirical observations (laboratory and field testings and/or natural analogs). 
Response: The models implemented in this total system performance assessment abstraction 
provide results consistent with output from detailed process-level models and/or empirical 
observations (laboratory testings), as described in Sections 6.3, 6.5, and 7. Section 7 provides 
comparisons of models developed in this model report with other models and experimental 
results. 
(3) DOE adopts well-documented procedures that have been accepted by the scientific 
community to construct and test the numerical models, used to simulate coupled 
thermal-hydrologic-chemical effects on radionuclide release. For example, DOE 
demonstrates that the numerical models used for high-level radioactive waste 
degradation and dissolution, and radionuclide release from the engineered barrier 
system, are adequate representations; include consideration of uncertainties; and are 
not likely to underestimate radiological exposures to the reasonably maximally 
exposed individual and releases of radionuclides into the accessible environment. 
Response: The EBS radionuclide transport abstraction uses well-documented procedures in 
Section 6.5 that have been accepted by the scientific community to construct and test the 
numerical models used to simulate radionuclide release. The abstraction demonstrates that the 
numerical models used for radionuclide release from the EBS include consideration of 
uncertainties and are not likely to underestimate radiological exposures to the reasonably 
maximally exposed individual and releases of radionuclides into the accessible environment. 
8.4 RESTRICTIONS FOR SUBSEQUENT USE 
This abstraction was developed specifically for application in TSPA-LA. Assumptions and 
approximations are made in order to integrate with and be consistent with other models and 
abstractions incorporated in TSPA-LA. Therefore, individual submodels should not be used 
independently outside of the TSPA-LA framework. This abstraction must be reevaluated if any 
models that feed into it are modified. 
Use of the two preliminary output DTNs: SN0403T0507703.015 and SN0409T0507703.017 is 
restricted to providing traceability in TSPA-LA. For any other application, the final output 
DTN: SN0410T0507703.018 is to be used. Differences between the preliminary and final 
DTNs are described in Appendix I. 

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9. INPUTS AND REFERENCES 
The following is a list of references cited in this document. Column 2 represents the unique six 
digit identifier numerical identifier (the Document Input Reference System number), which is 
placed in the text following the reference callout (e.g., BSC 2002 [DIRS 160819]). The purpose 
of these numbers is to assist in locating a specific reference. Within the reference list, multiple 
sources by the same author (e.g., BSC 2002) are sorted alphabetically by title. 
9.1 DOCUMENTS CITED 
Anderson, M.J. 2004. Mass for Nickel Gadolinium Neutron Absorber for 
Commercial Spent Nuclear Fuel (CSNF) Waste Packages--Initial Calculations (Not 
Yet Approved). Interoffice memorandum from M.J. Anderson (BSC) to C. Howard, 
September 14, 2004, 0914043170, with enclosure. ACC: MOL.20040928.0325. 
171637 
Anderson, M.P. and Woessner, W.W. 1992. Applied Groundwater Modeling, 
Simulation of Flow and Advective Transport. San Diego, California: Academic 
Press. TIC: 103227. 
123665 
Atkins, P.W. 1990. Physical Chemistry. 4th Edition. New York, New York: W. 
H. Freeman and Company. TIC: 245483. 
111464 
Baker, N.A.; and Grisak, G.E. 2004. Independent Model Validation Technical 
Review of the EBS-UZ Interface Sub-Model of the Radionuclide Transport 
Abstraction Model for the Yucca Mountain Project. Memo from N.A. Baker 
(INTERA) and G.E. Grisak (INTERA) to J. Schreiber (YMP) and C. Howard 
(YMP), July 27, 2004. ACC: MOL.20040730.0182. 
170953 
Balsley, S.D.; Brady, P.V.; Krumhansl, J.L.; and Anderson, H.L. 1998. Anion 
Scavengers for Low-Level Radioactive Waste Repository Backfills. Journal of Soil 
Contamination, 7, (2), 125-141. Boca Raton, Florida: Lewis Publishers. 
TIC: 249779. 
154439 
Bear, J. 1988. Dynamics of Fluids in Porous Media. New York, New York: Dover 
Publications. TIC: 217568. 
101379 
Bethke, C.M.; and Brady, P.V. 2000. How the Kd Approach Undermines Ground 
Water Cleanup. Ground Water, 38, (3), 435-443. Westerville, Ohio: National 
Ground Water Association. TIC: 249781. 
154437 
Bird, R.B.; Stewart, W.E.; and Lightfoot, E.N. 1960. Transport Phenomena. 
New York, New York: John Wiley & Sons. TIC: 208957. 
103524 
Brady, P.V.; Spalding, B.P.; Krupka, K.M.; Waters, R.D.; Zhang, P.; Borns, D.J.; 
and Brady, W.D. 1999. Site Screening and Technical Guidance for Monitored 
Natural Attenuation at DOE Sites. SAND99-0464. Albuquerque, New Mexico: 
Sandia National Laboratories. TIC: 249720. 
154421

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Briand, L.E.; Hirt, A.M.; and Wachs, I.E. 2001. Quantitative Determination of the 
Number of Surface Active Sites and the Turnover Frequencies for Methanol 
Oxidation over Metal Oxide Catalysts: Application to Bulk Metal Molybdates and 
Pure Metal Oxide Catalysts. Journal of Catalysis, 202, ([2]), 268-278. New York, 
New York: Academic Press. TIC: 253845 
161617 
Brown, R.L.; and Richards, J.C. 1970. Principles of Powder Mechanics, Essays on 
the Packing and Flow of Powders and Bulk Solids. Pages 17-20. New York, 
New York: Pergamon Press. TIC: 245119. 
131479 
BSC (Bechtel SAIC Company) 2001. Committed Material in Repository Drift. 
CAL-GCS-GE-000002 REV 00. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: MOL.20010412.0157. 
154441 
BSC 2001. Unsaturated Zone and Saturated Zone Transport Properties (U0100). 
ANL-NBS-HS-000019 REV 00 ICN 02. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: MOL.20020311.0017. 
160828 
BSC 2002. Test Plan for: Atlas Breached Waste Package Test and Drip Shield 
Experiments. SITP-02-EBS-005 REV 00. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: MOL.20020314.0181. 
158193 
BSC 2002. The Enhanced Plan for Features, Events, and Processes (FEPs) at 
Yucca Mountain. TDR-WIS-PA-000005 REV 00. Las Vegas, Nevada: Bechtel 
SAIC Company. ACC: MOL.20020417.0385. 
158966 
BSC 2003. Atlas Breached Waste Package and Drip Shield Experiments: Breached 
Drip Shield Tests. TDR-EBS-MD-000025 REV 00. Las Vegas, Nevada: Bechtel 
SAIC Company. ACC: DOC.20030619.0001. 
163406 
BSC 2003. Design and Engineering, Naval Long Waste Package Configuration. 
000-MW0-DNF0-00103-000-00A. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: ENG.20030929.0004. 
165159 
BSC 2003. Risk Information to Support Prioritization of Performance Assessment 
Models. TDR-WIS-PA-000009 REV 01 ICN 01, Errata 001. Las Vegas, Nevada: 
Bechtel SAIC Company. ACC: MOL.20021017.0045; DOC.20031014.0003. 
168796 
BSC 2004. Abstraction of Drift Seepage. MDL-NBS-HS-000019 REV 01. 
Las Vegas, Nevada: Bechtel SAIC Company. ACC: DOC.20041103.0003. 
169131 
BSC 2004. Clad Degradation  Summary and Abstraction for LA. 
ANL-WIS-MD-000021 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: DOC.20041004.0002. 
170023

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 9-3 November 2004 
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169987 
BSC 2004. D&E / PA/C IED Emplacement Drift Configuration and Environment. 
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170559 
BSC 2004. D&E / PA/C IED Interlocking Drip Shield and Emplacement Pallet. 
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169220 
BSC 2004. D&E/PA/C IED Typical Waste Package Components Assembly. 
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167207 
BSC 2004. D&E/PA/C IED Typical Waste Package Components Assembly. 
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169472 
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166947 
BSC 2004. Design and Engineering, 21-PWR Waste Package Configuration. 
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166953 
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167394 
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170710 
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167555

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 9-4 November 2004 
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168326 
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168275 
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169860 
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169984 
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168960

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 9-5 November 2004 
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169565 
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169861

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TIC: 250477. 
155700 
Onishi, Y.; Serne, R.J.; Arnold, E.M.; Cowan, C.E.; and Thompson, F.L. 1981. 
Critical Review: Radionuclide Transport, Sediment Transport, and Water Quality 
Mathematical Modeling; and Radionuclide Adsorption/Desorption Mechanisms. 
NUREG/CR-1322. Washington, D.C.: U.S. Nuclear Regulatory Commission. 
TIC: 249732. 
154420 
Perry, D.L.; Phillips, S.L.; and Chung, J.D. 1988. Potentiostatic Measurement of 
the Diffusion Coefficient of UO2
2+ in Carbonate Media. Inorganica Chimica Acta, 
149, 301-304. Lausanne, Switzerland: Elsevier. TIC: 246806. 
138732 
Perry, R.H.; Chilton, C.H.; and Kirkpatrick, S.D., eds. 1963. Chemical Engineers 
Handbook. 4th Edition. New York, New York: McGraw-Hill. TIC: 237828. 
119529

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ANL-WIS-PA-000001 REV 01 9-13 November 2004 
Perry, R.H.; and Chilton, C.H., eds. 1973 . Chemical Engineers Handbook. 
5th Edition. New York, New York: McGraw-Hill. TIC: 242591. 
104946 
Philip, J.R.; Knight, J.H.; and Waechter, R.T. 1989. Unsaturated Seepage and 
Subterranean Holes: Conspectus, and Exclusion Problem for Circular Cylindrical 
Cavities. Water Resources Research, 25, (1), 16-28. Washington, D.C.: American 
Geophysical Union. TIC: 239117. 
105743 
Pirson, S.J. 1963. Handbook of Well Log Analysis for Oil and Gas Formation 
Evaluation. Englewood Cliffs, New Jersey: Prentice-Hall. TIC: 245393. 
111477 
Porter, L.K.; Kemper, W.D.; Jackson, R.D.; and Stewart, B.A. 1960. Chloride 
Diffusion in Soils as Influenced by Moisture Content. Soil Science Society of 
America Proceedings, 24, (5), 460-463. Danville, Illinois: Soil Science Society of 
America. TIC: 246854. 
123115 
Reardon, E.J. 1981. Kds  Can They be Used to Describe Reversible Ion Sorption 
Reactions in Contaminant Migration? Ground Water, 19, (3), 279-286. 
Worthington, Ohio: Water Well Journal Publishing Company. TIC: 249726. 
154434 
Reimus, P.W.; Ware, S.D.; Benedict, F.C.; Warren, R.G.; Humphrey, A.; Adams, A.; 
Wilson, B.; and Gonzales, D. 2002. Diffusive and Advective Transport of H 3, C14, 
and Tc99 in Saturated, Fractured Volcanic Rocks from Pahute Mesa, Nevada. 
LA-13891-MS. Los Alamos, New Mexico: Los Alamos National Laboratory. 
TIC: 253905. 
163008 
Roberts, J. J.; and Lin, W. 1997. Electrical Properties of Partially Saturated 
Topopah Spring Tuffs: Water Distribution as a Function of Saturation. Water 
Resources Research, 33(4), 577-587. Washington, D.C.: American Geophysical 
Union. TIC: 239736. 
101710 
Rosch, F.; and Khalkin, V.A. 1990. Ion mobilities of Trivalent f-Elements in 
Aqueous Electrolytes. Radiochimica Acta, 51, 101-106. Munich, Germany: 
R. Oldenbourg Verlag. TIC: 246710. 
138739 
Russo, R.E.; Mao, X.; Borisov, O.V.; and Liu, H. 2000. Laser Ablation in Atomic 
Spectroscopy. Encyclopedia of Analytical Chemistry. Meyers, R.A., ed. 
Pages 9485-9506. Chichester, England: John Wiley & Sons. TIC: 250479. 
155697 
imunek, J.; Jarvis, N.J.; van Genuchten, M.Th.; and Gardenas, A. 2003. Review 
and Comparison of Models for Describing Non-Equilibrium and Preferential Flow 
and Transport in the Vadose Zone. Journal of Hydrology, 272, (1-4), 14-35. 
New York, New York: Elsevier. TIC: 255570. 
167469 
Singh, A.K.; Singh, H.; Singh, S.P.; and Sawhney, R.L. 2002. Numerical 
Calculation of Psychrometric Properties on a Calculator. Building and 
Environment, 37, (4), 415-419. New York, New York: Elsevier. TIC: 253846. 
161624

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 9-14 November 2004 
So, H.B.; and Nye, P.H. 1989. The Effect of Bulk Density, Water Content and Soil 
Type on the Diffusion of Chloride in Soil. Journal of Soil Science 40 (4), 743-749. 
Oxford, England: Blackwell Scientific. TIC: 255392. 
170588 
Stumm, W. 1992. Chemistry of the Solid-Water Interface, Processes at the 
Mineral-Water and Particle-Water Interface in Natural Systems. New York, 
New York: John Wiley & Sons. TIC: 237213. 
141778 
Tada, H.; Paris, P.C.; and Irwin, G.R. 1973. The Stress Analysis of Cracks 
Handbook. St. Louis, Missouri: Del Research Corporation. TIC: 247050. 
118706 
Tamura, H.; Tanaka, A.; Mita, K.; and Furuichi, R. 1999. Surface Hydroxyl Site 
Densities on Metal Oxides as a Measure for the Ion-Exchange Capacity. Journal of 
Colloid and Interface Science, 209, (1), 225-231. New York, New York: Academic 
Press. TIC: 253844. 
161625 
Tsukamoto, M.; Ohe, T.; Fujita, T.; Hesbol, R.; and Hermansson, H-P. 1994. 
Diffusion of Neptunium(V) in Loosely Compacted Sodium Bentonite. 
Radiochimica Acta, 66/67, 397-403. Mnchen, Germany: R. Oldenbourg Verlag. 
TIC: 246893. 
138747 
Wan, J.; and Wilson, J.L. 1994. Visualization of the Role of the Gas-Water 
Interface on the Fate and Transport of Colloids in Porous Media, Water Resources 
Research, 30 (1), 11 - 23. Washington, D.C.: American Geophysical Union. 
TIC: 246300. 
124994 
Weast, R.C.; and Astle, M.J., eds. 1981. CRC Handbook of Chemistry and Physics. 
62nd Edition. Boca Raton, Florida: CRC Press. TIC: 240722. 
100833 
Weast, R.C., ed. 1985. CRC Handbook of Chemistry and Physics. 66th Edition. 
Boca Raton, Florida: CRC Press. TIC: 216054. 
111561 
YMP (Yucca Mountain Site Characterization Project) 1998. Disposal Criticality 
Analysis Methodology Topical Report. YMP/TR-004Q, Rev. 00. Las Vegas, 
Nevada: Yucca Mountain Site Characterization Office. 
ACC: MOL.19990210.0236. 
104441 
9.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES 
10 CFR 63. 2002. Energy: Disposal of High-Level Radioactive Wastes in a 
Geologic Repository at Yucca Mountain, Nevada. Readily available. 
158535 
ASM (American Society for Metals) 1979. Properties and Selection: Nonferrous 
Alloys and Pure Metals. Volume 2 of Metals Handbook. 9th Edition. Metals Park, 
Ohio: American Society for Metals. TIC: 209800. 
154085

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 9-15 November 2004 
ASTM (American Society for Testing and Materials) A 20/A20M-99a. 1999. 
Standard Specification for General Requirements for Steel Plates for Pressure 
Vessels. West Conshohocken, Pennsylvania: American Society for Testing and 
Materials. TIC: 247403. 
147578 
ASTM A 588/A 588M-01. 2001. Standard Specification for High-Strength Low- 
Alloy Structural Steel with 50 ksi [345 MPa] Minimum Yield Point to 4in. 
[100-mm] Thick. West Conshohocken, Pennsylvania: American Society for Testing 
and Materials. TIC: 253998. 
162724 
ASTM A 759-00. 2001. Standard Specification for Carbon Steel Crane Rails. 
West Conshohocken, Pennsylvania: American Society for Testing and Materials. 
TIC: 253176. 
159971 
ASTM B 932-04. 2004. Standard Specification for Low-Carbon 
Nickel-Chromium-Molybdenum-Gadolinium Alloy Plate, Sheet, and Strip. 
West Conshohocken, Pennsylvania: American Society for Testing and Materials. 
TIC: 255846. 
168403 
ASTM G 1-90 (Reapproved 1999). 1999. Standard Practice for Preparing, 
Cleaning, and Evaluating Corrosion Test Specimens. West Conshohocken, 
Pennsylvania: American Society for Testing and Materials. TIC: 238771. 
103515 
AP-2.22Q, Rev. 1, ICN 1. Classification Analyses and Maintenance of the Q-List. 
Washington, D.C.: U.S. Department of Energy, Office of Civilian Radioactive 
Waste Management. ACC: DOC.20040714.0002. 
AP-2.27Q, Rev. 1, ICN 5. Planning for Science Activities. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20041014.0001. 
AP-SIII.2Q, Rev. 1, ICN 2. Qualification of Unqualified Data. Washington, D.C.: 
U.S. Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040127.0008. 
AP-SIII.10Q, Rev. 2, ICN 7. Models. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040920.0002. 
LP-SI.11Q-BSC, Rev. 0, ICN 01. Software Management. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20041005.0008 
9.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER (DTN) 
LA0003AM831341.001. Probability Distributions for Sorption Coefficients (Kds). 
Submittal date: 03/29/2000. 
148751

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 9-16 November 2004 
LA0311AM831341.001. Correlation Matrix for Sampling of Sorption Coefficient 
Probability Distributions. Submittal date: 11/06/2003. 
167015 
LA0408AM831341.001. Unsaturated Zone Distribution Coefficients (Kds) for U, 
Np, Pu, Am, Pa, Cs, Sr, Ra, and Th. Submittal date: 08/24/2004. 
171584 
LB0205REVUZPRP.001. Fracture Properties for UZ Model Layers Developed from 
Field Data. Submittal date: 05/14/2002. 
159525 
LB0207REVUZPRP.002. Matrix Properties for UZ Model Layers Developed from 
Field and Laboratory Data. Submittal date: 07/15/2002. 
159672 
LB0208UZDSCPLI.002. Drift-Scale Calibrated Property Sets: Lower Infiltration 
Data Summary. Submittal date: 08/26/2002. 
161788 
LB0208UZDSCPMI.002. Drift-Scale Calibrated Property Sets: Mean Infiltration 
Data Summary. Submittal date: 08/26/2002. 
161243 
LB03013DSSCP3I.001. 3-D Site Scale Calibrated Properties: Data Summaries. 
Submittal date: 01/27/2003. 
162379 
LB0302UZDSCPUI.002. Drift-Scale Calibrated Property Sets: Upper Infiltration 
Data Summary. Submittal date: 02/05/2003. 
161787 
LB0307FMRADTRN.001. Fracture-Matrix Partitioning Model: Spreadsheet 
Calculations. Submittal date: 07/31/2003. 
165451 
MO0003RIB00076.000. Physical and Chemical Characteristics of Type 316N 
Grade. Submittal date: 03/14/2000. 
153044 
MO0107TC239753.000. ASME Boiler and Pressure Vessel Code, Sec II B SB-575 
Specification for Low-Carbon Nickel-Molybdenum-Chromium, Low-Carbon. 
Submittal date: 07/23/2004. 
169973 
MO0107TC240032.000. Standard Specification for Pressure Vessel Plates, Carbon 
Steel, for Moderate- and-Lower-Temperature Service. Submittal date: 07/19/2001. 
169970 
MO0207EBSATBWP.021. Atlas Breached Waste Package and Drip Shield 
Experiments: Initial Tests for Rough Drip Shield Surface. Submittal date: 
07/31/2002. 
163399 
MO0207EBSATBWP.022. Atlas Breached Waste Package and Drip Shield 
Experiments: Initial Tests for Smooth Drip Shield Surface. Submittal date: 
07/31/2002. 
163400

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 9-17 November 2004 
MO0207EBSATBWP.023. Atlas Breached Waste Package and Drip Shield 
Experiments: Single Patch Q(Splash) and Q(Film) Tests on the Smooth Drip Shield 
Surface. Submittal date: 07/31/2002. 
163402 
MO0207EBSATBWP.024. Atlas Breached Waste Package and Drip Shield 
Experiments: Multiple Patch Tests for Smooth Drip Shield Surface. Submittal date: 
07/31/2002. 
163401 
MO0207EBSATBWP.025. Atlas Breached Waste Package and Drip Shield 
Experiments: Bounding Flow Rate Tests on the Smooth Drip Shield Surface. 
Submittal date: 07/31/2002. 
163403 
MO0208EBSATBWP.027. Atlas Breached Waste Package and Drip Shield 
Experiments: Multiple Patch Tests on the Rough Drip Shield Surface. Submittal 
date: 08/13/2002. 
163404 
MO0208EBSATBWP.028. Atlas Breached Waste Package and Drip Shield 
Experiments: Bounding Flow Rate Tests on the Rough Drip Shield Surface. 
Submittal date: 08/13/2002. 
163405 
MO0302UCC034JC.003. Graphical X-Ray Diffractometer Data and Mineral 
Analysis of Filtered Solids from Effluent Solution During Miniature Waste Package 
Corrosion. Submittal date: 02/10/2003. 
162871 
MO0312SPAPCEML.003. EBS P&CE Model Longevity of Materials Evaluation. 
Submittal date: 12/18/2003. 
167409 
MO0407SEPFEPLA.000. LA FEP List. Submittal date: 07/20/2004. 170760 
MO0409SPAACRWP.000. Aqueous Corrosion Rates for Non-Waste Form Waste 
Package Materials. Submittal date: 09/16/2004. 
172059 
SN0306T0504103.006. Revised Sorption Partition Coefficients (Kd Values) for 
Selected Radionuclides Modeled in the TSPA (Total System Performance 
Assessment). Submittal date: 06/30/2003. 
164131 
SN0309T0504103.010. Updated Iron Oxyhydroxide Colloid Concentration 
Parameters, Specific Surface Area (SA) of Iron Oxyhydroxide Colloids, Target Flux 
Out Ratio (FRN) and Forward Rate Constant (K) for Pu & Am Sorption to Iron 
Oxyhydroxide Colloids & Stationary Corrosion. Submittal date: 09/18/2003. 
165540 
SN0310T0505503.004. Initial Radionuclide Inventories for TSPA-LA. Submittal 
date: 10/27/2003. 
168761 
SN0404T0503102.011. Thermal Conductivity of the Potential Repository Horizon 
Rev 3. Submittal date: 04/27/2004. 
169129

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 9-18 November 2004 
9.4 OUTPUT DATA, LISTED BY DATA TRACKING NUMBER (DTN) 
SN0403T0507703.015. Model Inputs Used in Engineered Barrier System (EBS) 
Radionuclide Transport Abstraction, Version 1. Submittal date: 03/12/2004. 
(Preliminary developed data). 
SN0409T0507703.017. Model Inputs Used in Engineered Barrier System (EBS) 
Radionuclide Transport Abstraction. Submittal date: 09/27/2004. (Preliminary 
developed data). 
SN0410T0507703.018. Engineered Barrier System (EBS) Radionuclide Transport 
Abstraction Model Inputs. Submittal date: 11/03/2004. 
9.5 SOFTWARE CODES 
Golder Associates 2003. Software Code: GoldSim. V8.01 Service Pack 1. PC, 
Windows 2000. 10344-8.01 SP1-00. 
166572 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 
APPENDIX A 
MICROSOFT EXCEL SPREADSHEET MASSES OF MATERIALS 

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EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 A-1 November 2004 
MICROSOFT EXCEL SPREADSHEET MASSES OF MATERIALS 
In this spreadsheet, the mass of iron and the equivalent mass of Fe2O3 is calculated for four waste 
packages. The results are reported in Table 6.3-4. The calculation is done: 21-PWR (absorber 
plate), 44-BWR (absorber plate), 5-DHLW/DOE Short, and Naval Long. 
The procedure for determining the equivalent mass of Fe2O3 is to calculate the total mass of each 
type of iron-containing alloy, calculate the mass of iron in all components of each alloy based on 
the iron content of the alloy, sum the mass of iron in the waste package, and convert the iron 
mass to Fe2O3 mass using the stoichiometry and molecular weights. Only the components within 
the outer corrosion barrier are included in the calculation; the outer corrosion barrier is 
considered to be inert. 
For a 21-PWR waste package, the mass and number of each component are listed in Figures A-1 
and A-2 as shown in Table 4.1-17 (BSC 2004 [DIRS 169472], Table 2). This calculation uses 
the previous waste package design in which the absorber plates are composed of Neutronit, 
rather than the current design with Ni-Gd absorber plates (BSC 2004 [DIRS 170710]). The 
impact of using the previous design is discussed in Section 6.3.4.2.3, where it is shown that the 
differences in absorber plate design should have negligible net effect on radionuclides transport 
from the EBS. In Column E (Figure A-1), the total mass of the components is computed 
(e.g., E2=C2*D2). The total mass of all components is summed in Cell E23. The calculation is 
repeated for a 44-BWR waste package (BSC 2004 [DIRS 169472], Table 3) in Column K 
(Figure A-1), for a 5 DHLW/DOE Short waste package (BSC 2004 [DIRS 167207], Table 5) in 
Column Q (Figure A-2), and for a Naval Long waste package (BSC 2004 [DIRS 169472], 
Table 4) in Column W (Figure A-2). Consistent with the treatment for the 21-PWR waste 
package, the previous design with Neutronit absorber plates is considered for a 44-BWR waste 
package rather than the current design (BSC 2004 [DIRS 170838]). For the 5 DHLW/DOE 
Short waste package, a mass of 1 kg is erroneously used for the Interface Ring (Column O, 
Row 5 in Figure A-2); the correct mass is 44.6 kg (BSC 2004 [DIRS 167207], Table 5). 
Figure A-1. Spreadsheet Masses of Materials; Calculation of Mass of 21-PWR and 44-BWR Waste 
Package Components 

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ANL-WIS-PA-000001 REV 01 A-2 November 2004 
Figure A-2. Spreadsheet Masses of Materials; Calculation of Mass of 5-DHLW and Naval Long Waste 
Package Components and Materials 
In Rows 25-32, the calculation (Figure A-3) is repeated for a 21-PWR waste package for A 516 
carbon steel components only. The total mass of carbon steel components is shown in Cell E32. 
Similarly, the calculation is repeated in Rows 34-37 (Figure A-3) for Neutronit, with the total 
Neutronit mass shown in Cell E37; in Rows 43-48 for 316 SS, with the total 316 SS mass shown 
in Cell E48. The masses of Al 6061 and Alloy 22 are also calculated, but this information is not 
used because the aluminum alloy contains a negligible amount of iron, and the Alloy 22 is 
considered to be inert. The calculation is repeated for a 44-BWR waste package in Column K 
(Figure A-3), for a 5-DHLW Short waste package in Column Q (Figure A-2), and for a Naval 
Long waste package in Column W (Figure A-2). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 A-3 November 2004 
Figure A-3. Spreadsheet Masses of Materials; Calculation of Mass of 21-PWR and 44-BWR Waste 
Package Materials and Equivalent Mass of Fe2O3 
In Row 78, Columns C-E (Figure A-4), the iron content is calculated for the three alloys of 
interest (316 stainless steel, A 516 carbon steel, and Neutronit A 978, respectively). The iron 
content of these alloys is specified as Balance (see Table 4.1-10). It is calculated by summing 
the content of all nonferrous components of the alloys (Row 77, Columns C-E) and subtracting 
from 100 percent. 

