EBS Radionuclide Transport Abstraction Rev 00, ICN 02

ANL-WIS-PA-000001

September 2000

1. PURPOSE 
The purpose of this work is to develop the Engineered Barrier System (EBS) radionuclide 
transport abstraction model, as directed by a written development plan (CRWMS M&O 1999a). 
This abstraction is the conceptual model that will be used to determine the rate of release of 
radionuclides from the EBS to the unsaturated zone (UZ) in the total system performance 
assessment-license application (TSPA-LA). In particular, this model will be used to quantify the 
time-dependent radionuclide releases from a failed waste package (WP) and their subsequent 
transport through the EBS to the emplacement drift wall/UZ interface. 
The development of this conceptual model will allow Performance Assessment Operations 
(PAO) and its Engineered Barrier Performance Department to provide a more detailed and 
complete EBS flow and transport abstraction. The results from this conceptual model will allow 
PAO to address portions of the key technical issues (KTIs) presented in three NRC Issue 
Resolution Status Reports (IRSRs): (1) the Evolution of the Near-Field Environment (ENFE), 
Revision 2 (NRC 1999a), (2) the Container Life and Source Term (CLST), Revision 2 (NRC 
1999b), and (3) the Thermal Effects on Flow (TEF), Revision 1 (NRC 1998). The conceptual 
model for flow and transport in the EBS will be referred to as the EBS RT Abstraction in this 
analysis/modeling report (AMR). 
The scope of this abstraction and report is limited to flow and transport processes. More 
specifically, this AMR does not discuss elements of the TSPA-SR and TSPA-LA that relate to 
the EBS but are discussed in other AMRs. These elements include 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. In effect, this AMR provides the algorithms for transporting radionuclides 
using the flow geometry and radionuclide concentrations determined by other elements of the 
TSPA-SR model. The scope of the EBS RT Abstraction also does not include computational or 
numerical procedures for solving the process-level equations; rather, it identifies the important 
processes that must then be evaluated with process-level or component-level software using 
analytical or numerical solutions. 
Three iterations of the TSPA model are referred to in this AMR: (1) the viability assessment 
(TSPA-VA) that was completed and documented in 1998, (2) the site recommendation (TSPASR) 
that is currently underway, and (3) the license application (TSPA-LA) that will be submitted 
to the NRC. The text distinguishes between the current models and screening decisions for the 
TSPA-SR and the potential (future) changes to the EBS RT Abstraction for the TSPA-LA. 
The purpose of this Interim Change Notice (ICN) is to incorporate the recent design changes for 
the EBS into the EBS RT Abstraction. The recent design changes are: (1) an engineered backfill 
material will not be placed around the drip shield (DS), and (2) the DS design now includes posts 
that will connect adjacent DSs. In addition, new information on the block size from rockfalls 
and the dynamic response of the DS to such blocks has become available. Although the design 
basis for TSPA-SR is a repository without backfill (CRWMS M&O 2000a), sensitivity studies 
will also be performed for emplacement drifts with backfill. This AMR therefore presents 
abstractions for EBS flow and transport without backfill (the design basis) and with backfill.

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The emphasis in the EBS RT Abstraction is on a reasonable approach that bounds the response 
of the EBS. A reasonably bounding approach is appropriate for this abstraction because of the 
uncertainty in the response of a very complex engineered system over long periods of time. 
Areas where additional efforts can reduce the degree of conservatism or add more realism to the 
model have been identified, when appropriate. 
2. QUALITY ASSURANCE 
The Quality Assurance (QA) program applies to the development of documentation for the EBS 
RT Abstraction. A development plan, Develop the EBS Radionuclide Transport Abstraction 
Model for TSPA-LA (CRWMS M&O 1999a), has been completed for this work. The plan 
identifies the work package MYPS Number for this AMR as 1301213EM1. 
The PAO responsible manager has evaluated this technical document development activity in 
accordance with QAP-2-0, Conduct of Activities. The QAP-2-0 activity evaluation, Engineered 
Barrier System Performance Modeling (CRWMS M&O 1999b), has determined that the 
preparation and review of this technical document is subject to Quality Assurance Requirements 
and Description (QARD) DOE/RW-0333P (DOE 2000) requirements. Preparation of this 
conceptual model did not require the classification of items in accordance with QAP-2-3, 
Classification of Permanent Items. This activity is not a field activity. Therefore, an evaluation 
in accordance with NLP-2-0, Determination of Importance Evaluations, was not required. 
3. COMPUTER SOFTWARE AND MODEL USAGE 
3.1 COMPUTER SOFTWARE 
No codes or routines were developed for this analysis. No computer software was used to 
directly generate information for this AMR. 
3.2 MODELS 
The previous model used for EBS flow and transport is documented in Chapter 6 of the Total 
System Performance Assessment-Viability Assessment (TSPA-VA) Analyses Technical Basis 
Document (CRWMS M&O 1998a). This conceptual model document is being developed to 
supercede the concepts presented in Chapter 6 of the Technical Basis Document. More 
specifically, design changes since the TSPA-VA model was formulated have required 
reevaluation and, in some cases, substantial changes to the EBS flow and transport abstraction 
model. These design changes include the presence of a DS and the use of crushed tuff rather 
than concrete in the invert. The current baseline design is documented in (CRWMS M&O 
2000a).

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4. INPUTS 
4.1 DATA AND PARAMETERS 
For TSPA-Site Recommendation/License Application (TSPA-SR, TSPA-LA) analyses, requests 
were made by PAO to Waste Package Operations (WPO) and Engineered Barrier System 
Operations (EBSO) to obtain the appropriate information for EBS conceptual model 
development. Each organization responded using AP-3.14Q, Transmittal of Input, to provide the 
requested information (CRWMS M&O 1999c; CRWMS M&O 1999d; CRWMS M&O 2000s; 
CRWMS M&O 2000u). Because these inputs are not all qualified or accepted, they are 
considered TBV inputs. However, these inputs do contain some qualified and accepted data. 
Table 1 summarizes the relevant input parameters and the sources for these values. 
Table 1. Parameters for EBS Component Analyses and EBS RT Abstraction 
Model Input Value Source 
Angle of repose for Overton sand backfill 26 CRWMS M&O 1999c, Att. II to Item 
1 
Boltzmann constant 1.380658 x 10-23 J/K Lide 1997, p. 1-1 
Coefficient of linear thermal expansion for 
titanium grade 7 at 450F 
4.95 x 10-6 F-1= 
8.91 x 10-6 C-1 
ASME 1995, Table TE-5 
Cross-sectional area (nominal) for flow through 
a patch on the DS 
7.21 x 104 mm2 CRWMS M&O 2000b, Section 3.2.7 
Cross-sectional area (nominal) for flow through 
a patch on the WP 
2.346 x 104 mm2 CRWMS M&O 2000b, Section 3.2.7 
Diameter of the drift 5.5 m CRWMS M&O 1999c, Att. II to Item 
1 
Density of quartz sand (grain density) 2700 kg/m3 CRWMS M&O 1999c, Item 2A 
Density of tuff (invert grain density) 2530 kg/m3 CRWMS M&O 1999c, Item 2B 
Density of water at 0C 1000 kg/m3 Lide 1997, p. 6-3 
Distance between posts and mating holes for 
the DS 
5510 mm CRWMS M&O 2000c, Att. II, SK- 
0148 REV05 
Distance from edge of DS Plate-1 to center of 
post 
420 mm CRWMS M&O 2000c, Att. II, SK- 
0148 REV05 
Distance from edge of DS Connector Plate-1 to 
center of hole for posts 
175 mm CRWMS M&O 2000c, Att. II, SK- 
0148 REV05 
Width of the DS 2505 mm CRWMS M&O 2000c, Att. II, SK- 
0148 REV05 
Elementary electron charge 1.602 x 10-19 Coulomb Lide 1997, p. 1-1 
Maximum depth of invert 606 mm CRWMS M&O 1999d 
Length of DS 6105 mm CRWMS M&O 2000c, Att. II, SK- 
0148 REV05 
Porosity of quartz sand backfill 0.41 CRWMS M&O 1999c, Item 2A 
Porosity of crushed tuff rock in the invert 0.545 CRWMS M&O 1999c, Item 2B 
Self-diffusion coefficient of water at 25C 2.299 x 10-5 cm2/s Mills 1973, Table III 
Surface tension of water at 20C 0.0728 N/m Lide 1997, p. 6-3 
Thickness of DS Plate-1 15 mm CRWMS M&O 2000c, Att. II, SK- 
0148 REV05 
Viscosity of water at 20C 0.001 Pa-s Lide 1997, p. 6-3 
Width of DS connector guides 50 mm CRWMS M&O 2000c, Att. II, SK- 
0148 REV05

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Model Input Value Source 
WP inner lid to closure lid gap 30 mm CRWMS M&O 2000d, Att. I, SK- 
0175 REV02 and Att. II, SK-0192 
REV00; 
CRWMS M&O 2000e, Att. III, SK- 
0196 REV03; 
CRWMS M&O 2000f, Att. II, SK- 
0194 REV01 
WP outer layer thickness  21-PWR & 44-BWR 
packages 
2 cm CRWMS M&O 2000d, Att. I, SK- 
0175 REV02 and Att. II, SK-0192 
REV00 
WP outer layer thickness  Naval SNF and 
DHLW/DOE SNF packages 
2.5 cm CRWMS M&O 2000e, Att. III, SK- 
0196 REV03; 
CRWMS M&O 2000f, Att. II, SK- 
0194 REV01 
WP inner layer thickness 5 cm CRWMS M&O 2000d, Att. I, SK- 
0175 REV02 and Att. II, SK-0192 
REV00; 
CRWMS M&O 2000e, Att. III, SK- 
0196 REV03; 
CRWMS M&O 2000f, Att. II, SK- 
0194 REV01 
WP closure lid thickness 1.0 cm CRWMS M&O 2000d, Att. I, SK- 
0175 REV02 and Att. II, SK-0192 
REV00; 
CRWMS M&O 2000e, Att. III, SK- 
0196 REV03; 
CRWMS M&O 2000f, Att. II, SK- 
0194 REV01 
WP inner lid thickness  21-PWR & 44-BWR 
packages 
9.5 cm CRWMS M&O 2000d, Att. I, SK- 
0175 REV02 and Att. II, SK-0192 
REV00 
WP inner lid thickness  Naval SNF long 
package 
13.0 cm CRWMS M&O 2000f, Att. II, SK- 
0194 REV01 
WP inner lid thickness  DHLW/DOE SNF 
package 
8.0 cm CRWMS M&O 2000e, Att. III, SK- 
0196 REV03 
21 PWR Characteristics 
WP outer diameter 1.564 m CRWMS M&O 2000d, Att. I, SK- 
0175 REV02 
WP length 5.165 m CRWMS M&O 2000d, Att. I, SK- 
0175 REV02 
Distance from lowest point on WP to top of 
invert 
190 mm CRWMS M&O 2000c, Att. II, SK- 
0154 REV02 
Distance from DS to highest point on WP 582 mm CRWMS M&O 2000c, Att. II, SK- 
0154 REV02 
Distance from DS to highest point on WP if 
emplacement pallet collapses 
772 mm Sum of two previous lines 
WP porosity 0.672 CRWMS 1998b Table 5a 
44-BWR Characteristics 
WP outer diameter 1.594 m CRWMS M&O 2000d, Att. II, SK- 
0192 REV00 
WP length 5.165 m CRWMS M&O 2000d, Att. II, SK- 
0192 REV00 
Distance from lowest point on WP to top of 
invert 
193 mm CRWMS M&O 2000c, Att. II, SK- 
0154 REV02 
Distance from DS to highest point on WP 549 mm CRWMS M&O 2000c, Att. II, SK

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Model Input Value Source 
0154 REV02 
Distance from DS to highest point on WP if 
emplacement pallet collapses 
742 mm Sum of two previous lines 
5 DHLW/DOE SNF 
WP outer diameter 2.030 m CRWMS M&O 2000e, Att. III, SK- 
0196 REV03 
WP length (short package) 3.590 m CRWMS M&O 2000e, Att. III, SK- 
0196 REV03 
Distance from lowest point on WP to top of 
invert 
226 mm CRWMS M&O 2000c, Att. II, SK- 
0154 REV02 
Distance from DS to highest point on WP 80 mm CRWMS M&O 2000c, Att. II, SK- 
0154 REV02 
Distance from DS to highest point on WP if 
emplacement pallet collapses 
306 mm Sum of two previous lines 
Short emplacement pallet length 2500 mm CRWMS M&O 2000c, Att. III, SK- 
0189 REV00 
Naval SNF 
WP outer diameter 1.869 m CRWMS M&O 2000f, Att. II, SK- 
0194 REV01 
WP length 6.065 m CRWMS M&O 2000f, Att. II, SK- 
0194 REV01 
Distance from lowest point on WP to top of 
invert 
213 mm CRWMS M&O 2000c, Att. II, SK- 
0154 REV02 
Distance from DS to highest point on WP 254 cm CRWMS M&O 2000c, Att. II, SK- 
0154 REV02 
Distance from DS to highest point on WP if 
emplacement pallet collapses 
467 mm Sum of two previous lines 
4.2 CRITERIA 
Programmatic requirements for this document are listed in the Development Plan: Develop the 
EBS Radionuclide Transport Abstraction Model for TSPA-LA (CRWMS M&O 1999a). This 
Development Plan specifies that this document and all analyses described herein must adhere to 
the requirements of AP-3.10Q, Analyses and Models. This Plan also specifies that this AMR 
must address applicable NRC issue resolution status report (IRSR) acceptance criteria for three 
Key Technical Issues (KTIs): (1) Evaluation of the Near-Field Environment (ENFE) (NRC 
1999a), (2) Container Life and Source Term (CLST) (NRC 1999b), and (3) Thermal Effects on 
Flow (TEF) (NRC 1998). 
The following sections identify the NRC IRSR acceptance criteria for each of the three KTIs 
applicable to this Development Plan. Evaluations of these criteria are presented in Section 7.2. 
A listing of features, events and processes (FEPs) that apply to the EBS RT Abstraction is 
included in Section 4.2.4. 
The NRC IRSR acceptance criteria are presented separately for each KTI. This is appropriate 
because each KTI has a distinct set of acceptance criteria and because only selected subissues 
within each KTI are applicable to the EBS RT Abstraction. The subissues that apply to EBS RT 
Abstraction model development for the ENFE KTI are: (a) the effects of coupled thermalhydrologic-
chemical (THC) processes on seepage and flow, and (b) the effects of coupled THC 
processes on radionuclide transport through engineered and natural barriers. The subissues that

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apply for the CLST KTI are: (a) subissue 3: the rate at which radionuclides in spent nuclear fuel 
are released from the engineered barrier subsystem through the oxidation and dissolution of 
spent fuel, (b) subissue 4: the rate at which radionuclides in high-level waste glass are released 
from the engineered barrier subsystem, and (c) subissue 6: the effects of alternative engineered 
barrier subsystem design features on container lifetime and radionuclide release from the 
engineered barrier subsystem. The subissue that applies for the TEF KTI is subissue 3: does the 
U.S. Department of Energy total system performance assessment adequately account for thermal 
effects on flow? 
Several task-specific criteria were also used during the EBS conceptual model development. The 
criterion to evaluate the potential impact of thermal and mechanical processes on DS separation 
(see Section 6.5) is to compare the calculated separation distance with the possible slippage or 
overlap between adjacent DSs. This overlap is created by the connector plate attached to each 
DS. Mechanisms that result in separations that are much less than the overlap have been 
screened out of the EBS conceptual model for the TSPA-SR. The criteria selected to evaluate 
the bathtub geometry (see Section 6.6) as an alternative conceptual model are: (1) radionuclide 
concentration leaving the WP, and (2) radionuclide mass flux leaving the WP. These are 
reasonable performance measures because they directly effect the concentrations and fluxes of 
radionuclides released to the EBS and ultimately to the affected population. No other criteria 
have been used in developing the EBS RT Abstraction. 
4.2.1 NRC IRSR Criteria for the ENFE KTI 
The acceptance criteria for the ENFE KTI are presented for two of the five major subissues for 
this KTI. The two subissues that are directly relevant to the EBS RT Abstraction are: (1) IRSR 
Section 4.1  The Effects of Coupled Thermal-Hydrologic-Chemical Processes on Seepage and 
Flow, and (2) IRSR Section 4.4  The Effects of Coupled Thermal-Hydrologic-Chemical 
Processes on Radionuclide Transport Through Engineered And Natural Barriers. The subissues 
in Sections 4.2, 4.3 and 4.5 of the IRSR relate to the waste package chemical environment, to the 
impact of the chemical environment on radionuclide release (mobilization), and to the potential 
for nuclear criticality in the near-field, respectively. These subissues are not directly relevant to 
the EBS RT Abstraction and are not discussed in this AMR. 
The following sections present the technical and programmatic acceptance criteria from Sections 
4.1 and 4.4 of the IRSR that are applicable to this AMR. Note that a single listing of the 
acceptance criteria is possible because the criteria in Sections 4.1 and 4.4 are very similar. The 
main difference between the criteria in Sections 4.1 and 4.4 relates to microbial issues that are 
not relevant to the EBS RT Abstraction. 
4.2.1.1 Applicable Data and Model Justification Acceptance Criteria 
1. Consider both temporal and spatial variations in THC effects on EBS flow and 
transport processes. (NRC 1999a, Sections 4.1.1 and 4.4.1) 
2. Consider site characteristics in establishing initial and boundary conditions for 
conceptual models and simulations of coupled processes that may affect EBS flow and 
transport processes. (NRC 1999a, Sections 4.1.1 and 4.4.1)

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3. Collect sufficient data on the characteristics of the natural system and engineered 
materials, such as the type, quantity, and reactivity of materials, to establish initial and 
boundary conditions for conceptual models and simulations of THC coupled processes 
that may affect EBS flow and transport. (NRC 1999a, Sections 4.1.1 and 4.4.1) 
4. Use sensitivity and uncertainty analyses (including consideration of alternative 
conceptual models) to determine whether additional new data are needed to better 
define ranges of input parameters. (NRC 1999a, Sections 4.1.1 and 4.4.1) 
5. If the testing program for coupled THC processes on the chemical environment for 
radionuclide release from the engineered barrier system is not complete at the time of 
license application, or if sensitivity and uncertainty analyses indicate that additional 
data are needed, DOE has identified specific plans to acquire the necessary 
information as part of the performance confirmation program. (NRC 1999a, Sections 
4.1.1 and 4.4.1) 
4.2.1.2 Applicable Data Uncertainty and Verification Acceptance Criteria 
1. Use reasonable or conservative ranges of parameters or functional relations to 
determine effects of coupled THC processes on EBS flow and transport. Parameter 
values, assumed ranges, probability distributions, and bounding assumptions are 
technically defensible and reasonably account for uncertainties. (NRC 1999a, 
Sections 4.1.1 and 4.4.1) 
2. Consider uncertainty in data due to both temporal and spatial variations in conditions 
affecting coupled THC effects on EBS flow and transport processes. (NRC 1999a, 
Sections 4.1.1 and 4.4.1) 
3. Properly consider the uncertainties in the characteristics of the natural system and 
engineered materials, such as the type, quantity, and reactivity of materials, in 
establishing initial and boundary conditions for conceptual models and simulations of 
THC coupled processes that may affect EBS flow and transport. (NRC 1999a, 
Sections 4.1.1 and 4.4.1) 
4. The initial conditions, boundary conditions, and computational domain used in 
sensitivity analysis involving coupled THC effects on EBS flow and transport 
processes should be consistent with available data. (NRC 1999a, Sections 4.1.1 and 
4.4.1) 
5. DOE's performance confirmation program should assess whether the natural system 
and engineered materials are functioning as intended and anticipated with regard to 
coupled THC effects on radionuclide release from the engineered barrier system. 
(NRC 1999a, Sections 4.1.1 and 4.4.1) 
4.2.1.3 Model Uncertainty Acceptance Criteria 
1. Use appropriate models, tests, and analyses that are sensitive to the THC couplings 
under consideration for both natural and engineered systems as described in the

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following examples. The effects of THC coupled processes that may occur in the 
natural setting or due to interactions with engineered materials or their alteration 
products include: (i) Thermohydrologic (TH) effects on gas and water chemistry; (ii) 
hydrothermally driven geochemical reactions, such as zeolitization of volcanic glass 
and the precipitation and dissolution of lxides and hydroxides; (iii) dehydration of 
hydrous phases liberating moisture; (iv) effects of microbial processes; (v) effects of 
corrosion products on transport of radionculdies in the near field; and (v) changes in 
water chemistry that may result from interactions between cementatious or WP 
materials and groundwater, which, in turn, may affect the environment for EBS flow 
and transport. (NRC 1999a, Sections 4.1.1 and 4.4.1) 
2. Investigate alternative modeling approaches consistent with available data and current 
scientific understanding, and appropriately consider their results and limitations. 
(NRC 1999a, Sections 4.1.1 and 4.4.1) 
3. Provide a reasonable description of the mathematical models included in analyses of 
coupled THC effects on EBS flow and transport processes. The description should 
include a discussion of alternative modeling approaches not considered in its final 
analysis and the limitations and uncertainties of the chosen model. (NRC 1999a, 
Sections 4.1.1 and 4.4.1) 
4.2.1.4 Model Verification Acceptance Criteria 
1. The mathematical models for coupled THC effects on EBS flow and transport should 
be consistent with conceptual models based on inferences about the near-field 
environment, field data and natural alteration observed at the site, and expected 
engineered materials. (NRC 1999a, Sections 4.1.1 and 4.4.1) 
2. Appropriately adopted accepted and well-documented procedures to construct and test 
the numerical models should be used to simulate coupled THC effects on EBS flow 
and transport processes. (NRC 1999a, Sections 4.1.1 and 4.4.1) 
3. Abstracted models for coupled THC effects on EBS flow and transport processes 
should be based on the same assumptions and approximations shown to be appropriate 
for closely analogous natural or experimental systems. Abstracted model results 
should be verified through comparison to outputs of detailed process models and 
empirical observations. Abstracted model results should be compared with different 
mathematical models to judge robustness of results (NRC 1999a, Sections 4.1.1 and 
4.4.1) 
4.2.1.5 Integration Acceptance Criteria 
1. Consider all the relevant features, events and processes. The abstracted models should 
adequately incorporate important design features, physical phenomena, and couplings, 
and use consistent and appropriate assumptions throughout. (NRC 1999a, Sections 
4.1.1 and 4.4.1)

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2. The abstracted models should reasonably account for known temporal and spatial 
variations in conditions affecting coupled THC effects on seepage and flow. (NRC 
1999a, Sections 4.1.1 and 4.4.1) 
3. Assumptions may be used to simplify PA analyses if certain THC couplings are 
determined to be unimportant to performance. A firm technical basis will be provided 
if potentially important couplings are neglected. The technical basis can include 
activities such as independent modeling, laboratory and field data, or sensitivity 
studies. (NRC 1999a, Sections 4.1.1 and 4.4.1) 
4. The bases used for modeling assumptions and approximations will be documented and 
justified if simplifications for modeling coupled THC effects on seepage and flow are 
used for PA analyses instead of detailed process models. (NRC 1999a, Sections 4.1.1 
and 4.4.1) 
4.2.1.6 Programmatic Acceptance Criteria 
1. Data and models should be collected, developed, and documented under acceptable 
quality assurance (QA) procedures. (NRC 1999a, Sections 4.1.1 and 4.4.1) 
2. Deficiency reports should be closed concerning data quality on issues related to 
coupled THC effects on seepage and flow. (NRC 1999a, Sections 4.1.1 and 4.4.1) 
3. Expert elicitations should be conducted and documented in accordance with the 
guidance in NUREG-1562 (Kotra et al. 1996) or other acceptable approaches. (NRC 
1999a, Sections 4.1.1 and 4.4.1) 
4.2.2 NRC IRSR Criteria for the CLST KTI 
The acceptance criteria for the CLST KTI are presented as a set of general acceptance criteria 
plus specific acceptance criteria for each subissue under this KTI. All general acceptance criteria 
are presented in the next subsection, followed by the criteria applicable to EBS flow and 
transport for the subissues (3, 4 and 6) that are relevant to the EBS RT Abstraction. Subissues 3 
and 4 relate to the release of radionuclides from the EBS and subissue 6 relates to the effects of 
alternative EBS design features on radionuclide release. 
4.2.2.1 General Acceptance Criteria For All Subissues 
1. The collection and documentation of data, as well as development and documentation 
of analyses, methods, models, and codes, should be accomplished under approved 
quality assurance and control procedures and standards. (NRC 1999b, Section 4.0) 
2. Expert elicitations, when used, should be conducted and documented in accordance 
with the guidance provided in NUREG-1563 (Kotra et al. 1996) or other acceptable 
approaches. (NRC 1999b, Section 4.0)

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3. Sufficient data (field, laboratory, and natural analog) should be available to adequately 
define relevant parameters for the models used to evaluate performance aspects of the 
sub-issues. (NRC 1999b, Section 4.0) 
4. Sensitivity and uncertainty analyses (including consideration of alternative conceptual 
models) should be used to determine whether additional data would be needed to 
better define ranges of input parameters. (NRC 1999b, Section 4.0) 
5. Parameter values, assumed ranges, test data, probability distributions, and bounding 
assumptions used in the models should be technically defensible and can reasonably 
account for known uncertainties. (NRC 1999b, Section 4.0) 
6. Mathematical model limitations and uncertainties in modeling were defined and 
documented. (NRC 1999b, Section 4.0) 
7. Primary and alternative modeling approaches consistent with available data and 
current scientific understanding should be investigated and their results and limitations 
should be considered in evaluating the subissue. (NRC 1999b, Section 4.0) 
8. Model outputs should be validated through comparisons with outputs of detailed 
process models, empirical observations, or both. (NRC 1999b, Section 4.0) 
9. The structure and organization of process and abstracted models should adequately 
incorporate important design features, physical phenomena, and coupled processes. 
(NRC 1999b, Section 4.0) 
4.2.2.2 Applicable Acceptance Criteria for Subissues 3 and 4 
1. Identify and consider the likely processes for SNF or HLW degradation and the release 
of radionuclides from the EBS, as follows: dissolution of the irradiated UO2 matrix, 
with the consequent formation of secondary minerals and colloids; prompt release of 
radionuclides; degradation in the dry air environment; degradation and failure of fuel 
cladding; preferential dissolution of intermetallics in DOE SNF and HWL; and release 
of radionuclides from the WP emplacement drifts. (NRC 1999b, Sections 4.3.1 and 
4.4.1) 
2. Demonstrate that the numerical models used for SNF/HLW degradation and 
radionuclide release from the EBS are adequate representations, including 
consideration of uncertainties, of the expected SNF/HLW performance and are not 
likely to overestimate the actual performance in the repository environment. (NRC 
1999b, Sections 4.3.1 and 4.4.1) 
3. Conduct a consistent, sufficient, and suitable SNF/HLW corrosion and radionuclide 
release testing program at the time of the LA submittal. In addition, identify specific 
plans for further testing to reduce any significant area(s) of uncertainty as part of the 
performance confirmation program. (NRC 1999b, Sections 4.3.1 and 4.4.1)

