Drift-Scale Radionuclide Transport REV 01

September 2004

MDL-NBS-HS-000016


1. PURPOSE 
The purpose of this model report is to document the drift scale radionuclide transport model, 
taking into account the effects of emplacement drifts on flow and transport in the vicinity of the 
drift, which are not captured in the mountain-scale unsaturated zone (UZ) flow and transport 
models UZ Flow Models and Submodels (BSC 2004 [DIRS 169861), Radionuclide Transport 
Models Under Ambient Conditions (BSC 2004 [DIRS 164500]), and Particle Tracking Model 
and Abstraction of Transport Process (BSC 2004 [DIRS 170041]). The drift scale radionuclide 
transport model is intended to be used as an alternative model for comparison with the 
engineered barrier system (EBS) radionuclide transport model EBS Radionuclide Transport 
Abstraction (BSC 2004 [DIRS 169868]). For that purpose, two alternative models have been 
developed for drift-scale radionuclide transport. One of the alternative models is a dual-
continuum flow and transport model called the drift shadow model. The effects of variations in 
the flow field and fracture-matrix interaction in the vicinity of a waste emplacement drift are 
investigated through sensitivity studies using the drift shadow model (Houseworth et al. 2003 
[DIRS 164394]). In this model, the flow is significantly perturbed (reduced) beneath the waste 
emplacement drifts. However, comparisons of transport in this perturbed flow field with 
transport in an unperturbed flow field show similar results if the transport is initiated in the rock 
matrix. This has led to a second alternative model, called the fracture-matrix partitioning model, 
that focuses on the partitioning of radionuclide transport between the fractures and matrix upon 
exiting the waste emplacement drift. The fracture-matrix partitioning model computes the 
partitioning, between fractures and matrix, of diffusive radionuclide transport from the invert (for 
drifts without seepage) into the rock water. The invert is the structure constructed in a drift to 
provide the floor of the drift. 
The reason for introducing the fracture-matrix partitioning model is to broaden the conceptual 
model for flow beneath waste emplacement drifts in a way that does not rely on the specific flow 
behavior predicted by a dual continuum model and to ensure that radionuclide transport is not 
underestimated. The fracture-matrix partitioning model provides an alternative method of 
computing the partitioning of radionuclide releases from drifts without seepage into rock 
fractures and rock matrix. Drifts without seepage are much more likely to have a significant 
fraction of radionuclide releases into the rock matrix, and therefore warrant additional attention 
in terms of the partitioning model used for TSPA. 
The fracture-matrix partitioning model is intended to be used as the alternative model for 
comparison with the EBS radionuclide transport model (BSC 2004 [DIRS 169868]). This 
comparison is limited to waste emplacement drifts without seepage. The EBS radionuclide 
transport model is used in TSPA calculations to establish the radionuclide partitioning between 
fractures and matrix upon exiting the drifts, as well as the radionuclide mass flux from the drifts, 
under all drift seepage conditions. Following release from the drifts, subsequent TSPA transport 
calculations are conducted using mountain-scale flow and transport models that do not account 
for the presence of waste emplacement drifts or drift-shadow flow phenomena. 
MDL-NBS-HS-000016 REV 01 1-1 September 2004 

Drift-Scale Radionuclide Transport 
The following analysis and model reports are the sources of DTNs that provide direct inputs to 
this report: 
 Analysis of Hydrologic Properties Data (BSC 2004 [DIRS 170038]) 
 Calibrated Properties Model (BSC 2004 [DIRS 169857]) 
 UZ Flow Models and Submodels (BSC 2004 [DIRS 169861]) 
 Saturated Zone Flow and Transport Model Abstraction (BSC 2004 [DIRS 170042]) 
 Seepage Model for PA Including Drift Collapse (BSC 2004 [DIRS 167652]). 
The principal output of the fracture-matrix partitioning model is the distribution of radionuclide 
releases between the fractures and rock matrix from drifts with diffusive-dominated transport 
into the rock. Uncertainty in the fracture-matrix partitioning model is evaluated through the 
development of results over a suitable range of parameters that affect release fractions to the rock 
matrix and fractures. The distribution of radionuclide releases between fractures and matrix 
from drifts with advective-dominated transport into the rock is also provided. Data developed as 
inputs for the fracture-matrix partitioning model may also be used as input for the EBS 
radionuclide transport model (BSC 2004 [DIRS 169868]). 
The phenomenon of flow and transport in the vicinity of the waste emplacement drift are 
evaluated in this model report under ambient thermal, chemical, and mechanical 
conditions. This includes the effects of water diversion around an emplacement drift and the 
flow and transport behavior expected in a fractured rock below the drift. Model limitations for 
the fracture-matrix partitioning model include the following approximations: 
1. Fracture flow occurs beneath a waste emplacement drift within a distance less than the 
fracture spacing. Given fracture spacings that are, on average, less than one meter, the 
zone of reduced flow in the fracture-matrix partitioning model is much smaller than 
with the drift shadow model. 
2. The model is restricted to steady-state conditions (see Section 6.4). Therefore, the 
initial transient period is not treated, which is initially dominated by diffusive transfer 
into the rock. This initial radionuclide partitioning ratio will be approximately equal 
to the water content ratio of the fractures and matrix and will only asymptotically 
approach the partitioning ratio predicted by the fracture-matrix partitioning model. 
3. The effects of dryout during the boiling and re-wetting periods are ignored, during 
which fracture water saturations are disproportionately reduced in comparison with the 
matrix. This will lead to preferential entry of radionuclides to the matrix during the 
thermally-perturbed period. 
4. All fractures are flowing in the fracture-matrix partitioning model as opposed to the 
active fracture model, where only a subset of the fractures is flowing. This leads to 
greater contact between the invert and flowing fractures and, therefore, greater releases 
from the invert to the rock fractures. 
All of these limitations lead to a conservative prediction for fracture-matrix partitioning of 
radionuclide releases from drifts without seepage. 
MDL-NBS-HS-000016 REV 01 1-2 September 2004 

Drift-Scale Radionuclide Transport 
This report has been developed in accordance with Technical Work Plan for: Unsaturated Zone 
Transport Model Report Integration (Bechtel SAIC Company, LLC (BSC) 2004 
[DIRS 171282]), which includes planning documents for the technical work scope, content, and 
management of this Model Report in Section 1.2.3. The technical work scope for this Model 
Report calls for development of a process-level model representing diffusive release from the 
invert to the rocks, partitioned between fracture and matrix, as compared to the fracture-release 
approach used in the Site Recommendation. The plan for validation of the models documented 
in this Model Report is given in Section 2.2.4 (BSC 2004 [DIRS 171282]). See Section 7 for 
additional discussion. 
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Drift-Scale Radionuclide Transport 
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MDL-NBS-HS-000016 REV 01 1-4 September 2004 

Drift-Scale Radionuclide Transport 
2. QUALITY ASSURANCE 
Development of this model report and the supporting modeling activities have been determined 
to be subject to the Yucca Mountain Projects quality assurance program, as indicated in 
Technical Work Plan for: Unsaturated Zone Transport Model Report Integration (BSC 2004 
[DIRS 171282], Section 8.1). Approved quality assurance procedures identified in the TWP 
(BSC 2004 [DIRS 171282], Section 4) have been used to conduct and document the activities 
described in this model report. The TWP also identifies the methods used to control the 
electronic management of data (BSC 2004 [DIRS 171282], Section 8.4, WP ARTM01) during 
the modeling and documentation activities. 
This model report provides two models of drift-scale radionuclide transport in the unsaturated 
zone (UZ) below the repository. This natural barrier is classified in the Q-List (BSC 2004 
[DIRS 168361]) as Safety Category because it is important to waste isolation, as defined in 
AP-2.22Q, Classification Analyses and Maintenance of the Q-List. The report contributes to the 
analysis and modeling data used to support performance assessment (PA); the conclusions do not 
directly impact engineered features important to safety, as defined in AP-2.22Q. 
MDL-NBS-HS-000016 REV 01 2-1 September 2004 

Drift-Scale Radionuclide Transport 
INTENTIONALLY LEFT BLANK 
MDL-NBS-HS-000016 REV 01 2-2 September 2004 

Drift-Scale Radionuclide Transport 
3. USE OF SOFTWARE 
The major software codes and software routines used in this study are listed in Table 3-1. The 
superceded procedure AP-SI.1Q, Software Management, was used because this procedure 
governing the used of software was in effect at the time revision 00 was completed. There has 
been no additional use of software in the preparation of this revision 01. The software have been 
baselined in accordance with AP-SI.1Q, Software Management, are appropriate for the intended 
use, have been used strictly in the range of validation, and were obtained from Software 
Configuration Management. The iTOUGH2 V4.0 (LBNL 1999 [DIRS 139918]) and TOUGH2 
V1.11MEOS9NTV1.0 (LBNL 1999 [DIRS 113943]) programs are the primary software used to 
represent physical processes for the Drift-Scale Radionuclide Transport models. Flow 
simulations were performed with iTOUGH2 V4.0 (LBNL 1999 [DIRS 139918]) and flow and 
transport calculations were performed using TOUGH2 V1.11MEOS9NTV1.0 (LBNL 1999 
[DIRS 113943]). The range of use for iTOUGH2 V4.0 and TOUGH2 V1.11MEOS9NTV1.0 is 
for unsaturated, isothermal flow and tracer transport through fractured, porous rock. The routine 
CutDrift V1.0 (LBNL 2000 [DIRS 152816]) was used to cut a cylindrical drift shape into the 
rectangular grid. The routine AddBound V1.0 (LBNL 2000 [DIRS 152823]) was used to 
generate boundary grids for water and tracers to enter and leave the model grid. The routine 
EXT V1.0 (LBNL 1999 [DIRS 134141]) was used to postprocess the results of iTOUGH2 V4.0 
(LBNL 1999 [DIRS 139918]) for graphical display of the flow field results. The range of use for 
software CutDrift V1.0, AddBound V1.0, and EXT V1.0 are to pre-process the numerical grid 
and post-process the flow field output for graphical display. No software was used prior to 
qualification. 
The flow model calibration has been performed using the TOUGH family of software 
(BSC 2001 [DIRS 161316]), thus the compatibility of the parameters between the parameter 
development and their implementation in this report lead to the selection of the iTOUGH2 V4.0 
software over other possible software and computational methods. Transport calculations are 
then performed for steady-state flow conditions using the EOS9nT module of TOUGH2 
(TOUGH2 V1.11MEOS9NTV1.0 in Table 3-1) (Moridis et al. 1999 
[DIRS 123093]). Compatibility between the flow calculations with iTOUGH2 V4.0 and the 
transport calculations with TOUGH2 V.11MEOS9NTV1.0 lead to the selection of the iTOUGH2 
V4.0 software over other possible software and computational methods. Other direct finite 
difference approaches for treating the time dependence of the transport problem were not used 
because the Laplace transform method provides a semi-analytical treatment of the time 
derivatives that eliminates the need for time discretization or any restrictions on time-step 
size. The software CutDrift V1.0, AddBound V1.0, and EXT V1.0 pre- and post-processing 
software are commonly used with the TOUGH family of codes. There are no limitations on the 
use of this software within the range of use identified above. 
Table 3-1. Qualified Software Used in this Report 
Software Name Version Software Tracking Number DIRS 
Platform/Operating 
System 
iTOUGH2 4.0 10003-4.0-00 139918 SUN / SUNOS 5.5.1 
CutDrift 1.0 10375-1.0-00 152816 SUN / SUNOS 5.5.1 
MDL-NBS-HS-000016 REV 01 3-1 September 2004 

Drift-Scale Radionuclide Transport 
Table 3-1. Qualified Software Used in this Report (Continued) 
Software Name Version Software Tracking Number DIRS 
Platform/Operating 
System 
AddBound 1.0 10357-1.0-00 152823 SUN / SUNOS 5.5.1 
EXT 1.0 10047-1.0-00 134141 SUN / SUNOS 5.5.1 
TOUGH2 1.11MEOS9NTV1.0 10065-1.11MEOS9NTV1.0-00 113943 SUN / OSF1 V4.0 
Excel (v. 97-SR-1) and Mathcad (v. 11.0) spreadsheets and visual display graphics programs 
(Tecplot v. 7.0-4.0 for MS-WINDOWS) were also used. Tecplot was used to create Figures 6-1 
through 6-8, 6-13 through 6-20, 7-1, and 7-2. All information needed to reproduce the work 
using these standard software programs, including the input, computation, and output, is included 
in this report. Excel calculations are documented in Appendices A through I, and L. Mathcad 
calculations are discussed in Sections 6.4.3, 6.4.4, 6.4.6, and Appendices J and L. 
MDL-NBS-HS-000016 REV 01 3-2 September 2004 

Drift-Scale Radionuclide Transport 
4. INPUTS 
4.1 DIRECT INPUTS 
This section provides documentation for direct inputs to the Model Report. Other inputs are 
identified in the sections where they are used. Data input to the Model Report are referred to by 
Data Tracking Number (DTN). This format allows for all data of similar use in the Model 
Report to be kept in a single location, for readability of the document and simplicity for 
downstream users. 
Source DTNs for the hydrological and transport properties used in the calculations that are 
intended as an alternative model for the EBS Radionuclide Transport Model [EBS Radionuclide 
Transport Abstraction (BSC 2004 [DIRS 169868])] (see Section 6.4) are listed in 
Table 4-1. These data are summarized in Tables 4-2 through 4-6 for the repository UZ model 
layers tsw33 (Topopah Spring Tuff upper lithophysal), tsw34 (Topopah Spring Tuff middle 
nonlithophysal), tsw35 (Topopah Spring Tuff lower lithophysal), and tsw36 (Topopah Spring 
Tuff lower nonlithophysal). 
4.1.1 Fracture Frequency and Fracture Porosity 
Data for the mean and standard deviation of fracture frequency and fracture porosity for the 
tsw33, tsw34, tsw35, and tsw36 (see Table 4-2) are given in Table 6-5 of the report, Analysis of 
Hydrologic Properties Data (BSC 2004 [DIRS 170038] (indirect input); 
DTN: LB0205REVUZPRP.001 [DIRS 159525]). Fracture frequency is determined from 
qualified fracture property data developed from field data (BSC 2004 [DIRS 170038], 
Section 6.1). These include Detailed Line Survey (DLS) fracture data (collected from the 
Exploratory Studies Facility North and South Ramps, Main Drift, and Enhanced Characterization 
of the Repository Block (ECRB) Cross Drift, providing spatially varying frequency, length, and 
fracture dips and strikes) and fracture frequency data from boreholes. A combination of fracture 
porosity data derived from gas tracer tests in the Exploratory Studies Facility, fracture frequency 
data, fracture aperture estimates, and the geometry of fracture networks are used to develop 
representative fracture porosities for the UZ Model layers (BSC 2004 [DIRS 170038] (indirect 
input), Section 6.1). See Section 6.4.5 for a complete discussion of the uncertainty treatment for 
fracture frequency and fracture porosity. Fracture frequency data in the repository host rock 
provides estimates for the standard deviation of fracture frequency for the tsw33 and tsw34 
model units, but not for the tsw35 or tsw36. Data from other units shown in Table 4-3 are used 
to develop uncertainty data for the tsw35 and tsw36. 
Table 4-1. Inputs 
Input Type Description 
LB0205REVUZPRP.001 [DIRS 159525] Data Fracture frequency and porosity 
LB0208UZDSCPLI.002 [DIRS 161788] Data Matrix permeabilities, fracture van Genuchten m, 
and fracture residual saturation  lower infiltration 
scenario. 
LB0208UZDSCPMI.002 [DIRS 161243] Data Matrix permeabilities, fracture van Genuchten m, 
and fracture residual saturation  mean infiltration 
scenario. 
MDL-NBS-HS-000016 REV 01 4-1 September 2004 

Drift-Scale Radionuclide Transport 
Table 4-1. Inputs (Continued) 
Input Type Description 
LB0302UZDSCPUI.002 [DIRS 161787] Data Matrix permeabilities, fracture van Genuchten m, 
and fracture residual saturation  upper infiltration 
scenario. 
LB03023DSSCP9I.001 [DIRS 163044] Data Fracture and matrix flux and saturation, and matrix 
relative permeability (glacial transition climate, all 
infiltration scenarios) 
LB0406U0075FCS.002 [DIRS 170712] Data Flow focusing factor correlation 
LB0207REVUZPRP.002 [DIRS 159672] Data Matrix porosity, standard deviation for matrix porosity 
Weast and Astle 1979 [DIRS 102865] Established 
Fact 
Diffusion coefficients in aqueous solution 
SN0306T0502103.006 [DIRS 163944]; Data Diffusion coefficient in rock matrix 
BSC (2004 [DIRS 170042], 
Section 6.5.2.6, Equation 6-19) 
BSC 2001 [DIRS 156700], pp. 2325 Data Correlation for diffusion coefficient in invert materials 
Equation 37. 
Hilf 1975 [DIRS 169699], p. 257 Established Intergranular porosity of invert 
Fact 
BSC 2003 [DIRS 164101] 800-IED-WIS0-
00302-000-00A 
Design 
information 
Emplacement drift committed materials 
BSC 2004 [DIRS 168370] 800-IED-WIS0-Design Repository design layout information 
00103-000-00A Information 
BSC 2004 [DIRS 168489], 800-IED- Design Emplacement drift configuration 
MGR0-00201-000-00B Information 
Table 4-2. Fracture Frequency and Porosity Data for the Repository Host Rock 
UZ 
Model 
Layer 
Frequency 
(m-1) Porosity 
F sf Mean (-) Std (-) 
tsw33 0.81 1.03 5.8E-3 -
tsw34 4.32 3.42 8.5E-3 2.50E-03 
tsw35 3.16 -9.6E-3 -
tsw36 4.02 -1.3E-2 -
DTN: LB0205REVUZPRP.001 [DIRS 159525], BSC 2004 
[DIRS 170038] (indirect input). 
NOTE: Fracture properties developed from field data (Std 
refers to standard deviation for porosity). Note also 
that BSC 2004 [DIRS 170038] is supporting 
documentation for the direct input 
DTN: LB0205REVUZPRP.001 [DIRS 159525]. 
MDL-NBS-HS-000016 REV 01 4-2 September 2004 

Drift-Scale Radionuclide Transport 
Table 4-3. Fracture Frequency for Rock Units with Data on Standard Deviation 
Fracture frequency data 
UZ 
Model Layer 
Frequency 
(m-1) 
F sf 
tcw11 0.92 0.94 
tcw12 1.91 2.09 
tcw13 2.79 1.43 
ptn21 0.67 0.92 
ptn24 0.46 0.45 
ptn25 0.52 0.6 
ptn26 0.97 0.84 
tsw31 2.17 2.37 
tsw32 1.12 1.09 
tsw33 0.81 1.03 
tsw34 4.32 3.42 
DTN: LB0205REVUZPRP.001 [DIRS 159525]. 
BSC 2004 [DIRS 170038] (indirect input). 
4.1.2 Unsaturated Zone Flow 
Data on UZ flow in the repository were developed using the UZ Flow Model. The site-scale 
model incorporates the entire Yucca Mountain UZ; it accounts for the main stratigraphic units 
using layer-averaged rock properties and represents the major faults. Relevant rock properties of 
each hydrogeologic unit (for fractures, matrix, and fault zones) have been calibrated against 
saturation data, water-potential data, pneumatic-pressure data, perched-water data, temperature 
data, and geochemical data [Calibrated Properties Model (BSC 2004 [DIRS 169857] (indirect 
input), Section 6.1 and BSC 2004 [DIRS 169861] (indirect input), Sections 6.2 through 
6.5)]. The flow results also include the effects of preferential flow in the fracture network as 
implemented in the active fracture model (BSC 2004 [DIRS 169861] (indirect input), 
Section 6.1.2). The calibrations are conducted for lower, mean, and upper infiltration scenarios 
for the present-day climate to include this key uncertainty in the parameterization. The flow data 
used are for the lower, mean, and upper bound flow fields for the glacial transition 
climate. These data, which include the fracture and matrix flux and the fracture and matrix water 
saturations, are available in DTN: LB03023DSSCP9I.001 [DIRS 163044] and (BSC 2004 
[DIRS 169861] (indirect input)). The glacial transition lower, mean, and upper infiltration 
scenarios cover a range of conditions that encompass all of the monsoon scenarios and all but the 
present-day lower infiltration scenario. Furthermore, the majority of the compliance period 
(2,000 to 10,000 years) is modeled as being under glacial transition climate. Because of the 
predominance in time and wide range of the glacial transition infiltration scenarios, these three 
cases are used as representative for the low, mean, and high scenarios for the entire compliance 
period. In conjunction with the mountain-scale flow model results, a distribution for flow 
MDL-NBS-HS-000016 REV 01 4-3 September 2004 

Drift-Scale Radionuclide Transport 
focusing in the fracture continuum is also used to account for sub gridblock scale heterogeneity 
for the mountain-scale flow fields. 
4.1.3 Flow Focusing and Fracture Hydrologic Characteristics 
A flow focusing factor is included in the model to account for the effects of heterogeneity on 
flow at length scales relevant to drift-scale flow. These effects are not accounted for at the 
drift-scale (on the order of 10 m) because the horizontal dimensions of the mountain-scale 
numerical grid are on the order of 100m. The treatment of flow focusing is restricted to fracture 
flow because the effects are expected to be larger in the fractures, which are found to carry in 
excess of 90 percent of the total water flux in the UZ flow model results. Measurements of flow 
focusing are not available; therefore, models are used to describe the effects of the drift-scale 
heterogeneity on flow. The models used to investigate these effects were restricted to 2D and 3D 
domains for the upper portion Topopah Spring welded units, between the base of the Paintbrush 
non-welded (vitric tuff) PTn and the repository horizon. This domain was selected due to the 
more homogeneous, matrix-dominated, flow that is expected in the Paintbrush non-welded 
(vitric tuff) versus the strongly fracture-dominated flow expected in the Topopah Spring welded 
units. The model domains were on the order of 100 m in extent in all directions, with model grid 
spacing of less than 1 m (BSC 2004 [DIRS 167652] (indirect input), Section 6.8.1). 
The flow-focusing effect is represented in the fracture fluxes and water saturations, requiring the 
van Genuchten pore size distribution factor (m) shown in Table 4-4. This parameter is not 
treated as uncertain because of the uncertainty already investigated through flow model 
calibration (BSC 2004 [DIRS 169857] (indirect input) and BSC 2004 [DIRS 169861] (indirect 
input)). These investigations found that the same van Genuchten m could be used for all flow 
fields (low, mean, and high infiltration conditions) and match field data. Therefore, a constant 
value appears to be appropriate. Fracture residual water saturation (Table 4-4) is needed to 
define the effective saturation used in the van Genuchten relative permeability model and is 
treated as an uncertain parameter. The flow-focusing correlation, documented in BSC (2004 
[DIRS 167652] (indirect input), Section 6.8; DTN: LB0406U0075FCS.002 [DIRS 170712]), is 
given by the following: 
P - = 3137.0 F 4 + 4998.5 F 3 - 66.35 F 2 + 3.102 F - 434.11 
where F is the flow-focusing factor and P is the cumulative probability for the value of F (BSC 
2004 [DIRS 167652](indirect input), Figure 6-26). See Section 6.4.5 for a complete discussion 
of the uncertainty treatment for water flux, residual saturation, and flow focusing. 
Table 4-4. Fracture van Genuchten m and Residual Saturation, All Infiltration Cases 
Fracture 
UZ Model 
Layer 
Hydrogeologic 
Units 
Fracture 
van Genuchten m 
Residual 
Saturation 
tsw33 TUL 0.633 0.01 
tsw34 TMN 0.633 0.01 
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Drift-Scale Radionuclide Transport 
Table 4-4. Fracture van Genuchten m and Residual 
Saturation, All Infiltration Cases (Continued) 
Fracture 
UZ Model 
Layer 
Hydrogeologic 
Units 
Fracture 
van Genuchten m 
Residual 
Saturation 
tsw35 TLL 0.633 0.01 
tsw36 TM2 & TM1 0.633 0.01 
DTNs: LB0208UZDSCPLI.002 [DIRS 161788], 
LB0208UZDSCPMI.002 [DIRS 161243], and 
LB0302UZDSCPUI.002 [DIRS 161787]. 
NOTE: The fourth character of model layer is replaced by F or M in 
these DTNs, indicating fracture or matrix, respectively. 
4.1.4 Matrix Hydrologic Characteristics 
Data for matrix porosity and permeability (Table 4-5 and Table 4-6) are also used to evaluate 
matrix diffusion. Matrix porosity is taken from the hydrologic parameter set presented in 
Table 6-6 of Analysis of Hydrologic Properties Data (BSC 2004 [DIRS 170038] (indirect input); 
LB0207REVUZPRP.002 [DIRS 159672]). Note that the porosity data set selected for use in 
TSPA is thermal properties data set presented in LB0210THRMLPRP.001 [DIRS 160799] 
(indirect input). However, the values within the repository model units are (tsw33, tsw34, tsw35, 
and tsw36) are nearly identical. The reason for using the alternative data set is because this data 
set provides an estimate of the variance of the porosity, which is used to statistically sample 
matrix porosity. See Section 6.4.5 for a complete discussion of the uncertainty treatment. 
Table 4-5. Matrix Porosity Average and Standard Deviation, All Infiltration Cases 
UZ Model Layer 
Hydrogeologic 
Units 
Average Matrix 
Porosity 
Standard Deviation 
for Matrix Porosity 
tsw33 TUL 0.155 0.030 
tsw34 TMN 0.111 0.020 
tsw35 TLL 0.131 0.031 
tsw36 TM2 & TM1 0.103 0.025 
DTN: LB0207REVUZPRP.002 [DIRS 159672], BSC 2004 [DIRS 170038] (indirect input). 
Table 4-6. Matrix Permeability, All Infiltration Cases 
UZ Model 
Layer 
Hydrogeologic 
Units 
Average Matrix 
Permeability 
(m2)  lower 
infiltration case 
Average Matrix 
Permeability 
(m2)  mean 
infiltration case 
Average Matrix 
Permeability 
(m2)  upper 
infiltration case 
tsw33 TUL 1.60E-18 6.57E-18 2.39E-17 
tsw34 TMN 1.38E-19 1.77E-19 2.96E-19 
tsw35 TLL 2.33E-18 4.48E-18 8.55E-18 
tsw36 TM2 & TM1 5.58E-19 2.00E-19 7.41E-19 
DTNs: LB0208UZDSCPLI.002 [DIRS 161788], LB0208UZDSCPMI.002 
[DIRS 161243], and LB0302UZDSCPUI.002 [DIRS 161787]. 
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Drift-Scale Radionuclide Transport 
Matrix permeability is taken from the drift-scale calibrated property sets (BSC 2004 
[DIRS 169857] (indirect input), Tables 6-8, 6-9, and 6-10; DTNs: LB0208UZDSCPLI.002 
[DIRS 161788]; LB0208UZDSCPMI.002 [DIRS 161243]; and LB0302UZDSCPUI.002 
[DIRS 161787]). These permeability values are calibrated against water saturation and water 
potential values for the lower, mean, and upper bound infiltration cases using one-dimensional 
models and inverse modeling methods (BSC 2004 [DIRS 169857] (indirect input), 
Section 6.3.2). These cases represent the uncertainty in flux through the UZ and therefore the 
property sets calibrated to these different infiltration cases represent the uncertainty in the 
properties that are consistent with the calibration. The subsequent calibrations with the site-scale 
3D model did not affect the values of matrix permeability (BSC 2004 [DIRS 169861] (indirect 
input), Appendix A, Tables A-1, A-2, and A-3). 
4.1.5 Diffusion in Fractured Rock 
Mass transport in the rock fractures immediately in contact with the drift is treated as a 
steady-state diffusion process, as described in Section 6.4.1. Diffusion will occur through rock 
fractures immediately adjacent to a drift due to the residual water content (or greater) that is 
present in all fractures. Due to the limited direct information available concerning diffusion 
coefficients in partially saturated fractures, diffusion coefficients determined for the rock matrix 
are used as the expected values for diffusion coefficients in the neighboring partially saturated 
fractures. See Assumption 1 and Section 6.4.5 for a discussion of the justification for this 
approximation. 
Site-specific diffusion cell data were used to develop a correlation between the matrix diffusion 
coefficient, and the porosity and permeability of the rock matrix under saturated conditions, as 
discussed in Diffusive and Advective Transport of 3H, 14C, and 99Tc in Saturated, Fractured 
Volcanic Rocks from Pahute Mesa, Nevada (Reimus et al. 2002 [DIRS 163008] (indirect input) 
and Saturated Zone Flow and Transport Model Abstraction BSC 2004 [DIRS 170042], 
Section 6.5.2.6, Equation 6-19). 
The diffusing species 3HHO, Br-, and I-were used in the experiments to define the 
correlation. Samples of welded and nonwelded volcanic tuffs were taken from Pahute Mesa and 
the C-holes near Yucca Mountain. The ranges in porosity and permeability of these samples are 
approximately 0.05 to 0.3 and 10-18 m2 to 10-14 m2, respectively. The porosity and permeability 
of rock units in the repository horizon are in approximately the same range (porosity ranges from 
0.11 to 0.15 (BSC 2004 [DIRS 170038] (indirect input), Table 6-6) and permeability from 
10
-19 
m2 to 10-17 m2 (BSC 2004 [DIRS 169861] (indirect input), Table A-1). Reimus et al. 2002 
[DIRS 163008] (indirect input), Section 4, found that differences in rock type account for the 
largest variability in the effective diffusion coefficients, rather than variability between diffusing 
species, size, and charge. The highest predictability in determining a value of Dm occurs when 
both matrix porosity and log permeability are known, with log permeability as the most 
important predictive variable. The correlation is, 
log(D )=-49.3 +38.1 f+ log 165.0 10 (k )
m mm 
MDL-NBS-HS-000016 REV 01 4-6 September 2004 

Drift-Scale Radionuclide Transport 
where D is the effective matrix diffusion coefficient in cm2/s, f is the matrix porosity, and 
mm 
k is the matrix permeability in m2 (BSC 2004 [DIRS 170042], Section 6.5.2.6, Equation 6-19; 
m 
DTN: SN0306T0502103.006 [DIRS 163944]; Reimus et al. 2002 [DIRS 163008] (indirect 
input) Equation 2.5). The effects of changes in water saturation on diffusion are included 
through an adjustment of this correlation to one applicable to unsaturated conditions (see 
Section 6.4.5). 
4.1.6 Diffusion in the Invert 
Mass transport in the invert is modeled as a diffusion process. The water-filled pore space is 
treated as a single continuum. A correlation for the diffusion coefficient is given in the report, 
Invert Diffusion Properties Model (BSC 2001 [DIRS 156700] (indirect input), pp. 2325). The 
crushed tuff used for the invert will be a native material from the development of the 
emplacement drifts (refer to design information found in D&E / PA/C IED Emplacement Drift 
Configuration and Environment (BSC 2004 [DIRS 168489]); characteristics of the crushed tuff 
[Invert Configuration and Drip Shield Interface (CRWMS M&O 2000 [DIRS 136255] (indirect 
input), Section 6.5)]). Therefore, the matrix porosity of the granular material will be the same as 
the matrix porosity, f , from the repository host rock. The matrix porosity characteristics for 
mthe invert are taken from the tsw36 (see Table 4-5), as used in Advection Versus Diffusion in the 
Invert (BSC 2003 [DIRS 170881] (indirect input), Sections 5.8 and 6.4). The potential exists 
that materials from other host rock units may be used for the invert (BSC 2004 [DIRS 169565] 
(indirect input), Section 5.3.1.2). However, the sensitivity of the results in the fracture-matrix 
partitioning model to invert diffusion are shown to be very low (Section 6.4.6). Therefore, the 
use of matrix porosity of the tsw36 is sufficient for the purposes of this model. The expected 
value and range for the intergranular porosity of the crushed tuff, fIg, is shown in Table 4-7 (Hilf 
1975 [DIRS 169699], p. 257); BSC 2003 [DIRS 170881] (indirect input), Sections 4.1.4 
and 6.3). Uncertainty for fIg is discussed in Section 6.4.5. The uncertainty in the free-water 
diffusion coefficient is based on data from Weast and Astle (1979 [DIRS 102865]), which 
provides 38 free-water diffusion coefficients for 19 electrolytes in a range of aqueous solutions 
(see Table 4-8). These diffusion coefficients range in value from 7.1  10-10 m2/s to 3.87  
10-9 m2/s. This is a sufficiently wide range of free-water diffusion coefficients for radionuclides, 
based on reported values discussed in Section 6.4.5. See Section 6.4.5 for a complete discussion 
of the uncertainty treatment for diffusive mass transfer in the invert. 
Table 4-7. Intergranular Porosity of the Invert 
Source: 
NOTE: 
Mean 
Range 
0.45 
0.4 to 0.48 
Hilf (1975 [DIRS 169699], p. 257) BSC (2003 
[DIRS 170881] (indirect input), Sections 4.1.4 
and 6.3). 
Porosity is computed from the void ratio, e, in this 
reference as e/(1+e). The maximum void ratio 
for poorly graded sand (SP) is used from this 
reference to represent uncompacted tuff grains. 
MDL-NBS-HS-000016 REV 01 4-7 September 2004 

Drift-Scale Radionuclide Transport 
The correlation for the diffusive mass transfer coefficient is given by (BSC 2001 [DIRS 156700], 
pp. 2325): 
..
log.. DeI 
.. = log 849.1 .. D0 . I 
where DeI is the invert diffusive mass transfer coefficient, D0 is the free-water diffusion 
coefficient, and .I 
is the invert water content. The source document for this correlation is now 
cancelled, however, this expression is the same as that used in BSC 2004 [DIRS 169868] 
(indirect input), Eq. 6.3.4.1.1-16 when considering the mean value, except the coefficient, 1.849, 
differs by 0.8%. This difference is negligible given that the range of uncertainty in the invert 
diffusion coefficients can exceed an order of magnitude, as shown in Attachment E. Therefore, 
the correlation in BSC 2004 [DIRS 169868] (indirect input) corroborates the correlation used as 
suitable for its intended use. 
4.1.7 Design Information 
Design information on invert characteristics, cited in the in-drift configuration information 
exchange drawing, are given as follows: 
Design data on the dimensions of the drift and invert are presented in the in-drift configuration 
IED (BSC 2003 [DIRS 164101]), and shown in Figure 4-1 (BSC 2003 [DIRS 164101]). The 
depth of crushed tuff in the invert varies due to the curvature of the drift wall below the invert 
(Figure 4-1). The maximum depth of crushed tuff in the invert is 806 mm and the minimum 
depth is determined by that value, the drift diameter (5.5 m), and the width of the central clear 
space under the emplacement pallet (1674 mm). BSC 2003 [DIRS 164101] has been 
superseded. Nevertheless the dimensions shown therein and in Figure 4-1 are appropriate for 
use, because they are consistent with current IEDs: BSC 2004 [DIRS 168489] (indirect input) 
confirms the drift diameter value. The maximum depth of crushed tuff (806 mm) is prescribed 
for use in TSPA by Table 7 of Postclosure Modeling and Analyses Design Parameters (BSC 
2004 [DIRS 169885]) (indirect input). D&E/PA/C IED Interlocking Drip Shield and 
Emplacement Pallet (BSC 2004 [DIRS 169220]) (indirect input) confirms the nominal width of 
the emplacement pallet (2150 mm) as shown in Figure 4-1, and therefore is consistent with the 
clear space dimension of 1674 mm (that is, twice 837 mm). 
Information concerning the design layout is also needed. The percentages of each waste 
emplacement panel (1, 2, 3, and 4) within each of the four rock units (tsw33, tsw34, tsw35, and 
tsw36) is calculated from information on drift areas by geologic unit in D&E / PA/C IED 
Subsurface Facilities (BSC 2004 [DIRS 168370] 800-IED-WIS0-00103-000-00A). The total 
drift areas and percentages in each host rock unit are shown in Table 4-9. Note that in the IED 
geologic lithostratigraphic units are used. The correspondence between these units and the UZ 
flow model units are as follows: the tptpul is the tsw33, the tptpmn in the tsw34, the tptpll is the 
tsw35, and the tptpln is the tsw36. 
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Drift-Scale Radionuclide Transport 
Table 4-8. Free-Water Diffusion Coefficients 
Electrolytes 
Solute concentration (molarity) 
0.01 0.1 1 
HCl n.a. 3.05 3.436 
HBr n.a. 3.156 3.87 
LiCl 1.312 1.269 1.302 
LiBr n.a. 1.279 1.404 
LiNO3 1.276 1.24 1.293 
NaCl 1.545 1.483 1.484 
NaBr n.a. 1.517 1.596 
NaI n.a. 1.52 1.662 
KCl 1.917 1.844 1.892 
KBr n.a. 1.874 1.975 
KI n.a. 1.865 2.065 
KNO3 1.846 n.a. n.a. 
KClO4 1.79 n.a. n.a. 
CaCl2 1.188 1.11 1.203 
BaCl2 1.265 1.159 1.179 
Na2SO4 1.123 n.a. n.a. 
MgSO4 0.71 n.a. n.a. 
LaCl3 1.105 n.a. n.a. 
K4Fe(CN)4 1.183 n.a. n.a. 
Source: Weast and Astle 1979 [DIRS 102865], p. F-62. 
NOTE: Diffusion coefficient values for strong electrolytes =
2
actual value  105 cm/s. 
n.a. = data not available 
Table 4-9. Drift Areas and Percentage of Each Rock Unit within Waste Emplacement Panels 
Panel Drift Area (m2) %tsw33 %tsw34 %tsw35 %tsw36 
1 298850 0 40 60 0 
2* 1477867 0 5 91 4 
3** 1862136 12 22 66 0 
4 1344299 0 0 95 5 
Source: BSC (2004 [DIRS 168370], 800-IED-WIS0-00103-000-00A) (see also Appendix H). 
* including contingency area. 
** east and west portions of panel 3. 
MDL-NBS-HS-000016 REV 01 4-9 September 2004 

Drift-Scale Radionuclide Transport 
Source: BSC 2003 [DIRS 164101]. 
NOTE: All dimensions are in mm unless otherwise noted. 
Figure 4-1. In-Drift Configuration 
4.2 CRITERIA 
The licensing criteria for postclosure performance assessment are stated in 10 CFR 63.114 
[DIRS 156605]. The requirements to be satisfied by TSPA are identified in the Yucca Mountain 
Project Requirements Document (Canori and Leitner 2003 [DIRS 166275]). The acceptance 
criteria that will be used by the Nuclear Regulatory Commission (NRC) to determine whether the 
technical requirements have been met are identified in Yucca Mountain Review Plan, Final 
Report (YMRP; NRC 2003 [DIRS 163274]). The pertinent requirements and criteria for this 
model report are summarized in Table 4-10. 
MDL-NBS-HS-000016 REV 01 4-10 September 2004 

Drift-Scale Radionuclide Transport 
Table 4-10. Project Requirements and YMRP Acceptance Criteria Applicable to this Model Report 
Requirement 
Numbera Requirement Titlea 10 CFR 63 Link YMRP Acceptance Criteria 
PRD-002/T-015 Requirements for 10 CFR 63.114(a-c; e-g) Criteria 1 to 4 for Radionuclide 
Performance Assessment Transport in the Unsaturated 
Zone b 
a 
from Canori and Leitner (2003 [DIRS 166275]).
b 
from NRC (2003 [DIRS 163274], Section 2.2.1.3.7.3). 
The applicable acceptance criteria identified in Section 2.2.1.3.7.3 of the YMRP (NRC 2003 
[DIRS 163274]) are given below. 
Acceptance Criterion 1, System Description and Model Integration Are 
Adequate: 
(2) The description of the aspects of hydrology, geology, geochemistry, design 
features, physical phenomena, and couplings, that may affect radionuclide transport 
in the unsaturated zone, is adequate. For example, the description includes changes 
in transport properties in the unsaturated zone, from water-rock 
interaction. Conditions and assumptions in the total system performance 
assessment abstraction of radionuclide transport in the unsaturated zone are readily 
identified, and consistent with the body of data presented in the description; 
(6) Guidance in NUREG-1297 and NUREG-1298 (Altman et al. 1988 
[DIRS 103597] and [DIRS 103750]), or other acceptable approaches, is followed 
for peer review and data qualification. 
Acceptance Criterion 2, Data are Sufficient for Model Justification: 
(1) Geological, hydrological, and geochemical values, used in the license 
application, are adequately justified (e.g., flow-path length, sorption coefficients, 
retardation factors, colloid concentrations, etc.). Adequate descriptions of how the 
data were used, interpreted, and appropriately synthesized into the parameters are 
provided; 
Acceptance Criterion 3, Data Uncertainty Is Characterized and Propagated 
through the Model Abstraction: 
(1) Models use parameter values, assumed ranges, probability distributions, and 
bounding assumptions that are technically defensible, reasonably account for 
uncertainties and variabilities, and do not result in an under-representation of the 
risk estimate; 
(2) For those radionuclides where the total system performance assessment 
abstraction indicates that transport in fractures and matrix in the unsaturated zone is 
important to waste isolation: (i) estimated flow and transport parameters are 
appropriate and valid, based on techniques that may include laboratory 
MDL-NBS-HS-000016 REV 01 4-11 September 2004 

Drift-Scale Radionuclide Transport 
experiments, field measurements, natural analog research, and process-level 
modeling studies, conducted under conditions relevant to the unsaturated zone at 
Yucca Mountain; and (ii) models are demonstrated to adequately reproduce field 
transport test results. For example, if a sorption coefficient approach is used, the 
assumptions implicit in that approach are verified; 
(4) Uncertainty is adequately represented in parameter development for 
conceptual models, process-level models, and alternative conceptual models, 
considered in developing the abstraction of radionuclide transport in the unsaturated 
zone. This may be done either through sensitivity analyses or use of conservative 
limits; 
Acceptance Criterion 4, Model Uncertainty Is Characterized and Propagated 
through the Model Abstraction: 
(1) Alternative modeling approaches of features, events, and processes are 
considered and are consistent with available data and current scientific 
understanding, and the results and limitations are appropriately considered in the 
abstraction; 
(2) Conceptual model uncertainties are adequately defined and documented, and 
effects on conclusions regarding performance are properly assessed; 
(3) Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog 
information and process-level modeling studies; and the treatment of conceptual 
model uncertainty does not result in an under-representation of the risk estimate; 
and 
(4) Appropriate alternative modeling approaches are consistent with available 
data and current scientific knowledge, and appropriately consider their results and 
limitations, using tests and analyses that are sensitive to the processes 
modeled. For example, for radionuclide transport through fractures, the U.S. 
Department of Energy adequately considers alternative modeling approaches, to 
develop its understanding of fracture distributions and ranges of fracture flow and 
transport properties in the unsaturated zone. 
No Key Technical Issues were identified with respect to the work presented in this report. 
MDL-NBS-HS-000016 REV 01 4-12 September 2004 

Drift-Scale Radionuclide Transport 
Additional criteria identified in Technical Work Plan for: Unsaturated Zone Transport Model 
Report Integration (Bechtel SAIC Company, LLC (BSC) 2004 [DIRS 171282], Sections 3.3, 
3.4, and 3.5) are the Level of Accuracy, Precision, and Representativeness of Results, 
Completion Criteria and Other Requirements. The Level of Accuracy, Precision, and 
Representativeness of Results state: 
All reports addressed in this TWP will state the level of accuracy, precision, and 
representativeness for the results of the model, and how these were determined. Uncertainties 
associated with these models are a function of the specific application, and should be determined 
by the use of model-specific validation test cases. 
The level of accuracy and precision is addressed in Section 6.4.3. The level of 
representativeness is addressed in Sections 6.4 and 7.2.2. Uncertainties are treated in 
Sections 6.4.5, 6.6, and 7.2.3. 
The Completion Criteria state: 
This work will be done consistent with the activities performed as part of Technical Work Plan: 
Regulatory Integration Evaluation of Analysis and Model Reports Supporting the TSPA-LA (BSC 
2004 [DIRS 169377]) and will fulfill a portion of the Phase 2 work identified in that plan. It will 
also satisfy the requirements of AP-16.1Q, Condition Reporting and Resolution, to enable 
closure of the condition reports, if any, generated as a result of the Corrective Action Program 
noted in Section 1.2. 
This is addressed as a part of the Regulatory Integration Evaluation (BSC 2004 [DIRS 169377]) 
and the Other Requirements state: 
The boundary conditions for this work will be established in related process model documents 
and applicable Information Exchange Drawings. 
These Information Exchange Drawings are described in Section 4.1 
4.3 CODES, STANDARDS, AND REGULATIONS 
No specific formally established standards have been identified as applying to this modeling 
activity. 
MDL-NBS-HS-000016 REV 01 4-13 September 2004 

Drift-Scale Radionuclide Transport 
INTENTIONALLY LEFT BLANK
MDL-NBS-HS-000016 REV 01 4-14 September 2004 