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ANL-WIS-PA-000001 REV 01 A-4 November 2004 
DTN: MO0003RIB00076.000 [DIRS 153044]; DTN: MO0107TC240032.000 [DIRS 169970]. 
Source: Kgler 1991 [DIRS 155761], p.15. 
Figure A-4. Spreadsheet Masses of Materials; Elemental Weight Percent Compositions used in 
Calculation of Iron Content in Three Steel Alloys 
In Figure A-3, the total masses of 316 SS (from E48), of A 516 CS (from E32), and of Neutronit 
A 978 (from E37) in all 21-PWR components are listed in Column D, Rows 58-60, respectively. 
The iron content of all components for each alloy is calculated in Column E 
(e.g., E58=C58*D58/100). The total iron content in the three alloys is summed in Cell E61. 
The average iron content of all components constructed of these three alloys is calculated in 
Cell F61 (F61=E61*100/D61); this information is not used. 
The equivalent mass of Fe2O3 is computed in Cell E62 (Figure A-3) using the formula shown in 
Footnote d of Table 6.3-4: E62=E61*0.15969/0.055847/2. The results of these calculations 
(Rows 58-62, Columns C-F) are presented in Table 6.3-4 for a 21-PWR. These calculations are 
repeated for a 44-BWR waste package (Rows 58-62, Columns I-L; see Figure A-3), a 5-DHLW 
waste package (Rows 58-62, Columns O-R; Figure A-5), and for a Naval Long waste package 
(Rows 58-62, Columns U-X; Figure A-5). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 A-5 November 2004 
Figure A-5. Spreadsheet Masses of Materials; Calculation of Equivalent Mass of Fe2O3 in 5-DHLW and 
Naval Long Waste Packages 

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ANL-WIS-PA-000001 REV 01 A-6 November 2004 
INTENTIONALLY LEFT BLANK 

EBS Radionuclide Transport Abstraction 
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APPENDIX B 
IMPLEMENTATION OF RADIONUCLIDE SORPTION ONTO COLLOIDAL AND 
STATIONARY PHASES WITH FINITE DIFFERENCE SOLUTION 