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4. Establish an adequate program of monitoring radionuclide release from the WP during 
the performance confirmation period, to assure that assumptions and calculations of 
SNF/HLW dissolution and radionuclide release from the WP are appropriately 
substantiated. (NRC 1999b, Sections 4.3.1 and 4.4.1) 
4.2.2.3 Applicable Acceptance Criteria for Subissue 6 
1. Identify and consider the effects of backfill, and the timing of its emplacement, on the 
thermal loading of the repository, WP lifetime (including container corrosion and 
mechanical failure), and the release of radionuclides from the EBS. (NRC 1999b, 
Section 4.6.1) 
2. Identify and consider the effects of drip shields (with backfill) on WP lifetime, 
including extension of the humid-air corrosion regime, environmental effects, 
breakdown of drip shields and resulting mechanical impacts on WP, the potential for 
crevice corrosion at the junction between the WP and the drip shield, and the potential 
for condensate formation and dripping on the underside of the shield. (NRC 1999b, 
Section 4.6.1) 
3. Justify the use of test results for drip shields, ceramic coatings, and backfill materials 
not specifically collected for the YM side for the environmental conditions expected to 
prevail at the proposed YM repository. (NRC 1999b, Section 4.6.1) 
4.2.3 NRC IRSR Criteria for the TEF KTI 
The acceptance criteria for the TEF KTI are presented for subissue 3: does the U.S. Department 
of Energy total system performance assessment adequately account for thermal effects on flow? 
Subissue 3 has elements that are directly relevant to the EBS RT Abstraction. Subissues 1 and 2 
are generally concerned with thermohydrologic flow in the near-field rock environment and 
hence are less relevant to EBS flow and transport processes. 
The following section presents the acceptance criteria for the two programmatic acceptance 
criteria and for the first three technical acceptance criteria. Technical acceptance criteria 4 
through 7 are omitted because they are either covered in other general acceptance criteria or are 
not directly relevant to the EBS RT Abstraction. 
4.2.3.1 Acceptance Criteria For Subissue 3 
1. Develop and document analyses under acceptable QA procedures. (NRC 1998, 
Section 4.3.1). 
2. Justify the use of abstracted models in the TSPA. This justification may include, but is 
not necessarily limited to, the use of expert elicitation. Expert elicitations should be 
conducted and documented in accordance with NUREG1563 (Kotra et al., 1996) or 
other acceptable procedures. (NRC 1998, Section 4.3.1). 
3. Abstractions of process-level models may be used if predictions from the abstracted 
model are shown to conservatively bound process-level predictions. In particular, an

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abstracted model for influx of water into an emplacement drift may be used if the 
abstracted model is shown to bound process-level model predictions of the influx of 
water as liquid or vapor into an emplacement drift. (NRC 1998, Section 4.3.1). 
4. Demonstrate that sufficient data are available to adequately define relevant parameters, 
parameter values and conceptual models. Specifically, DOE should demonstrate that 
(NRC 1998, Section 4.3.1): 
- Uncertainties and variabilities in parameter values are accounted for using 
defensible methods. Provide the technical bases for parameter ranges, probability 
distributions or bounding values. Derive parameter values (single values, ranges, 
probability distributions, or bounding values) from site-specific data or an analysis 
showing that the assumed parameter values lead to a conservative effect on 
performance. 
- Demonstrate that analyses are consistent with site characteristics in establishing 
initial conditions, boundary conditions, and computational domains for conceptual 
models. 
5. Provide reasonably complete descriptions of the conceptual and mathematical models 
for the TSPA (NRC 1998, Section 4.3.1). Further, demonstrate that: 
- Performance affecting processes observed in available thermohydrologic tests and 
experiments have been identified and incorporated into the TSPA. Specifically, 
demonstrate that liquid water will not reflux into the underground facility or 
incorporate refluxing water into the TSPA and bound the potential adverse effects 
of: (i) corrosion of the WP; (ii) accelerated transport of radionuclides; and (iii) 
alteration of hydraulic and transport pathways that result from refluxing water. 
- Identify and incorporate Significant Geologic Repository Operations Area 
underground facility design features, such as the addition of backfill or drip 
shields, that can result in changes in TSP into the TSPA. 
- Define and document conceptual model uncertainties and assess their effects on 
conclusions regarding TSP. 
- Ensure that mathematical models are consistent with conceptual models, based on 
consideration of site characteristics. 
- Consider alternative models and modeling approaches to ensure that they are 
consistent with available data and current scientific understanding, that their 
limitations are defined, and that their results are appropriately considered. 
- Compare the results from different mathematical models to judge the robustness of 
results. 
4.2.4 YMP Features, Events and Processes (FEPs) 
Table 2 gives a listing of Yucca Mountain Project (YMP) FEPs (CRWMS M&O 2000g) that are 
relevant to the conceptual model for EBS flow and transport. YMP FEP # and NEA Category 
are part of the database search properties and are provided for convenience. Any resolution of 
these FEPs is discussed in Section 7.5. 
The focus of the FEPs for the EBS is on liquid-mediated transport of radionuclides. Gaseous 
transport of radionuclides has been screened out of the nominal scenario because of low

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consequence (CRWMS M&O 2000g, FEP 3.2.10.00.00). This FEP includes consideration of 
radiotoxic and chemotoxic species in the air as gas, vapor, particulates, or an aerosol. The 
radionuclide with the greatest potential for gaseous release is C-14. Bounding estimates of the 
potential dose of C-14 indicate that the maximum release of C-14 will be at least 5 orders of 
magnitude below the anticipated regulatory dose limit. It follows that gaseous transport is not 
included in the EBS RT Abstraction for the TSPA. 
As an aside, atmospheric transport due to volcanic ashfall is included in the TSPA-SR for the 
igneous intrusion scenario (CRWMS M&O 2000g, FEP 1.2.04.07.00, Ashfall). This scenario is 
not relevant to the EBS RT Abstraction because (a portion of) the EBS is destroyed by the 
igneous intrusion. 
Table 2. A Listing of YMP FEPs That Pertain to the EBS RT Abstraction 
YMP 
FEP # 
NEA 
Category FEP Name 
Screening 
Decision for EBS 
1.1.02.02.00 ID-1 Effects of pre-closure ventilation Include 
2.1.03.01.00 2.1.03a Corrosion of waste containers Include 
2.1.03.10.00 2.1.03k Container healing Exclude 
2.1.03.12.00 2.1.03i Container failure (long-term) Include 
2.1.04.01.00 2.1.04u Preferential pathways in the backfill Include 
2.1.04.02.00 2.1.04au Physical and chemical properties of backfill Include 
2.1.04.04.00 2.1.04az Mechanical effects of backfill Include 
2.1.04.05.00 2.1.04b Backfill evolution Include 
2.1.04.08.00 2.1.04t Diffusion in backfill Exclude 
2.1.04.09.00 3.2.07r Radionuclide transport through backfill Exclude 
2.1.06.05.00 2.1.05p Degradation of invert and pedestal Include 
2.1.06.06.00 WP-1 Effects and degradation of DS Include 
2.1.06.07.00 2.1.03o Effects at material interfaces Exclude 
2.1.07.01.00 2.1.07a Rockfall (large block) Exclude 
2.1.07.03.00 2.1.03bd Movement of containers Exclude 
2.1.07.06.00 2.1.07ad Floor buckling Exclude 
2.1.08.04.00 2.1.08e Condensation forms on backs of drifts Include 
2.1.08.05.00 2.1.08ad Flow through invert Include 
2.1.08.06.00 2.1.08y Wicking in waste and EBS Include 
2.1.08.07.00 2.1.03ax Pathways for unsaturated flow and transport in the waste 
and EBS 
Include 
2.1.08.09.00 2.1.08w Saturated groundwater flow in waste and EBS Exclude 
2.1.08.11.00 2.1.08m Resaturation of repository Include 
2.1.09.01.00 2.1.09k Properties of the potential carrier plume in the waste and 
EBS 
Include 
2.1.09.02.00 3.2.01i Interaction with corrosion products Exclude in EBS 
2.1.09.05.00 2.1.09bm In-drift sorption Exclude 
2.1.09.08.00 2.1.09bk Chemical gradients / enhanced diffusion in waste and EBS Exclude 
2.1.09.15.00 2.1.09c Formation of true colloids in waste and EBS Exclude in EBS 
2.1.09.19.00 3.2.04z Colloid transport and sorption in the waste and EBS Include 
2.1.09.20.00 3.2.04y Colloid filtration in the waste and EBS Exclude

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YMP 
FEP # 
NEA 
Category FEP Name 
Screening 
Decision for EBS 
2.1.09.21.00 3.2.08c Suspensions of particles larger than colloids Exclude 
2.1.11.05.00 2.1.11ac Differing thermal expansion of repository components Exclude 
2.1.11.09.00 2.1.11ad Thermal effects on liquid or two-phase fluid flow in the 
waste and EBS 
Include 
2.1.11.10.00 2.1.11ag Thermal effects on diffusion (Soret effect) in waste and 
EBS 
Exclude 
2.1.13.02.00 2.1.13b Radiation damage in waste and EBS Exclude 
2.2.07.06.00 ID-2 Episodic/pulse release from repository Include 
2.2.08.04.00 2.2.08c Redissolution of precipitates directs more corrosive fluids 
to containers 
Include 
4.3 CODES AND STANDARDS 
This AMR was prepared to comply with the DOE interim guidance (Dyer 1999, which directs 
the use of the proposed NRC high-level waste rule, 10 CFR Part 63. 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 ... . 
The relevant codes, standards, regulations and procedures for the development of the EBS RT 
Abstraction are listed in Section 8.2. 
5. ASSUMPTIONS 
The assumptions for the abstraction for EBS flow, for the abstraction for EBS transport, for the 
DS separation model, and for an alternative conceptual model of flow through the WP (called the 
bathtub model) are presented in Sections 5.1, 5.2, 5.3, and 5.4, respectively. Note that 
assumptions are often stated in their most general form to encompass the potential for future 
design changes or new experimental data, even though certain processes may not occur. For 
example, corrosive processes may result in patches, pits or stress corrosion cracks (SCCs) in the 
WP, although the local chemical environment or WP fabrication techniques may prevent certain 
failure modes from occurring in Alloy 22. 
5.1 EBS FLOW 
The assumptions for the conceptual model for EBS flow are listed below. The applicability of 
each assumption in the presence or absence of an engineered backfill material surrounding the 
DS is identified in the text. The presence or absence of backfill is indicated by the phrase 
backfilled EBS or nonbackfilled EBS, respectively.

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5.1.1 Capillary fluxes are estimated assuming pressure equilibrium at the interface 
between the quartz sand backfill and the host rock. 
The high capillarity of the Overton sand backfill relative to the capillarity for flowing 
fractures in the adjacent host rock results in the potential for backfill to wick water from the 
host rock. There is speculation as to whether sufficient connection exists between flowing 
fractures in the adjacent host rock and the backfill for wicking to occur. Simulations with 
the NUFT code assume sufficient connection for pressure equilibrium between the backfill 
and the host rock. (The NUFT code (Nitao 1998) provides numerical solutions for the 
coupled thermohydraulic response of the UZ and emplacement drifts, including the major 
components of the EBS). Until this issue is studied in more detail, the EBS RT Abstraction 
assumes a similar connection between the host rock and the backfill and includes a wicking 
flux in the PA calculations. This assumption is only relevant for the backfilled EBS; it is 
used in the discussions of capillary flow in Sections 6.2.1, 6.2.1.2, and 6.2.1.3. 
5.1.2 Condensation on the inside of the DS occurs when the temperature of the DS is less 
than the temperature of the invert. 
The inside of the DS will be filled with a mixture of air and water vapor. The source of the 
air is the general circulation of atmospheric gas through Yucca Mountain. The water vapor 
will be generated by evaporation from the invert. Water vapor can also be generated by 
evaporation from the surface of the WP, although the invert should be the dominant source 
while the DS is intact and diverts water away from the WP. Liquid water can condense on 
the inside of the DS when the temperature of the DS, TDS, is less than the dew point of this 
air/vapor mixture. 
Depending on vapor pressure gradients, the evaporated water from the invert can either 
move laterally away from the DS (i.e., to the right or left of the invert) or it can move 
upward to the inside of the DS. For example, the water vapor may move toward the drift 
walls by diffusing rapidly through the porous, high permeability materials in the invert and 
backfill. If this vapor condenses, it may do so in cooler regions where the relative humidity 
is high, perhaps on the walls of the drift. This flow pattern would tend to maintain wetter 
conditions on the outside of the DS, rather than beneath the DS. Note that the DS forms an 
inverted cap that will tend to trap any water vapor that moves upward. 
As a first order approximation, the space between the DS and WP can be treated as a closed 
system because of the geometry of the DS and invert. The vapor pressure of water beneath 
the DS will then be close to the equilibrium vapor pressure at the invert temperature, TINV. 
In this case, comparison of the temperature in the invert (TINV) and the temperature at the 
top of the DS (TDS) provides a suitable indicator of the potential for condensation on the 
inside of the DS. That is, condensation will occur if TINV >TDS. This is a physically 
reasonable approximation in terms of providing an indicator for the direction of vapor 
pressure gradients. This assumption is a reasonably bounding one because the possibility 
of water vapor transport laterally away from the DS or through gaps in the DS is ignored. 
This assumption is applicable to the backfilled and the nonbackfilled EBS; it is used in 
Section 6.3.3.

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A more accurate model of the evaporation/condensation process may be used in future 
TSPAs if experimental data from the ATLAS facility or computational data from NUFT 
analyses indicate that condensation is occurring. 
5.1.3 If condensation occurs, it is assumed that the condensation flux on the DS is equal 
to the evaporative flux in the invert. 
This is a reasonable bounding estimate if thermal conditions are relatively uniform beneath 
the DSs because some of the evaporative flux from the invert will escape through the 
backfill and host rock, rather than condense on the DS. If thermal conditions are 
nonuniform, then the local condensation flux could exceed the evaporation flux at some 
locations. This issue must be reevaluated for the final TSPA-LA design configuration. 
This assumption is used in Section 6.3.3 and is applicable to the backfilled and the 
nonbackfilled EBS. 
5.1.4 If condensation occurs, it is assumed that all the condensation flux drips from the 
crown of the DS onto the WP. 
This is a reasonably bounding assumption because droplets or thin films of liquid may flow 
down the sides of the DS, rather than fall on the WP. This assumption is used in Sections 
6.3.2 and 6.3.3 and is applicable to the backfilled and nonbackfilled EBS. 
5.1.5 The advective flow (of water) in the EBS cannot reach the WPs as long as the 
integrity of the DS is maintained. This assumption applies to the seepage flux in the 
nonbackfilled EBS and to the capillary and seepage fluxes for a backfilled EBS. 
Three lines of reasoning are presented in Section 6.2.2 to defend this assumption. 
5.1.6 Once the integrity of the DS is compromised, backfill is assumed to fill the axial 
space surrounding the WP. 
This assumption bounds the expected behavior of the EBS, as explained in Section 6.2.3.2. 
It is only applicable to the backfilled EBS. 
5.1.7 The total flux into the quartz sand backfill is equal to the sum of the seepage flux 
and the capillary flux multiplied by a factor between 0 and 1. The total flux into the 
nonbackfilled EBS is equal to the seepage flux; that is, the capillary flux is ignored 
when there is no backfill in the EBS. 
For the backfilled EBS, the total flux into the system is given by the seepage flux plus a 
contribution from the capillary flux. The capillary flux is calculated in a potentially very 
conservative framework for two reasons. First, there is speculation as to whether sufficient 
connection exists between flowing fractures in the adjacent host rock and the backfill for 
wicking to occur. Simulations with the NUFT code conservatively assume sufficient 
connection for pressure equilibrium between the backfill and the host rock, but the validity

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of this equilibrium condition is uncertain. Second, future design changes may specify a 
coarser backfill that has minimal wicking potential relative to the fractures in the host rock 
or possibly no backfill at all. Given this situation, the capillary flux will be multiplied by a 
factor between 0 and 1 to represent the variations in backfill materials, EBS design and the 
coupling with the fractures in the host rock. The value of this factor will be determined by 
the PAO for specific analyses and designs in future TSPAs for the backfilled EBS. This 
assumption is used in Section 6.2.1. 
The capillary flux is assumed to be zero for the nonbackfilled EBS because there is no 
medium to wick water from the fractures in the host rock. This means that the factor 
multiplying the capillary flux is zero and the total flux into the EBS is given by the seepage 
flux. This assumption is used in Section 6.2.1. 
5.1.8 Flow of water through the backfill is a quasi-steady process in a homogeneous 
porous medium. 
The overall flow through the backfill approaches a steady state condition because the 
inflow boundary condition (percolation flux) is generally constant. When the boundary 
condition does change, such as with a new climate, the flow will move to a new steady 
state condition. Breaching of the DS or WP can also change the flow geometry, but this 
effect is considered to be a perturbation to the overall capillary flux through the backfill. 
Finally, the fine Overton sand backfill should behave as a homogeneous, porous medium in 
the repository environment. This assumption is only applicable to the backfilled EBS and is 
used in Sections 6.2.1 and 6.2.4. 
5.1.9 The fluid flux through a patch or pit in the DS or WP is proportional to the ratio of 
the length of the penetration in the axial direction to the total axial length of the DS 
or WP. This assumption is equivalent to assuming that a patch or pit is always 
located on the side (90 from the crown) of the DS or WP and that it can collect all 
fluid that drips or flows from the crown towards the penetration if the axial locations 
of source and penetration coincide. 
Two types of fluxes are considered here: a dripping flux and a capillary-driven flux. A 
dripping flux may enter the EBS as a point source, either by dripping from fractures (i.e., 
seepage flux) or by dripping due to condensation. The simplest assumption is that the 
entire dripping flux could fall exactly at the crown of the DS or WP. This may not be an 
extreme assumption because preliminary experimental data from the ATLAS test facility 
seem to show that drips do occur preferentially from the region of the crown. While it is 
difficult to generalize from preliminary data, it is a reasonable bound to assume that 
dripping will fall at the crown and that a patch at any azimuthal location on the DS or WP 
will collect fluid if the axial location of the patch coincides with that of the drip. This 
argument is applicable to the backfilled and the nonbackfilled EBS. 
A similar assumption is also used for a capillary-driven flux in the backfilled EBS. The 
capillary flow through the sand backfill will be a complex, multidimensional flow field. 
Capillary effects should result in a more uniform distribution of effective sources for fluid 
flow through a penetration in the DS. However, assuming that the penetration is located on

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the side of the DS will again be a reasonable bounding estimate because any flux can enter 
the penetration if it is at the same axial location. 
This assumption is used in Sections 6.2.4 and 6.3.2. 
5.1.10 Fluid flux can pass through any patch on the surface of the WP, independent of its 
azimuthal location on the WP. Similarly, flow of a thin film through a stress 
corrosion crack (SCC) on the lid of the WP is independent of the location of the 
SCC on the lid. 
Two general types of openings or breaches can exist in the WP due to corrosion. These are 
(1) SCCs that penetrate the weld of the lid and (2) patches resulting from general corrosion. 
Section 6.3.1.2 provides a detailed discussion of these two types of openings. 
Fluid flux can pass through any patch on the surface of the WP, independent of its location 
on the upper or lower surface of the WP. This is a conservative assumption for the patches 
and pits on the lower half of the WP, where little inflow is expected to occur. Similarly, 
the dripping flux is assumed to flow through SCCs independent of location on the lid of the 
WP. This is again a bounding assumption for the SCCs because fluid is unlikely to reach 
any SCCs on the upper half of the lid. This assumption is applicable to the backfilled and 
the nonbackfilled EBS and is used in Sections 6.2.4 and 6.3.2. 
The fact that the fluid flux can advect through a single patch or pit is an additional 
bounding feature in the flow and transport model. This approach is consistent with the 
analyses showing that a flow-through model provides a bounding estimate with respect to a 
bathtub model for the WP (see Section 6.6). 
5.1.11 The nominal patch area on the DS is 7.21 x 104 mm2 and the nominal patch area on 
the WP is 2.346 x 104 mm2. The patches are assumed to be square for the purposes 
of the flux splitting algorithm. 
WAPDEG calculates corrosion assuming 500 nodes and 1000 nodes on the DS and WP, 
respectively (CRWMS M&O 2000b, Section 3.2.7, page 3-141). Each node represents a 
patch of the surface area for the corrosion calculation. The equivalent patch area is 
calculated as the total surface area divided by the number of nodes. These areas are referred 
to as nominal because there are four types of WPs in the repository. The nominal patch 
area is then scaled for the specific surface area of each type of WP. Patches are assumed to 
be square for the purpose of determining axial length for the flux splitting algorithm. This 
is a reasonable assumption for large patches on the surface. This assumption is used in 
Sections 6.2.4 and 6.3.2; it is applicable to the backfilled and the nonbackfilled EBS.. 
5.1.12 Diversion of flux around a breached DS or WP is based on continuity of liquid flux. 
This assumption means that the sum of the flux that is diverted and the flux that 
penetrates the DS or WP equals the incident flux on the DS or WP.

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This assumption is reasonable because continuity conserves liquid mass and because it is 
consistent with the response of a quasi-steady system. This assumption is used in Sections 
6.2.1.3, 6.2.4, 6.3.2 and 6.3.4; it is applicable to the backfilled and the nonbackfilled EBS.. 
5.1.13 SCCs through the welded lid are assumed to be in the radial direction. 
Tensile stress is required to drive an SCC through the thickness of the welded lid. Detailed 
finite-element analyses of the WP and welded lid show that tensile stresses exist for cracks 
oriented lengthwise in the radial direction. These same analyses also show that 
circumferentially-oriented cracks are highly unlikely to penetrate the lid because radial 
stress on the inside surface of the lid is compressive, not tensile. This assumption is used in 
Section 6.3.1.2.1 and is applicable to the backfilled and the nonbackfilled EBS.. 
5.1.14 The width of the weld on the inner surface of the outer lid of the WP is assumed to 
be 0.25 inches. 
This is a typical engineering value for a welding operation. This assumption is used in 
Section 6.3.1.2.1 and is applicable to the backfilled and the nonbackfilled EBS.. 
5.1.15 The fluid flux onto the closure lid of the WP is reasonably bounded by assuming 
that the WP is tilted at the maximum angle possible beneath the DS. This flux is 
given by the ratio of the projected length of the end cap in the axial direction to the 
projected length of the total WP in the axial direction. 
This maximum angle of tilt occurs when the skirt and lid end of the WP is elevated to the 
height of the inside of the DS while the other end rests on the invert. This assumption is 
used in Section 6.3.2 and is applicable to the backfilled and the nonbackfilled EBS.. 
5.1.16 All fluid that flows as a film on the closure lid of the WP is assumed to flow through 
a SCC, if present. 
This is a bounding assumption for several reasons. First, a film that completely spans the 
opening of a SCC creates a differential in capillary forces that will prevent any further 
ingress of flowing water into the WP. Second, the presence of corrosion products in the 
very small SCC may provide a capillary barrier for advective flux into the WP. In spite of 
these features, flow through a SCC has not been screened out. The potential for 
atmospheric pumping, hygroscopic salts in the WP, and the uncertainty about film 
thickness make it difficult to exclude fluid flow into the WP. The assumption that all the 
thin film flow can enter the WP is a reasonable bound for the TSPA-SR/TSPA-LA. This 
assumption is used in Section 6.3.2 and is applicable to the backfilled and the nonbackfilled 
EBS.. 
5.1.17 The potential for evaporation in and on the WP is ignored. 
The heat released by spent fuel has the potential to evaporate fluid on or in the WP. This is 
an important process because advective transport is not possible if evaporation eliminates

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advective fluxes. Detailed calculations of the evaporative process, including the 
complexities in the internal geometry of fuel pins within the WPs and the small conduits 
for water vapor to escape through SCCs, are currently being performed. Until these data 
are available, evaporative processes are conservatively ignored. This assumption is used in 
Sections 6.3.3 and 6.3.2; it is applicable to the backfilled and the nonbackfilled EBS.. 
5.1.18 The stainless steel components of the WP provide no resistance to corrosion or flow. 
These components include the inner liner and inner lid of the WP. 
Corrosion of the stainless steel inner shell will occur rapidly relative to corrosion of the 
Alloy 22 outer shell (CRWMS M&O 2000h). In this circumstance, no credit is allowed for 
the time to corrode any stainless steel component and a pathway through the WP is 
assumed to exist once the outer shell of Alloy 22 is breached. This assumption is a 
reasonably bounding assumption that is used in Sections 6.3.2 and 6.4.3.1; it is applicable 
to the backfilled and the nonbackfilled EBS.. 
5.1.19 Seismic damage to the WP and its emplacement pallet has been screened out.. 
The WP is a simple thick-walled cylindrical structure with end caps. The stainless steel 
inner shell is 5 cm thick and the Alloy 22 outer shell is 2 cm thick. This massive, compact 
structure will experience minimal strain and deformation from seismic loading in its asdesigned 
condition. Seismic damage can be ignored for the as-designed WP. 
Corrosion will reduce the structural integrity of the WP over time. At very early times, 
SCCs may penetrate the welded lids of the WP. SCCs may provide flow pathways into the 
WP, but should have negligible effect on the structural integrity of the WP. Similarly, 
general corrosion of the Alloy 22 will gradually reduce the thickness of the outer shell over 
longer time periods, but the 5 cm inner shell of stainless steel will still provide some 
strength for a partly corroded WP. 
After several patches penetrate the outer shell due to general corrosion, the WP will 
become increasingly susceptible to damage from a seismic event. A seismic event may 
even collapse a badly corroded WP, although the consequence for performance will be 
modest because there are already several patches through the outer and inner shells so that 
the changes in fluid flux through the WP and in radionuclide transport out of the WP 
should also be modest. 
The emplacement pallet is designed to transport the WP from the Waste Handling Building 
to the emplacement drift. It is also designed to facilitate retrieval of WPs. The pallet will, 
therefore, be lifted while loaded with a waste package. The pallet is fabricated from the 
same materials as the waste package (Alloy 22 plates and square stainless steel tubes) 
(CRWMS M&O 2000c, Section 6.2.1). System performance criteria for the emplacement 
pallet require that it maintain the nominal emplacement position of the WP for 300 years 
and that it maintain the nominal horizontal emplacement position of the WP for 10,000 
years (CRWMS M&O 2000c, Sections 6.2.2.1.1 and 6.2.2.1.2)

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Structural response calculations were performed for the emplacement pallet under 
lifting/retrieval and under static loads. In both cases, the stresses in the emplacement pallet 
are below one-third of the yield strength and one-fifth of the tensile strength of Alloy 22 or 
316L stainless steel. With this margin of safety and the fact that corrosion during the first 
300 years after emplacement is negligible, the pallet will support retrieval. (CRWMS M&O 
2000c, Sections 6.4 and 6.5) 
Horizontal movement of a WP over 10,000 years would primarily be due to seismic 
activity. The design of the emplacement pallet is anticipated to survive seismic ground 
motions, although seismic time histories were not available for structural response 
calculations to support the TSPA-SR. (CRWMS M&O 2000c, 6.2.2.1.2) 
It is then reasonable to screen out the seismic response of the WP and emplacement pallet 
from the EBS RT Abstraction for Rev 0 of the TSPA-SR. More detailed calculations for 
the structural response of the WP and emplacement pallet under seismic loads and in 
varying states of corrosion will be performed for the TSPA-LA. This assumption has been 
used in Sections 6.3.1 and 6.3.2; it is applicable to the backfilled and the nonbackfilled 
EBS. 
5.1.20 The advective flow for radionuclide transport is a one-dimensional process and 
always vertically downward. 
Advective transport will occur predominantly in the direction of advective flow (lateral 
dispersion can lead to transport perpendicular to the direction of flow). Advective flow in 
the backfill follows a complex, multi-dimensional pattern because of capillarity in the 
finely grained backfill. Similarly, the advective flow field from seepage (nonbackfilled 
EBS) will also be multi-dimensional because the fall of droplets and flow on thin films on 
the surfaces and openings of the DS and WP can also be highly chaotic and multidimensional. 
In spite of the complex flow patterns outside the WP, fluid must first enter a WP in order to 
mobilize radionuclides for advective transport. Once the radionuclides are mobilized 
within the WP, the advective flow will be predominantly directed downward from the WP 
to the invert and then to the UZ. Since advective transport through the backfill and DS can 
be ignored (because the radionuclides are not yet mobilized), the assumption of onedimensional, 
downward advective flow from WP to the UZ is a physically reasonable 
assumption for the EBS RT Abstraction. This assumption is inherent in the EBS flow 
abstraction discussed in Sections 6.2.1.3, 6.2.4, 6.3, 6.3.2, 6.3.3, and 6.3.4. This assumption 
is applicable to the backfilled EBS and the nonbackfilled EBS. 
5.2 RADIONUCLIDE TRANSPORT THROUGH THE EBS 
The key assumptions for the conceptual model for radionuclide transport are listed below. These 
assumptions are applicable to the backfilled EBS and the nonbackfilled EBS, with the exception 
of assumption 5.2.2.