Drift-Scale Radionuclide Transport 
5. ASSUMPTIONS 
The following assumptions are used in the absence of direct confirming data or evidence to 
perform the model activity. Other model assumptions are described in Section 6 of this model 
report. 
1. Diffusion in the rock matrix may be used as limiting upper values for diffusion in 
fractures. 
Diffusion coefficients in fracture water have not been directly determined. Generally 
speaking, diffusion in unsaturated geologic materials has been found to be sensitive to 
water content [Diffusion Coefficients in Gravel Under Unsaturated Conditions 
(Conca and Wright 1990 [DIRS 101582], p. 1,055; Dynamics of Fluids in Porous 
Media (Bear 1972 [DIRS 156269], Sections 4.8.2 and 4.8.3)]. Experimental evidence 
concerning diffusion in unsaturated granular materials is presented in Conca and 
Wright (1990 [DIRS 101582]). These experiments were performed on nonporous 
granular materials in which diffusion occurred through water films along the granular 
surfaces. The water content of these materials were on the order of 0.5 to 5 percent 
and diffusion coefficients ranged from about 10-13 m2/s to 10-11 m2/s (Conca and 
Wright 1990 [DIRS 101582], Figures 1013). The analogous water content of a 
fracture continuum is the fracture water saturation, which is also roughly in this range 
(see Appendix G). The range for matrix diffusion coefficients is about an order of 
magnitude larger (see Figure 6-23). This information suggests that the use of diffusion 
coefficients in the rock matrix as surrogates for diffusion coefficients in the fractures is 
conservative. Fractures in the welded tuff repository host rock are different than the 
nonporous granular materials investigated by Conca and Wright (1990 
[DIRS 101582]) due to differences in geometry and the connection to a porous rock 
matrix. Therefore, limiting values for diffusion coefficients in the fractures are taken 
to be the effective diffusion coefficients in the neighboring rock matrix. This 
assumption is used in Sections 6.3.2.2 and 6.4.5 and does not require further 
confirmation because the assumption represents a reasonable upper bound. 
2. Standard deviation of fracture frequency may be derived from the correlation with the 
mean value. 
Values for fracture frequency and the standard deviation for fracture frequency have 
been determined for several hydrogeologic model units in the unsaturated zone. These 
data show a strong correlation (see Figure 6-21). For two of the hydrogeologic model 
units addressed in this report (the tsw35 and tsw36), estimates of the mean fracture 
frequency are available, but not for the standard deviations. The correlation is used to 
estimate standard deviations for fracture frequency for these units. This assumption, 
used in Section 6.4.5, is considered adequate and does not require further 
confirmation. 
MDL-NBS-HS-000016 REV 01 5-1 September 2004 

Drift-Scale Radionuclide Transport 
3. A correlation between permeability, porosity, and effective diffusion coefficient 
developed for water-saturated rock matrix is extended to unsaturated conditions by 
using the effective permeability and water content in place of the permeability and 
porosity. 
This extension to unsaturated conditions is appropriate because for unsaturated flow, the 
character of the gas phase is not significant other than the space that it occupies. The gas phase 
could be replaced by solid (rock mineral) which would result in exact equivalence between the 
unsaturated water content and porosity and effective unsaturated permeability and permeability. 
This assumption, used in Section 6.4.5, is considered adequate does not require further 
confirmation because, as discussed for Assumption 1, the treatment of diffusion represents a 
reasonable upper bound. 
MDL-NBS-HS-000016 REV 01 5-2 September 2004 

Drift-Scale Radionuclide Transport 
6. MODEL DISCUSSION
This section begins with a summary of hydrogeologic conditions relevant to drift scale 
radionuclide transport as well as the drift shadow model and the fracture-matrix partitioning 
model in Section 6.1. Section 6.2 considers the features, processes, and events that the model 
report covers, followed by a description of the development of the shadow zone model in 
Section 6.3 and of the fracture-matrix partitioning model in Section 6.4. Section 6.5 presents an 
assessment of the effects of the air gap in the fracture. Section 6.6 compares the fracture-matrix 
partitioning model and the drift shadow model. 
6.1 INTRODUCTION 
Hydrogeology at Yucca Mountain 
Yucca Mountain consists of alternating layers of welded and nonwelded volcanic tuffs. The 
repository horizon lies in the unsaturated zone (UZ), approximately 300 m below the ground 
surface and 300 m above the water table. This horizon consists of welded tuffs composed of a 
dense porous rock matrix, which is highly fractured. Fracture permeability in the welded tuffs is 
on the order of darcies (~10-12 m2), and the rock matrix permeability is on the order of 
microdarcies (~10-18 m2) [Calibrated Properties Model (BSC 2004 [DIRS 169857], 
Table 6-8)]. Given these rock characteristics and the estimated range of water percolation rates 
of 1 to 11 mm/year [Simulation of Net Infiltration for Modern and Potential Future Climates 
(BSC 2004 [DIRS 170007], Table 6-10)], most of the water flux in the repository host rock is 
expected to flow in the fractures with a smaller component flowing through the rock 
matrix. Although most of the flow is in the fractures, more than 99 percent of the water volume 
resides in the rock matrix due to the larger porosity and water saturation in the matrix compared 
to the fractures. The key scientific notebooks (with relevant pages) used in this study are 
presented in Table 6-1. 
Table 6-1. Scientific Notebooks Used in this Model Report 
LBNL Scientific 
Notebook ID 
M&O Scientific 
Notebook ID Relevant Pages Citation 
YMP-LBNL-SZ-JEH-1 SN-LBNL-SCI-205-V1 115181; 193194 Houseworth 2003 [DIRS 163233] 
YMP-LBNL-SZ-JEH-2 SN-LBNL-SCI-239-V1 211231 Wang 2003 [DIRS 163234] 
YMP-LBNL-DSRT-JEH-1 SN-LBNL-SCI-236-V1 5145 Wang 2003 [DIRS 163234] 
Drift Shadow Alternative Model 
The Drift Shadow Alternative Model is developed in Section 6.3. The phenomenon of flow 
diversion around a cavity was investigated for a homogeneous porous medium by Philip et al. 
[Unsaturated Seepage and Subterranean Holes: Conspectus, and Exclusion Problem for 
Circular Cylindrical Cavities (Philip et al. 1989 [DIRS 105743])]. This diversion of flow was 
shown to result in flow velocities in a zone beneath the drift that are reduced relative to the 
undisturbed flow velocities away from the drift. In particular, the flow velocity at the base of the 
drift is exactly zero. The zone beneath the drift was also found to have lower water saturation 
MDL-NBS-HS-000016 REV 01 6-1 September 2004 

Drift-Scale Radionuclide Transport 
than the undisturbed zone. This region of reduced flow velocity and water saturation beneath the 
drift is known as the drift shadow (Philip et al. 1989 [DIRS 105743]). 
For a quasi-linear representation of the hydrogeologic properties, Philip et al. (1989 
[DIRS 105743]) found that the extent of the drift shadow is a function of the characteristic 
sorptive length scale and the drift radius. The quasi-linear model is a special case in which the 
logarithm of the relative permeability is linearly proportional to the capillary pressure, where the 
constant of proportionality is equal to 2, divided by the sorptive length scale. The shape of the 
drift shadow is governed by the ratio of the drift radius to the sorptive length scale. This ratio is 
a measure of the relative importance of gravitational forces compared with the capillary forces 
that define flow patterns around the drift. Philip et al. (1989 [DIRS 105743], p. 24) showed that 
the drift shadow becomes more elongated (relative to coordinates scaled by the drift radius) as 
the dimensionless ratio increases (i.e., the gravitational gradient becomes more 
dominant). Diagrams showing contours of equal flow velocity are given in Philip et al. (1989 
[DIRS 105743], Figure 3). Bordering the shadow, near the edge of the drift, a zone of enhanced 
flow occurs where the flow diverted from the top of the drift is focused. 
Capillary effects are much stronger in the matrix than in the fractures of a fractured rock. Based 
on the results of Philip et al. (1989 [DIRS 105743]), the fracture continuum is expected to 
behave as a gravity-dominated system and the rock matrix as a capillary-dominated system. 
Therefore, the reduction in flow below the drift is expected to be much more significant for the 
fracture continuum than for the matrix continuum. Furthermore, the very low water content of 
the fracture continuum below the drift, caused by very low saturation and porosity (compared to 
the matrix continuum), means that the vast majority of the water immediately below the drift will 
be in the rock matrix. 
In this report, the drift shadow model results suggest the use of the fracture-matrix partitioning 
model described below. This model is used as an alternative model for qualitative comparison 
with the Fracture-Matrix Partitioning Model described below. Comparisons between expected 
results for transport based on the fracture-matrix partitioning model method and the drift shadow 
model are used for model validation in Section 7. 
Fracture-Matrix Partitioning (Primary) Model 
Results of the drift shadow model rely on the use of the dual-continuum approach for drift-scale 
flow and transport in a fractured rock beneath a waste emplacement drift. A fracture-matrix 
partitioning model, developed in Section 6.4, considers the case in which fracture flow occurs in 
a region close to the base of the waste emplacement drift, relaxing the reliance on the 
dual-continuum process description of flow around a waste emplacement drift. The 
fracture-matrix partitioning model sets unperturbed fracture flow directly below the base of 
waste emplacement drifts. This approximation in neglecting the drift shadow effect on flow is 
based on the idea that the drift shadow may not be as spatially extensive as presented in 
Section 6.3, due to heterogeneity and anisotropy in fracture characteristics, as well as discrete 
fracture effects. Under these conditions, the partitioning of radionuclides from the waste 
emplacement drift to the rock fractures and matrix is an important process, given the more active 
hydrologic environment beneath waste emplacement drifts in this model. The fracture-matrix 
partitioning model establishes the fraction of radionuclides released to the rock fractures and 
MDL-NBS-HS-000016 REV 01 6-2 September 2004 

Drift-Scale Radionuclide Transport 
matrix. The output of this model can be used as an alternative model for comparison with the 
EBS Radionuclide Transport Model [EBS Radionuclide Transport Abstraction (BSC 2004 
[DIRS 169868])]. The transport model and the associated flow model used in total system 
performance assessment (TSPA) are mountain-scale models that do not represent the drifts and, 
therefore, do not include any effects of the drift shadow on flow or radionuclide transport 
beneath waste emplacement drifts. 
6.2 FEATURES, EVENTS, AND PROCESSES 
The following table of features, events, and processes (FEPs) was taken from the License 
Application (LA) FEP List (DTN: MO0407SEPFEPLA.000 [DIRS 170760]). The LA FEP List 
is a revision to the previous project FEP list [The Development of Information Catalogued in 
REV00 of the YMP FEP Database (Freeze et al. 2001 [DIRS 154365])] used to develop the list 
of FEPs in the Technical Work Plan for: Unsaturated Zone Transport Model Report Integration 
(BSC 2004 [DIRS 171282], Table 2.1.5-1). The selected FEPs are those taken from the LA FEP 
List that are relevant to the subject matter of this report. The cross-reference for each FEP to the 
relevant sections of this report is given below (Table 6-2). Screening arguments for both 
included and excluded FEPs are summarized in Features, Events, and Processes in UZ Flow and 
Transport (BSC 2004 [DIRS 170012]). 
Consistent with the use of this model report to only provide alternative conceptual models for 
comparison to the model implemented in TSPA (as described in Section 1), none of the FEPs 
shown in Table 6-2 is included in TSPA through the output of this report. Rather, the disposition 
of these FEPs is traceable through the output of two other model reports (BSC 2004 
[DIRS 169861] and BSC 2004 [DIRS 169131]). One FEP, 2.2.07.21.0A, is included in 
TSPA-LA through the outputs of (BSC 2004 [DIRS 169868]). That EBS radionuclide transport 
report may also take inputs developed in this document, and thereby inherently includes the 
FEPs associated with those inputs. 
Table 6-2. Features, Events, and Processes Addressed in This Report 
LA FEP Number FEP Name Cross Reference Section 
1.2.02.01.0A Fractures 6.3.2.3 and 6.4.5 
1.3.01.00.0A Climate change 6.4.6 
1.4.01.01.0A Climate modification increases recharge 6.4.6 
2.1.08.01.0A Water influx at the repository 6.3.2.2 and 6.4.5 
2.1.08.02.0A Enhanced influx at the repository 6.4.5 
2.2.03.01.0A Stratigraphy 6.4.5 
2.2.03.02.0A Rock properties of host rock and other units 6.3.2.3 and 6.4.5 
2.2.07.02.0A Unsaturated groundwater flow in the geosphere 6.3.3 and 6.4.1 
2.2.07.04.0A Focusing of unsaturated flow (fingers, weeps) 6.4.5 
2.2.07.08.0A Fracture flow in the UZ 6.3.3 and 6.4.1 
2.2.07.15.0B Advection and dispersion in the UZ 6.3.3.2 and 6.4.1 
2.2.07.20.0A Flow diversion around repository drifts 6.3.3.1 and 6.4.1 
MDL-NBS-HS-000016 REV 01 6-3 September 2004 

Drift-Scale Radionuclide Transport 
Table 6-2. Features, Events, and Processes Addressed in This Report (Continued) 
LA FEP Number FEP Name Cross Reference Section 
2.2.07.21.0A Drift shadow forms below repository 6.3.3.1 and 6.4.1 
2.2.08.05.0A Diffusion in the UZ 6.3.2.3 and 6.4.5 
2.2.08.08.0B Matrix diffusion in the UZ 6.3.2.3 and 6.4.5 
2.2.08.09.0B Sorption in the UZ 6.3.2.3 
6.3 DRIFT SHADOW ALTERNATIVE MODEL 
6.3.1 Conceptual Model and Numerical Implementation of the Drift Shadow Model 
This conceptual model used for the drift shadow model accounts for the effects of capillary, 
gravity, and viscous forces through the Darcy formulation for unsaturated flow. Transport 
processes are represented using mass conservation principles accounting for advection, diffusion, 
and sorption processes. The dual-permeability conceptual model is used to represent flow and 
transport in fractured rock. The dual-permeability model allows for flow and transport in a 
fracture continuum and a matrix continuum with advective and diffusive exchange between these 
continua. The conceptual model for fracture-matrix exchange also incorporates the active 
fracture model [An Active Fracture Model for Unsaturated Flow and Transport in Fractured 
Rocks (Liu et al. 1998 [DIRS 105729])], in which the fraction of flowing fractures is postulated 
to be a function of fracture saturation. This type of behavior is a result of flow instabilities 
caused by gravitational instability in combination with spatially heterogeneous properties, which 
leads to water flow in only a portion of the connected fracture system. One consequence of the 
active fracture model is a reduction in fracture-matrix interaction, needed to calibrate the 
dual-permeability flow model to observed matrix water saturations and potentials at Yucca 
Mountain [Calibrating Hydrogeologic Parameters for the 3-D Site-Scale Unsaturated Zone 
Model of Yucca Mountain, Nevada (Bandurraga and Bodvarsson 1999 [DIRS 103949])]. Thus, 
the drift-shadow conceptual model uses a standard continuum representation of flow and 
transport in a fractured rock. 
The conceptual flow and transport models are implemented numerically using an integral finite-
difference method. Flow calculations are carried out to steady-flow conditions using the 
iTOUGH2 V4.0 (LBNL 1999 [DIRS 139918]) EOS9 module [TOUGH2 Users Guide, Version 
2.0 (Pruess et al. 1999 [DIRS 160778])], which simulates unsaturated flow according to 
Richards equation [Capillary Conduction of Liquids Through Porous Mediums (Richards 
1931 [DIRS 104252])]. The flow model calibration has been performed using the TOUGH 
family of software (BSC 2001 [DIRS 161316]), thus the compatibility of the parameters between 
the parameter development and their implementation in this report lead to the selection of the 
iTOUGH2 V4.0 [DIRS 139918] software over other possible software and computational 
methods. Transport calculations are then performed for steady-state flow conditions using the 
EOS9nT module of TOUGH2 (TOUGH2 V1.11MEOS9NTV1.0 [DIRS 113943] in Table 3-1) 
[EOS9nT: A TOUGH2 Module for the Simulation of Water Flow and Solute/Colloid Transport in 
the Subsurface (Moridis et al. 1999 [DIRS 123093])]. The transport module first solves Richards 
equation to establish the steady-state flow field. The solute concentrations are sufficiently small 
MDL-NBS-HS-000016 REV 01 6-4 September 2004 

Drift-Scale Radionuclide Transport 
such that they have no dynamic effects on the flow (e.g., the density or viscosity). This allows 
transport equations to be decoupled from flow equations. Transport equations are solved using a 
Laplace transform method (Moridis et al. 1999 [DIRS 123093], Section 3.2) applicable to 
steady-state flow conditions. Compatibility between the flow calculations with iTOUGH2 V4.0 
(LBNL 1999 [DIRS 139918]) and the transport calculations with TOUGH2 
V.11MEOS9NTV1.0 (LBNL 1999 [DIRS 113943]) lead to the selection of the TOUGH2 V4.0 
software over other possible software and computational methods. Other direct finite-difference 
approaches for treating the time dependence of the transport problem were not used because the 
Laplace transform method provides a semi-analytical treatment of the time derivatives that 
eliminates the need for time discretization or any restrictions on time-step size. 
An important factor in the drift shadow problem, as discussed in Section 6.1, is the diversion of 
percolation flux around the drift such that water does not enter the drift. A considerable amount 
of theoretical and experimental work has been conducted to evaluate seepage for the waste 
emplacement drifts at Yucca Mountain [Evolutions of the Unsaturated Zone Testing at Yucca 
Mountain (Wang and Bodvarsson 2003 [DIRS 163215]); Inverse and Predictive Modeling of 
Seepage into Underground Openings (Finsterle et al. 2003 [DIRS 163214]); Seepage into 
Drifts with Mechanical Degradation (Li and Tsang 2003 [DIRS 163714]); Abstraction of Drift 
Seepage (BSC 2004 [DIRS 169131])]. This work indicates that the percolation flux 
encountering a drift will be completely diverted if the percolation flux is less than a value known 
as the seepage threshold. The seepage threshold depends on the capillary properties of the 
fracture system, the size and shape of the drift, and the heterogeneity in fracture properties. 
The drift shadow model is used in this report as an alternative model to the fracture-matrix 
partitioning model discussed in Section 6.4. Results of the drift shadow model are used for 
qualitative comparison with the fracture-matrix partitioning model as presented in Section 7. 
The model calculations were carried out using property sets (discussed in Section 6.3.2.3) 
available at the time the original calculations were performed (Houseworth 2003 
[DIRS 163233]). Additional documentation of the work presented in Section 6.3 is provided in 
Scientific Notebook by Houseworth (2003 [DIRS 163233], pp. 115181,; 193194). 
6.3.2 Numerical Grid, Boundary Conditions, and Parameter Development 
6.3.2.1 Numerical Grid 
The calculations presented here are for a two-dimensional, homogeneous, dual-permeability 
model of an emplacement drift. Figure 6.3-1 shows the grid used in the calculations developed 
using the software CutDrift V1.0 [DIRS 152816]. The area around the 5 m diameter drift uses a 
refined grid of 0.2 m  0.2 m. Farther from the drift, the grid coarsens to approximately 
2 m  2 m. Simulations for a single-continuum flow field around an open drift using the same 
spatial discretization were found to be in agreement with an analytical solution (Houseworth et 
al., 2003 [DIRS 164394], Section 3.1). This comparison indicates that the grid has sufficient 
spatial resolution. The drift is represented by two grid blocks that provide horizontal and vertical 
connections to the bordering rock grids after removing the grid blocks originally generated in the 
drift region. The depth to the bottom of the drift shadow model was chosen roughly on the 
character of the flow fields. At 45 meters below the drift, the flow field is found to have nearly 
returned to the unperturbed state (see Figures 6.2 through 6.4). 
MDL-NBS-HS-000016 REV 01 6-5 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 6-6 September 2004 
The 5 m drift diameter used in this calculation differs from the 5.5 m drift diameter in the current 
repository design. This smaller diameter may be used because the effects of a smaller drift 
diameter, given no drift seepage, will result in a conservative estimate of the effects of a drift on 
transport beneath the drift. This is because the magnitude of the drift shadow effect is a function 
of the size of the drift; as the drift becomes smaller, the effects of the drift on the flow beneath 
the drift also become smaller. 
102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
No-flowboundariesDrift,5mdiameterFree-drainageboundaryImposedfluxinfracturesandmatrix 
Output DTN: LB0307DSRADTRN.001. 
Figure 6-1. Grid and Boundary Conditions 
6.3.2.2 Boundary Conditions 
As shown in Figure 6-1, the model uses a no-flow symmetry condition along the vertical 
centerline of the drift. Similarly, the far lateral boundary is a no-flow boundary due to the 
symmetry condition reflecting the periodic, 81 m drift spacing. Note that the grid lines in 
Figure 6-1 illustrate the position of the grid centers, not the grid boundaries; thus the far lateral 
boundary is 40.5 m from the centerline. The bottom boundary condition is free gravity drainage 
(no capillary pressure gradient). The center of the drift is 17.5 m below the top of the model 
domain, and the drift has a radius of 2.5 m. Hydrological properties are assigned to the drift such 
that the capillary pressure is zero for all values of water saturation. 
Flow is introduced at the top boundary at a prescribed flow rate. For the dual-continuum model 
calculations, flow rates are prescribed separately for the fracture and matrix continua. This is 
necessary to develop a flow field compatible with results from the mountain-scale unsaturated 
zone flow model. The flow rates in Table 6-3 were chosen to cover a range of total flows while 
keeping matrix saturations within the range of observed values, approximately 0.80 to 
0.95 [Calibrated Properties Model (BSC 2001 [DIRS 161316]), Section 6.1.4]. For higher total 

Drift-Scale Radionuclide Transport 
percolation rates expected for future climates, BSC (2001 [DIRS 158726], Tables 6-23 and 6-24) 
shows that the percentage of the total percolation moving in the matrix is lower, however the 
absolute matrix flux increases as expected under wetter climate conditions. Therefore, the 
percentage of total flux in the matrix is adjusted to allow for more flow in the matrix than found 
at the lower percolation rates, short of saturating the matrix. Table 6-3 gives the values of flow 
rates investigated here. Note the cited fracture flow rate and matrix flow rate in Table 6-3 and 
elsewhere in this report refer to the flow rate maintained at the upper boundary of the model. 
Because of fracture-matrix interaction and flow diversion, the local flow rates at other locations 
in the model will vary. 
Table 6-3. Flow Rates Investigated 
Total Flow Rate (mm/yr) Fracture Flow Rate (mm/yr) Matrix Flow Rate (mm/yr) 
10 9.85 0.15 
10 9.15 0.85 
100 99.55 0.45 
100 98.4 1.6 
300 299.0 1.0 
Output DTN: LB0307DSRADTRN.001. 
6.3.2.3 Parameters 
Parameters used here for the drift-shadow model are from previous work for the Site 
Recommendation. Parameters for the License Application have changed; however, the general 
character of the rock remains the same, i.e., the fractures and matrix in the repository host rock 
are distinct continua with large differences in permeability, porosity, and capillary pressure 
characteristics. Differences in parameters between Site Recommendation and License 
Application do not impact the qualitative behavior of flow and transport in the drift shadow. This 
can be seen through the comparison of transport behavior as computed for Site Recommendation 
in BSC (2001 [DIRS 158726], Figures 6-54 through 6-56) and BSC (2004 [DIRS 169861], 
Figure 6.7-1). In particular, transport of radionuclides released in the drift shadow will be orders 
of magnitude longer than transport of radionuclides released to unperturbed fracture flow for 
either parameter set. Given that the drift shadow model presented here is only used for 
qualitative comparison with the fracture-matrix partitioning model discussed in Section 6.4, the 
older parameter set is adequate for the intended use of this alternative model. 
Capillary pressure and relative permeability functions of saturation for the fracture and matrix 
continua are based on the van Genuchten formulation [A Closed-Form Equation for Predicting 
the Hydraulic Conductivity of Unsaturated Soils (van Genuchten 1980 [DIRS 100610])]. The 
property set for the tsw35 hydrogeologic unit (BSC 2001 [DIRS 161316]), which corresponds to 
the lower lithophysal unit of the Topopah Spring tuff, is used in the flow calculations. This 
property set is used because about 80 percent of the waste emplacement areas in the repository 
reside in this unit (see Table 4-9 and Appendix H). The hydrological data are summarized in 
Tables 6-4 and 6-5 for the Topopah Spring Tuff Lower Lithophysal unit, one of the repository 
host rock units for waste emplacement drifts. Matrix and mountain-scale fracture properties are 
given in DTN: LB997141233129.001 [DIRS 104055]. 
MDL-NBS-HS-000016 REV 01 6-7 September 2004 

Drift-Scale Radionuclide Transport 
The calibrated property set for dual-permeability flow and transport calculations is based on 
permeability values obtained by calibrating a mountain-scale model against saturation, water 
potential, and pneumatic pressure data, using a large-scale model of Yucca Mountain 
[(Bandurraga and Bodvarsson 1999 [DIRS 103949]; Characterization and Prediction of 
Subsurface Pneumatic Response at Yucca Mountain, Nevada (Ahlers et al. 1999 
[DIRS 109715])]. Permeability measured at the drift scale has been found to be roughly one 
order of magnitude smaller than that inferred from measurements at the mountain scale (BSC 
2001 [DIRS 161316], Section 6.2). This difference results from the difference in sampling 
volume between mountain-scale and drift-scale measurements. Mountain-scale measurements 
capture the sparse, but highly permeable, fracture pathways not present in the typical smaller 
sampling volume. Because of the smaller length scales addressed in this model (tens of meters 
rather than hundreds of meters), the drift-scale fracture permeability is more appropriate. 
Drift-scale fracture permeability, shown in Table 6-6, was derived in the Calibrated Properties 
Model (BSC 2001 [DIRS 161316]; DTN: LB990861233129.001 [DIRS 110226]). All other 
properties at the drift scale were kept the same as the site-scale properties, as recommended in 
Calibrated Properties Model (BSC 2001 [DIRS 161316], Section 6.2). However, for 
fracture-matrix interaction to be approximately the same for the mountain-scale and drift-scale 
properties, the drift-scale active fracture parameter, ., must be increased from 0.41 to 0.81 (see 
Figure 6.3-4). This is a result of the change in fracture permeability between these property sets. 
An evaluation of the mountain-scale versus drift-scale properties with respect to the active 
fracture parameter is discussed further in Section 6.3.3.1. 
Table 6-4. Hydrological Properties for the tsw35Matrix Properties (Drift-Scale and Mountain-Scale) 
van van 
Permeability Porosity 
Genuchten 
a 
Genuchten 
m 
Residual 
saturation 
Satiated 
saturation 
Rock grain 
density 
km (m2) fm (-) am (1/Pa) mm (-) Slrm (-) Slsm (-) .g (kg/m3) 
3.04E-17 0.131 6.44E-6 0.236 0.12 1.00 2540 
DTN: LB997141233129.001 [DIRS 104055], BSC 2001 [DIRS 161316]. 
Table 6-5. Hydrological Properties for the tsw35Fracture Properties (Mountain-Scale Permeability) 
Fracture to 
Mountain-van van Active matrix 
scale Genuchten Genuchten Residual Satiated fracture connection 
permeability Porosity a m saturation saturation parameter Frequency area 
kf (m2) ff () 
af (1/Pa) mf (-) Slrf (-) Slsf (-) . (-) f (1/m) A (m2/m3) 
4.51E-11 1.5E-2 7.39E-4 0.611 0.01 1.00 0.41 3.16 9.68 
DTN: LB997141233129.001 [DIRS 104055], BSC 2001 [DIRS 161316], BSC 2001 [DIRS 159725]. 
MDL-NBS-HS-000016 REV 01 6-8 September 2004 

Drift-Scale Radionuclide Transport 
Table 6-6. Hydrological Properties for the tsw35Drift-Scale Fracture Permeability 
Drift-Scale Permeability 
kf (m2) 
1.29E-12 
DTN: LB990861233129.001 
[DIRS 110226], BSC 2001 
[DIRS 161316]. 
Transport calculations require the specification of matrix diffusion and sorption parameters. For 
TSPA, sorption and diffusion parameters have been characterized using a statistical approach to 
account for the variability found in measured values [Unsaturated Zone and Saturated Zone 
Transport Properties (U0100) (BSC 2001 [DIRS 160828])]. The parameters used in the 
calculations reported here have been chosen to be the expected (mean) values used in the site 
recommendation base case [Total System Performance Assessment for the Site Recommendation 
(CRWMS M&O 2000 [DIRS 153246], Section 3.7.3)]. The drift-shadow transport calculations 
presented here are for technetium, neptunium, and plutonium. These radionuclides were chosen 
because of their significance in dose calculations for TSPA (CRWMS M&O 2000 
[DIRS 153246], Figure 4.1-19a). Under the oxidizing conditions expected in the UZ, the aqueous 
form of technetium is the negatively charged pertechnetate ion (TcO4-), which is nonsorbing. 
Under the relevant geochemical conditions, aqueous neptunium has been found to be weakly 
sorbing to the volcanic rock, and aqueous plutonium has been found to be strongly sorbing (BSC 
2001 [DIRS 160828], Section 6.4.4.1.4). Therefore, the aqueous radionuclides investigated here 
span the range of expected sorption behavior. Matrix sorption coefficients are given in 
DTN: LA0003AM831341.001 [DIRS 148751]. Implementation of sorption coefficients in a 
transport model also requires specification of the rock bulk density. Rock bulk density in the 
tsw35 is given in DTN: LB997141233129.001 [DIRS 104055]. Note that sorption is only 
accounted for in the matrix because values for sorption in the fractures have not been measured 
and are difficult to estimate. 
Values for the effective diffusion coefficients in the matrix are taken from 
DTN: LA0003JC831362.001 [DIRS 149557]. The effective diffusion coefficient for technetium 
in tuff matrix is found to be smaller than for neptunium or plutonium. This is postulated to be a 
result of the large size and negative charge of the pertechnetate ion, leading to exclusion from a 
portion of the matrix pore space and a lower tortuosity. Parameters used for transport are given 
in Table 6-7. 
Table 6-7. Transport Properties for the tsw35 
Matrix Diffusion 
Coefficient (m2/s) 
Matrix Sorption Coefficient 
(m3/kg) 
Technetium 3.2  10-11 0 
Neptunium 1.6  10-10 3.0  10-4 
Plutonium 1.6  10-10 3.75  10-2 
DTNs: LA0003AM831341.001 [DIRS 148751] and LA0003JC831362.001 [DIRS 149557]. 
For diffusion in the fractures, a representative average diffusion coefficient in water, 1.6  
10-9 m2/s, is adjusted by the tortuosity, where the fracture tortuosity is approximated by the 
MDL-NBS-HS-000016 REV 01 6-9 September 2004 

Drift-Scale Radionuclide Transport 
matrix tortuosity (see Section 4.1.5 and 6.4.5). The free-water diffusion coefficient is based on 
the average of the values given in Table 4-8. No sorption is accounted for in the fractures owing 
to the limited information and likely limited effects on transport. 
Hydrodynamic dispersion is not expected to play a significant role in the transport of 
radionuclides in the fractures, because of the predominant role of differential advection resulting 
from fracture-matrix interaction as the main dispersive mechanism. The dispersive effects of 
fracture-matrix interaction are explicitly modeled, so they do not need to be represented in the 
form of a dispersion coefficient. Low velocities and short correlation lengths in the matrix make 
hydrodynamic dispersion negligible compared to molecular diffusion, which is included. With 
this in mind, hydrodynamic dispersion is not included in the model. 
The transport of aqueous radionuclides is calculated without including the effects of radioactive 
decay. For technetium, neptunium, and certain isotopes of plutonium, the half-lives are long 
relative to the transport times in the drift-shadow model. 
6.3.3 Results of Analysis 
6.3.3.1 Flow Field Results and Parameter Sets 
Unsaturated flow calculations were performed for a dual-continuum model using the 
mountain-scale and drift-scale property sets shown in Tables 6-4 to 6-6 and the flow rates shown 
in Table 6-3. The van Genuchten relative permeability relationship is used for these TOUGH2 
calculations. The repository design locates about 80 percent of the emplacement drifts in the 
tsw35 hydrogeologic unit (see Appendix H). Results of flow calculations using the 
mountain-scale property set are shown in Figure 6-2. 
i9 
8 
7 
6 
5 
4 
3 
2 
1 
l ll/yrl/yr 
i1 
2 
3 
4 
5 
6 
6 
78 
9 
water saturaton 
0.868 
0.862 
0.86 
0.859 
0.8585 
0.858 
0.857 
0.855 
0.85 
Saturation contours in the matrix 
Totapercoation fux = 10 mmMatrix percoation flux = 0.15 mmGamma = 0.41 
mountan-scale properties 
i9 
8 
7 
6 
5 
4 
3 
2 
1 
/
l/
1 
2 
3 
4 
5 
6 
7 
8 
9 
water saturaton 
0.02 
0.018 
0.0175 
0.0173 
0.017 
0.0165 
0.016 
0.015 
0.012 
Saturation contours in the fractures 
Total percolation flux = 10 mmyr 
Matrix percoation flux = 0.15 mmyr 
Gamma = 0.41 
mountain-scale properties 
Vertical Distance (m) 
-60 
-60 
102030405060 102030405060 
Horizontal Distance (m) Horizontal Distance (m) 
(a) (b) 
Figure 6-2. Fracture and Matrix Vertical Flux and Saturation Contours Using Mountain-Scale Property 
Set: (a) Matrix Saturation; (b) Fracture Saturation; (c) Matrix Flux (note 0.15 mm/yr = 
4.75  10-9 kg/m2-s); (d) Fracture Flux (note 9.85 mm/yr = 3.12  10-7 kg/m2-s) 
-10 
-10 
-20 
Vertical Distance (m) 
-20 
-30 
-30 
-40 
-40 
-50 
-50 
MDL-NBS-HS-000016 REV 01 6-10 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 6-11 September 2004 
102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
waterflux(kg/m2-s)
9-3E-098-4E-097-4.5E-096-4.75E-095-4.8E-094-4.95E-093-5.1E-092-5.5E-091-6E-09VerticalfluxcontoursinthematrixTotalpercolationflux=10mm/yrMatrixpercolationflux=0.15mm/yrGamma=0.41mountain-scaleproperties98765432156789102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
waterflux(kg/m2-s)
9-1E-088-5E-087-1.5E-076-2.5E-075-3.5E-074-4E-073-4.5E-072-5E-071-6E-07VerticalfluxcontoursinthefracturesTotalpercolationflux=10mm/yrMatrixpercolationflux=0.15mm/yrGamma=0.41mountain-scaleproperties123456789 
(c) (d) 
Output DTN: LB0307DSRADTRN.002. 
Figure 6-2. Fracture and Matrix Vertical Flux and Saturation Contours Using Mountain-Scale Property 
Set: (a) Matrix Saturation; (b) Fracture Saturation; (c) Matrix Flux (note 0.15 mm/yr = 
4.75  10-9 kg/m2-s); (d) Fracture Flux (note 9.85 mm/yr = 3.12  10-7 kg/m2-s) (Continued) 
The drift shadow is seen to be long and narrow for gravity-dominated fracture flow (Figures 6-2b 
and 6-2d), resulting in a decrease in fracture flow for several drift diameters below the drift. For 
example, the flow rate within about three drift diameters, on the drift centerline below the 
emplacement drift, is less than 50 percent of the undisturbed flow rate. The matrix, on the other 
hand, has a much shorter drift shadow (Figures 6-2a and 6-2c), with the flow rate in the matrix 
less than 50 percent of the undisturbed flow rate within approximately 0.2 drift diameters below 
the bottom of the drift (Figure 6-2c). 
The original drift-scale property set is the same as the modified drift-scale property set with the 
exception of the active fracture parameter, .. In the original drift-scale property set, . is assigned 
a value of 0.41, which is the same as for the mountain-scale property set. The vertical flow and 
water saturation contours for the original drift-scale property set are shown in Figure 6-3. 
However, as shown by comparing Figures 6-2 and 6-3, the resulting flow and saturation contours 
are substantially altered for the drift-scale property set. In particular, global vertical gradients of 
matrix water saturation and flow appearing in Figures 6-3a and 6-3c contrasts with the 
corresponding plots in Figures 6-2a and 6-2c. The water saturation contours in Figure 6-3 
indicate a much greater degree of fracture-matrix interaction than that found for the 
mountain-scale property set. This can be seen by the increase of matrix water saturation with 
depth. Given that the matrix properties are unchanged, the only mechanism that would explain 
this pattern is an increase in water flux from the fractures to the matrix. The flow model 
calibration against measured values of matrix water potential and saturation was conducted for 
the mountain-scale property set. Therefore, the original drift-scale property does not appear to be 
consistent with the field data. 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 6-12 September 2004 
102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
watersaturation90.91772680.91295270.90817860.90340450.8986340.89385630.88908220.88430810.879534SaturationcontoursinthematrixTotlpercolationflux=10mm/yrMatrixpercolationflux=0.15mm/yrGamma=0.41drift-scaleproperties12345678967548102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
watersaturation90.04580.04270.0460.03850.03540.0330.02520.0210.015SaturationcontoursinthefracturesTotalpercolationflux=10mm/yrMatrixpercolationflux(attop)0.15mm/yrGamma=0.41drift-scaleproperties98765432 
(a) (b) 
102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
waterflux(kg/m2-s)
8-5E-097-6E-096-7E-095-8E-094-9E-093-1E-082-1.1E-081-1.2E-0812345678432156VerticalfluxcontoursinthematrixTotalpercolationflux=10mm/yrMatrixpercolationflux=0.15mm/yrGamma=0.41drift-scaleproperties87102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
waterflux(kg/m2-s)
9-1E-088-5E-087-1.5E-076-2.5E-075-3.5E-074-4E-073-4.5E-072-5E-071-6E-07VerticalfluxcontoursinthefracturesTotalpercolationflux=10mm/yrMatrixpercolationflux=0.15mm/yrGamma=0.41drift-scaleproperties123456789 
(c) (d) 
Output DTN: LB0307DSRADTRN.002. 
Figure 6-3. Fracture and Matrix Vertical Flux and Saturation Contours using Drift-Scale Property Set 
and . = 0.41 (a) Matrix Saturation; (b) Fracture Saturation; (c) Matrix Flux; (d); Fracture Flux 
The differences in fracture-matrix interaction found for mountain-scale and drift-scale 
parameters may be understood from the van Genuchten relationships as modified for the active 
fracture model. As proposed in Liu et al. (1998 [DIRS 105729], Equation 1), the fraction of 
active fractures, fa, is defined by 
.eaSf= (Eq. 6-1) 

Drift-Scale Radionuclide Transport 
where . is an empirical parameter of the active fracture model. Se is the effective fracture 
saturation defined by 
Sf - S
r
S = (Eq. 6-2)
e 
1 - S
r 
where Sf is the fracture water saturation and Sr is the residual fracture water saturation. The 
active fracture parameter, ., is constrained to be less than or equal to one such that the saturation 
of the active fractures is less than or equal to one. Liu et al. (1998 [DIRS 105729], Equations 5 
and 9) derive the following relationships for fracture capillary pressure, Pc , and relative 
permeability, kr , using the van Genuchten formulation (van Genuchten 1980 [DIRS 100610]) in 
combination with the active fracture concept: 
1-m
S P (.-1) / m
()= 1 [S -1] (Eq. 6-3)
ce e
a 
m
S (1+.) /2 
2 
k ()= S [1 -{1 - S (1-.) / m }](Eq. 6-4)
ree e 
Figures 6-2 and 6-3 show that fracture water saturation is expected to be low, in the range of 0.01 
to 0.05. The effective water saturation range is even lower in magnitude. Therefore, it is 
appropriate to consider an expansion of the capillary pressure and relative permeability functions 
for low water saturation. The first-order expansions of the capillary pressure and relative 
permeability functions for low water saturation (such that S (1-.) / m is small) are 
() 1 S 
.
. 
1- m 
..
(.-1)
S P. m . (Eq. 6-5) 
ce e
a 
(
1 4 -.)+m(1+.) 
k ()S m 
S 
22m (Eq. 6-6)
re e 
Flux in the fractures, qf, can be approximated as free gravity drainage, i.e., the flux in the 
fractures equals the effective hydraulic conductivity. The effective hydraulic conductivity of the 
fractures is equal to the product of the saturated hydraulic conductivity, Ks, times the relative 
permeability. Using this approximation, the fracture saturation is given by 
2m 
(
S ..
. q .1 4 -.)+ m(1+.)
f 
(Eq. 6-7)
e . m K 2 ...
s 
Substituting this into Equation 6-5 gives 
(
1 2 -.)(1-m) 
(
1 4 -.)+m(1+.)
1 .
. m K 2 . 
P
a.
. qs .. 
(Eq. 6-8)
c 
f . 
MDL-NBS-HS-000016 REV 01 6-13 September 2004 

Drift-Scale Radionuclide Transport 
Note that the exponent of Ks is always positive. This relationship shows that for a fixed qf, as Ks 
decreases, Pc also decreases. This leads to a larger pressure difference between the fractures and 
matrix and, therefore, greater fracture-to-matrix imbibition flow as Ks decreases. This is 
consistent with the changes in fracture-matrix interaction observed in Figures 6-2 and 6-3 using 
the mountain-scale and drift-scale fracture permeabilities. 
The noted increase in fracture-matrix interaction suggests that the fracture-matrix interaction 
parameter, ., needs to be modified for use with the lower drift-scale fracture permeability. 
Measurements to establish . at the drift scale are not available. However, one of the key 
calibration metrics used to establish the value of . for the mountain-scale flow model is matrix 
saturation (BSC 2001 [DIRS 161316], Section 6). Figure 6-4 shows the matrix saturation 
contours using the drift-scale property set over a range of values for .. Increasing the value of . 
reduces fracture-matrix interaction. The matrix water saturation contours for the drift-scale 
properties with . set to 0.81 (Figure 6-4d) appear to be consistent with saturation contours for the 
mountain-scale property set (Figure 6-4a). Therefore, the modified drift-scale parameter set is 
believed to be more consistent with field observations. Note that the current calibrated properties 
values (BSC 2004 [DIRS 169857], Section 6, Tables 6-8 through 6-10) were developed using the 
lower drift-scale fracture permeabilities, and the values of . have increased from the previous 
values for the repository host rock units (BSC 2001 [DIRS 161316], Section 6, Tables 13-15). 
This is true even though matrix permeabilities are reduced in the current property set, which if 
everything else was held constant, would lead to a lower value of .. 
Calibration of the UZ Flow Model (Bandurraga and Bodvarsson 1999 [DIRS 103949], Section 4) 
and comparisons of geochemical composition of perched water (water from the fracture 
continuum) and matrix pore water [Analysis of Geochemical Data for the Unsaturated Zone 
(BSC 2003 [DIRS 168343], Section 7.5)] suggest that the fracture and matrix continua are only 
weakly connected. The UZ Flow Model requires reduced fracture-matrix interaction areas for 
calibration against field measurements of water saturation and potential (Liu et al. 1998 
[DIRS 105729], Section 1). Perched water and matrix pore waters are found to be significantly 
different in composition (BSC 2003 [DIRS 168343], Section 7.5), indicating a lack of 
geochemical equilibrium between the fracture and matrix continua. Although the hydrological 
and geochemical evidence indicates that the fracture and matrix continua are only weakly 
coupled, quantitative estimates of parameters reflecting this aspect of the fractured rock system 
are uncertain. Furthermore, this aspect of the system has a large impact on radionuclide transport 
in the drift shadow and beyond. 
Flow calculations for percolation rates of 10 mm/year and 100 mm/year have been performed 
and are used in the transport calculations discussed below. Flow behavior for higher total 
percolation rates also have been investigated. Complete diversion of seepage is found for total 
percolation rates up to 300 mm/year. Between the 300 and 350 mm/year total percolation rate, 
gravitational forces overcome the seepage threshold and water enters the drift. 
MDL-NBS-HS-000016 REV 01 6-14 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 6-15 September 2004 
102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
watersaturation90.86880.86270.8660.85950.858540.85830.85720.85510.85SaturationcontoursinthematrixTotalpercolationflux=10mm/yrMatrixpercolationflux=0.15mm/yrGamma=0.41mountain-scaleproperties1234566789102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
watersaturation90.91772680.91295270.90817860.90340450.8986340.89385630.88908220.88430810.879534SaturationcontoursinthematrixTotlpercolationflux=10mm/yrMatrixpercolationflux=0.15mm/yrGamma=0.41drift-scaleproperties12345678967548 
(a) (b) 
102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
watersaturation90.8880.87470.87260.8750.86940.86830.86520.86310.86SaturationcontoursinthematrixTotalpercolationflux=10mm/yrMatrixpercolationflux=0.15mm/yrGamma=0.61drift-scaleproperties1234567856789432102030405060HorizontalDistance(m)
-60-50-40-30-20-10VerticalDistance(m)
watersaturation90.86880.86270.8660.85950.858540.85830.85720.85510.85SaturationcontoursinthematrixTotalpercolationflux=10mm/yrMatrixpercolationflux=0.15mm/yrGamma=0.81drift-scaleproperties12451386679 
(c) (d) 
Output DTN: LB0307DSRADTRN.002. 
Figure 6-4. Matrix Saturation Contours Using Different Property Sets: (a) Mountain-Scale; (b) Drift-
Scale, . = 0.41; (c) Drift-Scale, . = 0.61; (d); Drift-Scale, . = 0.81 
6.3.3.2 Transport Results 
Transport calculations were run for a dual-permeability flow and transport system using the 
EOS9nT module of TOUGH2 (Moridis et al. 1999 [DIRS 123093]). In all cases, 1 kg of 
radionuclide is available for release from the waste emplacement drift. Connections are made 
from two cells inside the drift, where the radionuclides originate, to the fractures and rock matrix 
cells adjacent to the bottom of the drift and within 1.1 meter of the drift centerline (Houseworth 
2003 [DIRS 163233], p. 118). Radionuclides enter the fracture and matrix cells from the drift 
cells at rates determined by diffusive transport processes, because water does not flow through 
the drift cells. 