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EBS Radionuclide Transport Abstraction 
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IMPLEMENTATION OF RADIONUCLIDE SORPTION ONTO COLLOIDAL AND 
STATIONARY PHASES WITH FINITE DIFFERENCE SOLUTION 
CONCEPTUAL MODEL 
This colloid model accounts for both reversible and irreversible sorption onto the iron 
oxyhydroxide (designated FeO) mobile colloids and the immobile FeO corrosion products 
together with reversible sorption onto both waste form and groundwater (GW) colloids within 
the engineered barrier system (EBS). Figure B-1 shows the conceptual model of radionuclide 
sorption onto the iron oxy-hydroxide colloidal and stationary phases. The upstream domain is 
considered to be degraded fuel rods, including secondary mineral phases, in equilibrium with the 
aqueous phase at the radionuclide solubility limit predicted by the solubility limits model 
(BSC 2004 [DIRS 169425]). The radionuclides of concern are the Pu and Am isotopes. Since 
the material balance equations are written as a mass balance, the equations are valid for any 
solute species. Certain system parameters, such as solubility, decay rate, and partition 
coefficients, will be dependent on the species. In this appendix, the species used for subsequent 
analysis and discussion is Pu. 
There is no sorption considered in the upstream domain. Pu at its solubility limit is considered to 
transport by both advection and diffusion downstream into the corrosion product domain, where 
it can be involved in six separate reactions: 
 Reversible Pu sorption onto FeO colloidal particles 
 Reversible Pu sorption onto the stationary phase FeO corrosion products 
 Irreversible Pu sorption onto FeO colloidal particles 
 Irreversible Pu sorption onto the stationary phase FeO corrosion products 
 Reversible Pu sorption onto waste form colloids 
 Reversible Pu sorption onto GW colloids. 
Denote the concentrations (kg Pu m-3 water) for the Pu in the seven possible states as 
aq Pu c _ = concentration of Pu in aqueous solution 
c FeO Pu c _ _ = concentration of Pu in the FeO colloid state from reversible sorption 
CP FeO Pu c _ _ = concentration of Pu in the stationary FeO corrosion product state from 
reversible sorption 
c FeO Pu Irrv c _ _ _ = concentration of Pu in the FeO colloid state from irreversible sorption 
CP FeO Pu Irrv c _ _ _ = concentration of Pu in the stationary FeO corrosion products state from 
irreversible sorption 
c WF Pu c _ _ = concentration of Pu in the waste form colloid state from reversible 
sorption 
c GW Pu c _ _ = concentration of Pu in the GW colloid state from reversible sorption 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-2 November 2004 
and let 
s c = Pu solubility (concentration at the solubility limit) (kg Pu m-3 water). 
The concentrations (kg colloid m-3 water) of all colloids and stationary corrosion products are: 
c FeO c _ = concentration of FeO in the colloid state 
CP FeO c _ = concentration of FeO in the corrosion product state 
c WF c _ = concentration of waste form in the colloid state 
c GW c _ = concentration of GW in the colloid state. 
As indicated in Figure B-1, the mass in the fluid exiting the corrosion-product domain (reaction 
mixing cell) is expected to be proportioned such that the mass of Pu sorbed onto FeO colloids is 
some fraction of the total mass of Pu exiting the system in all formsaqueous, reversibly 
sorbed, and irreversibly sorbed. Observations in nature, such as the transport of Pu from the 
Benham test site (Kersting et al. 1999 [DIRS 103282]) suggest that this fraction is about 
95 percent. This is expressed as: 
95 . 0 
out flux mass total 
out flux mass colloid = = . . (Eq. B-1) 
This value of 95 percent is uncertain with an uncertainty range of 0.90 to 0.99 associated with it 
(BSC 2004 [DIRS 170025], Table 6-12, p. 6-72). It also may be a function of time, since the 
observation time for the Benham test is only about 50 years. 
upstream domain 
Pu 
Fuel rods 
Pu 
Pu 
Irrv_Pu_c 
reaction mixing cell 
colloids 
Pu 
Pu_aq 
Pu_c 
Corrosion Products 
Pu_aq 
Pu_CP Irrv_Pu_CP 
Pu_aq 
Pu_c 
Irrv_Pu_c 
Figure B-1. Conceptual Model Schematic 
Also of interest is the ratio of the mass flux leaving the mixing cell to the mass flux entering the 
mixing cell. This ratio of mass out to mass in is given by: 
in flux mass 
out flux mass = . , (Eq. B-2) 
and is a measure of the retardation due to sorption on the stationary corrosion products. The 
model is set up is such a way that most of the Pu mass entering the mixing cell is expected to be 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-3 November 2004 
sorbed onto the stationary FeO phase and only a small fraction of it flows downstream to the 
unsaturated zone. 
REACTIONS 
The reactions considered in this model are as follows, where i R , represents the bulk reaction rate 
of Pu for the ith reaction, in units (kg Pu m-3 yr-1): 
R1: ) Pu(FeO Pu(aq) irrev 
col . (Eq. B-3) 
R2: ) Pu(FeO Pu(aq) irrev 
CP . (Eq. B-4) 
R3: ) Pu(FeO Pu(aq) rev 
col . (Eq. B-5) 
R4: ) Pu(FeO Pu(aq) rev 
CP . (Eq. B-6) 
R5: ) Pu(WF Pu(aq) rev 
col . (Eq. B-7) 
R6: ) Pu(GW Pu(aq) rev 
col . (Eq. B-8) 
Note that the reactions in Equations B-5 through B-8 are reversible equilibrium reactions, 
therefore their reaction rates are undefined and not included in subsequent mass balance 
equations. Equilibrium mass-action relationships are imposed instead, for these four reactions. 
KINETIC REACTIONS 
The ith irreversible reaction rate (where i = 1 or 2), i R (kg Pu m-3 bulk-volume yr-1), is expressed 
in terms of the ith bulk surface area for the mineral phase involved in the reaction, i S (m2 
FeO m-3 bulk-volume), and the ith intrinsic (or surface) reaction rate, i r (kg Pu m-2 FeO yr-1): 
i i i r S R = . (Eq. B-9) 
The irreversible reaction of Pu onto FeO colloids is then 
1 c 1 r S R FeO_ = (Eq. B-10) 
and for the irreversible reaction of Pu onto FeO corrosion products 
2 2 r S R FeO_CP = . (Eq. B-11) 
The bulk surface area (m2 FeO m-3 bulk-volume) for FeO colloids and corrosion products are, 
respectively, 
w FeO_ FeO_c FeO_c S c S S f c 
 = (Eq. B-12) 
w FeO_CP FeO_CP FeO_CP S c S S f  = (Eq. B-13) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-4 November 2004 
where f is the porosity of the FeO matrix, w S is the water saturation and 
c FeO S _ 
 = specific surface area of FeO colloids (m2 FeO-colloid kg-1 FeO-colloid) 
CP FeO S _ 
 = specific surface area of FeO corrosion products 
(m2 FeO-CP kg-1 FeO-CP). 
The intrinsic or surface reaction rate (i.e., rate per unit mineral surface area) is considered to be 
the same for the colloidal and stationary phases, i.e., r r r = = 2 1 , and it only has a forward 
component, since the reaction is irreversible. Further, suppose that the reactions are first order in 
the solution concentration aq Pu c _ : 
Pu_aq kc r = , (Eq. B-14) 
where 
k = forward rate constant, (m3 water-volume m-2 FeO yr-1). 
The two irreversible reaction rates on a water volume basis are then 
aq Pu aq Pu c FeO c FeO 
w 
c R kc c S 
S
R 
_ 1 _ _ _ 
1  = = 
f 
(Eq. B-15) 
aq Pu aq Pu CP FeO CP FeO 
w 
c R kc c S 
S 
R 
_ 2 _ _ _ 
2  = = 
f 
, (Eq. B-16) 
where k c S R c FeO c FeO _ _ 1 
 = and k c S R CP FeO CP FeO _ _ 2 
 = are reaction rate constants (yr-1) for 
colloids and corrosion products, respectively. 
EQUILIBRIUM REACTIONS 
The four chemical species, ) Pu(FeOrev 
col , ) Pu(FeOrev 
CP , ) Pu(WFrev 
col and ) Pu(GWrev 
col , involved in 
reversible equilibrium sorption reactions, Equations B-5, B-6, B-7, and B-8, follow the law of 
mass action according to 
)] [Pu(aq 
)] [Pu(FeOrev 
col 
3 = eq K (Eq. B-17) 
)] [Pu(aq 
)] [Pu(FeOrev 
CP 
4 = eq K (Eq. B-18) 
)] [Pu(aq 
)] [Pu(WFrev 
col 
5 = eq K (Eq. B-19) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-5 November 2004 
)] [Pu(aq 
)] [Pu(GWrev 
col 
6 = eq K (Eq. B-20) 
where [Pu(j)] represents the thermodynamic activity of Pu in the jth phase (aqueous, colloidal, or 
corrosion product). Normally, these relationships are expressed for dilute solutions as a simple 
linear ( d K ) (water volume/mass FeO) type of isotherm in terms of concentrations: 
Pu_aq c FeO d c FeO Pu c K c _ _ _ _  = (Eq. B-21) 
Pu_aq CP FeO d CP FeO Pu c K c _ _ _ _  = (Eq. B-22) 
Pu_aq c WF d c WF Pu c K c _ _ _ _  = (Eq. B-23) 
Pu_aq c GW d c GW Pu c K c _ _ _ _  = (Eq. B-24) 
where 
c FeO Pu c _ _  = mass ratio of Pu sorbed onto FeO colloids (kg Pu kg-1 FeO-colloid) 
CP FeO Pu c _ _  = mass ratio of Pu sorbed onto FeO corrosion products (kg Pu kg-1 FeO-CP) 
c WF Pu c _ _  = mass ratio of Pu sorbed onto waste form colloids (kg Pu kg-1 WF-colloid) 
c GW Pu c _ _  = mass ratio of Pu sorbed onto GW colloids (kg Pu kg-1 GW-colloid). 
The mass ratio for these reversible sorption reactions can be converted to water volume 
concentrations by the following: 
c FeO Pu c FeO c FeO Pu c c c _ _ _ _ _  = (Eq. B-25) 
CP FeO Pu CP FeO CP FeO Pu c c c _ _ _ _ _  = (Eq. B-26) 
c WF Pu c WF c WF Pu c c c _ _ _ _ _  = (Eq. B-27) 
c GW Pu c GW c GW Pu c c c _ _ _ _ _  = (Eq. B-28) 
The reversible Pu equilibrium is expressed by the partition coefficients relating the aqueous state 
and the two reversible states given by Equations B-25 to B-28 as 
aq Pu c FeO d aq Pu c FeO d c FeO c FeO Pu c K c K c c _ _ _ _ _ _ _ _ _ = = (Eq. B-29) 
aq Pu CP FeO d aq Pu CP FeO d CP FeO CP FeO Pu c K c K c c _ _ _ _ _ _ _ _ _ = = (Eq. B-30) 
aq Pu c WF d aq Pu c WF d c WF c WF Pu c K c K c c _ _ _ _ _ _ _ _ _ = = (Eq. B-31) 
aq Pu c GW d aq Pu c GW d c GW c GW Pu c K c K c c _ _ _ _ _ _ _ _ _ = = (Eq. B-32) 
where c FeO d K _ _ , CP FeO d K _ _ , c WF d K _ _ and c GW d K _ _ are dimensionless partition coefficients. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-6 November 2004 
QUANTIFICATION OF CORROSION PRODUCTS 
The corrosion products are generated from the degradation of the waste packages. It is the 
corrosion product mass that provides the porous matrix for the transport of nuclides in the 
reaction mixing cell. The amount of corrosion products is time dependent. As modeled, the 
corrosion product density (kg m-3 solid) and mass (kg) are known. Let 
= CP FeO _ . corrosion product density 
= CP FeO m _ mass of corrosion product. 
The volume of corrosion products (kg m-3 solid) is then 
CP FeO 
CP FeO 
CP FeO 
m 
V 
_
_ 
_ . 
= . 
If the porosity of the corrosion product mass is specified as 
bulk 
pore 
V
V 
= f , 
then 
bulk
CP FeO 
V 
V _ 1 = - f . 
The bulk volume is computed from 
f - 
= 
1 
_ CP FeO 
bulk 
V 
V 
and the pore volume is 
CP FeO 
CP FeO 
bulk pore 
m 
V V 
_
_ 
1 . f 
f 
f 
- 
= = . 
The stationary corrosion products concentration is defined as 
pore 
CP FeO 
CP FeO V 
mass 
c _ 
_ = . 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-7 November 2004 
TRANSPORT EQUATIONS 
The mass balance equation for the Pu contained in the aqueous state, the reversible colloid state 
and the reversible corrosion product state with radionuclide decay (neglecting ingrowth) is (see 
development in Section 6.5.1.2): 
. .. 
. 
. .. 
. 
. 
. 
.
. 
- 
. 
+ + + . 
+ 
. 
+ + + + . 
x 
c 
D S 
x x 
c c c c 
u 
t 
c c c c c S 
aq Pu 
aq w 
c GW Pu c WF Pu c FeO Pu aq Pu 
c GW Pu c WF Pu CP FeO Pu c FeO Pu aq Pu w 
_ _ _ _ _ _ _ _ 
_ _ _ _ _ _ _ _ _ 
) ( 
) ( 
f 
f 
) ( 
) ( 
_ _ _ _ _ _ _ _ _ 2 1 
_ _ _ _ _ _ 
c GW Pu c WF Pu CP FeO Pu c FeO Pu aq Pu w 
c GW Pu c WF Pu c FeO Pu 
colloid w 
c c c c c S R R 
x 
c c c 
D S 
x 
+ + + + - - - = 
. .. 
. 
. .. 
. 
. 
+ + . 
.
. 
- 
.f 
f 
(Eq. B-33) 
where f is the porosity of the FeO matrix, w S is the water saturation, u is the Darcy velocity of 
the water (m yr-1), aq D is the diffusivity (m2 yr-1) of the Pu in solution, colloid D is the colloid 
diffusivity (m2 yr-1), and . is the radionuclide decay rate (yr-1). Now impose the reversible 
equilibrium of the Pu mass between the aqueous, colloid and corrosion products (Equations B-29 
and B-32) together with representing the irreversible reactions as functions of the aqueous phase 
Pu concentration (Equations B-15 and B-16). The mass balance (Equation B-33) on a bulk 
volume basis can be expressed in terms of the concentration in the aqueous state: 
( ) 
. _ _ _ _ _ _ _ _ _ 
_ 2 1 
_ 
_ _ _ _ _ _ 
_ 
_ 
_ _ _ _ _ _ 
_ 
_ _ _ _ _ _ _ _ 
) 1 ( 
) ( 
) 1 ( 
) 1 ( 
aq Pu c GW d c WF d CP FeO d c FeO d w 
aq Pu w 
aq Pu 
c GW d c WF d c FeO d colloid w 
aq Pu 
aq w 
aq Pu 
c GW d c WF d c FeO d 
aq Pu w 
c GW d c WF d CP FeO d c FeO d 
c K K K K S 
c R R S 
x 
c 
K K K D S 
x 
x 
c 
D S 
x 
x 
c 
K K K u 
t 
c S 
K K K K 
+ + + + - 
+ - = 
. .. 
. 
. .. 
. 
. 
. 
+ + 
.
. 
- 
. .. 
. 
. .. 
. 
. 
. 
.
. 
- 
. 
. 
+ + + + 
. 
. 
+ + + +
.f
f 
f
f 
f 
(Eq. B-34) 
The mass balance equations for the irreversible Pu in the colloid and corrosion product states are, 
respectively, 
c FeO Pu Irrv w aq Pu w 
c FeO Pu Irrv 
colloid w 
c FeO Pu Irrv c FeO Pu Irrv w 
c S c R S 
x 
c 
D S 
x x 
c 
u 
t 
c S 
_ _ _ _ 1 
_ _ _ _ _ _ _ _ _ 
.f f 
f 
f 
- = 
. .. 
. 
. .. 
. 
. 
. 
.
. 
- 
. 
. 
+ 
. 
. 
(Eq. B-35) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-8 November 2004 
and 
CP FeO Pu Irrv w aq Pu w 
CP FeO Pu Irrv w c S c R S 
t 
c S 
_ _ _ _ 2 
_ _ _ .f f 
f 
- = 
. 
. 
. (Eq. B-36) 
The boundary conditions require the upstream (left boundary cell, if flow is from left to right) 
conditions 
s c WF d c WF Pu 
s aq Pu 
c K c 
c c 
_ _ _ _
_ 
= 
= 
(Eq. B-37) 
0 _ _ _ _ _ _ _ _ _ _ _ _ = = = = = c GW Pu CP FeO Pu Irrv c FeO Pu Irrv CP FeO Pu c FeO Pu c c c c c , (Eq. B-38) 
where s c is the Pu solubility as defined earlier. In this model, no FeO or groundwater colloids 
exit in the upstream waste form cell. The solubility at the upstream location is dependent on the 
CO2 fugacity and pH at the upstream location (BSC 2004 [DIRS 169425], Section 8.1) and in 
general is time dependent: ) (t c c s s = . The right boundary cell is a free flow boundary with 
concentrations fixed at zero. For diffusion calculations it is required to specify down stream 
diffusion parameters (porosity, diffusivity, diffusive length and diffusive area). The initial 
conditions within the mixing cell are zero for all Pu concentrations. 
Both the colloid and corrosion product concentrations are chosen to be time dependent: 
) (
) ( 
) ( 
) ( 
_ _ 
_ _ 
_ _ 
_ _ 
t c c 
t c c 
t c c 
t c c 
c GW c GW 
c WF c WF 
CP FeO CP FeO 
c FeO c FeO 
= 
= 
= 
= 
(Eq. B-39) 
but are independent of the Pu concentrations. This implies that the reaction rates 1 R and 2 R are 
also time dependent. 
The mass balance equations are solved numerically by finite difference method. The calculation 
sequence for a time step is to solve Equation B-34 for aq Pu c _ . Reversible equilibrium 
Equations B-29 through B-32 then give c FeO Pu c _ _ , CP FeO Pu c _ _ , c WF Pu c _ _ and c GW Pu c _ _ . With 
aq Pu c _ known the mass balance Equations B-35 and B-36 for the irreversible components are 
solved. 
DIMENSIONLESS FORM OF TRANSPORT EQUATIONS 
In order to express the governing equations in dimensionless form, define dimensionless length, 
time and concentration, respectively, 
L x / = . 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-9 November 2004 
L
t u 
L S
ut
w 
= = 
f 
t 
s c c c / = , 
where L is the characteristic length (m) and 
w S
u u 
f 
= is the average linear advective velocity 
(m yr-1). The characteristic length would be the interval length or, for a finite difference 
solution, the grid block cell length. Make the change of variables to dimensionless space and 
time in the mass balance equations. If the colloid/corrosion product concentrations are taken to 
be constant (Equations B-39), then the Pu mass balance equation in the aqueous state is: 
( ) [ ] 
aq Pu c GW d c WF d CP FeO d c FeO d aq Pu 
aq Pu 
c GW d c WF d c FeO d colloid aq 
aq Pu 
c GW d c WF d c FeO d 
aq Pu 
c GW d c WF d CP FeO d c FeO d 
c K K K K c 
c 
K K K 
c 
K K K 
c 
K K K K 
_ _ _ _ _ _ _ _ _ _ 2 1 
2
_ 
2 
_ _ _ _ _ _ 
_ 
_ _ _ _ _ _ 
_ 
_ _ _ _ _ _ _ _ 
) 1 ( ) ( 
) 1 ( 
) 1 ( 
. + + + + - T + T - = 
. 
. 
+ + . + . - 
. 
. 
+ + + + 
. 
. 
+ + + + 
. 
. 
t 
(Eq. B-40) 
where 
rate advective
in water rate diffusive = = . 
L
u
L 
Daq 
aq , (Eq. B-41) 
rate advective 
colloids of rate diffusive 
2 
= = . 
L
u
L 
Dcolloid 
collid , (Eq. B-42) 
rate advective 
colloids to rate reaction 1 
1 = = T 
L
u
R , (Eq. B-43) 
rate advective 
products corrosion to rate reaction 2 
2 = = T 
L
u 
R , (Eq. B-44) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-10 November 2004 
rate advective 
rate decay = = . 
L
u
. 
. (Eq. B-45) 
The dimensionless form of the mass balance for the irreversible Pu concentrations 
(Equations B-5 and B-36) are: 
c FeO Pu Irrv aq Pu 
c FeO Pu Irrv 
colloid 
c FeO Pu Irrv c FeO Pu Irrv 
c c 
c c c 
_ _ _ _ 1 
2 
_ _ _ 
2 
_ _ _ _ _ _ 
. - T = 
. 
. 
. - 
. 
. 
+ 
. 
. 
. . t (Eq. B-46) 
CP FeO Pu Irrv aq Pu 
CP FeO Pu Irrv c c 
c 
_ _ _ _ 2 
_ _ _ . - T = 
. 
. 
t 
. (Eq. B-47) 
DIFFERENCE SOLUTION OF TRANSPORT EQUATIONS 
Consider a finite difference approximation of the governing mass balance equations. The 
discretization uses three spatial cells. The left or first cell represents the upstream boundary 
conditions. The second cell represents the mixing cell with reactions. The third or right cell 
represents the down stream boundary conditions. Since cells one and three represent boundary 
conditions, this discretization is a 0-dimensional or single cell representation of the processes. 
Let time step length be t . . Let superscript n, for example n 
aq Pu c _ , denote the concentration at 
the nth time step. The discretization uses a first order backward difference approximation for the 
time derivative and the advective transport term. The diffusive flux uses a second order 
approximation. This discretization is consistent with GoldSim (GoldSim Technology Group 
2002 [DIRS 160579]). In this model, diffusion of dissolved mass and waste form colloids occurs 
at the left boundary, and at the right boundary, diffusion of both dissolved mass and all colloids 
occur. In addition, the porosity and water saturation are time-independent but may vary 
spatially. If the discretization is fully implicit in concentrations and time dependent velocity, 
irreversible reactions and solubility, then the discrete form of Equation B-34 is solved for 1
_ 
+ n 
aq Pu c 
as: 
( ) [ ] 
( ) t K R R K D D K D D K U K 
t c K D D K U c K 
c 
n n 
col right aq right c WF d col left aq left 
n 
n
s c WF d col left aq left c WF d 
n n 
aq Pu 
n 
aq Pu 
. + + + + + + + + 
. + + + + 
= 
+ + + 
+ + 
+ 
1 
1 
2 
1 
1 3 _ _ _ _ _ _ 2 
1 
1 
1 
_ _ _ _ _ _ 
1 
_ 1 
1
_ 
1 
. 
(Eq. B-48) 
where 
t U 
V 
t U 
L S 
t u 
water w 
. = 
. 
= 
. 
f 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-11 November 2004 
is the Courant number (dimensionless), L is the characteristic length (m), water V is the volume of 
water in the cell (m3), U is the volumetric water flux (m3 yr-1), and U is the advective rate 
constant (yr-1). Further, 
c GW d c WF d CP FeO d c FeO d K K K K K _ _ _ _ _ _ _ _ 1 1 + + + + = 
c GW d c WF d c FeO d K K K K _ _ _ _ _ _ 2 1 + + + = 
c GW d c WF d c FeO d K K K K _ _ _ _ _ _ 3 + + = 
and 
s 
water 
w 
A 
V 
L
D S H 
D 
.. 
. 
.. 
. 
= 
f 
is the diffusive rate constant with respect to either the solution or colloid mass at either the right 
or left cell interface. Here, s A is the cross sectional area for diffusion (m2), and pore V is the pore 
volume of the cell (m3). .. 
. 
.. 
. 
L
D S H w f 
is the harmonic average: 
2 2 2 
2 
1 1 1 
1 
1 
D S
L 
D S
L L
D S H 
w w 
w 
f f 
f 
+ 
= .. 
. 
.. 
. 
at Cell 1 and Cell 2 interface, where 1 L and 2 L are the half-lengths (m) of Cells 1 and 2, 
respectively. The harmonic average of 
L
D Sw f 
guarantees the continuity of the diffusive flux at 
the cell interface. The diffusive rate constant subscript left or right refers to the left or right 
diffusive boundary conditions, while the subscript aq or colloid refers to diffusion of the 
dissolved mass or colloid mass, respectively. 
The reversible concentrations are determined from Equations B-29 through B-32 
1
_ _ _ 
1 
_ _ 
+ + = n 
aq Pu c FeO d 
n 
c FeO Pu c K c (Eq. B-49) 
1
_ _ _ 
1 
_ _ 
+ + = n 
aq Pu CP FeO d 
n 
CP FeO Pu c K c (Eq. B-50) 
1
_ _ _ 
1 
_ _ 
+ + = n 
aq Pu c WF d 
n 
c WF Pu c K c (Eq. B-51) 
1
_ _ _ 
1 
_ _ 
+ + = n 
aq Pu c GW d 
n 
c GW Pu c K c . (Eq. B-52) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-12 November 2004 
The discretization of the balance Equation B-35 for irreversible Pu mass on the colloids yields 
t D U 
tc R c 
c 
col right 
n 
n 
aq Pu 
n n 
c FeO Pu Irrv n 
c FeO Pu Irrv . + + + 
. + 
= + 
+ + 
+ 
) ( 1 _ 
1 
1
_ 
1 
1 _ _ _ 1 
_ _ _ . 
(Eq. B-53) 
and for irreversible Pu mass on the corrosion products, Equation B-36 yields 
t 
tc R c 
c 
n 
aq Pu 
n n 
CP FeO Pu Irrv n 
CP FeO Pu Irrv . + 
. + 
= 
+ + 
+ 
. 1 
1
_ 
1 
2 _ _ _ 1 
_ _ _ . (Eq. B-54) 
SAMPLE CALCULATION WITH TSPA REPRESENTATIVE PARAMETERS 
A sample calculation is performed to demonstrate the solution technique and illustrate the types 
of behavior that might be expected in this model. Parameter values that are representative of the 
TSPA-LA are used in this sample calculation and are given in Table B-1. Let the solubility, flow 
velocity, and irreversible reaction parameters be constant over time. 
For this set of parameters, the irreversible reactive rates, advective rate, diffusive rates, decay 
rate and the dimensionless colloids and corrosion product partition coefficients are: 
. 020 . 0 
60 . 0 
10 965 . 1 
20 . 0 
yr 10 875 . 2 
yr 10 229 . 2 
yr 10 229 . 2 
yr 09127 . 0 
yr 04367 . 0 
yr 786 
yr 02000 . 0 
_ _ 
_ _ 
4 
_ _ 
_ _ 
1 - 5 
1 - 5 
_ 
1 - 3 
_ 
1 - 
_ 
1 - 
1 - 
2 
-1 
1 
=
= 
 =
= 
 = 
 = 
 =
=
=
=
= 
-
-
- 
c GW d 
c WF d 
CP FeO d 
c FeO d 
col right 
aq right 
aq left 
K
K 
K
K
D
D
D 
U
R
R
. 
The simulation for the mixing cell (Cell 2) concentrations over a 1000-year time interval is 
shown in Figure B-2. The dominant rate constant, by several orders of magnitude, is the 
irreversible rate constant of the corrosion products, -1 
2 yr 786 = R . This is a result of the large 
mass of corrosion products and results in a relative large concentration of irreversibly sorbed Pu 
on the corrosion products, CP FeO Pu Irrv c _ _ _ . For this simulation, the amount of corrosion product 
mass is representative of the total mass of corrosion products in a waste package, and all the 
corrosion products are available at initial time. In the TSPA abstraction model, the corrosion 
product mass is time dependent and a function of the corrosion rates for the carbon and stainless 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-13 November 2004 
steel (see Section 6.5.3.2). A large mass of Pu is reversibly sorbed onto the corrosion products. 
This is a result of the large reversible partition coefficient for the corrosion products, 
19650 _ _ = CP FeO d K , which again is a result of the large corrosion product mass. For this 
simulation, almost all of the mass is sorbed onto the corrosion products. Only a small amount of 
mass remains in solution or is sorbed onto the colloids. The qualitative behavior of the 
concentrations in Figure B-2 shows the concentrations approach a limiting value, with the 
exception of the irreversibly sorbed mass on the corrosion products. This behavior is discussed 
in the next section, where the concentrations are expressed analytically as solutions of difference 
equations, and their asymptotic in time values are determined. 
Table B-1. Representative Parameter Values for Sample Calculation 
Parameter Value Units Description 
s c 1.0 mg l-1 Solubility 
w S 1.0 dimensionless Water saturation 
1 f 1.0 dimensionless Porosity of Cell 1 
2 f 0.4 dimensionless Porosity of Cell 2 
3 f 0.3 dimensionless Porosity of Cell 3 
U 0.1 m3 yr-1 Volumetric water flux 
c FeO d K _ _ 1  104 ml g-1 Colloid partition coefficient 
CP FeO d K _ _ 2.5  103 ml g-1 Corrosion product partition coefficient 
c WF d K _ _ 2  105 ml g-1 Waste form colloids partition coefficient 
c GW d K _ _ 2  105 ml g-1 Groundwater colloids partition 
coefficient 
c FeO S _ 
 100 m2 g-1 Specific surface area of FeO colloids 
CP FeO S _ 
 10 m2 g-1 Specific surface area of FeO corrosion 
products 
c FeO c _ 20 mg l-1 Concentration of FeO colloids 
CP FeO c _ 7.86  106 mg l-1 Concentration of FeO corrosion 
products 
c WF c _ 3.0 mg l-1 Concentration of waste form colloids 
c GW c _ 0.1 mg l-1 Concentration of groundwater colloids 
k 0.001 cm yr-1 Forward sorption rate constant 
pore V 2.290 m3 Pore volume 
12 s A 36.0 m2 Diffusive area between Cell 1 and Cell 
2 
23 s A 1.068 m2 Diffusive area between Cell 2 and Cell 
3 
1 L 0.001 m Half-length of Cell 1 diffusive path 
2 L 5.0 m Half-length of Cell 2 diffusive path 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-14 November 2004 
Table B-1. Representative Parameter Values for Sample Calculation (Continued) 
Parameter Value Units Description 
3 L 0.806 m Half-length of Cell 3 diffusive path 
aq D 2.3  10-9 m2 s-1 Aqueous diffusivity 
colloid D 2.3  10-11 m2 s-1 Colloid diffusivity 
. 2.875  10-5 yr-1 Radionuclide decay rate 
1.0E-09 
1.0E-08 
1.0E-07 
1.0E-06 
1.0E-05 
1.0E-04 
1.0E-03 
1.0E-02 
1.0E-01 
1.0E+00 
0 100 200 300 400 500 600 700 800 900 1000 
Time [yrs] 
Concentrations [kg/m3] 
c_Pu_aq 
c_Pu_FeO_c 
c_Pu_FeO_CP 
c_Pu_WF_c 
c_Pu_GW_c 
c_Irrv_Pu_FeO_c 
c_Irrv_Pu_FeO_CP 
Figure B-2. Concentrations with Respect to Pore Volume 
CLOSED FORM SOLUTIONS OF THE DIFFERENCE EQUATIONS 
If the solubility, advective flux, saturation, and irreversible rates are chosen to be constant over 
time, then the mass balance equation for the aqueous Pu, Equation B-48, is a first order linear 
constant coefficient nonhomogeneous difference equation. This equation is of the form 
2 _ 1 
1
_ a c a c n 
aq Pu 
n 
aq Pu + = + ` (Eq. B-55) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-15 November 2004 
where 
( )t K R R K D D K D D K U K 
K a 
col right aq right c WF d col left aq left . + + + + + + + + 
= 
1 2 1 3 _ _ _ _ _ _ 2 1 
1 
1 . 
( ) 
( )t K R R K D D K D D K U K 
tc K D D K U 
a 
col right aq right c WF d col left aq left 
s c WF d col left aq left c WF d 
. + + + + + + + + 
. + + + 
= 
1 2 1 3 _ _ _ _ _ _ 2 1 
_ _ _ _ _ _ 
2 
) 1 ( 
. 
. 
The difference equation (Equation B-55) with initial condition of zero concentration has the 
solution 
1 
1 2 
_ 1 
) 1 ( 
a
a a c 
n 
n 
aq Pu -
- 
= . (Eq. B-56) 
Since the condition 1 0 1 < < a is guaranteed, the solution n 
aq Pu c _ for large time is asymptotic to 
( ) 
. 
) 1 ( 
1 
lim 
1 2 1 3 _ _ _ _ _ _ 2 
_ _ _ _ _ _ 
1 
2 
_ 
K R R K D D K D D K U 
c K D D K U 
a 
a c 
col right aq right c WF d col left aq left 
s c WF d col left aq left c WF d 
n 
aq Pu n 
. + + + + + + + 
+ + + 
= 
- 
= 
8 . 
(Eq. B-57) 
The terms in this expression represent the effects of advection, diffusion, decay, and reversible 
and irreversible sorption reactions. 
The difference equation for the irreversible colloid concentration (Equation B-53) is first order 
linear and is written as: 
1
_ 2 _ _ _ 1 
1 
_ _ _ 
+ + + = n 
aq Pu 
n 
c FeO Pu Irrv 
n 
c FeO Pu Irrv c b c b c (Eq. B-58) 
where 
( ) t D U 
b 
col right . + + + 
= 
. _ 
1 1 
1 (Eq. B-59) 
( ) t D U 
t R b 
col right . + + + 
. 
= 
. _ 
1 
2 1 
(Eq. B-60) 
and 1
_ 
+ n 
aq Pu c is given by Equation B-56. The difference Equation B-58 with initial condition zero 
has solution 
.. 
. 
.. 
. 
-
- 
- 
- 
- 
- 
= 
+ + + 
1 1 
1 
1 
1 
1 
1 
1 
1 
1 
2 2 
_ _ _ 1 
1 
1 b a 
b a 
b 
b 
a 
b a c 
n n n 
n 
c FeO Pu Irrv . (Eq. B-61) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-16 November 2004 
Since 1 0 1 < < a and 1 0 1 < < b , this solution has asymptotic behavior 
) 1 )( 1 ( 
lim 
1 1 
2 2 
_ _ _ b a 
b a 
c n 
c FeO Pu Irrv n - - 
= 
8 . 
. (Eq. B-62) 
Thus 
n 
aq Pu n 
col right 
n 
aq Pu n 
n 
c FeO Pu Irrv n 
c 
D U 
R c 
b 
b c _ 
_ 
1 
_ 
1 
2 
_ _ _ lim lim 
1 
lim 
8 . 8 . 8 . + + 
= 
- 
= 
. 
. (Eq. B-63) 
The difference equation for the concentration of the irreversible mass on the corrosion products 
is first order linear and is written as 
1
_ 2 _ _ _ 1 
1 
_ _ _ 
+ + + = n 
aq Pu 
n 
CP FeO Pu Irrv 
n 
CP FeO Pu Irrv c e c e c (Eq. B-64) 
where 
t 
e 
. + 
= 
. 1 
1 
1 (Eq. B-65) 
t 
t R e 
. + 
. 
= 
. 1 
2 
2 . (Eq. B-66) 
If 0 > . , Equation B-64 with initial concentration of zero has solution 
.. 
. 
.. 
. 
-
- 
- 
- 
- 
- 
= 
+ + + 
1 1 
1 
1 
1 
1 
1 
1 
1 
1 
2 2 
_ _ _ 1 
1 
1 e a 
e a 
e 
e 
a 
e a c 
n n n 
n 
CP FeO Pu Irrv . (Eq. B-67) 
If 0 = . , Equation B-64 with initial concentration of zero has solution 
.. 
. 
.. 
. 
- 
- 
- + 
- 
= 
+ 
1 
1 
1 
1 
2 2 
_ _ _ 1 
1 
1 
1 a 
a n 
a 
e a c 
n 
n 
CP FeO Pu Irrv . (Eq. B-68) 
The solution Equation B-67 has asymptotic value 
aq Pu n 
n 
aq Pu n 
n 
CP FeO Pu Irrv n 
c R c 
e 
e c _ 
2 
_ 
1 
2 
_ _ _ lim lim 
1 
lim 
8 . 8 . 8 . 
= 
- 
= 
. 
, (Eq. B-69) 
while the solution Equation B-68 does not have a limiting value, but is unbounded as a function 
of the time index n. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-17 November 2004 
BOUNDARY FLUXES 
Now consider the two boundary flux conditions given in Equations B-1 and B-2. The left or 
upstream boundary flux accounts for advection/diffusion of Pu mass in solution (Pu_aq) and Pu 
mass sorbed to waste form colloids. In this analysis, upstream diffusion of colloids is ignored, 
although the TSPA-LA implementation does account for upstream colloid diffusion. The mass 
flux rates (kg yr-1) at this upstream left boundary for the nth time step are: 
Advective_Pu_aq (kg yr-1) = s porec V U 
Diffusive_Pu_aq (kg yr-1) = ) ( _ _ 
n 
aq Pu s pore aq left c c V D - 
Advective_Pu_WF_c (kg yr-1) = s c WF d pore c K V U _ _ 
Diffusive_Pu_WF_c (kg yr-1) = ) ( _ _ _ _ 
n 
aq Pu s c WF d pore col left c c K V D - . 
The right or downstream boundary flux has contributions from advection/diffusion of Pu in 
solution and colloid together with advection/diffusion of Irrv_Pu on colloids. There is no 
advective or diffusive flux associated with the immobile corrosion products. The mass flux rates 
(kg yr-1) at the right boundary assuming zero downstream concentrations are: 
Advective_Pu_aq (kg yr-1) = n 
aq Pu porec V U _ 
Diffusive_Pu_aq (kg yr-1) = n 
aq Pu pore aq right c V D _ _ 
Advective_Pu_FeO_c (kg yr-1) = n 
aq Pu c FeO d pore c K V U _ _ _ 
Diffusive_Pu_FeO_c (kg yr-1) = n 
aq Pu c FeO d pore col right c K V D _ _ _ _ 
Advective_Irrv_Pu_FeO_c (kg yr-1) = n 
c FeO Pu Irrv porec V U _ _ _ 
Diffusive_Irrv_Pu_FeO_c (kg yr-1) = n 
c FeO Pu Irrv pore col right c V D _ _ _ _ 
Advective_Pu_WF_c (kg yr-1) = n 
aq Pu c WF d pore c K V U _ _ _ 
Diffusive_Pu_WF_c (kg yr-1) = n 
aq Pu c WF d pore col right c K V D _ _ _ _ 
Advective_Pu_GW_c (kg yr-1) = n 
aq Pu c GW d pore c K V U _ _ _ 
Diffusive_Pu_GW_c (kg yr-1) = n 
aq Pu c GW d pore col right c K V D _ _ _ _ . 
The total flux at the left boundary (upstream) at the nth time step, n 
total bddy left F _ _ , is 
) ( _ _ _ _ 
n 
aq Pu s pore aq left s pore 
n 
total bddy left c c V D c V U F - + = 
) ( _ _ _ _ _ _ 
n 
aq Pu s c WF d pore col left s c WF d pore c c K V D c K V U - + + . 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-18 November 2004 
The condition discussed in Equation B-1 considers the ratio of the colloid mass to total mass flux 
out the right boundary. The right boundary colloidal flux, n 
colloid bddy right F _ _ , due to both reversibly 
and irreversibly sorbed Pu is: 
n 
c FeO Pu Irrv pore 
n 
aq Pu c FeO d pore 
n 
colloid bddy right c V U c K V U F _ _ _ _ _ _ _ _ + = 
n 
aq Pu c GW d pore 
n 
aq Pu c WF d pore c K V U c K V U _ _ _ _ _ _ + + 
n 
c FeO Pu Irrv pore col right 
n 
aq Pu c FeO d pore col right c V D c K V D _ _ _ _ _ _ _ _ + + 
n 
aq Pu c GW d pore col right 
n 
aq Pu c WF d pore col right c K V D c K V D _ _ _ _ _ _ _ _ + + . 
The total Pu flux at the right boundary, n 
total bddy right F _ _ , is 
n 
total bddy right F _ _ = n 
aq Pu pore aq right 
n 
aq Pu pore 
n 
colloid bddy right c V D c V U F _ _ _ _ _ + + . 
The right boundary ratio of colloid flux out to total flux out at time level n is 
n 
total bddy right 
n 
colloid bddy right 
n F 
F 
_ _ 
_ _ = . 
. 
Then 
n 
aq Pu 
n 
c Pu Irrv 
col right 
col right aq right 
n 
aq Pu 
n 
c Pu Irrv 
n 
c 
c 
D U 
K D D K U 
c 
c 
K 
_ 
_ _ 
_ 
3 _ _ 2 
_ 
_ _ 
3 
+ 
+ 
+ + 
+ 
= . . 
Now from Equation B-61 
. + + 
= 
8 . 
col right 
n 
aq Pu 
n 
c Pu Irrv 
n D U 
R 
c 
c 
_ 
1 
_ 
_ _ lim . 
The limiting value for the right boundary ratio of colloid flux to total flux is 
. 
. 
+ + 
+ 
+ 
+ + 
+ + 
+ 
= . = . 
8 . 
col right col right 
col right aq right 
col right 
n n 
D U 
R 
D U 
K D D K U 
D U 
R K 
_ 
1 
_ 
3 _ _ 2 
_ 
1 
3 
lim 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-19 November 2004 
or 
( ) 
( ) 1 
_ 
_ 
3 _ _ 2 
1 _ 3 
R 
D U 
D U 
K D D K U 
R D U K 
col right 
col right 
col right aq right 
col right 
+ . .
.
. 
. .
.
. 
+ 
+ + 
+ + 
+ + + 
= . 
. 
. 
. (Eq. B-70) 
This can be written as 
1 2 
1 1 
R p 
R p 
+
+ 
= . (Eq. B-71) 
where 
( ) . + + = col right D U K p _ 3 1 
( ) . .
.
. 
. .
.
. 
+ 
+ + 
+ + = 
col right 
col right 
col right aq right D U 
D U 
K D D K U p 
_ 
_ 
3 _ _ 2 2 
. 
. 
Note the limiting flux out ratio . satisfies 
1 
) ( 
0 
3 _ _ 2 
_ 3 < . < 
+ + 
+ 
< 
K D D K U 
D U K 
col right aq right 
col right , 
where the lower bound on . is obtained when 0 1 = R . Qualitatively, if the advective, diffusive, 
and decay rates dominate the reactive rate constant 1 R , then . is close to the minimum value. 
However, if the reactive rate constant dominates, then . is close to one. The latter is the 
expected qualitative behavior of the system as alluded to in the introduction of this appendix. 
For the parameter values given in Table B-1, the minimum value 4384 . 0 = . is obtained with 
0 1 = R . The limiting flux out ratio for Table B-1 parameter values is 5487 . 0 = . ; in other 
words, about 55 percent of the total Pu mass exiting the cell is sorbed onto colloids. Figure B-3 
shows the dependence of the flux out ratio . on the irreversible linear reaction rate constant k, 
where k c S R c FeO c FeO _ _ 1 
 = . The point obtained with the Table B-1 parameter values is also 
shown in Figure B-3. An increase of the irreversible linear reaction rate, k, of approximately one 
and a half orders of magnitude would increase the flux out ratio to approximately 95 percent. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-20 November 2004 
In the expression for irreversible sorption to colloids, k c S R c FeO c FeO _ _ 1 
 = , consider the 
irreversible linear reaction rate k a fitting parameter to match a specified flux out ratio . . Then 
the solution of Equation B-71 for k is: 
c FeO c FeO c S 
p p k 
_ _ 
1 2
 ) 1 ( . - 
- . 
= . (Eq. B-72) 
The result in Equation B-72 provides the fitting parameter, k, given a target flux ratio . . From 
the parameter values in Table B-1 and with 95 . 0 = . , the irreversible linear reaction rate is 
determined from Equation B-72 as -1 yr cm 04184 . 0 = k . The fitting parameter curve together 
with this point is shown in Figure B-4. 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
1.E-05 1.E-04 1.E-03 1.E-02 1.E-01 1.E+00 
Irreversible Linear Reaction Rate [cm/yr] 
Colloid Flux/Total Flux Out 
flux out ratio 
k=0.001 cm/yr 
Source: Worksheet: K-surface in Appendix F. 
Figure B-3. Limiting Flux Out Ratio as a Function of Irreversible Reaction Rate 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-21 November 2004 
1.E-04 
1.E-03 
1.E-02 
1.E-01 
1.E+00
0.4 0.5 0.6 0.7 0.8 0.9 1.0 
Omega: Colloid Flux to Total Flux Ratio 
k: Irreversible Reaction Rate Constant [cm/yr] 
irreversible rate 
fitting curve 
Omega = 0.95 
Source: Worksheet: adv_diff_decay in Appendix F. 
Figure B-4. Linear Reaction Rate from Colloid to Total Flux Out Ratio 
The ratio of the total flux out (right boundary) to total flux in (left boundary) at time level n is 
( ) 
( ) ( )n 
aq Pu c WF d col left aq left s c WF d col left aq left c WF d 
n 
c FeO Pu Irrv col right 
n 
aq Pu col right aq right 
n c K D D c K D D K U 
c D U c K D D K U 
_ _ _ _ _ _ _ _ _ _ _ 
_ _ _ _ _ 3 _ _ 2 
) 1 ( 
) ( 
+ - + + + 
+ + + + 
= . . 
This flux ratio has limiting value 
( ) 1 2 1 
_ 
_ 
2 
1 2 
K R R 
D U 
D U 
p 
R p 
col right 
col right . 
. 
+ + . .
.
. 
. .
.
. 
+ 
+ + 
+ 
+ 
= . . (Eq. B-73) 
The mass flux ratio . is calculated from Equation B-73 for the Table B-1 parameter values, but 
with irreversible linear reaction rate k = 0.04184 cm yr-1 obtained from the fit to 95 . 0 = . . 
Equation B-73 gives 
4 10 293 . 1 -  = . , 
which demonstrates that most of the Pu mass is reacted both reversibly and irreversibly to the 
corrosion products. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-22 November 2004 
CONVERGENCE ESTIMATES FOR CLOSED FORM SOLUTIONS 
Consider the convergence of the concentration in the aqueous state given by Equation B-56: 
( ) n n 
aq Pu a 
a 
a c 1 
1 
2 
_ 1 
1 
- 
- 
= 
with limit value (Equation B-57) 
1 
2 
_ 1 
lim 
a 
a cn 
aq Pu n - 
= 
8 . 
. 
The relative error estimate with tolerance e is given by 
e < 
- 
8 . 
8 . 
n 
aq Pu n 
n 
aq Pu 
n 
aq Pu n 
c 
c c 
_ 
_ _ 
lim 
lim 
. 
Then the error estimate is 
( ) 
e < = 
- 
- 
- 
- 
- n 
n 
a 
a 
a 
a 
a 
a 
a 
a 
1 
1 
2 
1 
1 
2 
1 
2 
1 
1 
1 1 
. 
The bounds 1 0 1 < < a implies 0 log 1 10 < a and the error estimate holds for 
1 10 
10 
log 
log 
a 
n 
e 
> 
or 
t 
a 
t n . > . = 
1 10 
10 
log 
log time 
e 
. (Eq. B-74) 
The time to converge to a given relative error tolerance for all reversible sorbed Pu 
concentrations is the same as the estimate for the aqueous concentration, inequality 
Equation B-74, since the reversibly sorbed concentration is a constant multiple of the aqueous 
concentration. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-23 November 2004 
Now consider the convergence of the irreversible Pu concentration on colloids, n 
c Pu Irrv c _ _ . An 
estimate of the relative error is given by 
. 1 1 
) 1 ( ) 1 ( 
1 
) 1 ( 
) 1 )( 1 ( 
) 1 )( 1 ( 1 
1 
1 
lim 
lim 
1 
1 
1 1 
1 1 
1 
1 1 
1 
1 1 
1 
1 1 
1 1 
1 
1 1 
1 1 
1 
1 
1 
1 
1
1 
1 
1 
1 1 
2 2 
1 1 
2 2 
1 1 
1 
1 
1 
1 
1 
1 
1 
1 
2 2 
_ _ 
_ _ _ _ 
e < 
- 
- 
+ 
- 
- 
= 
- 
- 
- 
- 
- 
= 
. .. 
. 
. .. 
. 
-
- 
- 
- 
- 
- = 
- - 
- - 
- .. 
. 
.. 
. 
-
- 
- 
- 
- 
- 
= 
- 
+ + 
+ + 
+ + + 
+ + + 
8 . 
8 . 
n n 
n n 
n n n 
n n n 
n 
c Pu Irrv n 
n 
c Pu Irrv n 
n 
c Pu Irrv 
a 
b a 
b b 
b a 
a 
b a 
a b 
b a 
b a 
b a 
b a 
b 
b b 
b a 
b a 
b a 
b a 
b a 
b a 
b 
b 
a 
b a 
c 
c c 
This estimate holds if 
1 
1
1 1 1 
1 2 1 
d 
e 
= 
-
- 
< + 
a
b a bn and 2 
1
1 1 1 
1 2 1 
d 
e 
= 
-
- 
< + 
b
b a an . 
These two estimates are satisfied if 
1 
log 
log , 
log 
log max Integer 1 
1 10 
2 10 
1 10 
1 10 + .. 
. 
.. 
. 
. .. 
. 
. .. 
. 
= + 
a b 
n 
d d 
or 
t 
a b 
t n . .. 
. 
.. 
. 
. .. 
. 
. .. 
. 
= . = 
1 10 
2 10 
1 10 
1 10 
log 
log , 
log 
log max Integer time 
d d 
. (Eq. B-75) 
For a relative error tolerance of 1 percent ( 01 . 0 = e ) and the parameter values in Table B-1, 
Figure B-5 shows the time to converge for time step size 0.1 to 1000 years for both the aqueous 
Pu concentration and irreversible colloid Pu concentration. For example, if the time step is 
small, say 10 years, the number of years to converge within the given tolerance for the aqueous 
phase concentration is 137 years, whereas the time to converge for the irreversible colloid 
concentration is 240 years. If the time step is increased to 100 years, then the time to converge 
to the aqueous phase concentration is 286 years (three time steps), whereas the time to converge 
to the irreversible colloid concentration is 500 years (5 time steps). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-24 November 2004 
1.E+00 
1.E+01 
1.E+02 
1.E+03 
1.E+04 
1.E-01 1.E+00 1.E+01 1.E+02 1.E+03 
Time Step Size [yrs] 
Time to Converge [yrs] 
c_Pu_aq 
c_irrv_Pu_c 
Source: Spreadsheet: time_to_conv.xls, Worksheet: plot_time_to_conv in Appendix F. 
Figure B-5. Time for Concentration to Converge with 1 Percent Relative Error Tolerance 
ESTIMATED SORPTION CAPACITY OF CORROSION MATERIALS 
It is important to know if the radionuclide mass is capable of saturating the sorption sites 
available on the FeO. Let 
CP FeO S _ 
 = specific surface area of FeO (m2 FeO kg-1 FeO) 
site . = adsorption site density (sites m-2 FeO) 
A N = Avogadros number (sites mol-1) 
Pu M = Pu molecular weight (g mol-1). 
Use the following values in this calculation: 
CP FeO S _ 
 = 10 m2 g-1 (representative, from Table B-1) 
site . = 2.3  1018 sites m-2 (Davis and Kent 1990 [DIRS 143280]) 
A N = 6  1023 sites mol-1 (Lide 2002 [DIRS 160832], p. 1-7) 
Pu M = 239 g mol-1 (Weast 1985 [DIRS 111561], p. B-125). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-25 November 2004 
Then the radionuclide mass (represented by Pu) that will be sorbed per unit mass of FeO is: 
. FeO kg Pu g 16 . 9 
mol 
sites 10 6 
mol 
Pu g 239 
m 
sites 10 3 . 2 
FeO g
m 10  
1 - 
23 
2 
18 
2 
= 
 