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5.2.1 Advective transport is represented as a one-dimensional process in the vertical 
direction and is always downward. 
This assumption is a direct consequence of assumption 5.1.20 and is included here for 
clarity. This assumption is used in Section 6.4. 
5.2.2 There is no transport through the quartz sand backfill. 
Upward diffusion, through the backfill, is physically impossible before the DS fails 
because there is no continuous fluid pathway for diffusion. After the DS fails, advection 
through the DS and into the WP will be the dominant flow mechanism. In this situation, it 
is reasonable to neglect any upward or lateral diffusive transport through the quartz sand 
backfill. Downward diffusive transport from the WP to the invert and UZ is then a 
physically reasonable assumption. This assumption is used in Section 6.4. This assumption 
is applicable to the backfilled EBS, although upward diffusion is also not expected for the 
nonbackfilled EBS because the minimal debris from rockfall will not provide a continuous 
pathway for liquid-based diffusion outside the DS. 
5.2.3 The effects of longitudinal and transverse dispersion are ignored. 
Longitudinal dispersion is ignored because of the small length of the flow path in the invert 
and because the representation of WP and invert as single mixing cells implies substantial 
dispersion in the numerical model. Transverse dispersion is ignored because it is a 
reasonably bounding assumption for the TSPA-LA. This assumption is used in Section 
6.4. 
5.2.4 The diffusion coefficient of all relevant radionuclides is bounded by the selfdiffusion 
coefficient for water. 
The basis for using the self-diffusion coefficient of water as a reasonably bounding value 
for the TSPA-SR is explained in Section 6.4.1.1. The value for the self-diffusion 
coefficient of water is TBV (MO0002SPASDC00.002). This assumption is used in Section 
6.4. 
5.2.5 The diffusion coefficient for a radionuclide in a porous, partly saturated medium is 
given by the self-diffusion coefficient for water times the product of porosity to the 
1.3 power and (liquid) saturation to the 1.849 power. That is, D = D0f1.3s1.849, 
where D0 is the self-diffusion coefficient of water, f is the porosity, and s is the 
liquid saturation. The basis for this assumption is explained in Section 6.4.1.2. 
The diffusion coefficient for a radionuclide in a porous, partly saturated medium is reduced 
from the self-diffusion coefficient in water by the effective cross-sectional area of the 
wetted liquid pathways. The reduction inherent in assumption 5.2.5 is an upper bound 
relative to Archies law, which predicts that the diffusion coefficient is reduced by f1.3s2 for 
a granular medium like unconsolidated sand. This assumption is used in Section 6.4.1.2.

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5.2.6 The nominal cross-sectional area of a (corroded) patch is 7.21 x 104 mm2 on the DS 
and 2.346 x 104 mm2 on the WP. 
WAPDEG calculates corrosion assuming 500 nodes and 1000 nodes on the DS and WP, 
respectively (CRWMS M&O 2000b, Section 3.2.7, page 3-141). The patch area is 
calculated as the total surface area divided by the number of nodes. This assumption is 
identical to assumption 5.1.11 and is repeated here because cross-sectional areas are an 
important parameter for diffusive transport. This assumption is used in Sections 6.2.4, 
6.3.2, and 6.4. 
5.2.7 Sorption of dissolved radionuclides is ignored in the WP and invert. That is, the 
partition coefficients for all dissolved radionuclides are assumed to be zero. Note 
that the creation of radionuclide-bearing colloids is allowed in the model. 
Corrosion products from the spent fuel and WP have the potential to retard selected 
radionuclides in the EBS. However, sorption of radionuclides is ignored in the EBS. This 
is a bounding assumption for the TSPA-SR and TSPA-LA because it maximizes the 
immediate release of radionuclides. This assumption is used in Section 6.4. 
5.2.8 Radionuclide transport through a SCC is limited to diffusive transport through a 
thin, continuous film that is always present. 
There are two cases to consider here: (1) at early times after closure, when SCCs represent 
the only flow path into the WP, and (2) at later times, after at least one patch appears on the 
surface of the WP. 
At early times, the location of SCCs in the weld of the closure lid and the physical 
geometry of the WP make it impossible to maintain an advective flux out of the WP. In 
other words, water can potentially flow in through a SCC by capillary forces, by 
atmospheric pumping or by hydrostatic head if the lid of the WP is tipped upward. 
However, these mechanisms and this geometry cannot support flow out of the WP because 
the SCCs are the only exit path at early times. 
Other features of the WP make advective flow through a SCC unlikely. For example, each 
SCC will fill with corrosion products that will further impede advective flow and the WP is 
sealed with a double lid configuration, leading to a potentially tortuous advective flow path. 
The geometry of the WP and SCCs and the other features of the system make an advective 
flow path through a SCC physically unrealistic at early times, when no patches exist on the 
WP. 
At late times, there is the possibility that advective flow could enter a SCC and exit through 
a patch. While this flow path is possible, the cross-sectional area of a typical SCC is orders 
of magnitude less than that of a patch, so any flow through the SCC is negligible compared 
to the general advective flux through patches. In addition, corrosion products will further

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reduce the flux through the SCC. It is then reasonable to ignore advective flux through the 
SCC at late times in the TSPA-SR model. 
In summary, the advective flux through an SCC can be neglected at both early and late 
times, so the only viable transport mechanism through an SCC is diffusive transport. In 
addition, the phenomenon of vapor pumping and the presence of hygroscopic salts in the 
waste make it impossible to eliminate the possibility of thin films forming a continuous 
liquid pathway that can support diffusive transport from the waste form through SCCs at all 
times. This assumption is used in Section 6.4.3. 
5.2.9 The invert is assumed to be adjacent to the WP for diffusive release calculations. 
This is a reasonably bounding assumption when advective fluxes in the EBS are zero. That 
is, diffusion cannot occur between the WP and invert without a continuous fluid pathway. 
This pathway does not exist at early times because the WP is supported on an emplacement 
pallet. However, a diffusive pathway is assumed to exist at all times in the EBS RT 
Abstraction. This assumption is used in Section 6.4. 
5.2.10 Diffusive transport occurs whenever an SCC exists in the WP. 
This assumption is a direct conclusion from assumptions 5.2.8 and 5.2.9, and is included 
to emphasize this feature of the diffusive transport model. The presence of a thin film of 
water in the SCCs at all times (see 5.2.8) and the direct physical link between the WP and 
invert (5.2.9) means that a continuous diffusive pathway exists between the waste form and 
the UZ whenever there is an SCC in the WP. In reality, the WP will not be in contact with 
the invert until the emplacement pallet fails, thin liquid films may not exist within the SCC 
when the waste form and WP are hotter than ambient temperature, corrosion products and 
precipitates may help to seal SCCs, and diffusion from the waste form to an SCC may be 
limited by the internal geometry of the waste form. Each of these mechanisms can restrict 
or eliminate the diffusive pathway between the waste form and the UZ, but are not 
incorporated into the TSPA-SR model. These mechanisms emphasize the conservatism of 
this assumption, which is used in Sections 6.4.3 and 6.4. 
5.3 DRIP SHIELD RESPONSE 
The key assumptions for the thermal and mechanical analysis of DS response are listed below. 
These assumptions are applicable to the backfilled EBS and the nonbackfilled EBS, except for 
assumption 5.3.3 
5.3.1 The relative displacement between adjacent DSs is limited by the dimensions of the 
posts in the lower DS and the holes in the overlapping (upper) DS connector plate. 
Thermal expansion or a seismic event may cause slippage between adjacent DSs. Each DS 
is not bolted to the invert and is not bolted to its nearest neighbors. However, the presence 
of posts on the top of the drip shield that mate with matching holes in the DS connector 
plate limits the relative displacement between adjacent DSs. This assumption is used in 
Section 6.5.1, Section 6.5.4 and in Attachment I.

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5.3.2 Adjacent DSs will not separate during the design basis earthquake. 
The new design for the DS has thick posts that fit into holes in the DS connector plate. 
These posts are more than 100 mm, or almost 4 inches, in diameter and more than 100 mm 
long. The DS connector plate is 15 mm thick. The posts and the connector plate are 
anticipated to be strong enough to ensure that adjacent DSs will not separate during a 
design basis earthquake. This assumption will be verified by ongoing analyses for the 
seismic response of the EBS. This assumption is used in Section 6.5.4. 
5.3.3 The sand backfill is effective in spreading the load from a rock fall. 
For the backfilled EBS, the backfill will act to distribute the load from a fallen block of 
rock over the full surface area of contact between sand and rock. This assumption is used 
in Section 6.5.3. 
5.3.4 The impact of rock fall on the degraded DS has been screened out from Rev 00 of 
the TSPA-SR. 
Rock fall will produce minor structural response in the as-emplaced DS, based on recent 
estimates of maximum block sizes from rockfall and detailed finite-element calculations of 
the dynamic response of the DS without backfill in the EBS (see Section 6.5.3). As the DS 
slowly degrades under general corrosion, the presence of rubble and debris from early-time 
rockfalls will distribute the load from subsequent rockfalls, reducing the potential for 
damage to a degraded DS. The impact of rock fall on the degraded DS has therefore been 
screened out from the TSPA-SR. This assumption is used in Section 6.5.3. 
5.4 BATHTUB MODEL 
The key assumptions for the primary analysis of the bathtub geometry as an alternative 
conceptual model are listed below. This analysis focuses on the response of the WP and the 
assumptions are independent of the presence or absence of backfill in the EBS. 
5.4.1 The seepage inflow rate, waste form dissolution rate, and radionuclide solubility are 
independent of time. 
This is a reasonable approach during the periods between climate changes, when 
groundwater conditions should be relatively constant. This assumption is used in Sections 
6.6.1 and 6.6.2. 
5.4.2 Kinetic effects are ignored in determining solubility limits for radionuclides. 
This assumption implies that radionuclide concentration is uniform in the WP and 
determined by a maximum solubility limit or a maximum dissolution rate. This assumption 
also implies that radionuclide concentration in the WP is well-mixed and hence uniform. 
This assumption is used throughout Sections 6.6.1 and 6.6.2.

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5.4.3 Once the bathtub has filled, steady state conditions prevail in the WP. 
This assumption is consistent with the expectation that the groundwater influx equals the 
outflux after the bathtub has filled. This assumption is used throughout Sections 6.6.1 and 
6.6.2. 
5.4.4 The WP penetrations (patches or pits) are large enough that they provide no 
resistance to liquid inflow or outflow. 
This assumption is consistent with the expectation that the groundwater influx equals the 
outflux after the bathtub has filled. This assumption is used in Sections 6.6.1.1, 6.6.1.2, 
6.6.2.1, and 6.6.2.2. 
5.4.5 The potential depletion of inventory is ignored. 
This assumption is used throughout Section 6.6. 
Secondary analyses in Section 6.6.2 consider a step change in seepage inflow rate, a step change 
in groundwater chemistry, or a different flow path geometry (i.e., alternative patch location). 
These alternatives require selective changes to the assumptions for the primary analyses. For 
example, the assumption of constant inflow rate for the primary analysis is modified for the 
alternative of changing inflow rate discussed in Section 6.6.2.1; however, all other assumptions 
remain the same and are applicable to the backfilled EBS or the nonbackfilled EBS. 
6. ANALYSIS/MODEL 
Given the complexity of the EBS and its components, it is useful to provide an overview of the 
EBS RT Abstraction for the TSPA-LA. This overview begins with a general description of the 
EBS components and is then divided into three parts: (1) the flow abstraction, (2) the transport 
abstraction, and (3) an abstraction for the thermal and mechanical response of the DS. Detailed 
discussion of the flow abstraction for the DS and the WP is provided in Sections 6.2 and 6.3, 
respectively. Section 6.4 describes the radionuclide transport abstraction. Section 6.5 presents 
the analyses related to DS separation under thermal and mechanical processes. 
Section 6.6 analyzes the response of an alternative conceptual model for flow through the WP. 
This alternative model, called the bathtub model, allows fluid to collect in the WP before being 
released. The results in Section 6.6 demonstrate that a flow through model is conservative 
relative to a bathtub model for most cases of interest to repository performance. The detailed 
discussions of the EBS RT Abstraction are therefore based on the flow through model, with the 
rationale for screening out the bathtub model given at the end of this section. 
6.1 INTRODUCTION AND OVERVIEW 
The EBS consists of a drip shield (DS), quartz sand backfill, the waste package (WP) on an 
emplacement pallet, and an invert filled with crushed tuff. An engineered backfill material will 
not be placed around the DS in the current baseline design (CRWMS M&O 2000a); however,

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sensitivity studies for the TSPA-SR will consider the system performance with a quartz sand 
backfill in the EBS. Each of the components of the EBS is designed to prevent or delay the 
mobilization and release of radionuclides into the geologic environment. For example, the DS is 
designed to redirect any seepage that flows into the drift away from the WP. This is beneficial 
for system performance because the WP lifetime is much greater in a dry rather than a wet 
environment. The invert supports the WP and emplacement pallet. It can act as a barrier to 
diffusive transport of radionuclides in liquids if the liquid saturation in the crushed tuff is low. 
The quartz sand backfill, if present, is designed to cushion the impact from potential rockfalls on 
the DS and WP. Figure 1 presents a typical cross-section of an emplacement drift and the major 
components of the EBS without backfill. 
The DS is fabricated from a highly corrosion resistant material (titanium) to provide long-term 
effectiveness. The WP is (partly) fabricated from another highly corrosion resistant material, 
nickel-based Alloy 22. The major corrosive processes are stress corrosion cracking in the welded 
lids of the WP and general corrosion for both the DS and WP. 
Before the drip shield fails, the only possible fluid pathway to the WP is from water vapor 
evaporating from the invert, condensing on the inside of the DS, and then dripping down onto the 
WP. This pathway is hypothetical because thermal-hydrologic calculations indicate that 
condensation will not occur; however, it is retained in the EBS RT Abstraction for completeness. 
Once the DS fails, the evaporative flux (if condensation occurs) will be augmented by the 
seepage flux from the roof of the drift and potentially by the capillary flux through the backfill, if 
backfill is present. Without backfill, the seepage flux will flow along the surface of the DS and 
will drip onto the WP if the seepage encounters a breach in the DS. If backfill is present, it will 
fall through any gaps or patches of corroded material in the DS, partly filling any space around 
the WP. Note that the cross-sectional area between the DS and WP is much less than the crosssectional 
area of backfill. The backfill is therefore likely to form a continuous flow path between 
the backfill outside the DS and the WP inside the DS. When this occurs, water may flow onto 
the WP because of capillary forces in the backfill. These capillary forces will be substantial for a 
backfill material with small particulate sizes, such as a quartz sand. 
If the backfill is a coarse material that acts as a capillary barrier, then the dominant flux into the 
EBS will be the seepage flux from the roof of the drift. Again, the DS must fail for this flux to 
fall or drip onto the WP through gaps between adjacent DSs or through patches in the DS.It is 
possible that DS failure may occur over the gap between adjacent WPs. This is a reasonable 
scenario because the overlap between adjacent DSs is located over the gap and this overlap is a 
potential leakage pathway. If the DS fails at the gap, the seepage flux or the backfill will fall 
directly to the invert, possibly avoiding the WP and channeling flow directly into the invert. The 
possibility that DS failure can occur over a gap, allowing fluid to bypass the WP, is 
conservatively ignored in the EBS RT Abstraction.

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Figure 1. Schematic Diagram of a Typical Emplacement Drift and the Major Components of the EBS 
After the WP fails, fluid can enter the WP, mobilize radionuclides in the waste form, and 
transport these radionuclides into the UZ. Diffusion is the primary transport mechanism at early 
times, when stress corrosion cracks (SCCs) are anticipated to be the only penetrations through 
the WP. Advective transport is also possible at late times, when substantial advective fluxes can 
pass through the corroded patches of the DS and WP. 
6.1.1 EBS Flow Abstraction 
The EBS has two potential sources of inflow. The first source is the seepage flux that drips from 
the crown (roof) of the drift. The second source is the capillary flux generated by the wicking 
forces between the rock fractures and the quartz sand backfill. Both fluxes are driven by 
downward infiltration through the existing fracture system at Yucca Mountain. Only the seepage 
flux will exist for the current repository design, without backfill.

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The seepage flux is conceptualized to flow from discrete fractures above the roof of the drift, 
falling vertically downward. The seepage flux will be represented in the TSPA-LA model 
through an existing abstraction (CRWMS M&O 2000i). For the backfilled EBS, the capillary 
flux is conceptualized to be wicked from the fractures in the host rock in direct contact with 
the backfill. In effect, the fine-grained backfill draws the liquid from the fractures on the sides of 
the drift and passes it into the lower walls and floor of the drift. The capillary flux will be 
represented in sensitivity studies for the TSPA-SR and TSPA-LA models through an abstraction 
of thermal-hydrologic calculations of backfilled repository response generated with NUFT 
(CRWMS M&O 2000j). 
These sources of inflow can flow through the EBS along 9 pathways, as shown in Figure 2. 
Seepage Flux 
Into The Drift 
Capillary Flux 
Into The Drift 
(Backfilled EBS Only) 
WP Lids 
WP Skirt 
Evaporation 
Unsaturated 
Zone 
Form 
Invert 
Void 
Waste 
Form 
Diversion 
Diversion 
5
9 
6 
7 
4 
4 
7 
3
8 
Unsaturated 
Zone 
Form 
6 
4 
1 2 
Backfill (If Present) 
WP 
DS 
Figure 2. Schematic of the Potential Flow Pathways in the EBS 
The nine pathways are: 
1. Seepage flux. This is the dripping flux from the crown (roof) of the drift. 
2. Capillary flux. This is the flux that is wicked into the drift due to the capillary forces 
between the fine-grained backfill and the fluid-filled fractures in the host rock. This flux 
is nonzero only if an engineered backfill material is placed around the DS. 
3. Flux through the DS. The flux through the DS is based on the presence of patches due to 
general corrosion and gaps between adjacent DSs due to seismic events. The number of 
patches through the DS is calculated independently of the EBS RT Abstraction by the 
WAPDEG code. The nominal size of a patch is fixed for the WAPDEG calculations; it is 
currently defined to be 7.21 x 104 mm2, based on the equivalent area of 500 nodes on the

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surface of the DS (CRWMS M&O 2000b). The fluid flux through any patches is given by 
the ratio of the axial length of the penetration(s) in the DS to the total axial length of the 
DS (see Section 6.2.4). 
4. Diversion around the DS. The portion of the flux that does not flow through the DS is 
assumed to bypass the EBS (per assumption 5.1.12), going straight into the UZ. 
5. Flux through the WP. The flux through the WP is based on the presence of SCCs and on 
patches due to general corrosion. The number of patches and SCCs through the WP is 
calculated independently of the EBS RT Abstraction by the WAPDEG code (CRWMS 
M&O 1998c). The nominal size of a patch is fixed for the WAPDEG calculations; it is 
currently defined to be 2.346 x 104 mm2, based on the equivalent area of 1000 nodes on 
the surface of the WP (CRWMS M&O 2000b). The area of each SCC, 4.08 x 10-6 m2, is 
calculated in Section 6.3.1.2.1. The flux through patches or SCCs is based on ratios of 
the appropriate flow lengths for the surface of the WP or for the lid and skirt of the WP, 
respectively (see Section 6.3.2). 
6. Diversion around the WP. The portion of the flux that does not flow into the WP is 
assumed to bypass the waste form (per assumption 5.1.12), going straight into the invert. 
7. Evaporative flux. The magnitude of the evaporative flux from the invert is based on the 
abstraction of NUFT data. If the DS is cooler than the invert, then all the evaporative 
flux is assumed to drip on the WP (per assumption 5.1.3). If the DS is hotter than the 
invert, then there is no dripping on the WP from the evaporative flux. 
8. Flux to the invert. All flux from the WP flows to the invert, independent of patch/pit 
location on the WP. The presence of the emplacement pallet is ignored. 
9. Flux to the UZ. All mass flux into the invert is released into the UZ. 
It is important to note that these pathways are time dependent, in the sense that DS gaps, DS 
penetrations, and WP penetrations will vary with time and local conditions in the repository. For 
example, at very early times there may be no penetrations through the DS, so fluid can reach the 
WP only if pathway 7, evaporation from the invert and condensation on the DS, is active. 
The conceptual model for flow through the EBS also includes two mixing cells: one for the WP 
(and internals) and a second for the invert. The two mixing cells are conceptualized to have a 
cylindrical, concentric one-dimensional geometry for volume calculations. The first cell has a 
diameter given by the diameter of the WP. The second cell (invert) wraps around the lower half 
of the WP and is 0.606 meters thick (CRWMS M&O 1999d). This is the maximum thickness of 
the invert directly beneath the WP (see Table 1). This value is appropriate because flow out of 
the WP is primarily vertically downward, centered over the thickest part of the invert. 
The WP mixing cell represents the source term for the TSPA-LA. Source term abstractions for 
radionuclide solubility, dissolution rate, cladding response and inventory by waste package type 
are defined in other AMRs. 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 from the EBS 
into the UZ. Note that the diversionary flows from the DS and WP (pathways 4 and 6) are not 
required outputs from the EBS RT Abstraction and are ignored by the TSPA-SR and TSPA-LA 
models. The parameters and formulas for calculating the fluxes in the various pathways are 
summarized in Table 3.