Drift-Scale Radionuclide Transport 
Breakthrough curves for transport to the bottom of the model (45 m below the bottom of the 
emplacement drift, as seen in Figure 6-1) are shown for technetium, neptunium, and plutonium 
in Figures 6-5a through 6-5d. These figures compare the transport results for total percolation 
rates of 10 mm/year and 100 mm/year for 2 matrix percolation cases each (see Table 6-3). 
Percolation flux = 10 mm/yr 
Matrix percolation flux = 0.15 mm/yr Percolation flux = 10 mm/yr 
Gamma = 0.81 Matrix percolation flux = 0.85 mm/yr 
Gamma = 0.81 
1 
102 103 104 105 106 107 108 
Tc 
Np 
Pu 
dri0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
Cumulative Breakthrough Fraction 
ft-scale properties
0.8 
0.7 
0.6 
0.5 
0.4 
0.1 
0.1 
0 
ve Breakthrough Fraction 
1 
102 103 104 105 106 107 
Tc 
Np 
Pu 
drilft-scae properties 
0.9 
0.9 
Cumulati
0.3 
0.2 
(a) 
(b)
Time (years) 
Time (years) 
Percolation flux = 100 mm/yr
Percolation flux = 100 mm/yr Matrix percolation flux = 1.6 mm/yr 
Matrix percolation flux = 0.45 mm/yr Gamma = 0.81 
Gamma = 0.81 
drift-scale properties 
1 
102 103 104 105 106 107 108 
Tc 
Np 
Pu 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
Cumulative Breakthrough Fraction 
102 103 104 105 106 107 108 
Tc 
Np 
Pu 
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
Cumulative Breakthrough Fraction 
drift-scale properties 
1 
0.9 
0.9 
0.1 
0.1 
(c) 
(d) 
Time (years)
Time (years) 
Output DTN: LB0307DSRADTRN.002. 
Figure 6-5. Breakthrough Curves for Drift Shadow Transport: (a) Total Percolation Flux = 10 mm/year, 
Matrix Percolation Flux = 0.15 mm/year; (b) Total Percolation Flux = 10 mm/year, Matrix 
Percolation Flux = 0.85 mm/year; (c) Total Percolation Flux = 100 mm/year, Matrix 
Percolation Flux = 0.45 mm/year; (d) Total Percolation Flux = 100 mm/year, Matrix 
Percolation Flux = 1.6 mm/year 
A comparison of the 50 percent breakthrough with approximate matrix advection-transport times 
can be made (Table 6-8). Approximate advection-transport times are computed from the flux 
introduced to the matrix divided by the approximate water content and retardation factor. 
Advective transport times are approximate, because flow rates vary as a result of the drift 
shadow effect and in response to fracture-matrix exchange. Nevertheless, flow patterns discussed 
MDL-NBS-HS-000016 REV 01 6-16 September 2004 

Drift-Scale Radionuclide Transport 
earlier indicate that the variations in flux and water saturation in the matrix are 
minor. Therefore, the approximate advective transport time is considered reasonable. The 
retardation factor is given by the relationship [derived from Groundwater (Freeze and Cherry 
1979 [DIRS 101173], p. 404] 
md
R = 1+
.(1 -f)K 
(Eq. 6-9)
fS 
w 
where .m is the grain density (2,540 kg/m3), f is the porosity (0.131), Kd is the sorption 
coefficient (see Table 6-7), and Sw is the water saturation (see Table 6-8). 
Table 6-8. Advective Transport Times and Computed Transport Times 
50% 
Breakthrough 
Time 
Total 
Percolation 
Flux 
Matrix 
Percolation 
Flux Water Retardation 
Advective 
Travel Time in 
(years) 
(Output-DTN: 
LB0307DSRA 
Radionuclide (mm/yr) (mm/yr) Saturation Factor Matrix (years) DTRN.002) 
Technetium 10 0.15 0.86 1 3.4E+04 3.6E+04 
Neptunium 10 0.15 0.86 6.9 2.3E+05 1.6E+05 
Plutonium 10 0.15 0.86 740 2.5E+07 1.7E+07 
Technetium 10 0.85 0.96 1 6.7E+03 7.5E+03 
Neptunium 10 0.85 0.96 6.3 4.2E+04 4.4E+04 
Plutonium 10 0.85 0.96 660 4.4E+06 4.6E+06 
Technetium 100 0.45 0.94 1 1.2E+04 9.6E+03 
Neptunium 100 0.45 0.94 6.4 7.9E+04 2.4E+04 
Plutonium 100 0.45 0.94 670 8.3E+06 2.5E+06 
Technetium 100 1.60 0.98 1 3.6E+03 4.4E+03 
Neptunium 100 1.60 0.98 6.2 2.2E+04 1.8E+04 
Plutonium 100 1.60 0.98 650 2.3E+06 1.9E+06 
Output DTN: LB0307DSRADTRN.002. 
In general, the advective travel time in the matrix is close to the value of the 50 percent 
breakthrough time for all percolation fluxes, suggesting that transport in the drift shadow is 
dominated by matrix advection. Because of the diversion of flow around the drift, radionuclides 
move from the drift to the rock by diffusion. Diffusive releases preferentially enter the matrix 
rather than the fractures because the water content (porosity times water saturation) in the matrix 
is roughly 1,000 times larger than in the fractures immediately beneath the drift. In some cases, 
the 50 percent breakthrough time is longer than the advective travel time. This happens for some 
of the technetium breakthrough curves (such as the case for 10 mm/year total flux with 
0.85 mm/year flux in the matrix) because the computed advective travel times in Table 6-8 
ignore the hydrodynamic effects of the drift shadow. For neptunium and plutonium, some of the 
50 percent breakthrough times are shorter than the advective travel times because of diffusive 
exchange between the matrix and the fractures. This occurs for the sorbing radionuclides, which 
have longer advective travel times and have more time for diffusive release from the matrix to 
the fractures. In the fractures, travel times are relatively short. 
MDL-NBS-HS-000016 REV 01 6-17 September 2004 

Drift-Scale Radionuclide Transport 
6.3.3.3 Transport Sensitivity Analysis 
Figure 6-6 compares breakthrough curves for technetium under different total percolation flux 
and matrix flux cases. The breakthrough curve sensitivity to total percolation flux is found to be 
low, with much greater sensitivity to the rate of percolation flux in the matrix. This result further 
substantiates the hypothesis that transport in the drift shadow is predominantly in the matrix. 
1 
0.9 
101 102 103 104 105
0 
300 
100 
100 
10 
10 
drili0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
ative Breakthrough Fract1.0 
1.6 
0.45 
0.85 
0.15 
Tc transport 
Gamma = 0.81 
ft-scale properties 
total fux matrx flux 
mm/yr mm/yr 
ion
Cumul
0.2 
0.1 
Time (years) 
Output DTN: LB0307DSRADTRN.002. 
Figure 6-6. Technetium Transport as a Function of Total Percolation Flux and Matrix Percolation Flux 
Figures 6-7a and 6-7b compare Tc transport in the drift shadow to transport in the unperturbed 
flow field for 10 mm/year and 100 mm/year total percolation fluxes. The releases in the 
unperturbed flow field were made in cells near the right-hand boundary of the model, at the same 
vertical coordinate as the bottom of the drift. Two types of releases were investigated; releases 
that are initiated in the fractures and releases that are initiated in the matrix. The drift-shadow 
breakthrough curve is shown for comparison. These results clearly demonstrate that releases to 
fractures transport at much greater velocities. These results also indicate that the drift-shadow 
effect is approximately equivalent to initiation of transport in the matrix. The dynamics of the 
drift shadow flow field have only a second-order effect on the breakthrough curves. 
Figure 6-8 shows a sensitivity calculation for the effects of the active fracture parameter, ., on 
breakthrough curves for Tc. This figure clearly shows that fracture-matrix interaction is a key 
factor in the rate of transport in the drift shadow. As . is reduced, the amount of fracture-matrix 
interaction increases, resulting in greater matrix-to-fracture diffusive exchange. Increased 
interaction results in more contaminant movement from the matrix to fractures in the shadow and 
as a result more transport in the fractures and, therefore, more rapid transport through the drift 
shadow 
MDL-NBS-HS-000016 REV 01 6-18 September 2004 

Drift-Scale Radionuclide Transport 
1
1 
0.9 
0.9 
10-1 100 101 102 103 104 1050 
/
i/
drift shadow 
no shadow -fracture release 
no shadow -matrix release 
Tc transport 
Percolation flux = 10 mmyr 
Gamma = 0.81 
Matrx percolation flux = 0.85 mmyr 
drift-scale properties
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
0.1 
0 
0.1 
Cumulative Breakthrough Fraction 
10-2 10-1 100 101 102 103 104 105 
l/
ii/
drift shadow 
no shadow -fracture release 
no shadow -matrix release 
Tc transport 
Percoation flux = 100 mmyr 
Gamma = 0.81 
Matrx percolaton flux = 1.6 mmyr 
drift-scale properties 
Cumulative Breakthrough Fraction 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
Time (years) Time (years) 
(a) (b) 
Output-DTN: LB0307DSRADTRN.002. 
Figure 6-7. Sensitivity Calculations Comparing Drift Shadow Transport with Transport in Unperturbed 
Flow Field: (a) Total Percolation Flux = 10 mm/year, Matrix Percolation Flux = 0.85 
mm/year; (b) Total Percolation Flux = 100 mm/year, Matrix Percolation Flux = 1.6 mm/year 
1 
0.9 
101 
102 
103 
104 
105
0 
/
l/
i0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
Cumulative Breakthrough Fraction 
Gamma = 0.81 
Gamma = 0.61 
Gamma = 0.41 
Tc transport 
Percolation flux = 10 mmyr 
Matrix percolation fux = 0.15 mmyr 
drft-scale properties 
0.1 
Time (years) 
Output DTN: LB0307DSRADTRN.002. 
Figure 6-8. Sensitivity Calculation for Technetium Transport Using Different Values of . 
6.4 FRACTURE-MATRIX PARTITIONING MODEL 
Results of sensitivity studies presented in Section 6.3 suggest that the main effect of the drift 
shadow is that, with no seepage, radionuclides are transported by diffusion into the fractures and 
matrix of the surrounding rock; because most of the water is in the matrix, most of the 
radionuclides are released to the matrix. The most important factor controlling the breakthrough 
MDL-NBS-HS-000016 REV 01 6-19 September 2004 

Drift-Scale Radionuclide Transport 
curves is the partitioning of the release between the fracture and matrix continua. The 
fracture-matrix partitioning model presented here focuses on the partitioning of releases from 
drifts between the rock fractures and matrix. The fracture-matrix partitioning model sets 
unperturbed fracture flow directly below the base of waste emplacement drifts. This 
approximation in neglecting the drift shadow effect on flow is based on the idea that the drift 
shadow may not be as spatially extensive as presented in Section 6.3, due to heterogeneity and 
anisotropy in fracture characteristics, as well as discrete fracture effects. As in Section 6.3, the 
fracture-matrix partitioning model is limited to drifts without seepage or other sources of water 
that may result in advective-dominated transport in the drift invert, i.e., transport through the 
drift invert to the rock is dominated by diffusion. For the initial release of radionuclides, the 
transient concentration front passing from the invert into the rock will initially be dominated by 
diffusion. However, as the concentration approaches a steady condition, transport in the rock 
will be dominated by advection. This is due to the reduction in the radionuclide concentration 
gradient at the drift wall over time for a steady radionuclide source concentration. The 
radionuclide concentration gradient at the drift wall relaxes for greater offset between the drift 
wall and the flowing fracture. The water content of the matrix is always dominant over the water 
content of the fractures, so diffusive exchange between the invert and the rock will 
predominantly enter the matrix. However, for the steady transport condition following the initial 
transient period, the final distribution of releases becomes a function of the water content and 
flux in the fractures and matrix. Because the unperturbed flux (no effects of the drift on the flow 
field) in the repository host rock is predominantly in the fractures, the distribution of releases 
from the invert between the fractures and matrix is controlled by the relative influence of the flux 
and the water content of the fractures and matrix. 
Note that calculations reported in Advection Versus Diffusion in the Invert (BSC 2003 
[DIRS 170881], Sections 6.66.8, Attachment X) indicate that even without drift seepage, water 
will enter the drift laterally from the rock into the crushed tuff invert as a result of capillary 
forces. The invert is a dual continuum in which the intragranular porosity (micropores) of the 
crushed tuff grains are the original porosity of the rock matrix and the intergranular porosity 
(macropores) between the crushed tuff grains has much larger pore spaces analogous to the rock 
fractures. The predicted flow pattern shows water entering laterally from the rock into the invert 
along the sides and then flowing out of the invert at the bottom of the drift. This flow is 
restricted to the micropores of the crushed tuff and the rock matrix (BSC 2003 [DIRS 170881], 
Section 6.11). The crushed tuff micropores are assigned the same capillary and permeability 
characteristics as the rock matrix, so from the perspective of flow, the rock matrix and 
micropores of the crushed tuff invert constitute a uniform and continuous flow domain. This is a 
reasonable approximation for diffusive transport through the intragranular porosity because the 
grains will be in capillary contact providing continuous diffusion pathways through the 
invert. Flow exchange from the crushed tuff micropores with the rock fractures and macropores 
of the crushed tuff is excluded by capillary pressure differences. A similar flow pattern between 
the rock fractures and crushed tuff macropores is not predicted due to the weaker capillarity of 
the fractures and the capillary barrier presented by the crushed tuff macropores relative to the 
rock fractures. The predicted micropore-matrix flow will lead to greater partitioning of 
radionuclide flux from the invert into the rock matrix than would be predicted by the 
fracture-matrix partitioning model, which is based on pure diffusive transport through the 
invert. This is because the advective transport process through the intragranular porosity delivers 
radionuclides to the rock matrix exclusively, as opposed to diffusion, which leads to 
MDL-NBS-HS-000016 REV 01 6-20 September 2004 

Drift-Scale Radionuclide Transport 
radionuclides entering both the rock fractures and rock matrix. Therefore, the neglect of this 
flow is conservative for the prediction of radionuclide partitioning from the drift into the rock 
fractures and matrix, and subsequent effects on radionuclide transport through the unsaturated 
zone. 
The results of the fracture-matrix partitioning model are to be used as an alternative model for 
comparison with the EBS Radionuclide Transport Model [EBS Radionuclide Transport 
Abstraction (BSC 2004 [DIRS 169868])]. 
6.4.1 Conceptual and Mathematical Model Development 
Figure 6-9 shows a diagram of the fracture-matrix partitioning model given this conceptual 
background. Beneath the waste package, the invert ranges in depth from 675 mm to 806 mm, 
with an average depth of 741 mm. The total invert depth variation is approximately 17 percent 
of the average depth beneath the waste package. Sensitivity to invert thickness is included in the 
model, but the second-order effects of the curvature of the drift-rock interface are not 
included. Rather than include the entire invert-rock interface, the model is restricted to a domain 
from the centerline of a fracture to a boundary at the midpoint between fractures 
(Figure 6-10). The boundary along the fracture centerline and the boundary along the midpoint 
between fractures are approximate symmetry boundaries. The top and bottom boundaries 
correspond to the top and bottom of the invert. 
675 mm 806 mm 
waste package 
waste package 
5500 mm diameter 
Invert section 
underlying the 
waste emplacement drift 
1674 mm 
Sources: BSC 2003 [DIRS 164101]. 
Figure 6-9. Schematic of Waste Emplacement Drift Configuration
MDL-NBS-HS-000016 REV 01 6-21 September 2004 

Drift-Scale Radionuclide Transport 
x 
y 
(x,y) = (0,0) 
top of invert 
fracture 
midpoint between 
fractures 
rock matrix 
invert 
one-half fracture spacing 
fracture water contact 
thickness with invert 
(exaggerated) 
Figure 6-10. Schematic Diagram of Modeling Domain 
The governing equation for steady diffusion in a homogeneous invert is [derived from The 
Mathematics of Diffusion (Crank 1975 [DIRS 122990], Equation 1.3, Section 1.3)] 
2 ( ,
. y x C)= 0 (Eq. 6-10) 
where C is the mass concentration of radionuclide and x and y are spatial coordinates. 
The boundary condition at the top of the invert has a fixed radionuclide concentration, 
Cx,ym )= C (Eq. 6-11)
( 
m
where ym is the y coordinate for the top of the invert and Cm is the radionuclide concentration at 
the top of the invert. No-flux boundary conditions are imposed on the lateral boundaries as a 
result of symmetry along these boundaries: 
. 
. 
x 
C(,0 ) =y 0 (Eq. 6-12) 
. 
. 
x 
C (h f, ) =y 0 (Eq. 6-13) 
where hf is the x coordinate for the midpoint between fractures. 
The boundary condition at the bottom of the invert is that the diffusive flux of radionuclides from 
the invert is equal to the radionuclide flux into the rock. This radionuclide flux into the rock is 
MDL-NBS-HS-000016 REV 01 6-22 September 2004 

Drift-Scale Radionuclide Transport 
split into two portions; flux into the rock matrix and flux into the fracture of the domain 
considered. To determine this flux, one must establish the vertical position of fracture flow 
relative to the waste emplacement drift. The high permeability and low capillary pressure of the 
fractures in the repository host rock are conditions conducive to gravity-driven flow. For 
fracture flow to move around the drift and contact the invert at a point underneath a waste 
package, the trajectory needs to be approximately 3 to 1 horizontal to vertical 
motion. Furthermore, the vertical projection for the portion of the invert beneath the waste 
package available for contact with horizontal flow is only about 13 cm (see Figure 6-9). Thus, 
flow in vertical fractures is not expected to have a sufficient lateral flow component to result in 
fracture flow immediately beneath a waste emplacement drift. However, under certain 
circumstances related to the local fracture connectivity, subhorizontal fractures may be capable 
of redirecting flow in a fracture network in a near-horizontal direction. Under these 
circumstances, the extent of the drift shadow could be substantially reduced compared with the 
model results presented in Sections 6.3.3.1 and 6.3.3.2. 
The limitation on where fracture flow may occur beneath a waste emplacement drift is associated 
with the probability of the vertical position of a subhorizontal fracture beneath a waste 
emplacement drift in association with a vertical fracture. Because of fracture spacing and the 
random relationship between fracture connections and the drift, the distance of a subhorizontal 
fracture connection to a vertical fracture beneath the waste emplacement drift, .yf , lies between 
0 and the fracture spacing (see Figure 6-11). This distance ( .yf ) has a uniform distribution, so 
the expected value for the vertical distance to the closest potential fracture flow beneath a waste 
emplacement drift is one-half the fracture spacing. 
yf 
w aste emplacement drift 
waste pack age 
Fixed 
rad ionu clide 
con centratio n 
bo un dary 
R adio nu clid e diffu sio n thr oug h 
stagn ant water in fractu re 
Rad ionu clide 
diffusio n 
thro ug h inver t 
R adionuclide advec tio n 
th rough r ock ma tr ix 
Figure 6-11. Schematic of Fracture Network, Waste Emplacement Drift, and Transport Processes 
MDL-NBS-HS-000016 REV 01 6-23 September 2004 

Drift-Scale Radionuclide Transport 
The radionuclide mass flux along any streamline through this connection (green circle in 
Figure 6-11), under steady flow and constant concentration conditions, will be equal to the 
fracture water flux times the concentration. Given that the water in the fracture between the drift 
and the connection is not flowing, the flux into the connection is diffusive and the water 
saturation of the fracture will be at its residual value. The steady-state flux balance along a 
fracture streamline is given by 
-Def .
.x C 0, )-C (x).
. 
=qwfC fn ()
fn
. (
f .
..y .x for 0<x <b (Eq. 6-14) 
where Def is the diffusion coefficient for steady diffusive flux in the fracture, Cfn is the 
radionuclide mass concentration at the connection point in the fracture network, and b is the 
half-water thickness in the fracture. Note that this water film thickness represents the residual 
saturation of the fracture, therefore, the fracture is unsaturated. Because the fracture is identified 
discretely rather than as a continuum, the local water flux in the discrete fracture, qwf, is equal to 
the continuum fracture flux (e.g., from a dual-permeability flow model) divided by the fracture 
water content, and thus is a velocity at points across the water film. Note that qwf is 
negative. Solving Equation 6-14 for Cfn gives 
x x C 0,) for 0<x <b (Eq. 6-15)
C 
fn ()= 
1 +
(-
( 
qwf ).yf 
D
ef 
Therefore, the radionuclide mass flux, qrad(x), into the fracture at the drift wall may be 
expressed as 
(
wf
xx
q ()=qwfC fn ()= 
q x C 0,) 
for 0<x <b (Eq. 6-16) 
rad 
1 -
qwf .y 
f 
D
ef 
Note that the effects of fracture-matrix exchange are neglected. However, neglecting this 
mechanism leads to greater radionuclide partitioning into the fracture at the drift wall. This is 
because the lower radionuclide concentrations in the fracture as compared to the matrix will lead 
to diffusive fracture-matrix transfers from the matrix to the fractures in the region immediately 
below the drift. Therefore, radionuclide flux into the fracture from the drift will be reduced 
because it will be in competition with radionuclide entry into the fracture from the rock matrix. 
Owing to the continuity of the matrix, the radionuclide flux into the matrix is equal to the matrix 
water flux, qm, times the radionuclide concentration at the drift boundary, 
x (
q ()=x C q 0, ) for b <x <hf (Eq. 6-17) 
rad m 
MDL-NBS-HS-000016 REV 01 6-24 September 2004 

Drift-Scale Radionuclide Transport 
Therefore, the balance between diffusive radionuclide flux in the invert and the advective 
radionuclide flux into the rock may be written in the form 
() (
D-
eI 
.C (x0, )=x C x q 0, ) (Eq. 6-18) 
.y 
where DeI is the effective diffusive mass-transfer coefficient for steady diffusive radionuclide 
flux in the invert. The generalized water flux function, q(x), is given by 
wf
x q =q for 0<x <b (Eq. 6-19) 
fe
()= 
qq 
.y 
f 
D
1- wf 
ef 
x q 
()=qm for b <x <hf (Eq. 6-20) 
A schematic water flux profile is shown in Figure 6-12. In the fracture water (x = 0 to x = b), the 
equivalent flux, qfe , is given by Equation 6- 19. The water flux in the matrix (x = b to x = hf) 
is given by Equation 6- 20. The generalized water flux function in the fracture domain (0 < x < 
b) has the water flux that would result in the same radionuclide mass transport by advection as 
occurs through the fracture by diffusion. 
0 
q (x) 
qfe 
qm 
0 b hf 
x 
Figure 6-12. Schematic Generalized Water Flux Profile at the Drift Wall 
Note that the fracture-matrix partitioning model does not include any representation of the air 
that is present in an unsaturated fracture at the invert-rock interface. Aqueous radionuclides 
cannot enter the rock through the gas phase, therefore, the presence of air in the fracture 
represents a barrier to radionuclide transfer to the rock. The justification for not including this 
feature of the unsaturated fracture in the model is given in Section 6.5. 
MDL-NBS-HS-000016 REV 01 6-25 September 2004 

Drift-Scale Radionuclide Transport 
6.4.2 Dimensionless Representation 
The model described by Equations 6-10 to 6-13 and 6-18 to 6-20 can be put into a dimensionless 
form, which reduces the number of independent parameters that need to be considered. The 
dimensionless concentration, Cd, is defined by 
C
C
d =-1 (Eq. 6-21)
C
m 
The range of Cd varies between 0 and -1. The reason for the normalization by subtracting 1 is to 
simplify the boundary condition at the top of the invert. The dimensionless distance coordinates, 
xd and yd, are given by 
dx =
fh 
x (Eq. 6-22) 
and 
dy =dmy - 
fh 
y (Eq. 6-23) 
where xd varies between 0 and 1 and yd between 0 and ydm = 
f 
m 
h 
y 
. 
Writing Equations 6-10 through 6-13 and 6-18 in terms of the dimensionless variables gives 
2
.dC(xd , y )= 0 (Eq. 6-24)
dd 
C
d (xd ,0)= 0 (Eq. 6-25) 
.Cd (,0 y )= 0 (Eq. 6-26)
.xd 
d 
.Cd (1, yd )= 0 (Eq. 6-27)
.xd 
.Cd (xd , y )= q (x )(C (xd , y )+ 1) (Eq. 6-28)
.y 
dm ddd dm 
d 
MDL-NBS-HS-000016 REV 01 6-26 September 2004 

Drift-Scale Radionuclide Transport 
.2 
2 .2 
where the dimensionless Laplacian operator is defined by = .+ and the
d 
.xd 
2 .y 2 
d 
dimensionless water flux, qd(xd), on the right-hand side of Equation 6-28 is defined as follows: 
q 
fehf
q =Pe fe = for 0<xd <bd (Eq. 6-29) 
D
d 
eI 
h q 
q =Pe = mf for bd <xd =1 (Eq. 6-30) 
D
dm 
eI 
1
q = 
2 
(Pe fe +Pem )for xd =bd (Eq. 6-31) 
d 
where 
b
bd = (Eq. 6-32) 
hf 
The average value at the boundary, xd =bd , is used to have a definition for the dimensionless 
water flux at all points in the domain. Based on the dimensionless form in Equations 6-24 
through 6-32, the following dimensionless groups may be identified: 
Pe= matrix  invert mass transfer Peclet number 
m 
Pe
fe = fracture  invert mass transfer Peclet number 
.
f =b =fracture water content
d 
y
dm = dimensionless invert depth. 
6.4.3 Solution Method 
The solution of Equation 6-24 subject to the boundary conditions defined in Equations 6-25 to 
6-28 may be obtained using an expansion in cosines and hyperbolic tangent functions. The 
general solution that satisfies Equation 6-24 and boundary conditions, Equations 6-25 to 6-27 is 
8 
Cd (xd , y )=y B +.Bj cos(jpx )sinh(jpy ) (Eq. 6-33) 
d 0 d dd 
j =1 
which may be verified by direct substitution. Substituting Equation 6-33 into Equation 6-28 
gives 
8 
()y )+.A cos (jpx )..
jp-qx
A0 (1 -qx ()tanh (jpydm )..
=qd ()(Eq. 6-34)
dddmj d dd xd 
j1
= 
MDL-NBS-HS-000016 REV 01 6-27 September 2004 

Drift-Scale Radionuclide Transport 
or 
8 
.
A M j = q (Eq. 6-35) 
ij di 
j=0
where 
Mi0=(1 - q (x )y ) (Eq. 6-36) 
d di dm 
M 
ij =cos( jpx )[ jp- q (x )tanh( jp y )] for i> 0 (Eq. 6-37) 
di ddi dm 
q =q (x ) (Eq. 6-38) 
di ddi 
Aj =Bj cosh( jp y ) (Eq. 6-39) 
dm 
The transformation from Bj to Aj is introduced to eliminate numerical difficulties in the 
evaluation of cosh( j p ydm ) and sinh( jp ydm ) for large j. The concentration at the invert-rock 
interface may be written as 
8 
Cd (xd , y )= y A +. Aj cos( jpx )tanh( jpy ) (Eq. 6-40) 
dm 0 dm ddm 
j=1 
The usual Fourier method for determining the coefficients, Aj, cannot be used because of the 
term in Equation 6-34 that involves the product of the cosine and the dimensionless water 
flux. However, a Fourier solution does exist, because if the steady concentration at the boundary 
yd =y were known, then the coefficients could be determined through standard methods 
dm 
using the orthogonality properties of the cosine series. An alternative method to determine the 
coefficients may be developed by noting that a finite range for j is expected to be sufficient in 
practice based on the similarity of this solution method with Fourier series and the known 
convergence characteristics of the Fourier series [A First Course in Partial Differential 
Equations (Weinberger 1965 [DIRS 163216], Section 18)]. For a finite sum from j = 0 to j = 
jmax, Equation 6-34 may be considered as a set of jmax+1 linear equations, corresponding to the set 
of points xd 0...xdj , in jmax+1 unknowns, A0 ... Aj , as shown in Equation 6-35. This solution 
max max 
method will be referred to as the discrete transform method. See Appendix L for a 
demonstration of the equivalence of the discrete transform method with the standard Fourier 
series method. Alternative solution methods include direct numerical approaches, such as the 
finite difference method. These methods were not selected because the solution to the problem is 
amenable using the semi-analytic approach presented here. 
MDL-NBS-HS-000016 REV 01 6-28 September 2004 

Drift-Scale Radionuclide Transport 
The cumulative dimensionless radionuclide flux in the fracture, Fdf, and in the matrix, Fdm, may 
be calculated by integrating the diffusive flux on the left hand side of Equation 6-28 over 
xd. Equation 6-33 is used for Cd(xd, yd) to compute the derivative evaluated at ydm. The result is 
j
max 
F
dfD = A b 0 +. Aj sin( jpb ) (Eq. 6-41) 
dd 
j =1 
j
max 
F
dmD =(1 - b )A -. Aj sin( jpb ) (Eq. 6-42) 
d 0 d 
j =1 
The cumulative dimensionless radionuclide flux in the fracture, Fdf, and in the matrix, Fdm, may 
also be calculated by integrating the advective flux on the right-hand side of Equation 6-28 over 
xd. Equation 6-40 is used for Cd(xd, ydm) and the flux in Equations 6-29 and 6-30 for the fracture 
and matrix, respectively. 
j
max .
.
F
dfA = Pefe . b (1 + A y )+.Aj tanh ( jpy ) sin ( jpbd ). (Eq. 6-43) 
d 0dm 
. j1jp dm 
.
= 
j
.
max .
F
dmA = Pe .(1 - b )(1 + A y )-.Aj tanh ( jpy ) sin ( jpbd ). (Eq. 6-44) 
m d 0dm 
. j1jp dm 
.
= 
The solution method presented below will involve calculating each of these advective and 
diffusive fluxes for the matrix and the fracture domains. The accuracy of the solution, meaning 
number of terms included in the expansion, is determined by comparing the results for the 
diffusive flux on the left hand side of Equation 6-28 and the advective flux on the right hand side 
of Equation 6-28. 
6.4.4 Solution Behavior 
A typical case is investigated here to provide insight into the solution behavior. This case, called 
nominal case 1, is parameterized as shown in Table 6-9. 
Table 6-9. Parameters for Nominal Case 
Parameter Value 
fracture water content 0.0001 
fracture Peclet number -1 
matrix Peclet number -0.004 
dimensionless invert depth 4 
Output-DTN: LB0307FMRADTRN.001. 
The dimensionless invert depth of 4 means that the invert is 4 times deeper than the fracture 
half-spacing (see definition of the dimensionless invert depth following Equation 6-23). The 
computational details leading to the results for the cases summarized here are given in a 
MDL-NBS-HS-000016 REV 01 6-29 September 2004 

Drift-Scale Radionuclide Transport 
scientific notebook by Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, pp. 5118). An 
example of the nominal-case calculations is presented in Appendix J. 
The concentration profile at the drift wall is shown for a nominal case 1 in Figure 6-13. The 
concentration drop at the left boundary results from the higher radionuclide mass flux entering 
the fracture. Lateral diffusive mass flux in the invert leads to additional radionuclide mass 
transfer into the fracture. The flux profile is shown in Figure 6-14, which shows the large flux 
near xd = 0 in the fracture zone. Note that the scale on this figure is selected to show how the 
flux profile behaves moving from the fracture to the matrix; the maximum value in the fracture 
zone is approximately 0.98. The matrix flux near the fracture is depressed on account of the 
reduced radionuclide concentration in the invert. 
0.983 
0.9825 
0.982 
C/Cm 
0.9815 
0.981 
0.9805 
0.98 
0 0.25 0.5 0.75 1 
Xd 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-13. Plot of C/Cm at the Solution Locations for the Fourier CoefficientsNominal Case 1 
Dimensionless radionuclide flux ratios are computed for both the flux in the invert at the drift 
wall and for the flux in the rock at the drift wall. The flux ratio on the invert side of the 
boundary is given by 
F
dfD
= 
F
P
rI 
dfD + FdmD 
and the flux ratio in the rock at the drift wall is given by 
F
dfA
P = 
F
r 
dfA + FdmA 
, 
MDL-NBS-HS-000016 REV 01 6-30 September 2004 

Drift-Scale Radionuclide Transport 
as computed from Equations 6-41 through 6-44. These two dimensionless flux ratios are the 
partitioning ratio between the fracture and the matrix in the rock beneath the invert. The 
diffusive and advective flux ratios are 0.024 and 0.022, respectively. The discrepancy between 
these flux terms provides an estimator for the accuracy of the discrete transform solution. For an 
infinite number of terms, the two flux ratios would be equal. 
0.003932 
0.00393 
0.003928 
-qd(1+ Cd) 
0.003926 
0.003924 
0.003922 
0 0.25 0.5 0.75 1 
Xd 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-14. Plot of Negative of Local Dimensionless Flux at the Solution Points for the Discrete 
Transform CoefficientsNominal Case 1 
The solution of Equation 6-35 may be evaluated through a comparison of the left-hand side and 
right-hand side at intermediate points to the solution points used for computing the discrete 
transform coefficients. The intermediate points lie along the drift wall boundary between the 
solution points , xdi, given in Equations 6-36 and 6-38. Figure 6-15 provides this comparison at 
different scales, to give a perspective on the entire solution as well as the fit near the fracture 
where rapid changes in the function occur. The series approximation to the curve is seen to have 
greater error and oscillations about the target function near the fracture, with a rapid reduction in 
differences moving away from the fracture. 
MDL-NBS-HS-000016 REV 01 6-31 September 2004 

Drift-Scale Radionuclide Transport 
-1 
0 
) 
() 
qd 
-1 
0 
() 
qd 
-0.75 
-0.5 
-0.25 
0.25 
flux profile; right hand side of Equation (35left-hand side of Equation 35-0.75 
-0.5 
-0.25 
0.25 
flux profile; right hand side of Equation (35) 
left-hand side of Equation 35
0 0.25 0.5 0.75 1 0 0.025 0.05 0.075 
Xd
(a) (b) Xd 
0.25 
0 
-0.25 
qd 
-0.5 
-0.75 
-1 
() 
flux profile; right hand side of Equation (35) 
left-hand side of Equation 35
0 0.0025 0.005 0.0075 0.01 
Xd
(c) 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-15. Comparison Plot at Intermediate Points to Solution for Discrete Transform Coefficients, qd, 
right-hand side of Equation 6-(35) (Solid Red Line) left-hand side of Equation 6-(35) (Dotted 
Blue Line) for 1,024 Terms (a) Entire Domain, (b) Region Near Fracture, and (c) Fracture 
Close-Up  Nominal Case 1 
The solution accuracy may also be evaluated through comparisons of the invert and rock 
radionuclide flux terms at the drift wall. For the solution points (xd) in the equation for the 
discrete transform coefficients, the flux in the invert and in the rock at the drift wall are 
identical. However, deviations between these flux terms at intermediate locations provide an 
indication of solution accuracy. In Figure 6-16, the comparison of these two fluxes is made at 
intermediate values of xd. This comparison points out that the calculations for diffusive flux in 
the invert are subject to oscillations of greater magnitude than the calculation for advective flux 
in the rock. This suggests that the advective flux ratio will provide a more accurate estimate than 
the diffusive flux ratio, even though both rely on the discrete Fourier transform solution. This 
occurs because the first-order terms for the advective radionuclide flux in Equations 6-43 and 
6-44 are a fairly good approximation to the full solutions. 
MDL-NBS-HS-000016 REV 01 6-32 September 2004

Drift-Scale Radionuclide Transport 
0 
1 
0 
1 
-0.25 
0.25 
0.5 
0.75 
dimensionless radionuclide flux in rock 
dimensionless radionuclide flux in invert 
-qrad 
-0.25 
0.25 
0.5 
0.75 
dimensionless radionuclide flux in rock 
dimensionless radionuclide flux in invert 
-qrad 
0 0.25 0.5 0.75 1 0 0.025 0.05 0.075 
(a) Xd (b) Xd 
1 
0.75 
0.5 
-qrad 
0.25 
0 
-0.25 
dimensionless radionuclide flux in rock 
dimensionless radionuclide flux in invert 
0 0.0025 0.005 0.0075 0.01 
Xd
(c) 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-16. Comparison Plot of Flux in the Invert (Dotted Blue Line) and Rock (Solid Red Line) at the 
Drift Wall for 1,024 Terms: (a) Entire Domain, (b) Region Near Fracture, and (c) Fracture 
Close-Up  Nominal Case 1 
The behavior of the solution with successively larger numbers of coefficients is shown in 
Figures 6-17 and 6-18. The solutions are seen to generally improve with larger numbers of 
coefficients. Table 6-10 gives the change in the dimensionless radionuclide flux ratio over a 
range of 1,024 to 4,096 Fourier coefficients. The value of the flux ratio as computed from the 
advective flux in the rock is found to change by less than 2 percent as compared to 4 percent for 
the diffusive flux ratio. The variability of the results (to be shown below) is on the order of a 
factor of 10, so the accuracy of the solution with 1,024 points is sufficient. Because of the 
greater stability of the flux ratio as computed from the advective flux in the rock, this ratio will 
be used to determine the flux ratios. 
MDL-NBS-HS-000016 REV 01 6-33 September 2004 

Drift-Scale Radionuclide Transport 
0.25 
(
()
flux profile; right hand side of Equation 35) 
left-hand side of Equation 35
0.25 
0 
0 
-0.25 
-0.25 
qd 
qd 
-0.5 
-0.5 
-0.75 
-0.75 
-1 
-1 
(
() 
flux profile; right hand side of Equation 35) 
left-hand side of Equation 35
0 0.0025 0.005 0.0075 0.01 0 0.0025 0.005 0.0075 0.01 
Xd Xd
(a) (b) 
0.25 
0 
-0.25 
qd 
-0.5 
-0.75 
-1 
() 
flux profile; right hand side of Equation (35) 
left-hand side of Equation 35
0 0.0025 0.005 0.0075 0.01 
Xd
(c) 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-17. Comparison Plot at Intermediate Points to Solution for Discrete Transform Coefficients, 
showing qd, right-hand side of Equation 6-(35) (Solid Red Line) left-hand side of 
Equation 6-(35) (Dotted Blue Line): (a) 1,024 Points, (b) 2,048 Points, and (c) 4,096 Points 
 Nominal Case 1 
MDL-NBS-HS-000016 REV 01 6-34 September 2004 

Drift-Scale Radionuclide Transport 
0 
1 
0 
1 
-0.25 
0.25 
0.5 
0.75 
dimensionless radionuclide flux in rock 
dimensionless radionuclide flux in invert 
-qrad 
-0.25 
0.25 
0.5 
0.75 
dimensionless radionuclide flux in rock 
dimensionless radionuclide flux in invert 
-qrad 
0 0.0025 0.005 0.0075 0.01 0 0.0025 0.005 0.0075 
Xd Xd
(a) (b) 
1 
0.75 
0.5 
-qrad 
0.25 
0 
-0.25 
dimensionless radionuclide flux in rock 
dimensionless radionuclide flux in invert 
0 0.0025 0.005 0.0075 0.01 
Xd
(c) 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-18. Comparison Plot of Flux in the Invert (Solid Red Line) and Rock (Dotted Blue Line) at the 
Drift Wall: (a) 1,024 Points, (b) 2,048 Points, and (c) 4,096 Points  Nominal Case 1 
Similar behavior is found for nominal case 2 with fracture water content of 0.0005 and all other 
parameters unchanged. Figures 6-19 and 6-20 show similar convergence characteristics for 
Nominal Case 2 as compared with Nominal Case 1. Again, the advective flux ratio is seen to be 
more stable in Table 6-11 over the selected number of coefficients. 
MDL-NBS-HS-000016 REV 01 6-35 September 2004 

Drift-Scale Radionuclide Transport 
Table 6-10. Advective and Diffusive Flux Ratios for Nominal Case 1 
Nominal Case 1 Results 
Number of Fourier Coefficients Advective Flux Ratio in Rock Diffusive Flux Ratio in Invert 
1024 0.02434 0.02211 
2048 0.02436 0.02301 
4096 0.02438 0.02213 
Output DTN: LB0307FMRADTRN.001. 
0.25 
() 
()
flux profile; right hand side of Equation 35left-hand side of Equation 35
0.25 
0 
0 
-0.25 
-0.25 
qd 
qd 
-0.5 
-0.5 
-0.75 
-0.75 
-1 
-1 
() 
() 
flux profile; right hand side of Equation 35left-hand side of Equation 35
0 0.0025 0.005 0.0075 0.01 0 0.0025 0.005 0.0075 
Xd Xd
(a) (b) 
0.25 
0 
-0.25 
qd 
-0.5 
-0.75 
-1 
flux profile 
Fourier representation of flux profile 
0 0.0025 0.005 0.0075 0.01 
Xd
(c) 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-19. Comparison Plot at Intermediate Points to Solution for Discrete Transform Coefficients, 
showing qd, right-hand side of Equation 6-(35) (Solid Red Line) left-hand side of 
Equation 6-(35) (Dotted Blue Line): (a) 1,024 Points, (b) 2,048 Points, and (c) 4,096 Points 
 Nominal Case 2 
MDL-NBS-HS-000016 REV 01 6-36 September 2004 

Drift-Scale Radionuclide Transport 
1 
dimensionless radionuclide flux in rock 
dimensionless radionuclide flux in invert 
1 
0.75 
0.75 
0.5 
0.5 
-qrad 
-qrad 
0.25 
0.25 
0 
0 
-0.25 
-0.25 
dimensionless radionuclide flux in rock 
dimensionless radionuclide flux in invert 
0 0.0025 0.005 0.0075 0.01 0 0.0025 0.005 0.0075 
Xd Xd
(a) (b) 
1 
0.75 
0.5 
-qrad 
0.25 
0 
-0.25 
dimensionless radionuclide flux in rock 
dimensionless radionuclide flux in invert 
0 0.0025 0.005 0.0075 0.01 
Xd
(c) 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-20. Comparison Plot of Flux in the Invert (Solid Red Line) and Rock (Dotted Blue Line) at the 
Drift Wall: (a) 1,024 Points, (b) 2,048 Points, and (c) 4,096 Points  Nominal Case 2 
MDL-NBS-HS-000016 REV 01 6-37 September 2004 

Drift-Scale Radionuclide Transport 
Table 6-11. Advective and Diffusive Flux Ratios for Nominal Case 2 
Nominal Case 2 Results 
Number of Fourier Coefficients Advective Flux Ratio in Rock Diffusive Flux Ratio in Invert 
1024 0.1109 0.0965 
2048 0.1108 0.1096 
4096 0.1109 0.1108 
Output DTN: LB0307FMRADTRN.001. 
6.4.5 Model Parameterization and Sampling 
Domain Investigated 
The model parameters are selected to represent the range of conditions expected across the waste 
emplacement locations. These locations encompass for model units within the Topopah Spring 
Tuff; tsw33 (Topopah Spring Tuff Upper Lithophysal), tsw34 (Topopah Spring Tuff Middle 
Nonlithophysal), tsw35 (Topopah Spring Tuff Lower Lithophysal), and the tsw36 (Topopah 
Spring Tuff Lower Nonlithophysal). The numerical grid for the mountain-scale site-scale model 
represents the waste emplacement locations through 433 gridblocks (excluding fault cells) that 
span the four model units (BSC 2004 [DIRS 169861], Figure 6.1-1). The percentage of waste 
emplacement within each of the model units is given in Appendix H, with more than 80 percent 
within the tsw35. 
Fracture Frequency 
The dimensionless invert depth is computed from the invert depth divided by the half of the 
fracture spacing, d h. Fracture half-spacing may be computed from 
f 
hf= 1 f -1 (Eq. 6-45)
2 
where f is the fracture frequency. The fracture frequency mean and standard deviation for the 
repository host rock units (BSC 2004 [DIRS 170038]; DTN: LB0205REVUZPRP.001 
[DIRS 159525]) are used to derive a sampled set of fracture spacings (see Section 4.1). A correlation 
of the data from all the model units having both the mean and the standard deviation in fracture 
frequency is shown in Figure 6-21. This figure shows a strong correlation between the average 
fracture frequency and the standard deviation in fracture frequency. The standard deviation in 
fracture frequency for the tsw35 and tsw36 are computed from the correlation in Figure 6-21. 
Fracture frequency is modeled as a lognormal distribution to account for the semi-infinite range of 
the fracture frequency. Details of the sampling method are given in Appendix A. 
Water Flux and Saturation 
Fracture and matrix flux and water saturation values are taken from the output of the UZ Flow Model 
for the repository host rock (see Section 4.1). The flow model provides 433 fracture and matrix flux 
pairs in the repository host rock, as discussed in Appendix B. The flow model output also provides 
the matrix relative permeability, which is used below for computing matrix diffusion. 
MDL-NBS-HS-000016 REV 01 6-38 September 2004 