.. 
. 
.. 
. 
.. 
. 
.. 
.  . .. 
. 
. .. 
. 
= 
A 
Pu site FeO 
N 
M S . 
The mass of FeO in a 21-PWR is estimated to be (Table 6.3-4): 
kg 19440 = FeO m 
and the radionuclide mass that can be sorbed is 
( ) 
Pu. kg 178 
FeO kg 19440 
FeO kg 
Pu g 16 . 9 sorbed mass de Radionucli 
= 
. .. 
. 
. .. 
. 
= 
This sorption capacity of the corrosion materials is dependent on the variability of the specific 
surface area, FeO S . The inventory mass of elements and their isotopes that is available to sorb 
irreversibly (Pu and Am) is estimated to be 83.6 kg per CSNF waste packages 
(DTN: SN0310T0505503.004 [DIRS 168761]). This estimate using representative parameter 
values shows that the mass of corrosion products is capable of sorbing all of the available 
radionuclide inventory. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 B-26 November 2004 
INTENTIONALLY LEFT BLANK 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 
APPENDIX C 
MICROSOFT EXCEL SPREADSHEET FLUX SPLIT DRIP SHIELD MODEL 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 C-1 November 2004 
MICROSOFT EXCEL SPREADSHEET FLUX SPLIT DRIP SHIELD MODEL 
SPREADSHEET FLUX SPLIT DRIP SHIELD MODEL WORKSHEET 
F CALCULATIONS 
DTN: MO0207EBSATBWP.023 [DIRS 163402]; DTN: MO0207EBSATBWP.024 [DIRS 163401]; 
DTN: MO0207EBSATBWP.025 [DIRS 163403]. 
Figure C-1. Spreadsheet Flux Split Drip Shield Model, Worksheet f calculations; Calculation of 
Experimental Breach Flow Fractions and Model Flow Fractions for Mean Minus One 
Standard Deviation Rivulet Spread Angle 
The purpose of this spreadsheet is to develop the drip shield flux splitting submodel using 
experimental data from the breached drip shield experiments. The data are analyzed to estimate 
an average and range of the rivulet spread angle, a. The disparity between measured fraction of 
dripping flux that enters a breach and the fraction calculated using the model (with the measured 
range of the rivulet spread angle) is then used to establish a range of uncertainty in the model. 
All descriptions for this worksheet (Figures C-1 to C-4) pertain to Rows 922. Equations in 
spreadsheet format are illustrated using Row 9. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 C-2 November 2004 
Column B: Drip location as indicated for each test in the designated DTN (Figure C-1). 
Column C: Breach or patch number most pertinent to this particular test, for which flow is 
analyzed in this row of the spreadsheet. 
Column D: Drip location, y, relative to the center of the breach listed in Column C. 
Column E: Vertical distance, x, from the drip shield crown to the top of the breach. 
Column F: Half-width, l , of the breach13.5 cm, same for all breaches. 
Column G: Measured mass of water, 1 F , dripped onto the drip shield during the test. It is 
assumed that half of the water that dripped onto the drip shield, 2 / 1 F , flowed 
down the side that contained the breach. 
Column H: Measured mass of water, 2 F , that flowed into the breach during the test. 
Column I: Fraction of water dripped onto the drip shield that flowed into the breach: 
1
2 
1 
2 2 
2 / F
F 
F
F fexpt = = . 
I9=H9*2/G9 
Column J: a tan x , where x is from Column E, and a is the spread angle. For Columns J-X, 
the value used for a is 8.8708 (Cell $M$7), which is one standard deviation less 
than the mean measured spread angle for these tests (see Worksheet Spread 
angles). 
J9=$E9*TAN(RADIANS($M$7)) 
Column K: Case number as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2. For Case 1, 
a tan x > l ; for Case 2, a tan x < l ; x is from Column E, and the half-width of the 
breach, l , is from Column F. 
K9=IF($F9>J9,1,2) 
Column L: Value of A y (Point A) as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2, 
corresponding to the leftmost point from which the edge of the fan from the 
rivulet can enter the left side of the breach: 
a tan ) 2 ( l l + - - = x yA 
L9=-$F9-($E9+2*$F9)*TAN(RADIANS($M$7)) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 C-3 November 2004 
Column M: Value of B y (Point B) as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2, 
corresponding to the leftmost point from which rivulets will enter the top edge of 
the breach. The value of B y depends on the Model Case number (Column K): 
a tan x yB + - = l Case 1. 
a tan x yB - = l Case 2. 
M9=IF(K9=1,(-$F9+$E9*TAN(RADIANS($M$7))), 
($F9-$E9*TAN(RADIANS($M$7)))) 
Column N: Value of C y (Point C) as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2, 
corresponding to the rightmost point from which rivulets will enter the top edge 
of the breach. The value of C y depends on the Model Case number (Column K): 
a tan x yC - = l Case 1. 
a tan x yC + - = l Case 2. 
N9=IF(K9=1,($F9-$E9*TAN(RADIANS($M$7))), 
(-$F9+$E9*TAN(RADIANS($M$7)))) 
Column O: Value of D y (Point D) as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2, 
corresponding to the rightmost point from which the edge of the fan from the 
rivulet can enter the right side of the breach: 
a tan ) 2 ( l l + + = x yD 
O9=$F9+($E9+2*$F9)*TAN(RADIANS($M$7)) 
Column P: Determines which region (designated as Fraction Case #) along the crown where 
the drip is located: 
1. A y y = 
2. l - = < y yA 
3. B y y < < - l 
4. C B y y y = = 
5. l < < y yC 
6. D y y < = l 
7. D y y = 
P9=IF(D9<=L9,1,IF(D9<=-F9,2,IF(D9<M9,3, 
IF(D9<=N9,4,IF(D9<F9,5,IF(D9<O9,6,IF(D9>=O9,7))))))) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 C-4 November 2004 
Figure C-2. Spreadsheet Flux Split Drip Shield Model, Worksheet f calculations; Calculation of Model 
Flow Fractions for Mean Minus One Standard Deviation Rivulet Spread Angle 
Columns R though X (Figure C-2) compute the fraction of dripping flux calc f that is predicted to 
flow into a breach, assuming the drip location is within each of seven regions along the crown. 
Although calc f is computed for all seven regions, it is valid in only one of the regions. The 
correct valid region is determined in Column P (Fraction Case #), and the appropriate value from 
Columns R through X is entered in Column Q. 
Column Q: calc f is the fraction of dripping flux onto the drip shield that is predicted by the 
drip shield flux splitting submodel, Equations 6.5.1.1.2-2 through 6.5.1.1.2-6 
or 6.5.1.1.2-19 through 6.5.1.1.2-23, for Cases 1 and 2, respectively. calc f is 
intended to be compared with expt f (Column I). The value of calc f is selected from 
Columns R through X, depending on the appropriate Fraction Case # (Column P). 
Q9=IF(P9=1,R9,IF(P9=2,S9,IF(P9=3,T9,IF(P9=4,U9, 
IF(P9=5,V9,IF(P9=6,W9,IF(P9=7,X9))))))) 

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Column R: Value of calc f in region 1 ( A y y = ), where . 0 = calc f 
R9=0 
Column S: Value of calc f in region 2 ( l - = < y yA ): 
a 
a 
tan ) 2 ( 2 
tan ) 2 ( 
l 
l l 
+ 
+ + + 
= 
x 
x y fcalc 
S9=(D9+F9+(E9+2*F9)*TAN(RADIANS($M$7)))/ 
(2*(E9+2*F9)*TAN(RADIANS($M$7))) 
Column T: Value of calc f in region 3 ( B y y < < - l ): 
a 
a 
tan 2 
tan 
x 
x y fcalc 
+ + 
= l 
T9=(D9+F9+E9*TAN(RADIANS($M$7)))/(2*E9*TAN(RADIANS($M$7))) 
Column U: Value of calc f in region 4 ( C B y y y = = ): 
a tan 2 
2 
x 
fcalc 
l = 
U9=IF(K9=1,1,(2*$F9/(2*$E9*TAN(RADIANS($M$7))))) 
Column V: Value of calc f in region 5 ( l < < y yC ): 
a 
a 
tan 2 
tan 
x 
x y fcalc 
+ + - 
= l 
V9=(-D9+F9+E9*TAN(RADIANS($M$7)))/(2*E9*TAN(RADIANS($M$7))) 
Column W: Value of calc f in region 6 ( D y y < = l ): 
a 
a 
tan ) 2 ( 2 
tan ) 2 ( 
l 
l l 
+ 
+ + + - 
= 
x 
x y fcalc 
W9=(-D9+F9+(E9+2*F9)*TAN(RADIANS($M$7)))/ 
(2*(E9+2*F9)*TAN(RADIANS($M$7))) 
Column X: Value of calc f in region 7 ( D y y = ) where 0 = calc f : 
X9=0 

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Figure C-3. Spreadsheet Flux Split Drip Shield Model, Worksheet f calculations; Calculation of Model 
Flow Fractions for Mean Rivulet Spread Angle 
Columns Y though AM (Figure C-3) repeat the calculations done in Columns J though X using 
the mean rivulet spread angle of 1527 . 13 = a  (Cell $AB$7). For Row 9, the spreadsheet 
equations are as follows: 
Y9=$E9*TAN(RADIANS($AB$7)) 
Z9=IF($F9>Y9,1,2) 
AA9=-$F9-($E9+2*$F9)*TAN(RADIANS($AB$7)) 
AB9=IF(Z9=1,(-$F9+$E9*TAN(RADIANS($AB$7))),($F9-$E9*TAN(RADIANS($AB$7)))) 
AC9=IF(Z9=1,($F9-$E9*TAN(RADIANS($AC$7))),(-$F9+$E9*TAN(RADIANS($AB$7)))) 
AD9=$F9+($E9+2*$F9)*TAN(RADIANS($AB$7)) 
AE9=IF(D9<=AA9,1,IF(D9<=- 
U9,2,IF(D9<AB9,3,IF(D9<=AC9,4,IF(D9<U9,5,IF(D9<AD9,6,IF(D9>=AD9,7))))))) 
AF9=IF(AE9=1,AG9,IF(AE9=2,AH9,IF(AE9=3,AI9,IF(AE9=4,AJ9,IF(AE9=5,AK9,IF(AE9 
=6,AL9,IF(AE9=7,AM9))))))) 

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AG9=0 
AH9=(D9+F9+(E9+2*F9)*TAN(RADIANS($AB$7)))/ 
(2*(E9+2*F9)*TAN(RADIANS($AB$7))) 
AI9=(D9+F9+E9*TAN(RADIANS($AB$7)))/(2*E9*TAN(RADIANS($AB$7))) 
AJ9=IF(Z9=1,1,(2*$F9/(2*$E9*TAN(RADIANS($AB$7))))) 
AK9=(-D9+F9+E9*TAN(RADIANS($AB$7)))/(2*E9*TAN(RADIANS($AB$7))) 
AL9=(-D9+F9+(E9+2*F9)*TAN(RADIANS($AB$7)))/ 
(2*(E9+2*F9)*TAN(RADIANS($AB$7))) 
AM9=0 
Columns AN though BB (Figure C-1) repeat the calculations done in Columns J though X using 
a rivulet spread angle of 2903 . 17 = a  (Cell $AQ$7), which is one standard deviation greater 
than the mean rivulet spread angle. For Row 9, the spreadsheet equations are as follows: 
AN9=$E9*TAN(RADIANS($AQ$7)) 
AO9=IF($F9>AN9,1,2) 
AP9=-$F9-($E9+2*$F9)*TAN(RADIANS($AQ$7)) 
AQ9=IF(AO9=1,(-$F9+$E9*TAN(RADIANS($AQ$7))),($F9- 
$E9*TAN(RADIANS($AQ$7)))) 
AR9=IF(AO9=1,($F9-$E9*TAN(RADIANS($AQ$7))), 
(-$F9+$E9*TAN(RADIANS($AQ$7)))) 
AS9=$F9+($E9+2*$F9)*TAN(RADIANS($AQ$7)) 
AT9=IF(AH9<=AP9,1,IF(AH9<=-AJ9,2,IF(AH9<AQ9,3,IF(AH9<=AR9,4, 
IF(AH9<AJ9,5,IF(AH9<AS9,6,IF(AH9>=AS9,7))))))) 
AU9=IF(AT9=1,AV9,IF(AT9=2,AW9,IF(AT9=3,AX9,IF(AT9=4,AY9,IF(AT9=5,AZ9,IF 
(AT9=6,BA9,IF(AT9=7,BB9))))))) 
AV9=0 
AW9=(D9+F9+(E9+2*F9)*TAN(RADIANS($AQ$7)))/ 
(2*(E9+2*F9)*TAN(RADIANS($AQ$7))) 
AX9=(D9+F9+E9*TAN(RADIANS($AQ$7)))/(2*E9*TAN(RADIANS($AQ$7))) 
AY9=IF(AO9=1,1,(2*$F9/(2*$E9*TAN(RADIANS($AQ$7))))) 
AZ9=(-D9+F9+E9*TAN(RADIANS($AQ$7)))/(2*E9*TAN(RADIANS($AQ$7))) 
BA9=(-D9+F9+(E9+2*F9)*TAN(RADIANS($AQ$7)))/ 
(2*(E9+2*F9)*TAN(RADIANS($AQ$7))) 
BB9=0 

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Figure C-4. Spreadsheet Flux Split Drip Shield Model, Worksheet f calculations; Calculation of Model 
Flow Fractions for Mean Plus One Standard Deviation Rivulet Spread Angle 
Rivulet spread measurements are listed in Column D, Rows 6-31 (Figure C-5), for 26 tests 
described in the indicated DTNs. The sketch to the right shows the relationships between 
measured rivulet spread (1/2 spread) and the 1/2 spread angle, a. The average, r , of the 
26 spread measurements (Cell D33) is 20.096 cm, with a standard deviation, s, of 6.674 cm. 
The uncertainty in the spread angle is incorporated into the drip shield flux splitting submodel by 
assigning a range for the rivulet spread of s  1  r . The mean rivulet spread and s  1  r are 
shown in Cells K6K8. The rivulet spread is converted to spread angle in Cells L6-L8 using the 
relation shown in the sketch that defines a: 
.. 
. 
.. 
. = - 
x 
wr 1 tan a , 

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where r w is the rivulet 1/2 spread (cm), and x is the distance from the crown to the spread 
measurement location (cm). The Microsoft Excel equation for the mean spread angle is: 
L6=DEGREES(ATAN(K6/($N$4))) 
where $N$4 = x = 86 cm for these tests. The Microsoft Excel function ATAN returns a value in 
radians, which must be converted to degrees using the DEGREES function. 
Also included in this worksheet is a sketch (Figure C-6) showing the dimensions and locations of 
breaches in the drip shield mockup used in the experiments. The sketch appears in the scientific 
notebook from the experiments (Howard 2002 [DIRS 161516], p. 14), and is also shown in 
Figure 4.1-1, Section 4.1.1. 
SPREADSHEET FLUX SPLIT DRIP SHIELD MODEL WORKSHEET 
SPREAD ANGLES 
DTN: MO0207EBSATBWP.023 [DIRS 163402]; DTN: MO0207EBSATBWP.024 [DIRS 163401]; 
DTN: MO0207EBSATBWP.025 [DIRS 163403]. 
Figure C-5. Spreadsheet Flux Split Drip Shield Model, Worksheet Spread angles; Calculation of 
Rivulet Spread Angle 

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Source: Howard 2002 [DIRS 161516], p. 14. 
Figure C-6. Spreadsheet Flux Split Drip Shield Model, Worksheet Spread Angles; Dimensions and 
Locations of Breaches in Drip Shield Mockup Used in Breached Drip Shield Experiments 

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SPREADSHEET FLUX SPLIT DRIP SHIELD MODEL WORKSHEET SUMMARY 
Source: BSC 2003 [DIRS 163406]. 
Figure C-7. Spreadsheet Flux Split Drip Shield Model, Worksheet Summary; Summary of Drip Shield 
Flux Splitting Submodel 
This worksheet, beginning with Figure C-7, summarizes the calculations in worksheets Spread 
angles and f calculations. 
The first table (Figure C-8), Measured Breach Flow Fractions and Calculated Breach Flow 
Fractions, Rows 25-43, Columns B-I, is identical to Table 6.5-2. Columns B-E are identical to 
the same respective columns described earlier for worksheet f calculations. Column F is 
identical to Column I in worksheet f calculations. Columns G-I summarize the calculated 
fraction of the dripping flux that the flux splitting submodel predicts should flow into the breach, 
for the minimum, mean, and maximum spread angles. The minimum spread angle is specified to 
be one standard deviation less than the mean of the measured spread angles. The maximum 
spread angle is specified to be one standard deviation greater than the mean of the measured 
spread angles. Column G is identical to Column Q of worksheet f calculations. Column H is 
identical to Column AF of worksheet f calculations. Column I is identical to Column AU of 
worksheet f calculations. 
Rows 3943, Columns FI, show the results of Microsoft Excel functions AVERAGE, 
STDEVA, MEDIAN, MIN, and MAX, respectively, as applied to Rows 25-38. 

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Figure C-8. Spreadsheet Flux Split Drip Shield Model, Worksheet Summary; Summary of Drip Shield 
Flux Splitting Submodel 
The second table (Figure C-9), Comparison of Measured and Calculated Breach Flows, is 
identical to Table 6.5-3. Column K is again the drip location. Column L is the fraction of 
dripping flux that flowed into a breach as measured experimentally; this is identical to Column F 
of the preceding table, or Column I in worksheet f calculations. The next three columns (M-O) 
show the difference between the predicted breach flow fraction, calc f , and the measured fraction, 
expt f , for the minimum, mean, and maximum rivulet spread angle. Columns P-R show the ratio 
expt calc f f / for the minimum, mean, and maximum rivulet spread angle. 
Rows 39-43, Columns L-R, show the results of Microsoft Excel functions AVERAGE, 
STDEVA, MEDIAN, MIN, and MAX, respectively, as applied to Rows 25-38. 

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Figure C-9. Spreadsheet Flux Split Drip Shield Model, Worksheet Summary; Summary of Drip Shield 
Flux Splitting Submodel Comparing Measured and Calculated Breach Flows 
Finally, a plot in worksheet Summary (Figure C-10) compares the calculated calc f with the 
measured expt f (Column F) for the minimum, mean, and maximum spread angles (Columns G, 
H, and I, respectively); the expt f and calc f values that are plotted in Figure C-10 are shown in 
Figure C-8. The diagonal line in the plot represents expt calc f f = . All values of calc f lie above the 
line expt calc f f = , indicating that the drip shield flux splitting submodel overestimates the flow 
into breaches. 

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Figure C-10. Spreadsheet Flux Split Drip Shield Model, Worksheet Summary; Comparison of 
Calculated and Measured Breach Flow Fractions for Drip Shield Flux Splitting Submodel 
for Minimum (8.87), Mean (13.15), and Maximum (17.29) Rivulet Spread Angles 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 
APPENDIX D 
MICROSOFT EXCEL SPREADSHEET FLUX SPLIT WASTE PACKAGE MODEL 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 

EBS Radionuclide Transport Abstraction 
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MICROSOFT EXCEL SPREADSHEET FLUX SPLIT WASTE PACKAGE MODEL 
SPREADSHEET FLUX SPLIT WASTE PACKAGE MODELWORKSHEET 
F CALCULATIONS 
DTN: MO0207EBSATBWP.023 [DIRS 163402]; DTN: MO0207EBSATBWP.025 [DIRS 163403]. 
Figure D-1. Spreadsheet Flux Split Waste Package Model, Worksheet f calculations; Calculation of 
Experimental Breach Flow Fractions and Model Flow Fractions for Mean Minus One 
Standard Deviation Rivulet Spread Angle 
The purpose of this spreadsheet is to develop the waste package flux splitting submodel using 
experimental data from the breached drip shield experiments. The data are analyzed to estimate 
an average and range of the rivulet spread angle, a. The disparity between measured fraction of 
dripping flux that enters a breach and the fraction calculated using the model (with the measured 
range of the rivulet spread angle) is then used to establish a range of uncertainty in the model. 
Whereas the drip shield submodel is based on data from on-crown drip locations, the waste 
package submodel uses off-crown drip data, for which the drip location is some distance away 
from the crown of the drip shield mockup. 
All descriptions for this worksheet pertain to Rows 9-34. Equations in spreadsheet format are 
illustrated using Row 9. 
Column B: Test type. The first three columns (B-D) help identify uniquely each test as 
described in the designated DTN. 

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Column C: Test date. 
Column D: Drip location as indicated for each test in the designated DTN. 
Column E: Breach or patch number most pertinent to this particular test, for which flow is 
analyzed in this row of the spreadsheet. 
Column F: Drip location relative to drip shield center. Applies only to Bounding tests, further 
defining the drip location as specified in the DTN. 
Column G: Breach location relative to drip shield center. Applies only to Bounding tests, 
further defining the breach location as specified in the DTN. 
Column H: Drip location, y, relative to the center of the breach listed in Column E. 
Column I: Vertical distance, x, from the drip location to the top of the breach. 
Column J: Half-width, l , of the breach13.5 cm, same for all breaches. 
Column K: Measured mass of water, 1 F , dripped onto the drip shield during the test. For the 
on-crown drips, it is assumed that half of the water that dripped onto the drip shield, 
2 / 1 F , flowed down the side that contained the breach. For these off-crown tests, 
the full dripping flux is assumed to flow down the side where the drip is located. 
Column L: Measured mass of water, 2 F , that flowed into the breach during the test. 
Column M: Fraction of water dripped onto the drip shield that flowed into the breach: 
1
2 
F
F fexpt = . 
M9=L9/K9 
Columns N through AB perform calculations that result in calc f , the fraction of dripping flux that 
is predicted by the model to flow into a breach. 
Column N: a tan x , where x is from Column I, and a is the spread angle. For Columns N-AB, 
the value used for a is 5.5037 (Cell $Q$7), which is one standard deviation less 
than the mean measured spread angle for these tests (see Worksheet Spread 
angles). 
N9=$I9*TAN(RADIANS($Q$7)) 
Column O: Case number as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2. For Case 1, 
a tan x > l ; for Case 2, a tan x < l ; x is from Column I, and the half-width of the 
breach, l , is from Column J. 