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Table 3. Summary of Parameters for EBS Flow Pathways 
Flow Pathway Flow Parameters Data Sources & Notes 
1. Seepage flux, F1 Seepage flux is a function of fracture 
properties, rock properties, and the 
percolation flux. 
(CRWMS M&O 2000i) provides 
time-dependent and locationdependent 
values of seepage 
flux. 
2. Capillary flux, F2 Capillary flux is a function of the 
moisture potential, fm, of the quartz 
sand backfill, the infiltration flux, 
and the fracture properties of the 
host rock. 
Capillary flux into the EBS is reduced 
by a factor, a. This factor is chosen 
between 0 and 1 to reflect the 
differences in capillary flux for 
various design options, including 
the option for zero flux when there 
is no backfill in the EBS. 
fm, T and RH will be abstracted 
from calculations with the NUFT 
code (CRWMS M&O 2000j). T is 
temperature and RH is relative 
humidity. 
3. Flux through the DS, F3 LDS_Patch  axial length of patches due 
to general corrosion of Ti 
LDS_Pit  0 because pH<10 
LDS_SCC  probably 0 for Ti 
LDS_Gap  axial length of total gap in 
the DS 
F3 = (F1 + aF2) x (LDS_SCC + LDS_Patch 
+ LDS_Pit + LDS_Gap)/LDS; 
LDS is the axial length of the DS. 
a is a factor between 0 and 1 based 
on the design and backfill 
properties; 
WAPDEG (CRWMS M&O 1998c) 
will provide the number of 
patches, pits and SCCs on the 
DS; 
Patch size is 7.21 x 104 mm2 
(CRWMS M&O 2000b); 
LDS Patch = (7.21 x 104)0.5 = 269 mm 
LDS Gap is calculated from a seismic 
response model (see Section 
6.5.4) 
Limit F3 such that F3  (F1 + F2). 
4. Diversion around DS, F4 F4 = F1 + aF2 - F3. Continuity of liquid flux. Limit F4 
such that F4  0. 
5. Flux into the WP, F5 LWP_Patch  axial length of all patches 
due to general corrosion 
of Alloy 22 
LWP_Pit  probably 0 for Alloy 22 
LWP SCC  projected axial length of 
closure lid directly 
exposed to fluid flux 
F5 = (F3 + F7) x (LWP_Patch + 
LWP_Pit)/LWP + (F3 + F7) x (LWP 
SCC)/(LWP + LWP_SCC) for the 
baseline design (no backfill); 
F5 = (F3 + F7) x (LWP_Patch + 
LWP_Pit)/LWP + F7 (LWP SCC)/(LWP + 
LWP_SCC) for a backfilled EBS. 
LWP is the axial length of the WP. 
WAPDEG will provide the number 
of patches, pits and SCCs on the 
WP; 
patch size is constant: 2.346 x 104 
mm2 (CRWMS M&O 2000b); 
LWP Patch = (2.346 x 104)0.5 = 153 
mm 
LWP_SCC is calculated based on the 
maximum tilt angle of the WP 
and the diameter of the closure 
lid (see Section 6.3.2) 
Limit F5 such that F5  F3 + F7. 
6. Diversion around the WP, F6 F6 = F3 + F7 - F5 Continuity of liquid flux. Limit F6 
such that F6  0. 
7. Evaporative flux, F7 If TDS < TInvert, then F7 is the 
evaporative flux calculated by NUFT; 
else F7 = 0. 
Data for temperatures and 
evaporative flux are based on an 
abstraction of NUFT calculations 
(CRWMS M&O 2000j). 
8. Flux to the invert, F8 F8 = F5 Steady state, flow-through 
assumption for WP (outflow = 
inflow in steady state; this is 
conservative for release; see 
Section 6.6)

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Flow Pathway Flow Parameters Data Sources & Notes 
9. Flux to the UZ, F9 F9 = F6 + F8  F7 Steady state flow-through 
assumption for invert. Consistent 
with flow-through assumption for 
WP. Note that only F8 can transport 
radionuclides through the invert. 
6.1.2 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 UZ, as shown in Figure 3. Transport can 
occur through advection when there is a fluid flux through the WP and invert. Transport can also 
occur by diffusion, even in the absence of a liquid flux, if there is a continuous liquid pathway 
via thin films in the waste form, in SCCs in the lid of the WP, and in the invert. 
Invert 
Waste 
Form
9
8 
Unsaturated 
Zone 
Form 
WP 
WP Lids 
WP Skirt 
Figure 3. Schematic of the Transport Pathways in the EBS 
The advection-dispersion equation for transport of nonreactive constituents in a homogeneous 
medium with one-dimensional flow is given by (Freeze and Cherry 1979, pp. 389-390 and 
Appendix X): 
, 2 
2 
* 
t 
C 
x
C 
v 
x
C 
D 
 
 
= 
 
 
- 

 
(Eq. 6.1.2-1) 
where C is the solute concentration [M/L3], D* is the coefficient of molecular diffusion in Freeze 
and Cherry [L2/T], v is the average linear water velocity [L/T], and x is the one-dimensional 
coordinate [L]. This equation assumes that dispersivity and retardation are negligible, consistent 
with the assumptions 5.2.3 and 5.2.7. The first term on the left-hand side of equation 6.1.2-1 
corresponds to transport by diffusion; the second term on the left-hand side corresponds to 
transport by advection. Table 4 summarizes the transport modes and transport parameters for the 
two transport pathways in the EBS

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Table 4. Summary of Transport Modes and Parameters for the EBS Transport Pathways 
Transport Pathway Transport Modes Transport Parameters and Data Sources 
8. WP to invert (F8) Diffusion through SCCs 
(no advective transport 
through SCCs); 
Diffusion and advection 
through patches; 
Diffusion and advection 
through pits (no pits are 
expected in Alloy 22) 
Fluid flux for advection = F8: 
Diffusive area for each SCC is given by 4.08 x 10-6 m2 
(see Sections 6.3.1.2.1 and 6.4.3); 
Diffusive area for each patch is 2.346 x 104 (mm)2 
(1000 nodes on the surface of the WP); 
Diffusive length in WP is 135 mm to 185 mm 
depending on WP type (see Section 6.4.3) 
Diffusion coefficient (all radionuclides): 
- 2.299 x 10-5 cm2/s at 25C (see Section 6.4.1.1) 
- Corrected for porosity and saturation by f1,3s1.849, 
where f is porosity and s is the liquid saturation (see 
Section 6.4.1.2). 
- Temperature correction defined in Section 6.4.1.3 
- Reduced by a factor of 100 if radionuclide is bound to 
a colloid (see Section 6.4.2). 
9. Invert to UZ (F9) Diffusion and advection 
through the invert; 
Flow cross-sectional areas 
given by: 
AInvert = p(RWP)LWP 
AUZ = p(RWP + Drinvert)LWP 
where RWP is radius of 
WP, LWP is length of WP, 
and Drinvert is the 
thickness of the invert 
(0.606 m) 
Fluid flux for advection = F9 = F8; 
Diffusive length = 0.606 m (max thickness of invert; 
see Table 1); 
Diffusion coefficient: 
- 2.299 x 10-5 cm2/s at 25C (see Section 6.4.1.1); 
- Corrected for porosity and saturation by f1.3s1.849, 
where f is porosity and s is the liquid saturation (see 
Section 6.4.1.2). 
- Temperature correction defined in Section 6.4.1.3; 
- Reduced by a factor of 100 if radionuclide is bound 
to a colloid (see Section 6.4.2). 
The flow cross-sectional areas, Ainvert and Auz, assume 
a cylindrical geometry corresponding to the low half 
of the WP lying on the invert. Ainvert is one-half the 
surface area of the WP and AUZ is the corresponding 
surface area at a radius equal to the radius of the 
WP plus the thickness of the invert. 
The invert diffusion calculation uses radionuclide 
concentrations in the WP as the boundary condition 
at the top of the invert and a swept away (effectively 
zero) radionuclide concentration at the interface with 
the UZ. 
For the nonbackfilled EBS, there will be no upward transport of radionuclides because there is 
no solid medium with a liquid pathway above the DS. For the backfilled EBS, it is anticipated 
that there will be negligible upward transport through the quartz sand backfill under any 
conditions. Upward diffusion through the backfill is impossible before the DS fails because a 
continuous flow path does not exist between the WP and backfill. After the DS fails, upward 
diffusion will be negligible in comparison to the downward advective flux through the DS. (It is 
theoretically possible that radionuclides can follow a U shaped flow pattern in the backfill. In 
the pattern, radionuclides could move downward into the invert, laterally beyond the DS and 
upward into the backfill. Transport along this pathway will be negligible because the capillary 
flux downward through the backfill should dominate any upward diffusion from the invert.) 
Colloid-facilitated transport of radionuclides is included as an additional source term for the EBS 
RT Abstraction. Radionuclide transport from the WP occurs in a fluid containing colloids and 
dissolved radionuclides. There are three types of colloids in the EBS: (a) waste form colloids, 
(b) colloids due to corrosion products, and (c) groundwater colloids. The waste form colloids

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may have irreversibly attached (embedded) or reversibly attached (sorbed) radionuclides. The 
corrosion and groundwater colloids may have reversibly attached radionuclides. 
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 porosity, liquid saturation and 
temperature are also included in calculating the diffusion coefficient. 
The corrosion products from the WP and spent fuels have the potential to be strong sorbers for 
the actinides. Including sorption in the WP and invert will be beneficial to performance because 
this process can retain radionuclides in the EBS and delay release to the UZ. However, the 
effects of retardation are conservatively ignored in the EBS RT Abstraction. 
6.1.3 Thermal and Mechanical Abstraction for Drip Shield Response 
The thermal and mechanical response of the DS has been evaluated for five mechanisms: (1) 
thermal expansion, (2) floor heave, (3) rock fall, (4) seismic response, and (5) emplacement 
pallet failure. 
Thermal expansion, floor heave and rock fall will produce minor structural response in relation 
to the potential slippage or overlap between adjacent DSs for the as-emplaced DS configuration. 
These mechanisms have therefore been screened out from the TSPA-SR, as explained in 
Sections 6.5.1, 6.5.2, and 6.5.3. 
Seismic response has also been screened out, as discussed in Section 6.5.4. The DS design 
includes strong posts that will provide a positive mechanical connection between adjacent DSs. 
With this mechanical connection, seismically-induced separation between adjacent DSs is very 
unlikely until the DS fails catastrophically from general corrosion. Analyses for the TSPA-LA 
will evaluate the structural response of the DSs to the design basis earthquake. 
Emplacement pallet failure has the potential to shift the DS if the WP falls to the invert and rolls 
into contact with a DS. Emplacement pallet failure is very likely from general corrosion during 
long time periods. In addition, failure is even more likely during an earthquake, when the 
ground motions may increase the load on the emplacement pallet and impart additional 
momentum to the WP. The presence of posts that mate with holes in the DS connector plate 
provide additional stability to the system of overlapping DSs. Given this additional stability, the 
response to pallet failure is also screened out for the TSPA-SR until results from seismic 
analyses for the TSPA-LA are available (see Section 6.5.5). 
6.2 FLUX IN THE BACKFILL & THROUGH THE DRIP SHIELD (F1  F4) 
6.2.1 Water Movement Into and Through a Drift (F1, F2, and F4) 
Water movement from the land surface and down through the UZ at Yucca Mountain is 
conceptualized to occur through a system of fractures (Liu et al., 1998). 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 (CRWMS M&O 2000k). Consideration of the

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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 1 (CRWMS M&O 2000a). 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 WPs are to be placed on emplacement pallets that hold them in 
place above the invert. A titanium DS surrounds the WPs. The space between the WP and the 
DS, which will be referred to as the axial space, is designed to remain air filled. The current 
repository design does not include an engineered backfill material (CRWMS M&O 2000a). The 
previous design concept used Overton sand, a fine to medium grained sand, as the backfill 
material. 
At early times, any water that enters the drift is vaporized and expelled due to the heat output of 
the WPs. According to modeling of water movement through the EBS (CRWMS M&O 2000l), 
much of the water that enters the drift remains as liquid once thermal output has subsided after 
approximately 3,000 years. With the nonbackfilled EBS, this water can drip onto the DS and is 
diverted around the WP, into the invert. For the backfilled EBS, this water migrates through the 
backfill and exits through the bottom portion of the drift. 
Water enters the drift by either one of two mechanisms  by seepage from the roof of the drift or 
by wicking inward from the sides of the drift if backfill is present. In this section, each of these 
mechanisms is considered in turn, followed by a discussion of water diversion around the DS. 
6.2.1.1 Seepage Flux (F1) 
The Seepage Models for PA Including Drift Collapse (CRWMS M&O 2000k) 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, as 
expected. 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 theory 
for seepage exclusion around cylindrical cavities introduced by Philip et al. (1989). They 
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. Indeed, the drift-scale UZ 
flow modeling results show a propensity for flow to diverge around the drifts. 
Abstraction of Drift Seepage (CRWMS M&O 2000i) provides the rationale for calculating the 
seepage flux into the repository, accounting for thermal effects and spatial variability. Here, 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. 
6.2.1.2 Capillary Flux (F2) 
For the backfilled EBS, the high capillarity of the Overton sand relative to the flowing fractures 
in the adjacent host rock results in the potential for backfill to wick water from the host rock. 
This capillary wicking effect can result in a focussing of flow through the backfill. In fact, 
results of thermal-hydrologic simulations of EBS flow using NUFT (CRWMS M&O 2000l)

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show water fluxes through the backfill that are several times the percolation flux. Further, this 
modeling yields capillary pressure gradients that indicate flow of water is from the host rock into 
the backfill. The response to wicking is in marked contrast to the seepage from the roof, where 
the cylindrical shape of the roof diverts water and only a subset of the drifts permit seepage. 
With wicking, the effect of the capillarity-induced wicking flux permits appreciable water fluxes 
through the backfill surrounding every WP. 
There is speculation as to whether sufficient connection exists between flowing fractures in the 
adjacent host rock and the backfill for wicking to occur. The NUFT simulations assume 
sufficient connection for there to be equilibrium in regard to pressures between the backfill and 
the host rock (see assumption 5.1.1). Until this issue is studied in more detail, the potential for 
wicking flux is included in the PA calculations. 
6.2.1.3 Diversion Around The Drip Shield (F4) 
The DS has been designed to divert liquid water that may enter the drift away from the WP. If 
the DS 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. Upon 
being deflected by the DS, it continues to move downward through the invert and into the UZ. 
For the nonbackfilled EBS, the diversion around the DS occurs as thin films or droplets and any 
flow that enters the invert will be concentrated at the sides of the DS while the DS is intact. For 
the backfilled EBS, the diversion around the drip shield is a milti-dimensional flow through a 
porous medium (the backfill). This flow is driven by gravity, by capillary forces in the backfill, 
and by capillary forces within the fractures adjacent to the emplacement drifts. Flow into the 
invert will be more uniformly distributed along the backfill-invert interface than for the 
nonbackfilled EBS. 
For the backfilled EBS, water that enters the backfill by capillary wicking moves laterally under 
capillary pressure gradients toward the DS, and downward under gravity. In the absence of 
appreciable seepage from the roof, capillary forces can wick small amounts of water upward into 
the backfill above the DS. (The flow models are symmetric about the centerline of the drift, so 
flow cannot cross from the right-hand side to the left-hand side of a drift. Rather, the potential 
flow path is laterally upward, from the sides of the drift toward the centerline, followed by a turn 
so flow moves downward along the center line, around the top of the drip shield and downward 
again along the vertical side of the DS without crossing the centerline.) Liquid saturation levels 
may become elevated at the backfill/invert interface if the (coarse) crushed tuff in the invert acts 
as a capillary barrier relative to the (finer) sand backfill; however, this is probably a localized 
effect for the overall capillary flow through the EBS. 
When backfill is present, the small amount of liquid directly above the DS will tend to evaporate 
until the thermal output from the WP becomes negligible. The NUFT simulations show that the 
flux near the top of the DS is relatively small due to the comparatively long flow path over which 
the capillary pressure drop is spread. Much higher flux rates are seen along the side of the DS, 
below the spring line, because of the shorter, more direct flow path from the walls of the drift. 
(The spring line refers to the line through the two points on the drift wall that are 90 around 
from the crown (topmost point) of the drift. It represents the widest span across the drift at its 
mid-height.)

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As water migrates downward around the DS, it encounters the invert. For the nonbackfilled EBS, 
the diversion around the DS probably occurs as droplets and thin films. This diversion will be 
concentrated along the sides of the DS while it is intact. If backfill is present, the diversion 
around the DS will act like a flow in a porous medium. In addition, a fine textured backfill 
overlying the coarse textured invert creates a capillary barrier to flow. Local values for 
saturation and pressure above the invert increase until sufficient to overcome the capillary forces 
of the backfill and drive water into the invert. A capillary fringe is then created in the backfill 
above the invert. The majority of water migrates through the invert although the buildup of the 
capillary fringe creates sufficient pressure for some portion of the water to migrate back into the 
host rock directly. Once in the invert, water migrates quickly through, probably as fingered flow 
into the host rock at the bottom of the drift. 
The algorithm for calculating the flux diversion around a breached drip shield is discussed in 
Section 6.2.4. 
6.2.2 Drip Shield Effectiveness 
Design drawings for the DS are given in sketch SK-0148 REV05 (CRWMS M&O 2000c, 
Attachment II). The DS has roughly the shape of a mailbox with vertical sides and a top section 
that is curved for strength and to shed water. On one end, a DS connector guide and two mating 
posts are attached to the top of the curved section. The connector guide is a square rib, 50 mm 
wide, that is attached to and extends across the curved top section. This rib provides extra 
stiffness to the end of the DS and can deflect seepage down the sides of the DS. Each post is 
shaped like a truncated cone that is wider at its base and tapers to a diameter of 100 mm across 
the top. On the other end of the DS, a connector plate is attached. The connector plate is 15 mm 
thick and has two, 119 mm diameter holes that mate with the posts of the adjacent DS. The 
connector plate also has two square ribs, approximately 300 mm apart, that are attached to the 
underside of the connector plate. Each rib is 50 mm wide. 
Adjacent DSs are interlocked with one another. This is accomplished by lowering the connector 
plate of one DS over the upward extending guide rib of the previously emplaced DS such that the 
posts mate with the holes in the DS connector plate. The overlap between adjacent DSs will be 
595 mm (see Attachment I). 
The gaps that will exist between DSs in this interlocking design can, potentially, provide a 
pathway for water to penetrate the DS system. The potential for such leakage under design 
conditions is considered here, followed by consideration of the ways in which the integrity of the 
DS might become compromised. This discussion is limited to considering the top of the DS 
because it is reasonable that any water entering the contact between DSs from the side would 
simply flow down the vertical sides of the DSs, never contacting the waste. 
Three lines of reasoning support the contention that the DS will be successful in excluding liquid 
water migration from the backfill to the WP under design conditions: analogy, geometry, and 
experimentation. 
Analogy  When backfill is present, consider an extremely simplified and conservative 
abstraction of the current system, where the DS provides sufficient mechanical support to hold

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the backfill in place while providing no barrier to water flow. Such a system would be analogous 
to the top of the drift -- a geologic medium that transmits water above a cylindrical, air-filled 
cavern. As stated above, such a system diverts water around the air-filled cavern. The extent to 
which the system completely excludes water is a function of the seepage flux, the capillarity of 
the geologic medium, and the diameter (Philip et al., 1989). In comparison with the drift roof, 
the backfill has greater capillarity and the DS has a smaller diameter and receives a smaller flux - 
- all of which favor the exclusion of water. (Due to diversion of flow, the seepage flux is always 
less than the focussed percolation flux above the drift. Based on results of the NUFT 
calculations (CRWMS M&O 2000l), the flux at the top of the drip shield due to capillary 
wicking tends to be quite small compared to the seepage flux.) 
Geometry  Now consider a more realistic system where the titanium walls of the DS form a 
barrier to flow. Water flux through the DS will now be limited to the gap where adjacent DSs 
interlock. If extremely high seepage flux conditions exist, then the flow can be driven into this 
gap. First, the water must travel laterally 595 mm to get beyond the overlap between the DSs. 
As this water travels, it must remain precisely along the crown of this gap between the DSs. If 
there is any deviation, the sloping sides of the DS impose gravity forces that will cause the water 
to flow down the sides and into the invert. Second, the upward extending guide rib provides a 
barrier to flow along the crown. Sufficient water pressure must be provided to push water up and 
over this barrier. Furthermore, the guide ribs provide surfaces of contact with the DS and the 
connector plate. These contact surfaces maintain continuity down along the sloping sides of the 
top portion of the DS. 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 DSs. Note also that the air-filled voids (having no capillarity) in 
between and beyond the guide ribs provide an additional barrier to flow. This analogy is 
appropriate for both the nonbackfilled EBS and the backfilled EBS. 
Experimentation -- The first quarter-scale test of the DS conducted to date at the Atlas facility 
(Howard 2000) provide additional evidence. This first test was conducted without backfill; 
water was dripped onto the DS from the roof of the drift. Without the benefit of the capillarity of 
the backfill to help divert water and with a simplified DS design (overlapping but not 
interlocking), water did not penetrate the DS. Some water did, however, flow as a thin film 
within the overlap between the DSs. Nevertheless, no dripping occurred inside the DS and the 
WP remained dry. 
Additional flow modeling and experimental studies with high seepage fluxes are recommended 
to provide quantitative evidence demonstrating the effectiveness of the DS. 
6.2.3 Drip Shield Breaching 
The advective flow of water into the EBS has been shown to be effectively segregated from the 
WPs as long as the integrity of the DS is maintained. Once holes form in the DS or adjacent DSs 
separate, seepage can drip through onto the WP for the nonbackfilled EBS or the air-filled space 
between the DS and the WP is assumed to fill with backfill if it is present. The consequence of 
DS failure is that a portion of the water flux through the backfill now migrates through the DS 
and comes into contact with the WP.

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6.2.3.1 Breaching Mechanisms 
The thermal and mechanical response of the DS may produce gaps between adjacent sections of 
DS. These breaching mechanisms are analyzed in Section 6.5. 
6.2.3.2 Sand Filling of a Breached Drip Shield (Backfilled EBS) 
Once the integrity of the DS is compromised, the gas-filled space or gap between the DS and the 
WP may become filled with backfill. While the angle of repose of the backfill might limit its 
entry into the gap, the potential for repeated seismic events makes it unlikely that backfill will 
not be able to fill most if not all of the gap volume. 
The main reason for assuming that backfill sand fills the gap (per assumption 5.1.6) is to have a 
bounding model for flow through the EBS. Having sand fill the gap space creates a connected 
pathway from the backfill through the breaches in the DS to the WP. A connected sand pathway 
creates a capillary flow path that channels flow through the DS and onto the WP. In addition, the 
capillary barrier created by having an air-filled gap under the DS no longer exists if there is a 
connected sand pathway through the DS. 
It is also reasonable that at least some of the gap volume will be filled with backfill because the 
volume of backfill is much greater than the gap volume. These volumes (per unit length) are 
equal to the cross-sectional areas. The gap cross-sectional area around a 21-PWR WP can be 
calculated as follows. The area under the DS can be bounded as the width at its base times the 
height to the crown of the DS. The width at the base is given by (334 + 1644 + 334) = 2312 mm 
and the height at the crown is given by (1834 + 582) = 2416 mm The total area beneath the DS 
is then less than their product, 5.59 m3. Subtracting the cross-sectional area of the 1644-mm 
diameter WP, 2.12 m3, leaves a gap cross-sectional area of 3.46 m3 between WP and DS. All 
dimensions are based on sketch SK-0154 REV 02 in CRWMS M&O 2000c; the invert is 
assumed to be a barrier for the backfill but the presence of the emplacement pallet is ignored. 
Compare this with the cross-sectional area of the backfill, which has been computed to be 13.23 
m2 (CRWMS M&O 1999d, page 3 of 3). The amount of available backfill is then almost 4 times 
greater than the gap volume (per axial unit of length), so there is ample backfill to at least partly 
fill the gap volume once the DS is breached. 
An alternative approach is to consider the mechanistic details of how sand might fall into the gap 
beneath the DS for the purpose of exploring potential limits to the connectedness between sand 
above the DS and sand that has fallen through the DS. The attempt to limit connectedness might 
include arguments about the height of the penetrations in the DS relative to the elevation of the 
WP, the presence of separations between WPs that could allow backfill to fall directly to the 
invert, the angle of repose for sand (especially wet sand), or arguments considering the minimum 
dimensions for breaches to the DS required for sand to fall through. Further, geologic 
cementation processes in the backfill might limit the ability of sand to fall through the breached 
DS if breaching were to occur at sufficiently late times after closure. 
However, the likelihood of recurring seismicity over the long time scales of the performance 
assessment will help to shake sand through any opening in the DS and make arguments about 
angles of repose for sand untenable. It is then unlikely that the sand backfill will be unable to fall

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through the penetrations from general corrosion. The significant uncertainties regarding rates of 
cementation make it difficult to limit sand migration into the gap beneath the DS due to 
cementation. Finally, the randomness of patch location on the DS and the relatively small 
separation between adjacent WPs relative to their length imply that patch location and WP 
separation are unlikely to prevent at least some connectivity across the DS. 
Furthermore, angle of repose arguments are a double-edged sword because slope in the backfill 
created by the angle of repose may also be used to support a focussing of water flow. The 
process of spilling sand through a breach in the DS creates crossbedding (similar to that seen on 
the lee side of a sand dune). This crossbedding (micro-scale laminations of alternating coarse 
and fine textures aligned parallel to the slope) creates, in effect, a series of small-scale capillary 
barriers. This results in a preference for flow to occur parallel to slope and toward the breached 
feature. McCord et al. (1991 and 1997) have demonstrated the effect of hillslope and 
crossbedding under stable flow conditions. Also, Glass and Nicholl (1996) used a lab 
experiment to show the effect of crossbedding for fingered (unstable) flow. The strength of 
texture variations across laminae is inversely proportional to the degree of sorting. The wellsorted 
nature of the Overton sand (CRWMS M&O 2000m) implies that the capillary effect of 
crossbedding will be somewhat minimized. 
In summary, attempting to limit the connectedness of sand through the DS and to maintain the 
capillary barrier of the gap is not defensible and might require adding significant complexity to 
the analysis. In contrast, invoking the assumption of sand completely filling the axial space upon 
DS breaching (per assumption 5.1.6) is a reasonable bound and makes the analysis of water flux 
through the DS relatively straightforward, as discussed in Section 6.2.4. 
6.2.4 Water Flux Through and Around a Breached Drip Shield (F3 and F4) 
Once the DS has been breached, a portion of the water flux (F3) will pass through the DS and 
have access to the WP. The flux through the backfill is assumed to be the sum of the seepage 
flux (F1) and the flux due to capillary wicking (F2) (per assumption 5.1.7). The seepage flux is 
supplied according to the Abstraction of Drift Seepage (CRWMS M&O 2000i) and is always 
present in the EBS. If the EBS is backfilled, the capillary wicking flux is also supplied from the 
NUFT abstraction as the flux at the side of the DS. (Actually, since NUFT invokes symmetry 
and simulates flow over one half of the drift, the capillary wicking flux is twice the calculated 
flux at the side of the DS.) 
The total calculated flux onto the DS is probably conservative for the backfilled EBS. Since 
both the seepage flux and the capillary wicking flux are calculated in separate simulations, 
summing them can result in overestimating the flux through the backfill. For example, a nonnegligible 
seepage flux entering from the top of the backfill will change the flow field, at least 
partly satiating the capillarity of the backfill and reducing the capillary wicking flux. However, 
this effect is not included in this EBS RT Abstraction. 
- A Note about the Seepage Flux with Backfill  Because fracture flow is the dominant 
mechanism for flow in the host rock, water will necessarily come into the drift as point 
sources. In an extreme case, the entire seepage flux enters the drift through a single point 
source. Carrying this extreme case still further, it is possible that density unstable flow

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conditions prevail and the seepage flux entering the backfill migrates as fingered flow. 
Conditions required for fingered flow are a function of the seepage flux, the capillarity of the 
backfill material, and the initial moisture content. The lower the seepage flux, the less 
capillarity, and the lower the initial moisture content, the higher the propensity for fingering. 
In comparison with uniform flow, the occurrence of fingered flow lowers the probability that 
the seepage flux will encounter multiple breaches in the DS, but the fluxes through the DS 
would be much higher if a finger encounters a breach. 
The low probability/high consequence fingered flow events are likely to be averaged over the 
total repository for several reasons. First, the seepage flux is conceptualized to vary spatially 
over the approximately 10,000 WPs in the repository so that it is not always a single point 
source at a fixed location throughout time. Second, the presence of engineered backfill or 
natural backfill from rockfalls will tend to produce more uniform flow conditions with higher 
initial saturation in the backfill, reducing the likelihood of focussed flow. Third, the 
preliminary data on general corrosion of titanium shows that this process is not a function of 
direct liquid contact with the DS. Given these factors, the low probability/high consequence 
fingered flow events will be averaged out since seepage and breaches will vary spatially over 
the approximately 10,000 WPs in the repository. It therefore seems reasonable to consider 
uniform fluxes encountering the DS. 
- A Note about the Capillary Wicking Flux  As a first order approximation, the flux at the side 
of the DS is used as a surrogate for the flux that would reach the WP due to capillary wicking 
in the absence of a DS. This is probably an overestimation. Extending the flow lines farther 
laterally to intersect the WP would likely result in fluxes lower than those seen at the side of 
the DS. Additional NUFT simulations could be undertaken to demonstrate this point. 
However, until such simulations are undertaken, the best surrogate available for flow is 
capillary flux through the DS. 
As a reasonable approximation, the flux through the DS is scaled by the axial length of the DS 
penetration as compared to the total axial length of the DS. This approximation is conservative 
because it is equivalent to assuming that the penetration is at the side of the DS and intercepts 
fluid flux over all azimuthal angles at the relevant axial location (per assumption 5.1.9). The 
flux through the DS (F3) is then given by: 
( ) , 
L 
L L L L 
F F F 
DS 
Gap _ DS Pit _ DS Patch _ DS SCC _ DS + + + 
+ = 2 1 3 a (Eq. 6.2.4-1) 
where F1 is the seepage flux, F2 is the capillary flux, LDS_SCC is the total axial length of all SCCs 
in the DS, LDS_Patch is the total axial length of all patches in the DS, LDS_Pit is the total axial length 
of all pits in the DS, LDS_Gap is the axial length of any gaps between adjacent DSs, and LDS is the 
axial length of the DS. The parameter a is a factor between 0 and 1 based on the design and 
backfill properties; the rationale for including this parameter is discussed in Section 5.1 (see 
assumption 5.1.7). Equation 6.2.4-1 is applicable to the backfilled EBS and the nonbackfilled 
EBS. 
Once the flux through the DS is known, the flux diverted around the DS is calculated assuming 
continuity of flow:

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. F F F F 3 2 1 4 - + = a (Eq. 6.2.4-2) 
This quasi-static approach is consistent with assumption 5.1.12 and is applicable to the backfilled 
and the nonbackfilled EBS. 
6.3 FLUX INTO AND AROUND THE WASTE PACKAGE (F5  F9) 
The conceptual model for the TSPA-SR is based on the presence of continuous flow paths 
through the patches, SCCs and pits that penetrate the WP. More specifically, the TSPA-SR 
conceptual model assumes that vertical flow of seepage into the WP, through the waste form and 
out of the WP is not impeded by the location of patches, SCCs and pits on the surface of the WP 
(see assumption 5.1.10). In other words, there is no long-term build-up and retention of liquid 
within the WP for flow and transport. There is also no significant resistance to the flow through 
the waste form. The TSPA-SR approach attempts to maximize the immediate release and 
mobilization of radionuclides, as explained in Section 6.6. 
Radionuclides cannot be released from the WP if there are no openings through either the wall or 
lid of the WP. Section 6.3.1 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 or through the WP or 
whether transport out of the WP will be by advection and/or diffusion. Section 6.3.2 describes 
the flux of liquid around or through the WP. Section 6.3.3 describes the alternative pathway for 
liquid to reach the waste package; namely, evaporation from the invert and condensation on the 
inside of the DS can provide a source of liquid even when there are no openings in the DS. 
Section 6.3.4 describes the flux of liquid through the invert. 
The flux abstraction for the WP is independent of the use of an engineered backfill around the 
DS. The algorithms in this section are therefore applicable to the backfilled and nonbackfilled 
EBS. 
6.3.1 Breaching of the Waste Package 
6.3.1.1 Waste Package Design 
Although WPs vary depending on the waste form they contain, the majority of design features 
are shared in common. These commonalties are described here. The cylindrical WP is 
constructed with a double-shelled wall. The inner shell is a 5 cm thick shell of stainless steel that 
provides structural integrity for the WP. The outer shell is a 2 cm or 2.5 cm thick layer of Alloy 
22 that provides resistance to corrosion. This cylinder is sealed with two lids that are welded 
onto the open end. The inner lid is composed of stainless steel and the outer lid is composed of 
Alloy 22. There is a 3 cm air gap between the inner and outer lids. All WPs also have a 
protective skirt that extends at least 24 cm beyond the lids. This skirt is an extension of the 
Alloy 22 outer shell. Design sketches of the 21-PWR and 44-BWR WPs are documented in 
CRWMS M&O 2000d. Design sketches of the short and long DHLW/DOE SNF WPs are 
documented in CRWMS M&O 2000e. Design sketches of the naval SNF WP are documented in 
CRWMS M&O 2000f.