Drift-Scale Radionuclide Transport 
Fracture Frequency 
Standard Deviation of Fracture Frequency 
(1/m)
4 
3.5 
3 
2.5 
2 
1.5 
1 
iFracture Frequency 
Data 
Linear regresson to 
data 
y = 0.831x 
R2 = 0.783 
0.5 
0 
0.00 1.00 2.00 3.00 4.00 5.00 
Fracture Frequency (1/m) 
Output-DTN: LB0307FMRADTRN.001. 
NOTE: Linear regression forced through origin. 
Figure 6-21. Fracture Frequency Correlation 
Flow Focusing 
In addition to the average flow rates predicted by the mountain-scale model, flow focusing at the 
drift scale is including through a flow-focusing factor. This factor (see Section 4.1) is sampled 
and used in combination with the sampled fracture water flux from the mountain-scale model 
(BSC 2004 [DIRS 167652], Figure 6-26; DTN: LB0406U0075FCS.002 [DIRS 170712]). 
P- = 3137.0 F 4 + 4998.5 F 3 - 66.35 F 2 + 3.102 F - 434.11 (Eq. 6-46) 
where F is the flow focusing factor and P is the cumulative probability for the value of 
F. Details of the sampling method are given in Appendix C. Fracture saturations are adjusted 
for flow focusing through the van Genuchten relationship (van Genuchten, 1980 [DIRS 100610], 
Equation 8) and the approximation of unit gradient flow in the fractures: 
2 
g k 
S 
1 .. 1 . m . 
fm .
q = 2 . 1 -. 1 - S fn 
.
. ..
. (Eq. 6-47)
f .fn 
. .
. 
. 
MDL-NBS-HS-000016 REV 01 6-39 September 2004 

Drift-Scale Radionuclide Transport 
where g is the acceleration of gravity, . is the kinematic viscosity of water, Sfn is the normalized 
S
-
S
f 
fr 
, Sf is the physical fracture saturation, Sfr is the residual fracture 
fracture saturation 
-
S
1 
fr 
saturation (Sfr is a significant fraction of the typical ambient Sf), m is the van Genuchten pore 
size distribution factor, and qf is the fracture water flux. Adjusting qf by the flow focusing factor, 
F, gives 
2
.
.
m
1 
1 
Fq 
f 
g k 
S
f 
.
= 
..
.
..
.
1
..
. 
.
1
-
S
-
(Eq. 6-48)
2 
fna 
m 
fna
..
.
.
where Sfna is the adjusted normalized fracture saturation. Taking the ratio of Equations 48 to 47 
gives 
2
.
.
m
1 
1 
m 
fna
.
-
1
..
. 
..
.
1
..
. 
.
S 
S
-
2 
fna
..
.
F
=
(Eq. 6-49)
2
.
.
m
1
1
..
.
...
..
. 
1
.
S 
S
-
1
-
2 
fn 
m 
fn
..
.
.
Using the fact that fracture saturations are low, the numerator may be expanded for small Sfna 
1 
m
(such that S fma is small) and solved for Sfna , as detailed in Appendix G: 
2m 
2
.
.
4
+
m
...
1
-
m
..
.
F
2
m 
..
.
S
1 
2 
fn 
1
-
S
1 
m 
fn 
...
...
...
.
.
.
S 
(Eq. 6-50)
=
fna
.
..
.
...
.
.
.
. 
Fracture and Matrix Porosity 
Fracture porosity is needed to define the fracture water velocity and to define the fracture water 
content in contact with the drift invert. A standard deviation in fracture porosity is available only 
for the tsw34 model unit. The standard deviation for the other host rock units are computed from 
the ratio of the standard deviation to the mean in the tsw34, multiplied by the average porosity 
for each host rock unit. The fracture porosity is described by a beta distribution to reflect the 
physical limits of 0 and 1 for this parameter. Details of the sampling method are given in 
Appendix D. A similar sampling is performed for matrix porosity as described in Appendix D. 
MDL-NBS-HS-000016 REV 01 6-40 September 2004 

Drift-Scale Radionuclide Transport 
Fracture Residual Saturation 
The fracture saturation at the drift wall is given the same value as that in the flowing fracture 
beneath the drift. Although physical saturations are reported from the flow model, flow 
calibrations are based on permeability and capillary pressure relationships that are a function of 
normalized saturation. Therefore, the uncertainty in the normalized fracture saturation is 
accounted for via the lower, mean, and upper infiltration cases, but this does not account for 
uncertainty in the residual saturation. The value for residual water saturation in fractures is 
available in the calibrated hydrological property sets (DTN: LB03023DSSCP9I.001 
[DIRS 163044]), which for all infiltration cases is 0.01. Currently, there are no data from Yucca 
Mountain that could be used to assess the uncertainty in residual fracture saturation. In general, 
experiments may be expected to overestimate residual wetting-phase saturations because it is 
difficult to assess the end of a drainage process. The wetting phase tends to maintain continuity 
during the drainage process [Hydraulic Continuity of Residual Wetting Phase in Porous Media 
(Dullien et al. 1986 [DIRS 163221], p. 201)], which leads to drainage experiments that only 
asymptotically approach residual saturation at an ever-decreasing rate. Therefore, the time scales 
for laboratory experiments become a factor in the determination of the residual 
saturation. Dullien et al. (1986 [DIRS 163221], p. 203) investigated residual wetting-phase 
saturation in sandstones and found that with increasing capillary pressure, the wetting-phase 
saturation continued to drop, and no irreducible saturation could be determined. The 
uncertainty in residual saturation in fractures is modeled using a log-uniform distribution with a 
range of 0.001 to 0.1. This distribution has a median of 0.01 and spans the range of residual 
saturation values measured for higher permeability capillary media [Residual Equilibrium 
Saturation of Porous Media (Dombrowski and Brownell 1954 [DIRS 163222], Figure 7, 
p. 1,213)]. Sampling for fracture water saturation, including the uncertainty in residual 
saturation is described in Appendix G. The magnitude of the residual water saturation is found 
to be a significant fraction of the typical total fracture water saturation. 
Diffusion Coefficient for the Invert 
The invert diffusion coefficient was developed based on an empirical correlation with the water 
content (BSC 2001 [DIRS 156700], pp. 2325, Equation (37)): 
.
log..
. DeI 
.. = log 849.1 . (Eq. 6-51)
. D0 . 
I 
where D0 is the diffusion coefficient in water factor and .I 
is the invert water content. The 
coefficient in this correlation, 1.849 was more recently updated to a value of 1.863 (BSC 2003 
Section 6.2 [DIRS 170881]). For a typical invert water content of 0.046, the change in exponent 
results in a difference in DeI of about 4 percent. However, the total uncertainty range for DeI 
spans a factor of 43 due to uncertainties in invert water content and the free-water diffusion 
coefficient (see Appendix E). Therefore, the effect of the difference in the exponent is 
negligible. The invert water content is found to be essentially equal to the intergranular solid 
content (1 minus the intergranular porosity) times the matrix porosity of the invert material 
grains, or (1-fIg )fm (BSC 2003 [DIRS 170881], Section 6.4). The tuff matrix material for the 
invert will be taken from the tsw36 repository host rock horizon (BSC 2003 [DIRS 170881], 
MDL-NBS-HS-000016 REV 01 6-41 September 2004 

Drift-Scale Radionuclide Transport 
Sections 5.8 and 6.4). Therefore, the matrix porosity in the invert is sampled based on the 
variability in matrix porosity in the Tptpln lithostratigraphic unit, which is equivalent to the TM2 
and TM1 hydrogeologic units (Analysis of Hydrologic Properties Data, BSC 2004 
[DIRS 170038], Table 6-1). A suitable range of values for the intergranular porosity is estimated 
to be 0.4 to 0.48 (Hilf 1975 [DIRS 169699], p. 257; BSC 2003 [DIRS 170881], 
Section 4.1.4). The range of porosities is derived from values of the maximum void ratios for 
poorly graded sand (SP) as given in Hilf (1975 [DIRS 169699], p. 257). The maximum void 
ratio for poorly graded sand is used to represent the possible range void ratios for uncompacted 
tuff grains. Porosity is computed from the void ratio e as e/(1+e). Intergranular porosity is 
sampled as a uniform random distribution over the range identified in Section 4.1.1. The 
uncertainty in D0 is based on the range of values for strong electrolyte diffusion coefficients in 
aqueous solution (Weast and Astle 1979 [DIRS 102865]) given in Section 4.1.1. This is a 
sufficiently wide range of free-water diffusion coefficients for radionuclides, based on reported 
values of 2.2  10-9 m2/s for tritiated water [Diffusion of Helium in Water-Saturated, 
Compacted Sodium Montmorillonite (Sato et al. 2001 [DIRS 164047])], 1.9  10-9 m2/s for 
pertechnetate (TcO4 ) [Ionic Diffusion Coefficients of Cs+, Pb2+, Sm3+, Ni2+, SeO42-and TcO4 
in Free Water Determined from Conductivity Measurements (Sato et al. 1996 [DIRS 163213])], 
and 1.1  10-9 m2/s for bicarbonate [Electrochemical Systems (Newman 1973 
[DIRS 148719])]. These are sampled as a lognormal distribution to account for the semi-infinite 
range of this parameter. Details concerning the sampling methods used for the diffusive mass 
transfer coefficient are given in Appendix E. 
Diffusion Coefficients in Fractured Rock 
Diffusion coefficients in fracture water have not been directly determined. Generally speaking, 
diffusion in unsaturated geologic materials has been found to be sensitive to water content 
(Conca and Wright 1990 [DIRS 101582], p. 1,055; Bear 1972 [DIRS 156269], Sections 4.8.2 
and 4.8.3). Experimental evidence concerning diffusion in unsaturated granular materials is 
presented in Conca and Wright (1990 [DIRS 101582]). These experiments were performed on 
nonporous granular materials in which diffusion occurred through water films along the granular 
surfaces. The water content of these materials ranged from 0.5 to 5 percent and diffusion 
coefficients ranged from about 10-13 m2/s to 10-11 m2/s (Conca and Wright 1990 [DIRS 101582], 
Figures 1013). The analogous water content of a fracture continuum is the fracture water 
saturation, which is also roughly in this range (see Appendix G). The range for matrix diffusion 
coefficients is about an order of magnitude larger (see Figure 6-23). This information suggests 
that the use of diffusion coefficients in the rock matrix as surrogates for diffusion coefficients in 
the fractures is conservative. Fractures in the welded tuff repository host rock are different than 
the nonporous granular materials investigated by Conca and Wright (1990 [DIRS 101582]) due 
to differences in geometry and the connection to a porous rock matrix. As discussed in 
Section 4.1.5, limiting values for diffusion coefficients in the fractures are taken to be the 
effective diffusion coefficients in the neighboring rock matrix. Distributions for matrix diffusion 
coefficients for cations and anions are given in Appendix I. Additional corroborative 
information on diffusion coefficients in rock matrix is given in Reimus et al. (2002 
[DIRS 163008]), where a correlation for diffusion in the rock matrix was developed based on 
laboratory and field data. The correlation establishes a quantitative relationship between the 
porosity and permeability of a saturated rock matrix to the effective diffusion coefficient. This 
correlation may be extended for unsaturated conditions by using the water content as an 
MDL-NBS-HS-000016 REV 01 6-42 September 2004 

Drift-Scale Radionuclide Transport 
equivalent parameter for porosity under saturated conditions and the unsaturated effective 
permeability for the saturated permeability. This extension to unsaturated conditions is 
appropriate because for unsaturated flow, the character of the gas phase is not significant other 
than the space that it occupies. The gas phase could be replaced by solid (rock mineral) which 
would result in exact equivalence between the unsaturated water content and porosity and 
effective unsaturated permeability and permeability. The correlation is then (BSC 2004 
[DIRS 170042], Equation 6-19; Reimus et al. 2002 [DIRS 163008], Equation 2.5) 
log( D )=- 49.3 + 38.1 .+ log 165.0 ( k ) (Eq. 6-52)
m mw 
where Dm is the effective diffusion coefficient in cm2/s, . is the matrix water content, and kw is
mthe effective permeability to water in m2. Data confirm that this correlation provides a 
reasonable estimate for matrix diffusion in Yucca Mountain volcanic rocks 
(DTN: SN0306T0502103.006 [DIRS 163944]; BSC 2004 [DIRS 170042], Section 6.5.2.6) The 
data from Reimus et al. (2002 [DIRS 163008]) suggests that the range of diffusion coefficients 
for tritium, bicarbonate, and pertechnetate individually are roughly similar to the range of mean 
values for each. This suggests that a single broad distribution scaled by the range of values 
between cations and anions from DTN: LA0003JC831362.001 [DIRS 149557] would provide a 
better representation of the uncertainty in matrix diffusion. To capture this in a single 
distribution, consider the following transformation: 
X = log..
. D0 ..
. (Eq. 6-53)
. Dm. 
where D0 is the limiting upper value for Dm. This value is given in DTN: LA0003JC831362.001 
[DIRS 149557] as 10-9 m2/s. The average for X is 

= log( D )- log( D ) (Eq. 6-54)
X 0 m 
If we stipulate that the variable X ranges from 0 to infinity, then Dm is constrained to be less than 
10-9 m2/s. 
Given the semi-infinite range for X, it can be sampled as a lognormal distribution. This 
introduces the second logarithmic transformation, Y, 
Y =ln( X ) (Eq. 6-55) 
The mean for Y is taken to be 
=ln( ) (Eq. 6-56)
YX 
such that the mean is unchanged by the transformation to a lognormal distribution. The 
distribution of diffusion coefficients based on Equations 53 and 55 and a normal distribution for 
Y is called the primary distribution. Distribution parameters for Y may be obtained by setting 
log( D ) to be the log of the geometric mean of the mean values in DTN: LA0003JC831362.001
m 
MDL-NBS-HS-000016 REV 01 6-43 September 2004 

Drift-Scale Radionuclide Transport 
[DIRS 149557] and then adjusting the standard deviation for Y such that it covers the range of 
values represented by cations and anions in DTN: LA0003JC831362.001 [DIRS 149557]. The 
standard deviation of 0.3 for Y results in a spread for the distribution that is representative of the 
spread of values in DTN: LA0003JC831362.001 [DIRS 149557], as shown in Figure 6-22. 
Cumulative Probability for Matrix Diffusion 
Diffusion Coefficient m2/s 
1.00E-09 
1.00E-10 
diiiidipriiiion 
strbuton for anons 
stribution for cations 
mary dstrbut
1.00E-11 
1.00E-12
0.000 0.200 0.400 0.600 0.800 1.000
Cumulative Probability 
DTN: LA0003JC831362.001 [DIRS 149557]. 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-22. Cumulative Probability for Matrix Diffusion 
See Appendix I for a discussion of the methods used to generate the distributions for cations, 
anions, and the Reimus correlation. The range of values for the UZ may be examined using 5th 
and 95th percentile values for water content and effective matrix permeability. Doing this, the a 
low distribution may be computed based on Equation 6-52 by assigning the mean using the 5th 
percentile water content and effective matrix permeability and a high distribution may be 
based on the 95th percentile of values of these quantities. The results are shown in Figure 6-23. 
MDL-NBS-HS-000016 REV 01 6-44 September 2004 

Drift-Scale Radionuclide Transport 
Cumulative Probability for Matrix Diffusion 
Diffusion Coefficient m2/s 
1.00E-09 
1.00E-10 
1.00E-11 
iiiiiipriiiile 
priiiile 
distrbuton for anons 
distrbuton for catons 
mary distrbuton - 5th percentmary distrbuton - 95th percent
1.00E-12
0.000 0.200 0.400 0.600 0.800 1.000
Cumulative Probability 
DTN: LA0003JC831362.001 [DIRS 149557]. 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-23. Comparison of Cation/Anion Distributions with Primary Distributions at 5th and 95th 
Percentile for Effective Permeability, Mean Glacial Transition Climate 
See Appendix I for a discussion of the methods used to generate the low and high distributions 
for the Reimus correlation. The data used to develop the distributions in 
DTN: LA0003JC831362.001 [DIRS 149557] were from diffusion measurements under 
saturated conditions. As a consequence, the generally lower values represented by the Reimus 
distributions are expected. The comparison with measured diffusion coefficients for tritium, 
technetium, and bicarbonate (Table 6-12) is given in Figure 6-24. Again, the correlations for the 
UZ are lower than the measured values, which were all performed under saturated conditions. 
MDL-NBS-HS-000016 REV 01 6-45 September 2004 

Drift-Scale Radionuclide Transport 
iiiD iii/siion fiion fiii)
) technetium 
data 
) bidata 
Cumulatve Probability for Matrx Diffusion 
1.00E-12 
1.00E-11 
1.00E-10 
1.00E-09 
0.000 0.200 0.400 0.600 0.800 1.000 
Cumulatve Probability 
ffu s o n C o e ffic e n t m 2 
distrbutor anions 
distrbutor catons 
primary distrbution - 5th 
percentile 
primary distrbution - 95th 
percentile 
Reimus (2002 tritium data 
Reimus (2002Reimus (2002carbonate 
Source: Reimus et al. 2002 [DIRS 163008], Table 2-4. 
DTN: LA0003JC831362.001 [DIRS 149557]. 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-24. Comparison of the Distributions with Diffusion Data 
Table 6-12. Diffusion Data from Reimus et al. (2002 [DIRS 163008], Table 2-4) 
Sample Description 
3H Diffusion coefficient, 
cm2/s 
99Tc Diffusion coefficient, 
cm2/s 
14C Diffusion coefficient, 
cm2/s 
UE20c 2856D 1.1E-06 8.0E-07 6.0E-07 
UE20c 2856E 8.5E-07 6.0E-07 4.5E-07 
UE20c 2856F 9.0E-07 5.0E-07 3.3E-07 
UE20c 2856F 2.3E-06 2.5E-06 1.7E-06 
UE20c 2856F 1.3E-06 1.2E-06 8.0E-07 
UE20c 2858A 1.2E-06 9.0E-07 3.0E-06 
UE20c 2858A 1.0E-06 4.0E-07 1.7E-06 
UE20c 2809A 7.5E-07 n.a. n.a. 
UE20c 2809B* 1.4E-06 n.a. n.a. 
UE20c 2751A 1.4E-06 6.0E-07 5.0E-06 
MDL-NBS-HS-000016 REV 01 6-46 September 2004 

Drift-Scale Radionuclide Transport 
Table 6-12. Diffusion Data from Reimus et al. (2002 [DIRS 163008], Table 2-4) (Continued) 
Sample Description 
3H Diffusion coefficient, 
cm2/s 
99Tc Diffusion coefficient, 
cm2/s 
14C Diffusion coefficient, 
cm2/s 
UE20c 2751B* 1.3E-06 5.0E-07 5.0E-06 
UE20c 2908A 3.0E-06 2.7E-06 1.3E-06 
UE20c 2908D* 2.4E-06 2.1E-06 2.5E-06 
UE20f 2842 5.5E-07 5.0E-07 1.5E-07 
UE18t 1003A 1.3E-06 n.a. n.a. 
UE18t 1003B* 7.0E-07 n.a. n.a. 
UE18t 1387.5A 8.5E-07 4.5E-07 3.0E-06 
UE18t 1387.5A 8.5E-07 6.5E-07 1.8E-06 
UE18t 1387.5B 8.0E-07 6.0E-07 6.1E-06 
UE18t 1387.5B 9.5E-07 9.0E-07 3.0E-06 
UE18t 1390 9.0E-07 5.5E-07 7.5E-06 
UE18t 1390 7.5E-07 4.0E-07 1.1E-05 
UE18r 2228A 4.4E-07 3.5E-07 6.0E-06 
UE18r 2228A 4.3E-07 3.2E-07 6.0E-06 
UE18r 2228B 3.5E-07 1.3E-06 2.0E-05 
PM1 4823A 3.5E-06 1.2E-06 1.5E-06 
PM1 4823B* 3.5E-06 1.3E-06 5.0E-06 
PM2 4177A 2.1E-06 8.0E-07 1.4E-06 
PM2 4177A 8.0E-07 2.5E-07 1.4E-06 
PM2 4177B 2.3E-06 5.0E-06 3.5E-06 
PM2 4177B 9.0E-07 4.5E-07 1.0E-06 
PM2 4177C* 2.0E-06 4.0E-06 1.0E-05 
PM2 4177C* 1.0E-06 2.8E-07 2.0E-06 
NOTE: *Denotes diffusion cell with a mineralized fracture surface. 
n.a. = data not available. 
See Appendix I for a discussion of the methods used to compare these distributions with the 
measurements. 
Water content is derived from the sampled water saturation (Appendix B) times the sampled 
matrix porosity (Appendix D) for the model unit. The effective permeability is computed from 
the relative permeability and matrix permeability 
k =k k (Eq. 6-57)
w mrw 
where km is the saturated permeability of the matrix and krw is the relative permeability from the 
flow model output. The matrix permeability is not sampled because the flow and saturation 
information is consistent only with the mean values. Details concerning the sampling methods 
used for the matrix diffusion coefficient are given in Appendix F. 
MDL-NBS-HS-000016 REV 01 6-47 September 2004 

Drift-Scale Radionuclide Transport 
The parameters derived are combined to provide values of the dimensionless parameters 
identified in Section 6.4.2 across the flow model grid locations within the repository host 
rock. Computation of these parameters across the grid locations is described in Appendix G. 
A summary of the parameters used for the fracture-matrix partitioning model, initially presented 
in Section 4 of this report, is given in Table 6-13. 
Table 6-13. Inputs for the Fracture-Matrix Partitioning Model 
Input 
Name Input Description Input Source 
Value or 
Distribution 
Type of 
Uncertainty 
f fracture frequency LB0205REVUZPRP.001 log-normal epistemic 
[DIRS 159525] 
Sfr fracture residual saturation LB0208UZDSCPLI.002 [DIRS 161788], 
LB0208UZDSCPMI.002 
log-uniform epistemic 
[DIRS 161243], LB0302UZDSCPUI.002 
[DIRS 161787] 
Sf fracture saturation LB03023DSSCP9I.001 [DIRS 163044] empirical epistemic 
F flow focusing factor DTN LB0406U0075FCS.002 
[DIRS 170712]; BSC 2004 
[DIRS 167652], Section 6.8 
empirical epistemic 
m fracture van Genuchten pore 
size distribution parameter 
LB0208UZDSCPLI.002 [DIRS 161788], 
LB0208UZDSCPMI.002 
[DIRS 161243], LB0302UZDSCPUI.002 
[DIRS 161787] 
single value n.a. 
qwf water flux in fracture LB03023DSSCP9I.001 [DIRS 163044] empirical epistemic 
f f 
fracture porosity LB0205REVUZPRP.001 
[DIRS 159525] 
beta epistemic 
mf matrix porosity LB0207REVUZPRP.002 
[DIRS 159672] 
beta epistemic 
Sm matrix saturation LB03023DSSCP9I.001 [DIRS 163044] empirical epistemic 
km matrix saturated permeability LB03023DSSCP9I.001 [DIRS 163044] empirical epistemic 
krm matrix relative permeability LB03023DSSCP9I.001 [DIRS 163044] empirical epistemic 
Dm diffusion in rock matrix SN0306T0502103.006 [DIRS 163944]; ln- log- normal epistemic 
BSC 2004 [DIRS 170042], 
Equation 6-19. 
qm water flux in matrix LB03023DSSCP9I.001 [DIRS 163044] empirical epistemic 
fIginvert intergranular porosity Hilf 1975 [DIRS 169699], p. 257; BSC 
2003 [DIRS 170881], Sections 4.1.4 
and 6.3 
uniform epistemic 
D0 free-water diffusion coefficient Weast and Astle 1979 [DIRS 102865], 
p. F-62 
log-normal epistemic 
DeI Invert diffusion correlation BSC 2001 [DIRS 156700], pp. 2325 n.a. n.a. 
ym invert depth BSC 2003 [DIRS 164101] uniform epistemic 
n.a. waste emplacement areas in 
each host rock unit 
BSC 2004 [DIRS 168370] single value n.a. 
NOTE: n.a. = not applicable. 
MDL-NBS-HS-000016 REV 01 6-48 September 2004 

Drift-Scale Radionuclide Transport 
6.4.6 Model Results 
Calculations are performed for the lower, mean, and upper scenarios of the glacial transition 
climate. This climate is the largest fraction of the compliance period and is the portion of the 
compliance period when radionuclide transport is more probable. Furthermore, mean infiltration 
rates for the glacial transition scenarios range from 2.4 to 32 mm/year [UZ Flow Models and 
Submodels (BSC 2004 [DIRS 169861]), Table 6.1-2]. This range nearly encompasses the entire 
mean infiltration range infiltration scenarios from monsoon and present-day climates, which 
range from 1.3 to 19 mm/year (BSC 2004 [DIRS 169861], Table 6.1-2). Therefore, using results 
derived for the glacial transition climate for the lower, mean, and upper infiltration scenarios, 
respectively, under modern and monsoon climate, are not expected to result in an underestimate 
of radionuclide transport. 
As discussed in Section 6.4.5, parameter uncertainty is included in the model development 
through sampling of the 433 different repository locations that have been assigned 
parameters. The sampling is performed to provide a representation of the frequency distribution 
of the fraction of the total radionuclide flux from a drift that enters the fractures. A set of 24 
samples was randomly selected for each climate scenario. This total number of samples allows 
for taking one sample each from the tsw33 and tsw36 host rock horizons in a representative 
proportion to the tsw34 (3 samples) and the tsw35 (19 samples), based on the repository 
layout. Estimation theory indicates that for 95 percent confidence limits, 24 samples provide an 
estimate of the mean that is within 
96.1 

S  = 41.0 S (Eq. 6-58) 
24 -1 
[Introduction to Mathematical Statistics (Hogg and Craig 1978 [DIRS 163236], pp. 212215)], 
where S is the sample standard deviation. The details of the sampling methods used for each 
infiltration case are given in Appendix H. 
Computed results for each climate scenario are shown in Figures 6-25a-c using the 
dimensionless flux ratios as discussed in Section 6.4.4. Calculation details are given in Wang 
(2003 [DIRS 163234], SN-LBNL-SCI-236-V1, pp. 101145), but the method used is the same as 
discussed in Section 6.4.4 and Appendix J. Results for the lower and mean infiltration scenarios 
are more similar and, in general, have a larger proportion released to the fractures than the higher 
infiltration case. This difference primarily results from the influence of the higher matrix water 
flux on the transport from the drift into the rock matrix under the higher infiltration 
scenario. The variation in fracture flux and water saturation among the different infiltration 
scenarios is found to have a second-order effect on fracture-matrix partitioning. 
MDL-NBS-HS-000016 REV 01 6-49 September 2004 

Drift-Scale Radionuclide Transport 
(a) 
ii0 1 
is 
Ii0 1 
isFracture-Matrix Partitioning Glacial 
Transiton Lower Infiltraton Scenario 
0.00E+00 
1.00E-01 
2.00E-01 
3.00E-01 
4.00E-01 
5.00E-01 
6.00E-01 
7.00E-01 
8.00E-01 
9.00E-01 
1.00E+00 
0.2 0.4 0.6 0.8 
Cumulatve Probability 
Fraction Released to FractureFracture-Matrix Partitioning Glacial 
Transition Lowernfltration Scenario 
1.00E-04 
1.00E-03 
1.00E-02 
1.00E-01 
1.00E+00 
0.2 0.4 0.6 0.8 
Cumulatve Probability 
Fraction Released to Fracture 
(b) 
0 0.4 0.8 1 0 1 
liFracture-Matrix Partitioning Glacial 
Transition Mean Infiltration Scenario 
0.00E+00 
1.00E-01 
2.00E-01 
3.00E-01 
4.00E-01 
5.00E-01 
6.00E-01 
7.00E-01 
8.00E-01 
9.00E-01 
1.00E+00 
0.2 0.6 
Cumulative Probability 
Fraction Released to Fractures 
Fracture-Matrix Partitioning Glacial 
Transition Mean Infiltration Scenario 
1.00E-04 
1.00E-03 
1.00E-02 
1.00E-01 
1.00E+00 
0.2 0.4 0.6 0.8 
Cumuatve Probability 
Fraction Released to Fractures 
(c) 
lii0 1 
is 
0 1 
ilFracture-Matrix Partitioning -
Glacia Transition Upper Infltraton Scenario 
0.00E+00 
1.00E-01 
2.00E-01 
3.00E-01 
4.00E-01 
5.00E-01 
6.00E-01 
7.00E-01 
8.00E-01 
9.00E-01 
1.00E+00 
0.2 0.4 0.6 0.8 
Cumulatve Probability 
Fraction Released to FractureFracture-Matrix Partitioning Glacial 
Transition Upper Infiltration Scenario 
1.00E-04 
1.00E-03 
1.00E-02 
1.00E-01 
1.00E+00 
0.2 0.4 0.6 0.8 
Cumulatve Probability 
Fraction Reeased to Fractures 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-25. Fracture-Matrix Partitioning Distributions for the (a) Lower, (b) Mean, and (c) Upper 
Glacial-Transition Infiltration Scenarios  Linear Scale on Left-Hand Side; Logarithmic 
Scale on Right-Hand Side 
MDL-NBS-HS-000016 REV 01 6-50 September 2004 

Drift-Scale Radionuclide Transport 
Distributions are based on the values for fracture-matrix partitioning and then ordered, to 
establish an empirical cumulative probability distribution. The distribution for the upper 
scenario has smaller releases to the fractures because of the larger advective water flux in the 
matrix. The average matrix water flux for the upper infiltration scenario is 0.08 mm/year 
compared with average matrix fluxes for the mean and lower scenarios of 0.035 and 
0.027 mm/year, respectively. Furthermore, the median matrix fluxes for the upper, mean, and 
lower infiltration scenarios are 6.6, 1.6, and 1.6 mm/year, respectively. The similarity of the 
matrix flux for the lower and mean scenarios is the main reason for the similarity in the flux 
partitioning between the fractures and matrix. The other factors, such as the fracture Peclet 
number and fracture water content, tend to be random variables defined by the invert and fracture 
diffusion coefficients, offset of fracture flow from the drift, and residual fracture saturation not 
strongly affected by the infiltration scenario. Figures 6-25ac show that the lower and mean 
scenarios result in distributions similar to the upper scenario. A comparison of the lower and 
mean scenarios is given in Figure 6-26. 
(b) 
ii0 1 
liiiliiiFracture-Matrx Partitioning Glacial 
Transition Lower and Mean Infiltration Scenaros 
1.00E-04 
1.00E-03 
1.00E-02 
1.00E-01 
1.00E+00 
0.2 0.4 0.6 0.8 
Cumulative Probability 
Fraction Released to Fractures 
Samped Dstrbuton Lower 
Samped Dstrbuton Mean 
Fracture-Matrix Partitioning Glacial 
Transition Lower and Mean Infiltration Scenarios 
1.00E+00 
9.00E-01 
8.00E-01 
7.00E-01 
Fraction Released to Fractures 
6.00E-01 
5.00E-01 
4.00E-01 
3.00E-01 
2.00E-01 
1.00E-01 
0.00E+00 
0 0.2 0.4 0.6 0.8 1 
Cumulative Probability 
liiliiSamped Distrbuton Lower 
Samped Distrbuton Mean 
(a) 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-26. Comparison of Lower and Mean Scenarios  (a) Linear Scale on Left-Hand Side; 
(b) Logarithmic Scale on Right-Hand Side 
The comparisons in Figure 6-26a show on a linear scale that the distributions are fairly 
similar. The logarithmic plot shows the comparison with error bars set by the relative error in 
the mean. The overlap of the confidence limits for the lower and mean cases suggests combining 
these distributions into a single distribution. This distribution is shown in Figure 6-27. 
MDL-NBS-HS-000016 REV 01 6-51 September 2004 

Drift-Scale Radionuclide Transport 
(a) 
iFracture-Matrix Parttioning Glacial 
Transition Lower and Mean Infiltration Scenarios 
0.00E+00 
1.00E-01 
2.00E-01 
3.00E-01 
4.00E-01 
5.00E-01 
6.00E-01 
7.00E-01 
8.00E-01 
9.00E-01 
1.00E+00 
0.000E+00 2.000E-01 4.000E-01 6.000E-01 8.000E-01 1.000E+00 
Cumulative Probability 
Fraction Released to Fractures 
(b) 
iiiFracture-Matrx Parttionng Glacial 
Transition Lower and Mean Infiltration Scenarios 
1.00E-04 
1.00E-03 
1.00E-02 
1.00E-01 
1.00E+00 
0.000E+00 2.000E-01 4.000E-01 6.000E-01 8.000E-01 1.000E+00 
Cumulative Probability 
Fraction Released to Fractures 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-27. Composite Distribution from the Lower and Mean Scenarios  (a) Linear Scale on Left-Hand 
Side; (b) Logarithmic Scale on Right-Hand Side 
The uncertainty in the sampled distributions is shown in Figure 6-28. This uncertainty is based 
on the 95th percentile confidence interval estimates as presented in Equation 6-58. 
(a) 
iitiFracture-Matrix Partitionng - 
Glacial Transon Lower and Mean Infiltration Scenarios 
1.00E-04 
1.00E-03 
1.00E-02 
1.00E-01 
1.00E+00 
0.000E+00 2.000E-01 4.000E-01 6.000E-01 8.000E-01 1.000E+00 
Cumulative Probability 
Fraction Released to Fractures 
(b) 
0 1 
iFracture-Matrix Partitioning Glacial 
Transition Upper Infiltration Scenario 
with Uncertainty Estimates 
1.00E-04 
1.00E-03 
1.00E-02 
1.00E-01 
1.00E+00 
0.2 0.4 0.6 0.8 
Cumulatve Probability 
Fraction Released to Fractures 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-28. Fracture-Matrix Partitioning Distributions with 95th Percentile Confidence Intervals: (a) 
Composite Distribution for the Lower and Mean Infiltration Scenarios and (b) Distribution for 
the Upper Infiltration Scenario 
The combined distribution of percentage released to fractures for lower and mean infiltration 
scenarios under the glacial transition climate was derived for infiltration rates of 2.5 and 
17.8 mm/year (Simulation of Net Infiltration for Modern and Potential Future Climates, BSC 
2004 [DIRS 170007], Table 6-19). Present-day and monsoon climates range from 1.3 to 
19.8 mm/year (BSC 2004 [DIRS 170007], Tables 6-10 and 6-14). Therefore, the combined 
distribution given in Figure 6-28a is applicable over all climates and infiltration scenarios except 
for the glacial transition upper infiltration case. For the glacial transition upper infiltration 
scenario, the distribution shown in Figure 6-28b is applicable. 
MDL-NBS-HS-000016 REV 01 6-52 September 2004 

Drift-Scale Radionuclide Transport 
Table 6-14. Cumulative Distributions for Fracture-Matrix Partitioning Factor: (a) Composite Distribution 
for the Glacial Transition Lower and Mean Infiltration Scenarios; (b) Distribution for the 
Glacial Transition Upper Infiltration Scenario 
(a) Lower and Mean Infiltration Scenario (b) Upper Infiltration Scenario 
Cumulative Probability Sampled Distribution Cumulative Probability Sampled Distribution 
0.000E+00 0.00 0 0.00 
2.041E-02 3.33E-04 0.040 1.53E-04 
4.082E-02 7.60E-04 0.080 1.84E-03 
6.122E-02 1.55E-03 0.120 1.91E-03 
8.163E-02 1.58E-03 0.160 2.56E-03 
1.020E-01 1.67E-03 0.200 3.45E-03 
1.224E-01 2.53E-03 0.240 4.08E-03 
1.429E-01 2.63E-03 0.280 4.32E-03 
1.633E-01 3.41E-03 0.320 5.79E-03 
1.837E-01 4.22E-03 0.360 5.98E-03 
2.041E-01 4.86E-03 0.400 7.08E-03 
2.245E-01 4.97E-03 0.440 7.14E-03 
2.449E-01 7.86E-03 0.480 7.21E-03 
2.653E-01 9.08E-03 0.520 7.37E-03 
2.857E-01 1.02E-02 0.560 9.81E-03 
3.061E-01 1.139E-02 0.600 1.02E-02 
3.265E-01 1.141E-02 0.640 1.40E-02 
3.469E-01 1.209E-02 0.680 1.68E-02 
3.673E-01 1.214E-02 0.720 1.82E-02 
3.878E-01 1.39E-02 0.760 1.95E-02 
4.082E-01 1.52E-02 0.800 1.98E-02 
4.286E-01 1.55E-02 0.840 2.18E-02 
4.490E-01 1.63E-02 0.880 2.83E-02 
4.694E-01 1.69E-02 0.920 3.34E-02 
4.898E-01 1.99E-02 0.960 5.44E-02 
5.102E-01 2.79E-02 1 1.00E+00 
5.306E-01 3.24E-02 
5.510E-01 3.77E-02 
5.714E-01 4.63E-02 
5.918E-01 4.82E-02 
6.122E-01 4.94E-02 
6.327E-01 5.04E-02 
6.531E-01 5.26E-02 
6.735E-01 5.85E-02 
6.939E-01 7.61E-02 
7.143E-01 8.34E-02 
7.347E-01 9.68E-02 
7.551E-01 1.52E-01 
7.755E-01 1.66E-01 
7.959E-01 2.00E-01 
8.163E-01 2.72E-01 
8.367E-01 3.58E-01 
8.571E-01 3.77E-01 
8.776E-01 4.49E-01 
8.980E-01 4.53E-01 
9.184E-01 4.88E-01 
9.388E-01 4.90E-01 
9.592E-01 5.50E-01 
9.796E-01 7.34E-01 
1.000E+00 1.00E+00 
Output DTN: LB0307FMRADTRN.001. 
NOTE: A fourth significant figure is given for the sampled distribution values where three significant 
figures result in a repeated value. 
MDL-NBS-HS-000016 REV 01 6-53 September 2004 

Drift-Scale Radionuclide Transport 
Table 6-15. Statistics for the Fracture-Matrix Partitioning Factor Distributions: (a) Lower and Mean 
Infiltration Scenarios for Glacial Transition Climate; (b) Upper Infiltration Scenario for 
Glacial Transition Climate 
(a) Lower and Mean Infiltration 
Scenario (b) Upper Infiltration Scenario 
Average of FractureMatrix 
Partitioning Factors 1.16E-01 1.27E-02 
Standard Deviation of Fracture-
Matrix Partitioning Factors 1.82E-01 1.25E-02 
95th Percentile Confidence Interval 
(Equation 6-58) 7.45E-02 5.11E-03 
95th Percentile Confidence 
IntervalPercentage of Average 64.5% 40.2% 
Output DTN: LB0307FMRADTRN.001. 
The sensitivity of the results to the invert diffusive mass transfer coefficient have been 
investigated to address the potential effects of different invert materials on the fracture-matrix 
partitioning. The modeling results for the partitioning coefficient (the fraction of the 
radionuclide releases that enter the fractures) are plotted against the diffusive mass transfer 
coefficient for the invert in Figure 6-29. The sensitivity results show that the fraction released to 
fractures has only a very weak correlation with the invert diffusive mass transfer coefficient. 
Invert properties affect the partitioning results only through the invert diffusive mass transfer 
coefficient. Furthermore, the invert diffusive mass transfer coefficient is only affected by the 
invert porosities (Section 6.4.5). Therefore, the main results that are derived using properties of 
the invert intragranular porosity from the tsw36 are also applicable if the invert consists of 
materials from the other host rock units having different intragranular porosities, i.e. the tsw33, 
tsw34, and tsw35. 
Partitioning Sensitivity to Invert 
Diffusive Mass Transfer Coefficient 
0
-0.5
-1
-1.5
-2
-2.5
-3
R2 = 0.0002 
-3.5
-4
1.5 22.5 33.5 
Log(Invert Diffusion Coefficient (mm^2/yr)) 
Output DTN: LB0307FMRADTRN.001. 
Figure 6-29. Fracture-Matrix Partitioning Sensitivity to Invert Diffusive Mass Transfer Coefficient 
Log(Fraction Released to 
Fractures) 
MDL-NBS-HS-000016 REV 01 6-54 September 2004 

Drift-Scale Radionuclide Transport 
6.5 EFFECTS OF AIR IN FRACTURE 
The results found for the model as discussed in Section 6.4 may be compared with the first-order 
model predictions from Equations 43 and 44. The fracture-matrix partitioning ratio, Pr, to first 
order is: 
b Pe d
P = 
Pe ( 1- b 
fe 
)+ b Pe 
(Eq. 6-59) 
r 
m d fed 
A comparison of the predictions for the fracture-matrix partitioning model based on 
Equation 6-59 with the results in Section 6.4 is given below. Inputs for this calculation are 
presented in Appendix H. 
Table 6-16. Comparison of First-Order Model to Full Model 
Average Fracture-Matrix Partitioning Ratio 
Full model First-order model 
Lower case 8.61E-02 8.92E-02 
Mean case 1.45E-01 1.51E-01 
Upper case 1.27E-02 1.33E-02 
The results indicate that the first-order model explains most of the partitioning behavior. The 
first-order model is independent of the Fourier coefficients, as shown in Equation 6-59. 
Therefore, the solution is not sensitive to the details of the boundary conditions and location of 
the water film along the invert-rock boundary. 
If the air gap in the fracture is included, the first-order solution becomes: 
b Pe d
P = 
Pe ( 1-f 
fe )+ b Pe 
(Eq. 6-60) 
ra 
m f fed 
where P is the partitioning ratio including the air gap and f f is the fracture porosity. 
ra
Equation 6-60 may be written in terms of P giving,
r
P
r
P = (Eq. 6-61) 
ra 
1-( 1- P )...
ff - bd ...
r 
. 1- bd . 
The ratio of P to P is unity for P = 1 and is largest for P = 0. The maximum ratio is 
rarrr
ra
P = 1- bd (Eq. 6-62) 
P 1-f f
r 
MDL-NBS-HS-000016 REV 01 6-55 September 2004 

Drift-Scale Radionuclide Transport 
However, ff and bdare both much less than 1 so Equation 6-60 may be approximated as, 
P
ra 
P 
= 1+ff - bd (Eq. 6-63) 
r 
Therefore, the maximum relative error is, 
P - P
ra r 
=ff - bd (Eq. 6-64) 
P
r 
which is less than the fracture porosity. This result supports the model approximation that the 
solution is not sensitive to the placement of the no-flux boundary either immediately adjacent to 
the water film (as in the model presented in Section 6.4) or displaced from this water film by an 
air gap in the fracture. 
6.6 COMPARISON OF FRACTURE-MATRIX PARTITIONING MODEL AND DRIFT 
SHADOW MODEL 
Sections 6.3 and 6.4 present two models concerning the behavior of flow and transport in the 
region beneath waste emplacement drifts. In Section 6.3, the drift shadow model uses the 
dual-continuum method to show that a substantial perturbation to the flow field exists beneath 
waste emplacement drifts. A large zone of reduced flow is found for the fracture continuum, 
with a much smaller perturbation to the flow for the matrix continuum. The transport through 
the drift shadow is found to be much slower than transport initiated in unperturbed fracture flow. 
Sensitivity studies indicate that this behavior is largely due to initiation of transport in the matrix 
and the subsequent slow migration of radionuclides through the matrix to the fractures. 
The fracture-matrix partitioning model presented in Section 6.4 is based on the premise that 
fracture flow around a drift does not behave like a homogeneous continuum, but that 
heterogeneity, anisotropy, and discrete fracture effects may result in water movement in the 
fractures much closer to the waste emplacement drift than found in Section 6.3. With the 
approximation of fracture flow close to the base of the waste emplacement drift, partitioning of 
releases from the drifts is not necessarily dominated by the relatively large matrix water content 
as compared with the fracture water content. The dynamics of the flow field in this model result 
in a competition between the fracture and matrix continua for radionuclide releases, and that 
leads to greater partitioning of the releases to the fractures. The greater releases of radionuclides 
to fractures and the more active flow system in the fracture-matrix partitioning model leads to 
more rapid transport of radionuclides in the UZ. Therefore, the fracture-matrix partitioning 
model was chosen to be used for validation of the EBS radionuclide transport abstraction model 
[EBS Radionuclide Transport Abstraction (BSC 2004 [DIRS 169868])] so that radionuclide 
transport in the unsaturated zone is not underestimated. 
MDL-NBS-HS-000016 REV 01 6-56 September 2004 

Drift-Scale Radionuclide Transport 
7. VALIDATION 
The drift-scale radionuclide transport model is intended to be used as an alternative model for 
comparison with the engineered barrier system (EBS) radionuclide transport model (EBS 
Radionuclide Transport Abstraction, BSC 2004 [DIRS 169868]). For that purpose, two 
alternative models have been developed for drift-scale radionuclide transport. One of the 
alternative models is a dual-continuum flow and transport model called the drift shadow 
model. The effects of variations in the flow field and fracture-matrix interaction in the vicinity 
of a waste emplacement drift are investigated through sensitivity studies using the drift shadow 
model (Houseworth et al. 2003 [DIRS 164394]). In this model, the flow is significantly 
perturbed (reduced) beneath the waste emplacement drifts. However, comparisons of transport 
in this perturbed flow field with transport in an unperturbed flow field show similar results if the 
transport is initiated in the rock matrix. This has led to a second alternative model, called the 
fracture-matrix partitioning model, that focuses on the partitioning of radionuclide transport 
between the fractures and matrix upon exiting the waste emplacement drift. The fracture-matrix 
partitioning model computes the partitioning of diffusive radionuclide transport from the invert 
(for drifts without seepage) into the rock water in the fractures and matrix. 
This section describes the validation of the fracture-matrix partitioning model. Note that the 
term model as presented in this section refers to both the mathematical model and its underlying 
conceptual model. This model is intended to support validation of the TSPA component model 
Radionuclide Transport from Waste Package to Drift Wall through Invert through comparisons 
of the fracture-matrix partitioning results for drifts without seepage. AP-2.27Q, Planning for 
Science Activities (Attachment 3, Table 1) requires Level I validation for models supporting that 
TSPA component. The criteria for confidence building during model development are given in 
Technical Work Plan for: Unsaturated Zone Transport Model Report Integration (BSC 2004 
[DIRS 171282], Section 2.2.4), consistent with AP-SIII.10Q, Models, Paragraph 5.3.2b). The 
general criteria for post-model development validation are given in AP-SIII.10Q, Models, 
Paragraph 5.3.2c). As specified in Attachment 3 of AP-2.27Q, the Level I post-development 
model validation must implement a single, appropriate method from this list. 
The results of the fracture-matrix partitioning model as shown in Figure 6-28 are intended to be 
used as an alternative model for comparison with the EBS radionuclide transport model. This 
use is limited to conditions applicable to the fracture-matrix partitioning model, which means 
drifts without seepage or other sources of advective transport (excluding the capillary driven 
flow between the rock matrix and the intragranular porosity of the invert, as discussed in 
Section 6.4). The range of intended use is for drifts without seepage or other sources of 
significant advective transport inside the drift (such as condensate flow). The range of use also 
encompasses the range of possible flow conditions in the rock and parameter ranges as discussed 
in Section 6.4.5. The level of confidence required is limited as a result of the expectation that a 
large fraction of the drifts will either have advective radionuclide transport through the invert 
from water seeping into the drifts and/or from condensation [(BSC 2004 [DIRS 169131], 
Tables 6.8-1 and 6.8-2; In-Drift Natural Convection and Condensation (BSC 2004 
[DIRS 164327], Section 6.3.7)] and because this is an alternative model that does not provide 
direct input to TSPA. As a result, the diffusive transport mechanism investigated in the 
fracture-matrix partitioning model is not expected to have a significant impact on performance; 
MDL-NBS-HS-000016 REV 01 7-1 September 2004 