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O9=IF($J9>N9,1,2) 
Column P: Value of A y (Point A) as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2, 
corresponding to the leftmost point from which the edge of the fan from the rivulet 
can enter the left side of the breach: 
a tan ) 2 ( l l + - - = x yA 
P9=-$J9-($I9+2*$J9)*TAN(RADIANS($Q$7)) 
Column Q: Value of B y (Point B) as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2, 
corresponding to the leftmost point from which rivulets will enter the top edge of 
the breach. The value of B y depends on the Model Case number (Column O): 
a tan x yB + - = l Case 1. 
a tan x yB - = l Case 2. 
Q9=IF(O9=1,(-$J9+$I9*TAN(RADIANS($Q$7))), 
($J9-$I9*TAN(RADIANS($Q$7)))) 
Column R: Value of C y (Point C) as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2, 
corresponding to the rightmost point from which rivulets will enter the top edge of 
the breach. The value of C y depends on the Model Case number (Column O): 
a tan x yC - = l Case 1. 
a tan x yC + - = l Case 2. 
R9=IF(O9=1,($J9-$I9*TAN(RADIANS($Q$7))), 
(-$J9+$I9*TAN(RADIANS($Q$7)))), 
Column S: Value of D y (Point D) as described in Sections 6.5.1.1.2.1 and 6.5.1.1.2.2, 
corresponding to the rightmost point from which the edge of the fan from the rivulet 
can enter the right side of the breach: 
a tan ) 2 ( l l + + = x yD 
S9=$J9+($I9+2*$J9)*TAN(RADIANS($Q$7)) 

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Column T: Determines which region (designated as Fraction Case #) along the drip shield 
relative to the center of the breach where the drip is located: 
1. A y y = 
2. l - = < y yA 
3. B y y < < - l 
4. C B y y y = = 
5. l < < y yC 
6. D y y < = l 
7. D y y = 
T9=IF($H9<=P9,1,IF($H9<=-$J9,2,IF($H9<Q9,3, 
IF($H9<=R9,4,IF($H9<$J9,5,IF($H9<S9,6,IF($H9>=S9,7))))))) 
Figure D-2. Spreadsheet Flux Split Waste Package Model, Worksheet f calculations; Calculation of 
Model Flow Fractions for Mean Minus One Standard Deviation Rivulet Spread Angle 
Columns V though AB compute the fraction of dripping flux calc f that is predicted to flow into a 
breach, assuming the drip location is within each of seven regions listed above under Column T. 
Although calc f is computed for all seven regions, it is valid in only one of the regions. The 

EBS Radionuclide Transport Abstraction 
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correct valid region is determined in Column T (Fraction Case #), and the appropriate value from 
Columns VAB is entered in Column U. 
Column U: calc f is the fraction of dripping flux onto the drip shield that is predicted by the drip 
shield flux splitting submodel, Equations 6.5.1.1.2-2 through 6.5.1.1.2-6 or 
6.5.1.1.2-19 through 6.5.1.1.2-23, for Cases 1 and 2, respectively. calc f is intended 
to be compared with expt f (Column M). The value of calc f is selected from 
Columns V through AB, depending on the appropriate Fraction Case # (Column T). 
U9 =IF(T9=1,V9,IF(T9=2,W9,IF(T9=3,X9,IF(T9=4,Y9, 
IF(T9=5,Z9,IF(T9=6,AA9,IF(T9=7,AB9))))))) 
Column V: Value of calc f in region 1 ( A y y = ), where . 0 = calc f 
V9=0 
Column W: Value of calc f in region 2 ( l - = < y yA ): 
a 
a 
tan ) 2 ( 2 
tan ) 2 ( 
l 
l l 
+ 
+ + + 
= 
x 
x y fcalc 
W9 =(H9+J9+(I9+2*J9)*TAN(RADIANS($Q$7)))/ 
(2*(I9+2*J9)*TAN(RADIANS($Q$7))) 
Column X: Value of calc f in region 3 ( B y y < < - l ): 
a 
a 
tan 2 
tan 
x 
x y fcalc 
+ + 
= l 
X9=(H9+J9+I9*TAN(RADIANS($Q$7)))/(2*I9*TAN(RADIANS($Q$7))) 
Column Y: Value of calc f in region 4 ( C B y y y = = ): 
a tan 2 
2 
x 
fcalc 
l = 
Y9=IF(O9=1,1,(2*$J9/(2*$I9*TAN(RADIANS($Q$7))))) 
Column Z: Value of calc f in region 5 ( l < < y yC ): 
a 
a 
tan 2 
tan 
x 
x y fcalc 
+ + - 
= l 
Z9=(-H9+J9+I9*TAN(RADIANS($Q$7)))/(2*I9*TAN(RADIANS($Q$7))) 

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Column AA: Value of calc f in region 6 ( D y y < = l ): 
a 
a 
tan ) 2 ( 2 
tan ) 2 ( 
l 
l l 
+ 
+ + + - 
= 
x 
x y fcalc 
AA9=(-H9+J9+I9*TAN(RADIANS($Q$7)))/ 
(2*I9*TAN(RADIANS(AA9$Q$7))) 
Column AB: Value of calc f in region 7 ( D y y = ) where 0 = calc f : 
AB9=0 
Figure D-3. Spreadsheet Flux Split Waste Package Model, Worksheet f calculations; Calculation of 
Model Flow Fractions for Mean Rivulet Spread Angle 
Columns AC though AQ repeat the calculations done in Columns N though AB using the mean 
rivulet spread angle of 7326 . 13 = a  (Cell $AF$7). For Row 9, the spreadsheet equations are as 
follows: 
AC9=$I9*TAN(RADIANS($AF$7)) 

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AD9=IF($J9>AC9,1,2) 
AE9=-$J9-($I9+2*$J9)*TAN(RADIANS($AF$7)) 
AF9=IF(AD9=1,(-$J9+$I9*TAN(RADIANS($AF$7))),($J9-$I9*TAN(RADIANS($AF$7)))) 
AG9=IF(AD9=1,($J9-$I9*TAN(RADIANS($AF$7))),(-$J9+$I9*TAN(RADIANS($AF$7)))) 
AH9=$J9+($I9+2*$J9)*TAN(RADIANS($AF$7)) 
AI9=IF($H9<=AE9,1,IF($H9<=-$J9,2,IF($H9<AF9,3, 
IF($H9<=AG9,4,IF($H9<$J9,5,IF($H9<AH9,6,IF($H9>=AH9,7))))))) 
AJ9=IF(AI9=1,AK9,IF(AI9=2,AL9,IF(AI9=3,AM9,IF(AI9=4,AN9,IF(AI9=5,AO9,IF(AI9=6,A 
P9,IF(AI9=7,AQ9))))))) 
AK9=0 
AL9=(H9+J9+(I9+2*J9)*TAN(RADIANS($AF$7)))/ 
(2*(I9+2*J9)*TAN(RADIANS($AF$7))) 
AM9=(H9+J9+I9*TAN(RADIANS($AF$7)))/(2*I9*TAN(RADIANS($AF$7))) 
AN9=IF(AD9=1,1,(2*$J9/(2*$I9*TAN(RADIANS($AF$7))))) 
AO9=(-H9+J9+I9*TAN(RADIANS($AF$7)))/(2*I9*TAN(RADIANS($AF$7))) 
AP9=(-H9+J9+(I9+2*J9)*TAN(RADIANS($AF$7)))/ 
(2*(I9+2*J9)*TAN(RADIANS($AF$7))) 
AQ9=0 
Columns AR though BF (next page) repeat the calculations done in Columns N though AB using 
a rivulet spread angle of 9614 . 21 = a  (Cell $AU$7), which is one standard deviation greater 
than the mean rivulet spread angle. For Row 9, the spreadsheet equations are as follows: 
AR9=$I9*TAN(RADIANS($AU$7)) 
AS9=IF($J9>AR9,1,2) 
AT9=-$J9-($I9+2*$J9)*TAN(RADIANS($AU$7)) 
AU9=IF(AS9=1,(-$J9+$I9*TAN(RADIANS($AU$7))),($J9-$I9*TAN(RADIANS($AU$7)))) 
AV9=IF(AS9=1,(-$J9+$I9*TAN(AV9RADIANS($AU$7))),($J9- 
$I9*TAN(RADIANS($AU$7)))) 
AW9=$J9+($I9+2*$J9)*TAN(RADIANS($AU$7)) 
AX9=IF($H9<=AT9,1,IF($H9<=-$J9,2,IF($H9<AU9,3,IF($H9<=AV9,4, 
IF($H9<$J9,5,IF($H9<AW9,6,IF($H9>=AW9,7))))))) 
AY9=IF(AX9=1,AZ9,IF(AX9=2,BA9,IF(AX9=3,BB9,IF(AX9=4,BC9,IF(AX9=5,BD9,IF 
(AX9=6,BE9,IF(AX9=7,BF9))))))) 
AZ9=0 

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BA9=(H9+J9+(I9+2*J9)*TAN(RADIANS($AU$7)))/ 
(2*(I9+2*J9)*TAN(RADIANS($AU$7))) 
BB9=(H9+J9+I9*TAN(RADIANS($AU$7)))/(2*I9*TAN(RADIANS($AU$7))) 
BC9=IF(AS9=1,1,(2*$J9/(2*$I9*TAN(RADIANS($AU$7))))) 
BD9=(-H9+J9+I9*TAN(RADIANS($AU$7)))/(2*I9*TAN(RADIANS($AU$7))) 
BE9=(-H9+J9+(I9+2*J9)*TAN(RADIANS($AU$7)))/ 
(2*(I9+2*J9)*TAN(RADIANS($AU$7))) 
BF9=0 
Figure D-4. Spreadsheet Flux Split Waste Package Model, Worksheet f calculations; Calculation of 
Model Flow Fractions for Mean Plus One Standard Deviation Rivulet Spread Angle 

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SPREADSHEET FLUX SPLIT WASTE PACKAGE MODELWORKSHEET 
SPREAD ANGLES 
DTN: MO0207EBSATBWP.023 [DIRS 163402]; DTN: MO0207EBSATBWP.025 [DIRS 163403]. 
Figure D-5. Spreadsheet Flux Split Waste Package Model, Worksheet Spread angles; Calculation of 
Rivulet Spread Angle 
In this worksheet, the mean and range of the rivulet spread angle a is determined from spread 
measurements. The drip locations are off-crown, at the 16.5 and 33 positions on the drip shield 
mockup. These angles are the angular distances from the crown about the center of curvature of 
the drip shield; thus, the crown is at 0, and the transition from the curved top surface to the 
vertical side of the drip shield is located about 60 from vertical. The actual distance (arc length) 
from the crown to the 16.5 line is 43 cm; from the crown to the 33 line the distance is 86 cm; 
and from the crown to the transition line the distance is 150 cm. The distance x from the drip 
location to the spread measurement location (the 33 line or the transition line) is shown in 
Columns E and H, respectively. 
Columns B and C identify the pertinent tests as described in the designated DTNs. In each test, 
the spread of rivulets to the right and to the left of the drip location was measured. The spread 
distance measured at the 33 line is listed in Columns F and G. The spread distance measured at 
the transition line is listed in Columns I and J. For drips at the 33 location, no rivulet spread 
was measured, although splattering upslope may have resulted in some rivulets appearing at the 
drip location. 
The sketch below from the scientific notebook for the experiments (Howard 2002 
[DIRS 161516], p. 14) indicates the dimensions and locations of breaches on the drip shield 
mockup used in the tests. This sketch is also shown in Figure 4.1-1, Section 4.1.1. 

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Source: Howard 2002 [DIRS 161516], p. 14. 
Figure D-6. Spreadsheet Flux Split Waste Package Model, Worksheet Spread angles; Dimensions 
and Locations of Breaches in Drip Shield Mockup Used in Breached Drip Shield 
Experiments 

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Figure D-7. Spreadsheet Flux Split Waste Package Model, Worksheet Spread angles; Calculation of 
Rivulet Spread Angles and Statistical Measures 
In Column M, Rows 928 (Figure D-7), all of the spread measurements (right and left) at the 
33 line are listed for the 16.5 drip location from the Q(film) and Bounding tests. In Rows 
31-47 (Figure D-7), the spread from 16.5 drips measured at the transition are listed for the 
Q(film) and Bounding tests. In Rows 5059, the spread from 33 drips measured at the 
transition are listed for the Bounding tests. In Column N, the distance, x, from the drip location 
to the measurement location is listed. In Column O, the spread angle, a, is computed from the 
rivulet spread, r w (cm): 
.. 
. 
.. 
. = - 
x 
wr 1 tan a , 
The spreadsheet equation for Row 9 is: 
O9=DEGREES(ATAN(M9/N9)) 

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In Column R (Figures D-7 and D-8), the mean spread angle and standard deviation are shown for 
comparison for three groups of datadrip location at 16.5 measured at 33, drip location at 16.5 
measured at the transition line, and drip location at 33 measured at the transition line. The 
statistics for all measurements are computed in Column U. The mean rivulet spread angle 
(Cell U19) and the bounds on the range for spread angle as defined by the mean minus one 
standard deviation (Cell U21) and the mean minus one standard deviation (Cell U22) are used in 
Worksheet f calculations as the basis of the waste package flux splitting submodel to compute 
the predicted fraction of dripping flux that flows into a breach, calc f . 
Figure D-8. Spreadsheet Flux Split Waste Package Model, Worksheet Spread angles; Calculation of 
Rivulet Spread Angles 

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SPREADSHEET FLUX SPLIT WASTE PACKAGE MODELWORKSHEET 
SUMMARY 
Source: BSC 2003 [DIRS 163406]. 
Figure D-9. Spreadsheet Flux Split Waste Package Model, Worksheet Summary; Summary of 
Waste Package Flux Splitting Submodel 
This worksheet, beginning with Figure D-9, summarizes the calculations in Worksheets Spread 
angles and f calculations. 
In the first table (Figure D-10), Measured Breach Flow Fractions and Calculated Breach Flow 
Fractions, Columns B, C, D, and E are identical to Columns D, E, H, and I described earlier for 
Worksheet f calculations. Column F ( expt f ) is identical to Column M in Worksheet 
f calculations. Columns GI summarize the calculated fraction of the dripping flux that the 
flux splitting submodel predicts should flow into the breach, for the minimum, mean, and 
maximum spread angles. The minimum spread angle is specified to be one standard deviation 
less than the mean of the measured spread angles. The maximum spread angle is specified to be 
one standard deviation greater than the mean of the measured spread angles. Column G is 
identical to Column U of Worksheet f calculations. Column H is identical to Column AJ of 
Worksheet f calculations. Column I is identical to Column AY of Worksheet f calculations. 
Rows 5054, Columns FI, show the results of Microsoft Excel functions AVERAGE, 
STDEVA, MEDIAN, MIN, and MAX, respectively, as applied to Rows 25-49. 

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Figure D-10. Spreadsheet Flux Split Waste Package Model, Worksheet Summary; Summary of 
Waste Package Flux Splitting Submodel 
In the second table (Figure D-11), Comparison of Measured and Calculated Breach Flows, 
Column K is again the drip location. Column L is the fraction of dripping flux ( expt f ) that 
flowed into a breach as measured experimentally; this is identical to Column F of the preceding 
table, or Column M in Worksheet f calculations. The next three columns (M-O) show the 
difference between the predicted breach flow fraction, calc f , and the measured fraction, expt f , for 
the minimum, mean, and maximum rivulet spread angle. Columns P-R show the ratio expt calc f f / 
for the minimum, mean, and maximum rivulet spread angle. 

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Rows 50-54, Columns L-R, show the results of Microsoft Excel functions AVERAGE, 
STDEVA, MEDIAN, MIN, and MAX, respectively, as applied to Rows 25-49. 
Figure D-11. Spreadsheet Flux Split Waste Package Model, Worksheet Summary; Summary of 
Waste Package Flux Splitting Submodel Comparing Measured and Calculated Breach 
Flows 

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ANL-WIS-PA-000001 REV 01 D-16 November 2004 
Lastly, a plot in Worksheet Summary (Figure D-12) compares the calculated calc f with the 
measured expt f for the minimum, mean, and maximum spread angles; the expt f and calc f values 
that are plotted in Figure D-12 are shown in Figure D-10. The diagonal line in the plot 
represents expt calc f f = . Most values of calc f lie above the line expt calc f f = , indicating that the 
waste package flux splitting submodel tends to overestimate the flow into breaches. 
Figure D-12. Spreadsheet Flux Waste Package Shield Model, Worksheet Summary; Comparison of 
Calculated and Measured Breach Flow Fractions for Waste Package Flux Splitting 
Submodel for Minimum (5.50), Mean (13.73), and Maximum (21.96) Rivulet Spread 
Angles 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 
APPENDIX E 
MICROSOFT EXCEL SPREADSHEET FLUX SPLITTING VALIDATION 

EBS Radionuclide Transport Abstraction 
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MICROSOFT EXCEL SPREADSHEET FLUX SPLITTING VALIDATION 
SPREADSHEET FLUX SPLITTING VALIDATIONWORKSHEET SPLASH 
RAD VS NUMBER 
Figure E-1. Spreadsheet Flux Splitting ValidationWorksheet Splash Rad vs Number; Effect of 
Number of Drips on Splash Radius 
In this worksheet (Figures E-1 to E-3), the effect of the number of drips on the splash radius is 
analyzed using data from dripping on the crown in the rough drip shield tests. This analysis is 
used for validation of the drip shield flux splitting submodel. The splash distance or radius (cm) 
to the left and to the right of the drip location are listed in Columns A and B, respectively. The 
number of drips in each test is given in Column C. The type of measurementinner cluster (I) or 
outer fringe (O)is indicated in Column D. These data and the DTN from which they were 
obtained (MO0207EBSATBWP.021 [DIRS 163399]) are also presented in Table 7.1-1. In 
Row 26, the sum of the splash radii is shown. Rows 27, 28, and 29 give the mean, standard 
deviation, and median for each column. The mean, standard deviation, and median for all 40 
splash radius measurements are listed in Column G, Rows 11, 12, and 13, respectively. 
The plot to the right in Figure E-1, which is reproduced as Figure 7.1-1, shows the dependence of 
splash radius on the number of drips. As indicated beneath the figure, the data are the same as in 
the table, but organized by type of measurement further down in this worksheet. The Trendline 
tool in Microsoft Excel is used to fit a quadratic curve to the inner cluster and outer fringe data. 
The correlation coefficient is shown for each curve, and the correlation equation is shown for the 
inner cluster curve. A second degree polynomial was chosen for the Trendline in order to 
display the expected behaviorthe splash radius should increase with the number of drips, but 
eventually reach a maximum. A functional form such as ( ) ax e y y - - = 1 max may be more 
appropriate, but because this is nonlinear in the fitting parameter a, a simple linear least squares 
fit using Trendline is not possible. Since the object is simply to demonstrate a correlation, a 
more accurate fit to the data is not necessary. 

EBS Radionuclide Transport Abstraction 
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In Figure E-2, the experimental data from the top of the worksheet are reorganized by type of 
measurement and, in Figure E-3, all left and right measurements are consolidated for plotting in 
the plot at the top of the worksheet (shown in Figure E-1). 
Figure E-2. Spreadsheet Flux Splitting ValidationWorksheet Splash Rad vs Number; Effect of 
Number of Drips on Splash Radius; Data Organized by Type of Measurement 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 E-3 November 2004 
Figure E-3. Spreadsheet Flux Splitting ValidationWorksheet Splash Rad vs Number; Effect of 
Number of Drips on Splash Radius; All Left and Right Measurements Are Consolidated 
SPREADSHEET FLUX SPLITTING VALIDATIONWORKSHEET SPLASH 
RADIUS 
For validation of the drip shield and waste package flux splitting submodels, splash radius data 
are analyzed for measurements on the rough drip shield surface, with dripping on the crown and 
at off-crown locations. Data for crown drip locations are used for the drip shield submodel 
validation, and off-crown drip locations are used for the waste package submodel validation. 
The statistics (mean, standard deviation, median, mean plus one standard deviation, and mean 
minus one standard deviation) are shown in Column I, Rows 1923 for crown drip locations, and 
in Rows 37-41 for off-crown locations. The data actually used in the model validation are the 
minimum and maximum values for more than 20 drips, Cells H11 and I9, respectively, for crown 
locations, and Cells H31 and I36, respectively, for off-crown locations. 

EBS Radionuclide Transport Abstraction 
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DTN: MO0207EBSATBWP.021 [DIRS 163399]. 
Figure E-4. Spreadsheet Flux Splitting ValidationWorksheet Splash Radius; Splash Radius 
Determination 

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SPREADSHEET FLUX SPLITTING VALIDATIONWORKSHEET ROUGH DS 
This worksheet provides calculations for validation of the drip shield flux splitting submodel 
based on data from rough drip shield surface tests. An overall view of the worksheet is shown in 
Figure E-5 to show the layout of the worksheet, and individual tables are then presented more 
legibly and described in detail on following pages. 
DTN: MO0208EBSATBWP.027 [DIRS 163404]; DTN: MO0208EBSATBWP.028 [DIRS 163405]. 
Figure E-5. Spreadsheet Flux Splitting ValidationWorksheet Rough DS; Worksheet Overview 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 E-6 November 2004 
DTN: MO0208EBSATBWP.027 [DIRS 163404]; DTN: MO0208EBSATBWP.028 [DIRS 163405]. 
Figure E-6. Spreadsheet Flux Splitting ValidationWorksheet Rough DS; Calculation of Experimental 
Breach Flow Fractions 
Figure E-7. Spreadsheet Flux Splitting ValidationWorksheet Rough DS; Summary of Experimental 
Breach Flow Fractions 

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Tests are identified in Figure E-6 in Column A. Columns B and C are raw datathe initial and 
final water mass in the input water container. Column D is the difference between Columns B 
and C (e.g., D8=B8-C8), giving the mass of water dripped onto the drip shield. Columns E and 
F are the initial and final masses of water in the Breach B4 collection vessel. The difference, in 
Column G (e.g., G8=F8-E8), is the mass of water that flowed into B4. In Column H 
(Figure E-7), the fraction of the dripping flux that flowed into B4, expt f (B4), is calculated for 
tests in which the flow into B4 was greater than zero (e.g., H8=2*G8/D8). Because the dripping 
was onto the crown, it is assumed that only half of the total input (i.e., D8/2) flowed down the 
side of the drip shield where B4 was located. 
Columns I and J are the initial and final masses of water in the Breach B5 collection vessel. The 
difference, in Column G (e.g., K8=J8-I8), is the mass of water that flowed into B5. In 
Column N, the fraction of the dripping flux that flowed into B5, expt f (B5), is calculated for tests 
in which the flow into B5 was greater than zero (e.g., N10=2*K10/D10). Because the drip 
location was the crown, it is assumed that only half of the total input (i.e., D10/2) flowed down 
the side of the drip shield where B5 was located. 
The input water mass and flows into Breaches B4 and B5 are summarized in Table 7.1-3. 
In Column P, all values of expt f are consolidated. The mean, standard deviation, and median for 
the 12 data values are given in Rows 21, 22, and 23, respectively. The values of expt f are listed 
in Table 7.1-4. 
DTN: MO0208EBSATBWP.027 [DIRS 163404]; DTN: MO0208EBSATBWP.028 [DIRS 163405]. 
Figure E-8. Spreadsheet Flux Splitting ValidationWorksheet Rough DS; Rivulet Spread Distances 
Rivulet spread distances for each test are listed in Figure E-8, Columns D and E, Rows 28-40, for 
drips originating on the crown of the rough drip shield surface. The spread data are reorganized 
in Column B, starting in Row 52 (see Figure E-9). All spread data measured 86 cm from the drip 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 E-8 November 2004 
location are listed first, followed by all data measured 136 cm from the drip location. The 
corresponding x-distance is listed in Column C, starting in Row 52. In Column E, the spread 
distances, r w , are converted to spread angles using the formula: 
.. 
. 
.. 
. = - 
x 
wr 1 tan a . 
In Cell E52, for example, the Microsoft Excel equation is: E52=ATAN(B52/C52). The result 
is the spread angle in radians, which is converted to degrees in Column F 
(e.g., F52=DEGREES(E52)). The mean spread angle for 86-cm drips is given in Cell I55 
(I55=AVERAGE(F52:F63)) and for 136-cm drips in Cell I69 (I69=AVERAGE(F65:F75)). 
Statistics are computed for all individual spread angle data in Column F, Rows 77-82: 
F77=AVERAGE(F52:F75) 
F78=STDEVA(F52:F75) 
F79=F77-F78 
F80=F77+F78 
F81=MIN(F52:F75) 
F82=MAX(F52:F75) 
As shown in F79 and F80, the range for the spread angle is zero (rounding down) to 14.4. 
Figure E-9. Spreadsheet Flux Splitting ValidationWorksheet Rough DS; Rivulet Spread Data 
Reorganized 

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Figure E-10. Spreadsheet Flux Splitting ValidationWorksheet Rough DS; Calculation of Rivulet 
Spread Angles 
In Column H, Rows 28-40 (see Figure E-10), the average rivulet spread is computed for each 
experiment (e.g., H28=(D28+E28)/2). Column I is the distance from the crown to the point 
where the rivulet spread was measured (identical to Column C). The spread angle is computed 
in Column J, Rows 28-40, (e.g., J28=ATAN(H28/I28)). In Column K, Rows 28-40, the 

EBS Radionuclide Transport Abstraction 
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average spread angle in radians is converted to degrees (e.g., K28=DEGREES(J28)). In 
Worksheet Splash Rad vs Number, the minimum splash radius for tests using 20 or more drips 
was 3.5 cm, for a total splash distance of 7 cm. This is used as the effective drip shield length in 
Column L, where calc f is obtained using the formula 
.. 
. 
.. 
. + = 
.. 
. 
.. 
. + = 
2 
tan 1 
7
5 . 13 
2 
tan 1 
a 
a 
L 
fcalc 
l 
L28=13.5*(1+TAN(J28)/2)/7 
The maximum splash radius tests using 20 or more drips was 48 cm in Worksheet Splash Rad 
vs. Number, giving a total splash distance of 96 cm. This is used as the effective drip shield 
length in Column M, 
.. 
. 
.. 
. + = 
.. 
. 
.. 
. + = 
2 
tan 1 
96
5 . 13 
2 
tan 1 
a 
a 
L 
fcalc 
l 
M28=13.5*(1+TAN(J28)/2)/96 
The values of calc f in Columns L and M are the same as VD f F / following Equation 7.2.1-1. As 
shown in the statistics (Rows 4647), VD f F / ranges from 0.147 to 2.078. 
In Column N, Rows 2840, the values of expt f are transferred from Column P, Rows 920. In 
Column O, the ratio calc expt f f / is computed (e.g., O28=N28/L28) for the minimum effective 
drip shield length of 7 cm. In Column P, the ratio calc expt f f / is computed (e.g., P28=N28/M28) 
for the maximum effective drip shield length of 96 cm. This ratio is identical to the uncertainty 
factor DV f in Equation 7.2.1-2. As shown in the statistics (Rows 4647), VD f F/ for the 
experimental data ranges from 0.0 to 8.306 

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SPREADSHEET FLUX SPLITTING VALIDATIONWORKSHEET ROUGH OFF 
CROWN WP MODEL 
This worksheet provides calculations for validation of the waste package flux splitting submodel 
based on data from the rough drip shield surface tests. An overall view of the worksheet is 
shown in Figure E-11, and individual tables are then described in detail. 
Figure E-11. Spreadsheet Flux Splitting ValidationWorksheet Rough off crown WP model; 
Worksheet Overview 

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DTN: MO0208EBSATBWP.027 [DIRS 163404]; DTN: MO0208EBSATBWP.028 [DIRS 163405]. 
Figure E-12. Spreadsheet Flux Splitting ValidationWorksheet Rough off crown WP model; 
Calculation of Rivulet Spread Angles 
In Figure E-12, Columns A and B, Rows 1030, identify the tests reported in indicated DTNs. 
In Columns C and H, the value of x, the distance from the drip location to the measurement 
point, is listed. Rivulet spread measured to the left and right of the drip location is shown in 
Columns D and F, respectively, for measurements at the 33 line. Measurements at the transition 
line are listed in Columns I and K. Portions of this table are reproduced in Table 7.1-8. 
The spread distance, r w , is converted to spread angle, a, in Columns E, G, J, and L: 
.. 
. 
.. 
. = - 
x 
wr 1 tan a . 
An example of the Microsoft Excel equation used for this calculation is: 
E11=DEGREES(ATAN(D11/C11)) 
where the DEGREES function converts the result of the inverse tangent function ATAN from 
radians to degrees. 
In Figure E-13, Column O, Rows 1138, the spread angles measured at the 33 line are ordered 
by drip rate. The nominal drip rate is that used in the Multiple Patch tests, and the high and 
low drip rates were used in the Bounding Flow Rate tests. The mean, standard deviation, and 
median are computed for each of the three drip rates. 
In Column S, the spread angles from Column O are repeated, and statistics (mean, standard 
deviation, median, and mean plus or minus one standard deviation) are computed for the entire 
set in Rows 3135. The drip rate is indicated in Column R, where M indicates the nominal 
drip rate. 