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The stainless steel inner layer of the WP is assumed to have no resistance to corrosion, forming 
an immediate flow pathway once the outer (Alloy 22) shell has been breached (per assumption 
5.1.18). Similarly, it is assumed that the closure weld on the inner stainless steel lid has no 
resistance to corrosion and the inner lid has failed once the outer lid has failed. 
6.3.1.2 Types of Openings 
Two general types of openings can exist in the WP due to corrosion. These are (1) radial SCCs 
that penetrate the weld of the lid and (2) patches resulting from general corrosion. Each of these 
types of openings is discussed in turn below. 
6.3.1.2.1 Stress Corrosion Cracks 
SCCs 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). SCCs may be important at 
early times because they can occur relatively quickly relative to the formation of a penetrating 
patch from general corrosion. 
SCCs will typically form along two orientations. Radial stresses can generate circumferential 
cracks while hoop stresses can generate radial cracks. Only radial SCCs are considered in the 
EBS RT Abstraction because the formation of circumferential cracks that penetrate the thickness 
of the lid is highly 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 (CRWMS M&O 2000n, Fig. 11 - Profile 1- 
1). In this condition, circumferential cracks cannot propagate through the thickness of the lid 
weld and are therefore not considered in the EBS RT Abstraction. 
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 d (CRWMS M&O 
2000n, Section 5). The equation given by Tada et al. (1973) can be used to calculate the gap, d 
[L], for a crack with length 2a in an infinite sheet under plane stress load: 
, 
2 ) 1 ( 2 2 
E 
a a s u 
d 
- 
= (Eq. 6.3.1-1) 
where E is the modulus of elasticity [M/L/T2], u is Poisson's ratio [-], 2a is the crack length [L] 
and sa is the applied stress [M/L/T2]. Appropriate values for E and u for Alloy 22 are given in 
Table 1. 
The residual tensile stress is higher on the outside surface than on the inside surface (CRWMS 
M&O 2000n, Fig. 13, Profile 1-1). The resulting shape of the crack is then an ellipsoidal cone 
where 2a is the length of the long axis and do and di are the short axis lengths for the outside and 
inside surfaces, respectively. The depth d of the crack is taken to be the lid thickness. Figure 4 
is a schematic diagram of the geometry of the ellipsoidal cone crack.

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d 
2a
d
o
d
i 
Figure 4. Schematic of the Dimensions for an Ellipsoidal Crack 
Values of sa, the residual stress, and 2a are still subject to design changes and improved 
calculations; however a range of values can be estimated. One approach is to estimate the 
maximum length 2a of a radial crack based on the width of the heat-affected zone around the 
weld between lid and WP. The width of the heat-affected zone is estimated to be about twice the 
width of the weld or 0.50 inches (1.27 cm). A second approach is to identify the region of high 
residual stress from finite-element simulations. The width of the region of high residual stress on 
the outer surface of the lid is approximately 4 cm (Tang et al., 1999). Table 5 gives the 
calculated gap width, based on Equation 6.3.1-1, for both approaches based on typical residual 
stresses at the inner and outer surface of the lid for a 21 PWR WP (CRWMS 2000n, Fig. 13). 
The second approach is recommended for the EBS RT Abstraction because it is conservative 
relative to the first approach. 
Table 5. Gap Width for a Range of Residual Stresses at 400F (~200C) in a 21-PWR Container 
Parameter 
Inner 
Surface 
Outer 
Surface 
Hoop stress 40 ksi 50 ksi 
Gap width for a 1.27 cm long crack 33 mm  41 mm 
Gap width for a 4 cm long crack  104 mm  130 mm 
*1 ksi = 1,000 psi 
The cross-sectional area of the SCC is important for transport by diffusion. The bounding 
(largest) cross-sectional area is defined by conditions at the outer surface of the 4 cm long crack. 
The area of this ellipse is pab, where 2a is 4 cm and b is one-half of the larger gap width on the 
last line in Table 5. The cross-sectional area is then p(0.02 m)(65 x 10-6 m) or 4.08 x 10-6 m2. 
The width (gap) of the SCCs can also be used as an indicator to determine whether or not water 
can flow into the WP through a SCC. However, the potential for flow through a SCC may vary 
with dust or corrosion products in the crack and with the effects of temperature and mineral 
content on viscosity and surface tension. Given the complexity of this situation, it is reasonable 
to bound the response by assuming that any fluid that contacts a crack will flow through the 
crack and into the WP (per assumption 5.1.10 and 5.1.16). This fluid is also assumed to form a 
continuous liquid pathway for diffusive transport of radionuclides out of the WP (per assumption 
5.2.8). 
Film flow on the WP exists if condensation generates droplets on the inner surface of the DS or 
if the EBS design has no backfill. This dripping water is assumed to be capable of contacting an 
SCC only if the drip falls inside the skirt of the WP (see Figure 2 or 3). This is a reasonable 
limitation because of the effect of gravity and because all WPs are conservatively assumed to be

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tilted at their maximum angle to provide a bounding estimate of the dripping flux inside the skirt 
(per assumption 5.1.15). Once a drop or thin film is inside the skirt, it will flow around and 
down the skirt into any SCCs. The EBS RT Abstraction conservatively assumes that all dripping 
flux inside the skirt enters the SCCs and WP, independent of film thickness (assumption 5.1.16). 
The dripping flux has the greatest potential to fall inside the skirt if the WP is tilted upward. 
Possible mechanisms for tilting are emplacement pallet collapse due to corrosion or a seismic 
event that causes one end of the WP to fall off its emplacement pallet. The EBS RT Abstraction 
conservatively assumes that all WPs become tilted, lid-end upward, at the maximum angle 
possible. This maximum angle of tilt occurs when the skirt end of the WP is elevated to the 
height of the inside of the DS while the other end rests against the invert. 
For the backfilled EBS, a capillary flux can reach a SCC only if the backfill forms a continuous 
pathway from the outer surface of the DS to the skirt. In effect, the free space around the WP 
and its skirt must fill with backfill to provide this flow pathway. The EBS flow abstraction 
conservatively assumes that, once there is a patch from general corrosion of the DS, this 
pathway forms and liquid can flow through the SCCs and wet the waste form. 
Crack apertures will fill with corrosion products over time. The capillary forces in these 
corrosion products may then act as a Richards barrier, preventing advective inflow through the 
crack if there is no fluid pathway through fine granular material between the two lids of the WP. 
The formation of corrosion products is conservatively neglected in considering flow into SCCs. 
6.3.1.2.2 Patches from General Corrosion 
The EBS design includes two corrosion-resistant materials, titanium and Alloy-22. The main 
corrosion mechanism for both materials is expected to be general corrosion, although research is 
continuing into the potential for pitting corrosion due to extreme near-field geochemical 
environments and for SCC due to damage from rockfall or seismic events. 
The timing and location of patches from general corrosion is predicted by the WAPDEG 
software. These predictions are based on discretizing the response of the DS with 500 nodes and 
the WP with 1,000 nodes (see assumption 5.1.11). The equivalent area per patch for the EBS RT 
Abstraction is calculated as the total surface area divided by the number of nodes on the surface. 
The axial length of each patch is calculating assuming a square geometry for each patch. The 
data on timing, location (upper or lower surface of WP), size and length of patches is available as 
a boundary condition for the EBS RT Abstraction. 
6.3.1.3 Impact of Heat Generation 
Heat generated by the waste form has the potential to evaporate water within the WP. In this 
situation, water cannot collect inside the WP and cannot support advective transport of 
radionuclides. Preliminary estimates indicate that the available heat can evaporate incoming 
water for several thousand years and possibly longer. However, complexities in the internal 
geometry of the WPs (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 SCCs) make it difficult to 
say definitively that all incoming water will be evaporated.

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Since the temperature of the WP drops relatively rapidly in the first 3,000 years (CRWMS M&O 
2000l), the potential for evaporation in the WP has been ignored in Rev 0 of the TSPA-SR. This 
approach is conservative because evaporation might stop advection as a transport mechanism. It 
is potentially nonconservative if evaporation from the surface of the WP is followed by 
condensation on the DS, resulting in a refluxing of water that could accelerate corrosion of the 
WP. The current approach (no evaporation) is considered reasonable for the Rev 0 of the TSPASR 
until additional results become available. 
6.3.2 Flux Through and Around the WP (F5 and F6) 
The flux into the waste package, F5, is conceptualized to be the sum of two parts: the flux 
through SSCs and the flux through patches and/or pits in the WP. The flux through SSCs 
currently has two sources: (1) evaporation from the invert and condensation on the inside of the 
DS (F7), and (2) a dripping flux from seepage for the nonbackfilled EBS. When backfill is 
present, the advective (capillary) flux around the WP (F3) cannot contribute to flow through a 
SCC because the small size of the SCC excludes individual grains of sand so that the SCC and 
any corrosion products inside the SCC are anticipated to be a barrier to capillary flow from the 
backfill. The sources of flux through patches and pits includes the condensation on the DS (F7) 
and the advective (capillary) flux thorough the backfill around the WP (F3). The flux through 
SCCs and the flux through patches/pits are described in turn. 
The value of the SCC flux into the WP is not required by the model because transport through 
the SCCs is solely by diffusion and because the presence of water vapor and hygroscopic salts on 
the waste form are assumed to generate a continuous, thin film pathway for diffusive transport 
(per assumption 5.2.8). However, it is useful to provide an abstraction of the dripping flux for 
future use. The flux through the SCC is proportional to the ratio of the length of the exposed lid 
within the skirt to the length of the exposed WP (per assumption 5.1.15). Length is appropriate 
here, rather than area, because only the dripping flux from condensation or from seepage without 
backfill can fall within the skirt and this dripping flux is conceptualized to fall from the crown of 
the invert. In effect, the flux is a line source so a ratio of lengths is used to partition the dripping 
flux between the WP and the skirt. The calculation for the nonbackfilled EBS is as follows: 
, 
) sin( 
) sin( 
) ( 7 3 j 
j 
LID WP 
LID 
SCC L 
F F F 
l 
l
+ 
+ = (Eq. 6.3.2-1) 
where FSCC is the flux through the SCC, (F3 + F7) is the sum of the seepage flux (no backfill 
design) and the condensation flux (if present), LID l is the diameter of the lid within the skirt, 
WP L is the total axial length of the WP, and j is the maximum tilt angle of the WP. The 
corresponding formula for the backfilled EBS does not include the flux F3 because capillarity of 
the backfill prevents this flux from entering the small SCCs: 
. 
) sin( 
) sin( 
7 j 
j 
LID WP 
LID 
SCC L 
F F 
l 
l
+ 
= (Eq. 6.3.2-2) 
The maximum tilt angle is defined as the angle of the WP when the top edge of the skirt touches 
the crown of the DS and the bottom corner of the WP is in contact with the invert. This angle

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can be calculated from simple trigonometry and the data for the four types of WPs in Table 1. 
The equation for calculating the maximum tilt angle, j, is given by
, ) cos( ) sin( h D D L WP WP WP D + = + j j (Eq. 6.3.2-3) 
where LWP is the length of the waste package [L], DWP is the outer diameter of the waste package 
[L], and Dh is the distance from the DS to the top of the WP if the emplacement pallet collapses 
[L]. This equation can be rewritten into a form suitable for iterative solution on a hand 
calculator: 
. 
)) cos( 1 ( 
) sin( 
WP 
WP 
L 
h D D + - 
= 
j 
j (Eq. 6.3.2-4) 
With a given (or old) value of j, evaluate the right-hand side of Equation 6.3.2-4 to determine 
the new values of sin(j) and then of j itself. Repeated substitutions of the latest value for j into 
the right-hand side of Equation 6.3.2-4 and calculation of a new value for j results in an iterative 
process that converges to 3 significant places in about 4 iterations. The values of j for the four 
types of WPs are presented in Table 6. Note that the maximum tilt angles are relatively small, so 
only a small fraction of any dripping flux will fall within the lid of the WP. 
Table 6. Maximum Tilt Angle for the Four Types of Waste Packages. 
Type of WP 
Length of 
WP, LWP 
(meters) 
Outer Diameter 
of WP, DWP 
(meters) 
Distance from DS 
To Top of WP, Dh 
(meters) 
Maximum Tilt Angle, 
j 
(degrees) 
21-PWR 5.165 1.564 0.772 8.80 
44 BWR 5.165 1.594 0.742 8.45 
5 HLW/DOE SF 3.590 2.030 0.306 5.01 
Naval SNF 6.065 1.869 0.467 4.47 
The fluid flux through patches and pits in the WP is proportional to the total axial length of all 
patches and pits to the total axial length of the WP (per assumption 5.1.9). The presence of a gap 
between adjacent WPs is conservatively neglected in the TSPA-SR model. The calculated flux 
through the WP is then given by: 
, ) ( _ _ 
7 3 5 SCC 
WP 
Pit WP Patch WP F 
L 
L L 
F F F + 
+ 
+ = (Eq. 6.3.2-4) 
where F5 is the flux into the WP, F3 is the flux through the DS, F7 is the condensation flux (if 
any), LWP_Patch is the total axial length of all patches on the WP, LWP_Pit is the total axial length of 
all pits on the WP, and LWP is the total axial length of the WP. FSCC is given by Equation 6.3.2-1. 
Finally, the flux that is diverted around the WP, F6, is calculated using continuity of the quasistatic 
flow (assumption 5.1.12) around and into the WP: 
. F F F F 5 7 3 6 - + = (Eq. 6.3.2-5)

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6.3.3 Evaporation from the Invert and Condensation on the Drip Shield (F7) 
The evaporation/condensation pathway, F7, is possible when the free space between DS and WP 
is not blocked by a backfill material. In other words, water vapor can evaporate from the invert 
and move upward to the underside of the DS if this pathway is not blocked by backfill. This 
pathway is therefore possible at all times for the nonbackfilled EBS or at early time for the 
backfilled EBS, before the DS is breached and sand can enter the space between DS and WP. 
Liquid water may reach the WP due to condensation on the inside of the DS. A substantial 
portion of the water draining through the backfill migrates through the invert. In proximity to 
thermal output from the WP, some of this water will evaporate. This water vapor convects 
following temperature gradients. In the high humidity environment of the subsurface, this water 
will condense once it moves away from the heat source. If the water vapor convects downward 
and laterally away, then the interior of the DS will remain dry. If, however, convection proceeds 
upward toward the DS, then condensation could occur. The manner in which convection 
proceeds will be a function of the thermal conductivities of the various media in the vicinity 
(invert, backfill, and host rock) and the geometry of the system (for instance, the relative 
proximity of the WP to the invert and the top of the DS). 
The inside of the DS will be filled with a mixture of air and water vapor. Liquid water can 
condense on the inside of the DS when the temperature of the DS, TDS, is less than the dew point 
of this air/vapor mixture at the DS surface. Note that the DS forms an inverted cap that will tend 
to trap any water vapor that moves upward from the invert. 
As a first order approximation, the space between the DS and WP can be treated as a closed 
system because of the geometry of the DS and invert. The vapor pressure of water beneath the 
DS will then be close to the equilibrium vapor pressure at the invert temperature, TINV. In this 
case, comparison of the temperature in the invert (TINV) and the temperature at the top of the DS 
(TDS) provides a suitable indicator of the potential for condensation on the inside of the DS. That 
is, condensation will occur if TINV >TDS. This is a physically reasonable approximation in terms 
of providing an indicator for the direction of vapor pressure gradients and the potential for 
condensation on the DS. 
The potential for condensation is abstracted very simply using the output of NUFT. A NUFT 
calculation is supplied for each group of WPs in the repository. The NUFT calculations and 
abstraction provide the average temperature in the invert and the temperature at the crown of the 
DS as a function of time. The criterion for condensation is then 
- If TDS>TINV , then F7 = 0 (no condensation occurs), 
- Otherwise, the condensation flux is equal to the evaporative flux, F7. 
Note that all the evaporative flux from the invert drips from the inside of the DS onto the WP. 
This approach provides a reasonable bound because the possibility of water vapor transport 
laterally away from the DS is ignored. 
It is also possible that liquid will evaporate from the WP; however, the invert is envisioned as the 
main source of water vapor, particularly during the main thermal pulse. The main thermal pulse 
occurs during the first 3,000 years after repository closure (CRWMS M&O 2000l), when failure

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of the DS will be quite infrequent. In this situation, seepage and capillary fluxes will be diverted 
away from the WP and into the invert, so the invert will be the main source for the evaporative 
flux. 
6.3.4 Flux Into and Through the Invert (F8 and F9) 
The flux leaving the WP, F8, is equal to the flux entering the WP, F5. Similarly, the liquid flux 
leaving the invert, F9, is equal to the sum of the diversion around the WP, F6 and the flux leaving 
the WP, F8, minus any evaporative flux leaving the invert, F7. That is, 
, F F 5 8 = (Eq. 6.3.4-1) 
and . F F F F F 3 7 8 6 9 = - + = (Eq. 6.3.4-2) 
The equality of F8 and F5 is based on quasi-static flow (i.e., outflow equals inflow). The equality 
of F9 and F3 is consistent with the definitions of F6 and F8 and with the quasi-static assumption, 
which implies that the flux through the DS equals the flux out of the invert. Note that only the 
flux leaving the WP, F8, can transport radionuclides through the invert. These flux calculations 
are independent of the presence or absence of backfill around the DS. 
6.4 TRANSPORT THROUGH THE EBS 
The waste form is the source of all radionuclides in the repository system. Radionuclides can be 
transported downward, through the invert and into the UZ, as shown in Figure 3. Transport can 
occur through advection when there is a fluid flux through the WP, and by diffusion through 
continuous fluid pathways in the WP. These two transport processes (diffusion and advection) 
may not be active simultaneously because they are a function of the type of penetrations through 
the DS and WP and the local seepage conditions. For example, diffusion would be the only 
viable transport mechanism through SCCs or through patches that form in a humid environment 
without a seepage flux. Both advective and diffusive transport are viable through a patch with a 
significant seepage flux. 
The emphasis in this AMR is on flow and transport of radionuclides through the EBS after the 
radionuclides are mobilized. This AMR does not define elements of the TSPA, 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. In effect, this AMR provides the algorithms for 
transporting radionuclides using the flow geometry and radionuclide concentrations determined 
by other elements of the TSPA-SR. 
Transport through the quartz sand backfill, if present, is expected to be negligible. Upward 
diffusion through the backfill is unlikely before the DS fails for two reasons. First, a direct, 
continuous flow path does not exist between the WP and the backfill. Second, transport through 
a more circuitous flow path, such as laterally across the invert and up into the backfill is unlikely 
given the downward (capillary) flux through the backfill. After the DS fails, upward diffusion is 
expected to be negligible in comparison to the downward advective flux through the DS.

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For the nonbackfilled EBS, any seepage is diverted by intact portions of the DS and enters the 
invert near the base of the DS. This concentration of the seepage flux could enhance advective 
transport beneath the sides of the DS. However, the effect of this enhancement on a radionuclide 
plume directly beneath the WP will be limited by geometry and by capillarity or dispersion. The 
distance from the centerline of the WP to the foot of the DS, approximately 1250 mm, is much 
greater than the depth of the invert, 606 mm. The plume will then be separated from the diverted 
seepage unless capillary forces or dispersion are very strong in the invert. But if capillary forces 
or dispersion are very strong, then the diverted flow will also be rapidly spread through the 
invert, eliminating the enhanced advective flux. The impact of the diverted flux on transport of 
radionuclides across the invert does not appear significant and is neglected in the EBS Transport 
Abstraction. 
For the backfilled EBS, the seepage flux into the drifts is spread more uniformly than for the 
nonbackfilled design by capillary forces in the backfill. The backfill provides a more uniform 
distribution of flow into the invert between the sides of the DS and the walls of the drift, 
reducing the possibility of an enhanced advective flux. 
The diffusion coefficient for radionuclide transport is based on the self-diffusion coefficient of 
water at 25C. This is a bounding value for all radionuclides, as discussed in Section 6.4.1.1. 
The effects of porosity and liquid saturation on the diffusion coefficient are incorporated using 
the formulation in Section 6.4.1.2. The effects of temperature on this bounding value are 
corrected using the formulation in Section 6.4.1.3. 
Advective transport is very straightforward in the EBS RT Abstraction because of the 
conservative assumptions for the TSPA-SR model. In particular, mobilized radionuclides will be 
transported with the local fluid flux from the WP (F8) through the invert to the UZ (F9). (Note 
that the v in Equation 6.1.2-1 can be interpreted as a flux rate per unit cross-sectional area, or 
[L3/T/L2} = [L/T]). There are no corrections for dispersive effects or chemical sorption because 
horizontal dispersion is conservatively ignored in the EBS RT Abstraction and because the 
partition coefficients for all radionuclides are conservatively set to zero in the WP and invert (see 
Section 5.2). 
Diffusive transport through the invert is calculated in a conservative manner. Diffusive transport 
through any barrier depends on the difference in concentrations across the barrier. For the invert, 
this difference is based on the concentration in the WP and the concentration at the bottom of the 
drift, i.e., the interface with the UZ. The radionuclide concentration in the WP is given by the 
appropriate dissolution rate or solubility limit for each radionuclide or the partition coefficient 
for each colloid. The concentration at the interface with the UZ is set to a value very close to 0 
in order to maximize diffusive transport. The boundary condition at the UZ interface is 
implemented by defining a flow cell with a small volume of water but a very high advective flux, 
effectively sweeping all radionuclides away from the lower boundary. This swept away 
boundary condition will maximize diffusive transport, particularly if the advective flux through 
the WP and invert is low. 
Given the simplicity of the transport models, the discussion in this section focuses on the 
calculation of the diffusion coefficient for diffusive transport.

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6.4.1 Diffusion Coefficient Abstraction 
The TSPA-LA model requires an abstraction for the diffusion coefficient in the WP and invert as 
a function of radionuclide, porosity, saturation, temperature, and concentration. The 
recommended abstraction for diffusion coefficient is as follows: 
 Use the free water diffusion coefficient for self-diffusion of water, 2.299 x 10-5 cm2/sec 
(Mills 1973, Table III), as a bounding value for all radionuclides at 25C. The rationale 
for choosing this value is presented in Section 6.4.1.1. The value of the self-diffusion 
coefficient of water is TBV (MO0002SPASDC00.002). 
 Correct the diffusion coefficient for the porosity and (liquid) saturation of the invert. 
The correction for porosity and saturation is conservatively represented, based on 
Archies law and experimental data for granular media. The rationale for this approach 
and its conservatism is presented in Section 6.4.1.2. 
 Correct the diffusion coefficient for temperature variation using the formulation in 
Section 6.4.1.3 (CRWMS M&O 2000o). 
 Ignore the effects of concentrated solutions for Rev 0 (see Section 6.4.1.4). The 
maximum correction 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 selfdiffusion 
coefficient for all radionuclides. It will be neglected for the TSPA-SR. 
6.4.1.1 Self-Diffusion Coefficient of Water 
The self-diffusion coefficient of water provides a conservative bound for the diffusion of ionic 
and neutral inorganic, and organo-metal species that may be released from a WP. This assertion 
is based on: 
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 99 ionic species, only 3 species, H+, OH-, and ODhave 
diffusion coefficients that are larger than the self-diffusion of water at 25C (Mills and 
Lobo, 1989; Appendix I, 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; 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 is 
conservative.