Drift-Scale Radionuclide Transport 
hence the required level of confidence in the model validation is relatively low, commensurate 
with a Level I validation. 
Section 7.1 discusses confidence building during model development which establishes the 
reasons for confidence in the fracture-matrix partitioning model. Section 7.2 provides a detailed 
discussion of post-development validation activities, including the underlying rationale for 
comparison with the drift shadow model, a summary discussion of the rationale for introducing 
the fracture-matrix partitioning model to account for uncertainties in the drift shadow model; and 
demonstration of the conservative results obtained from the fracture-matrix partitioning model in 
comparison with the drift shadow model. This conservatism is tied to the effects of the 
partitioning on UZ transport, and the justification of a conservative model is based on the 
following points: 
1. The drift shadow model is approximately equivalent to 100% matrix release, as shown 
in Figure 6-7. 
2. Transport for fracture release is orders of magnitude faster than for matrix release, 
shown in Figure 6-7 for the drift shadow model and in Figure 7-2 for the site-scale UZ 
transport model. Note that the results for the drift shadow model domain are not 
quantitatively the same as for the site-scale model domain. This is a result of the drift 
shadow model being limited to fractured rock within the tsw35 rock unit and does not 
account for the effects of the full path length to the water table, other rock units, and 
other hydrogeologic features, as represented in the site-scale unsaturated zone 
transport model results. 
3. The fracture matrix partitioning model results in a non-negligible fraction of releases 
to the fractures for non-seeping drifts, as shown by the partitioning factor to fractures 
in Figure 6-28. Furthermore, this figure indicates that the model propagates a wide 
range of uncertainty from the input parameters into the output partitioning factor. 
7.1 CONFIDENCE BUILDING DURING MODEL DEVELOPMENT TO ESTABLISH 
SCIENTIFIC BASIS AND ACCURACY FOR INTENDED USE 
For Level I validation, Section 2.2.4 of BSC (2004 [DIRS 171282]) specifies the following steps 
for Confidence Building During Model Development: The development of the model should be 
documented in accordance with the requirements of Section 5.3.2b) of AP-SIII.10Q. The 
development of the fracture-matrix partitioning model has been conducted according to all of the 
applicable requirements, as follows: 
1. Selection of input parameters and/or input data, and a discussion of how the selection 
process builds confidence in the model. [AP-SIII.10Q 5.3.2(b) (1)] 
The types and quality of data selected as input builds confidence in the model. The 
inputs to the fracture-matrix partitioning model are presented in Section 4.1. The 
inputs describing hydrologic properties have been taken from site-specific 
measurements, e.g. fracture frequency and fracture porosity as discussed in 
Section 4.1.1, laboratory measurements on analogous materials, e.g. matrix diffusion 
as discussed in Section 4.1.5, or from models based on accepted scientific principles 
MDL-NBS-HS-000016 REV 01 7-2 September 2004 

Drift-Scale Radionuclide Transport 
and calibrated to site-specific data, e.g. water flux and water saturation in the rock as 
discussed in Section 4.1.2. Other sources of information including scientific data from 
handbooks, e.g. free-water diffusion coefficients as discussed in Section 4.1.6, and 
design information is taken from IEDs, e.g. the repository layout relative to the host 
rock units as discussed in Section 4.1.7. Thus, this criterion is appropriately 
addressed. 
2. Description of calibration activities, and/or initial boundary condition runs, 
convergences, and a discussion of how the activity or activities build confidence in the 
model. Inclusion of a discussion of impacts of any non-convergence runs 
[(AP-SIII.10Q 5.3.2(b)(2)]. 
The construction of the fracture-matrix partitioning model is discussed in detail in 
Section 6.4, with specific information on boundary conditions given in Section 6.4.1. 
Given that the model is steady-state, initial conditions are not applicable. Model 
calibration was not performed because the model was compared to an alternative 
conceptual model (i.e., the drift shadow model) in lieu of test data. Model run 
convergence for the fracture-matrix partitioning model is described in Section 6.4.4. 
The convergence variations were found to be on the order of a few percent 
(Section 6.4.4), significantly less than 50 percent specified in the criterion and 
significantly less than the uncertainty in model output, which is found to be on the 
order of a factor of 10 to 100 (Section 6.4.6). Therefore, the criterion for calibration 
and run convergence is met. 
3. Discussion of the impacts of uncertainties to the model results. 
[(AP-SIII.10Q 5.3.2(b)(3)]. 
Addressing Future States/Uncertainty - The effects of future climates and 
uncertainties are addressed in ways which build confidence in the models. Changes in 
future climate are expected to result in changes in flow and water saturation in the 
unsaturated zone, as discussed in Section 6.4.6. However, the range of uncertainty in 
climate conditions for the glacial-transition climate state was found to be comparable 
to that for the range of conditions under all climate states. The glacial-transition 
climate state is also expected to occur for most of the compliance period (from 2000 to 
10,000 years). Furthermore, the effects of changes in hydrologic conditions were 
found to be relatively small except for the wettest conditions anticipated under the 
glacial-transition climate state. Therefore, the fracture-matrix partitioning model 
could be based on the range of conditions under the glacial-transition climate state 
only. 
Parameter uncertainty in the fracture-matrix partitioning model is defined for 
parameters that affect the model output as discussed in Section 6.4.5. The uncertainty 
is based on direct, site-specific measurements, e.g. matrix porosity, inferences from 
analogous measurements, e.g. diffusion under saturated conditions in analogous rock 
samples, and uncertainty in model output, e.g. models of unsaturated flow using 
site-specific measurements and uncertainties. Uncertainty is either sampled directly, 
e.g. fracture frequency, or is treated as discrete states as in the UZ flow model output. 
MDL-NBS-HS-000016 REV 01 7-3 September 2004 

Drift-Scale Radionuclide Transport 
Because model uncertainty in the fracture-matrix partitioning model is incorporated by 
using a conservative approximation to flow processes in a fracture network beneath a 
waste emplacement drift, as discussed above under Addressing the Use of 
Assumptions/ Simplifications, the treatment of uncertainty builds confidence. 
Addressing the Propagation of Uncertainty - Uncertainties are propagated in a way 
which builds confidence. The uncertainty in parameters are sampled directly using a 
Monte Carlo methodology to derive the uncertainty in the output from the 
fracture-matrix partitioning model as presented in Section 6.4.6. Furthermore, the 
uncertainty resulting from the finite sample size used for the Monte Carlo analysis is 
also addressed. The uncertainty in model output is shown in Figure 6-28 and also is 
presented in Table 6-14. The range of uncertainty in the partitioning factor may be 
represented by the ratio of the mean plus one standard deviation divided by the mean 
minus one standard deviation. For the lower-mean climate states this range of 
uncertainty is on the order of 100; for the upper climate state this range of uncertainty 
is on the order of 10. These results show that uncertainty in the inputs translates into a 
broad range of uncertainty in the output of the fracture-matrix partitioning model. 
Therefore, the criterion for discussing the impacts of uncertainty is addressed. 
7.2 POST-DEVELOPMENT MODEL VALIDATION TO SUPPORT THE SCIENTIFIC 
BASIS OF THE MODEL 
Post-development model validation activities followed the model validation plan described in 
Section planned in the Technical Work Plan for: Unsaturated Zone Transport Model Report 
Integration (BSC 2004 [DIRS 171282], Section 2.2.4). The method chosen for model validation 
is corroboration with alternative models. In particular, BSC (2004 [DIRS 171282], 
Section 2.2.4) states for corroboration with alternative models: 
Results of the fracture-matrix partitioning model, in which flow is undisturbed immediately 
below the drift, will be evaluated. A comparison of this case with the dual-continuum model 
provides information on the sensitivity of the radionuclide partitioning to matrix and fractures 
upon leaving the waste emplacement drift, as a function of the flow field characteristics. The 
alternative model that results in greater radionuclide releases to the fractures will be used as an 
alternative model for validation of the EBS Radionuclide Transport Model. A discussion of the 
model uncertainties will also be provided. 
This model validation is based on a conservative model approach as discussed in 
Section 5.3.1b)2) in AP-SIII.10Q. 
7.2.1 Rationale for Selecting the Drift Shadow Model as the Alternative Conceptual 
Model 
The drift-shadow model is used as the alternative conceptual model to validate the 
fracture-matrix partitioning model. The drift shadow model is a standard process-based 
representation of flow and transport processes in fractured rock that represent a reasonable, 
credible, technical approach using scientific principles. The specific drift shadow model 
presented in Section 6.3 provides a detailed process-level description of the phenomena of 
MDL-NBS-HS-000016 REV 01 7-4 September 2004 

Drift-Scale Radionuclide Transport 
unsaturated flow and transport in a fractured rock near a waste emplacement drift [Flow and 
Transport in the Drift Shadow in a Dual-Continuum Model (Houseworth et al. 2003 
[DIRS 164394])]. This model accounts for the presence of fractures and a porous rock matrix 
using a standard process-based description of unsaturated flow in a dual continuum that predicts 
the hydrodynamic effects of a waste emplacement drift on unsaturated flow patterns. The model 
parameters are based on the drift-scale calibrated properties parameter set, with an adjustment to 
the active fracture parameter as discussed in Section 6.3.3.1 to account for the effects of the 
lower fracture permeability on fracture-matrix interaction as compared with the mountain-scale 
fracture permeabilities. Similarly, transport is modeled using a standard process-based 
description for an unsaturated dual-continuum using parameters applicable to advection, 
diffusion, sorption, and fracture-matrix interaction. The model uses the same conceptual basis as 
described in Conceptual and Numerical Models for UZ Flow and Transport (BSC 2004 
[DIRS 170035]). The fundamental process representations for flow and transport used by the 
drift shadow model are the same as those used for other drift-scale models as discussed in 
Seepage Model for PA Including Drift Collapse (BSC 2004 [DIRS 167652]); Seepage 
Calibration Model and Seepage Testing Data (BSC 2004 [DIRS 170034]); Drift-Scale THC 
Seepage Model (BSC 2004 [DIRS 169856]); Drift-Scale Coupled Processes (DST and TH 
Seepage) Models (BSC 2004 [DIRS 170338]); and Drift Scale THM Model (BSC 2004 
[DIRS 169864]), as well as mountain-scale models as discussed in UZ Flow Models and 
Submodels (BSC 2004 [DIRS 169861]); Radionuclide Transport Models Under Ambient 
Conditions (BSC 2004 [DIRS 164500]); and Mountain-Scale Coupled Processes 
(TH/THC/THM) (BSC 2004 [DIRS 169866]). Therefore, there is substantial precedent for using 
the drift shadow model for describing flow and transport in a fractured rock. 
The drift shadow flow model predictions for flow patterns in a single continuum have been 
found to quantitatively agree with an analytical model for unsaturated flow around a drift 
(Houseworth et al. 2003 [DIRS 164394], Figure 2), as shown in Figure 7-1. Figure 7-1a presents 
flow patterns for the case where capillary forces are relatively strong compared with gravity 
forces, as in the rock matrix at Yucca Mountain. Figure 7-1b presents flow patterns for the case 
where capillary forces are relatively weak compared with gravity forces, as in the fractures at 
Yucca Mountain. Although the drift shadow model presented in Section 6 uses a 
dual-continuum to represent a fractured rock, the flow patterns for the matrix continuum and 
fracture continuum in the dual-continuum model in Figures 6-2 through 6-4 are similar to those 
shown in Figure 7-1. The dual-continuum behavior in the rock matrix and fractures is similar to 
the single-continuum solutions because fracture-matrix interaction has only a small effect on the 
flow patterns. Therefore, the scientific basis of the drift shadow model is found to be adequate. 
MDL-NBS-HS-000016 REV 01 7-5 September 2004 

Drift-Scale Radionuclide Transport 
(a) 
(2D) .06 Jul 2004 .
0 5 10 15 20 
Horizontal Distance (m) 
-30 
-25 
-20 
-15 
-10 
Vertical Distance (m)
Vertical flux (mm/yr) 
9 -0.08 
8 -0.16 
7 -0.24 
6 -0.31 
5 -0.4 
4 -0.48 
3 -0.63 
2 -0.95 
1 -1.6 
Flow in the Drift Shadow 
Percolation flux = -0.32 mm/yr 
Dimensionless capillary-gravity number (s) = 0.25 
Red -analytical solution 
Green -numerical solution 
9 
8 
7 
6 
6 
54 
7 
8 
9 
3(2D).06Jul2004. 
(b) 
(2D) .06 Jul 2004 .
0 10 20 30 40 
Horizontal Distance (m) 
-50 
-40 
-30 
-20 
-10 
Vertical Distance (m)
Vertical flux (mm/yr) 
9 -2.5 
8 -5 
7 -7.5 
6 -10.1 
5 -12.5 
4 -14.4 
3 -20 
2 -30 
1 -50 
Red -analytical solution 
Green -numerical solution 
Flow in the Drift Shadow 
Percolation Flux = -10 mm/yr 
Dimensionless capillary-gravity number (s) = 8 
9 
8 
7 
6 
5 
4 
3 
2 
6 
(2D).06Jul2004.
Source: Houseworth et al. 2003 [DIRS 164394], Figure 2. 
Figure 7-1. Comparison of the Numerical Model for a Single-Continuum With the Analytical Model of 
Philip et al. (1989 [DIRS 105743]) a) Flow Contours Representative of Rock Matrix b) Flow 
Contours Representative of Rock Fractures 
7.2.2 Rationale for Introducing the Fracture-Matrix Partitioning Model 
The primary reason for not directly using the drift shadow model in the TSPA is that there is 
presently a lack of relevant observational data and that it is difficult to obtain such data from in 
situ tests. Existing data for natural analogs presented in BSC (2004 [DIRS 169218]) are not 
relevant or useful for the drift-scale radionuclide transport problem. In addition, not all features 
of fractured rock have been explored in the drift shadow model. For example, heterogeneity of 
the fracture network and potential effects of discrete fractures may lead to a reduction in the 
extent of the drift shadow. Given these limitations and the potentially large beneficial effect of 
drift-scale processes on reducing radionuclide transport rates through the UZ, a more flexible 
modeling approach is appropriate. To that end, the fracture-matrix partitioning model has been 
developed to limit the reliance on process descriptions of flow and transport in the fractures near 
a waste emplacement drift. This necessarily results in approximations from the standpoint of the 
theoretical framework used for the drift shadow model. The fracture-matrix partitioning model 
uses the following approximations that lead to greater flow and transport in fractures beneath a 
waste emplacement drift: 
1. Fracture flow occurs beneath a waste emplacement drift within a distance less than the 
fracture spacing. Given fracture spacings that are, on average, less than one meter, the 
zone of reduced flow is greatly reduced in comparison with the shadow zone predicted 
by the drift shadow model. 
2. The initial transient period, which is initially dominated by diffusive transfer into the 
rock, is not treated. This initial radionuclide partitioning ratio will be equal to the 
water content ratio of the fractures and matrix, and will only asymptotically approach 
the predicted fracture-matrix partitioning ratio. 
MDL-NBS-HS-000016 REV 01 7-6 September 2004

Drift-Scale Radionuclide Transport 
3. The effects of dryout during the boiling and rewetting periods are ignored, during 
which fracture water saturations are disproportionately reduced in comparison with the 
matrix. This will lead to preferential entry of radionuclides to the matrix during this 
thermally perturbed period. 
4. All fractures are flowing in the fracture-matrix partitioning model as opposed to the 
active fracture model, where only a subset of the fractures is flowing. This leads to 
greater contact between the invert and flowing fractures and, therefore, greater releases 
from the invert to the rock fractures. 
7.2.3 Validation Results 
The results of the fracture matrix partitioning model clearly lead to more rapid radionuclide 
transport through the UZ as compared with the drift shadow model. The probability distribution 
for the partitioning ratio between the fractures and matrix for the drift interface model allows a 
non-zero fraction of the releases initially into the fractures, which will lead to relatively rapid 
transport through the UZ for that release fraction. Differences in transport times from the 
repository to the water table for fracture versus matrix release are shown in Figure 7-2 for 
present-day mean climate using the site-scale transport process model. This figure shows that 
releases to fractures will lead to significantly more rapid transport than releases to matrix. By 
comparison, the drift shadow model predicts transport times, shown in Figure 6-5 (a) and (b), 
similar to or longer than those shown in Figure 7-2 for matrix release. 
In summary, the fracture-matrix partitioning model is valid based on the following results: 
1. The transport results shown in Figure 6-7 demonstrate that releases to the matrix in an 
undisturbed flow field behave similarly to transport through the drift shadow. The 
figure also shows that releases to fractures in an undisturbed flow field travel through 
the model domain in about one year compared with several thousand years for releases 
to the matrix or the drift shadow. Transport times are also found to be substantially 
longer for matrix release as compared with fracture release in the mountain-scale UZ 
transport results shown in Figure 7-2. Note that the results for the drift shadow model 
domain are not quantitatively the same as for the site-scale model domain. This is a 
result of the drift shadow model being limited to fractured rock within a single 
repository host-rock unit and does not account for the effects of the full path length to 
the water table, other rock units, and other hydrogeologic features, as represented in 
the site-scale unsaturated zone transport model results. 
2. The drift shadow model results in Figures 6-5 and 6-6 shows that transport times 
through the model domain are thousands to tens of thousands of years for essentially 
all radionuclides under a wide range of fracture and matrix flow conditions. 
MDL-NBS-HS-000016 REV 01 7-7 September 2004 

Drift-Scale Radionuclide Transport 
1 
0.9 
Fractional Mass Breakthrough
100 101 102 103 104 105 1060 
[
0.2 
0.3 
0.4 
0.5 
0.6 
0.7 
0.8 
Tc -fracture release 
Tc -matrix release 
Np -fracture release 
Np -matrix release 
DTN: LB03033DUZTRAN.001 DIRS 170372] 
0.1 
Time (years) 
Source: Modified from Figure 6.7-3 BSC 2004 [DIRS 169861]). 
NOTE: Radionuclide decay not included in transport calculation. 
Figure 7-2. Breakthrough Curves for Fracture and Matrix Release. 
3. As can be seen in Table 6-14, the fracture-matrix partitioning model gives a 
distribution of releases to fractures ranging from roughly 0.1 percent to 50 percent for 
the 5th to 95th percentile values, with a mean of 11.6 percent for all climate scenarios 
except for the glacial-transition upper climate scenario. The distribution of releases 
for the glacial-transition upper climate scenario is roughly 0.02 percent to 5 percent for 
the 5th to 95th percentile values, with an average of 1.27 percent. These releases to 
undisturbed fracture flow will result in transport through the near-drift region 
(drift-shadow model domain) that are orders of magnitude faster than releases to the 
matrix or in the drift shadow model. 
For all of these reasons, based on points 1, 2, and 3, the fracture-matrix partitioning model will 
result in a fast component of transport not found in the drift shadow model and leads to a 
conservative representation of drift-scale transport as compared to the drift shadow model. This 
satisfies the post-development model validation requirements presented in the technical work 
plan (BSC 2004 [DIRS 171282], Section 2.2.4) that the alternative model results in greater 
MDL-NBS-HS-000016 REV 01 7-8 September 2004 

Drift-Scale Radionuclide Transport 
radionuclide releases to the fractures will be used as an alternative model for validation of the 
EBS radionuclide transport model. 
7.3 VALIDATION SUMMARY 
The fracture-matrix partitioning model has been validated by applying acceptance criteria as 
described above. Activities requirements for confidence building during model development 
have been satisfied (Section 7.1). Also, the post-development validation requirement defined in 
the BSC (2004 [DIRS 171282], Section 2.2.4) has been fulfilled, including corroboration of 
model results with the alternative conceptual model (Section 7.2). The model development and 
post-development validation activities described establish the scientific bases for the 
fracture-matrix partitioning model. No future activities need to be accomplished for model 
validation. Based on this, the fracture-matrix partitioning model is considered to be adequate 
and sufficiently accurate for the intended purpose and validate the level of confidence required 
by the models relative importance to the potential performance of the repository system. 
MDL-NBS-HS-000016 REV 01 7-9 September 2004 

Drift-Scale Radionuclide Transport 
INTENTIONALLY LEFT BLANK
MDL-NBS-HS-000016 REV 01 7-10 September 2004 

Drift-Scale Radionuclide Transport 
8. CONCLUSIONS 
The diversion of all percolating water around a waste emplacement drift results in an 
environment of greatly diminished flow inside the drift. In such an environment, the primary 
transport mechanism for radionuclides to migrate from the drift to the surrounding rock is by 
diffusion. Because of the relatively large water content of the matrix in comparison with the 
fractures, diffusive releases from waste emplacement drifts are highly partitioned to the 
matrix. Transport time for radionuclides initiated in the matrix has been found to be orders of 
magnitude longer than for radionuclides initiated in undisturbed fracture flow. The average (or 
50 percent) breakthrough times in the submodel presented in Section 6.3.3.2 are dominated by 
matrix advection. Simulation results show that for these cases, most of the radionuclide mass 
still remains in the matrix at breakthrough. Therefore, the effects of the drift shadow on 
transport extend beyond the existing model boundary. For radionuclide releases from drifts 
without seepage, the results presented in this section indicate that transport times to the water 
table will be thousands to tens of thousands of years for nonsorbing radionuclides (such as 
technetium). For sorbing radionuclides, the transport times are considerably longer, according to 
the degree of sorption. For a weakly sorbing radionuclide such as neptunium, transport times are 
tens of thousands to hundreds of thousands of years. For a strongly sorbing radionuclide such as 
plutonium, transport times range from millions to tens of millions of years. 
Sensitivity calculations show that the main effect of the drift shadow on transport is that 
radionuclide transport is initiated in the matrix. Subsequent effects of the drift shadow on the 
dynamics of the fracture or matrix flow fields have much less influence on transport. The long 
transport pathways in the matrix primarily result from initiation of transport in the matrix 
combined with the relatively disconnected nature of the fracture and matrix continua. Varying 
degrees of fracture-matrix interaction in the dual-permeability model are shown to have a 
significant influence on transport in the drift shadow. 
The lack of observational evidence for the drift shadow has led to the development of the 
fracture-matrix partitioning model. In this model, the sensitivity results from the drift shadow 
model are used to focus the discussion of drift-scale transport on the behavior of radionuclide 
releases from drifts without seepage. In particular, the most important factor is the initiation of 
transport in the fractures or the matrix. The fracture-matrix partitioning model allows for 
undisturbed fracture flow to occur some distance beneath the drift, flow that is scaled by the 
fracture spacing to account for uncertainty in the drift shadow effect. Additional uncertainty is 
captured through sampling distributions for the following factors: 
1. Fracture and matrix water flux and saturation and matrix effective permeability over a 
wide range of average flow rates representing uncertainty in the UZ flow fields 
2. Flow-focusing effects to account for uncertainty in variations in flow at the drift scale, 
which is smaller than the spatial resolution of the mountain-scale flow model 
3. Invert thickness, porosity characteristics, and molecular diffusion rates that influence 
diffusive characteristics of the invert 
MDL-NBS-HS-000016 REV 01 8-1 September 2004 

Drift-Scale Radionuclide Transport 
4. Matrix diffusion rates, including the influence of partial matrix saturation 
5. Fracture and matrix porosity and fracture residual saturation. 
The fracture-matrix partitioning model assesses the fraction of releases from drifts without 
seepage to the fractures and matrix in the underlying rock. This assessment is based on a 
steady state transport model where radionuclides diffuse through the crushed tuff invert in the 
drift to the fractures and matrix in the underlying rock. Due to the discrete nature of fractures 
and blockage of fracture flow by the drift, fracture flow is offset from the base of the drift by a 
fraction of the fracture spacing. Conversely, the continuous nature of the rock matrix leads to 
advective water flux in the rock immediately below the drift. Thus, diffusive releases from the 
invert are transported away from the drift by advection in the rock matrix and by diffusion 
through the fractures to the point where fracture flow begins. The developed partitioning 
distributions are shown in Figure 6-28. These distributions are a result of uncertainties in the 
inputs (see Table 6-14). Similarity in the partitioning distribution for the lower and mean 
infiltration scenarios leads to the composite distribution for the fracture-matrix partitioning in 
6-28a. The upper infiltration scenario leads to a distinct distribution as shown in 6-28b. 
Uncertainties in the distributions resulting from sampling uncertainties are indicated by the error 
bars in Figure 6-28. 
Output from this report for the drift shadow model is captured in Output-DTNs: 
LB0307DSRADTRN.001 and LB0307DSRADTRN.002 and in Output-
DTN: LB0307FMRADTRN.001 for the fracture-matrix partitioning model. 
Following release from the drifts to the rock, the radionuclide transport process in TSPA is 
simulated using the particle-tracking model, which does not account for the effects of the drift on 
the flow field [Particle Tracking Model and Abstraction of Transport Processes (BSC 2004 
[DIRS 170041])]. Thus, radionuclides are transported from the drifts in the undisturbed, UZ 
flow field. Use of these results for the partitioning of fracture-matrix releases is restricted to 
drifts with radionuclide releases dominated by diffusion, which in general are drifts without 
seepage. 
Confirmatory information comparing the drift shadow model flow predictions with an analytical 
model are given in Section 7.1. Confirmatory information from the mountain-scale UZ transport 
model concerning the effects of initiating transport in the rock fractures or rock matrix is given in 
Section 7.3. 
8.1 BARRIER DESCRIPTION 
The findings in this model report support the conclusion that for drifts without seepage, 
radionuclide releases from the drift to the rock will be preferentially partitioned to the rock 
matrix. Furthermore, initiation of transport in the rock matrix has a significant effect on the 
subsequent transport through the unsaturated zone. The difference in transport times through the 
drift-scale model domain for radionuclide transport initiated in rock matrix versus the fractures 
for undisturbed flow conditions is thousands to tens of thousands of years. The preferential 
release of radionuclides from drifts without seepage to the rock matrix results in substantial 
delays in radionuclide transport, leading to the conclusion that the presence of the drift, with or 
MDL-NBS-HS-000016 REV 01 8-2 September 2004 

Drift-Scale Radionuclide Transport 
without a drift shadow, plays an important role in the delay of radionuclide transport. The 
magnitude of this effect on performance of the repository is a function of fraction of drifts that 
do not seep. 
8.2 HOW THE ACCEPTANCE CRITERIA ARE ADDRESSED 
2.2.1.3.7.3 Radionuclide Transport in the Unsaturated Zone 
Acceptance Criterion 1, System Description and Model Integration Are 
Adequate. 
(2) The description of the aspects of hydrology, geology, geochemistry, design 
features, physical phenomena, and couplings, that may affect radionuclide transport 
in the unsaturated zone, is adequate. For example, the description includes changes 
in transport properties in the unsaturated zone, from water-rock 
interaction. Conditions and assumptions in the total system performance 
assessment abstraction of radionuclide transport in the unsaturated zone are readily 
identified, and consistent with the body of data presented in the description; 
Descriptions of the aspects of processes and features that affect radionuclide transport in the 
unsaturated zone are provided in the following sections as indicated: hydrology (Sections 6.1, 
6.3.1, 6.4, 6.4.1), geology (Sections 6.3.2.3, 6.4.5), geochemistry (Section 6.3.2.3), design 
features (6.3.2.1, 6.4.1, 6.4.5), physical phenomena (6.1, 6.3.1, 6.4.1), and couplings 
(Sections 1, 7.2). The adequacy of these descriptions is demonstrated by their consistency with 
the available data. The methodology accounts for these factors at a level consistent with the 
available data and uncertainty, such that the potential for radionuclide transport in the 
unsaturated zone (UZ) is not underestimated. This includes the introduction of the 
fracture-matrix partitioning model, as discussed in Section 7.2, to address limitations in the 
available data and the potential effects of different flow patterns on radionuclide partitioning 
between the fractures and rock matrix upon existing the drift. Distributions for flow and 
transport parameters have been developed to account for the level of uncertainty in the available 
data, as discussed in Section 6.4.5. 
(6) Guidance in NUREG-1297 and NUREG-1298 (Altman et al. 1988 
[DIRS 103597] and [DIRS 103750]), or other acceptable approaches, is followed 
for peer review and data qualification. 
This report was developed using processes and procedures consistent with the QARD, which 
commits to the requirements in NUREG-1297 and NUREG-1298. This report was developed in 
accordance with AP-SIII.10Q, Models, which implements those commitments for model reports. 
Acceptance Criterion 2, Data are Sufficient for Model Justification. 
(1) Geological, hydrological, and geochemical values, used in the license 
application, are adequately justified (e.g., flow-path length, sorption coefficients, 
retardation factors, colloid concentrations, etc.). Adequate descriptions of how the 
data were used, interpreted, and appropriately synthesized into the parameters are 
provided; 
MDL-NBS-HS-000016 REV 01 8-3 September 2004 

Drift-Scale Radionuclide Transport 
Data are sufficient to support the geological, hydrological, and geochemical values because they 
are based on supporting reports that define the model units, associated hydrological properties, 
and resulting flow field predictions. Specifically, the use of qualified fracture property data to 
determine fracture frequency and fracture porosity is discussed in Section 4.1.1, data on flow in 
the unsaturated zone are discussed in Section 4.1.2, a flow focusing factor for flow in fractures 
and other fracture hydrologic characteristics are discussed in Section 4.1.3, data for matrix 
porosity and permeability are discussed in Section 4.1.4, data used to develop a correlation 
between the matrix diffusion coefficient and the porosity and permeability of the rock matrix 
under saturated conditions are discussed in Section 4.1.5, data used for diffusion in the crushed 
tuff invert are discussed in Section 4.1.6, and design data used in the evaluation of transport 
from the invert to the rock is discussed in Section 4.1.7, Descriptions, of how the data are used, 
interpreted, and synthesized into parameters are given in Sections 4.1, 6.3.2.3 and 6.4.5. The 
results are adjusted to account for effects of scale between the mountain-scale flow model and 
the drift-scale phenomena considered in this report (Sections 6.3.3.1 and 6.4.5). 
Acceptance Criterion 3, Data Uncertainty Is Characterized and Propagated 
through the Model Abstraction. 
(1) Models use parameter values, assumed ranges, probability distributions, and 
bounding assumptions that are technically defensible, reasonably account for 
uncertainties and variabilities, and do not result in an under-representation of the 
risk estimate; 
The parameters used are based on and consistent with available data from Yucca Mountain as 
presented in Sections 6.3.2.3 and 6.4.5. Section 6.3.5 contains discussions of how capillary 
pressure and relative permeability functions of saturation for the fracture and matrix continua are 
based on the van Genuchten relation; how the property set for dual-permeability flow and 
transport calculations was calibrated; how matrix diffusion and sorption parameters were 
characterized statistically to span the range of sorption behavior; how the free-water diffusion 
coefficient was derived from data; how the dispersive effects fracture-matrix interaction are 
explicitly modeled; and why parameters from the Site Recommendation are still valid for the 
drift-shadow model. Section 6.4.5 contains discussions of how data or relations were used to 
calculate the model parameters which represent the range of conditions expected across the 
waste emplacement location, i.e. fracture frequency, water flux and saturation, flow focusing, 
fracture residual saturation, diffusion coefficient for the invert, and diffusion coefficient in 
fractured rock. Uncertainties and variabilities in parameters are evaluated, reasonably accounted 
for, and adequately represented as discussed in Section 6.4.5 and Appendices A through I. 
(2) For those radionuclides where the total system performance assessment 
abstraction indicates that transport in fractures and matrix in the unsaturated zone is 
important to waste isolation: (i) estimated flow and transport parameters are 
appropriate and valid, based on techniques that may include laboratory 
experiments, field measurements, natural analog research, and process-level 
modeling studies, conducted under conditions relevant to the unsaturated zone at 
Yucca Mountain; and (ii) models are demonstrated to adequately reproduce field 
transport test results. For example, if a sorption coefficient approach is used, the 
assumptions implicit in that approach are verified; 
MDL-NBS-HS-000016 REV 01 8-4 September 2004 

Drift-Scale Radionuclide Transport 
Two models are considered for transport in fractures and matrix: (1) the fracture-matrix 
partitioning model introduced in Section 6.1 and described in Section 6.4; and (2) the 
dual-permeability conceptual model described in Section 6.3. For both models, the estimated 
flow and transport parameters are appropriate and valid because they are based on and consistent 
with available data from Yucca Mountain, including field measurements for hydrological 
properties of fractures and laboratory measurements of the hydrological and transport properties 
of the rock matrix (Sections 6.3.2.3 and 6.4.5). Process-level modeling studies were conducted 
to calibrate some of the hydrological parameters as discussed in Section 4.1. 
(4) Uncertainty is adequately represented in parameter development for conceptual 
models, process-level models, and alternative conceptual models, considered in 
developing the abstraction of radionuclide transport in the unsaturated zone. This 
may be done either through sensitivity analyses or use of conservative limits; 
Uncertainty is adequately represented in the model parameters used because they are based on 
and consistent with the scenarios and range of available data from Yucca Mountain. An 
extensive assessment of parameter uncertainties and variabilities was conducted and 
implemented in the model calculations to ensure that these factors are adequately represented in 
the model (see Sections 6.4.5, 6.4.6, and Appendices A through I). 
Acceptance Criterion 4, Model Uncertainty Is Characterized and Propagated 
through the Model Abstraction. 
(1) Alternative modeling approaches of features, events, and processes are 
considered and are consistent with available data and current scientific 
understanding, and the results and limitations are appropriately considered in the 
abstraction; 
The alternative models of fracture-matrix partitioning and dual permeability are considered and 
are consistent with available data and current scientific understanding of observed features and 
processes. The results and limitations are appropriately considered in the abstraction, as 
described in Sections 6.3.1 and 6.4. This includes treatment of the effects of fractures both as a 
continuum and as discrete features and alternative representations of flow processes in fractures. 
(2) Conceptual model uncertainties are adequately defined and documented, and 
effects on conclusions regarding performance are properly assessed; 
Conceptual model uncertainties are identified, principally in terms of the effects of fracture flow 
in the vicinity of the waste emplacement drift in Sections 6.3.1 and 6.4. The effects of these 
uncertainties on conclusions regarding performance are conservatively addressed in Sections 7 
and 8. 
(3) Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog 
information and process-level modeling studies; and the treatment of conceptual 
model uncertainty does not result in an under-representation of the risk estimate; 
and 
MDL-NBS-HS-000016 REV 01 8-5 September 2004 

Drift-Scale Radionuclide Transport 
Conceptual model uncertainty is addressed by considering the alternative models of 
fracture-matrix partitioning and dual permeability, which include standard flow and transport 
models for unsaturated rock that are consistent with available data and current scientific 
knowledge and conservative modeling methods intended to bound conceptual model 
uncertainties (Section 7 and 8). The fracture matrix alternative model is the more conservative 
of the two because it incorporates approximations which predict increased flow and transport in 
fractures beneath a waste emplacement drift, as discussed in Section 7.3. The more conservative 
representation between the alternative models is selected for use in downstream products such 
that the identified model uncertainty does not result in an underestimate of radionuclide transport 
(Sections 7 and 8). 
(4) Appropriate alternative modeling approaches are consistent with available data 
and current scientific knowledge, and appropriately consider their results and 
limitations, using tests and analyses that are sensitive to the processes 
modeled. For example, for radionuclide transport through fractures, the U.S. 
Department of Energy adequately considers alternative modeling approaches, to 
develop its understanding of fracture distributions and ranges of fracture flow and 
transport properties in the unsaturated zone. 
Alternative modeling approaches are appropriate because they include standard flow and 
transport models for unsaturated rock that are consistent with available data and current scientific 
knowledge. These alternative models result in an understanding of fracture distributions, ranges 
of fracture flow, and transport properties in the unsaturated zone as discussed in Section 8. As 
discussed in Section 7.1, the drift shadow model accounts for the presence of fractures and a 
porous rock matrix by using a standard process-based description of unsaturated flow in a dual 
continuum, and model parameters are based on the drift-scale calibrated properties parameter set. 
As discussed in Section 7.2, the fracture-matrix partitioning model was developed to limit 
reliance on process descriptions of flow and transport in the fractures near a waste emplacement 
drift and incorporates approximations which conservatively predict increased flow and transport 
in fractures beneath a waste emplacement drift, as discussed in Section 7.3. 
MDL-NBS-HS-000016 REV 01 8-6 September 2004 

Drift-Scale Radionuclide Transport 
9. INPUTS AND REFERENCES 
9.1 DOCUMENTS CITED 
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Altman, W.D.; Donnelly, J.P.; and Kennedy, J.E. 1988. Peer Review for High-Level 103597
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Drift-Scale Radionuclide Transport 
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Drift-Scale Radionuclide Transport 
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169856 
MDL-NBS-HS-000001, Rev. 03. Las Vegas, Nevada: Bechtel SAIC Company. 
BSC (Bechtel SAIC Company) 2004. EBS Radionuclide Transport Abstraction. 169868 
ANL-WIS-PA-000001, Rev. 01. Las Vegas, Nevada: Bechtel SAIC Company. 
BSC (Bechtel SAIC Company) 2004. Features, Events, and Processes in UZ Flow and 170012 
Transport. ANL-NBS-MD-000001, Rev. 03. Las Vegas, Nevada: Bechtel SAIC 
Company. 
BSC (Bechtel SAIC Company) 2004. In-Drift Natural Convection and 164327 
Condensation. MDL-EBS-MD-000001, Rev. 00. Las Vegas, Nevada: Bechtel SAIC 
Company. 
BSC (Bechtel SAIC Company) 2004. Mountain-Scale Coupled Processes 169866 
(TH/THC/THM). MDL-NBS-HS-000007, Rev. 02. Las Vegas, Nevada: Bechtel SAIC 
Company. 
BSC (Bechtel SAIC Company) 2004. Multiscale Thermohydrologic Model. 169565 
ANL-EBS-MD-000049, Rev. 02. Las Vegas, Nevada: Bechtel SAIC Company. 
BSC (Bechtel SAIC Company) 2004. Natural Analogue Synthesis Report. 169218 
TDR-NBS-GS-000027 REV 01. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: DOC.20040524.0008. 
BSC (Bechtel SAIC Company) 2004. Particle Tracking Model and Abstraction of 170041 
Transport Process. MDL-NBS-HS-000020, Rev. 01. Las Vegas, Nevada: Bechtel 
SAIC Company. 
BSC (Bechtel SAIC Company) 2004. Postclosure Modeling and Analyses Design 169885 
Parameters. TDR-MGR-MD-000037 REV 00. Las Vegas, Nevada: Bechtel SAIC 
Company. 
BSC (Bechtel SAIC Company) 2004. Q-List. 000-30R-MGR0-00500-000-000 168361 
REV 00. Las Vegas, Nevada: Bechtel SAIC Company. ACC: ENG.20040721.0007. 
BSC (Bechtel SAIC Company) 2004. Radionuclide Transport Models Under Ambient 164500 
Conditions. MDL-NBS-HS-000008, Rev. 02. Las Vegas, Nevada: Bechtel SAIC 
Company. 
BSC (Bechtel SAIC Company) 2004. Saturated Zone Flow and Transport Model 170042 
Abstraction. MDL-NBS-HS-000021, Rev. 02. Las Vegas, Nevada: Bechtel SAIC 
Company. 
MDL-NBS-HS-000016 REV 01 9-3 September 2004 

Drift-Scale Radionuclide Transport 
BSC (Bechtel SAIC Company) 2004. Seepage Calibration Model and Seepage Testing 170034 
Data. MDL-NBS-HS-000004, Rev. 03. Las Vegas, Nevada: Bechtel SAIC Company. 
BSC (Bechtel SAIC Company) 2004. Seepage Model for PA Including Drift 167652 
Collapse. MDL-NBS-HS-000002, Rev. 03. Las Vegas, Nevada: Bechtel SAIC 
Company. 
BSC (Bechtel SAIC Company) 2004. Simulation of Net Infiltration for Present-Day 170007 
and Potential Future Climates. MDL-NBS-HS-000023, Rev. 00. Las Vegas, Nevada: 
Bechtel SAIC Company. 
BSC (Bechtel SAIC Company) 2004. Technical Work Plan for: Regulatory Integration 169377 
Evaluation of Analysis and Model Reports Supporting the TSPA-LA. TWP-MGR-PA-
000014 REV 00. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: DOC.20040408.0004. 
BSC (Bechtel SAIC Company) 2004. Technical Work Plan for: Unsaturated Zone 171282 
Transport Model Report Integration. TWP-MGR-HS-000002 REV 00 ICN 
01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: DOC.20040816.0001. 
BSC (Bechtel SAIC Company) 2004. UZ Flow Models and Submodels. 169861
MDL-NBS-HS-000006, Rev. 02. Las Vegas, Nevada: Bechtel SAIC Company. 
Canori, G.F. and Leitner, M.M. 2003. Project Requirements Document. 166275
TER-MGR-MD-000001 REV 02. Las Vegas, Nevada: Bechtel SAIC 
Company. ACC: DOC.20031222.0006. 
Conca, J.L. and Wright, J. 1990. Diffusion Coefficients in Gravel Under Unsaturated 101582
Conditions. Water Resources Research, 26, (5), 1055-1066. Washington, D.C.: 
American Geophysical Union. TIC: 237421. 
Crank, J. 1975. The Mathematics of Diffusion. 2nd Edition. 1983 Reprint. Oxford, 122990
England: Clarendon Press. TIC: 9662. 
CRWMS M&O 2000. Invert Configuration and Drip Shield Interface. TDR-EDS-ST-136255
000001 REV 00. Las Vegas, Nevada: CRWMS M&O. ACC: MOL.20000505.0232. 
CRWMS M&O 2000. Total System Performance Assessment for the Site 153246
Recommendation. TDR-WIS-PA-000001 REV 00 ICN 01. Las Vegas, Nevada: 
CRWMS M&O. ACC: MOL.20001220.0045. 
Dombrowski, H.S. and Brownell, L.E. 1954. Residual Equilibrium Saturation of 163222
Porous Media. Industrial & Engineering Chemistry, 46, (6), 1207-1219. Easton, 
Pennsylvania: American Chemical Society. TIC: 254309. 
MDL-NBS-HS-000016 REV 01 9-4 September 2004 

Drift-Scale Radionuclide Transport 
Dullien, F.A.L.; Lai, F.S.Y.; and MacDonald, I.F. 1986. Hydraulic Continuity of 163221 
Residual Wetting Phase in Porous Media. Journal of Colloid and Interface 
Science, 109, (1), 201-218. New York, New York: Academic Press. TIC: 254308. 
Finsterle, S.; Ahlers, C.F.; Trautz, R.C.; and Cook, P.J. 2003. Inverse and Predictive 163214 
Modeling of Seepage into Underground Openings. Journal of Contaminant Hydrology, 
62-63, 89-109. New York, New York: Elsevier. TIC: 254205. 
Freeze, G.A.; Brodsky, N.S.; and Swift, P.N. 2001. The Development of Information 154365 
Catalogued in REV00 of the YMP FEP Database. TDR-WIS-MD-000003 REV 00 ICN 
01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: MOL.20010301.0237. 
Freeze, R.A. and Cherry, J.A. 1979. Groundwater. Englewood Cliffs, New Jersey: 101173
Prentice-Hall. TIC: 217571. 
Hilf, J.W. 1975. Compacted Fill. Chapter 7 of Foundation Engineering 169699
Handbook. Winterkorn, H.F. and Fang, H.-Y., eds. New York, New York: 
Van Nostrand Reinhold. TIC: 248400. 
Hogg, R.V. and Craig, A.T. 1978. Introduction to Mathematical 163236
Statistics. 4th Edition. New York, New York: Macmillan. TIC: 254311. 
Houseworth, J. 2003. UZ PMR for SR - Shadow Zone. Scientific Notebook SN-LBNL-163233
SCI-205-V1. ACC: MOL.20030319.0086. 
Houseworth, J.E.; Finsterle, S.; and Bodvarsson, G.S. 2003. Flow and Transport in the 164394
Drift Shadow in a Dual-Continuum Model. Journal of Contaminant Hydrology, 62-63, 
133-156. New York, New York: Elsevier. TIC: 254205. 
Li, G. and Tsang, C-F. 2003. Seepage into Drifts with Mechanical Degradation. 163714
Journal of Contaminant Hydrology, 62-63, 157-172. New York, New York: 
Elsevier. TIC: 254205. 
Liu, H.H.; Doughty, C.; and Bodvarsson, G.S. 1998. An Active Fracture Model for 105729
Unsaturated Flow and Transport in Fractured Rocks. Water Resources Research, 34, 
(10), 2633-2646. Washington, D.C.: American Geophysical Union. TIC: 243012. 
Moridis, G.J.; Wu, Y-S.; and Pruess, K. 1999. EOS9nT: A TOUGH2 Module for the 123093
Simulation of Water Flow and Solute/Colloid Transport in the Subsurface. LBNL-
42351. Berkeley, California: Lawrence Berkeley National Laboratory. TIC: 246520. 
Newman, J. 1973. Electrochemical Systems. Englewood Cliffs, New Jersey: 148719
Prentice-Hall. TIC: 210201. 
NRC (U.S. Nuclear Regulatory Commission) 2003. Yucca Mountain Review Plan, 163274
Final Report. NUREG-1804, Rev. 2. Washington, D.C.: U.S. Nuclear Regulatory 
Commission, Office of Nuclear Material Safety and Safeguards. TIC: 254568. 
MDL-NBS-HS-000016 REV 01 9-5 September 2004 