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In Column U, the spread angles from Columns J and L are consolidated for measurements at the 
transition line. The drip rate used in each test is indicated in Column T. (The values in this 
column are currently incorrect, since they are just copies of the incorrect results in Column L and 
incorrectly recalculated values from Column J, where the actual Column J values are correct.) 
All 50 spread angle measurements are compiled in Column W, with statistics (mean, standard 
deviation, median, and mean plus or minus one standard deviation) computed for the entire set in 
Rows 63-67 (Figure E-14). The mean plus or minus one standard deviation are used as the 
spread angle range in Section 7.1.1.2 for determination of the uncertainty in the waste package 
flux splitting submodel validation. 
Figure E-13. Spreadsheet Flux Splitting ValidationWorksheet Rough off crown WP model; Additional 
Calculations of Rivulet Spread Angles 

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Figure E-14. Spreadsheet Flux Splitting ValidationWorksheet Rough off crown WP model; Statistics 
of Rivulet Spread Angles 
DTN: MO0208EBSATBWP.027 [DIRS 163404]; DTN: MO0208EBSATBWP.028 [DIRS 163405]. 
Figure E-15. Spreadsheet Flux Splitting ValidationWorksheet Rough off crown WP model; 
Calculation of Experimental Breach Flow Fractions 
For the tests identified in Columns A and B, Rows 5070 (Figure E-15), the initial and final 
water mass in the input water container are listed in Columns C and D, and the amount of water 
dripped onto the drip shield is calculated in Column E (e.g., E50=C50-D50). The initial and 
final mass of water in the Breach B4 collection vessel is listed in Columns F and G, respectively, 
and the amount of water collected from flow into Breach B4 is calculated in Column H 
(e.g., H52=G52-F52). The fraction of water dripped onto the drip shield that flowed into 
Breach B4, expt f (B4), is computed in Column I for the tests in which the inflow was greater than 
zero (e.g., I52=H52/E52). 

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Figure E-16. Spreadsheet Flux Splitting ValidationWorksheet Rough Off Crown WP Model; 
Summary of Experimental Breach Flow Fractions 
The initial and final mass of water in the Breach B5 collection vessel is listed in Figure E-16, 
Columns I and J, respectively, and the amount of water collected from flow into Breach B5 is 
calculated in Column L (e.g., L50=K50-J50). The fraction of water dripped onto the drip shield 
that flowed into Breach B5, expt f (B5), is computed in Column M for the tests in which the 
inflow was greater than zero (e.g., M50=L50/E50). 
The 20 values of expt f are compiled in Column P, with statistics (mean, standard deviation, 
median, and mean plus or minus one standard deviation) presented in Rows 73-76. 
The input water, breach inflows, and expt f for each breach are reproduced in Table 7.1-10. 

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INTENTIONALLY LEFT BLANK 

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APPENDIX F 
MICROSOFT EXCEL SPREADSHEETS TRANSPORT_CALC_ALL_COLLOIDS, 
FLUX_OUT_RATIO.XLS, AND TIME_TO_CONV.XLS 