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The compilation below (Table 7) lists a selection of diffusion coefficients for some trivalent 
lanthanides and actinides. Table 7 also includes some anions not listed in most compilations but 
relevant and/or analogous to those expected for radionuclides released from the WP. The listing 
shows that, except for I2 and TcO4
-, the diffusion coefficients for these species are far smaller 
than the self-diffusion of water, and that the hydroxyl and/or carbonate complexes of the metal 
species would be expected to have even smaller diffusion coefficients. 
Table 7. Compilation of Diffusion Coefficients for Molecular Iodine, Yttrium, Technetium, and Lanthanide 
and Actinide Species 
Species D, cm2/s Comments Reference 
Y3+ 5.7 x 10-6 25C (Mills and Lobo, 1989); pg. 220. 
TcO4
- 1.48 x 10-5 25C (Mills and Lobo, 1989); pg. 105. 
I2 1.36 x 10-5 25C; 0.075 M H2SO4 (Cantrel, Chaouche, and Chopin-Dumas, 
1997); Table 5. 
La3+ 5.42 x 10-6 25C; 0.1 M NaClO4 (Rosch and Khalkin, 1990); calculated 
from mobility data reported in Table 1; 
pg. 103.a 
La3+ 6.18 x 10-6 25C (Mills and Lobo, 1989); pg. 93. 
Ce(III)-carbonate 2.68 x 10-6 5.5 M K2CO3, pH 13, 
presumably at 25C. 
(Haltier, Fourest, and David, 1990); 
pg. 111. 
Ce(IV)-carbonate 1.56 x 10-6 5.5 M K2CO3, pH 13, 
presumably at 25C. 
(Haltier, Fourest, and David, 1990); 
pg. 111. 
Eu3+ 4.38 x 10-6 25C; 0.1 M NaClO4 (Rosch and Khalkin, 1990); calculated 
from mobility data reported in Table 1; 
pg. 103.a 
Gd3+ 5.24 x 10-6 25C; 0.1 M NaClO4 (Rosch and Khalkin, 1990); calculated 
from mobility data reported in Table 1; 
pg. 103.a 
Tb3+ 5.01 x 10-6 25C; 0.1 M NaClO4 (Rosch and Khalkin, 1990); calculated 
from mobility data reported in Table 1; 
pg. 103.a 
Tm3+ 5.10 x 10-6 25C; 0.1 M NaClO4 (Rosch and Khalkin, 1990); calculated 
from mobility data reported in Table 1; 
pg. 103.a 
Yb3+ 5.23 x 10-6 25C; 0.1 M NaClO4 (Rosch and Khalkin, 1990); calculated 
from mobility data reported in Table 1; 
pg. 103.a 
Lu3+ 5.01 x 10-6 25C; 0.1 M NaClO4 (Rosch and Khalkin, 1990); calculated 
from mobility data reported in Table 1; 
pg. 103.a 
UO2(CO3)3
4- 3.6 x 10-6 1 M total carbonate, 22 C (Perry, Phillips, and Chung, 1988); 
pg. 302. 
UO2(CO3)3
4- 3.0 x 10-6 0.2 M total carbonate, pH 9.8, 
25C 
(Perry, Phillips, and Chung, 1988); 
pg. 302. 
UO2(CO3)3
5- 3.81 x 10-6 0.75 M Na2CO3, 0.6 M 
NaClO4, pH 11.5, presumably 
at 25C 
(Haltier, Fourest, and David, 1990); pg. 
110. 
UO2
++ 6.8 x 10-6 25C (Millard and Hedges, 1996); pg. 2141. 
UO2-carbonate 1.9 x 10-6 Calculated using Stokes- 
Einstein with a radius of 
8  at 10C 
(Millard and Hedges, 1996); pg. 2141. 
Np(V)-carbonate 7 x 10-6 Calculated using Stokes- 
Einstein with a radius of 
3.4  at 25C 
(Tsukamoto, Ohe, et al., 1994); pg. 469.

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Species D, cm2/s Comments Reference 
Am3+ 5.78 x 10-6 25C; 0.1 M NaClO4 (Rosch and Khalkin, 1990); calculated 
from mobility data reported in Table 1; 
pg. 103.a 
Am3+ 5.95 x 10-6 25C, in 0.0002 M Nd(ClO4)3 (Mills and Lobo, 1989); pg. 131. 
Cf3+ 4.39 x 10-6 25C; 0.1 M NaClO4 (Rosch and Khalkin, 1990); calculated 
from mobility data reported in Table 1; 
pg. 103.a 
Cf3+ 5.50 x 10-6 25C, in 0.0002 M Nd(ClO4)3 (Mills and Lobo, 1989); pg. 132. 
Es3+ 5.50 x 10-6 25C, in 0.0002 M Nd(ClO4)3 (Mills and Lobo, 1989); pg. 132. 
aCalculation of diffusion coefficients from reported ionic mobilities (Rosch and Khalkin 1990; Table 1). The mobilities were 
measured in 0.1 M NaClO4 at various pHs (below the pH of hydrolysis). The mobilities 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, T is the temperature in Kelvin, z is the valence of the ion, e is the elementary 
charge, and u is the mobility (Atkins 1990, Box 25.1, Einstein relation, page 765). 
Future TSPA_SR or TSPA-LA models might use four diffusion coefficients to provide a more 
realistic model. 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 x 10-5 cm2/s, 1.2 x 10-5 
cm2/s, 0.7 x 10-5 cm2/s, respectively, as shown in Figure 5. 
Figure 5. Limiting Diffusion Coefficients for Anions and Simple (Non-Complexed) Cations. Selected from 
Mills and Lobo (1989), Appendix I, Tables 1.1 to 1.6; pgs. 314 to 319 
6.4.1.2 Correction for Porosity and Saturation 
The reduction in the free water diffusion coefficient for a partly saturated porous medium can be 
estimated from Archies law (CRWMS M&O 2000o). Archies law gives the diffusion 
coefficient, D, as a function of porosity and saturation in a partly saturated, granular medium as: 
, 2 3 . 1 
0 s D D f = (Eq. 6.4.1-1) 
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

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where f is the porosity, and s is the (liquid) saturation of the porous medium. D0 is the free 
water diffusion coefficient, corresponding to the value of D when porosity and saturation are 
both 1.0. The value of the exponents for f and s correspond to the values for unconsolidated 
sand and are not directly applicable to the crushed tuff in the invert. 
Conca and Wright (1992) have measured the dependence of diffusion coefficient on volumetric 
moisture content for granular materials from Yucca Mountain, including crushed tuff. A 
statistical analysis produced an excellent fit to Conca and Wrights data (CRWMS M&O 2000o) 
using a power law dependence on moisture content. The statistical fit to the data is given by the 
following equation: 
( ) ), 2 )(log 849 . 1 ( log 
0 
- =   
 
  
 
q 
D
D 
(Eq. 6.4.1-2) 
where q is the volumetric moisture content. The independent variables for this fit are defined in 
Equation 31 and the slope of the curve is given by Equation 37 of (CRWMS M&O 2000o). The 
volumetric moisture content (%) is defined in Equation 28 of the same reference as 
. 100 s f q = (Eq. 6.4.1-3) 
The volumetric moisture content is the ratio of the liquid volume to the total volume, expressed 
in Equation 6.4.1-3 as a percent. Substituting Equation 6.4.1-3 into Equation 6.4.1-2 and 
simplifying: 
( ) ), 2 100 )(log 849 . 1 ( log 
0 
- =   
 
  
 
s 
D
D f (Eq. 6.4.1-4) 
( ) ), 2 ) log( 100 )(log 849 . 1 ( log 
0 
- + =   
 
  
 
s 
D
D f (Eq. 6.4.1-5) 
), log( ) 849 . 1 ( log 
0 
s 
D
D f =   
 
  
 
(Eq. 6.4.1-6) 
( ) . log log 849 . 1 
0 
s 
D
D f =   
 
  
 
(Eq. 6.4.1-7) 
Equation 6.4.1-7 is equivalent to: 
, ) ( 849 . 1 
0 
s 
D
D f = (Eq. 6.4.1-8) 
or rearranging . 849 . 1 849 . 1 
0 s D D f = (Eq. 6.4.1-9) 
The functional form of Equation 6.4.1-9 is identical to Equation 6.4.1-1, although the exponents 
are different, partly due to differences in the media. 
Archies law (Equation 6.4.1-1) has two independent variables, f and s, with values of the 
exponents appropriate for unconsolidated sand. The statistical analysis of Conca and Wrights 
data combines a variety of materials into a single fit for a single parameter, moisture content; 
porosity is not considered as an independent variable. Until a multi-parameter statistical analysis

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of the data is available, it is conservative to use the following representation for diffusion 
coefficient as a function of porosity and saturation: 
. 849 . 1 3 . 1 
0 s D D f = (Eq. 6.4.1-10) 
This equation has the exponent for saturation determined from the statistical fit and the exponent 
for porosity determined from Archies law. Equation 6.4.1-10 is conservative relative to the 
statistical fit, in the sense that it will lead to a higher value for the diffusion coefficient than 
Equation 6.4.1-9 for the same values of f and s. 
The statistical fit for the diffusion coefficient has uncertainty because of the scatter of data points 
about Equation 6.4.1-9 (see Figure 3 in CRWMS M&O 2000o). This uncertainty approximates a 
normal distribution for the residuals to Equation 6.4.1-2, as shown in Figure 4 of CRWMS M&O 
2000o. This distribution has a mean value of 0.0 and a standard deviation of 0.223 (Equation 38 
in CRWMS M&O 2000o). This uncertainty can be incorporated by adding a factor to Equation 
6.4.1-10 as follows: 
. 10 ) 223 . 0 , 0 ( 849 . 1 3 . 1 
0 
= = = s f a ND s D D (Eq. 6.4.1-11) 
where ND represents a normal distribution with mean, a, of 0 and standard deviation, s, of 
0.223. ND is in the exponent in Equation 6.4.1-11 because the residuals are calculated in the loglog 
space of the fit for Equation 6.4.1-2. This normal distribution can be sampled for each 
realization of the TSPA-SR calculations, thereby incorporating the effective uncertainty of the 
experimental data into the diffusion coefficient. 
6.4.1.3 Correction for Temperature 
The following equations correct the diffusion coefficient for temperature: 
, 
0
0 
0 
h
hT 
T T
T 
D
D = (Eq. 6.4.1-12) 
where DT is the diffusion coefficient at temperature T, D0 is the free water diffusion coefficient at 
temperature T0, hT is the viscosity of water at temperature T, and h0 is the viscosity of water at 
temperature T0. The temperature dependence of viscosity is given by: 
, 
168 
) 293 ( 001053 . 0 ) 293 ( 3272 . 1 
log 
2 
20 
10 - 
- - - 
=   
 
  
 
T 
T T T 
h
h 
(Eq. 6.4.1-13a) 
or , 10 ) 10 002 . 1 ( 168 
) 293 ( 001053 . 0 ) 293 ( 3272 . 1 
3 
2 
  
 
  
 
- 
- - - 
- = T 
T T 
T x h (Eq. 6.4.1-13b) 
where h20 = 1.002x10-3 Pa-s.

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All temperatures are in Kelvin. Equations 6.4.1-12 and 6.4.1-13 correspond to Equations 13 and 
12 in CRWMS M&O 2000o, respectively. 
6.4.1.4 Correction for Concentrated Aqueous Solutions 
Data in the AIP Handbook (Grey 1972, 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 molar solution and the 
coefficient for potassium iodide increases from 2.00 in a dilute solution to 2.533 at 3.5 molar. 
The percent increase for potassium iodide, 26.7%, is the greatest of any in Table 2p-2, excluding 
HCl. HCl has been excluded from consideration because it is not representative of the type of 
radionuclides released from the WP. 
This correction factor is partly contained in the conservatism inherent in using the self-diffusion 
coefficient for water as a bounding value for all radionuclides. The correction for concentrated 
aqueous solutions is therefore being neglected in the TSPA-SR. 
6.4.2 Colloidal Transport 
Radionuclide transport from the WP 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 (CRWMS M&O 2000p): (a) waste form colloids, (b) colloids due to corrosion products, 
and (c) groundwater colloids. The waste form colloids may have irreversibly attached 
(embedded) or reversibly attached (sorbed) radionuclides. The corrosion and groundwater 
colloids may have reversibly attached radionuclides only. The stability and mass concentrations 
of colloids are functions of the ionic strength and pH of the groundwater or local fluid chemistry 
in the WP and invert. 
The mass of radionuclides irreversibly attached to the waste form colloids is determined from 
reactions within the WP (CRWMS M&O 2000p). 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 fluid 
. Mass concentration of colloid material in the fluid 
. Radionuclide distribution coefficient (Kd) of a specific radionuclide on a specific 
colloid mineralogical type 
The concentrations of colloids in the drifts and EBS has also been determined (CRWMS M&O 
2000q). 
Colloidal transport of radionuclides occurs by advective and diffusive processes. Advective 
transport moves colloids (and the associated radionuclides) at the same velocity as the liquid flux 
leaving the WP and passing through the invert. Diffusive transport moves colloids based on the 
concentration gradient across the invert and the diffusion coefficient in the invert material. The 
concentration gradient across the invert is calculated conservatively because the concentration at 
the bottom of the invert (interface with the UZ) is determined by the swept away boundary 
condition. The colloidal diffusion coefficient is estimated as the diffusion coefficient for the 
corresponding dissolved radionuclide divided by 100. The factor of 100 is based on an

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approximation for the ratio of the ionic radii for a dissolved species versus that for a colloid 
(CRWMS M&O 2000p, Section 6.17). 
6.4.3 Transport Through Stress Corrosion Cracks 
Two cases are considered for transport through SCCs. In the first case, there is a dripping flux 
on the WP but no backfill is in contact with the WP. This first case can happen if there is a 
dripping flux due to condensation and the DS is intact so that quartz sand backfill cannot fill the 
annular space around the WP. This first case is also applicable after the DS fails for a design 
without backfill. In the second case, backfill is in contact with the lid and SCCs after DS failure. 
6.4.3.1 Dripping Flux Only 
Transport through SCCs in the WP is limited to diffusion. Once SCCs form in the lid of the WP, 
all surfaces inside the WP are assumed to be coated with a thin film of water (per assumption 
5.2.8). This thin film provides the medium for diffusion from the waste form, through the SCC, 
and out of the WP. 
This approach is consistent with several features of the EBS RT Abstraction. First, the dripping 
flux onto the skirt area of the WP will flow into the SCCs, independent of gap size or film 
thickness. Second, corrosion products will quickly build up within the SCCs, helping to 
maintain a continuous fluid layer through capillary processes and possible condensation within 
the crack. Third, the WPs are angled with the lid-end upward to maximize any dripping flux into 
the SCC. Fourth, the WP configuration (lid-end upward) means that fluid can pool inside the 
WP. However, there is no pressure or head gradient driving advective flow out of the WP when 
only SCCs are present, so this will be only diffusive transport. 
If both SCCs and patches are present, then fluid can flow in through the SCCs and out through 
the patch. This advective path will be negligible compared to patch-to-patch advective flow 
because the cross-sectional area of a single SCC, 4.08 x 10-6 m2 or 4.08 mm2, is about 6,130 
times smaller than the cross-sectional area of a single patch, 25,010 mm2. The advective flow 
through SCCs is again negligible in this case as in the previous case. Radionuclide transport out 
through the SCCs is limited to diffusive transport. Once radionuclides are released through 
diffusion, they will then be transported by advection through the invert. 
It is probable that some WPs will be oriented with the lid-end downward. In this situation, the 
skirt shields the SCCs from vertical drips, making it quite difficult for any droplets or thin films 
that might be generated by a dripping flux to reach the SCCs. Even considering the potentially 
chaotic nature of droplet flow and the possible presence of dust and particulates on the surface of 
the WP, the flow must wrap around the edges of the skirt and move transverse to the 
gravitational gradient in a physically significant amount to reach the SCC and affect EBS 
performance. This behavior is considered unlikely, unless experimental data indicate a strong 
potential for transverse movement of droplets and thin films. 
The most recent WP designs have three lids: an inner lid made of stainless steel, a closure lid 
made of Alloy 22, and an extended lid made of Alloy 22 (CRWMS M&O 2000a). The extended 
lid was added late in the TSPA-SR process and is not represented by the EBS RT Abstraction. 
The new design configuration, with two lids of Alloy 22, may provide improved resistance to

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stress corrosion cracking and diffusive transport; however, these effects are not included in the 
EBS RT Abstraction. 
Within the WP, the diffusive length is taken to be the thickness of the inner lid and the closure 
lid plus the air gap between the lids. This length is 170 mm for the Naval SNF package, 135 mm 
for the 21-PWR WP and the 44-BWR WP, and 120 mm for the 5-HLW/DOE SNF short CRM 
WP (CRWMS M&O 2000f, 2000d and 2000e, respectively). 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 5. The maximum cross-sectional area of each crack for diffusive transport is calculated 
to be 4.08 x 10-6 m2 (see Section 6.3.1.2.1). 
6.4.3.2 Transport with Backfill 
As discussed in Section 6.2.3.2, breaching of the DS causes backfill to enter the axial space 
surrounding the WP. Water flux through the backfill surrounding the WP brings water up to, but 
not into, the SCCs. The backfill itself cannot penetrate a SCC because the low end of the grain 
size distribution for the Overton sand is 100 mm, about the same size as the maximum crack 
width. Since a capillary barrier is formed above the invert (fine backfill over coarse invert), the 
saturation of the backfill in direct contact with the SCCs is expected to be high. The SCCs 
should also be highly saturated with water because of the presence of corrosion products in the 
crack. 
In this situation, flow may be drawn through the SCC by capillary forces. If SCCs are the only 
penetrations through the WP, liquid can pool inside the WP if the lid-end is tilted upward. 
Substantial advective flux out of the SCC is unlikely in this configuration, so radionuclide 
release through the SCC will then be primarily by diffusion. Once released from the WP, 
radionuclides will then be transported by advection and diffusion through the invert. Note that 
the diffusive pathway through the invert is always present because the WP is assumed to be in 
contact with the invert (per assumption 5.2.9). 
If both SCCs and patches are present, then fluid can flow in through the SCCs and out through 
the patches. This advective path will be negligible compared to patch-to-patch advective flow 
because the cross-sectional area of a single SCC, 4.08 x 10-6 m2 or 4.08 mm2, is about 6,130 
times smaller than the cross-sectional area of a single patch, 25,010 mm2. The advective flow 
through SCCs is again negligible in this case as in the previous case. Radionuclide transport out 
through the SCCs is limited to diffusive transport. Once radionuclides are released through 
diffusion, they will then be transported by advection and diffusion through the invert. 
The diffusive lengths and areas for these cases are identical to the values calculated in Section 
6.4.3.1. 
6.5 DRIP SHIELD RESPONSE 
The thermal and mechanical response of the DS has been evaluated for five mechanisms: (1) 
thermal expansion, (2) floor heave, (3) rock fall, (4) seismic response, and (5) emplacement 
pallet failure. Each of these mechanisms has the potential to separate or displace adjacent DSs, 
thereby reducing the effectiveness of the DS as a barrier to seepage and flow.

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Each of these five mechanisms has been screened out of the TSPA-SR performance assessment. 
The maximum displacement from thermal expansion is less than the clearance between adjacent 
DSs, so that expansion will not alter the geometry or functionality of the DSs. The potential 
displacements from floor heave are much less than the overlap between adjacent DSs and much 
less than the height of the DS connector guide that blocks flow between adjacent DSs. Rock fall 
results in minor structural displacements for only the largest rock sizes, but never alters the basic 
geometry of the DS system. Seismic events and failure of the emplacement pallet are not 
expected to damage the DS as a flow barrier because a system of posts and mating holes 
provides a mechanical connection between adjacent DSs. This mechanical connection is 
anticipated to be strong enough to hold adjacent DSs together during a seismic event or after 
failure of the emplacement pallet. The reasoned arguments and calculations that support these 
screening decisions are described next. 
These screening decisions are also reasonable because future DS design changes will ensure that 
the DS is effective as an engineered barrier to flow and seepage. The design of the DS will 
continue to be refined for the License Application if the Yucca Mountain site is designated by 
the President. The design will be refined based on the results from the TSPA-SR calculations 
and based on design criteria that are currently under development, such as the design basis 
earthquake. These refinements will ensure that the thermal and mechanical effects discussed 
here do not impair the effectiveness of the DS as an engineered barrier. 
6.5.1 Thermal Expansion 
Thermal expansion will produce a change in the dimensions of the DS, particularly during the 
first few thousand years when DS and WP temperatures are most elevated over ambient 
conditions. The change in length due to thermal expansion will be greatest in the axial direction 
because that is the longest dimension of the DS. The response in the axial direction is also of 
most interest for DS separation. 
The coefficient of linear thermal expansion is defined as the length change per reference length 
per degree of temperature change. The coefficient for titanium Grade 7 is (ASME 1995, Table 
TE-5): 
( ). C 8.91x10 1 6 - -  = 
D
D
T l 
l 
(Eq. 6.5.1-1) 
The axial length of the DS between posts is 5510 mm. The maximum temperature at the top of 
the DS is 216C at 35 years after closure (CRWMS M&O 2000r, Table 6-7). Then the maximum 
length change, l D max, is given by: 
, 6 . 10 ) 216 )( 5510 )( 10 91 . 8 ( 6 
max mm mm x = = D - l (Eq. 6.5.1-2) 
where the as-emplaced temperature of the DS is set to zero to maximize the length change. 
This length change should be compared to the potential clearance or slippage between adjacent 
DSs. If the length change from thermal expansion is less than the potential clearance, then 
thermally-generated stresses will not develop. But if the length change from thermal expansion

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exceeds the potential clearance, then the impact of thermally-generated stresses must be 
considered. 
The clearance between adjacent DSs is determined by the clearance between the post and its 
mating hole on the DS connector plate. The connector plate does not lie directly on top of the 
adjacent DS because the connector guide, which is 50 mm high, separates these components in 
the vertical direction. The diameter of the post 50 mm above the top surface of the DS is 105.5 
mm (see Attachment I). The diameter of the mating hole is 119 mm. So the clearance between 
the mating hole and post, 13.5 mm, is greater than the maximum thermal expansion, 10.6 mm, 
and no thermal stresses are expected to develop in the DS. 
The effect of thermal expansion on DS separation has therefore been screened out from the 
TSPA-SR model. 
6.5.2 Floor Heave 
A ground support analysis for the TSPA-VA calculated the vertical and horizontal closure for an 
unsupported emplacement drift with a thermal loading of 85 metric tons of uranium per acre 
(MTU/acre). Vertical closure refers to the change in the distance between the top and bottom of 
the drift. Similarly, horizontal closure refers to the change in distance between the left and right 
sides of the drift at the springline. Net vertical closure is between 8 mm inward to 7 mm outward 
for the combined in situ and thermal loads at 150 years (CRWMS M&O 1998d, Section 7.6.2.1.2 
and Figure 7-15a). Net horizontal closure is of the same order of magnitude. Seismic loading 
did not have a significant impact on drift closure (CRWMS M&O 1998d, Section 7.6.2.1.3). 
The DS will continue to function properly provided that floor heave does not cause a fluid 
pathway to form between adjacent DSs. If this pathway forms, then water may drip on the WP 
or may wet the WP through capillary action if the EBS design has backfill and if this backfill 
forms a continuous pathway between the DSs. Either circumstance will negate the DS as an 
engineered barrier . 
The vertical displacements from floor heave are small relative to the overlap between adjacent 
DSs. The overlap is 595 mm, as shown in Attachment I. The length of overlap is then more than 
70 times greater than the displacement from floor heave. In addition, there is a DS connector 
guide that is located on the top side of the DS, below the DS Connector Plate-1. This guide acts 
as a barrier to the flow of water or backfill in the axial direction. It is 50 mm wide by 50 mm 
high, substantially greater than the displacement from floor heave. The length of the overlap and 
the presence of the guide make it very unlikely that water can flow between the DSs after floor 
heave or that sand backfill (if present) can completely fill the overlap between shields due to 
floor heave. 
The effect of floor heave on DS separation has therefore been screened out from the TSPA-SR 
model. 
6.5.3 Rock Fall for the As-Emplaced DS Configuration 
The potential ranges and distributions of rock falls have been analyzed for the Tptpmn, Tptpll, 
and Tptpln stratigraphic units under static and seismic loads for a tunnel orientation of 75

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degrees to the azimuth (CRWMS M&O 2000s, Sections 2 through 4). The range of block 
volumes from rock fall under static loads varies from 0.01 m3 to 10.63 m3 for the Tptpln unit 
(CRWMS M&O 2000s, pages 22 and 32). A level 3 seismic loads has only a modest effect, 
increasing the maximum block size to 15.45 m3 for the Tptpln stratigraphic unit (CRWMS M&O 
2000s, page 37). The 10.63 m3 block weights 25.63 MT; the 15.45 m3 block weighs 37.23 MT. 
The Tptpln unit has the largest block sizes for these three stratigraphic units. 
The largest block volumes are relatively improbable. For example, the 90th percentile block 
volume under static load is 0.50 m3, 0.27 m3, and 2.05 m3 for the Tptpmn, Tptpll, and Tptpln 
stratigraphic units, respectively (CRWMS M&O 2000s, pages 5, 20, and 24). A similar behavior 
also holds under the level 1, 2 or 3 seismic loadings. These distributions imply that most rockfall 
will be small blocks, essentially rubble, around the drip shield. The presence of this rubble is 
important because it will help to cushion the impacts from larger blocks. However, no credit is 
taken for the presence of rubble in the structural response calculations. 
The transient, dynamic response of the DS to impact from a large rock block has been evaluated 
with a detailed finite-element model (CRWMS M&O 2000t). These analyses considered blocks 
weighing 2 MT, 4 MT, 6 MT, 8 MT, and 52 MT and also considered on-center and off-center 
rock falls. The DS does not fail catastrophically for either the on-center or the off-center impacts 
(CRWMS M&O 2000t, Figures III-7 and III-15). In fact, it is seen to retain its basic mail box 
shape. However, there is some permanent deformation. For example, the permanent 
displacement of the crown of the DS is approximately 70 mm for a 6 MT block and 80 mm for a 
52 MT block. (CRWMS M&O 2000t, Figures III-10 and III-16). 
The finite-element analyses are conservative, particularly near the ends of the DS, because the 
overlap between adjacent DSs is ignored. The overlap will tend to reduce the permanent 
displacement of the crown locally, providing added stability for a part of the DS that is critical as 
a flow barrier. The degree of conservatism in ignoring the overlap has not been quantified. 
A second effect from rock fall has also been considered in these analyses. The permanent 
deformation from the rock fall generates stress concentrations and damaged regions with a 
potential for stress corrosion cracking. The number of potential cracks per DS has been 
predicted from the detailed stress fields in the finite-element calculations (CRWMS M&O 2000t, 
Table 6-1). In theory, these cracks can form advective pathways for liquid flow that can bypass 
the DS. In practice, a dense passive corrosion oxide film is expected to fill any through-wall 
SCCs in Titanium Grade 7 that form after a rock fall (CRWMS M&O 2000u, Item No. 4). In 
addition, evaporation of J-13 water slowly flowing through such a crack will lead to rapid scaling 
by calcite deposition. The ingrowth of corrosion products and the calcite deposition are expected 
to result in a very tightly plugged crack that cannot pass a significant advective flux through the 
DS (CRWMS M&O 2000u, Item No. 4). 
The DS will continue to function properly provided that the deflection of the crown does not 
cause a continuous fluid pathway to form between adjacent DSs. The permanent vertical 
displacements from rock fall are small relative to the overlap between adjacent DSs, 595 mm 
(see Attachment I). In addition, the basic shape of the DS is essentially unchanged for the 
impact of even the largest blocks. It is therefore unlikely that a rock fall will damage the DS to 
the point that it will not function as a flow barrier.