Drift-Scale Radionuclide Transport 
Philip, J.R.; Knight, J.H.; and Waechter, R.T. 1989. Unsaturated Seepage and 105743 
Subterranean Holes: Conspectus, and Exclusion Problem for Circular Cylindrical 
Cavities. Water Resources Research, 25, (1), 16-28. Washington, D.C.: American 
Geophysical Union. TIC: 239117. 
Pruess, K.; Oldenburg, C.; and Moridis, G. 1999. TOUGH2 Users Guide, Version 160778 
2.0. LBNL-43134. Berkeley, California: Lawrence Berkeley National 
Laboratory. TIC: 253038. 
Reimus, P.W.; Ware, S.D.; Benedict, F.C.; Warren, R.G.; Humphrey, A.; Adams, A.; 163008
Wilson, B.; and Gonzales, D. 2002. Diffusive and Advective Transport of 3H, 14C, and
99Tc in Saturated, Fractured Volcanic Rocks from Pahute Mesa, Nevada. LA-13891-
MS. Los Alamos, New Mexico: Los Alamos National Laboratory. TIC: 253905. 
Richards, L.A. 1931. Capillary Conduction of Liquids Through Porous Mediums. 104252
Physics, 1, 318-333. [New York, New York: American Physical 
Society]. TIC: 225383. 
Sato, H.; Yui, M.; and Yoshikawa, H. 1996. Ionic Diffusion Coefficients of Cs+, 163213
Pb2}+, Sm3+, Ni2+, SeO2- 4 and TcO-4 in Free Water Determined from Conductivity 
Measurements. Journal of Nuclear Science and Technology, 33, (12), 950-
955. Tokyo, Japan: Atomic Energy Society of Japan. TIC: 254307. 
Sato, S.; Otsuka, T.; Kuroda, Y.; Higashihara, T.; and Ohashi, H. 2001. Diffusion of 164047
Helium in Water-Saturated, Compacted Sodium Montmorillonite. Journal of Nuclear 
Science and Technology, 38, (7), 577-580. [Tokyo, Japan: Atomic Energy Society of 
Japan]. TIC: 254463. 
van Genuchten, M.T. 1980. A Closed-Form Equation for Predicting the Hydraulic 100610
Conductivity of Unsaturated Soils. Soil Science Society of America Journal, 44, (5), 
892-898. Madison, Wisconsin: Soil Science Society of America. TIC: 217327. 
Wang, J.S. 2003. Scientific Notebooks Referenced in Model Report U0230 Drift-163234
Scale Radionuclide Transport MDL-NBS-HS-000016 REV 00. Interoffice 
correspondence from J.S. Wang (BSC) to File, August 18, 2003, with 
attachments. ACC: MOL.20030818.0293. 
Wang, J.S.Y. and Bodvarsson, G.S. 2003. Evolution of the Unsaturated Zone Testing 163215
at Yucca Mountain. Journal of Contaminant Hydrology, 62-63, 337-360. New York,
New York: Elsevier. TIC: 254205. 
Weast, R.C. and Astle, M.J., eds. 1979. CRC Handbook of Chemistry and 102865
Physics. 60th Edition. 2nd Printing 1980. Boca Raton, Florida: CRC 
Press. TIC: 245312. 
Weinberger, H.F. 1965. A First Course in Partial Differential Equations. New York, 163216
New York: John Wiley & Sons. TIC: 254310. 
MDL-NBS-HS-000016 REV 01 9-6 September 2004 

Drift-Scale Radionuclide Transport 
9.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES 
10 CFR 63. Energy: Disposal of High-Level Radioactive Wastes in a Geologic 156605 
Repository at Yucca Mountain, Nevada. Readily available. 
AP-2.22Q, Rev. 1. Classification Analyses and Maintenance of the Q-List. Washington, 
D.C.: U.S. Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20030807.0002. 
AP-2.27Q, Rev. 1, ICN 4. Planning for Science Activities. Washington, D.C.: U.S. Department 
of Energy, Office of Civilian Radioactive Waste Management. ACC: DOC.20040610.0006. 
AP-SI.1Q, Rev. 5, ICN 1. Software Management. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. ACC: DOC.20030708.0001. 
AP-SIII.10Q, Rev. 2, ICN 7. Models. Washington, D.C.: U.S. Department of Energy, Office of 
Civilian Radioactive Waste Management. ACC: DOC.20040920.0002. 
9.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER 
LA0003AM831341.001. Probability Distributions for Sorption Coefficients 148751 
(Kds). Submittal date: 03/29/2000. 
LA0003JC831362.001. Preliminary Matrix Diffusion Coefficients for Yucca 149557 
Mountain Tuffs. Submittal date: 4/10/2000. 
LB0205REVUZPRP.001. Fracture Properties for UZ Model Layers Developed from 159525 
Field Data. Submittal date: 05/14/2002. 
LB0207REVUZPRP.002. Matrix Properties for UZ Model Layers Developed from 159672 
Field and Laboratory Data. Submittal date: 07/15/2002. 
LB0208UZDSCPLI.002. Drift-Scale Calibrated Property Sets: Lower Infiltration 161788 
Data Summary. Submittal date: 08/26/2002. 
LB0208UZDSCPMI.002. Drift-Scale Calibrated Property Sets: Mean Infiltration 161243 
Data Summary. Submittal date: 08/26/2002. 
LB0210THRMLPRP.001. Thermal Properties of UZ Model Layers: Data 160799 
Summary. Submittal date: 10/25/2002. 
LB03023DSSCP9I.001. 3-D Site Scale UZ Flow Field Simulations for 9 Infiltration 163044 
Scenarios. Submittal date: 02/28/2003. 
LB0302UZDSCPUI.002. Drift-Scale Calibrated Property Sets: Upper Infiltration 161787 
Data Summary. Submittal date: 02/05/2003. 
MDL-NBS-HS-000016 REV 01 9-7 September 2004 

Drift-Scale Radionuclide Transport 
LB03033DUZTRAN.001. TC and NP Distributions/Transport in UZ 170372 
Flow-Fields. Submittal date: 03/28/2003. 
LB0406U0075FCS.002. Flow Focusing in Heterogeneous Fractured Rock: 170712 
Summaries. Submittal date: 06/30/2004. 
LB990861233129.001. Drift Scale Calibrated 1-D Property Set, FY99. Submittal 110226 
date: 08/06/1999. 
LB997141233129.001. Calibrated Basecase Infiltration 1-D Parameter Set for the 104055 
UZ Flow and Transport Model, FY99. Submittal date: 07/21/1999. 
MO0407SEPFEPLA.000. LA FEP List. Submittal date: 07/20/2004. 170760 
SN0306T0502103.006. Data Spreadsheets to Support Parameter Uncertainty 163944 
Development. Submittal date: 06/05/2003. 
9.4 OUTPUT DATA, LISTED BY DATA TRACKING NUMBER 
LB0307DSRADTRN.001. Drift Shadow Model: Simulations. Submittal date: 07/24/2003. 
LB0307DSRADTRN.002. Drift Shadow Model: Data Summaries. Submittal date: 07/24/2003. 
LB0307FMRADTRN.001. Fracture-Matrix Partitioning Model: Spreadsheet Calculations. 
Submittal date: 07/31/2003. 
9.5 SOFTWARE CODES 
LBNL (Lawrence Berkeley National Laboratory) 1999. Software Code: EXT. V1.0. 134141 
Sun. 10047-1.0-00. 
LBNL (Lawrence Berkeley National Laboratory) 1999. Software Code: 139918 
iTOUGH2. V4.0. SUN, DEC. 10003-4.0-00. 
LBNL (Lawrence Berkeley National Laboratory) 1999. Software Code: 113943 
TOUGH2. V1.11 MEOS9nTV1.0. MAC, SUN, DEC/Alpha, 
PC. 10065-1.11MEOS9NTV1.0-00.
LBNL (Lawrence Berkeley National Laboratory) 2000. Software Routine: 152823 
AddBound. V1.0. SUN w/Unix OS. 10357-1.0-00. 
LBNL (Lawrence Berkeley National Laboratory) 2000. Software Routine: 152816 
CutDrift. V1.0. SUN w/Unix OS. 10375-1.0-00. 
MDL-NBS-HS-000016 REV 01 9-8 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX A 
SAMPLING FOR FRACTURE FREQUENCY (OR FRACTURE SPACING) 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
SAMPLING FOR FRACTURE FREQUENCY (OR FRACTURE SPACING) 
This appendix provides additional information pertaining to Section 6.4.5 of the main 
text. Fracture frequency sampling uses the mean and standard deviations as given in 
Table A-1. The standard deviations for the tsw35 and tsw36 units are computed using the 
correlation shown in Figure 6-21. The mean and standard deviation for the natural logarithm of f 
is related to the mean and standard deviation for f through the following relationships (Hogg and 
Craig 1978 [DIRS 163236], pp. 180 and 432) (see Appendix K for detailed derivation): 
2 
f 
2 
s
 
+
1 ln 
...
. 
.
1
()
f
 
f 
...
ln( f

) 
=
ln
- 
(Eq. A-1) 
2 
2 
2 
f 
f 

s 
1 ln 
...
. 
.
..
.
ln( f )
s 
(Eq. A-2) 
+
= 
Table A-1. Fracture Frequency and Standard Deviation 
Frequency (m-1) 
Std Dev Frequency 
(m-1) Equation A-1 Equation A-2 
UZ Model Layer fsf  ln(f) sln(f) 
tsw33 0.81 1.03 -0.692 0.981 
tsw34 4.32 3.42 1.22 0.698 
tsw35 3.16 2.63 0.887 0.725 
tsw3[67] 4.02 3.34 1.13 0.725 
DTN: LB0205REVUZPRP.001 [DIRS 159525]. 
Output DTN: LB0307FMRADTRN.001. 
The sampling for the lognormal distribution uses the rational approximation of the inverse 
cumulative probability distribution for a Gaussian random variable as given in Equation 26.2.23 
of Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables 
(Abramowitz and Stegun 1972 [DIRS 103280]). See Scientific Notebook by Wang (2003 
[DIRS 163234], SN-LBNL-SCI-236-V1, pp. 4042) for a discussion of the generation of 
Gaussian random numbers. Table A-2 presents a portion of the output from the formulation as 
performed in an Excel spreadsheet for the tsw35 model unit. See Wang (2003 [DIRS 163234], 
SN-LBNL-SCI-236-V1, p. 46) and Output-DTN: LB0307FMRADTRN.001 for the complete 
output. 
The sequence of calculations is as follows: 
Column A: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. These are the cumulative probabilities, p. 
Column B: The normalized Gaussian random number corresponding to the cumulative 
probability in Column A. 
MDL-NBS-HS-000016 REV 01 A-1 September 2004 

Drift-Scale Radionuclide Transport 
Column C: The corresponding random natural logarithm of fracture frequency is derived from 
the normalized Gaussian random variable through the normalization definition: 
f =xpsln( f ) +ln( f ) (Eq. A-3) 
where ln( f ) and sln( f ) are defined in Equations A-1 and A-2. 
In Excel, this is 
Crn=Brn*$I$rn+$H$rn 
Column D: This column calculates the fracture frequency through the identity 
f = )) exp(ln( (Eq. A-4) 
f 
In Excel, this is 
Drn=exp(Crn) 
Column E: The fracture half-spacing, in millimeters, is computed from the fracture frequency 
based on the relationship 
1000
h
f = (Eq. A-5) 
2 f 
In Excel, this is 
Ern=1000/(2*Drn) 
Column F: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. 
Column G: The distance beneath the drift where fracture flow occurs, in millimeters, is defined 
by a uniform random distribution between 0 and the fracture spacing. Therefore, this is just the 
uniform random number between 0 and 1 in Column O, multiplied by the corresponding fracture 
spacing. In Excel, this is 
Grn=2*Ern*Frn 
Column H: Contains the value of ln( f ) as computed from Equation A-1 
Column I: Contains the value of sln( f ) as computed from Equation A-2. 
MDL-NBS-HS-000016 REV 01 A-2 September 2004 

Drift-Scale Radionuclide Transport 
Table A-2. Fracture Frequency and Spacing in the tsw35 
A B C D E F G H I 
Distance 
for 
Fixed 
Uniform 
xP - norm. 
Gaussian 
x  
Gaussian Fracture 
Fracture 
Half-
Fixed 
Uniform 
fracture 
flow Standard 
1 
Random 
Number (P) 
random 
number 
random 
number 
frequency 
(m-1) 
Spacing 
(mm) 
Random 
Number (P) 
beneath 
drift (mm) 
mean ln(f) 
tsw35 
deviation 
ln(f) tsw35 
2 5.8511E-01 2.1459E-01 1.04E+00 2.84E+00 1.76E+02 4.5126E-01 1.59E+02 8.87E-01 7.25E-01 
3 5.4439E-01 1.1124E-01 9.68E-01 2.63E+00 1.90E+02 9.1458E-01 3.48E+02 
4 6.4091E-01 3.6045E-01 1.15E+00 3.15E+00 1.59E+02 3.3211E-01 1.05E+02 
5 5.9792E-01 2.4755E-01 1.07E+00 2.91E+00 1.72E+02 8.5178E-01 2.93E+02 
6 3.5424E-01 -3.7345E-01 6.16E-01 1.85E+00 2.70E+02 5.2193E-01 2.82E+02 
7 2.0906E-01 -8.0950E-01 3.00E-01 1.35E+00 3.70E+02 6.2457E-02 4.63E+01 
8 3.6657E-01 -3.4052E-01 6.40E-01 1.90E+00 2.64E+02 6.0227E-01 3.18E+02 
9 2.4803E-01 -6.8040E-01 3.94E-01 1.48E+00 3.37E+02 9.8595E-02 6.65E+01 
10 1.3127E-01 -1.1205E+00 7.47E-02 1.08E+00 4.64E+02 5.1294E-01 4.76E+02 
11 3.9488E-01 -2.6619E-01 6.94E-01 2.00E+00 2.50E+02 7.5245E-01 3.76E+02 
12 3.5507E-01 -3.7123E-01 6.18E-01 1.85E+00 2.70E+02 5.5208E-02 2.98E+01 
13 3.2690E-01 -4.4805E-01 5.62E-01 1.75E+00 2.85E+02 4.1146E-01 2.35E+02 
14 7.3161E-01 6.1735E-01 1.33E+00 3.80E+00 1.32E+02 1.6819E-01 4.43E+01 
15 3.7473E-01 -3.1891E-01 6.56E-01 1.93E+00 2.60E+02 1.0001E-03 5.19E-01 
16 4.3275E-01 -1.6904E-01 7.64E-01 2.15E+00 2.33E+02 3.3327E-02 1.55E+01 
17 2.2638E-01 -7.5058E-01 3.43E-01 1.41E+00 3.55E+02 5.1599E-01 3.66E+02 
18 4.8791E-01 -3.0228E-02 8.65E-01 2.38E+00 2.11E+02 7.7558E-01 3.27E+02 
19 9.6566E-01 1.8210E+00 2.21E+00 9.09E+00 5.50E+01 1.4702E-01 1.62E+01 
20 9.9064E-01 2.3515E+00 2.59E+00 1.34E+01 3.74E+01 7.1911E-02 5.38E+00 
21 7.6046E-01 7.0750E-01 1.40E+00 4.05E+00 1.23E+02 4.8032E-01 1.18E+02 
22 6.5544E-01 3.9961E-01 1.18E+00 3.24E+00 1.54E+02 4.3202E-01 1.33E+02 
23 2.8080E-01 -5.8009E-01 4.66E-01 1.59E+00 3.14E+02 6.6853E-02 4.19E+01 
24 9.7585E-01 1.9751E+00 2.32E+00 1.02E+01 4.92E+01 7.7782E-01 7.65E+01 
25 9.9035E-01 2.3403E+00 2.58E+00 1.32E+01 3.77E+01 1.9658E-01 1.48E+01 
26 4.8014E-01 -4.9667E-02 8.51E-01 2.34E+00 2.13E+02 8.7179E-01 3.72E+02 
27 6.7670E-01 4.5806E-01 1.22E+00 3.38E+00 1.48E+02 1.0364E-01 3.06E+01 
28 6.7628E-02 -1.4940E+00 -1.96E-01 8.22E-01 6.08E+02 5.7641E-02 7.01E+01 
29 3.8513E-01 -2.9160E-01 6.76E-01 1.97E+00 2.54E+02 3.0107E-01 1.53E+02 
30 6.0259E-01 2.5965E-01 1.08E+00 2.93E+00 1.71E+02 9.8363E-01 3.36E+02 
Output DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 A-3 September 2004 

Drift-Scale Radionuclide Transport 
INTENTIONALLY LEFT BLANK
MDL-NBS-HS-000016 REV 01 A-4 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX B 
FRACTURE AND MATRIX FLUXES AND WATER SATURATIONS 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
FRACTURE AND MATRIX FLUXES AND WATER SATURATIONS 
This appendix provides additional information pertaining to Section 6.4.5 of the main 
text. Fracture and matrix water saturations and fluxes and matrix relative permeabilities are 
available from the UZ Flow Model results. As discussed in Section 4.1.2, the lower, mean, and 
upper infiltration scenarios for the glacial transition climate are evaluated. Table B-1 gives an 
example of the fluxes, saturations, and matrix relative permeabilities for mean infiltration 
scenario for model grid cells within the waste emplacement horizon, excluding fault zones. The 
values are arranged by rock unit (tsw33, tsw34, tsw35, and tsw36). The flux for a given cell is a 
vector with three components; therefore, the component with the maximum fracture flux (and 
corresponding matrix flux) was selected for each cell. See Scientific Notebook by Wang (2003 
[DIRS 163234], SN-LBNL-SCI-236-V1, pp. 4752) for a discussion of how these values were 
extracted from the 3-D flow fields. Table B-1 gives a portion of the values extracted for the 
tsw33 and tsw34 model units. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, pp. 
5053) and Output-DTN: LB0307FMRADTRN.001 for the complete output. 
The matrix saturations and matrix relative permeabilities as presented here may be used as input 
for the TSPA to support the EBS Radionuclide Transport Model [EBS Radionuclide Transport 
Abstraction BSC 2004 [DIRS 169868])]. This is contained in the Flow and Saturation Data 
from UZ Flow Model.xls spreadsheet in the output DTN: LB0307FMRADTRN.001. 
Table B-1. Fracture and Matrix Fluxes, Saturations, and Matrix Relative PermeabilityGlacial Transition 
Mean 
A B C D E F G H 
1 
Rock 
Unit 
Fracture 
Cell Name 
Fracture Flux 
(mm/yr) 
Fracture 
Saturation 
Matrix Cell 
Name 
Matrix Flux 
(mm/yr) 
Matrix 
Saturation 
Matrix Relative 
Permeability 
2 tsw33 F012Bl76 5.3967E+00 1.3240E-02 M012Bl76 2.4032E-01 9.3761E-01 1.1223E-01 
3 tsw33 F012Bl78 5.7350E+00 1.3264E-02 M012Bl78 1.4520E-01 9.0879E-01 7.1708E-02 
4 tsw33 F012Cl72 4.8155E+00 1.3061E-02 M012Cl72 1.3236E+00 9.9786E-01 5.4681E-01 
5 tsw33 F012Cl74 6.6185E+00 1.3454E-02 M012Cl74 5.1798E-01 9.7267E-01 2.1822E-01 
6 tsw33 F012Cm70 9.7583E+00 1.3937E-02 M012Cm70 5.0937E-01 9.7432E-01 2.2678E-01 
7 tsw33 F012Dg58 1.0083E+01 1.4374E-02 M012Dg58 2.2577E-01 9.3205E-01 1.0250E-01 
8 tsw33 F012Dl68 1.3328E+01 1.4453E-02 M012Dl68 5.3696E-01 9.7656E-01 2.3933E-01 
9 tsw33 F012Dl70 6.9879E+00 1.3254E-02 M012Dl70 5.5948E-01 9.7693E-01 2.4154E-01 
10 tsw33 F012Dl71 3.5104E+00 1.2386E-02 M012Dl71 1.2656E+00 9.9586E-01 4.7057E-01 
11 tsw33 F012Dl75 4.4996E+00 1.2746E-02 M012Dl75 2.6302E-01 9.4760E-01 1.3303E-01 
12 tsw33 F012Dl77 4.2020E+00 1.2657E-02 M012Dl77 2.1155E-01 9.3789E-01 1.1275E-01 
13 tsw33 F012Dl79 5.5142E+00 1.3038E-02 M012Dl79 4.4544E-01 9.6898E-01 2.0103E-01 
14 tsw33 F012Ef89 1.8602E+01 1.4758E-02 M012Ef89 1.4086E-01 9.5004E-01 1.3891E-01 
15 tsw33 F012Eg 2 1.5102E+01 1.5319E-02 M012Eg 2 1.1983E-01 9.2449E-01 9.0951E-02 
16 tsw33 F012Eg14 4.0953E+00 1.2794E-02 M012Eg14 5.8384E-02 9.0131E-01 6.4266E-02 
17 tsw33 F012Eg25 4.2045E+00 1.2854E-02 M012Eg25 5.3101E-02 8.5649E-01 3.4394E-02 
18 tsw33 F012Eg36 6.6068E+00 1.3531E-02 M012Eg36 1.1091E-01 9.1961E-01 8.4365E-02 
19 tsw33 F012Eg47 7.4195E+00 1.3779E-02 M012Eg47 1.6404E-01 9.1500E-01 7.8658E-02 
20 tsw33 F012Eh 1 2.5267E+01 1.6781E-02 M012Eh 1 1.8512E-01 9.3937E-01 1.1556E-01 
21 tsw33 F012El73 4.1465E+00 1.2600E-02 M012El73 4.8153E-01 9.7170E-01 2.1347E-01 
22 tsw33 F012Fg26 4.5607E+00 1.2340E-02 M012Fg26 1.0880E-01 9.4168E-01 1.2012E-01 
MDL-NBS-HS-000016 REV 01 B-1 September 2004 

Drift-Scale Radionuclide Transport 
Table B-1. Fracture and Matrix Fluxes, Saturations, and Matrix Relative PermeabilityGlacial Transition 
Mean (Continued) 
A B C D E F G H 
Rock 
Unit 
Fracture 
Cell Name 
Fracture Flux 
(mm/yr) 
Fracture 
Saturation 
Matrix Cell 
Name 
Matrix Flux 
(mm/yr) 
Matrix 
Saturation 
Matrix Relative 
Permeability 
23 tsw33 F012Fg59 3.4216E+01 1.6465E-02 M012Fg59 3.2473E-01 9.6741E-01 1.9434E-01 
24 tsw33 F012Fg70 3.3638E+01 1.6356E-02 M012Fg70 2.1330E-01 9.5857E-01 1.6265E-01 
25 tsw33 F012Fg80 2.0564E+01 1.6174E-02 M012Fg80 1.4723E-01 9.3185E-01 1.0217E-01 
26 tsw33 F012Fg90 1.9384E+01 1.6000E-02 M012Fg90 1.3500E-01 9.2880E-01 9.7324E-02 
27 tsw34 F0013g 3 3.5168E+00 1.4929E-02 M0013g 3 1.2727E-02 9.5988E-01 2.0111E-01 
28 tsw34 F0013g48 2.6890E+01 2.2664E-02 M0013g48 1.5652E-02 9.7120E-01 2.5171E-01 
29 tsw34 F0013g91 1.4310E+01 1.9454E-02 M0013g91 1.4594E-02 9.6798E-01 2.3541E-01 
30 tsw34 F0013h 2 9.6354E+00 1.9077E-02 M0013h 2 6.9779E-02 9.6752E-01 2.3319E-01 
Output DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 B-2 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX C 
SAMPLING FOR FLOW FOCUSING FACTOR 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
SAMPLING FOR FLOW FOCUSING FACTOR 
This appendix provides additional information pertaining to Section 6.4.5 of the main text. The 
cumulative probability distribution for the flow-focusing factor is given by BSC (2004 
[DIRS 167652], Figure 6-26; DTN: LB0406U0075FCS.002 [DIRS 170712]): 
P- = 3137.0 F 4 + 4998.5 F 3 - 66.35 F 2 + 3.102 F - 434.11 (Eq. C-1) 
where F is the flow-focusing factor and P is the cumulative probability in as a percentage. The 
correlation is limited to a range of F between approximately 0.12 to 5. The equation is evaluated 
and interpolated to evenly spaced values of P, 1, 2, 3, , 100. Then, the factor is sampled using 
a uniform random number scaled between 1 and 100 and truncated to an integer. This factor 
does not depend on any particular properties of the host rock. Table C-1 presents a portion of the 
output from the formulation as performed in an Excel spreadsheet. See Wang (2003 
[DIRS 163234], SN-LBNL-SCI-236-V1, p. 54) and DTN: LB0307FMRADTRN.001 for the 
complete output. 
The flow-focusing factor as presented here may be used as input for the TSPA to support the 
EBS Radionuclide Transport Model [EBS Radionuclide Transport Abstraction BSC 2004 
[DIRS 169868])]. This is contained in the Flow Focusing Factor.xls spreadsheet in the output 
DTN: LB0307FMRADTRN.001. 
The sequence of calculations are described here: 
Column A: This column contains a series of values for the normalized flux generated between 
0.12 and 5.02. 
Column B: The cumulative probability is computed from the relationship given in 
Equation C-1. In Excel, this is calculated as 
Brn=-11.434 +102.3*Arn-35.66*Arn^2+5.4998*Arn^3-0.3137*Arn^4 
Column C: A series of evenly spaced values of the cumulative probability. 
Column D: The normalized flux is interpolated to the evenly spaced values in Column C. This 
is done using the following Excel formula: 
Drn=Arn+(Crn-Brn)*((A(rn+1)-Arn)/(B(rn+1)-Brn)) 
Column E: A uniform random number between 1 and 100 is used to randomly select a 
normalized flux. The Excel formula is 
Ern=1+99*RAND(), 
which is copied and saved in Column E. 
MDL-NBS-HS-000016 REV 01 C-1 September 2004 

Drift-Scale Radionuclide Transport 
Column F: Round off the random number to an integer. The Excel formula is 
Frn=ROUND(Ern,0) 
Column G: Use the random integer to find the corresponding normalized flux. The Excel 
formula is 
Grn=INDEX(D$3:D$103,Frn) 
Table C-1. Flow-Focusing Factor 
A B C D E F G 
1 
Normalized 
Flux 
Cumulative 
Probability 
(%) 
Cumulative 
Probability 
(%) 
Interpolated 
Normalized 
Flux 
Fixed 
Uniform 
Random 
Number 
Uniform 
Random 
Integer 
Flow 
Focusing 
Factor 
2 1.16E-01 8.81E-07 0.00E+00 1.16E-01 7.8382E+01 78 1.47E+00 
3 1.20E-01 3.38E-01 1.00E+00 1.27E-01 9.1213E+01 91 2.10E+00 
4 1.30E-01 1.27E+00 2.00E+00 1.38E-01 5.2710E+01 53 8.51E-01 
5 1.40E-01 2.20E+00 3.00E+00 1.49E-01 6.2073E+01 62 1.04E+00 
6 1.50E-01 3.13E+00 4.00E+00 1.60E-01 3.7861E+01 38 5.96E-01 
7 1.60E-01 4.04E+00 5.00E+00 1.71E-01 2.6944E+01 27 4.38E-01 
8 1.80E-01 5.86E+00 6.00E+00 1.82E-01 2.0972E+01 21 3.60E-01 
9 1.90E-01 6.75E+00 7.00E+00 1.93E-01 5.6278E+01 56 9.09E-01 
10 2.00E-01 7.64E+00 8.00E+00 2.04E-01 8.8144E+01 88 1.91E+00 
11 2.10E-01 8.53E+00 9.00E+00 2.15E-01 8.6708E+01 87 1.85E+00 
12 2.20E-01 9.40E+00 1.00E+01 2.27E-01 8.6516E+00 9 2.15E-01 
13 2.30E-01 1.03E+01 1.10E+01 2.38E-01 8.9982E+01 90 2.03E+00 
14 2.40E-01 1.11E+01 1.20E+01 2.50E-01 6.3578E+01 64 1.08E+00 
15 2.60E-01 1.28E+01 1.30E+01 2.62E-01 5.0222E+01 50 7.95E-01 
16 2.70E-01 1.37E+01 1.40E+01 2.74E-01 5.7781E+01 58 9.49E-01 
17 2.80E-01 1.45E+01 1.50E+01 2.86E-01 3.7505E+01 38 5.96E-01 
18 2.90E-01 1.54E+01 1.60E+01 2.98E-01 4.0043E+01 40 6.27E-01 
19 3.00E-01 1.62E+01 1.70E+01 3.10E-01 1.1477E+01 11 2.38E-01 
20 3.10E-01 1.70E+01 1.80E+01 3.22E-01 3.7317E+00 4 1.60E-01 
21 3.30E-01 1.86E+01 1.90E+01 3.35E-01 4.9257E+00 5 1.71E-01 
22 3.40E-01 1.94E+01 2.00E+01 3.47E-01 6.5344E+01 65 1.10E+00 
23 3.50E-01 2.02E+01 2.10E+01 3.60E-01 2.9530E+01 30 4.79E-01 
24 3.60E-01 2.10E+01 2.20E+01 3.72E-01 4.2111E+01 42 6.59E-01 
25 3.80E-01 2.26E+01 2.30E+01 3.85E-01 4.7234E+01 47 7.42E-01 
26 3.90E-01 2.34E+01 2.40E+01 3.98E-01 7.4482E+01 74 1.34E+00 
27 4.00E-01 2.41E+01 2.50E+01 4.12E-01 7.9962E+01 80 1.55E+00 
28 4.20E-01 2.56E+01 2.60E+01 4.25E-01 4.3791E+01 44 6.92E-01 
29 4.30E-01 2.64E+01 2.70E+01 4.38E-01 1.5301E+01 15 2.86E-01 
30 4.40E-01 2.71E+01 2.80E+01 4.52E-01 8.8079E+01 88 1.91E+00 
Output-DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 C-2 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX D 
SAMPLING FOR FRACTURE AND MATRIX POROSITY 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
SAMPLING FOR FRACTURE AND MATRIX POROSITY 
This appendix provides additional information pertaining to Section 6.4.5 of the main 
text. Fracture and matrix average porosity values and standard deviations are given in 
Section 4.1.1. No standard deviations are available for fracture porosity in the tsw33, tsw35, and 
tsw36. Therefore, values were computed such that the ratio of the standard deviation to the mean 
in these units is the same as the ratio for the tsw34. The average and standard deviations for 
fracture and matrix porosities are given in Table D-1. 
Table D-1. Fracture and Matrix Porosity Data 
UZ 
Model Layer 
Average fracture 
porositya (-) 
Fracture porosity 
Std deviationa (-) 
Average Matrix 
Porosityb 
Standard Deviation 
for Matrix Porosityb 
tsw33 5.8E-3 1.71E-03c 0.155 0.030 
tsw34 8.5E-3 2.50E-03 0.111 0.020 
tsw35 9.6E-3 2.82E-03c 0.131 0.031 
tsw3[67] 1.3E-2 3.82E-03c 0.103 0.025 
a 
DTN: LB0205REVUZPRP.001 [DIRS 159525]. 
b DTN: LB0207REVUZPRP.002 [DIRS 159672]. 
Derived values  see text above. 
Porosities are modeled using the beta distribution, with the mean values and standard deviations 
as indicated in Table D-1 and for all cases, a maximum of 1 and a minimum of 0. 
The sampling for the beta distribution uses the approximation for the inverse as given in 
Equation 26.5.22 of Abramowitz and Stegun (1972 [DIRS 103280]). This method requires the 
generation of a Gaussian random number. Gaussian random numbers are computed using the 
rational approximation for the inverse cumulative probability distribution for a Gaussian random 
variable, as given in Equation 26.2.23 of Abramowitz and Stegun (1972 [DIRS 103280]). See 
Scientific Notebook by Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, pp. 4042) for a 
discussion of the generation of Gaussian random numbers. Table D-2 presents a portion of the 
output from the formulation as performed in an Excel spreadsheet for the fracture and matrix 
porosities of the tsw35 model unit. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, 
p. 59) and DTN: LB0307FMRADTRN.001 for the complete output. 
The sequence of calculations are as follows: 
Column A: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. These are the cumulative probabilities, p . 
Column B: The normalized Gaussian random number corresponding to the cumulative 
probability in Column A. 
Column C: The parameter . in the beta inverse function is given by Abramowitz and Stegun 
(1972 [DIRS 103280], Equation 26.5.22): 
2 -
.= 
yp 3 
(Eq. D-1) 
6 
MDL-NBS-HS-000016 REV 01 D-1 September 2004 

Drift-Scale Radionuclide Transport 
where yp is defined in Column B. In Excel, this is 
Crn=(Brn^2-3)/6 
Column D: The parameter w in the beta inverse function is given by Abramowitz and Stegun 
(1972 [DIRS 103280], Equation 26.5.22): 
1 
=
y 
p
(
)
.
+
h 
1 
1 
5 
2
-
..
.
1
..
. 
..
. 
+
.
..
. 
(Eq. D-2) 
2 
-
-
w 
h 
2b
-
1 
2 
6 
3h
a
-
In Excel, this is 
Drn= (Brn*(($J$2+Crn)^0.5)/$J$2)-((2*$I$2-1)^(-1)-(2*$H$2-1)^(-1))*(Crn+(5/6)-2/(3*$J$2)) 
Column E: The beta random number, xp, is given by Abramowitz and Stegun (1972 
[DIRS 103280], Equation 26.5.22): 
a 
(Eq. D-3) 
2

x 
p 
be 
w
a
+
In Excel, this is 
Ern=$H$2/($H$2+$I$2*EXP(2*Drn)) 
Column F: Contains the value of the mean porosity, f, from Table D-1 
Column G: Contains the value of the porosity standard deviation, sf, from Table D-1 
Column H: The beta distribution parameter a is derived from Abramowitz and Stegun (1972 
[DIRS 103280], Equation 26.1.33) (see Appendix K for a detailed derivation of Equations (D-4) 
and (D-5)): 
..
. 
)
1
(
f

1
-
.
.
f

- 
(Eq. D-4) 
f

=
..
.
a
In Excel, this is 
2 
f
s 
H2=F2*((F2*(1-F2)/G2^2)-1) 
Column I: The beta distribution parameter b is given by Abramowitz and Stegun (1972 
[DIRS 103280], Equation 26.1.33): 
..
. 
)
1 
.
(
f

1
-
f

.
b
=
-
(
1
f

..
. 
)
2 
f
s
- 
(Eq. D-5) 
MDL-NBS-HS-000016 REV 01 D-2 September 2004 

Drift-Scale Radionuclide Transport 
In Excel, this is 
I2=(1-F2)*((F2*(1-F2)/G2^2)-1) 
Column J: The parameter h in the beta inverse function is given by Abramowitz and Stegun 
(1972 [DIRS 103280], Equation 26.5.22): 
-
1
1 
1
=
h2
...
2 
1 
..
. 
(Eq. D-6) 
+
a
-
1 
2b
-
In Excel, this is 
J2=2*((2*H2-1)^(-1)+(2*I2-1)^(-1))^(-1) 
Table D-2. Fracture Porosity in the tsw35 
A B C D E F G H I J 
1 
Fixed 
Uniform 
Random 
Number 
(P) 
yP normalized 
Gaussian 
random 
number 
Beta inverse 
param. -. 
Beta 
inverse 
param. -
w 
xP -
Beta 
random 
number 
(Fracture 
Porosity) 
mean 
fracture 
porosity 
- tsw35 
standard 
deviation 
fracture 
porosity - 
tsw35 
Beta 
dist. 
Param. - 
a 
Beta 
dist. 
Param. b 
Beta 
inverse 
param. -
h 
2 6.1798E-01 2.9975E-01 -4.8503E-01 6.02E-02 8.52E-03 9.60E-03 2.82E-03 1.15E+01 1.18E+03 4.35E+01 
3 4.6680E-01 -8.3116E-02 -4.9885E-01 1.88E-03 9.56E-03 
4 6.3399E-01 3.4200E-01 -4.8051E-01 6.68E-02 8.41E-03 
5 6.5133E-01 3.8846E-01 -4.7485E-01 7.41E-02 8.29E-03 
6 8.7752E-01 1.1628E+00 -2.7465E-01 2.00E-01 6.45E-03 
7 3.6128E-01 -3.5460E-01 -4.7904E-01 -3.82E-02 1.04E-02 
8 3.3315E-01 -4.3080E-01 -4.6907E-01 -4.92E-02 1.06E-02 
9 5.7646E-02 -1.5752E+00 -8.6467E-02 -2.06E-01 1.44E-02 
10 3.4838E-01 -3.8926E-01 -4.7475E-01 -4.32E-02 1.05E-02 
11 6.3949E-01 3.5665E-01 -4.7880E-01 6.91E-02 8.37E-03 
12 6.3466E-01 3.4378E-01 -4.8030E-01 6.71E-02 8.40E-03 
13 2.1067E-01 -8.0391E-01 -3.9229E-01 -1.02E-01 1.18E-02 
14 1.8567E-01 -8.9384E-01 -3.6684E-01 -1.15E-01 1.20E-02 
15 6.9110E-01 4.9856E-01 -4.5857E-01 9.15E-02 8.01E-03 
16 5.2111E-01 5.2811E-02 -4.9954E-01 2.23E-02 9.18E-03 
17 7.6460E-02 -1.4296E+00 -1.5940E-01 -1.87E-01 1.39E-02 
18 1.2759E-01 -1.1380E+00 -2.8418E-01 -1.48E-01 1.29E-02 
19 2.2382E-01 -7.5911E-01 -4.0396E-01 -9.59E-02 1.16E-02 
20 3.9235E-01 -2.7278E-01 -4.8760E-01 -2.62E-02 1.01E-02 
21 4.7861E-01 -5.3507E-02 -4.9952E-01 6.31E-03 9.48E-03 
22 2.9629E-01 -5.3472E-01 -4.5235E-01 -6.42E-02 1.09E-02 
MDL-NBS-HS-000016 REV 01 D-3 September 2004 

Drift-Scale Radionuclide Transport 
Table D-2. Fracture Porosity in the tsw35 (Continued) 
A B C D E F G H I J 
Fixed 
Uniform 
Random 
Number 
(P) 
yP normalized 
Gaussian 
random 
number 
Beta inverse 
param. -. 
Beta 
inverse 
param. -
w 
xP -
Beta 
random 
number 
(Fracture 
Porosity) 
mean 
fracture 
porosity 
- tsw35 
standard 
deviation 
fracture 
porosity - 
tsw35 
Beta 
dist. 
Param. - 
a 
Beta 
dist. 
Param. b 
Beta 
inverse 
param. h 
23 2.9692E-02 -1.8858E+00 9.2682E-02 -2.45E-01 1.56E-02 
24 8.1567E-01 8.9887E-01 -3.6534E-01 1.56E-01 7.04E-03 
25 9.1682E-01 1.3842E+00 -1.8064E-01 2.38E-01 5.98E-03 
26 3.2410E-01 -4.5583E-01 -4.6537E-01 -5.28E-02 1.07E-02 
27 2.3452E-01 -7.2378E-01 -4.1269E-01 -9.09E-02 1.15E-02 
28 4.4601E-01 -1.3546E-01 -4.9694E-01 -5.93E-03 9.71E-03 
29 4.5832E-01 -1.0442E-01 -4.9818E-01 -1.30E-03 9.62E-03 
30 3.6776E-01 -3.3734E-01 -4.8103E-01 -3.57E-02 1.03E-02 
Output DTN: LB0307FMRADTRN.001. 
Table D-3. Matrix Porosity in the tsw35 
A B C D E F G H I J 
1 
Fixed 
Uniform 
Random 
Number 
(P) 
yP normalized 
Gaussian 
random 
number 
Beta inverse 
param. -. 
Beta 
inverse 
param. -
w 
xP -
Beta 
random 
number 
(Matrix 
Porosity) 
mean 
matrix 
porosity 
- tsw35 
standard 
deviation 
matrix 
porosity - 
tsw35 
Beta 
dist. 
Param. - 
a 
Beta 
dist. 
Param. b 
Beta 
inverse 
param. -
h 
2 8.2838E-01 9.4770E-01 -3.5031E-01 1.45E-01 1.01E-01 1.31E-01 3.10E-02 1.54E+01 1.02E+02 5.19E+01 
3 1.4598E-01 -1.0538E+00 -3.1491E-01 -1.31E-01 1.64E-01 
4 9.2170E-01 1.4169E+00 -1.6542E-01 2.15E-01 8.93E-02 
5 2.3816E-01 -7.1196E-01 -4.1552E-01 -8.68E-02 1.52E-01 
6 1.9194E-01 -8.7064E-01 -3.7367E-01 -1.08E-01 1.57E-01 
7 2.3945E-01 -7.0779E-01 -4.1651E-01 -8.62E-02 1.52E-01 
8 8.6837E-01 1.1188E+00 -2.9138E-01 1.70E-01 9.69E-02 
9 5.1569E-01 3.9223E-02 -4.9974E-01 1.46E-02 1.28E-01 
10 7.6814E-01 7.3249E-01 -4.1058E-01 1.13E-01 1.07E-01 
11 1.3291E-01 -1.1128E+00 -2.9361E-01 -1.39E-01 1.66E-01 
12 5.2042E-01 5.1084E-02 -4.9957E-01 1.63E-02 1.27E-01 
13 3.0449E-01 -5.1112E-01 -4.5646E-01 -6.02E-02 1.45E-01 
14 6.2932E-01 3.2962E-01 -4.8189E-01 5.52E-02 1.19E-01 
15 7.8249E-01 7.8041E-01 -3.9849E-01 1.20E-01 1.06E-01 
16 2.1576E-02 -2.0227E+00 1.8187E-01 -2.52E-01 2.00E-01 
17 1.0799E-01 -1.2374E+00 -2.4479E-01 -1.55E-01 1.70E-01 
18 7.6286E-01 7.1526E-01 -4.1473E-01 1.10E-01 1.08E-01 
MDL-NBS-HS-000016 REV 01 D-4 September 2004 

Drift-Scale Radionuclide Transport 
Table D-3. Matrix Porosity in the tsw35 (Continued) 
A B C D E F G H I J 
Fixed 
Uniform 
Random 
Number 
(P) 
yP normalized 
Gaussian 
random 
number 
Beta inverse 
param. -. 
Beta 
inverse 
param. -
w 
xP -
Beta 
random 
number 
(Matrix 
Porosity) 
mean 
matrix 
porosity 
- tsw35 
standard 
deviation 
matrix 
porosity - 
tsw35 
Beta 
dist. 
Param. - 
a 
Beta 
dist. 
Param. b 
Beta 
inverse 
param. h 
19 2.3410E-01 -7.2515E-01 -4.1236E-01 -8.85E-02 1.53E-01 
20 3.1982E-01 -4.6778E-01 -4.6353E-01 -5.44E-02 1.44E-01 
21 1.5005E-01 -1.0362E+00 -3.2104E-01 -1.29E-01 1.63E-01 
22 8.6802E-01 1.1172E+00 -2.9199E-01 1.70E-01 9.69E-02 
23 6.3793E-02 -1.5240E+00 -1.1290E-01 -1.91E-01 1.81E-01 
24 7.1773E-01 5.7574E-01 -4.4475E-01 9.03E-02 1.12E-01 
25 2.6452E-02 -1.9361E+00 1.2476E-01 -2.42E-01 1.96E-01 
26 1.2687E-03 -3.0192E+00 1.0192E+00 -3.70E-01 2.40E-01 
27 6.7080E-01 4.4170E-01 -4.6748E-01 7.11E-02 1.16E-01 
28 1.7696E-01 -9.2694E-01 -3.5680E-01 -1.15E-01 1.59E-01 
29 8.9801E-02 -1.3422E+00 -1.9975E-01 -1.68E-01 1.74E-01 
30 1.4850E-01 -1.0429E+00 -3.1873E-01 -1.30E-01 1.64E-01 
Output DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 D-5 September 2004 