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MICROSOFT EXCEL SPREADSHEETS TRANSPORT_CALC_ALL_COLLOIDS, 
FLUX_OUT_RATIO.XLS, AND TIME_TO_CONV.XLS 
SPREADSHEET TRANSPORT_CALC_ALL_COLLOIDS.XLS 
The purpose of this spreadsheet is to implement the colloid model that represents the sorption of 
radionuclides onto the oxy-hydroxide (designated FeO) corrosion material within the engineered 
barrier system (EBS). The model accounts for both reversible and irreversible sorption onto the 
FeO mobile colloids and the immobile corrosion products together with reversible sorption onto 
both waste form and groundwater (GW) colloids. This description refers to equations in 
Appendix B, Implementation of Radionuclide Sorption onto Colloidal and Stationary Phases 
with Finite Difference Solution. 
Description of Input Values 
The first 29 rows of the worksheet (see Figure F-1 for an image of the worksheet) contain 
parameter input values. Column D contains the typical values input from the GoldSim model. 
Column B contains values from Column D that are scaled appropriately for the current 
calculations. 
Row 2: c_s [kg/m^3], 
s c = Pu solubility 
$B$2=$D$2/1000 
Row 3: phi_1 
1 _ cell f , 
bulk 
pore 
V
V 
= f , porosity of the upstream boundary 
$B$3=$D$3 
Row 4: phi_2 
2 _ cell f , 
bulk 
pore 
V
V 
= f , porosity of the corrosion product mass 
$B$4=$D$4 
Row 5: phi_3 
3 _ cell f , 
bulk 
pore 
V
V 
= f , porosity of the downstream boundary 
$B$5=$D$5 
Row 6: u [m^3/yr] 
volumetric water flux, U Table B-1 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-2 November 2004 
$B$6=$D$6 
Row 7: Kd_FeO_c [m^3/kg] 
partition coefficient in the FeO colloid state 
$B$7=$D$7/1000 
Row 8: Kd_FeO_CP [m^3/kg] 
partition coefficient in the stationary FeO corrosion product state 
$B$8=$D$8/1000 
Row 9: Kd_WF_c [m^3/kg] 
partition coefficient in the waste form colloid state 
$B$9=$D$9/1000 
Figure F-1. Spreadsheet Transport_Calc_all_colloids.xls; Summary of Inputs 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-3 November 2004 
Row 10: Kd_GW_c [m^3/kg] 
partition coefficient in the GW colloid state 
$B$10=$D$10/1000 
Row 11: mass_FeO_CP [kg] 
= CP FeO m _ mass of corrosion product 
$B$11=$D$11/1000 
Row 12: V_pore [m^3] 
CP FeO 
CP FeO 
bulk pore 
m 
V V 
_
_ 
1 . f 
f 
f 
- 
= = , pore volume 
$B$12=$D$12/1000 
Row 13: c_FeO_c [kg/m^3] 
c FeO Pu c _ _ , concentration of Pu in the FeO colloid state from reversible sorption 
$B$13=$D$13/1000 
Row 14: c_FeO_CP [kg/m^3] 
CP FeO Pu c _ _ , concentration of Pu in the stationary FeO corrosion product state from 
reversible sorption 
$B$14=$D$14/1000 
Row 15: c_WF_c [kg/m^3] 
c WF Pu c _ _ , concentration of Pu in the waste form colloid state from reversible sorption 
$B$15=$D$15/1000 
Row 16: c_GW_c [kg/m^3] 
c GW Pu c _ _ , concentration of Pu in the GW colloid state from reversible sorption 
$B$16=$D$16/1000 
Row 17: rate [m/yr] 
k, forward rate constant (m3 water m-2 FeO yr-1) 
$B$17=$D$17/100 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-4 November 2004 
Row 18: S_FeO_c [m^2/kg] 
= FeO S specific surface area of FeO (m2 kg-1) in the colloid state 
$B$18=$D$18*1000 
Row 19: S_FeO_CP [m^2/kg] 
= FeO S specific surface area of FeO (m2 kg-1) in the corrosion product state 
$B$19=$D$19*1000 
Row 20: d_FeO [kg/m^3] 
= CP FeO _ . corrosion product (FeO) density (kg m-3) 
$B$20=$D$20 
Row 21: diffus_aq [m^2/yr] 
aq D = aqueous diffusivity (m2 yr-1) 
$B$21=$D$21*31558000 
Row 22: diffus_colloid [m^2/yr] 
colloid D = colloid diffusivity (m2 yr-1) 
$B$22=$D$22*31558000 
Row 23: diff_length_1 [m] 
1 L = diffusive length for cell_1 
$B$23=$D$23 
Row 24: diff_length_2 [m] 
2 L = diffusive length for cell_2 
$B$24=$D$24 
Row 25: diff_length_3 [m] 
3 L = diffusive length for cell_3 
$B$25=$D$25 
Row 26: diff_area_1_2 [m^2] 
12 s A = diffusive area at cell_1 and cell_2 interface 
$B$26=$D$26 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-5 November 2004 
Row 27: diff_area_2_3 [m^2] 
23 s A = diffusive area at cell_2 and cell_3 interface 
$B$27=$D$27 
Row 28: decay [1/yr] 
., decay rate (yr-1) 
$B$28=$D$28 
Row 29: delt [yr] 
t . , time step length 
$B$29=$D$29 
Rows 30 through 53 contain additional derived parameters for the mixing cell colloid model. 
Figure F-2. Spreadsheet Transport_Calc_all_colloids.xls; Additional Derived Parameters 
Row 30: R_bar_1 [1/yr] 
k c S R c FeO c FeO _ _ 1 
 = , reaction rate for colloids 
$B$30=$B$18*$B$13*$B$17 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-6 November 2004 
Row 31: R_bar_2 [1/yr] 
k c S R CP FeO CP FeO _ _ 2 
 = , reaction rate constants for corrosion products 
$B$31=$B$19*$B$14*$B$17 
Row 32: U_bar [1/yr] 
U is the advective rate constant 
$B$32=$B$6/$B$12 
Row 33: Kd_bar_FeO_c 
advective dimensionless partition coefficient in the FeO colloid state 
$B$33=$B$13*$B$7 
Row 34: Kd_bar_FeO_CP 
advective dimensionless partition coefficient in the FeO corrosion product state 
$B$34=$B$14*$B$8 
Row 35: Kd_bar_WF_c 
advective dimensionless partition coefficient in the waste form colloid state 
$B$35=$B$15*$B$9 
Row 36: Kd_bar_GW_c 
advective dimensionless partition coefficient in the GW colloid state 
$B$36=$B$16*$B$10 
Row 37: K_bar_1 
c GW d c WF d CP FeO d c FeO d K K K K K _ _ _ _ _ _ _ _ 1 1 + + + + = , combination of dimensionless 
partition coefficients 
$B$37=1+$B$33+$B$34+$B$35+$B$36 
Row 38: K_bar_2 
c GW d c WF d c FeO d K K K K _ _ _ _ _ _ 2 1 + + + = , combination of dimensionless partition 
coefficients 
$B$38=1+$B$33+$B$35+$B$36 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-7 November 2004 
Row 39: K_bar_3 
c GW d c WF d c FeO d K K K K _ _ _ _ _ _ 3 + + = , combination of dimensionless partition 
coefficients 
$B$39=$B$33+$B$35+$B$36 
Row 40: Diff_left_aq 
aqueous diffusive rate constant for left diffusive boundary condition 
$B$40=($B$26/($B$23/($B$3*$B$21)+$B$24/($B$4*$B$21)))/$B$12 
Row 41: Diff_left_c 
colloid diffusive rate constant for left diffusive boundary condition 
$B$41=($B$26/($B$23/($B$3*$B$22)+$B$24/($B$4*$B$22)))/$B$12 
Row 42: Diff_right_aq 
aqueous diffusive rate constant for right diffusive boundary condition 
$B$42=($B$27/($B$24/($B$4*$B$21)+$B$25/($B$5*$B$21)))/$B$12 
Row 43: Diff_right_colloid 
colloid diffusive rate constant for right diffusive boundary condition 
$B$43=($B$27/($B$24/($B$4*$B$22)+$B$25/($B$5*$B$22)))/$B$12 
Row 44: denom_a_1_2 
denominator of a1 in Equation B-55 (see Row 45) 
$B$44=$B$37+($B$32*$B$38+$B$40+$B$41*$B$35+$B$42+$B$43*$B$39 
+$B$30+$B$31+$B$28*$B$37)*$B$29 
Row 45: a_1 
first order linear constant coefficient for Equation B-55, 
( )t K R R K D D K D D K U K 
K a 
col right aq right c WF d col left aq left . + + + + + + + + 
= 
1 2 1 3 _ _ _ _ _ _ 2 1 
1 
1 . 
B$45=$B$37/$B$44 
Row 46: a_2 
first order linear constant coefficient for Equation B-55, 
( ) 
( )t K R R K D D K D D K U K 
tc K D D K U 
a 
col right aq right c WF d col left aq left 
s c WF d col left aq left c WF d 
. + + + + + + + + 
. + + + 
= 
1 2 1 3 _ _ _ _ _ _ 2 1 
_ _ _ _ _ _ 
2 
) 1 ( 
. 
$B$46=(($B$32*(1+$B$35)+$B$40+$B$41*$B$35)*$B$29*$B$2)/$B$44 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-8 November 2004 
Row 47: b_1 
irreversible colloid coefficient (Equation B-59) for Equation B-58, 
( ) t D U 
b 
col right . + + + 
= 
. _ 
1 1 
1 
$B$47=1/(1+($B$32+$B$43+$B$28)*$B$29) 
Row 48: b_2 
irreversible colloid coefficient (Equation B-60) for Equation B-58, 
( ) t D U 
t R b 
col right . + + + 
. 
= 
. _ 
1 
2 1 
$B$48=($B$30*$B$29)*$B$47 
Row 49: e_1 
irreversible corrosion products coefficient (Equation B-65) for Equation B-64, 
t 
e 
. + 
= 
. 1 
1 
1 
$B$49=1/(1+$B$28*$B$29) 
Row 50: e_2 
irreversible corrosion products coefficient (Equation B-66) for Equation B-64, 
t 
t R e 
. + 
. 
= 
. 1 
2 
2 
$B$50=($B$31*$B$29)*$B$49 
Row 51: Omega 
95 . 0 
out flux mass total 
out flux mass colloid = = . (Equation B-1) 
$B$51=0.95 
Row 52: k_fit_Omega [cm/yr] 
c FeO c FeO c S 
p p k 
_ _ 
1 2
 ) 1 ( . - 
- . 
= , fitting parameter, k, given a target flux ratio . , 
Equation B-72 
$B$52=100*($E$44*$B$51-$E$43)/((1-$B$51)*$B$18*$B$13) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-9 November 2004 
Row 53: p1/p2 
1 2 
1 1 
R p 
R p 
+
+ 
= . (Equation B-71) 
$B$53=$E$43/$E$44 
The values of parameters in Column E & G Rows 43 through 52 under the heading limiting 
values pertain to the equations and discussion in Section Boundary Fluxes in Appendix B. 
Row 43, Column E: p_1 
( ) . + + = col right D U K p _ 3 1 
$E$43=$B$39*($B$32+$B$43+$B$28) 
Row 44, Column E: p_2 
( ) . .
.
. 
. .
.
. 
+ 
+ + 
+ + = 
col right 
col right 
col right aq right D U 
D U 
K D D K U p 
_ 
_ 
3 _ _ 2 2 
. 
$E$44=($B$32*$B$38+$B$42+$B$43*$B$39)*($B$32+$B$43+$B$ 
28)/($B$32+$B$43) 
Row 45, Column E: lim c_Pu_aq 
1 
2 
_ 1 
lim 
a 
a cn 
aq Pu n - 
= 
8 . 
$E$45=$B$46/(1-$B$45) 
Row 46, Column E: lim c_irr_c 
) 1 )( 1 ( 
lim 
1 1 
2 2 
_ _ _ b a 
b a cn 
c FeO Pu Irrv n - - 
= 
8 . 
$E$46=($B$30*$E$45)/($B$32+$B$43+$B$28) 
Row 47, Column E: lim c_rev_c 
n 
aq Pu n c FeO d 
n 
c FeO Pu n 
c K c _ _ _ _ _ lim lim 
8 . 8 . 
= 
$E$47=$B$33*$E$45 
Row 48, Column E: lim c_irr_CP 
n 
aq Pu n 
n 
aq Pu n 
n 
CP FeO Pu Irrv n 
c R c 
e 
e c _ 
2 
_ 
1 
2 
_ _ _ lim lim 
1 
lim 
8 . 8 . 8 . 
= 
- 
= 
. 
$E$48=$E$45*$B$31/$B$28 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-10 November 2004 
Row 49, Column E: lim c_rev_CP 
n 
aq Pu n CP FeO d 
n 
CP FeO Pu n 
c K c _ _ _ _ _ lim lim 
8 . 8 . 
= 
$E$49=$B$34*$E$45 
Row 50, Column E: flux out ratio 
1 2 
1 1 
R p 
R p 
+
+ 
= . 
$E$50=($E$43+$B$30)/($E$44+$B$30) 
Row 51, Column E: flux out/flux in 
( ) 1 2 1 
_ 
_ 
2 
1 2 
K R R 
D U 
D U 
p 
R p 
col right 
col right . 
. 
+ + . .
.
. 
. .
.
. 
+ 
+ + 
+ 
+ 
= . 
$E$51=($E$44+$B$30)/($E$44+($B$32+$B$43+$B$28)*($B$30+$ 
B$31+$B$28*$B$37)/($B$32+$B$43)) 
Row 52, Column E: irrv_col/rev_col 
1 
) ( 
0 
3 _ _ 2 
_ 3 < . < 
+ + 
+ 
< 
K D D K U 
D U K 
col right aq right 
col right 
$E$52=($B$32+$B$43)*$E$46/(($B$32+$B$43)*$B$39*$E$45) 
Row 44, Column G: tolerance 
relative error estimate with tolerance e 
$G$44 =G44 
Row 45, Column G: Pu_aq time [yr] 
t 
a 
t n time . > . = 
1 10 
10 
log 
log e 
(Equation B-74) 
$G$45 =$B$29*LOG10($G$44)/LOG10($B$45) 
Row 46, Column G: delta_1 
1 
1
1 1 1 
1 2 1 
d 
e 
= 
-
- 
< + 
a
b a bn 
$G$46 =0.5*$G$44*ABS(($B$47-$B$45)/(1-$B$45)) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-11 November 2004 
Row 47, Column G: delta_2 
2 
1
1 1 1 
1 2 1 
d 
e 
= 
-
- 
< + 
b
b a an 
$G$47 =0.5*$G$44*ABS(($B$47-$B$45)/(1-$B$47)) 
Row 48, Column G: t_1 
1 10 
1 10 
log 
log 
b
d 
$G$48 =LOG10($G$46)/LOG10($B$47) 
Row 49, Column G: t_2 
1 10 
2 10 
log 
log 
a
d 
$G$49 =LOG10($G$47)/LOG10($B$45) 
Row 50, Column G: irrv_Pu_c time [yr] 
time to converge to a given relative error tolerance, 
t 
a 
t n time . > . = 
1 10 
10 
log 
log e 
$G$50 =INT(MAX($G$48,$G$49))*$B$29 
Rows 58 thru 158 and Columns A through AC contain calculated solutions and equation terms, 
iterated in time, for the mixing cell colloid model. Images of this section of the spreadsheet are 
included at the end of this appendix (Figures F-3 through F-14). 
A58 through A158 are the model times, time(n+1) = time(n)+delt, $A$59=$A58+$B$29 
Column B: c_Pu_aq 
B$59=$B$45*$B58+$B$46 
Column C: c_Pu_FeO_c 
C$59 =$B$33*$B59 
Column D: c_Pu_FeO_CP 
D$59 =$B$34*$B59 
Column E: c_Pu_WF_c 
E$59 =$B$35*$B59 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-12 November 2004 
Column F: c_Pu_GW_c 
F$59 =$B$36*$B59 
Column G: c_irrv_Pu FeO_c 
G$59 =$B$47*$G58+$B$48*$B59 
Column H: c_irrv_Pu FeO_CP 
H$59 =$B$49*$H58+$B$50*$B59 
Column I: c_Pu_Fluid1 [mg/L] 
I$59 =1000*($B59+$C59+$E59+$F59) 
Column J: c_Pu_FeO_c [g/kg] 
J$59 =1000*$C59/$B$13 
Column K: c_Pu_FeO_CP [g/kg] 
K$59 =1000*$D59/$B$14 
Column L: c_PU_WF_c [g/kg] 
L$59 =1000*$E59/$B$15 
Column M: c_Pu_GW_c [g/kg] 
M$59 =1000*$F59/$B$16 
Column N: c_Irrv_Pu_c [g/kg] 
N$59 =1000*$G59/$B$13 
Column O: c_Irrv_Pu_CP [g/kg] 
O$59 =1000*$H59/$B$14 
Column P: time 
P$59 =$A59 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-13 November 2004 
Column Q: left_bddy_flux [kg] 
) ( _ _ _ _ 
n 
aq Pu s pore aq left s pore 
n 
total bddy left c c V D c V U F - + = 
) ( _ _ _ _ _ _ 
n 
aq Pu s c WF d pore col left s c WF d pore c c K V D c K V U - + + 
Q$59=($B$32*(1+$B$35)*$B$2+($B$40+$B$41*$B$35)*($B$2-$B59))*$B 
$12*$B$29 
Column R: right_bddy colloid flux [kg] 
n 
colloid bddy right F _ _ = n 
c FeO Pu Irrv pore 
n 
aq Pu c FeO d pore c V U c K V U _ _ _ _ _ _ + 
n 
aq Pu c GW d pore 
n 
aq Pu c WF d pore c K V U c K V U _ _ _ _ _ _ + 
n 
c FeO Pu Irrv pore col right 
n 
aq Pu c FeO d pore col right c V D c K V D _ _ _ _ _ _ _ _ + + 
n 
aq Pu c GW d pore col right 
n 
aq Pu c WF d pore col right c K V D c K V D _ _ _ _ _ _ _ _ + 
R$59 =($B$32+$B$43)*($B$39*$B59+$G59)*$B$12*$B$29 
Column S: right bddy total flux [kg] 
n 
total bddy right F _ _ = n 
aq Pu pore aq right 
n 
aq Pu pore 
n 
colloid bddy right c V D c V U F _ _ _ _ _ + + 
S$59 =$R59+($B$32+$B$42)*$B59*$B$12*$B$29 
Column T: col_out/total_out 
n 
total bddy right 
n 
colloid bddy right 
n F 
F 
_ _ 
_ _ = . 
T$59 =$R59/$S59 
Column U: flux_out/flux_in 
U$59 =$S59/$Q59 
Column V: change mass [kg] 
V$59 =(($B59-$B58)+($C59-$C58)+($D59-$D58)+($E59-$E58)+($F59- 
$F58))*$B$12 
Column W: in - out [kg] 
W$59=$Q59-(($B$32+$B$43)*$B$39+$B$32+$B$42)*$B59*$B$12*$B$29 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-14 November 2004 
Column X: react/decay [kg] 
X$59 =-($B$30+$B$31+$B$28*$B$37)*$B$12*$B$29*$B59 
Column Y: PU mass balance 
Y$59 =$V59-$W59-$X59 
Column Z: change mass [kg] 
Z$59 =(($G59-$G58)+($H59-$H58))*$B$12 
Column AA: in-out [kg] 
AA$59 =-($B$32+$B$43)*$G59*$B$12*$B$29 
Column AB: react/decay [kg] 
AB$59 =(($B$30+$B$31)*$B59-$B$28*($G59+$H59))*$B$12*$B$29 
Column AC: Irrv_Pu mass balance 
AC$59 =$Z59-$AA59-$AB59 
Figure F-3. Spreadsheet Transport_Calc_all_colloids.xls; Calculated Solutions and Equation Terms, 
Iterated in Time, for Mixing Cell Colloid Model, Time 0  290 Years 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-15 November 2004 
Figure F-4. Spreadsheet Transport_Calc_all_colloids.xls; Additional Calculated Solutions and Equation 
Terms, Iterated in Time, for Mixing Cell Colloid Model, Time 0  290 Years 
Figure F-5. Spreadsheet Transport_Calc_all_colloids.xls; Final Calculated Solutions and Equation 
Terms, Iterated in Time, for Mixing Cell Colloid Model, Time 0  290 Years 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-16 November 2004 
Figure F-6. Spreadsheet Transport_Calc_all_colloids.xls; Calculated Solutions and Equation Terms, 
Iterated in Time, for Mixing Cell Colloid Model, Time 300  630 Years 
Figure F-7. Spreadsheet Transport_Calc_all_colloids.xls; Additional Calculated Solutions and Equation 
Terms, Iterated in Time, for Mixing Cell Colloid Model, Time 300  630 Years 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-17 November 2004 
Figure F-8. Spreadsheet Transport_Calc_all_colloids.xls; Final Calculated Solutions and Equation 
Terms, Iterated in Time, for Mixing Cell Colloid Model, Time 300  630 Years 
Figure F-9. Spreadsheet Transport_Calc_all_colloids.xls; Calculated Solutions and Equation Terms, 
Iterated in Time, for Mixing Cell Colloid Model, Time 640  970 Years 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-18 November 2004 
Figure F-10. Spreadsheet Transport_Calc_all_colloids.xls; Additional Calculated Solutions and 
Equation Terms, Iterated in Time, for Mixing Cell Colloid Model, Time 640  970 Years 
Figure F-11. Spreadsheet Transport_Calc_all_colloids.xls; Final Calculated Solutions and Equation 
Terms, Iterated in Time, for Mixing Cell Colloid Model, Time 640  970 Years 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-19 November 2004 
Figure F-12. Spreadsheet Transport_Calc_all_colloids.xls; Calculated Solutions and Equation Terms, 
Iterated in Time, for Mixing Cell Colloid Model, Time 980  1000 Years 
Figure F-13. Spreadsheet Transport_Calc_all_colloids.xls; Additional Calculated Solutions and 
Equation Terms, Iterated in Time, for Mixing Cell Colloid Model, Time 980  1000 Years 
Figure F-14. Spreadsheet Transport_Calc_all_colloids.xls; Final Calculated Solutions and Equation 
Terms, Iterated in Time, for Mixing Cell Colloid Model, Time 980  1000 Years 
SPREADSHEET FLUX_OUT_RATIO.XLS 
The purpose of this spreadsheet is to demonstrate the use of the irreversible linear reaction rate 
constant to fit a specified flux out ratio. The spreadsheet calculates and plots the figures 
Limiting Flux Out Ratio as a function of Irreversible Reaction Rate and Linear reaction rate 
from colloid to total flux out ratio. 
The calculations for flux out ratio as a function of k, linear irreversible reaction rate, are done in 
Worksheet adv_diff_decay. The calculations for k as a function of flux out ratio are done in 
Worksheet K-surface. This description refers to equations from Appendix B, Implementation 
of Radionuclide Sorption onto Colloidal and Stationary Phases with Finite Difference Solution. 
Description of Input Values 
The first 29 rows of the worksheet contain the input data values with the exception of Row 12, 
where pore volume is computed. Column D contains input values typical of the TSPA-LA. 
Column B contains values from Column D that are scaled for unit conversion of mass (kg), 
length (m), and time (yr). An image of the first 31 rows of the Microsoft Excel spreadsheet is 
shown in Figure F-15. 
Row 2: c_s [kg/m^3] 
s c (mg L-1) = Pu solubility 
$B$2=$D$2/1000 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-20 November 2004 
Row 3: phi_1 
1_ f , porosity of the waste form cell_1 
$B$3=$D$3 
Row 4: phi_2 
2_ f , porosity of the corrosion product mass in waste form cell_2 
$B$4=$D$4 
Row 5: phi_3 
3_ f , porosity of the invert 
$B$5=$D$5 
Row 6: u [m^3/yr] 
u , volumetric water flux 
$B$6=$D$6 
Figure F-15. Spreadsheet flux_out_ratio.xls, Worksheet K-surface; Summary of Inputs 
Row 7: Kd_FeO_c [m^3/kg] 
c FeO d K _ _ , partition coefficient in the FeO colloid state 
$B$7=$D$7/1000 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-21 November 2004 
Row 8: Kd_FeO_CP [m^3/kg] 
CP FeO d K _ _ , partition coefficient in the stationary FeO corrosion product state 
$B$8=$D$8/1000 
Row 9: Kd_WF_c [m^3/kg] 
c WF d K _ _ , partition coefficient in the waste form colloid state 
$B$9=$D$9/1000 
Row 10: Kd_GW_c [m^3/kg] 
c GW d K _ _ , partition coefficient in the GW colloid state 
$B$10=$D$10/1000 
Row 11: mass_FeO_CP [kg] 
CP FeO m _ , mass of corrosion products 
$B$11=$D$11/1000 
Row 12: V_pore [m^3] 
CP FeO 
CP FeO 
bulk pore 
m 
V V 
_
_ 
1 . f 
f 
f 
- 
= = , pore volume 
$B$12=$D$12/1000 
$D$12=$D$4*$D$11/($D$20*(1-$D$4)) 
Row 13: c_FeO_c [kg/m^3] 
c FeO Pu c _ _ , concentration of FeO colloids 
$B$13=$D$13/1000 
Row 14: c_FeO_CP [kg/m^3] 
CP FeO Pu c _ _ , concentration of FeO corrosion product 
$B$14=$D$14/1000 
Row 15: c_WF_c [kg/m^3] 
c WF Pu c _ _ , concentration of waste form colloids 
$B$15=$D$15/1000 
Row 16: c_GW_c [kg/m^3] 
c GW Pu c _ _ , concentration of GW colloid state 
$B$16=$D$16/1000 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-22 November 2004 
Row 17: k [m/yr] 
k, intrinsic or surface reaction rate (m3 m-2 yr-1) 
$B$17=$D$17/100 
Row 18: S_FeO_c [m^2/kg] 
= c FeO S _ 
 specific surface area of FeO colloids (m2 kg-1) 
$B$18=$D$18*1000 
Row 19: S_FeO_CP [m^2/kg] 
= CP FeO S _ 
 specific surface area of FeO corrosion products (m2 kg-1) 
$B$19=$D$19*1000 
Row 20: d_FeO [kg/m^3] 
= CP FeO _ . density of FeO 
$B$20=$D$20 
Row 21: diffus_aq [m^2/yr] 
aq D = aqueous diffusivity 
$B$21=$D$21*31558000 
Row 22: diffus_colloid [m^2/yr] 
colloid D = colloid diffusivity 
$B$22=$D$22*31558000 
Row 23: diff_length_1 [m] 
1 L = diffusive length for cell_1 
$B$23=$D$23 
Row 24: diff_length_2 [m] 
2 L = diffusive length for cell_2 
$B$24=$D$24 
Row 25: diff_length_3 [m] 
3 L = diffusive length for cell_3 
$B$25=$D$25 
Row 26: diff_area_1_2 [m^2] 
12 s A = diffusive area at cell_1 and cell_2 interface 
$B$26=$D$26 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-23 November 2004 
Row 27: diff_area_2_3 [m^2] 
23 s A = diffusive area at cell_2 and cell_3 interface 
$B$27=$D$27 
Row 28: decay [1/yr] 
., decay rate 
$B$28=$D$28 
Row 29: delt [yr] 
t . , time step length 
$B$29=$D$29 
Rows 30 through 51 contain additional derived parameters for the colloid model. Images of 
Rows 32 through 100 are shown at the end of the description of this spreadsheet. 
Row 30: R_bar_1 [1/yr] 
k c S R c FeO c FeO _ _ 1 
 = , reaction rate constant for colloids 
$B$30=$B$18*$B$13*$B$17 
Row 31: R_bar_2 [1/yr] 
k c S R CP FeO CP FeO _ _ 2 
 = , reaction rate constant for corrosion products 
$B$31=$B$19*$B$14*$B$17 
Row 32: U_bar [1/yr] 
U = advective rate constant 
$B$32=$B$6/$B$12 
Row 33: Kd_bar_FeO_c 
dimensionless partition coefficient in the FeO colloid state 
$B$33=$B$13*$B$7 
Row 34: Kd_bar_FeO_CP 
dimensionless partition coefficient in the FeO corrosion product state 
$B$34=$B$14*$B$8 
Row 35: Kd_bar_WF_c 
dimensionless partition coefficient in the waste form colloid state 
$B$35=$B$15*$B$9 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-24 November 2004 
Row 36: Kd_bar_GW_c 
dimensionless partition coefficient in the GW colloid state 
$B$36=$B$16*$B$10 
Row 37: K_bar_1 
c GW d c WF d CP FeO d c FeO d K K K K K _ _ _ _ _ _ _ _ 1 1 + + + + = , combination of dimensionless 
partition coefficients 
$B$37=1+$B$33+$B$34+$B$35+$B$36 
Row 38: K_bar_2 
c GW d c WF d c FeO d K K K K _ _ _ _ _ _ 2 1 + + + = , combination of dimensionless partition 
coefficients 
$B$38=1+$B$33+$B$35+$B$36 
Row 39: K_bar_3 
c GW d c WF d c FeO d K K K K _ _ _ _ _ _ 3 + + = , combination of dimensionless partition 
coefficients 
$B$39=$B$33+$B$35+$B$36 
Row 40: Diff_left_aq [1/yr] 
diffusive rate constant, left interface in water 
$B$40=($B$26/($B$23/($B$3*$B$21)+$B$24/($B$4*$B$21)))/$B$12 
Row 41: Diff_right_aq 
diffusive rate constant, right interface in water 
$B$41=($B$27/($B$24/($B$4*$B$21)+$B$25/($B$5*$B$21)))/$B$12 
Row 42: Diff_right_colloid 
diffusive rate constant, right interface colloids 
$B$42=($B$27/($B$24/($B$4*$B$22)+$B$25/($B$5*$B$22)))/$B$12 
Row 43: Omega 
out flux mass total 
out flux mass colloid = . 
$B$43=($B$44+$B$30)/($B$45+$B$30) 
Row 44: p_1 
( ) . + + = col right D U K p _ 3 1 
$B$44=$B$39*($B$32+$B$42+$B$28) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-25 November 2004 
Row 45: p_2 
( ) . .
.
. 
. .
.
. 
+ 
+ + 
+ + = 
col right 
col right 
col right aq right D U 
D U 
K D D K U p 
_ 
_ 
3 _ _ 2 2 
. 
$B$45=($B$32*$B$38+$B$41+$B$42*$B$39)*($B$32+$B$42+$B$28)/($B$3 
2+$B$42) 
Row 46: delta 
scale value for k = 2.0 
Row 47: comments 
Rows 48 through 81 are values for the flux out ratio calculated as a function of the irreversible 
forward reaction rate, Equation B-71. Column A contains the values of k, and Column B 
contains the corresponding values of flux out ratio. 
$A$48=0 
$A$49=1.E-5 
$A50 = $B$46*$A49 
Row 50 is dragged down through Row 81. 
Then in Column B the flux out ratio, 
out flux mass total 
out flux mass colloid = . , is calculated as a function of the 
irreversible reaction rate value: 
$B48 = ($B$44+$B$18*$B$13*$A48*0.01)/($B$45+$B$18*$B$13*$A48*0.01) 
The factor 0.01 converts the irreversible reaction rate constant from units of cm yr-1 to m yr-1. 
The above expression is then dragged down through Row 81. 
Figure B-3 in Appendix B, Limiting Flux Out Ratio as a Function of Irreversible Reaction 
Rate, is plotted, where: 
x-axis: $A$49:$A$73 
y-axis: $B$49:$B$73 
The point k = 0.001 cm yr-1 is 
x-axis: $D$17:$D$17 
y-axis: $B$43:$B$43 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-26 November 2004 
In Worksheet K-surface, Rows 1 through 46 are the same as for Worksheet adv_diff_decay. 
In Worksheet K-surface, Rows 48 through 100 (Figure F-16), values for the irreversible 
forward reaction rate, k, are calculated as a function of the flux out ratio, . , Equation B-72. 
Column A contains the values of flux out ratio, and Column B contains the corresponding values 
of k. 
$A$48: minimum flux out ratio when k = 0, 
2
1 
p
p = . 
$A$48 = $B$44/$B$45 
$A49 to $A100: uniform spacing of omega values between the minimum and 1. 
$A49 = $A48+(1-$A$48)/53. 
$A49 is dragged down to row 100. 
$B48 to $B101: irreversible reaction rate. 
c FeO c FeO c S 
p p k 
_ _ 
1 2
 ) 1 ( . - 
- . 
= 
$B48 = 100*($B$35*$A48-$B$44)/((1-$A48)*$B$18*$B$13) 
(The factor of 100 is a conversion from meters to cm.) 
$B$48 is dragged down through $B$100 
Figure B-4 in Appendix B, Linear Reaction Rate from Colloid to Total Flux Out Ratio, is the 
plot in Worksheet K-surface, where 
x-axis: $A$49:$A$100 
y-axis: $B$49:$B$100 
The point labeled Omega = 0.95 is 
x-axis: $B$43:$B$43 
y-axis: $D$17:$D$17 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-27 November 2004 
Figure F-16. Spreadsheet flux_out_ratio.xls, Worksheet K-surface; Calculation of Irreversible Forward 
Reaction Rate, k, as Function of Flux Out Ratio, . 
SPREADSHEET TIME_TO_CONV.XLS 
The purpose of this spreadsheet is to demonstrate the time to converge for the Pu concentration 
in solution and the irreversible Pu concentration on colloids. The spreadsheet verifies the 
convergence estimate discussed in Section Convergence Estimates For Closed Form Solutions 
in Appendix B. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-28 November 2004 
The calculations are done in Worksheet time_to_conv, while the plot is in Worksheet 
plot_time_to_conv. This description will refer to equations from Appendix B, 
Implementation of Radionuclide Sorption onto Colloidal and Stationary Phases with Finite 
Difference Solution. 
Description of Input Values 
The first 29 rows of each worksheet contain the input data values, with the exception of Row 12, 
where pore volume is computed. Column D contains input values representative of TSPA-LA. 
Column B contains values from column D that are scaled for unit conversion of mass (kg), 
length (m), time (yr). An image of Rows 1 through 33 is shown on the next page. 
Row 2: c_s [kg/m^3] 
s c (mg L-1) = Pu solubility 
$B$2=$D$2/1000 
Row 3: phi_1 
1_ f , porosity of the waste form cell_1 
$B$3=$D$3 
Row 4: phi_2 
2_ f , porosity of the corrosion product mass in waste form cell_2 
$B$4=$D$4 
Row 5: phi_3 
3_ f , porosity of the invert 
$B$5=$D$5 
Row 6: u [m^3/yr] 
u = volumetric water flux (m3 yr-1) 
$B$6=$D$6 
Row 7: Kd_FeO_c [m^3/kg] 
c FeO d K _ _ , partition coefficient in the FeO colloid state 
$B$7=$D$7/1000 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-29 November 2004 
Figure F-17. Spreadsheet time_to_conv.xls, Worksheet time_to_conv; Summary of Inputs 
Row 8: Kd_FeO_CP [m^3/kg] 
CP FeO d K _ _ , partition coefficient in the stationary FeO corrosion product state 
$B$8=$D$8/1000 
Row 9: Kd_WF_c [m^3/kg] 
c WF d K _ _ , partition coefficient in the waste form colloid state 
$B$9=$D$9/1000 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-30 November 2004 
Row 10: Kd_GW_c [m^3/kg] 
c GW d K _ _ , partition coefficient in the GW colloid state 
$B$10=$D$10/1000 
Row 11: mass_FeO_CP [kg] 
CP FeO m _ mass of corrosion products 
$B$11=$D$11/1000 
Row 12: V_pore [m^3] 
CP FeO 
CP FeO 
bulk pore 
m 
V V 
_
_ 
1 . f 
f 
f 
- 
= = , pore volume 
$B$12=$D$12/1000 
$D$12=$D$4*$D$11/($D$20*(1-$D$4)) 
Row 13: c_FeO_c [kg/m^3] 
c FeO Pu c _ _ , concentration of FeO colloids 
$B$13=$D$13/1000 
Row 14: c_FeO_CP [kg/m^3] 
CP FeO Pu c _ _ , concentration of FeO corrosion product 
$B$14=$D$14/1000 
Row 15: c_WF_c [kg/m^3] 
c WF Pu c _ _ , concentration of waste form colloids 
$B$15=$D$15/1000 
Row 16: c_GW_c [kg/m^3] 
c GW Pu c _ _ , concentration of GW colloid state 
$B$16=$D$16/1000 
Row 17: k [m/yr] 
k, intrinsic or surface reaction rate (pore-vol/area-FeO/time) 
$B$17=$D$17/100 
Row 18: S_FeO_c [m^2/kg] 
= c FeO S _ 
 specific surface area of FeO colloids (m2 kg-1) 
$B$18=$D$18*1000 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-31 November 2004 
Row 19: S_FeO_CP [m^2/kg] 
= CP FeO S _ 
 specific surface area of FeO corrosion products (m2 kg-1) 
$B$19=$D$19*1000 
Row 20: d_FeO [kg/m^3] 
= CP FeO _ . density of FeO 
$B$20=$D$20 
Row 21: diffus_aq [m^2/yr] 
aq D = aqueous diffusivity 
$B$21=$D$21*31558000 
Row 22: diffus_colloid [m^2/yr] 
colloid D = colloid diffusivity 
$B$22=$D$22*31558000 
Row 23: diff_length_1 [m] 
1 L = diffusive length for cell_1 
$B$23=$D$23 
Row 24: diff_length_2 [m] 
2 L = diffusive length for cell_2 
$B$24=$D$24 
Row 25: diff_length_3 [m] 
3 L = diffusive length for cell_3 
$B$25=$D$25 
Row 26: diff_area_1_2 [m^2] 
12 s A = diffusive area at cell_1 and cell_2 interface 
$B$26=$D$26 
Row 27: diff_area_2_3 [m^2] 
23 s A = diffusive area at cell_2 and cell_3 interface 
$B$27=$D$27 
Row 28: decay [1/yr] 
., decay rate 
$B$28=$D$28 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-32 November 2004 
Row 29: delt [yr] 
t . , time step length 
$B$29=$D$29 
Rows 30 through 51 contains additional derived parameters for the colloid model. An image of 
Rows 34 through 61 is shown in Figure F-18. 
Figure F-18. Spreadsheet time_to_conv.xls, Worksheet time_to_conv; Additional Derived Parameters 
and Results for Colloid Model 
Row 30: R_bar_1 [1/yr] 
k c S R c FeO c FeO _ _ 1 
 = , reaction rate constant for colloids 
$B$30=$B$18*$B$13*$B$17 
Row 31: R_bar_2 [1/yr] 
k c S R CP FeO CP FeO _ _ 2 
 = , reaction rate constant for corrosion products 
$B$31=$B$19*$B$14*$B$17 
Row 32: U_bar [1/yr] 
U advective rate constant 
$B$32=$B$6/$B$12 
Row 33: Kd_bar_FeO_c 
dimensionless partition coefficient in the FeO colloid state 
$B$33=$B$13*$B$7 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-33 November 2004 
Row 34: Kd_bar_FeO_CP 
dimensionless partition coefficient in the FeO corrosion product state 
$B$34=$B$14*$B$8 
Row 35: Kd_bar_WF_c 
dimensionless partition coefficient in the waste form colloid state 
$B$35=$B$15*$B$9 
Row 36: Kd_bar_GW_c 
dimensionless partition coefficient in the GW colloid state 
$B$36=$B$16*$B$10 
Row 37: K_bar_1 
c GW d c WF d CP FeO d c FeO d K K K K K _ _ _ _ _ _ _ _ 1 1 + + + + = , combination of dimensionless 
partition coefficients 
$B$37=1+$B$33+$B$34+$B$35+$B$36 
Row 38: K_bar_2 
c GW d c WF d c FeO d K K K K _ _ _ _ _ _ 2 1 + + + = , combination of dimensionless partition 
coefficients 
$B$38=1+$B$33+$B$35+$B$36 
Row 39: K_bar_3 
c GW d c WF d c FeO d K K K K _ _ _ _ _ _ 3 + + = , combination of dimensionless partition 
coefficients 
$B$39=$B$33+$B$35+$B$36 
Row 40: Diff_left_aq [1/yr] 
diffusive rate constant, left interface in water 
$B$40=($B$26/($B$23/($B$3*$B$21)+$B$24/($B$4*$B$21)))/$B$12 
Row 41: Diff_left_colloid [1/yr] 
diffusive rate constant, left interface colloids 
$B$41=($B$26/($B$23/($B$3*$B$22)+$B$24/($B$4*$B$22)))/$B$12 
Row 42: Diff_right_aq [1/yr] 
diffusive rate constant, right interface in water 
$B$41=($B$27/($B$24/($B$4*$B$21)+$B$25/($B$5*$B$21)))/$B$12 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-34 November 2004 
Row 43: Diff_right_colloid [1/yr] 
diffusive rate constant, right interface colloids 
$B$42=($B$27/($B$24/($B$4*$B$22)+$B$25/($B$5*$B$22)))/$B$12 
Row 44: denom_a_1_2 
denominator of Equation B-48 
$B$44=$B$37+($B$32*$B$38+$B$40+$B$41*$B$35+$B$42+$B$43*$B$39 
+$B$30+$B$31+$B$28*$B$37)*$B$29 
Row 45: a_1 
first coefficient for Equation B-55, 
( )t K R R K D D K D D K U K 
K a 
col right aq right c WF d col left aq left . + + + + + + + + 
= 
1 2 1 3 _ _ _ _ _ _ 2 1 
1 
1 . 
$B$45=$B$37/$B$44 
Row 46: a_2 
second coefficient for Equation B-55, 
( ) 
( )t K R R K D D K D D K U K 
tc K D D K U 
a 
col right aq right c WF d col left aq left 
s c WF d col left aq left c WF d 
. + + + + + + + + 
. + + + 
= 
1 2 1 3 _ _ _ _ _ _ 2 1 
_ _ _ _ _ _ 
2 
) 1 ( 
. 
$B$46=(($B$32*(1+$B$35)+$B$40+$B$41*$B$35)*$B$29*$B$2)/$B$44 
Row 47: b_1 
first coefficient for Equation B-58, ( ) t D U 
b 
col right . + + + 
= 
. _ 
1 1 
1 
$B$47=1/(1+($B$32+$B$43+$B$28)*$B$29) 
Row 48: b_2 
second coefficient for Equation B-58, ( ) t D U 
t R b 
col right . + + + 
. 
= 
. _ 
1 
2 1 
$B$48=($B$30*$B$29)*$B$47 
Row 49: e_1 
first coefficient for Equation B-64, 
t 
e 
. + 
= 
. 1 
1 
1 
$B$49=1/(1+$B$28*$B$29) 
Row 50: e_2 
second coefficient for Equation B-64, 
t 
t R e 
. + 
. 
= 
. 1 
2 
2 
$B$50=($B$31*$B$29)*$B$49 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-35 November 2004 
Row 51: convergence relative error tolerance 1% = 0.01. 
Rows 54 through 61 calculates the times to converge to limit value for Pu_aq concentration and 
Irrv_Pu_c concentration as a function of time step size. The time step size (yr) varies by order of 
magnitude increments from 110-3 to 1104. 
Column A: delt_time 
Row 54: assign time step value 110-3 
Rows 55: $A55 = 10*$A54 
This value is dragged down through Row 61 
Column B: denom_a_1_2 
denominator in the calculation for a_1 and a_2 coefficients. 
$B54=$B$37+($B$32*$B$38+$B$40+$B$41*$B$35+$B$42+$B$43*$B$39+ 
$B$30+$B$31+$B$28*$B$37)*$A54 
This value is dragged down through Row 61 
Column C: a_1 
coefficient in Pu_aq concentration Equation B-56. 
Row 54: $C54 = $B$37/$B54 
This result is dragged down through Row 61 
Column D: time Pu_aq [yrs] 
time for Pu_aq concentration to converge, estimate Equation B-74. 
Row 54: $D54 = $A54*LOG10($B$51)/LOG10($C54) 
This result is dragged down through Row 61 
Column E: b_1 
coefficient in Irrv_Pu_c concentration, Equation B-59. 
Row 54: $E54 = 1/(1+($B$32+$B$43+$B$28)*$A54) 
This result is dragged down through Row 61 
Column F: delta_1 
intermediate tolerance 1 d in estimate for Irrv_Pu_c concentration convergence. 
Row 54: $F54 = 0.5*$B$51*ABS(($E54-$C54)/(1-$C54)) 
This result is dragged down through Row 61 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-36 November 2004 
Column G: delta_2 
intermediate tolerance 2 d in estimate for Irrv_Pu_c concentration convergence. 
Row 54: $G54 = 0.5*$B$51*ABS(($E54-$C54)/(1-$E54)) 
This result is dragged down through Row 61 
Column H: t_1 
intermediate result 
) ( log 
) ( log 
1 10 
1 10 
b
d 
Equation B-75. 
Row 54: $H54 = LOG10($F54)/LOG10($E54) 
This result is dragged down through row 61 
Column I: t_2 
intermediate result 
) ( log 
) ( log 
1 10 
2 10 
a
d 
Equation B-75. 
Row 54: $G54 = LOG10($G54)/LOG10($C54) 
This result is dragged down through Row 61 
Column J: time [yrs] 
time for Irrv_Pu_c concentration to converge to given tolerance, Equation B-75. 
Row 54: $J54 
=$A54*INT(MAX(LOG10($F54)/LOG10($E54),LOG10($G54)/LOG10($C54))) 
This result is dragged down through Row 61. 
The plot of the time to converge (shown in Figure F-19) is in Worksheet plot_time_to_conv 
and is Figure B-5 of Appendix B. 
Time to converge for Pu_aq concentration is 
x-axis: $A$54:$A$61 
y-axis: $D$54:$D$61 
Time to converge for Irrv_Pu_colloids is 
x-axis: $A$54:$A$61 
y-axis: $J$54:$J$61 
Note that the x-axis scale is from 110-3 to 1103 years, so only Rows 54 through 60 are shown 
in the figure. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-37 November 2004 
Figure F-19. Spreadsheet time_to_conv.xls, Worksheet plot_time_to_conv; Plot of Colloid Model 
Results 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 F-38 November 2004 
INTENTIONALLY LEFT BLANK 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 
APPENDIX G 
MICROSOFT EXCEL SPREADSHEET INVERT DIFFUSION COEFFICIENT 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 G-1 November 2004 
MICROSOFT EXCEL SPREADSHEET INVERT DIFFUSION COEFFICIENT 
SPREADSHEET INVERT DIFFUSION COEFFICIENT WORKSHEET MODEL 
The purpose of this spreadsheet is to perform a statistical analysis of the dependence of diffusion 
coefficients, D (cm2 s-1), on volumetric moisture content, . (percent, 100 m3 water m-3 bulk 
volume), as described in Section 6.3.4.1.1. The diffusion data are fit to an equation of the form 
n 
D D .. 
. 
.. 
. = 
100 0 
. 
, (Eq. G-1) 
where 0 D is the self-diffusion coefficient of water (2.299  10-5 cm2 s-1) (Mills 1973 
[DIRS 133392], Table III), and the fitting parameter is the exponent, n. To perform a least 
squares fit of the data, this equation is linearized in terms of n: 
.. 
. 
.. 
. = . .. 
. 
. .. 
. 
100 
log log 10 
0 
10 
. 
n 
D
D . (Eq. G-2) 
Column A, Rows 1 through 125, of the spreadsheet, shown in Figures G-1 through G-4, contains 
the moisture content values, . (percent) (Conca and Wright 1992 [DIRS 100436]; Conca et al. 
1993 [DIRS 170709]), that are listed in Table 4.1-14. The corresponding diffusion coefficient 
values listed in Table 4.1-14 are in Column B, Rows 1 through 125. In Column C, the quantity 
100 / . is computed (e.g., C3=A3/100], and 0 / D D is computed in Column D 
(e.g., D3=B3/0.00002299). The log term on the right hand side of Equation G-2, containing 
the moisture content, is computed Column E (e.g., E3=LOG10(A3)-2). In Column F, the 
left-hand side of Equation G-2 is calculated (e.g., D3=LOG10(D3)). 
The least squares fit of the data is done using the Microsoft Excel Trendline tool. In Figure G-5, 
the results in Column F are plotted on the y-axis against the corresponding values in Column E 
on the x-axis in the plot located between Rows 132 and 154 of the worksheet. The type of 
regression is linear. The Trendline features, Set intercept = 0, Display equation on chart, 
and Display R-squared value on chart are clicked on. In particular, the Set intercept = 0 
feature results in a fit to Equation G-2, in which the intercept is constrained to be zero. 
As shown on the charts, the fitting parameter, n, has a value of 1.863. The correlation 
coefficient, R2, is 0.915, indicating a strong correlation between the diffusion coefficient and the 
volumetric moisture content. The regression equation is: 
863 . 1 
0 100 
.. 
. 
.. 
. = 
. D D , (Eq. G-3) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 G-2 November 2004 
In Column G, the error, or deviation of each data point from the fitted equation, is calculated 
(e.g., G3=F3-1.862899*E3)); i.e., for data point i, the calculation in Column G is the 
deviation i e: 
.. 
. 
.. 
. - . .. 
. 
. .. 
. 
= 
100 
log 863 . 1 log 10 
0 
10 
. 
e 
D
D 
i . (Eq. G-4) 
In Cell G128, the average of the 125 values of i e is computed: G128=AVERAGE(G3:G127). 
The standard deviation of the i e, Cell G129 is computed: G129=STDEV(G3:G127). 
Figure G-1. Spreadsheet Invert Diffusion Coefficient, Worksheet Model; Invert Diffusion Coefficient 
Input Data (Water Content 1.50 to 6.93 Percent) 