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The effect of rock fall on the as-emplaced DS has therefore been screened out from the TSPASR. 
In the as-emplaced condition, there appears to be an adequate margin of safety to ensure 
that the deflection of the crown does not cause a continuous fluid pathway to form and that SCCs 
will not provide significant advective pathways through the DS. The effect of rock fall has also 
been screened out as the DS degrades, pending more complete analyses of DS response. 
6.5.4 Seismic Response 
Seismic events are not expected to damage the DS as a flow barrier. The latest DS design has a 
system of posts and mating holes that provide a direct, mechanical connection between adjacent 
DSs (CRWMS M&O 2000c, Att. II, SK-0148 REV05). Full separation of adjacent DSs also 
requires a vertical clearance of at least 1.2 meters (CRWMS M&O 2000c, Section 6.1.1 and 
Figure 3). These features are anticipated to be strong enough to hold adjacent DSs together 
during the vibratory/ground motions general by the design basis earthquake in the emplacement 
drifts. The effects of seismic events on the DS as a flow barrier have been screened out of the 
TSPA-SR. 
6.5.5 Emplacement Pallet Failure 
Failure of the emplacement pallet has the potential to shift the DS if the WP falls to the invert 
and rolls into contact with the shield. This scenario is more likely during an earthquake, when 
the ground motions may increase the load on the pallet and impart additional momentum to the 
WP. 
The ability of a heavy WP to roll over the failed or corroded pieces of the emplacement pallet 
during an earthquake has not been analyzed. In addition, the potential DS displacements from a 
rolling WP, with or without backfill, have not been analyzed. The latest DS design has a system 
of posts and mating holes that provide a mechanical connection between adjacent DSs. Full 
separation of adjacent DSs also requires a vertical clearance of at least 1.2 meters (CRWMS 
M&O 2000c, Section 6.1.1 and Figure 3). These features are anticipated to be strong enough to 
hold adjacent DSs together after failure of the emplacement pallet. Detailed structural response 
calculations for the DS response to pallet failure may be performed before the TSPA-LA; in the 
interim, the effects of pallet failure on the DS as a flow barrier have been screened out of the 
TSPA-SR. 
An alternative scenario for pallet failure could occur if only one end of the pallet fails while the 
WP is still supported near its midpoint. In this case, the WP could swing upward after pallet 
failure, knocking the DS out of alignment and forming a fluid pathway. This alternative scenario 
is very unlikely because (1) the current pallet design does not support the WP near its midpoint, 
only at the ends (see CRWMS M&O 2000c, Attachment III), and (2) the 21 PWR, 44 BWR and 
Naval SNF WPs are emplaced closer to the invert than to the DS, so it is physically impossible to 
contact the DS. For example, the 21 PWR WP is 19 cm above the invert but 58.2 cm below the 
drip shield, so that a 19 cm swing upward at one end will not cause contact between DS and WP. 
The 5 DHLW package might contact the DS because its clearance from the DS (8 cm) is less 
than its height above the invert (22.6). However, the location of the ends of the emplacement 
pallet prevents this from happening. Assume that one end of the pallet has failed completely,

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that the other end is intact, and that the package is centered on the emplacement pallet. When the 
end of the package on the failed side of the pallet drops 22.6 cm to the invert, the other end of the 
package will rise only a fraction of this distance. This fraction depends on the length of the short 
DHLW WP, 359 cm (CRWMS M&O 2000e), and the length of the short emplacement pallet, 
250 cm (CRWMS M&O 2000c). The fraction is then the ratio of the lengths from the intact end 
of the pallet to the rising and falling ends of the package. These lengths are 54.5 cm and 304.5 
cm, respectively, for a package centered on the emplacement pallet. The fraction is then 
(54.4/304.5) = 0.179 and the end of the package rises by (0.179)(22.6cm), or about 4 cm. This is 
still less than the distance from the DS so the DHLW short package will not contact the DS. A 
similar calculation shows that the DHLW long package moves less than the DHLW short 
package, so it will also not contact the DS. 
In this circumstance, this alternative scenario has been screened out of the TSPA-SR model. 
6.6 BATHTUB MODEL FOR THE WASTE PACKAGE 
The conceptual model for the TSPA-SR is based on the presence of continuous flow paths 
through the patches, SCCs and pits that penetrate the WP. More specifically, the TSPA-SR 
conceptual model assumes that vertical flow of seepage into the WP, through the waste form and 
out of the WP is not impeded by the location of patches, SCCs and pits on the surface of the WP 
(see assumption 5.1.10). There is no long-term build-up and retention of liquid within the WP 
for flow and transport. There is also no significant resistance to the flow through the waste form. 
The TSPA-SR approach attempts to maximize the immediate release and mobilization of 
radionuclides into the local groundwater environment. The TSPA-SR approach will be referred 
to as the flow through geometry. 
An alternative conceptual model to the flow through geometry is the bathtub geometry 
(Mohanty et al. 1996). The bathtub geometry allows seepage to collect within the WP 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 fails 
abruptly beneath the water line. 
The bathtub effect will be most important during the first 20,000 years after repository closure 
because only a few patches or pits are anticipated to penetrate the DS and WP during this time 
frame. In this situation, there may be penetrations through the top of the WP while the bottom 
surface remains intact, leading to retention of liquid. At longer duration, say 100,000 years or 
greater, 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 types of radionuclide release 
mechanisms: dissolution rate limited and solubility limited. Tc-99 is typical of dissolution rate 
limited radionuclides: the Tc-99 released due to waste dissolution can always be dissolved in the 
available groundwater because the solubility limit of Tc-99 is very high. Np-237 is typical of the 
second type of radionuclide, where all the release from dissolution is limited by the low 
solubility.

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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 groundwater 
chemistry, and a step change in flow geometry, as would occur if a patch suddenly failed beneath 
the waterline. The basic geometry and flow pattern for the primary bathtub model is shown in 
Figure 6 (from Mohanty et al. 1996, Figure 2-7). qin is identical with F5 in Table 3 and in 
Section 6.3.2. 
qin = F5 
qout 
Liquid Overflow Level 
Figure 6. Schematic of the Bathtub Geometry for the Waste Package 
6.6.1 Primary Case 
6.6.1.1 Dissolution-Rate-Limited Radionuclide 
Consider the system shown in Figure 6, with a constant inflow rate, qin, and assume that Vtub is 
the total volume of liquid that can be retained within the WP before it overflows. The response 
of the WP will be a two step process. During Step 1, the package is filling with liquid and the 
outflow rate, qout, is zero. This condition continues until the WP fills with liquid at a time, Tfill, 
given by Vtub/qin. After time Tfill, the amount of liquid inside the WP remains constant and qout = 
qin. This is a steady state condition, consistent with the assumption that qin is constant and that 
liquid does not continue to accumulate within the package. Note that the following analysis 
assumes there is complete contact between the liquid and the waste form within the WP. This 
assumption is consistent with the use of a single mixing cell to represent the waste package for 
the TSPA-SR model. 
During Step 1, for time t such that , 0 fill T t < < the release of a radioisotope into the groundwater 
inside the WP can be represented as 
, Df m = & (Eq. 6.6.1-1) 
where m& is the rate of release of radionuclide into the liquid [M/T], 
D is the dissolution rate of the waste form [M/T], and 
f is the mass fraction of radioisotope released per unit mass of waste form (-) 
(f is less than one for a waste form with multiple radionuclides). 
During the fill period qout is zero, so the mass, m(t), of radioisotope dissolved within the liquid in 
the WP at time t is given by 
, ) ( Dft t m = (Eq. 6.6.1-2) 
because D and f are constant. Similarly the volume of liquid in the WP at time t, V(t), is given by

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, ) ( t q t V in = (Eq. 6.6.1-3) 
so the concentration of dissolved isotope in the WP, c(t), is 
. 
) ( 
) ( 
) ( 
in in q
Df 
t q
Dft 
t V 
t m 
t c = = = (Eq. 6.6.1-4) 
Note that the concentration, c(t), is constant during the fill phase because the values of D, f, and 
qin are assumed to be constant. This result for c(t) is not surprising because the dissolved mass, 
m, and the volume of liquid, V, are linear functions of the time, so their ratio remains constant. 
The result in Equation 6.6.1-4 will hold for each dissolution-rate-limited radioisotope in the 
waste form, although the numerical value of c will differ because the mass fraction, f, is different 
for each isotope. Note that the equations in Section 6.6 generally apply to the ith isotope in the 
waste form, although the subscript has been dropped for simplicity. 
During Step 2, when t > Tfill, the radioisotope mass within the WP is a balance between the 
release of radioisotope into the groundwater within the WP and the loss of radioisotope due to 
outflow from the WP: 
). (t c q Df m out - = & (Eq. 6.6.1-5) 
Substituting for the definition of c(t) from Equation 6.6.1-4: 
, 
) (
tub 
out V 
t m 
q Df m - = & (Eq. 6.6.1-6) 
a first order differential equation with constant coefficients. The solution to this equation for 
constant qin, with qout = qin, is derived in Attachment II and given by: 
. ) ( ) ( fill fill DfT T m t m = = (Eq. 6.6.1-7) 
It follows that . 
) ( 
) ( 
) ( 
in tub
fill 
q
Df 
V 
DfT 
t V 
t m 
t c = = = (Eq. 6.6.1-8) 
Note that the dissolved mass in the WP is constant for fill T t > . In addition, the concentration of 
dissolved radionuclide is constant for all time t > 0, as shown by Equations 6.6.1-4 and 6.6.1-8. 
These results are reasonable because the WP is in steady state for fill T t > . This means that the 
inflow rate equals the outflow rate and that any loss of dissolved radionuclide mass in the 
outflow from the WP 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, 
c(t), and the same release flux, given by c(t)qout, as the bathtub geometry. The sole difference

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between the flow-through and bathtub models is that the flux from the flow-through model starts 
from t = 0 while the flux from the bathtub model is zero until time Tfill. 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. 
The flow-through model is conservative relative to the bathtub model for radionuclide transport. 
The flow-through transport model assumes advective transport with no sorption of radionuclides. 
These assumptions are consistent with those used elsewhere in this AMR. With these 
assumptions, the flow-through transport model releases radionuclides with no delay into the 
invert and UZ, in contrast to the delay inherent in the bathtub model. 
6.6.1.2 Solubility-Limited Radionuclide 
The response for a solubility-limited radionuclide is similar to that for a dissolution-rate-limited 
radionuclide, in the sense that the bathtub model delays the release from the WP but does not 
change the dose rate. 
During Step 1, , 0 fill T t < < the amount of radionuclide dissolved in the groundwater in the WP 
can be represented as 
, in sq m = & (Eq. 6.6.1-9) 
where s is the solubility limit of the radionuclide. Assuming constant groundwater chemistry 
(assumption 5.4.1), the solubility will be constant and the mass, m, of radioisotope retained in the 
WP at time t is 
. ) ( t sq t m in = (Eq. 6.6.1-10) 
The volume of liquid in the WP at time t, V(t), is given by 
, ) ( t q t V in = (Eq. 6.6.1-11) 
so that the concentration of dissolved isotope in the WP is 
. 
) ( 
) ( 
) ( s 
t q 
t sq 
t V 
t m 
t c 
in
in = = = (Eq. 6.6.1-12) 
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 will vary. 
For t > Tfill, the mass balance within the WP is given by: 
. 
) ( 
) ( out 
tub 
in out in q 
V 
t m 
sq q t c sq m - = - = & (Eq. 6.6.1-13)

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The solution to Equation 6.6.1-13 with qout = qin is given by: 
, ) ( tub sV t m = (Eq. 6.6.1-14) 
with . ) ( s t c = (Eq. 6.6.1-15) 
Again the dissolved mass in the WP is constant for fill T t > and the concentration of dissolved 
radionuclide is constant at the solubility limit for all times t > 0 (see Equations 6.6.1-12 and 
6.6.1-15). 
The comparable flow-through model has the same radionuclide concentration, s, and the same 
release flux, given by sqout, 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 
Tfill. The bathtub model introduces a delay in the response but does not change the dose rate. 
Again, the flow-through model is conservative relative to the bathtub model because 
radionuclides are released with no delay time to the EBS. 
6.6.2 Secondary Cases 
The secondary cases evaluate the response of the bathtub model when changes occur in the 
groundwater inflow rate, in groundwater chemistry, or in the flow geometry. 
6.6.2.1 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 
the concentration within the WP remains unchanged at the solubility limit. The only change in 
the system is that the radionuclide mass flux out of the WP changes instantaneously from cqout to 
cqout, new. 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-ratelimited 
radionuclide. In this case the mass released per unit time remains constant because the 
dissolution rate remains constant, but the radionuclide concentration will come to a new 
equilibrium value. This new equilibrium value can be determined by Equation 6.6.1-8, with the 
product of concentration and liquid inflow remaining constant:
. , , Df q c q c old in old new in new = = (Eq. 6.6.2-1) 
If the inflow rate decreases, the final concentration will increase because their product remains 
constant. A flow-through model will have an instantaneous increase in concentration, while the 
bathtub model will show an exponential growth to the new concentration. The flow-through 
model is then conservative for concentration released into the EBS.

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The exponential growth to the new concentration can be seen as follows. The replacement of 
old groundwater with concentration cold with new groundwater with concentration cnew can 
be represented through a parameter b, the volume fraction of old groundwater to Vtub, the total 
liquid volume in the bathtub. The rate of change of the volume of old groundwater, Vold, is given 
by: 
. , , new in new out 
old q q 
dt 
dV b b - = - = (Eq. 6.6.2-2) 
Equation 6.6.2-2 represents the loss of old groundwater through outflow, with the factor b 
representing the (decreasing) volume fraction of old groundwater that is lost. Since by 
definition, 
, 
tub 
old 
V
V  b (Eq. 6.6.2-3) 
and substituting this definition into the left-hand side of Equation 6.6.2-2, it follows that: 
. , b 
b 
tub 
new in 
V 
q 
dt 
d - = (Eq. 6.6.2-4) 
The solution to Equation 6.6.2-4 is an exponential decay of b from 1 to 0, which corresponds to 
an exponential decay of c from cold to cnew. 
If the inflow rate increases, the concentration will decrease. A flow-through model will have an 
instantaneous decrease in concentration, while the bathtub model will exponentially relax to the 
new concentration. The flow-through model is then less conservative for concentration released 
into the EBS. Note that the mass of radionuclide mobilized is identical, as implied by Equation 
6.6.2-1; but the dissolved concentration will vary with the amount of fluid flowing through the 
system. The TSPA-SR model passes mass to the UZ, rather than concentration, so the difference 
between the flow through model and the bathtub model for this case is probably not critical to 
performance. 
Finally, a change in inflow rate during the initial period, when the bathtub is filling, only affects 
the value of Tfill and hence the delay until the bathtub fills, after which it will behave as described 
in Section 6.6.1. 
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 conservative than the flow-through 
model when the inflow rate decreases (and concentration increases). If the inflow rate increases 
(and concentration and probably dose decreases), the bathtub model will be more conservative 
than the flow-through model.

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6.6.2.2 Change in Groundwater Chemistry 
Consider a step change in groundwater 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 groundwater composition. Eventually the old groundwater will be flushed out and 
replaced with the new groundwater, resulting in new concentrations within the bathtub. 
The replacement of old with new groundwater can be represented through a parameter b, 
representing the volume fraction of old groundwater to Vtub, the total liquid volume in the 
bathtub. The rates of change of the volumes of old and new groundwater are given by: 
, out 
old q 
dt 
dV b - = (Eq. 6.6.2-5) 
and , ) 1 ( out in 
new q q 
dt 
dV b - - = (Eq. 6.6.2-6) 
where Vold and Vnew represent the volumes of groundwater with the old and new chemistries, 
respectively. Equation 6.6.2-5 represents the loss of old groundwater through outflow, with the 
factor a representing the volume fraction of old groundwater that is lost. Equation 6.6.2-6 
represents the addition of new groundwater through 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 b b + = - = (Eq. 6.6.2-7) 
By definition , 
tub 
old 
V
V  b (Eq. 6.6.2-8) 
and substituting this definition into the left-hand equation in 6.6.2-7 it follows that: 
. 
1 b b 
b 
fill tub 
in 
T V
q 
dt 
d - = - = (Eq. 6.6.2-9) 
The solution to Equation 6.6.2-9 with the boundary condition 1 ) 0 ( = b , is given by 
, ) ( fill T
t 
e t 
- 
= b (Eq. 6.6.2-10) 
It follows that the old and new volumes of groundwater are given by: 
fill T
t 
tub old e V V 
- 
= (Eq. 6.6.2-11)

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and . 1   

 
  

 
- = 
- 
fill T
t 
tub new e V V (Eq. 6.6.2-12) 
These equations say that the volume fraction of groundwater with the old chemistry decays 
exponentially with the characteristic time Tfill. Alternatively, the volume fraction of new 
groundwater increases to 1.0 with a characteristic time of Tfill for the exponential growth given 
by Equation 6.6.2-12. 
The impact of changing groundwater chemistry on dissolution rate or solubility is much more 
difficult to predict analytically because chemical interactions are very nonlinear. More 
specifically, the pH of mixtures of groundwaters will not be proportional to a 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. 
Nonlinear response makes it particularly difficult to predict the time-dependent response for 
(say) 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 
T
t 
old e s e s t s (Eq. 6.6.2-13) 
Consider the response when . old new s s >> 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 snew, Equation 6.6.2-13 becomes 
) ( old new s s >> . 1 ) (   

 
  

 
-  
- 
fill T
t 
new e s t s (Eq. 6.6.2-14) 
In effect the initial solubility is negligible compared to snew, and solubility at late times increases 
to snew from below. Alternatively, if , old new s s << 
) ( new old s s >> . ) ( new 
T
t 
old s e s t s fill +  
- 
(Eq. 6.6.2-15) 
Here the solubility will decay towards a much smaller value in the new groundwater mixture. 
While the details of the time-dependent behavior are unknown, the starting and ending states 
must be accurate and Equations 6.6.2-14 and 6.6.2-15 provide a simplified approximation to the 
transition from one chemical regime to another. Note also that the dissolution rate could replace 
solubility in Equations 6.6.2-13 through 6.6.2-15, and the same general conclusions would hold.

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In summary, the response of the bathtub model to a change in groundwater chemistry will be 
slower than that for a flow-through model, where the solubility or dissolution rate will change 
abruptly with a step change in groundwater chemistry. The bathtub damps or delays the 
response to a change in groundwater chemistry over a time scale on the order of perhaps Tfill to 
7Tfill. The upper estimate of 7Tfill corresponds to an exponential factor of e-7 or 0.0009, at which 
point Equation 6.6.2-15 should have asymptoted to snew. 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 is conservative when solubility increases because the bathtub geometry 
delays the increase in radionuclide concentrations and mass fluxes from the WP to the EBS. 
Note that 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 conservative when 
solubility or dissolution rate decreases is therefore of less importance for performance 
assessment and is of secondary importance in selecting the conceptual model for flow through 
the WP. 
6.6.2.3 Change in Patch Geometry 
The geometry for the bathtub model allows seepage to collect within the WP before being 
released to the EBS. In the primary model (Figure 6), the patch is positioned such that release is 
governed by the condition in out q q = after the package fills with liquid. 
An alternative conceptual model does not have an existing patch on the side of the package, but 
instead allows the second patch to fail abruptly beneath the water line. While the radionuclide 
concentration within the WP is unchanged by the alternative location, failure will result in the 
sudden release of a larger pulse (mass) of radionuclides at the failure time of the second patch. 
Mathematically, the flux of radionuclides leaving the WP in the primary model, Fpri, is given by: 
, 
fill 
tub 
in out pri T
V 
c cq cq F = = = (Eq. 6.6.2-16) 
and the flux of radionuclides leaving the WP in the alternative model, Falt, is given by: 
, 
T 
V 
c F tub 
alt D 
= (Eq. 6.6.2-17) 
where DT is the time to empty the retained liquid through the second patch. In theory, it is 
possible that DT << Tfill, so that Falt >> Fpri. 
Equations 6.6.2-16 and 6.6.2-17 have the same value for radionuclide concentration, c, in the 
retained liquid because the chemistry of the groundwater is independent of patch location. 
Equations 6.6.2-16 and 6.6.2-17 also assume that the second patch in the alternative conceptual 
model fails when the volume of liquid is identical to the capacity of the WP in the primary 
model.

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It is worth noting that 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 returns to the same flux as the flow-through model. In other words, the flowthrough 
model represents a time average of the response of the bathtub model. From this 
viewpoint, the potential difference Falt and Fpri will be partly mitigated by the sorption and 
diffusion processes in the unsaturated and saturated zones. The potential difference between Falt 
and Fpri will also be small if the second patch fails shortly after the first penetration because there 
will be less retained liquid. 
This alternative scenario can also be thought of as being equivalent to the appearance of 
additional penetrations in the WP. This analogy is appropriate because additional penetrations in 
the WP increase the groundwater flux into the waste form, resulting in higher releases to the 
EBS. The main effect of the alternative conceptual model is to generate this increase earlier. 
This is not considered a major difference because there is a very wide range of variability in 
corrosion rates for the TSPA-SR model (CRWMS M&O 2000h). The effect of the alternative 
conceptual model can then be reasonably considered to be captured within this variability. 
The results and observations in this section (6.6.2.3) and throughout Section 6.6 are appropriate 
for the general boundary conditions considered here. In other words, this comparison is based on 
the full fluid flux into the WP having access to all radioisotopes in the waste. An alternative 
conceptual model, in which radionuclides are mobilized in a rind of corrosion products around 
the fuel pellets, will partly mitigate 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 rind of corrosion products. The situation is then 
similar to that mentioned at the end of Section 6.6.2.1, where mass transfer to the UZ is the 
dominant issue, rather than dissolved concentration. 
6.6.3 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 groundwater 
chemistry, and a change in flow geometry, as would occur if a patch suddenly failed 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 WP 
to the EBS in comparison to the flow-through model for the primary case. The flowthrough 
model is conservative 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

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concentration and mass flux associated with the new inflow rate. The flow-through 
model is conservative 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. 
 The response of the bathtub model to a step change in groundwater chemistry 
(secondary case 2) is to delay the change in concentration and mass flux associated with 
the new groundwater chemistry. Analytical models cannot define the exact time delay, 
which will be sensitive to nonlinear chemical effects when groundwaters mix. Limiting 
cases, when 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 is conservative with respect to the bathtub geometry when 
solubility or dissolution rate increase with changing groundwater chemistry. The flowthrough 
model is conservative because it has an instantaneous change to the higher 
equilibrium value while the bathtub geometry delays the change until the old 
groundwater is flushed out of the WP. Note that the case of increasing radionuclide 
concentrations and fluxes is of primary interest from a performance or regulatory 
viewpoint, so the lack of conservatism of the flow-through model for decreasing 
solubility or dissolution rate is ignored here. 
 The response of the bathtub model when a second patch opens instantaneously beneath 
the water level in the WP (secondary case 3) has been analyzed. The impact of the 
instantaneous opening is to release a pulse (additional mass) 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 WP. Note that 
there is a wide range of variability in corrosion rates for the TSPA-SR model, and the 
impact from the instantaneous opening is probably encompassed in the uncertainty in 
corrosion rates. 
The impact of this alternative flow path has therefore been screened out of TSPA-SR 
analyses because of the potential mitigation from sorption and diffusion and because the 
variability of corrosion rates provides substantial uncertainty in radionuclide fluxes from 
the WP.

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7. CONCLUSIONS 
The EBS RT Abstraction for the flow of water and the transport of radionuclides in the EBS has 
been defined in this AMR. This model is a reasonably bounding model because it is designed to 
overestimate flow through the DS and into the WP and transport out of the EBS. Future efforts 
will refine some of the approximations in the current model in order to have a more realistic yet 
still conservative approach for licensing calculations. 
7.1 CONCEPTUAL MODEL SUMMARY 
Radionuclide transport out of the waste form and WP, through the invert, and into the UZ is 
dependent on a complex series of events in the repository. After the WPs 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 and wick into the drifts and subsequently contact some of the DSs. Over 
time, the DS, WP, and other components of the EBS are expected to degrade, leading to the 
mobilization and transport of radionuclides through the EBS to the UZ. The primary transport 
medium through the EBS is anticipated to be water. Either a thin film or moving water is 
necessary for radionuclide transport out of the WP and through the invert to the UZ. 
A number of key factors will affect the mobilization and transport of radionuclides through the 
EBS: 
 Performance of the DSs 
 Performance of the WPs 
 Protection provided by cladding 
 Waste form degradation rates 
 Entry and movement of water through WPs 
 Solubilities of radionuclides 
 Transport of radionuclides through and out of the WPs 
 Transport of radionuclides through the invert below the WPs 
 Colloidal transport of radionuclides 
Once a DS is breached, water may contact the WP. Once a WP is breached, water may enter the 
package as water vapor or as drips. If the cladding around spent fuel pins or the canister around 
a vitrified waste form is also breached, radionuclides may start to dissolve in the water. The 
dissolved concentration of each radionuclide mobilized from the waste form cannot exceed the 
radionuclide solubility limit, unless suspended colloids are included. Colloids may be important 
for two reasons: they may increase the release of radionuclides from the WP, and they may 
increase the transport velocity of radionuclides. Radionuclides mobilized in water as dissolved 
or colloidal species may then be transported by advective and diffusive transport from the waste 
form, through the WP, and out of breaches in the WPs. Once outside the package, the 
radionuclides will be transported through the invert predominantly by diffusion, if water is not 
flowing through the invert, or by advection, if an appreciable amount of water is flowing through 
the invert.