Drift-Scale Radionuclide Transport 
INTENTIONALLY LEFT BLANK
MDL-NBS-HS-000016 REV 01 D-6 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX E 
SAMPLING FOR INVERT DIFFUSIVE MASS TRANSFER COEFFICIENTS
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
SAMPLING FOR INVERT DIFFUSIVE MASS TRANSFER COEFFICIENTS 
This appendix provides additional information pertaining to Section 6.4.5 of the main text. The 
invert diffusive mass-transfer coefficient is based upon the correlation presented in Invert 
Diffusion Properties Model (BSC 2001 [DIRS 156700], pp. 2325, Equation (37)): 
..
log.. DeI 
.. = log 849.1 . 
(Eq. E-1) . D0 . I 
where DeI is the invert diffusive mass-transfer coefficient, D0 is the coefficient of diffusion in 
water, and .I is the invert water content. As discussed in Section 6.4.5, the invert water content 
is related to the invert grain microporosity, times the fraction of the bulk volume occupied by the 
grains, i.e.: 
. I =( 1-f )f (Eq. E-2) 
Ig m 
where f Igis the intergranular porosity of the invert and f is the microporosity of the grains. The
m
invert material is planned to be taken from the tsw36 unit, and the sampling for the porosity of 
this material is discussed in Appendix D. The intergranular porosity has an expected value of 
0.45 (BSC 2003 [DIRS 170881], Section 6.3) and a range from 0.4 to 0.48. A distribution 
representative of these characteristics can be produced by noting that a uniform random sample 
between 0.4 and 0.45 will on average produce a value of 0.425. Similarly, a uniform random 
sample between 0.45 and 0.48 will on average produce a value of 0.465. If samples are drawn 
from these two distributions in some proportion, x , for the range of 0.4 to 0.45 and (1-x) for the 
range of 0.45 to 0.48, then an overall average of 0.45 will be achieved if x = 0.375. 
Table E-1 presents a portion of the output from the formulation as performed in an Excel 
spreadsheet for the fracture and matrix porosities of the tsw35 model unit. See Wang 
(2003 [DIRS 163234], SN-LBNL-SCI-236-V1, p. 64) and DTN: LB0307FMRADTRN.001 for 
the complete output. The sequence of calculations are as follows: 
Column A: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. 
Column B: Scale the random number in Column B to between 0.4 and 0.45 
Brn=0.4+Arn*0.05 
Column C: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. 
Column D: Scale the random number in Column E to between 0.45 and 0.48 
Drn=0.45+Crn*0.03 
MDL-NBS-HS-000016 REV 01 E-1 September 2004 

Drift-Scale Radionuclide Transport 
Column E: Calculate the weighted average of columns B and D to give the invert intergranular 
porosity. 
Ern=0.375*Brn+0.625*Drn 
The statistical properties for the diffusion coefficient in water, D0, are derived from the data from 
Weast and Astle 1979 [DIRS 102865], presented in Section 4.1.1. The diffusion coefficient is 
sampled as a lognormal distribution, with the mean and standard deviation of log(D0) being 4.69 
and 0.150, respectively, where D0 is in mm/year. 
See Scientific Notebook by Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, pp. 4042) for 
a discussion of the generation of Gaussian random numbers. Table E-2 presents a portion of the 
output from the formulation as performed in an Excel spreadsheet for the diffusion 
coefficient. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, p. 67) and DTN: 
LB0307FMRADTRN.001 for the complete output 
The sequence of calculations are as follows: 
Column A: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. These are the cumulative probabilities, p. 
Column B: The normalized Gaussian random number corresponding to the cumulative 
probability in Column A. 
Column C: The corresponding random base-10 logarithm of fracture frequency is derived from 
the normalized Gaussian random variable through the normalization definition: 
f =xpslog(D0) +log(D0 ) (Eq. E-3) 
where log(D0) and slog(D0) are the mean and variance of log(D ) .
0 
In Excel, this is 
Crn=Brn*$F$2+$E$2 
Column D: This column calculates the diffusion coefficient through the identity 
D0 =10log(D0 ) 
(Eq. E-4) 
In Excel, this is 
Drn=10^(Crn) 
MDL-NBS-HS-000016 REV 01 E-2 September 2004 

Drift-Scale Radionuclide Transport 
Table E-1. Intergranular Porosity 
A B C D E 
Random Random 
1 
Fixed Uniform 
Random 
Number (P) 
Porosity 
between 0.4 and 
0.45 
Fixed Uniform 
Random 
Number (P) 
Porosity 
between 0.45 
and 0.48 
Intergranular 
porosity 
2 4.1774E-01 4.2089E-01 4.7017E-01 4.6411E-01 4.48E-01 
3 8.1015E-01 4.4051E-01 3.8268E-01 4.6148E-01 4.54E-01 
4 7.0390E-01 4.3519E-01 2.6241E-01 4.5787E-01 4.49E-01 
5 1.9219E-01 4.0961E-01 1.5264E-01 4.5458E-01 4.38E-01 
6 6.8994E-01 4.3450E-01 7.1428E-01 4.7143E-01 4.58E-01 
7 1.5716E-01 4.0786E-01 8.3342E-02 4.5250E-01 4.36E-01 
8 6.6607E-01 4.3330E-01 4.5951E-01 4.6379E-01 4.52E-01 
9 6.5736E-01 4.3287E-01 5.7148E-02 4.5171E-01 4.45E-01 
10 1.0713E-01 4.0536E-01 2.5464E-01 4.5764E-01 4.38E-01 
11 2.9326E-01 4.1466E-01 1.8206E-01 4.5546E-01 4.40E-01 
12 2.8986E-01 4.1449E-01 4.8610E-01 4.6458E-01 4.46E-01 
13 8.9896E-01 4.4495E-01 8.8812E-01 4.7664E-01 4.65E-01 
14 9.2404E-01 4.4620E-01 2.3375E-01 4.5701E-01 4.53E-01 
15 2.1126E-01 4.1056E-01 4.6330E-01 4.6390E-01 4.44E-01 
16 9.7667E-01 4.4883E-01 1.5419E-01 4.5463E-01 4.52E-01 
17 8.7149E-02 4.0436E-01 3.6447E-02 4.5109E-01 4.34E-01 
18 1.0232E-01 4.0512E-01 9.8288E-01 4.7949E-01 4.52E-01 
19 9.1436E-02 4.0457E-01 2.3091E-01 4.5693E-01 4.37E-01 
20 2.0876E-01 4.1044E-01 1.6027E-01 4.5481E-01 4.38E-01 
21 4.6890E-01 4.2344E-01 9.6731E-01 4.7902E-01 4.58E-01 
22 2.4024E-01 4.1201E-01 4.6734E-01 4.6402E-01 4.45E-01 
23 7.3021E-01 4.3651E-01 9.8400E-01 4.7952E-01 4.63E-01 
24 5.9356E-01 4.2968E-01 8.7017E-02 4.5261E-01 4.44E-01 
25 5.8208E-01 4.2910E-01 8.1004E-01 4.7430E-01 4.57E-01 
26 8.3132E-01 4.4157E-01 6.2164E-01 4.6865E-01 4.58E-01 
27 6.5032E-01 4.3252E-01 3.1289E-01 4.5939E-01 4.49E-01 
28 3.9302E-02 4.0197E-01 1.1715E-01 4.5351E-01 4.34E-01 
29 1.9354E-01 4.0968E-01 7.8522E-01 4.7356E-01 4.50E-01 
30 7.4822E-03 4.0037E-01 8.6992E-01 4.7610E-01 4.48E-01 
Output DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 E-3 September 2004 

Drift-Scale Radionuclide Transport 
Table E-2. Free-Water Diffusion Coefficients 
A B C D E F 
xP - norm. Free-water 
Fixed Uniform Gaussian x - Gaussian Diffusion standard 
1 
Random 
Number (P) 
random 
number 
random 
number 
Coefficient 
(mm2/yr) 
mean log(D0) 
(mm2/yr) 
deviation 
log(D0) 
2 8.6421E-01 1.0995E+00 4.85E+00 7.16E+04 4.69E+00 1.50E-01 
3 2.3687E-01 -7.1615E-01 4.58E+00 3.82E+04 
4 4.7360E-01 -6.6043E-02 4.68E+00 4.79E+04 
5 4.7725E-01 -5.6898E-02 4.68E+00 4.80E+04 
6 3.1923E-01 -4.6944E-01 4.62E+00 4.16E+04 
7 3.2902E-01 -4.4220E-01 4.62E+00 4.20E+04 
8 4.9136E-01 -2.1600E-02 4.69E+00 4.86E+04 
9 8.4999E-01 1.0364E+00 4.85E+00 7.01E+04 
10 9.5489E-01 1.6946E+00 4.94E+00 8.79E+04 
11 2.0629E-01 -8.1919E-01 4.57E+00 3.69E+04 
12 1.4971E-01 -1.0377E+00 4.53E+00 3.42E+04 
13 5.3725E-01 9.3274E-02 4.70E+00 5.06E+04 
14 5.0698E-01 1.7446E-02 4.69E+00 4.93E+04 
15 2.5667E-01 -6.5333E-01 4.59E+00 3.91E+04 
16 9.7563E-01 1.9712E+00 4.99E+00 9.68E+04 
17 8.2452E-01 9.3265E-01 4.83E+00 6.76E+04 
18 8.5117E-01 1.0414E+00 4.85E+00 7.02E+04 
19 5.1257E-01 3.1418E-02 4.69E+00 4.95E+04 
20 1.2745E-01 -1.1386E+00 4.52E+00 3.31E+04 
21 5.9803E-01 2.4783E-01 4.73E+00 5.34E+04 
22 4.2537E-01 -1.8780E-01 4.66E+00 4.59E+04 
23 8.0602E-01 8.6319E-01 4.82E+00 6.60E+04 
24 1.7123E-01 -9.4925E-01 4.55E+00 3.53E+04 
25 8.3000E-01 9.5408E-01 4.83E+00 6.81E+04 
26 6.0404E-01 2.6339E-01 4.73E+00 5.36E+04 
27 4.4891E-01 -1.2814E-01 4.67E+00 4.69E+04 
28 9.1953E-01 1.4022E+00 4.90E+00 7.95E+04 
29 9.5815E-01 1.7300E+00 4.95E+00 8.90E+04 
30 1.7662E-01 -9.2825E-01 4.55E+00 3.55E+04 
Output-DTN: LB0307FMRADTRN.001. 
The invert diffusion coefficient is computed using the intergranular porosity and matrix porosity 
from tsw36 (Appendix D), Equations E-1 and E-2, and the free-water diffusion 
coefficient. Table E-2 presents a portion of the output from the formulation as performed in an 
Excel spreadsheet for the invert diffusive mass transfer coefficient. See Wang (2003 
[DIRS 163234], SN-LBNL-SCI-236-V1, p. 69) and DTN: LB0307FMRADTRN.001 for the 
complete output. The ratio of the maximum to minimum of the sampled diffusion coefficients 
spans a factor of approximately 43. 
MDL-NBS-HS-000016 REV 01 E-4 September 2004 

Drift-Scale Radionuclide Transport 
The sequence of calculations are described here: 
Column A: Intergranular Porosity 
Column B: Matrix Porosity (tsw36) 
Column C: Invert water content computed from Equation E-2. In Excel, this is 
Crn=(1-Arn)*Brn 
Column D: Free-water diffusion coefficient 
Column E: Invert diffusive mass transfer coefficient computed from Equation E-1. In Excel, 
this is 
Ern=Drn*Crn^1.849 
Table E-3. Invert Diffusive Mass Transfer Coefficients 
A B C D E 
Free-Water Invert Diffusive 
Diffusion Mass Transfer 
1 
Intergranular 
Porosity 
Matrix Porosity - 
tsw36 
Invert Water 
Content 
Coefficient 
(mm/r) 
Coefficient 
(mm2/yr) 
2 4.48E-01 1.51E-01 8.34E-02 7.16E+04 7.25E+02 
3 4.54E-01 9.24E-02 5.05E-02 3.82E+04 1.53E+02 
4 4.49E-01 8.54E-02 4.70E-02 4.79E+04 1.68E+02 
5 4.38E-01 9.61E-02 5.40E-02 4.80E+04 2.18E+02 
6 4.58E-01 8.26E-02 4.48E-02 4.16E+04 1.34E+02 
7 4.36E-01 1.35E-01 7.60E-02 4.20E+04 3.58E+02 
8 4.52E-01 1.09E-01 5.99E-02 4.86E+04 2.67E+02 
9 4.45E-01 8.37E-02 4.65E-02 7.01E+04 2.41E+02 
10 4.38E-01 1.23E-01 6.89E-02 8.79E+04 6.24E+02 
11 4.40E-01 1.31E-01 7.31E-02 3.69E+04 2.93E+02 
12 4.46E-01 6.76E-02 3.75E-02 3.42E+04 7.89E+01 
13 4.65E-01 1.15E-01 6.18E-02 5.06E+04 2.94E+02 
14 4.53E-01 1.05E-01 5.76E-02 4.93E+04 2.51E+02 
15 4.44E-01 1.75E-01 9.71E-02 3.91E+04 5.24E+02 
16 4.52E-01 7.95E-02 4.35E-02 9.68E+04 2.94E+02 
17 4.34E-01 5.44E-02 3.08E-02 6.76E+04 1.09E+02 
18 4.52E-01 1.33E-01 7.27E-02 7.02E+04 5.51E+02 
19 4.37E-01 1.12E-01 6.30E-02 4.95E+04 2.99E+02 
20 4.38E-01 1.32E-01 7.39E-02 3.31E+04 2.68E+02 
21 4.58E-01 1.33E-01 7.18E-02 5.34E+04 4.10E+02 
22 4.45E-01 9.39E-02 5.22E-02 4.59E+04 1.95E+02 
MDL-NBS-HS-000016 REV 01 E-5 September 2004 

Drift-Scale Radionuclide Transport 
Table E-3. Invert Diffusive Mass Transfer Coefficients (Continued) 
A B C D E 
Free-Water Invert Diffusive 
Diffusion Mass Transfer 
Intergranular 
Porosity 
Matrix Porosity - 
tsw36 
Invert Water 
Content 
Coefficient 
(mm/r) 
Coefficient 
(mm2/yr) 
23 4.63E-01 1.38E-01 7.42E-02 6.60E+04 5.38E+02 
24 4.44E-01 1.09E-01 6.08E-02 3.53E+04 1.99E+02 
25 4.57E-01 3.70E-02 2.01E-02 6.81E+04 4.94E+01 
26 4.58E-01 1.23E-01 6.67E-02 5.36E+04 3.59E+02 
27 4.49E-01 4.55E-02 2.51E-02 4.69E+04 5.14E+01 
28 4.34E-01 1.02E-01 5.79E-02 7.95E+04 4.09E+02 
29 4.50E-01 5.68E-02 3.13E-02 8.90E+04 1.47E+02 
30 4.48E-01 1.25E-01 6.90E-02 3.55E+04 2.53E+02 
Output DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 E-6 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX F 
SAMPLING FOR MATRIX DIFFUSION COEFFICIENTS 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
SAMPLING FOR MATRIX DIFFUSION COEFFICIENTS 
This appendix provides additional information pertaining to Section 6.4.5 of the main 
text. Matrix diffusion coefficients are derived based on the correlation discussed in Section 6.4.5 
(Equation 6-52): 
log( D )=- 49.3 + 38.1 .+ log 165.0 ( k ) (Eq. F-1) 
m mw 
where Dm is in cm2/s and kw is in m2. The water-content values of the matrix are derived from 
the matrix porosities given in Appendix D, times the matrix water saturations given in 
Appendix B. The effective permeability to water is derived using the equation given in 
Section 6.4.5 (Equation 6-57): 
k =k k (Eq. F-2) 
w mrw 
where the matrix permeabilities are given in Table 4-6. A portion of the output from the above 
relationship for matrix diffusion coefficient for each of the model grid locations are shown in 
Table F-1. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, p. 84) and 
DTN: LB0307FMRADTRN.001 for the complete output. 
The sequence of calculations is given here: 
Column A: Cell name from Appendix B. 
Column B: Matrix water saturation from Appendix B. 
Column C: Matrix porosity from Appendix D. 
Column D: Matrix water content equals matrix water saturation, times matrix porosity. In
Excel, this is 
Drn=Brn*Crn 
Column E: Matrix relative permeability from Appendix B 
Column F: The effective permeability is computed using Equation F-2. In Excel, this is 
Frm=$N$2*Ern 
Column G: The logarithm of the mean matrix diffusion coefficient is computed using 
Equation F-1. In Excel, this is 
Grn=-3.49+1.38*Drn+0.165*LOG(Frn) 
Column H: The matrix diffusion coefficient is computed from the identity 
m
D =10log(D ) (Eq. F-3) 
m
MDL-NBS-HS-000016 REV 01 F-1 September 2004 

Drift-Scale Radionuclide Transport 
and converted from cm2/s to mm2/year. In Excel, this is 
Hrn=(10^Grn)*100*3600*24*365.25 
Column I: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. These are the cumulative probabilities, p. 
Column J: The normalized Gaussian random number corresponding to the cumulative 
probability in Column H. 
Column K: The distributed random variable, Y, in Equation 6-55 is defined by 
log ln
...
.
.
. 
. 
D0 
D
m 
.
.
. 
. 
..
.
Y
= 
(Eq. F-4) 
.
.
where Dm is given in Column G and D0 = 10-9 m2/s = 31557.6 mm2/year. In Excel, this is 
Krn=ln(log(31558/Hrn)) 
Column L: The corresponding random value of Y is derived from the normalized Gaussian 
random variable through the normalization definition: 
Y
=
s
x 
pY
+
Y (Eq. F-5) 
where Y and sY are the mean and variance for Y. As discussed in Section 6.4.5, sY=0.3. 
In Excel, this is 
Lrn=Jrn*$O$rn+Krn 
Column M: Inverting Equation F-4, the random value of Y is transformed back to a diffusion 
coefficient through the relationship 
D
m 
=
D010- 
exp
)
(
Y 
In Excel, this is 
Mrn=31558*10^(-exp(Lrn)) 
Column N: Matrix permeability from Table 4-6 
Column O: Standard deviation for Y 
MDL-NBS-HS-000016 REV 01 F-2 September 2004 

Table F-1. Matrix Diffusion Coefficients in the tsw35, Mean Infiltration Scenario 
Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 F-3 September 2004 
A B C D E F G H I J K L M N O 
1 Cell Name 
Matrix 
Water 
Saturation 
Matrix 
Porosity 
Matrix 
Water 
Content 
Relative 
Permeability 
Effective 
Permeability 
m2 
log(Dm) 
cm2/s Dm mm2/yr 
Fixed 
Uniform 
Random 
Number (P) 
Normalized 
Gaussian 
Random 
Number Mean of Y Sampled Y 
Sampled Dm 
mm2/yr 
Perme 
-ability 
m2 
Std 
Dev Y 
2 F0014f19 8.5119E-01 1.01E-01 8.64E-02 1.1513E-02 5.16E-20 -6.55E+00 8.83E+02 2.8703E-02 -1.9006E+00 4.40E-01 -1.30E-01 4.18E+03 4.48E-3.00E-
3 F0014f31 8.3762E-01 1.64E-01 1.37E-01 9.1980E-03 4.12E-20 -6.50E+00 1.00E+03 1.0475E-01 -1.2551E+00 4.05E-01 2.83E-02 2.95E+03 
4 F0014f67 8.3178E-01 8.93E-02 7.43E-02 8.3545E-03 3.74E-20 -6.59E+00 8.06E+02 9.7688E-01 1.9937E+00 4.66E-01 1.06E+00 4.00E+01 
5 F0014f80 8.3701E-01 1.52E-01 1.27E-01 9.1054E-03 4.08E-20 -6.51E+00 9.67E+02 1.9728E-01 -8.5123E-01 4.15E-01 1.59E-01 2.12E+03 
6 F0014g17 8.3776E-01 1.57E-01 1.32E-01 9.2192E-03 4.13E-20 -6.51E+00 9.84E+02 6.8327E-01 4.7643E-01 4.10E-01 5.53E-01 5.77E+02 
7 F0014g83 8.3757E-01 1.52E-01 1.27E-01 9.1904E-03 4.12E-20 -6.51E+00 9.69E+02 5.6143E-01 1.5428E-01 4.14E-01 4.60E-01 8.21E+02 
8 F0014h13 8.3672E-01 9.69E-02 8.11E-02 9.0624E-03 4.06E-20 -6.58E+00 8.34E+02 4.4206E-02 -1.7042E+00 4.56E-01 -5.53E-02 3.57E+03 
9 F0014h21 8.3566E-01 1.28E-01 1.07E-01 8.9063E-03 3.99E-20 -6.54E+00 9.03E+02 3.6072E-01 -3.5609E-01 4.34E-01 3.27E-01 1.29E+03 
10 F0014h67 8.4732E-01 1.07E-01 9.10E-02 1.0797E-02 4.84E-20 -6.55E+00 8.86E+02 8.3538E-01 9.7559E-01 4.39E-01 7.32E-01 2.63E+02 
11 F0014h77 8.4210E-01 1.66E-01 1.40E-01 9.9040E-03 4.44E-20 -6.49E+00 1.02E+03 4.6970E-01 -7.5832E-02 3.99E-01 3.76E-01 1.10E+03 
12 F0014h82 8.3832E-01 1.27E-01 1.07E-01 9.3047E-03 4.17E-20 -6.54E+00 9.09E+02 1.4114E-01 -1.0752E+00 4.32E-01 1.09E-01 2.42E+03 
13 F0014i13 8.3837E-01 1.45E-01 1.22E-01 9.3129E-03 4.17E-20 -6.52E+00 9.54E+02 3.7451E-01 -3.1949E-01 4.18E-01 3.23E-01 1.31E+03 
14 F0014i18 8.3830E-01 1.19E-01 9.97E-02 9.3013E-03 4.17E-20 -6.55E+00 8.89E+02 2.6836E-01 -6.1745E-01 4.38E-01 2.53E-01 1.63E+03 
15 F0014i48 8.3729E-01 1.06E-01 8.88E-02 9.1484E-03 4.10E-20 -6.57E+00 8.56E+02 7.5006E-01 6.7438E-01 4.49E-01 6.51E-01 3.81E+02 
16 F0014l54 8.3708E-01 2.00E-01 1.67E-01 9.1172E-03 4.08E-20 -6.46E+00 1.10E+03 5.5094E-01 1.2776E-01 3.77E-01 4.16E-01 9.63E+02 
17 F0014l56 8.3869E-01 1.70E-01 1.43E-01 9.3628E-03 4.19E-20 -6.49E+00 1.02E+03 4.1410E-02 -1.7349E+00 3.99E-01 -1.22E-01 4.11E+03 
18 F0014l57 8.3979E-01 1.08E-01 9.06E-02 9.5337E-03 4.27E-20 -6.56E+00 8.67E+02 8.9647E-01 1.2619E+00 4.45E-01 8.24E-01 1.66E+02 
19 F0014m62 8.4322E-01 1.53E-01 1.29E-01 1.0090E-02 4.52E-20 -6.50E+00 9.88E+02 4.7281E-01 -6.8031E-02 4.08E-01 3.88E-01 1.06E+03 
20 F0014m63 8.3760E-01 1.44E-01 1.21E-01 9.1946E-03 4.12E-20 -6.52E+00 9.48E+02 6.9257E-01 5.0273E-01 4.20E-01 5.71E-01 5.36E+02 
21 F0014m64 8.4056E-01 1.63E-01 1.37E-01 9.6557E-03 4.33E-20 -6.50E+00 1.01E+03 8.9833E-01 1.2723E+00 4.03E-01 7.84E-01 2.03E+02 
22 F0014m65 8.4299E-01 9.69E-02 8.17E-02 1.0051E-02 4.50E-20 -6.57E+00 8.51E+02 7.1121E-01 5.5653E-01 4.51E-01 6.18E-01 4.41E+02 
23 F0014n24 8.6049E-01 1.81E-01 1.56E-01 1.3442E-02 6.02E-20 -6.45E+00 1.13E+03 9.5768E-01 1.7248E+00 3.69E-01 8.87E-01 1.18E+02 
24 F0014n26 8.5652E-01 1.12E-01 9.57E-02 1.2580E-02 5.64E-20 -6.53E+00 9.23E+02 6.3064E-01 3.3310E-01 4.28E-01 5.28E-01 6.37E+02 
25 F0014o29 8.4453E-01 1.96E-01 1.66E-01 1.0310E-02 4.62E-20 -6.45E+00 1.12E+03 7.0273E-01 5.3187E-01 3.72E-01 5.32E-01 6.26E+02 
26 F0014o31 8.5044E-01 2.40E-01 2.04E-01 1.1370E-02 5.09E-20 -6.39E+00 1.28E+03 7.1114E-01 5.5635E-01 3.30E-01 4.97E-01 7.16E+02 
27 F014Af20 8.3851E-01 1.16E-01 9.70E-02 9.3349E-03 4.18E-20 -6.55E+00 8.82E+02 3.6621E-01 -3.4147E-01 4.41E-01 3.38E-01 1.25E+03 
28 F014Af43 8.3937E-01 1.59E-01 1.34E-01 9.4685E-03 4.24E-20 -6.50E+00 9.94E+02 7.4439E-01 6.5661E-01 4.07E-01 6.04E-01 4.68E+02 
29 F014Af56 8.3128E-01 1.74E-01 1.45E-01 8.2857E-03 3.71E-20 -6.50E+00 1.01E+03 8.2489E-01 9.3409E-01 4.03E-01 6.83E-01 3.30E+02 
30 F014Af68 8.3726E-01 1.64E-01 1.37E-01 9.1432E-03 4.10E-20 -6.50E+00 9.98E+02 4.9809E-01 -4.7678E-03 4.05E-01 4.04E-01 1.00E+03 
Output-DTN: LB0307FMRADTRN.001. 

Drift-Scale Radionuclide Transport 
INTENTIONALLY LEFT BLANK 
MDL-NBS-HS-000016 REV 01 F-4 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX G 
SAMPLING FOR FRACTURE AND MATRIX PECLET NUMBERS, FRACTURE 
WATER CONTENT, AND DIMENSIONLESS INVERT DEPTH 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
SAMPLING FOR FRACTURE AND MATRIX PECLET NUMBERS, FRACTURE 
WATER CONTENT, AND DIMENSIONLESS INVERT DEPTH 
This appendix provides additional information pertaining to Section 6.4.5 of the main 
text. Fracture Peclet numbers are computed using Equations 19 and 29 from the main 
text. These are: 
q
wf 
(Eq. G-1) 
-
(
.
)
q 
fe 
=
q 
y 
f
wf
1
+
D
ef 
and 
h
q 
fe 
f
Pe 
(Eq. G-2) 
=
fe 
D
eI 
Fracture flow is adjusted using the flow-focusing factor in Appendix C 
q
wfa 
=
q
wf 
F (Eq. G-3) 
and the fracture saturation is adjusted as shown in Equation 6-50 in the main text. 
2m 
2
.
.
4
+
m 
.
. 
..
. 
..
. 
....
. 
1
..
.
m
1
F 
2
m 
..
.
S
1 
2 
fn 
.
.
..
. 
...
. 
...
. 
S 
S
-
1
- 
(Eq. G-4) 
m
=
fna 
fn 
where Sfn is the normalized fracture saturation 
S
-
S
f 
fr
S 
(Eq. G-5) 
=
fn 
S
1
-
fr 
and the adjusted physical saturation, Sfa, is given by 
)
(
1SS
S
=
S
- 
(Eq. G-6) 
+
fa 
fr 
fr 
fna 
The fixed parameters used are given in Table 4-4. 
The fracture residual saturation is sampled as discussed in Section 6.4.5. A portion of the output 
for the sampling of fracture residual saturation is shown in Table G-1. See Wang (2003 
[DIRS 163234], SN-LBNL-SCI-236-V1, p. 62) and DTN: LB0307FMRADTRN.001 for the 
complete output. 
The fracture percolation flux and fracture saturation as presented here may be used as input for 
the TSPA to support the EBS Radionuclide Transport Model [EBS Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 G-1 September 2004 

Drift-Scale Radionuclide Transport 
Abstraction BSC 2004 [DIRS 169868])]. This is contained in the Fracture Flux and Water 
Content with Flow Focusing r1.xls spreadsheet in the output DTN: LB0307FMRADTRN.001. 
The fracture residual saturation as presented here may be used as input for the TSPA to support 
the EBS Radionuclide Transport Model [EBS Radionuclide Transport Abstraction BSC 2004 
[DIRS 169868])]. This is contained in the Fracture Residual Saturation.xls spreadsheet in the 
output DTN: LB0307FMRADTRN.001. 
The matrix percolation flux as presented here may be used as input for the TSPA to support the 
EBS Radionuclide Transport Model [EBS Radionuclide Transport Abstraction BSC 2004 
[DIRS 169868])]. This is contained in the Matrix Peclet Number.xls spreadsheet in the output 
DTN: LB0307FMRADTRN.001. 
The sequence of calculations is as follows: 
Column A: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. 
Column B: The uniform random number in Column A, which ranges between 0 and 1, is 
converted to a uniform random number between -3 and -1. In Excel, this is 
Brn=-3+2*Arn 
Column C: The sampled Sfr is computed from the relationship 
S 
fr = 10RN 
where RN is the random number between -3 and -1 in Column B. In Excel, this is 
Crn=10^Brn 
Table G-1. Sampled Fracture Residual Saturations 
A B C 
1 
Fixed Uniform Random 
Number 
Uniform Random 
Number between -3 and 
-1 Sampled Sfr 
2 9.5775E-01 -1.0845E+00 8.2318E-02 
3 9.4855E-01 -1.1029E+00 7.8906E-02 
4 8.4093E-01 -1.3181E+00 4.8068E-02 
5 8.1139E-01 -1.3772E+00 4.1954E-02 
6 2.4515E-01 -2.5097E+00 3.0924E-03 
7 6.0656E-01 -1.7869E+00 1.6335E-02 
8 1.6459E-01 -2.6708E+00 2.1339E-03 
9 8.3698E-01 -1.3260E+00 4.7201E-02 
10 1.7917E-01 -2.6417E+00 2.2821E-03 
11 7.5053E-01 -1.4989E+00 3.1700E-02 
12 3.5867E-01 -2.2827E+00 5.2161E-03 
13 9.4585E-01 -1.1083E+00 7.7927E-02 
14 7.8309E-01 -1.4338E+00 3.6828E-02 
15 4.9868E-01 -2.0026E+00 9.9396E-03 
MDL-NBS-HS-000016 REV 01 G-2 September 2004 

Drift-Scale Radionuclide Transport 
Table G-1. Sampled Fracture Residual Saturations (Continued) 
A B C 
Fixed Uniform Random 
Number 
Uniform Random 
Number between -3 and 
-1 Sampled Sfr 
16 8.3823E-01 -1.3235E+00 4.7475E-02 
17 5.1569E-01 -1.9686E+00 1.0749E-02 
18 5.2289E-01 -1.9542E+00 1.1112E-02 
19 9.0574E-01 -1.1885E+00 6.4787E-02 
20 4.4778E-01 -2.1044E+00 7.8627E-03 
21 6.5841E-01 -1.6832E+00 2.0740E-02 
22 6.1984E-01 -1.7603E+00 1.7365E-02 
23 5.8284E-02 -2.8834E+00 1.3079E-03 
24 9.6211E-01 -1.0758E+00 8.3987E-02 
25 9.6423E-01 -1.0715E+00 8.4814E-02 
26 2.8823E-01 -2.4235E+00 3.7711E-03 
27 6.7397E-01 -1.6521E+00 2.2281E-02 
28 2.0593E-01 -2.5881E+00 2.5815E-03 
29 4.4110E-01 -2.1178E+00 7.6241E-03 
30 4.4855E-01 -2.1029E+00 7.8905E-03 
Output-DTN: LB0307FMRADTRN.001. 
A portion of the output for the fracture flux and water content sampling for the mean infiltration 
scenario are shown in Table G-2. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, 
p. 88) and DTN: LB0307FMRADTRN.001 for the complete output. 
The sequence of calculations is given here: 
Column A: Rock unit. 
Column B: Cell name. 
Column C: Fracture flux (negative of) from Appendix B. 
Column D: Flow focusing factor from Appendix C. 
Column E: Fracture saturation from Appendix B. 
Column F: Fracture normalized saturation using Equation G-5. In Excel this is 
Frn=(Ern-$M$2)/(1-$M$2) 
Column G: Adjusted normalized fracture saturation using Equation G-4. In Excel, this is 
Grn= ((Drn/($N$2^2))*Frn^0.5*(1-(1-Frn^(1/$N$2))^$N$2)^2)^(2*$N$2/(4+$N$2)) 
Column H: Sampled fracture residual saturation (see above). 
Column I: Adjusted physical fracture saturation using Equation G-6. In Excel, this is 
MDL-NBS-HS-000016 REV 01 G-3 September 2004 

Drift-Scale Radionuclide Transport 
Irn= Hrn+Grn*(1-Hrn) 
Column J: Fracture porosity from Appendix D. 
Column K: Adjusted fracture water velocity, which is equal to the fracture flux, times the flow-
focusing factor, divided by the fracture porosity and the adjusted physical fracture saturation. In 
Excel, this is 
Krn= Drn*Crn/(Irn*Jrn) 
Column L: Fracture water content. In Excel, this is 
Lrn=Irn*Jrn 
Column M: Fracture residual saturation from Table 4-4. 
Column N: Fracture van Genuchten pore size distribution factor, m, from Table 4-4. 
MDL-NBS-HS-000016 REV 01 G-4 September 2004 

Drift-Scale Radionuclide Transport 
Table G-2. Fracture Flux and Water Content for Mean Infiltration Scenario 
A B C D E F G H I J K L M N 
1 
Rock 
Unit Cell Name qf (mm/yr) F Sf Sfn Sfna 
Sampled 
Sfr Sfa .f 
qwf 
(mm/yr) 
Fracture 
Water 
Content Sfr m 
2 tsw33 F012Bl76 -5.3967E+00 1.47E+00 1.32E-02 3.27E-03 3.64E-03 8.2318E-02 8.57E-02 5.98E-03 -1.55E+04 5.12E-04 0.01 0.633 
3 tsw33 F012Bl78 -5.7350E+00 2.10E+00 1.33E-02 3.30E-03 4.04E-03 7.8906E-02 8.26E-02 4.70E-03 -3.11E+04 3.89E-04 
4 tsw33 F012Cl72 -4.8155E+00 8.51E-01 1.31E-02 3.09E-03 2.96E-03 4.8068E-02 5.09E-02 7.40E-03 -1.09E+04 3.77E-04 
5 tsw33 F012Cl74 -6.6185E+00 1.04E+00 1.35E-02 3.49E-03 3.52E-03 4.1954E-02 4.53E-02 4.21E-03 -3.59E+04 1.91E-04 
6 tsw33 F012Cm70 -9.7583E+00 5.96E-01 1.39E-02 3.98E-03 3.45E-03 3.0924E-03 6.53E-03 3.62E-03 -2.46E+05 2.36E-05 
7 tsw33 F012Dg58 -1.0083E+01 4.38E-01 1.44E-02 4.42E-03 3.53E-03 1.6335E-02 1.98E-02 5.48E-03 -4.07E+04 1.09E-04 
8 tsw33 F012Dl68 -1.3328E+01 3.60E-01 1.45E-02 4.50E-03 3.40E-03 2.1339E-03 5.53E-03 8.18E-03 -1.06E+05 4.52E-05 
9 tsw33 F012Dl70 -6.9879E+00 9.09E-01 1.33E-02 3.29E-03 3.20E-03 4.7201E-02 5.03E-02 2.82E-03 -4.49E+04 1.41E-04 
10 tsw33 F012Dl71 -3.5104E+00 1.91E+00 1.24E-02 2.41E-03 2.88E-03 2.2821E-03 5.15E-03 6.95E-03 -1.87E+05 3.58E-05 
11 tsw33 F012Dl75 -4.4996E+00 1.85E+00 1.27E-02 2.77E-03 3.28E-03 3.1700E-02 3.49E-02 5.49E-03 -4.36E+04 1.91E-04 
12 tsw33 F012Dl77 -4.2020E+00 2.15E-01 1.27E-02 2.68E-03 1.76E-03 5.2161E-03 6.97E-03 4.11E-03 -3.16E+04 2.86E-05 
13 tsw33 F012Dl79 -5.5142E+00 2.03E+00 1.30E-02 3.07E-03 3.73E-03 7.7927E-02 8.14E-02 4.79E-03 -2.88E+04 3.90E-04 
14 tsw33 F012Ef89 -1.8602E+01 1.08E+00 1.48E-02 4.81E-03 4.91E-03 3.6828E-02 4.16E-02 5.88E-03 -8.23E+04 2.44E-04 
15 tsw33 F012Eg 2 -1.5102E+01 7.95E-01 1.53E-02 5.37E-03 5.05E-03 9.9396E-03 1.49E-02 6.52E-03 -1.23E+05 9.75E-05 
16 tsw33 F012Eg14 -4.0953E+00 9.49E-01 1.28E-02 2.82E-03 2.78E-03 4.7475E-02 5.01E-02 4.80E-03 -1.62E+04 2.41E-04 
17 tsw33 F012Eg25 -4.2045E+00 5.96E-01 1.29E-02 2.88E-03 2.50E-03 1.0749E-02 1.32E-02 4.03E-03 -4.71E+04 5.32E-05 
18 tsw33 F012Eg36 -6.6068E+00 6.27E-01 1.35E-02 3.57E-03 3.14E-03 1.1112E-02 1.42E-02 4.52E-03 -6.44E+04 6.43E-05 
19 tsw33 F012Eg47 -7.4195E+00 2.38E-01 1.38E-02 3.82E-03 2.58E-03 6.4787E-02 6.72E-02 4.84E-03 -5.44E+03 3.25E-04 
20 tsw33 F012Eh 1 -2.5267E+01 1.60E-01 1.68E-02 6.85E-03 4.15E-03 7.8627E-03 1.20E-02 6.55E-03 -5.14E+04 7.84E-05 
21 tsw33 F012El73 -4.1465E+00 1.71E-01 1.26E-02 2.63E-03 1.62E-03 2.0740E-02 2.23E-02 8.15E-03 -3.89E+03 1.82E-04 
22 tsw33 F012Fg26 -4.5607E+00 1.10E+00 1.23E-02 2.36E-03 2.43E-03 1.7365E-02 1.98E-02 3.55E-03 -7.18E+04 7.02E-05 
23 tsw33 F012Fg59 -3.4216E+01 4.79E-01 1.65E-02 6.53E-03 5.34E-03 1.3079E-03 6.64E-03 7.72E-03 -3.20E+05 5.13E-05 
24 tsw33 F012Fg70 -3.3638E+01 6.59E-01 1.64E-02 6.42E-03 5.73E-03 8.3987E-02 8.92E-02 4.17E-03 -5.95E+04 3.73E-04 
25 tsw33 F012Fg80 -2.0564E+01 7.42E-01 1.62E-02 6.24E-03 5.75E-03 8.4814E-02 9.01E-02 6.26E-03 -2.71E+04 5.64E-04 
26 tsw33 F012Fg90 -1.9384E+01 1.34E+00 1.60E-02 6.06E-03 6.57E-03 3.7711E-03 1.03E-02 3.97E-03 -6.36E+05 4.10E-05 
27 tsw34 F0013g 3 -3.5168E+00 1.55E+00 1.49E-02 4.98E-03 5.61E-03 2.2281E-02 2.78E-02 1.13E-02 -1.73E+04 3.15E-04 
28 tsw34 F0013g48 -2.6890E+01 6.92E-01 2.27E-02 1.28E-02 1.16E-02 2.5815E-03 1.41E-02 1.16E-02 -1.13E+05 1.64E-04 
29 tsw34 F0013g91 -1.4310E+01 2.86E-01 1.95E-02 9.55E-03 6.78E-03 7.6241E-03 1.44E-02 8.94E-03 -3.18E+04 1.28E-04 
30 tsw34 F0013h 2 -9.6354E+00 1.91E+00 1.91E-02 9.17E-03 1.09E-02 7.8905E-03 1.87E-02 4.37E-03 -2.25E+05 8.19E-05 
Output-DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 G-5 September 2004 

Drift-Scale Radionuclide Transport 
A portion of the output for the fracture Peclet number is shown in Table G-3 for the mean 
infiltration scenario. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, p. 89) and DTN: 
LB0307FMRADTRN.001 for the complete output. 
The sequence of calculations is given here: 
Column A: Rock unit. 
Column B: Cell name. 
Column C: The adjusted fracture flux (qwf) as shown in Table G-2. 
Column D: Fracture half-spacing from Appendix A. 
Column E: Distance to fracture flow below drift from Appendix A. 
Column F: Effective diffusion coefficient in the fracture from Appendix F. 
Column G: Effective fracture velocity using Equation F-1. In Excel, this is 
Grn= Crn/(1+(-Crn*Ern/Frn)) 
Column H: Diffusive mass transfer coefficient for the invert from Appendix E. 
Column I: Fracture Peclet number computed using Equation F-2. In Excel, this is 
Irn= Grn*Drn/Hrn 
Table G-3. Fracture Peclet Number for the Mean Infiltration Scenario 
A B C D E F G H I 
1 
Rock 
Unit Cell Name qwf (mm/yr) hf (mm) .yf (mm) 
Def 
(mm2/yr) qfe (mm/yr) 
DeI 
(mm2/yr) Pefe 
2 tsw33 F012Bl76 -1.55E+04 1.26E+03 5.70E+02 3.31E+02 -5.81E-01 7.25E+02 -1.01E+00 
3 tsw33 F012Bl78 -3.11E+04 4.14E+03 4.88E+03 2.27E+03 -4.65E-01 1.53E+02 -1.26E+01 
4 tsw33 F012Cl72 -1.09E+04 4.60E+02 5.36E+02 6.23E+02 -1.16E+00 1.68E+02 -3.18E+00 
5 tsw33 F012Cl74 -3.59E+04 1.35E+03 1.59E+03 2.53E+03 -1.59E+00 2.18E+02 -9.90E+00 
6 tsw33 F012Cm70 -2.46E+05 1.84E+03 1.83E+03 4.63E+03 -2.53E+00 1.34E+02 -3.49E+01 
7 tsw33 F012Dg58 -4.07E+04 8.46E+02 1.27E+03 7.77E+02 -6.13E-01 3.58E+02 -1.45E+00 
8 tsw33 F012Dl68 -1.06E+05 4.10E+02 5.88E+02 1.12E+03 -1.91E+00 2.67E+02 -2.93E+00 
9 tsw33 F012Dl70 -4.49E+04 8.27E+02 1.18E+02 5.82E+01 -4.95E-01 2.41E+02 -1.70E+00 
10 tsw33 F012Dl71 -1.87E+05 5.00E+02 1.88E+01 3.80E+03 -2.02E+02 6.24E+02 -1.62E+02 
11 tsw33 F012Dl75 -4.36E+04 2.84E+03 5.37E+03 2.54E+03 -4.73E-01 2.93E+02 -4.60E+00 
12 tsw33 F012Dl77 -3.16E+04 4.09E+02 6.79E+02 2.80E+03 -4.12E+00 7.89E+01 -2.14E+01 
13 tsw33 F012Dl79 -2.88E+04 2.55E+03 3.22E+03 1.54E+03 -4.78E-01 2.94E+02 -4.16E+00 
14 tsw33 F012Ef89 -8.23E+04 3.36E+02 5.01E+02 2.82E+03 -5.62E+00 2.51E+02 -7.51E+00 
MDL-NBS-HS-000016 REV 01 G-6 September 2004 

Drift-Scale Radionuclide Transport 
Table G-3. Fracture Peclet Number for the Mean Infiltration Scenario (Continued) 
A B C D E F G H I 
Rock 
Unit Cell Name qwf (mm/yr) hf (mm) .yf (mm) 
Def 
(mm2/yr) qfe (mm/yr) 
DeI 
(mm2/yr) Pefe 
15 tsw33 F012Eg 2 -1.23E+05 1.10E+03 5.94E+02 6.67E+02 -1.12E+00 5.24E+02 -2.36E+00 
16 tsw33 F012Eg14 -1.62E+04 4.82E+02 5.22E+01 1.09E+03 -2.08E+01 2.94E+02 -3.40E+01 
17 tsw33 F012Eg25 -4.71E+04 7.49E+02 7.20E+02 3.05E+02 -4.24E-01 1.09E+02 -2.93E+00 
18 tsw33 F012Eg36 -6.44E+04 6.35E+02 4.83E+02 7.93E+02 -1.64E+00 5.51E+02 -1.89E+00 
19 tsw33 F012Eg47 -5.44E+03 1.60E+03 7.33E+02 8.73E+02 -1.19E+00 2.99E+02 -6.39E+00 
20 tsw33 F012Eh 1 -5.14E+04 1.49E+03 1.36E+03 1.58E+03 -1.16E+00 2.68E+02 -6.48E+00 
21 tsw33 F012El73 -3.89E+03 6.33E+02 7.25E+02 3.81E+03 -5.25E+00 4.10E+02 -8.11E+00 
22 tsw33 F012Fg26 -7.18E+04 1.79E+03 2.45E+03 1.29E+03 -5.25E-01 1.95E+02 -4.82E+00 
23 tsw33 F012Fg59 -3.20E+05 1.21E+03 3.60E+02 2.41E+03 -6.68E+00 5.38E+02 -1.51E+01 
24 tsw33 F012Fg70 -5.95E+04 1.94E+03 1.23E+03 3.09E+03 -2.51E+00 1.99E+02 -2.45E+01 
25 tsw33 F012Fg80 -2.71E+04 2.17E+02 2.59E+01 1.36E+03 -5.22E+01 4.94E+01 -2.30E+02 
26 tsw33 F012Fg90 -6.36E+05 1.23E+03 2.41E+03 3.28E+03 -1.36E+00 3.59E+02 -4.66E+00 
27 tsw34 F0013g 3 -1.73E+04 1.48E+02 2.91E+02 3.13E+01 -1.07E-01 5.14E+01 -3.10E-01 
28 tsw34 F0013g48 -1.13E+05 1.66E+02 1.45E+01 8.82E+01 -6.08E+00 4.09E+02 -2.47E+00 
29 tsw34 F0013g91 -3.18E+04 1.66E+02 8.55E+01 1.90E+03 -2.22E+01 1.47E+02 -2.50E+01 
30 tsw34 F0013h 2 -2.25E+05 1.85E+02 1.12E+02 6.04E+02 -5.38E+00 2.53E+02 -3.93E+00 
Output-DTN: LB0307FMRADTRN.001. 
The matrix Peclet number is computed using Equation 6-30 from the main text, which is 
h q 
Pe =mf (Eq. G-7) 
D
m 
eI 
An example of the sampling for the matrix Peclet number is shown in Table G-4. See Wang 
(2003 [DIRS 163234], SN-LBNL-SCI-236-V1, p. 91) for the file directory information 
containing the complete results. 
The sequence of calculations is as follows: 
Column A: Rock unit. 
Column B: Cell name. 
Column C: Matrix flux from Appendix B. 
Column D: Fracture half-spacing from Appendix A. 
Column E: Diffusive mass-transfer coefficient for the invert from Appendix V. 
MDL-NBS-HS-000016 REV 01 G-7 September 2004 