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ANL-WIS-PA-000001 REV 01 G-3 November 2004 
Figure G-2. Spreadsheet Invert Diffusion Coefficient, Worksheet Model; Invert Diffusion Coefficient 
Input Data (Water Content 7.30 to 11.60 Percent) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 G-4 November 2004 
Figure G-3. Spreadsheet Invert Diffusion Coefficient, Worksheet Model; Invert Diffusion Coefficient 
Input Data (Water Content 11.60 to 17.50 Percent) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 G-5 November 2004 
Figure G-4. Spreadsheet Invert Diffusion Coefficient, Worksheet Model; Invert Diffusion Coefficient 
Input Data (Water Content 17.50 to 66.30 Percent) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 G-6 November 2004 
Source: Conca and Wright 1992 [DIRS 100436]; Conca et al. 1993 [DIRS 170709]. 
Figure G-5. Spreadsheet Invert Diffusion Coefficient, Worksheet Model; Plot of Fitted Invert Diffusion 
Coefficient Data 
In the plot in Figure G-6 between Rows 169 and 191, the lines for the mean and for the mean 
plus or minus three standard deviations are added to the plot shown earlier. The lines are drawn 
over the range of the data, i.e., for 100 / . from 0.015 to 0.663 (Column C, Rows 159 to 166). 
The y-values for the Trendline fit are computed as ( ) 863 . 1 
0 100 / / . = D D 
(e.g., D159=(C159^1.863)), and the values plotted are ( ) 0 10 / log D D 
(e.g., G159=LOG10(D159)). For the mean curve, the y-values are computed as 
( ) 033 . 0 863 . 1 
0 10 100 / / . = D D (e.g., D163=(C163^1.863)*10^(0.033)), and the values plotted are 
again ( ) 0 10 / log D D (e.g., G163=LOG10(D163)). For the mean plus three standard deviations 
curve, the y-values are computed as ( ) ) 218 . 0 ( 3 033 . 0 863 . 1 
0 10 100 / / + = . D D 
(e.g., G161=(C161^1.863)*10^(0.033+3*0.218)), and the values plotted are again 
( ) 0 10 / log D D (e.g., G161=LOG10(D161)). The mean minus three standard deviations curve is 
done similarly. This plot is shown as Figure 6.3-4 in Section 6.3.4.1.1. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 G-7 November 2004 
Source: Conca and Wright 1992 [DIRS 100436]; Conca et al. 1993 [DIRS 170709]. 
Figure G-6. Spreadsheet Invert Diffusion Coefficient, Worksheet Model; Plotted Results of Invert 
Diffusion Coefficient Data, Showing Uncertainty Range as Mean 3 Standard Deviations 
The data are further analyzed in Figure G-7 to demonstrate that the deviations approximately 
follow a normal distribution. Under the Microsoft Excel menu item Tools, Data Analysis is 
clicked, and Histogram is selected under Analysis Tools. In the Histogram window, the error 
data (Column G, Rows 3 to 127) are entered for the Input Range. For the Bin Range, Column I, 
Rows 3 to 22, is entered. The frequency distribution is output in Column J, Rows 3 to 22. For 
comparison, a theoretical normal distribution is computed over the same range in Column M: 
( ) 2 2 2 / 
2 
1 ) , ; ( s  
p s 
s  - - = x e x f , (Eq. G-5) 
where x is the bin value, the mean 033 . 0   , and the standard deviation 218 . 0  s . 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 G-8 November 2004 
The Microsoft Excel formula is (for Cell M3, for example): 
M3=EXP(-((I3-0.0329438386573088)^2)/(2*0.218121819319092^2))/ 
(0.218121819319092*(2*PI())^0.5) 
Figure G-7. Spreadsheet Invert Diffusion Coefficient, Worksheet Model; Further Analysis of Invert 
Diffusion Coefficient Data 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 G-9 November 2004 
SPREADSHEET INVERT DIFFUSION COEFFICIENT 
WORKSHEET VALIDATION 
In this worksheet (Figure G-8), diffusion coefficient data (Column B) from Tables A-1 and A-2 
of The Determination of Diffusion Coefficient of Invert Materials (CRWMS M&O 2000 
[DIRS 156680]) are plotted against water content (Column A), along with the results of the 
analysis in Worksheet Model. The purpose of this worksheet is partially to validate the 
diffusion coefficient submodel by showing that the model overestimates the value of the invert 
diffusion coefficient, thereby overestimating diffusive releases of radionuclides through the 
invert. The model curve fit (Equation 6.3.4.1.1-16), also shown on p. G-7 and in Figure 6.3-4 in 
Section 6.3.4.1.1, is reproduced in Columns D-G, Rows 3 and 4, and plotted in the figure below. 
Source: CRWMS M&O 2000 [DIRS 156680], Tables A-1 and A-2. 
Figure G-8. Spreadsheet Invert Diffusion Coefficient, Worksheet Validation; Validation of Invert 
Diffusion Coefficient Data 

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INTENTIONALLY LEFT BLANK 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 
APPENDIX H 
QUALIFICATION OF DIFFUSION COEFFICIENT DATA 

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QUALIFICATION OF DIFFUSION COEFFICIENT DATA 
DESCRIPTION OF DATA TO BE QUALIFIED 
The data reported in Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 
[DIRS 170709]) consist of measured diffusion coefficients of unsaturated soil, gravel, bentonite, 
rock, and crushed tuff from Yucca Mountain, over a broad range of water contents. These data 
have been collected and analyzed using standard scientific practices. The diffusivity data for 
various granular media at volumetric moisture contents ranging between 1.5 percent and 
66.3 percent are given in Section 4.1.2, Table 4.1-14. These measured data have been used to 
analyze the dependence of the diffusion coefficient on volumetric moisture content for a variety 
of granular materials (Section 6.3.4.1.1). These data are qualified in accordance with the data 
qualification plan included in this appendix. 
CORROBORATING DATA 
The diffusion coefficient data for crushed tuff materials from The Determination of Diffusion 
Coefficient of Invert Materials (CRWMS M&O 2000 [DIRS 156680]) are used to qualify the 
data reported by Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 
[DIRS 170709]). The diffusion coefficient data found in The Determination of Diffusion 
Coefficient of Invert Materials (CRWMS M&O 2000 [DIRS 156680]) were collected in the 
DOE Atlas Facility. The tests were performed by the EBS Testing Department under 
YMP-approved procedures using the Unsaturated Flow Apparatus. The Unsaturated Flow 
Apparatus method is reported to be an accurate and fast indirect method of determining diffusion 
coefficients in porous media (Conca and Wright 1992 [DIRS 100436], p. 7). The method uses 
measurements of electrical conductivity, at specified volumetric moisture content, which is 
converted to diffusion coefficient. The Determination of Diffusion Coefficient of Invert 
Materials (CRWMS M&O 2000 [DIRS 156680]) reports that the error on the reported data is 
within 7 percent. The reported data are shown in Table H-1. 
DATA EVALUATION CRITERIA 
The diffusion coefficient data from Conca and Wright (1992 [DIRS 100436]) and Conca et al. 
(1993 [DIRS 170709]) will be considered qualified if they are within one order of magnitude of 
the values reported in The Determination of Diffusion Coefficient of Invert Materials 
(CRWMS M&O 2000 [DIRS 156680]); or if greater differences are observed, they result in 
more conservative results with regard to radionuclide releases. 
COMPARISON OF THE DIFFUSION COEFFICIENT DATA IN CONCA AND 
WRIGHT (1992 [DIRS 100436]) AND CONCA ET AL. (1993 [DIRS 170709]) TO CRWMS 
M&O (2000 [DIRS 156680]) 
The data reported by Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 
[DIRS 170709]) (shown in Section 4.1.2, Table 4.1-14) consist of diffusion coefficient data for 
the range of 1.5 percent to 66.3 percent volumetric moisture content. The data from The 
Determination of Diffusion Coefficient of Invert Materials (CRWMS M&O 2000 
[DIRS 156680]) ranges between 0.2 percent and 32.13 percent. Figure H-1 shows a plot of 
moisture content versus diffusion coefficient for data from both sources. The figure shows that 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 H-2 November 2004 
overall the Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 [DIRS 170709]) 
data have higher diffusion coefficient values over the measured range of water content. The 
differences are highest at low water content. At water content values below 10 percent, the 
Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 [DIRS 170709]) diffusion 
coefficient values are higher by as much as two orders of magnitude. For water content values 
above 10 percent, the Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 
[DIRS 170709]) diffusion coefficient data show higher but comparable values. 
The differences in diffusion coefficient at low water content values can be partly attributed to the 
measurement technique. As discussed in Section 6 of The Determination of Diffusion Coefficient 
of Invert Materials (CRWMS M&O 2000 [DIRS 156680]), errors in measurement are higher at 
low diffusion coefficient values. Conca and Wright (1992 [DIRS 100436], p. 10) also reported 
that, at low water content, reductions in water content result in sharp declines in the measured 
diffusion coefficient as surface films become thin and discontinuous, and pendular water 
elements become small. Measurement differences could also be attributed to the different porous 
medium samples used. The Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 
[DIRS 170709]) data include various material samples whereas the determination report 
(CRWMS M&O 2000 [DIRS 156680]) data are for crushed tuff only. The data from both 
sources show some scatter. The diffusion coefficient data of Conca and Wright (1992 
[DIRS 100436]) and Conca et al. (1993 [DIRS 170709]) are thus comparable to those of the 
determination report (CRWMS M&O 2000 [DIRS 156680]) for volumetric water content values 
above 10 percent. For low volumetric water content values, the differences are greater. 
However, the higher diffusion coefficient values of Conca and Wright (1992 [DIRS 100436]) 
and Conca et al. (1993 [DIRS 170709]) will result in predicted radionuclide releases being 
higher. 
The Conca and Wright (1992 [DIRS 100436]) data have been published in a peer-reviewed 
journal (Applied Hydrology), and thus has undergone strict review. The data are shown plotted 
in Figure 2 of Conca and Wright (1992 [DIRS 100436]). 
The Conca et al. (1993 [DIRS 170709]) data have been published in the proceedings of the 
Scientific Basis for Nuclear Waste Management XVI Symposium held November 30 to 
December 4, 1992. This symposium was organized by the Materials Research Society, which 
was formed in 1973. The most recent Scientific Basis for Nuclear Waste Management XVI 
Symposium is XXVII, the proceedings of which were published in 2004. Papers published in the 
proceedings undergo peer review prior to publication and must be presented at the meeting in 
order to be published. 
SUMMARY OF QUALIFICATION 
The diffusion coefficient data of Conca and Wright (1992 [DIRS 100436]) and Conca et al. 
(1993 [DIRS 170709]) have been evaluated in the context of their use in radionuclide transport 
modeling, and are considered qualified for use within this report per AP-SIII.2Q, Qualification of 
Unqualified Data, Attachment 3, on the basis of: 
 Availability of corroborating dataThe corroborating data are YMP-generated data using 
the same measurement technique. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 H-3 November 2004 
 Reliability of data sourcesThe data are published in a peer-reviewed journal and in a 
peer-reviewed symposium proceedings. 
 Data demonstrate properties of interestThe published data, diffusion coefficients in 
crushed rock, are the data required for the model of transport in the invert. 
The above comparison of the diffusion coefficient data of Conca and Wright (1992 
[DIRS 100436]) and Conca et al. (1993 [DIRS 170709]) with the corroborating data from 
CRWMS M&O 2000 [DIRS 156680] shows that the data evaluation criteria have been met. The 
data to be qualified are within one order of magnitude of the values in the corroborating source 
for volumetric water content values above 10 percent (Figure H-1). The differences between the 
two data sets are greater than one order of magnitude below 10 percent; however, the higher 
diffusion coefficient values of Conca and Wright (1992 [DIRS 100436]) and Conca et al. (1993 
[DIRS 170709]) will result in predicted radionuclide releases being higher. Therefore, the Conca 
and Wright (1992 [DIRS 100436]) and Conca et al. (1993 [DIRS 170709]) diffusion coefficient 
data shown on Table 4.1-14 are judged to be qualified for use in this report. Use of these data in 
other applications would require a comparable evaluation for that specific use. 
Table H-1. Diffusion Coefficient of Crushed Tuff Invert Materials 
Sample 
Volumetric Moisture 
Content (%) 
Diffusion Coefficient 
(cm2 s-1) 
1 32.13 2.02  10-6 
2 18.15 5.40  10-7 
3 9.26 4.05  10-8 
4 7.03 6.75  10-9 
5 6.97 7.45  10-9 
6 6.89 6.73  10-9 
7 6.75 5.42  10-9 
8 6.63 4.39  10-9 
9 6.63 3.76  10-9 
10 6.23 3.40  10-9 
11 6.00 3.43  10-9 
12 5.55 2.04  10-9 
13 5.46 2.04  10-9 
14 8.29 2.24  10-9 
15 7.54 6.81  10-9 
16 7.36 6.21  10-9 
17 7.22 4.38  10-9 
18 6.84 2.19  10-9 
19 6.11 1.55  10-9 
20 5.41 9.97  10-10 
21 4.45 6.19  10-10 
22 3.64 5.00  10-10 
23 0.29 1.24  10-10 
24 0.20 1.25  10-10 
Source: CRWMS M&O 2000 [DIRS 156680]. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 H-4 November 2004 
1.E-10 
1.E-09 
1.E-08 
1.E-07 
1.E-06 
1.E-05 
1.E-04 
0 10 20 30 40 50 60 70 
Volumetric Moisture Content (%) 
Diffusion Coefficient (cm2/s) 
Conca and Wright (1992); 
Conca et al. (1993) 
CRWMS M&O (2000) 
Source: Conca and Wright 1992 [DIRS 100436]; Conca et al. 1993 [DIRS 170709]; CRWMS M&O 2000 
[DIRS 156680]. 
Figure H-1. Comparison of Diffusion Coefficients 
DATA QUALIFICATION PLAN 
A facsimile of the data qualification plan developed for the above qualification effort is provided 
in Figure H-2. The original is included in the records package for this model report. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 H-5 November 2004 
Figure H-2. Data Qualification Plan 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 H-6 November 2004 
INTENTIONALLY LEFT BLANK 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 November 2004 
APPENDIX I 
COMPARISON OF OUTPUT DTNS 

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ANL-WIS-PA-000001 REV 01 November 2004 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 I-1 November 2004 
COMPARISON OF OUTPUT DTNs 
The output from this report consists of two preliminary output DTNs: SN0403T0507703.015 
and SN0409T0507703.017, and a final output DTN: SN0410T0507703.018. In this appendix, 
the differences between the two preliminary output DTNs are discussed. In addition, the final 
output DTN is compared with the second preliminary DTN. These comparisons provide 
traceability for TSPA-LA applications that were initially developed based on the preliminary 
output DTNs. 
The output in these DTNs consists of the tables from Section 8 (Conclusions) of the EBS RT 
Abstraction. Each of these tables is compared in this appendix. Numerous editorial revisions 
were made in converting the first preliminary version of the DTN to the second preliminary 
version; because these editorial revisions have no impact on TSPA-LA results, they are not 
discussed in this appendix. 
TABLE 57 (DTN: SN0403T0507703.015) VS. TABLE 8.1-1 (DTN: SN0409T0507703.017) 
Table 57 (Summary of EBS Flow Abstraction) in DTN: SN0403T0507703.015 corresponds to 
Table 8.1-1 in DTN: SN0409T0507703.017. The key differences in this table between the two 
DTN versions are the expressions for the flux through the drip shield, F2, and the flux into the 
waste package, F4. In preliminary DTN: SN0403T0507703.015, F2 is expressed as: 
F2 = F1 LDS_Patch fDS/(2LDS). (Eq. I-1) 
The parameters are defined in the Table 57 in DTN: SN0403T0507703.015. This equation is 
technically correct, but it is expressed more completely in DTN: SN0409T0507703.017 as: 
F2 = min[F1NbDSLDS_Patch f 'DS/(2LDS), F1]. (Eq. I-2) 
The parameters are defined in the Table 8.1-1 in DTN: SN0409T0507703.017. Equation I-2 
replicates Equation 6.5.1.1.2-37 in the EBS RT Abstraction. Equations I-1 and I-2 give the same 
result when the number of corrosion patches in the drip shield, bDS N , is one, which is the case in 
the WAPDEG model of drip shield failure (BSC 2004 [DIRS 169996], Section 6.3). The min 
function in Equation I-2 provides a numerical check to prevent an unrealistic result of F2 > F1 
from being obtained if the parameter values used in the equation were to give that result. 
The same discussion applies to the flux into the waste package. In 
DTN: SN0403T0507703.015, F4, is expressed as: 
F4 = F2 LWP_Patch fWP/(2LWP). (Eq. I-3) 
The parameters are defined in the Table 57 in DTN: SN0403T0507703.015. 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 I-2 November 2004 
This equation is technically correct, but it is expressed more completely in 
DTN: SN0409T0507703.017 as: 
F4 = min[F2NbWPLWP_Patchf 'WP/(2LWP), F2]. (Eq. I-4) 
The parameters are defined in the Table 8-1 in DTN: SN0409T0507703.017. Equation I-4 
replicates Equation 6.5.1.1.3-1 in the EBS RT Abstraction. The difference between Equations I-3 
and I-4 is the definition of LWP_Patch. In Equation I-3, LWP_Patch, is the length of all corrosion 
patches in the waste package, whereas in Equation I-4, LWP_Patch is the length of each corrosion 
patch; thus, the product NbWPLWP_Patch in Equation I-4 is equal to LWP_Patch in Equation I-3. The 
min function in Equation I-4 provides a numerical check to prevent an unrealistic result of 
F4 > F2 from being obtained if the parameter values used in the equation were to give that result. 
In the Flow Parameter column for Flow Pathway 8 in Table 57 in DTN: SN0403T0507703.015, 
a flux F9 is erroneously included in the equation and is deleted in the final DTN. Since this flux 
does not exist, its inclusion in the preliminary DTN has no impact on the TSPA-LA calculation. 
The references and comments in the Data Sources & Notes column in Table 8.1-1 in 
DTN: SN0409T0507703.017 are updated from Table 57 in DTN: SN0403T0507703.015; these 
updates have no impact on TSPA-LA calculations. 
TABLE 58 (DTN: SN0403T0507703.015) VS. TABLE 8.1-2 (DTN: SN0409T0507703.017) 
In DTN: SN0409T0507703.017, the cross-sectional area for radionuclide transport is clarified in 
Table 8.1-2, with references to sections in the report. In DTN: SN0403T0507703.015, the same 
parameter is referred to as the flow cross-sectional area in Table 58 and described in vague terms 
that prompted a revised description in the final DTN. References are updated in 
DTN: SN0409T0507703.017 Table 8.1-2. None of these changes has any impact on TSPA-LA 
calculations. 
TABLE 59 (DTN: SN0403T0507703.015) VS. TABLE 8.2-1 (DTN: SN0409T0507703.017) 
In Table 57 in DTN: SN0403T0507703.015, the lower end of the range on sampled parameter 
Diff_Path_Length_CP_CDSP is erroneously shown as 0.02 m; this error is also found in 
Table 63 in DTN: SN0403T0507703.015. Because the correct value, 0.025 m, is included in the 
database used for TSPA-LA, this error has no impact on TSPA-LA. In the corresponding table 
in DTN: SN0409T0507703.017, Table 8.2-1, the range for this parameter is not shown, since it 
is given correctly in Table 8.2-3. 
References to parameter sources and sections in the EBS RT Abstraction are updated in 
DTN: SN0409T0507703.017. These changes have no impact on TSPA-LA calculations. 
TABLE 60 (DTN: SN0403T0507703.015) VS. TABLE 8.2-2 (DTN: SN0409T0507703.017) 
Table 8.2-2 in DTN: SN0409T0507703.017 (Kd values for corrosion products) is identical to 
Table 60 in DTN: SN0403T0507703.015. Therefore, there is no impact on TSPA-LA 
calculations. 

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ANL-WIS-PA-000001 REV 01 I-3 November 2004 
TABLES 61 & 62 (DTN: SN0403T0507703.015) VS. TEXT (DTN: SN0409T0507703.017) 
Tables 61 and 62 in DTN: SN0403T0507703.015 (Kd values and correlations for the invert) are 
replaced in DTN: SN0409T0507703.017 with text clarifying that TSPA-LA is to use UZ Kd 
values for the invert. This change has no impact on TSPA-LA calculations. 
TABLE 63 (DTN: SN0403T0507703.015) VS. TABLE 8.2-3 (DTN: SN0409T0507703.017) 
In Table 63 in DTN: SN0403T0507703.015, sampled parameter Diff_Path_Length_CP_CDSP 
is erroneously shown as having a lower end of the range of 0.02 m. Because the correct value, 
0.025 m, is included in the database used for TSPA-LA, this error has no impact on TSPA-LA. 
The correct range is shown in Table 8.2-3 in DTN: SN0409T0507703.017. References are 
updated in Table 8.2-3 in DTN: SN0409T0507703.017. These changes have no impact on 
TSPA-LA calculations. 
TABLE 64 (DTN: SN0403T0507703.015) VS. TABLE 8.2-4 (DTN: SN0409T0507703.017) 
References are updated in Table 8.2-4 in DTN: SN0409T0507703.017. Three parameters were 
added to this table to provide a source for the values used in TSPA-LA: DS_Total_Length 
(5805 mm), Invert_Viscosity_Ref_Temp (298.15 K), and Interface_Scale_Factor (1  10-6). 
These changes have no impact on TSPA-LA calculations. No other changes were made in 
converting Table 64 to Table 8.2-4. 
TABLE 65 (DTN: SN0403T0507703.015) VS. TABLE 8.2-5 (DTN: SN0409T0507703.017) 
The following changes were made to convert Table 65 to Table 8.2-5. References to the 
equations in the EBS RT Abstraction were added to the Input Description column. In the 
Parameter Description for Equation 8-1, clarification of the definition of ND, the truncated 
normal distribution, was added. In Equation 8-2, the range of validity was added to the 
definition of temperature. In Equation 8-3, the definition of m . was changed from fraction to 
percent, and the equation was modified accordingly by changing the term m . 138 .0 to 
m . 00138 . 0 . Equation 8-7 was completely revised in order to clarify the calculation of corrosion 
product mass as computed in TSPA-LA over each time interval, from 0 t , when breach occurs, to 
1 f t and 2 f t , the lifetimes of each type of steel. These changes have no impact on TSPA-LA 
calculations. 
TABLE 66 (DTN: SN0403T0507703.015) VS. TABLE 8.2-6 (DTN: SN0409T0507703.017) 
Table 8.2-6 DTN: SN0409T0507703.017 (Invert Diffusion Coefficient Alternative conceptual 
Model Parameters) is identical to Table 66 in DTN: SN0403T0507703.015. Therefore, there is 
no impact on TSPA-LA calculations. 

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ANL-WIS-PA-000001 REV 01 I-4 November 2004 
TABLE 67 (DTN: SN0403T0507703.015) VS. TABLE 8.2-7 (DTN: SN0409T0507703.017) 
Equation 8-8 was reformulated in the EBS RT Abstraction and revised accordingly in 
Table 8.2-7. Because this is an alternative conceptual model, this change has no impact on 
TSPA-LA calculations. Equation 8-9, the definitions of intra . and min . were changed from 
fractions to percent. This change has no impact on the results. 
TABLE 8.1-1 (DTN: SN0410T0507703.018)VS. TABLE 8.1-1 (DTN: SN0409T0507703.017) 
The differences in this table (Summary of EBS Flow Abstraction) between the two DTN 
versions are the expressions for the flux through the drip shield, 2 F , and the flux into the waste 
package, 4 F . In DTN: SN0409T0507703.017, 2 F is expressed as: 
( ) [ ] 1 _ 1 2 , 2 / min F L f L N F F DS DS Patch DS bDS ' = . (Eq. I-5) 
The parameters are defined in Table 8.1-1 in both DTNs. Because Patch DS L _ is defined as the 
axial half-length of each corrosion patch, the factor of 2 should not appear in the denominator. 
This equation is presented correctly in DTN: SN0410T0507703.018 as: 
[ ] 1 _ 1 2 , / min F L f L N F F DS DS Patch DS bDS ' = . (Eq. I-6) 
Similarly, in DTN: SN0409T0507703.017, 4 F is expressed in Table 8.1-1 as: 
( ) [ ] 2 _ 2 4 , 2 / min F L f L N F F WP WP Patch WP bWP ' = . (Eq. I-7) 
This equation is presented correctly in Table 8.1-1 in DTN: SN0410T0507703.018 as: 
[ ] 2 _ 2 4 , / min F L f L N F F WP WP Patch WP bWP ' = . (Eq. I-8) 
These differences have no impact because the correct equations (Equations I-6 and I-8) have 
been implemented in the TSPA. 
TABLE 8.2-5 (DTN: SN0410T0507703.018)VS. TABLE 8.2-5 (DTN: SN0409T0507703.017) 
The differences in this table (Calculated Model Inputs Used in the EBS Radionuclide Transport 
Abstraction) between the two DTN versions include Equation 8-5 for the effective water 
saturation of corrosion products. In DTN: SN0409T0507703.017, this equation is: 
( ) 45 . 2 / 1 6 
, ln 10 312 . 1 - - -  = RH s S CP CP we . (Eq. I-9) 
This equation, developed in an earlier draft of Section 6.5.1.2.1.4.2 as Equation 6.5.1.2.1-27, is 
incorrect. The correct equation (as shown in Section 6.5.1.2.1.4.2, Equation 6.5.1.2.1-27 of this 
report), is given in DTN: SN0410T0507703.018 as: 
( ) 45 . 2 / 1 6 
, ln 10 28 . 3 - - -  = RH s S CP CP we . (Eq. I-10) 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 I-5 November 2004 
In addition, in DTN: SN0409T0507703.017, parameter CP s is defined in Table 8.2-5 as having 
units of (m2 g-1). The correct units for use in this parameter are given in 
DTN: SN0410T0507703.018 as (m2 kg-1). 
The impact of this correction has been assessed in a Technical Management Review Board 
(TMRB) Decision Proposal (BSC 2004 [DIRS 172219]). Because the water saturation in the 
waste package corrosion products is used to calculate the diffusion coefficient, this correction 
has a direct impact on dose estimates. In the preliminary assessment, using Equation I-10 
instead of Equation I-9 increases the total peak mean annual dose from all scenario classes by 10 
percent (BSC 2004 [DIRS 172219]). 

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 01 I-6 November 2004 
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