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The conceptual model for flow through the EBS identifies nine key flow pathways. These 
pathways and their relationships are summarized in the following list and in Table 8. Sections 
6.1.1, 6.2, and 6.3 contain a detailed technical discussion of the EBS flow abstraction. 
 Seepage Flux and Capillary FluxThese are the input fluxes or boundary conditions. 
The seepage flux is valid for the nonbackfilled EBS (the design baseline for TSPA-SR, 
CRWMS M&O 2000a) or for a backfilled EBS. The capillary flux is only applicable to 
the backfilled EBS. 
 Through the DS to the WPFlux through the DS is based on the ratio of the axial 
lengths of breaches in the DS to the total axial length of the DS. The number of patches 
and pits in the DS and WP are calculated by the WP Degradation software (WAPDEG). 
 DS to Unsaturated Zone (Diversion around DS)Any seepage flux that doesnt go 
through the DS is assumed to bypass the EBS and flow straight into the UZ. 
 Through the WP to the WFFlux into the WP is proportional to the product of the flux 
through the DS and the ratio of the lengths of patches and pits in the WP to the total 
axial length of the WP. 
 WP to Invert (Diversion around WP)Flow that doesnt go through the WP is diverted 
to the invert. 
 Invert to WP (Evaporation)If the DS is cooler than the invert, all the evaporative flux 
from the invert is assumed to drip on the WP. If the DS is hotter than the invert, there is 
no dripping on the WP from the evaporative flux. Current thermal-hydrologic 
calculations indicate that condensation does not occur on the underside of the DS. 
 Waste Form to InvertAll the flux from the WP flows to the invert, independent of 
patch/pit location on the WP. 
 Invert to UZAll the flux into the invert is released into the UZ. 
Table 8. Summary of EBS Flow Abstraction 
Flow Pathway Flow Parameters Data Sources & Notes 
1. Seepage flux, F1 Seepage flux is a boundary condition 
for the EBS flow abstraction 
(CRWMS M&O 2000i) provides 
time-dependent and locationdependent 
values of seepage 
flux. 
2. Capillary flux, F2 Capillary flux is a boundary condition 
for the EBS flow abstraction. 
Capillary flux will be determined by 
abstraction of computational 
results from the NUFT code 
(CRWMS M&O 2000j). 
3. Flux through the DS, F3 F3 = (F1 + aF2) x (LDS_SCC + LDS_Patch 
+ LDS_Pit + LDS_Gap)/LDS; 
a is a factor between 0 and 1 based 
on the design and backfill 
properties, if present; 
(see Section 6.2.4) 
WAPDEG (CRWMS M&O 1998c) 
will provide the number of 
patches, pits and SCCs on the 
DS; 
patch size is constant: 7.21 x 104 
mm2 (CRWMS M&O 2000b); 
LDS Patch = (7.21 x 104)0.5 = 269 mm 
LDS Gap is calculated from a seismic 
response model (see Section 
6.5.4) 
4. Diversion around DS, F4 F4 = F1 + aF2 - F3. 
(see Section 6.2.4) 
Continuity of liquid flux (quasisteady 
flow) 
5. Flux into the WP, F5 F5 = (F3 + F7) x (LWP_Patch + 
LWP_Pit)/LWP + (F3 + F7) x (LWP 
SCC)/(LWP + LWP_SCC) for the 
WAPDEG will provide the number 
of patches, pits and SCCs on the 
WP;

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Flow Pathway Flow Parameters Data Sources & Notes 
baseline design (no backfill); F5 = 
(F3 + F7) x (LWP_Patch + 
LWP_Pit)/LWP + F7 (LWP SCC)/(LWP + 
LWP_SCC) if the EBS is backfilled. 
(see Section 6.3.2) 
patch size is constant: 2.346 x 104 
mm2 (CRWMS M&O 2000b); 
LWP Patch = (2.346 x 104)0.5 = 158 
mm 
LWP_SCC is calculated based on the 
maximum tilt angle of the WP 
and the diameter of the closure 
lid (see Section 6.3.2) 
6. Diversion around the WP, F6 F6 = F3 + F7 - F5 
(see Section 6.3.2) 
Continuity of liquid flux (quasisteady 
flow) 
7. Evaporative flux, F7 If TDS < TInvert, then F7 is the 
evaporative flux calculated by NUFT; 
else F7 = 0. 
(see Section 6.3.3) 
Data for temperatures and 
evaporative flux are based on an 
abstraction of NUFT calculations 
(CRWMS M&O 2000j). 
8. Flux to the invert, F8 F8 = F5 
(see Section 6.3.4) 
Quasi-steady, flow-through 
assumption for WP 
9. Flux to the UZ, F9 F9 = F6 + F8  F7 
(see Section 6.3.4) 
Quasi-steady flow-through 
assumption for invert. Note that 
only F8 can transport radionuclides 
through the invert. 
The waste form is the source of all radionuclides in the potential repository system. 
Radionuclides can be transported downward, through the invert and into the UZ. Transport can 
occur through advection when there is a fluid flux through the WP, and by diffusion through thin 
films in the WP when there are SCCs in the lids of the package. The concentration of each 
radionuclide during transport is limited by the sum of its (dissolved) solubility limit and the 
presence of any colloidal particles that may act as reversible or irreversible carriers for the 
radionuclide. 
Transport through the quartz sand backfill, if present, is anticipated to be negligible under any 
conditions. Before the DS fails, upward diffusion through the backfill will be negligible for two 
reasons. First, a continuous, direct flow path does not exist between the WP and the backfill 
while the DS is intact. Second, the circuitous pathway that goes down to the invert, laterally 
across the invert and then upward through the backfill will most likely be dominated by any 
seepage or capillary fluxes moving through the backfill toward the UZ. After the DS fails 
upward diffusion will be negligible in comparison to the downward advective flux through the 
DS. 
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 porosity and time-dependent saturation 
in the invert are conservatively 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 estimated to be the diffusion coefficient for a dissolved species divided 
by a factor of 100. 
No credit is taken for the potential for sorption in the waste form, WP or invert. Partition 
coefficients for all radionuclides are conservatively set to zero in the WP and invert. 
The conceptual model for transport through the EBS focuses on the flow from the waste form to 
invert and from the invert to the UZ. The transport pathways and transport processes (advection

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or diffusion) are summarized in Table 9. Sections 6.1.2 and 6.4 contain a detailed technical 
discussion of the EBS transport abstraction. 
Table 9. Summary of EBS Transport Abstraction 
Transport Pathway Transport Modes Transport Parameters and Data Sources 
1. Through 7. None No transport is expected along pathways 1. through 7. 
(see Section 6.4) 
8. WP to invert (F8) Diffusion through SCCs; 
Diffusion and advection 
through patches; 
Diffusion and advection 
through pits (if present) 
Fluid flux for advection = F8: 
No retardation in waste form/WP; 
No lateral or forward dispersion; 
Colloidal particles will transport radionuclides. 
Diffusive area for each SCC is given by 4.08 x 10-6 m2 
(see Sections 6.3.1.2.1 and 6.4.3); 
Diffusive area for each patch is 2.346 x 104 (mm)2 
(1000 nodes on the surface of the WP); 
Diffusive length in WP is 135 mm to 185 mm 
depending on WP type (see Section 6.4.3) 
Diffusion coefficient (all radionuclides): 
- 2.299 x 10-5 cm2/s at 25C (see Section 6.4.1.1) 
- Corrected for porosity, saturation and temperature 
(see Sections 6.4.1.2 and 6.4.1.3) 
- Reduced by a factor of 100 if radionuclide is bound 
to a colloid (see Section 6.4.2) 
9. Invert to UZ (F9) Diffusion and advection 
through the invert; 
Fluid flux for advection = F9 = F8; 
No retardation in waste form/WP; 
No lateral or forward dispersion; 
Colloidal particles will transport radionuclides. 
Diffusive length = 0.606 m (max thickness of invert; 
see Table 1); 
Diffusion coefficient (all radionuclides): 
- 2.299 x 10-5 cm2/s at 25C (see Section 6.4.1.1) 
- Corrected for porosity, saturation and temperature 
(see Sections 6.4.1.2 and 6.4.1.3) 
- Reduced by a factor of 100 if radionuclide is bound 
to a colloid (see Section 6.4.2). 
The flow cross-sectional areas, Ainvert and Auz, assume 
a cylindrical geometry corresponding to the low half 
of the WP lying on the invert. Ainvert is one-half the 
surface area of the WP and AUZ is the corresponding 
surface area at a radius equal to the radius of the 
WP plus the thickness of the invert. 
The invert diffusion calculation uses radionuclide 
concentrations in the WP as the boundary condition 
at the top of the invert and a swept away (effectively 
zero) radionuclide concentration at the interface with 
the UZ. 
The thermal and mechanical response of the DS is an important factor in EBS performance. The 
thermal and mechanical response of the DS has been evaluated for five mechanisms: (1) thermal 
expansion, (2) floor heave, (3) rock fall, (4) seismic response, and (5) emplacement pallet failure. 
The latest DS design (CRWMS M&O 2000c, Att. II, SK-0148 REV05) has a system of posts and 
mating holes that provide a strong, mechanical connection between adjacent DSs and ensure the 
performance of the DS as a flow barrier for the EBS. 
Thermal expansion has been screened out because there is enough clearance between the posts 
and their mating holes to accommodate the maximum axial expansion. Floor heave and rock fall

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will produce minor structural response in relation to the potential overlap between adjacent DSs. 
These mechanisms have therefore been screened out from the TSPA-SR. The system of posts 
and mating holes is anticipated to be strong enough to hold adjacent DSs together during the 
vibratory/ground motions general by the design basis earthquake and during the potential effects 
from failure of the emplacement pallet. The DS design will continue to be refined if the Yucca 
Mountain site is designated by the President. Detailed structural response calculations may be 
performed before the TSPA-LA; in the interim, the effects of seismic events on the DS as a flow 
barrier have been screened out of the TSPA-SR. 
7.2 MODEL VALIDATION 
The emphasis in this AMR is on a reasonable approach that bounds the response of the EBS. The 
EBS RT Abstraction is a conceptual model for flow and transport through the EBS. It is based 
on typical flow processes, such as the seepage/flow of liquid water through the EBS and the 
potential for condensation on the underside of the DS. The transport abstraction is based on the 
diffusive and advective processes for dissolved and colloidal species that are commonly 
considered for contaminant transport calculations. The use of reasonable bounds is appropriate 
because of the uncertainty in the response of a very complex engineered system over long 
periods of time. 
The EBS RT Abstraction is valid and appropriate for its intended use because it is designed to be 
represent fundamental flow and transport processes in a bounding or conservative framework. 
The following features provide confidence in the Abstraction: 
 The flow splitting algorithm is based on a quasi-steady approach. This approach is 
appropriate for slowly varying flow systems that are close to steady state conditions, as 
will exist for most of the lifetime of the repository. The steady state approach preserves 
conservation of mass for the seeping fluid and enhances immediate release of 
radionuclides from the WP. 
 The transport abstraction is based on the diffusive and advective processes that are 
commonly used in a wide variety of situations (Freeze and Cherry, 1979). The 
conceptual models for contaminant transport are widely accepted in the scientific 
community. 
 The model for the diffusion coefficient is based on an extensive data set for a variety of 
granular materials, including crushed tuff (Conca and Wright, 1992). These data include 
the effects of saturation and porosity and are directly applicable to the invert. The model 
for the diffusion coefficient also corrects for the effect of temperature through the Nernst 
Einstein equation, a well-accepted approach. 
 The results from multi-dimensional thermal hydraulic models provide abstracted 
boundary conditions for EBS flow processes. For example, these boundary conditions 
define the seepage flux into the EBS as a function of time and location in the repository 
and define the saturation in the invert as a function of time and location. This approach 
couples the EBS abstraction with the most detailed descriptions of thermal hydraulic 
processes in the drifts and near-field that are currently available. . 
Many details of EBS flow and transport have substantial uncertainty, particularly when complex 
processes are represented as a one-dimensional abstraction. It is appropriate to use bounding

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approximations when substantial uncertainties are thought to exist. Following are the 
noteworthy bounding approximations or conservatisms in this abstraction: 
 Seepage through the DS always falls on a WP. DS placement in the current potential 
repository design is such that the overlap between adjacent DSs should be above the 
small axial gap between adjacent packages (CRWMS M&O 2000a). It is then possible 
that seepage through the DS will fall directly to the invert, missing the WP entirely. 
This feature is conservatively ignored. 
 Seepage is assumed to uniformly wet the DS and WP. The pathways for seepage into 
the drifts are fractures or fracture sets. As a result, seepage will vary spatially and 
temporally over the approximately 10,000 waste packages in the potential repository. 
Therefore, the response of groups of waste packages is represented as averages for 
performance assessment. In addition, it is assumed that any breach is located so that it 
will collect all fluid that drips onto the drip shield or waste package at the same axial 
location as the breach. This assumption conservatively ignores the fact that fluid 
dripping onto the lower portion of the drip shield or waste package will not flow through 
a breach high on the drip shield or waste package. It also conservatively ignores the fact 
that seepage on the left half of a drip shield or waste package cannot flow through a 
breach on the right half. 
 Diffusive transport is maximized because transport is always possible through 
SCCs and because the WP is in contact with the invert. The waste form is assumed 
to be covered with a thin liquid film that supports diffusive transport at all times. In 
addition, the WP is assumed to be in contact with the invert, providing a continuous 
liquid pathway for diffusion. Radionuclides will then be released by diffusion through a 
SCC, even when the DS is intact and there is no advective flux into the WP. Note that 
this transport pathway will also function when the package is hot and in-package 
evaporation may be significant enough to dry out the thin liquid films on the waste form. 
 Release of radionuclides through advective transport is independent of the location 
of breaches on the WP. Advective transport out of the WP is based on a flow-through 
model that is independent of the location of penetrations through the WP or the DS. 
This means that a WP with only one penetration or a WP with one or more penetrations 
on its upper surface and none on its lower surface will still have advective transport into 
the invert. 
 Evaporation within and on the WP is ignored. Diffusive or advective transport will 
cease if the heat from the waste form can evaporate any thin liquid films on the waste 
form or evaporate a small seepage flux on the surface of the WP. The potential for 
evaporation to eliminate radionuclide transport is conservatively ignored in the EBS RT 
Abstraction. 
 Bounding value for diffusion coefficient. The use of a bounding diffusion coefficient 
for all radionuclides may overestimate the diffusion coefficient of actinide complexes by 
an order of magnitude. The effect of porosity and liquid saturation on the free water 
diffusion coefficient has been included in a conservative manner. These assumptions 
enhance diffusion.

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7.3 EVALUATION OF NRC ISSUE RESOLUTION STATUS REPORT CRITERIA 
This document defines the abstraction model for flow of liquid and transport of radionuclides 
through the EBS. Being conceptual in nature, it is not possible to evaluate many of the IRSR 
acceptance criteria in Section 4.2. For example, sensitivity studies have not yet been performed 
with the full TSPA-SR model and are beyond the scope of this document. 
The relevance of this AMR to the NRC IRSR criteria for the ENFE KTI is as follows: 
From Section 4.2.1.1 (Applicable Data and Model Justification Acceptance Criteria), Criteria 
1, 2, and 3 are addressed by this abstraction. With regard to Criteria 3, much of the data used 
in this abstraction needs further work in terms of its completeness and its quality assurance. 
Criteria 4 and 5 are outside the scope of this AMR. 
From Section 4.2.1.2 (Applicable Data Uncertainty and Verification Acceptance Criteria), 
Criteria 1, 2, and 3 are addressed by this abstraction. With regard to Criterion 2, much of the 
data used in this abstraction needs further work in terms of its completeness and its quality 
assurance. Criteria 4 and 5 are outside the scope of this AMR. 
For Section 4.2.1.3 (Model Uncertainty Acceptance Criteria), Criteria 2 and 3 are addressed 
by this AMR. Note that other alternative modeling approaches may be considered in 
response to future design changes for the EBS. Criterion 1 is outside the scope of this AMR. 
For Section 4.2.1.4 (Model Verification Acceptance Criteria), Criterion 1 is addressed by this 
abstraction. Criteria 2 and 3 require computational testing that is beyond the scope of this 
AMR. 
For Section 4.2.1.5 (Integration Acceptance Criteria), Criteria 1 and 2 are addressed by this 
abstraction. Criteria 3 and 4 require computational testing and sensitivity studies that are 
beyond the scope of this AMR. 
For Section 4.2.1.6 (Programmatic Acceptance Criteria), Criterion 1 is addressed by this 
abstraction. With regard to Criterion 2, much of the data used in this abstraction needs further 
work in terms of its completeness and its quality assurance. Criterion 3 is not applicable to 
this AMR because expert elicitation has not been used to develop this abstraction. 
The relevance of this AMR to the NRC IRSR criteria for the CLST KTI is as follows: 
For Section 4.2.2.1 (General Acceptance Criteria for All Subissues), Criteria 1, 3, 5, 6, 7, and 
9 are addressed in this AMR. Again, much of the data used in this abstraction needs further 
work in terms of its completeness and its quality assurance before Criterion 3 can be 
resolved. Criteria 2, 4 and 8 are outside the scope of this AMR. 
For Section 4.2.2.2 (Applicable Acceptance Criteria for Subissues 3 and 4), these criteria are 
not directly addressed in this AMR. The emphasis in these criteria is on the mobilization of 
radionuclides from SNF and HLW, rather than transport through the EBS to the UZ. Criteria 
2, 3, and 4 involve detailed calculations or testing and are beyond the scope of this AMR.

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The final element of Criterion 1, release of radionuclides from the WP emplacement drifts, is 
addressed by this AMR. 
For Section 4.2.2.3 (Applicable Acceptance Criteria for Subissue 6), criteria 1 and 2 are 
addressed by this AMR. Criterion 3 is beyond the scope of this AMR. 
The relevance of this AMR to the NRC IRSR criteria for the TEF KTI is as follows: 
For Section 4.2.3.1 (Acceptance Criteria for Subissue 3), criteria 1, 2, 3, and 4 are addressed 
by this AMR. With regard to the need for sufficient data in criterion 4, much of the data used 
in this abstraction needs additional work in terms of its completeness and quality assurance 
before this criterion can be resolved with the NRC. 
7.4 TO BE VERIFIED (TBV) IMPACT 
There can be significant impacts to this conceptual model due to potential changes in TBV 
inputs. There is one TBV input item defined in this AMR that pertains to these impacts: the selfdiffusion 
coefficient of water at 25C (2.399 x 10-5 cm2/s) (MO0002SPASDC00.002). 
The self-diffusion coefficient of water is used as a bounding value for the diffusion coefficient of 
all radionuclides considered in the TSPA-SR. The numerical value of the self-diffusion 
coefficient directly impacts the magnitude of diffusive transport through the EBS to the UZ. 
This document may be affected by technical product input information that requires 
confirmation. Any changes to the document that may occur as a result of completing the 
confirmation activities will be reflected in subsequent revisions. The status of the input 
information quality may be confirmed by review of the Document Input Reference System 
database. 
7.5 FEPS EVALUATION 
Although the FEPs found in Table 2 are discussed in this document, they cannot be fully 
resolved until the results with this conceptual model are evaluated through a complete analysis 
and sensitivity study of results from the TSPA-SR.

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8. INPUTS AND REFERENCES 
8.1 DOCUMENTS CITED 
ASME (American Society of Mechanical Engineers) 1995. Materials. Section II of 1995 
ASME Boiler and Pressure Vessel Code. New York, New York: American Society of 
Mechanical Engineers. TIC: 245287. 
Atkins P.W. 1990. Physical Chemistry. 4th Edition. New York, New York: W. H. Freeman and 
Company. TIC: 245483. 
Cantrel, L.; Chaouche, R.; and Chopin-Dumas, J. 1997. "Diffusion Coefficients of Molecular 
Iodine in Aqueous Solutions." Journal Chemical Engineering Data, 42, 216-220. Washington, 
D.C.: American Chemical Society. TIC: 246757. 
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. 
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EBS Radionuclide Transport Abstraction 
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CRWMS M&O 1999d. Request for Repository Subsurface Design Information to Support TSPASR. 
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CRWMS M&O 2000k. Seepage Model for PA Including Drift Collapse. MDL-NBS-HS-000002 
REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19990721.0525.

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 00 ICN 02 91 of 95 September 2000 
CRWMS M&O 2000l. Multiscale Thermohydrologic Model. ANL-EBS-MD-000049 REV 00. 
Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20000609.0267. 
CRWMS M&O 2000m. Water Diversion Model. ANL-EBS-MD-000028 REV 00. Las Vegas, 
Nevada: CRWMS M&O. ACC: MOL.20000107.0329. 
CRWMS M&O 2000n. Stress Corrosion Cracking of the Drip Shield, the Waste Package Outer 
Barrier and the Stainless Steel Structural Material. Input Transmittal 00218.T. Las Vegas, 
Nevada: CRWMS M&O. ACC: MOL.20000411.0232. 
CRWMS M&O 2000o. Invert Diffusion Properties Model. ANL-EBS-MD-000031 REV 01. Las 
Vegas, Nevada: CRWMS M&O. ACC: MOL.20000912.0208. 
CRWMS M&O. 2000p. Waste Form Colloid-Associated Concentrations 
Limits: Abstraction and Summary. ANL-WIS-MD-000012 REV 00, Las Vegas, Nevada: 
CRWMS M&O. ACC: MOL.20000525.0397.. 
CRWMS M&O 2000q. In-Drift Colloids and Concentrations. ANL-EBS-MD-000042 REV 00. 
Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20000509.0242. 
CRWMS M&O 2000r. Drift Scale Thermal Analysis. CAL-WIS-TH-000002 REV 00. Las 
Vegas, Nevada: CRWMS M&O. ACC: MOL.20000420.0401. 
CRWMS M&O 2000s. Preliminary Rock Block Information. Input Transmittal 00154.T. Las 
Vegas, Nevada: CRWMS M&O. ACC: MOL.20000403.0429. 
CRWMS M&O 2000t. Rock Fall on Drip Shield. CAL-EDS-ME-000001 REV 00. Las Vegas, 
Nevada: CRWMS M&O. ACC: MOL.20000509.0276. 
CRWMS M&O 2000u. Rock Fall Calculations for Drip Shield. Input Transmittal PA-WP- 
00056.Tb. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20000518.0135. 
Freeze, R.A. and Cherry, J.A. 1979. Groundwater. Englewood Cliffs, New Jersey: Prentice-Hall. 
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Electrolytes at 25C. American Institute of Physics Handbook. 3rd Edition. Page 2-223. New 
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Number-247425.

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Haltier, E.; Fourest, B.; and David, F. 1990. "Spectroelectrochemical Study of Uranium and 
Cerium in Carbonate Media ." Radiochimica Acta, 51, 107-112. Mnchen, Germany: R. 
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through V3. ACC: MOL.20000302.0344. 
Lide, D.R. and Frederikse, H.P.R., eds. 1997. CRC Handbook of Chemistry and Physics. 78th 
Edition. Boca Raton, Florida: CRC Press. TIC: 243741. 
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Flow and Transport in Fractured Rocks." Water Resources Research, 34, (10), 2633-2646. 
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McCord, J.T.; Stephens, D.B.; and Wilson, J.L. 1991. "Hysteresis and State-Dependent 
Anisotropy in Modeling Unsaturated Hillslope Hydrologic Processes." Water Resources 
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Recharge Estimation Using Environmental Tracers: Numerical Modeling Investigation." Water 
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238284. 
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Archaeological Bone." Geochimica et Cosmochimica Acta, 60, (12), 2139-2152. New York, 
New York: Pergamon Press. TIC: 246791. 
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238072.

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ANL-WIS-PA-000001 REV 00 ICN 02 94 of 95 September 2000 
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Environment. Rev. 2. Washington, D.C.: U.S. Nuclear Regulatory Commission. ACC: 
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8.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER 
MO0002SPASDC00.002. Self-Diffusion Coefficient of Water. Submittal date: 02/24/2000.

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 00 ICN 02 95 of 95 September 2000 
9. ATTACHMENTS 
Attachment Title 
I Overlap And Clearance Between Adjacent Drip Shields 
II Analytic Solution for the Primary Case, t > Tfill

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 00 ICN 02 I-1 September 2000 
I. OVERLAP AND CLEARANCE BETWEEN ADJACENT DRIP SHIELDS

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 00 ICN 02 I-2 September 2000 
The overlap between adjacent DSs is calculated from sketch SK-0148 REV 05 in Attachment II 
of CRWMS M&O 2000c.  The design configuration is shown schematically in Figure I.1. The 
overlap between adjacent DSs can be calculated as the sum of the following dimensions: 
 Distance from edge of DS connector plate-1 to center of mating hole 175 mm 
 Distance from edge of DS plate-1 to center of post 420 mm 
Overlap 595 mm 
Figure I.1. Geometry for Calculation of Overlap Between Drip Shields 
The clearance between adjacent DSs can be calculated as the difference in diameter of the 
mating hole in the DS Connector Plate-1 and the diameter of the post in the DS plate-1. This 
calculation must include the curvature of the top of the DS, the vertical offset produced by the 
DS Connector Guide, and the taper on the post. The geometry for the calculations is shown in 
Figure I.2, based on sketch SK-0148 REV 05 in Attachment II of CRWMS M&O 2000c. 
Figure I.2. Schematic (Not to Scale) for Calculation of Clearance Between Post and 
DS Connector Plate-1 
Drip Shield Connector Guide 
175 mm 
Drip Shield Connector Plate-1 
Drip Shield Plate-1 
420 mm 
Mating Hole 
Post 
137 
Drip Shield Plate-1 
f100 mm Drip Shield Connector Plate-1 
50 mm Vertical Offset Produced 
by DS Connector Guide 
200 mm 
~45

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 00 ICN 02 I-3 September 2000 
The post has a 2 taper, based on the 137 angle between the DS Plate-1 and the side of the post. 
Then the diameter of the post, D, as a function of h, the distance from the top of the post, is given 
by: 
) 2 tan( 2 100  + = h D (I-1) 
The definitions of D and h are illustrated in Figure I.3. 
Figure I.3. Definitions of D and h for calculating clearance. 
The distance from the top of the post to the bottom of the DS Connector Plate-1 is given by: 
mm. 3 . 79 50 2 50 200 = - - = h (I-2) 
This calculation is based on the total height of the post (200 mm) minus two lengths. The first 
length is the vertical displacement for the offset of 50 mm, which is 502 because of the 45 
angle of the DS plates. The second length is the vertical displacement at the center of the post, 
which is 50 mm because the radius of the post is 50 mm and because the angle of the DS plates 
is 45. The diameter of the post at the bottom surface of the DS Connector Plate-1 is then: 
mm D 5 . 105 ) 2 tan( ) 3 . 79 ( 2 100 =  + = (I-3) 
h 
D 
502 
50

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 00 ICN 02 II-1 September 2000 
II. ANALYTIC SOLUTION FOR THE PRIMARY CASE, t > Tfill

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 00 ICN 02 II-2 September 2000 
For t > Tfill, the mass balance within the WP is given by: 
, 
) (
tub 
out V 
t m 
q Df m - = & (Eq. 6.6.1-6) 
or rearranging terms and using the condition that , in out q q = 
. ) ( Df t m 
V
q 
m 
tub 
in = + & (Eq. II-1) 
Multiply Equation II-1 by the integrating factor , 
t 
V
q
tub 
in 
e 
. ) ( 
t 
V
q 
t 
V
q 
tub 
in 
t 
V
q 
tub 
in 
tub 
in 
tub 
in 
Dfe t m e 
V
q 
e m = + & (Eq. II-2) 
or . ) ( 
t 
V
q 
t 
V
q 
tub 
in 
tub 
in 
Dfe e t m 
dt 
d = 
  

 
  

 
(Eq. II-3) 
Integrating Equation II-3 from time Tfill to time t: 
 = - t 
T 
t 
V
q 
T 
V
q 
fill 
t 
V
q 
fill 
tub 
in 
fill 
tub 
in 
tub 
in 
dt Dfe e T m e t m , ) ( ) ( (Eq. II-4) 
. ) ( ) (   

 
  

 
-   
 
  
 
= - fill 
tub 
in 
tub 
in 
fill 
tub 
in 
tub 
in T 
V
q 
t 
V
q 
in
tub 
T 
V
q 
fill 
t 
V
q 
e e 
q 
DfV 
e T m e t m (Eq. II-5) 
The initial condition for Equation II-5, corresponding to t = Tfill, is determined by conditions at 
the end of the fill period. From Equation 6.6.1-2, the mass of radioisotope dissolved within the 
liquid at time Tfill is given by: 
. 
q 
V 
Df DfT ) T ( m 
in 
tub 
fill fill = = (Eq. II-6) 
It follows that 
  

 
  

 
- = - fill 
tub 
in 
tub 
in 
fill 
tub 
in 
tub 
in T 
V
q 
t 
V
q 
fill 
T 
V
q 
fill 
t 
V
q 
e e T m e T m e t m ) ( ) ( ) ( (Eq. II-7)

EBS Radionuclide Transport Abstraction 
ANL-WIS-PA-000001 REV 00 ICN 02 II-3 September 2000 
  

 
  

 
= 
t 
V
q 
fill 
t 
V
q 
tub 
in 
tub 
in 
e T m e t m ) ( ) ( (Eq. II-8) 
and therefore , ) ( ) ( fill fill DfT T m t m = = (Eq. II-9) 
if Equation II-8 is to hold at all values of the time, t. Equation II-9 is the same as Equation 6.6.1- 
7 in Section 6.6.1.