Drift-Scale Radionuclide Transport 
Column F: Matrix Peclet number computed using Equation G-7. In Excel, this is 
Frn= Crn*Drn/Ern 
Table G-4. Matrix Peclet Numbers for Mean Infiltration Scenario 
A B C D E F 
1 
Rock 
Unit Cell Name qm (mm/yr) hf (mm) 
DeI 
(mm2/yr) Pem 
2 tsw33 M012Bl76 -2.4032E-01 1.26E+03 7.25E+02 -4.18E-01 
3 tsw33 M012Bl78 -1.4520E-01 4.14E+03 1.53E+02 -3.93E+00 
4 tsw33 M012Cl72 -1.3236E+00 4.60E+02 1.68E+02 -3.63E+00 
5 tsw33 M012Cl74 -5.1798E-01 1.35E+03 2.18E+02 -3.22E+00 
6 tsw33 M012Cm70 -5.0937E-01 1.84E+03 1.34E+02 -7.02E+00 
7 tsw33 M012Dg58 -2.2577E-01 8.46E+02 3.58E+02 -5.34E-01 
8 tsw33 M012Dl68 -5.3696E-01 4.10E+02 2.67E+02 -8.25E-01 
9 tsw33 M012Dl70 -5.5948E-01 8.27E+02 2.41E+02 -1.92E+00 
10 tsw33 M012Dl71 -1.2656E+00 5.00E+02 6.24E+02 -1.01E+00 
11 tsw33 M012Dl75 -2.6302E-01 2.84E+03 2.93E+02 -2.55E+00 
12 tsw33 M012Dl77 -2.1155E-01 4.09E+02 7.89E+01 -1.10E+00 
13 tsw33 M012Dl79 -4.4544E-01 2.55E+03 2.94E+02 -3.87E+00 
14 tsw33 M012Ef89 -1.4086E-01 3.36E+02 2.51E+02 -1.88E-01 
15 tsw33 M012Eg 2 -1.1983E-01 1.10E+03 5.24E+02 -2.51E-01 
16 tsw33 M012Eg14 -5.8384E-02 4.82E+02 2.94E+02 -9.55E-02 
17 tsw33 M012Eg25 -5.3101E-02 7.49E+02 1.09E+02 -3.67E-01 
18 tsw33 M012Eg36 -1.1091E-01 6.35E+02 5.51E+02 -1.28E-01 
19 tsw33 M012Eg47 -1.6404E-01 1.60E+03 2.99E+02 -8.81E-01 
20 tsw33 M012Eh 1 -1.8512E-01 1.49E+03 2.68E+02 -1.03E+00 
21 tsw33 M012El73 -4.8153E-01 6.33E+02 4.10E+02 -7.44E-01 
22 tsw33 M012Fg26 -1.0880E-01 1.79E+03 1.95E+02 -9.99E-01 
23 tsw33 M012Fg59 -3.2473E-01 1.21E+03 5.38E+02 -7.32E-01 
24 tsw33 M012Fg70 -2.1330E-01 1.94E+03 1.99E+02 -2.08E+00 
25 tsw33 M012Fg80 -1.4723E-01 2.17E+02 4.94E+01 -6.47E-01 
26 tsw33 M012Fg90 -1.3500E-01 1.23E+03 3.59E+02 -4.61E-01 
27 tsw34 M0013g 3 -1.2727E-02 1.48E+02 5.14E+01 -3.67E-02 
28 tsw34 M0013g48 -1.5652E-02 1.66E+02 4.09E+02 -6.35E-03 
29 tsw34 M0013g91 -1.4594E-02 1.66E+02 1.47E+02 -1.65E-02 
30 tsw34 M0013h 2 -6.9779E-02 1.85E+02 2.53E+02 -5.10E-02 
Output-DTN: LB0307FMRADTRN.001. 
The dimensionless invert depth is computed from the invert depth, divided by the fracture 
half-spacing. The variation in the invert depth is sampled as a uniform random number between 
675 mm and 806 mm (see Figure 6-9). A portion of the output for the dimensionless invert 
depth is shown in Table G-5. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, p. 94) 
and DTN: LB0307FMRADTRN.001 for the complete output. 
MDL-NBS-HS-000016 REV 01 G-8 September 2004 

Drift-Scale Radionuclide Transport 
The sequence of calculations is as follows: 
Column A: Rock unit. 
Column B: Cell name. 
Column C: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. 
Column D: Generate random invert depth between 675 and 806 mm. In Excel, this is 
Drn= 675+(806-675)*Crn 
Column E: Fracture half-spacing from Appendix A. 
Column F: Dimensionless invert depth is computed from the ratio of the invert depth to the 
fracture half-spacing. In Excel, this is 
Frn= Drn/Ern 
Table G-5. Dimensionless Invert Depth (Independent of Infiltration Scenario) 
A B C D E F 
Fixed 
Uniform Invert 
1 
Rock 
Unit Cell Name 
Random 
Number 
Depth 
(mm) hf (mm) 
Dimensionless 
Invert Depth 
2 tsw33 F012Bl76 5.3041E-01 7.44E+02 1.26E+03 5.91E-01 
3 tsw33 F012Bl78 1.7330E-01 6.98E+02 4.14E+03 1.68E-01 
4 tsw33 F012Cl72 2.3364E-01 7.06E+02 4.60E+02 1.53E+00 
5 tsw33 F012Cl74 7.5332E-01 7.74E+02 1.35E+03 5.72E-01 
6 tsw33 F012Cm70 5.8412E-01 7.52E+02 1.84E+03 4.08E-01 
7 tsw33 F012Dg58 8.0829E-01 7.81E+02 8.46E+02 9.23E-01 
8 tsw33 F012Dl68 4.2416E-01 7.31E+02 4.10E+02 1.78E+00 
9 tsw33 F012Dl70 8.3845E-01 7.85E+02 8.27E+02 9.50E-01 
10 tsw33 F012Dl71 6.5790E-01 7.61E+02 5.00E+02 1.52E+00 
11 tsw33 F012Dl75 4.3296E-01 7.32E+02 2.84E+03 2.57E-01 
12 tsw33 F012Dl77 2.7310E-01 7.11E+02 4.09E+02 1.74E+00 
13 tsw33 F012Dl79 3.7391E-01 7.24E+02 2.55E+03 2.83E-01 
14 tsw33 F012Ef89 3.6039E-01 7.22E+02 3.36E+02 2.15E+00 
15 tsw33 F012Eg 2 6.4304E-01 7.59E+02 1.10E+03 6.91E-01 
16 tsw33 F012Eg14 5.1883E-01 7.43E+02 4.82E+02 1.54E+00 
17 tsw33 F012Eg25 6.3216E-01 7.58E+02 7.49E+02 1.01E+00 
18 tsw33 F012Eg36 6.1548E-01 7.56E+02 6.35E+02 1.19E+00 
19 tsw33 F012Eg47 8.8158E-01 7.90E+02 1.60E+03 4.93E-01 
MDL-NBS-HS-000016 REV 01 G-9 September 2004 

Drift-Scale Radionuclide Transport 
Table G-5. Dimensionless Invert Depth (Independent of Infiltration Scenario 
(Continued) 
A B C D E F 
Fixed 
Uniform Invert 
Rock 
Unit Cell Name 
Random 
Number 
Depth 
(mm) hf (mm) 
Dimensionless 
Invert Depth 
20 tsw33 F012Eh 1 1.8140E-01 6.99E+02 1.49E+03 4.68E-01 
21 tsw33 F012El73 7.6937E-01 7.76E+02 6.33E+02 1.23E+00 
22 tsw33 F012Fg26 2.3021E-01 7.05E+02 1.79E+03 3.94E-01 
23 tsw33 F012Fg59 1.1181E-01 6.90E+02 1.21E+03 5.69E-01 
24 tsw33 F012Fg70 3.0337E-01 7.15E+02 1.94E+03 3.68E-01 
25 tsw33 F012Fg80 6.3025E-01 7.58E+02 2.17E+02 3.49E+00 
26 tsw33 F012Fg90 9.3048E-01 7.97E+02 1.23E+03 6.50E-01 
27 tsw34 F0013g 3 4.4532E-01 7.33E+02 1.48E+02 4.94E+00 
28 tsw34 F0013g48 6.5840E-01 7.61E+02 1.66E+02 4.58E+00 
29 tsw34 F0013g91 3.3859E-01 7.19E+02 1.66E+02 4.34E+00 
30 tsw34 F0013h 2 5.0435E-01 7.41E+02 1.85E+02 4.01E+00 
Output-DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 G-10 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX H 
SAMPLING FOR THE PARAMETER SETS USED IN THE CALCULATION OF 
FRACTURE-MATRIX RADIONUCLIDE FLUX DISTRIBUTIONS FROM WASTE 
EMPLACEMENT DRIFTS 
MDL-NBS-HS-000016 REV 01 September 2004 

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MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
SAMPLING FOR THE PARAMETER SETS USED IN THE CALCULATION OF 
FRACTURE-MATRIX RADIONUCLIDE FLUX DISTRIBUTIONS FROM WASTE 
EMPLACEMENT DRIFTS 
This appendix provides additional information pertaining to Sections 6.4.6 and 6.5 of the main 
text. Each case investigated for the calculation of the radionuclide fracture-matrix flux fraction, 
for radionuclide transport from the waste emplacement drift invert into the rock, requires four 
dimensionless parameters. These were the parameters given at the end of Section 6.4.2; they are 
repeated here: 
Pe= matrix  invert mass transfer Peclet number 
m 
Pe
fe = fracture  invert mass transfer Peclet number 
.
f = fracture water content 
y
dm = dimensionless invert depth 
The design information in Table 4-9 (BSC 2004 [DIRS 168370], 800-IED-WIS0-00103-000-
00A) may be used to compute the percentage of total waste-emplacement drift area in each of the 
four rock units (tsw33, tsw34, tsw35, and tsw36). Note that in the IED geologic 
lithostratigraphic units are used. The correspondence between these units the UZ flow model 
units are as follows: the tptpul is the tsw33, the tptpmn in the tsw34, the tptpll is the tsw35, and 
the tptpln is the tsw36. The total percentage of waste emplacement in each of the four rock units 
is shown in Table H-1: 
Table H-1. Percentage of Waste Emplacement in Each Rock Unit 
Total 
Drift Area Drift Area Drift Area Drift Area Drift Area Drift Area 
(m2) %tsw33 %tsw34 %tsw35 %tsw36 tsw33 (m2) tsw34 (m2) tsw35 (m2) tsw36 (m2) (m2) 
Panel 1 298850 0 40 60 0 0 119172 179678 0 
Panel 2 1477867 0 5 91 4 0 80213 1341147 56507 
Panel 3 1862136 12 22 66 0 224398 416618 1221120 0 
Panel 4 1344299 0 0 95 5 0 0 1271323 72976 
224398 616003 4013268 129483 4983152 
Overall Fractions = 4.5% 12.4% 80.5% 2.6% 
Source: Table 4-9. 
The percentages are rounded to the nearest percent, except for tsw33, which is truncated to 4 
percent such that the total is 100 percent. For a total of 24 samples, this leads to the following 
expected number of samples in each rock unit as given in Table H-2: 
MDL-NBS-HS-000016 REV 01 H-1 September 2004 

Drift-Scale Radionuclide Transport 
Table H-2. Number of Samples in Each Rock Unit 
Number of 
Rock unit 
samples in each 
rock unit 
Tsw33 1 
Tsw34 3 
Tsw35 19 
Tsw36 1 
Random sampling for each of these dimensionless parameters at every model grid across a 
laterally continuous section through the repository horizon is presented in Appendix G. These 
parameters are assembled and sampled to provide the cases computed for fracture-matrix release 
fractions. The sampling selects 24 random parameter sets from each infiltration scenario. To 
ensure sampling from all host rock units, one random sample is drawn from each of the tsw33 
and tsw36, three random samples from the tsw34, and 19 random samples from the tsw35. The 
Peclet numbers and fracture water film thicknesses selected here are used as inputs for the 
calculations performed in Section 6.5. A portion of the output for the sampled values are given 
in Table H-3. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, p. 100) and 
DTN: LB0307FMRADTRN.001 for the complete output. 
The sequence of calculations is given here: 
Column A: Rock unit. 
Column B: Fracture cell name. 
Column C: Matrix cell name. 
Column D: Fracture Peclet number from Appendix G. 
Column E: Matrix Peclet number from Appendix G. 
Column F: Fracture water content from Appendix G. 
Column G: Dimensionless invert depth from Appendix G. 
Column H: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. 
Column I: Convert cumulative probability in Column H to an integer between 1 and 25 for the 
tsw33, between 26 and 95 for the tsw34, between 96 and 428 for the tsw35 and between 429 and 
433 for the tsw36. In Excel, this is 
Irn= INT(1+25*Hrn) for the tsw33 in row 2 
Irn= INT(26+95*Hrn) for the tsw34 in rows 3, 4, and 5 
MDL-NBS-HS-000016 REV 01 H-2 September 2004 

Drift-Scale Radionuclide Transport 
Irn= INT(96+428*Hrn) for the tsw35 in rows 6 through 24 
Irn= INT(429+433*Hrn) for the tsw36 in row 25 
Column J: Find selected rock type from Column A. In Excel, this is 
Jrn= INDEX(A$2:A$434,$Irn) 
Column K: Find selected Fracture Peclet number from Column D. In Excel, this is 
Krn= INDEX(D$2:D$434,$Irn) 
Column L: Find selected Matrix Peclet number from Column E. In Excel, this is 
Lrn= INDEX(E$2:E$434,$Irn) 
Column M: Find selected fracture water content from Column F. In Excel, this is 
Mrn= INDEX(F$2:F$434,$Irn) 
Column N: Find selected dimensionless invert depth from Column G. In Excel, this is 
Nrn= INDEX(G$2:G$434,$Irn) 
Values selected in columns K, L, and M are used as input for the calculations discussed in 
Section 6.5. 
MDL-NBS-HS-000016 REV 01 H-3 September 2004 

Drift-Scale Radionuclide Transport 
Table H-3. Sampled Parameter Sets for Mean Infiltration Scenarios 
A B C D E F G H I J K L M N O 
1 
Rock 
Unit 
Fracture 
Cell Name 
Matrix Cell 
Name 
Fracture 
Peclet 
Number, 
Peef 
Matrix 
Peclet 
Number, 
Pem 
Fracture 
Water 
Content, 
.f 
Dimensionless 
Invert Depth, 
ydm 
Fixed 
Uniform 
Random 
Number 
Uniform 
Random 
Integer 
ranging 
over cells 
in each 
rock unit 
Selected 
Rock 
Type 
Selected 
Fracture 
Peclet 
Number, 
Pefe 
Selected 
Matrix 
Peclet 
Number, 
Pem 
Selected 
Fracture 
Water 
Content, 
.f 
Selected 
Dimensionless 
Invert Depth, 
ydm 
Case 
Number 
2 tsw33 F012Bl76 M012Bl76 -1.01E+00 -4.18E-01 5.12E-04 5.91E-01 3.2628E-01 9 tsw33 -1.62E+02 -1.01E+00 3.58E-05 1.52E+00 1 
3 tsw33 F012Bl78 M012Bl78 -1.26E+01 -3.93E+00 3.89E-04 1.68E-01 9.4126E-01 91 tsw34 -4.05E+01 -2.62E-02 4.27E-04 3.62E+00 2 
4 tsw33 F012Cl72 M012Cl72 -3.18E+00 -3.63E+00 3.77E-04 1.53E+00 5.0552E-01 61 tsw34 -2.87E+00 -5.99E-03 4.18E-04 8.14E+00 3 
5 tsw33 F012Cl74 M012Cl74 -9.90E+00 -3.22E+00 1.91E-04 5.72E-01 5.7828E-01 66 tsw34 -2.45E+00 -4.48E-03 6.15E-05 7.78E+00 4 
6 tsw33 F012Cm70 M012Cm70 -3.49E+01 -7.02E+00 2.36E-05 4.08E-01 5.8022E-01 289 tsw35 -4.37E+01 -1.90E-02 5.84E-04 3.91E+00 5 
7 tsw33 F012Dg58 M012Dg58 -1.45E+00 -5.34E-01 1.09E-04 9.23E-01 5.2025E-01 269 tsw35 -6.49E+00 -1.33E-02 2.23E-04 5.38E+00 6 
8 tsw33 F012Dl68 M012Dl68 -2.93E+00 -8.25E-01 4.52E-05 1.78E+00 6.5149E-01 312 tsw35 -1.47E+00 -3.96E-02 4.51E-05 1.17E+00 7 
9 tsw33 F012Dl70 M012Dl70 -1.70E+00 -1.92E+00 1.41E-04 9.50E-01 8.8356E-01 390 tsw35 -8.82E-01 -2.00E-02 7.78E-05 1.92E+00 8 
10 tsw33 F012Dl71 M012Dl71 -1.62E+02 -1.01E+00 3.58E-05 1.52E+00 3.2712E-01 204 tsw35 -2.29E+01 -6.15E-02 1.57E-04 1.59E+00 9 
11 tsw33 F012Dl75 M012Dl75 -4.60E+00 -2.55E+00 1.91E-04 2.57E-01 9.5806E-01 415 tsw35 -8.53E+00 -3.56E-02 5.23E-05 1.68E+00 10 
12 tsw33 F012Dl77 M012Dl77 -2.14E+01 -1.10E+00 2.86E-05 1.74E+00 4.3343E-01 240 tsw35 -1.66E+00 -5.90E-03 5.62E-05 6.82E+00 11 
13 tsw33 F012Dl79 M012Dl79 -4.16E+00 -3.87E+00 3.90E-04 2.83E-01 5.3805E-01 275 tsw35 -2.63E+00 -6.72E-03 9.60E-04 5.35E+00 12 
14 tsw33 F012Ef89 M012Ef89 -7.51E+00 -1.88E-01 2.44E-04 2.15E+00 8.3590E-01 374 tsw35 -4.99E+00 -1.13E-02 1.19E-04 1.69E+00 13 
15 tsw33 F012Eg 2 M012Eg 2 -2.36E+00 -2.51E-01 9.75E-05 6.91E-01 5.9247E-01 293 tsw35 -1.20E+02 -7.27E-03 7.44E-05 3.62E+00 14 
16 tsw33 F012Eg14 M012Eg14 -3.40E+01 -9.55E-02 2.41E-04 1.54E+00 4.0651E-01 231 tsw35 -9.89E-01 -3.08E-02 4.39E-04 2.17E+00 15 
17 tsw33 F012Eg25 M012Eg25 -2.93E+00 -3.67E-01 5.32E-05 1.01E+00 3.3043E-01 206 tsw35 -1.95E+00 -1.85E-02 1.10E-04 1.08E+00 16 
18 tsw33 F012Eg36 M012Eg36 -1.89E+00 -1.28E-01 6.43E-05 1.19E+00 4.4509E-02 110 tsw35 -3.46E+01 -7.85E-03 6.74E-04 3.32E+00 17 
19 tsw33 F012Eg47 M012Eg47 -6.39E+00 -8.81E-01 3.25E-04 4.93E-01 5.7180E-01 286 tsw35 -3.34E+00 -2.03E-02 5.61E-05 2.99E+00 18 
20 tsw33 F012Eh 1 M012Eh 1 -6.48E+00 -1.03E+00 7.84E-05 4.68E-01 8.5478E-01 380 tsw35 -2.09E-01 -9.65E-03 1.17E-04 2.36E+00 19 
21 tsw33 F012El73 M012El73 -8.11E+00 -7.44E-01 1.82E-04 1.23E+00 2.3670E-01 174 tsw35 -4.59E+00 -2.77E-02 6.28E-05 1.33E+00 20 
22 tsw33 F012Fg26 M012Fg26 -4.82E+00 -9.99E-01 7.02E-05 3.94E-01 6.6134E-01 316 tsw35 -1.14E+01 -8.15E-03 6.06E-04 5.43E+00 21 
23 tsw33 F012Fg59 M012Fg59 -1.51E+01 -7.32E-01 5.13E-05 5.69E-01 2.3843E-01 175 tsw35 -3.26E+00 -7.18E-03 8.70E-05 4.54E+00 22 
24 tsw33 F012Fg70 M012Fg70 -2.45E+01 -2.08E+00 3.73E-04 3.68E-01 8.1817E-01 368 tsw35 -6.11E+00 -6.35E-02 1.29E-04 9.09E-01 23 
25 tsw33 F012Fg80 M012Fg80 -2.30E+02 -6.47E-01 5.64E-04 3.49E+00 4.2699E-01 431 tsw36 -7.60E+00 -1.16E-02 1.28E-04 3.65E+00 24 
26 tsw33 F012Fg90 M012Fg90 -4.66E+00 -4.61E-01 4.10E-05 6.50E-01 
27 tsw34 F0013g 3 M0013g 3 -3.10E-01 -3.67E-02 3.15E-04 4.94E+00 
28 tsw34 F0013g48 M0013g48 -2.47E+00 -6.35E-03 1.64E-04 4.58E+00 
29 tsw34 F0013g91 M0013g91 -2.50E+01 -1.65E-02 1.28E-04 4.34E+00 
30 tsw34 F0013h 2 M0013h 2 -3.93E+00 -5.10E-02 8.19E-05 4.01E+00 
Output-DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 H-4 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX I 
DISTRIBUTIONS FOR MATRIX DIFFUSION AND MEASURED MATRIX 
DIFFUSION COEFFICIENTS 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
DISTRIBUTIONS FOR MATRIX DIFFUSION AND MEASURED MATRIX 
DIFFUSION COEFFICIENTS 
This appendix provides additional information pertaining to Section 6.4.5 of the main 
text. Anion and cation distributions for matrix diffusion coefficients are sampled from a beta 
distribution, using the distribution statistics shown here: 
Table I-1. Matrix Diffusion Distributions 
Solute Min (m2/s) Max (m2/s) Mean (m2/s) Std Dev (m2/s) 
Distribution 
Type 
Anions 0 1.0 E-9 3.2 E-11 1.0 E-11 Beta 
Cations 0 1.0 E-9 1.6 E-10 0.5 E-10 Beta 
DTN: LA0003JC831362.001 [DIRS 149557]. 
The distributions are generated by sampling 1,000 values from each beta distribution. The 
sampling for the beta distribution uses the approximation for the inverse as given in 
Equation 26.5.22 of Abramowitz and Stegun (1972 [DIRS 103280]). This method requires the 
generation of a Gaussian random number. Gaussian random numbers are computed using the 
rational approximation for the inverse cumulative probability distribution for a Gaussian random 
variable, as given in Equation 26.2.23 of Abramowitz and Stegun (1972 [DIRS 103280]). See 
Scientific Notebook by Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, pp. 4042) for a 
discussion of the generation of Gaussian random numbers. A portion of the output with the 
results for anions are given in Table I-2. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-
V1, p. 75) and Output-DTN: LB0307FMRADTRN.001 for the complete output. The sequence 
of calculations is given here: 
Column A: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. These are the cumulative probabilities, p . 
Column B: The normalized Gaussian random number corresponding to the cumulative 
probability in Column A. 
Column C: The parameter . in the beta inverse function is given by Abramowitz and Stegun 
(1972 [DIRS 103280], Equation 26.5.22) 
2 -
.= 
yp 3 
(Eq. I-1) 
6 
where yp is defined in Column B. In Excel, this is 
Crn=(Brn^2-3)/6 
MDL-NBS-HS-000016 REV 01 I-1 September 2004 

Drift-Scale Radionuclide Transport 
Column D: The parameter w in the beta inverse function is given by Abramowitz and Stegun 
(1972 [DIRS 103280], Equation 26.5.22) 
1 
=
y 
p
(
)
.
+
h 
1 
1 
5 
2
-
..
1
..
..
+
.
..
(Eq. I-2) 
2 
-
-
w 
h 
2b
-
1 
2 
6 
3h
a
-
In Excel, this is 
Drn= (Brn*(($K$2+Crn)^0.5)/$K$2)-((2*$J$2-1)^(-1)-(2*$I$2-1)^(-1))*(Crn+(5/6)-2/(3*$K$2)) 
Column E: The beta random number, xp, is given by Abramowitz and Stegun (1972 
[DIRS 103280], Equation 26.5.22) 
a 
(Eq. I-3) 
2

x 
p 
be 
w
a
+
In Excel, this is 
Ern=$I$2/($I$2+$J$2*EXP(2*Drn)) 
Column F: Contains the ordered values computed in Column E. 
Column G: Contains the value of the mean matrix diffusion coefficient, , from Table- I-1. 
Dm 
Column H: Contains the value of the matrix diffusion coefficient standard deviation, , from
sDm 
Table I-1. 
Column I: The beta distribution parameter a is derived from Abramowitz and Stegun (1972 
[DIRS 103280], Equation 26.1.33) (for detailed derivation, see Appendix K) 
..
. 
)
1 
-
(
s 
1 
2 
.
.

Dm

Dm
- 
(Eq. I-4) 
...
a
=

Dm 
Dm 
In Excel, this is 
I2=G2*((G2*(1-G2)/H2^2)-1) 
Column J: The beta distribution parameter b is derived from Abramowitz and Stegun (1972 
[DIRS 103280], Equation 26.1.33) (for detailed derivation, see Appendix K) 
..
. 
)
1 
-
(
s 
1 
2 
.
.

Dm

Dm
b
=
-
(
1

Dm 
..
. 
)
- 
(Eq. I-5) 
Dm 
MDL-NBS-HS-000016 REV 01 I-2 September 2004 

Drift-Scale Radionuclide Transport 
In Excel, this is 
J2=(1-G2)*((G2*(1-G2)/H2^2)-1) 
Column K: The parameter h in the beta inverse function is given by Abramowitz and Stegun 
(1972 [DIRS 103280], Equation 26.5.22) 
1 .-1
. 1
h= 2.+. (Eq. I-6) 
. 2a - 12b - 1. 
In Excel, this is 
K2=2*((2*I2-1)^(-1)+(2*J2-1)^(-1))^(-1) 
The Reimus et al. (2002 [DIRS 163008]) correlation is sampled according to the scheme outlined 
in Section 6.4.5 and Equations 6-52 through 6-56, which are shown here: 
log(D )=-49.3 + 38.1 .+ log 165.0 (k ) (Eq. I-7) 
m mw 
.
X = log..
. D0 
.. (Eq. I-8) 
. Dm. 

= log(D )- log(D ) (Eq. I-9) 
X 0 m 
Y =ln(X ) (Eq. I-10) 
=ln( ) (Eq. I-11) 
YX 
Here, D0 is a limiting value of Dm taken to be 10-9 m2/s (see Table I-1). The sampling follows a 
lognormal distribution scheme for the variable X, in which the variable Y in Equation I-10 is 
normally distributed. This sampled variable is reduced to the matrix diffusion coefficient using 
Equations I-8 and I-10. Gaussian random numbers are computed using the rational 
approximation for the inverse cumulative probability distribution for a Gaussian random variable 
as given in Equation 26.2.23 of Abramowitz and Stegun (1972 [DIRS 103280]). See Scientific 
Notebook by Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, pp. 4042) for a discussion 
of the generation of Gaussian random numbers. A portion of the output is shown in 
Table I-3. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, p. 76) and 
DTN: LB0307FMRADTRN.001 for the complete output. 
MDL-NBS-HS-000016 REV 01 I-3 September 2004 

Drift-Scale Radionuclide Transport 
Table I-2. Anion Matrix Diffusion Coefficient Distribution 
A B C D E F G H I J K 
1 
Fixed 
Uniform 
Random 
Number 
(P) 
yP normalized 
Gaussian 
random 
number Lambda w 
xP -Beta 
random 
number 
(Dm, m2/s) 
Ordered 
Distribution 
(Dm, m2/s) 
Mean Dm - 
m2/s 
Standard 
deviation 
Dm m2/s a b h 
2 5.7681E-01 1.9336E-01 -4.94E-01 4.73E-02 2.91E-11 9.49E-12 3.20E-11 1.00E-11 1.02E+01 3.20E+11 3.90E+01 
3 1.5444E-02 -2.1589E+00 2.77E-01 -2.91E-01 5.73E-11 9.78E-12 
4 8.9037E-01 1.2287E+00 -2.48E-01 2.25E-01 2.04E-11 1.23E-11 
5 5.6024E-01 1.5127E-01 -4.96E-01 4.05E-02 2.95E-11 1.32E-11 
6 3.7359E-01 -3.2192E-01 -4.83E-01 -3.41E-02 3.43E-11 1.33E-11 
7 2.4730E-01 -6.8273E-01 -4.22E-01 -8.86E-02 3.82E-11 1.34E-11 
8 9.0546E-01 1.3135E+00 -2.12E-01 2.41E-01 1.98E-11 1.35E-11 
9 7.0270E-01 5.3178E-01 -4.53E-01 1.03E-01 2.60E-11 1.37E-11 
10 4.1033E-01 -2.2629E-01 -4.91E-01 -1.94E-02 3.33E-11 1.41E-11 
11 1.0581E-01 -1.2493E+00 -2.40E-01 -1.70E-01 4.50E-11 1.42E-11 
12 3.9859E-01 -2.5657E-01 -4.89E-01 -2.41E-02 3.36E-11 1.49E-11 
13 8.0209E-01 8.4894E-01 -3.80E-01 1.58E-01 2.33E-11 1.49E-11 
14 5.1719E-01 4.2995E-02 -5.00E-01 2.31E-02 3.06E-11 1.49E-11 
15 5.6921E-01 1.7402E-01 -4.95E-01 4.42E-02 2.93E-11 1.50E-11 
16 4.4208E-01 -1.4540E-01 -4.96E-01 -6.73E-03 3.24E-11 1.52E-11 
17 8.4520E-01 1.0160E+00 -3.28E-01 1.87E-01 2.20E-11 1.53E-11 
18 9.3388E-01 1.5056E+00 -1.22E-01 2.76E-01 1.84E-11 1.53E-11 
19 8.3627E-01 9.7919E-01 -3.40E-01 1.81E-01 2.23E-11 1.53E-11 
20 2.0787E-01 -8.1365E-01 -3.90E-01 -1.08E-01 3.97E-11 1.54E-11 
21 6.9208E-01 5.0136E-01 -4.58E-01 9.82E-02 2.63E-11 1.57E-11 
22 5.2997E-01 7.5015E-02 -4.99E-01 2.82E-02 3.02E-11 1.57E-11 
23 8.1050E-02 -1.3983E+00 -1.74E-01 -1.91E-01 4.68E-11 1.58E-11 
24 2.0226E-01 -8.3341E-01 -3.84E-01 -1.11E-01 3.99E-11 1.58E-11 
25 6.0195E-01 2.5798E-01 -4.89E-01 5.79E-02 2.85E-11 1.59E-11 
26 9.4478E-01 1.5966E+00 -7.52E-02 2.94E-01 1.78E-11 1.61E-11 
27 9.0122E-01 1.2887E+00 -2.23E-01 2.36E-01 1.99E-11 1.61E-11 
28 6.8250E-02 -1.4892E+00 -1.30E-01 -2.03E-01 4.80E-11 1.62E-11 
29 4.9429E-01 -1.4281E-02 -5.00E-01 1.40E-02 3.11E-11 1.63E-11 
30 5.9879E-01 2.4979E-01 -4.90E-01 5.65E-02 2.86E-11 1.63E-11 
Output-DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 I-4 September 2004 

Drift-Scale Radionuclide Transport 
The sequence of calculations is as follows: 
Column A: Uniform random numbers generated by the Excel spreadsheet function RAND() and 
saved. These are the cumulative probabilities, p. 
Column B: The normalized Gaussian random number corresponding to the cumulative 
probability in Column A. 
Column C: The corresponding random value of Y is derived from the normalized Gaussian 
random variable through the normalization definition: 
f =xpsY + (Eq. I-12) 
Y 
In Excel, this is 
Crn=Brn*$I$2+$H$2 
where Y 
and sY are defined as discussed below. 
Column D: This column calculates the fracture frequency through the inverse of (Eq. I-11) 
X =exp(Y ) (Eq. I-13) 
In Excel, this is 
Drn=exp(Crn) 
Column E: The matrix diffusion coefficient is obtained from a known value of X using 
Equation I-8. In Excel, this is 
Ern=10^(-Drn-9) (Eq. I-14) 
Column F: The cumulative probability based on rank. In Excel, this is 
Frn=F(rn-1)+$F$2 
and 
F1=1/1001 
Column G: The values from Column E in ascending order. 
Column H: Contains the value of Y 
(see below). 
Column I: Contains the value of sY (see below). 
MDL-NBS-HS-000016 REV 01 I-5 September 2004 

Drift-Scale Radionuclide Transport 
The mean value for the case shown in Figure 6-22 is equal to the log(Dm), which is equal to the 
logarithm of the square root of the product of the mean values from Table I-1. The standard 
deviation is then adjusted to provide a distribution with a spread representative of the anion and 
cation curves shown in Figure 6-22. The mean value for Y is then computed from Equations I-9 
and I-11. The high and low cases shown in Figure 6-23 are computed using mean values for 
log( Dm) computed from Equation I-7, using the 5th and 95th percentile matrix water content and 
matrix effective permeability computed in the mean infiltration scenario from Appendix F and 
converting to m2/s. The data shown in Figure 6-24 are from DTN: LA0003JC831362.001 
[DIRS 149557] and from Reimus et al. (2002 [DIRS 163008]). Both data sets contain values of 
Dm for pertechnetate (technetium) and tritium. Data for bicarbonate diffusion come from Reimus 
et al. (2002 [DIRS 163008]). These data are combined and ordered to generate a cumulative 
probability distribution, where the cumulative probability is defined by the order number of the 
sequence divided by the number of samples plus 1. 
MDL-NBS-HS-000016 REV 01 I-6 September 2004 

Drift-Scale Radionuclide Transport 
Table I-3. Matrix Diffusion Coefficient Distribution using Reimus et al. (2002 [DIRS 163008]) Correlation 
A B C D E F G H I 
1 
Fixed 
Uniform 
Random 
Number 
(P) 
xP -
normalized 
Gaussian 
random 
number 
x -
Gaussian 
random 
number 
Transformation 
to -
9-logDm 
Transformation 
to Dm 
Cumulative 
Probability 
Ordered Dm 
for Reimus 
mean high 
Transformed 
mean 
Standard 
deviation 
2 5.3281E-01 8.2139E-02 2.79E-01 1.32E+00 4.76E-11 9.99E-04 7.89E-13 2.54E-01 3.00E-01 
3 4.6699E-01 -8.2631E-02 2.30E-01 1.26E+00 5.52E-11 2.00E-03 1.04E-12 
4 3.3136E-01 -4.3574E-01 1.24E-01 1.13E+00 7.38E-11 3.00E-03 1.34E-12 
5 9.3271E-01 1.4966E+00 7.03E-01 2.02E+00 9.53E-12 4.00E-03 1.42E-12 
6 6.3809E-01 3.5292E-01 3.60E-01 1.43E+00 3.68E-11 5.00E-03 1.61E-12 
7 8.6930E-01 1.1232E+00 5.91E-01 1.81E+00 1.56E-11 5.99E-03 1.63E-12 
8 4.5888E-01 -1.0301E-01 2.24E-01 1.25E+00 5.62E-11 6.99E-03 2.00E-12 
9 2.0184E-01 -8.3491E-01 4.02E-03 1.00E+00 9.91E-11 7.99E-03 2.09E-12 
10 8.4635E-01 1.0209E+00 5.61E-01 1.75E+00 1.77E-11 8.99E-03 2.42E-12 
11 5.7322E-01 1.8423E-01 3.10E-01 1.36E+00 4.33E-11 9.99E-03 2.43E-12 
12 3.3340E-01 -4.3010E-01 1.25E-01 1.13E+00 7.35E-11 1.10E-02 2.66E-12 
13 1.2658E-01 -1.1428E+00 -8.84E-02 9.15E-01 1.21E-10 1.20E-02 2.76E-12 
14 9.0245E-01 1.2958E+00 6.43E-01 1.90E+00 1.25E-11 1.30E-02 2.76E-12 
15 6.4196E-01 3.6326E-01 3.63E-01 1.44E+00 3.64E-11 1.40E-02 3.14E-12 
16 9.9078E-01 2.3570E+00 9.62E-01 2.62E+00 2.42E-12 1.50E-02 3.23E-12 
17 5.1764E-01 4.4122E-02 2.68E-01 1.31E+00 4.93E-11 1.60E-02 4.08E-12 
18 9.3863E-01 1.5437E+00 7.18E-01 2.05E+00 8.92E-12 1.70E-02 4.20E-12 
19 7.0570E-01 5.4049E-01 4.17E-01 1.52E+00 3.04E-11 1.80E-02 4.33E-12 
20 6.8929E-01 4.9342E-01 4.03E-01 1.50E+00 3.19E-11 1.90E-02 4.88E-12 
21 2.9941E-01 -5.2571E-01 9.68E-02 1.10E+00 7.91E-11 2.00E-02 4.97E-12 
22 4.4436E-01 -1.3961E-01 2.13E-01 1.24E+00 5.80E-11 2.10E-02 5.04E-12 
23 7.3649E-04 -3.1802E+00 -7.00E-01 4.97E-01 3.19E-10 2.20E-02 5.11E-12 
24 8.9592E-01 1.2588E+00 6.32E-01 1.88E+00 1.31E-11 2.30E-02 5.11E-12 
25 3.2285E-01 -4.5932E-01 1.17E-01 1.12E+00 7.52E-11 2.40E-02 5.20E-12 
26 7.2163E-01 5.8732E-01 4.31E-01 1.54E+00 2.90E-11 2.50E-02 5.45E-12 
27 9.9740E-01 2.7953E+00 1.09E+00 2.98E+00 1.04E-12 2.60E-02 5.50E-12 
28 6.8463E-01 4.8028E-01 3.99E-01 1.49E+00 3.24E-11 2.70E-02 5.52E-12 
29 7.1169E-01 5.5794E-01 4.22E-01 1.52E+00 2.99E-11 2.80E-02 5.89E-12 
30 7.9956E-01 8.3989E-01 5.06E-01 1.66E+00 2.19E-11 2.90E-02 6.01E-12 
Output-DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 I-7 September 2004 

Drift-Scale Radionuclide Transport 
INTENTIONALLY LEFT BLANK 
MDL-NBS-HS-000016 REV 01 I-8 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX J 
EXAMPLE OF CALCULATION FOR FRACTURE-MATRIX PARTITIONING 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
EXAMPLE OF CALCULATION FOR FRACTURE-MATRIX PARTITIONING 
This appendix provides additional information pertaining to Section 6.4.4 of the main text. The 
calculation tool used to solve Equations 40 through 44 is Mathcad V11. The implementation of 
Mathcad for nominal cases 1 with 1,024 points is given on the following pages. 
MDL-NBS-HS-000016 REV 01 J-1 September 2004 

Drift-Scale Radionuclide Transport 
NOMINAL CASE 1 - 1024 
Values used for calculation 
Pefe - := 1Pefe is the fracture Peclet number 
Pe m 0.004- := Pem is the matrix Peclet number 
. f := 0.0001 .f is the fracture water content 
ydm := 4.00 ydm is the dimensionless invert thickness 
b d := . f bd is the dimensionless fracture water thickness 
jmax := 1023 jmax+1 is the number of Fourier coefficients 
Distance coordinate along drift wall 
i := 0.. ji is reference number for the coordinates along the drift wall 
max 
j := 0.. jj is the reference number for the Fourier coefficients 
max
i
:=
xdi jxdi is the dimensionless distance along the drift wall 
max 
Sample values for verification of xdi 
- 4 - 3 
xd0 
= 0 xd1 
= 9.775 10 xd2 
= 1.955 10 ..... xd1022 
= 0.999 
xd1023 
= 1 
MDL-NBS-HS-000016 REV 01 J-2 September 2004 

Drift-Scale Radionuclide Transport 
Solution for Fourier coefficients 
qdi 
:= Pefe + 0.5 Pem - Pefe).F. xdi 
- bd . -F. bd - xdi 
.+ 1. Eq. (29), (30), (31) from main 
( ...... 
qdi is the dimensionless 
Note that the Heaviside step function water flux profile at the 
(F) is defined to be 1 at x=0. Therefore, 
invert-rock interface 
the combination of step functions, 
0.5(F(x)-F(-x)+1), is needed to make 
qdi = 0.5*(Pefe+Pem) at xdi=bd 
Sample values for verification of qd 
- 3 - 3 - 3 - 3 
qd0 
- = 1qd1 
=-4 10 qd2 
=-4 10 .... qd1022 
=-4 10 qd1023 
=-4 10 
Mij:= F(). 1 - ymdqdi 
.+F(j1)cos . jp  xdi 
.. jp  - qdi 
tanh ymdp). 
,-j 
.
- ( j
. Eq. (36) from main 
. ... 
Mi,j is the coefficient 
matrix for A 
Sample values for verification of Mi,j 
33 
= 5 M01= 4.142 ,= 3.212 10M0 1023 = 3.215 10
M00, .... M0 1022 ,
, 
33 
= 1.016 M11= 3.146 , =-3.211 10M1 1023 =-3.214 10
M10, .... M1 1022 ,
, 
33 
= 1.016 M21= 3.146 ,= 3.211 10M2 1023 = 3.214 10
M20, .... M2 1022 ,
, 
.. 
. =-1.134 103 
.
M511 511 
. ,
.
33 
= 1.016 M1022 1 - = 3.146.... , =-3.211 10= 3.214 10
M1022 0 , M1022 1022 M1022 1023 
,, 
33 
= 1.016 M1023 1 - = 3.146.... ,= 3.211 10=-3.214 10
M1023 0 , M1023 1022 M1023 1023 
,, 
MDL-NBS-HS-000016 REV 01 J-3 September 2004 

Drift-Scale Radionuclide Transport 
A := M- 1 qd From Eq. (35) in main A is the vector of 
Fourier coefficients 
Verification of matrix solution for Fourier coefficients, A. 
CheckA is a vector of the residuals for M*A-qd 
CheckA := M A - qd
 
Plot of residuals for M*A-qd 
0 200 400 600 800 1000 12005 .10 15 
0 
5 .10 15 
1 .10 14 
CheckAi 
i 
MDL-NBS-HS-000016 REV 01 J-4 September 2004 

Drift-Scale Radionuclide Transport 
Calculations for cumulative dimensionless flux and flux ratio in fractures and matrix 
. jmax A . 
j .
.+
FdfA := Pefe.f(1A0 ymd)+. jp  
tanh ( jp  ymd)sin( jp  bd) Eq. (6-43) from main 
..
. j = 1 .
- 5 
=-9.801 10
FdfA FdfA is the total dimensionless mass 
flux into the fracture at the drift wall on 
rock side of boundary 
Partial sum for verification of FdfA 
. 8A .
j 
.
+
CheckFdfA := Pefe..f(1A0 ymd)+. jp  
tanh ( jp  ymd)sin( jp  bd)
. . 
. j = 1 .
- 3 - 4 - 4
A=-4.407 10 A=-3.034 10 A=-1.518 10
01 2
- 4 - 5 - 5
A=-1.012 10 A=-7.591 10 A=-6.073 10
34 5
- 5 - 5 - 5
A=-5.061 10 A=-4.338 10 A=-3.796 10
67 8
- 5
CheckFdfA =-9.815 10 
. jmax A . 
j .
.- +
FdmA := Pem (1bd)(1A0 ymd)-. jp  
tanh ( jp  ymd)sin( jp  bd). Eq. (6-44) from main 
.
. j = 1 .
FdmA is the total dimensionless mass 
FdmA =-3.929 10- 3 flux into the matrix at the drift wall on rock 
side of boundary 
Partial sum for verification of FdfA 
. 8A .
j
-+ .
CheckFdmA := Pem .(1bd)(1A0 ymd)-. jp  
tanh ( jp  ymd)sin( jp  bd)
. . 
. j = 1 . 
- 3
CheckFdmA =-3.929 10 
MDL-NBS-HS-000016 REV 01 J-5 September 2004 

Drift-Scale Radionuclide Transport 
FdfA Dimensionless flux ratio on 
= 0.02434 
rock side of boundary
FdmA + FdfA 
Eq. (6-41) from main 
j
max 
FdfD is the total dimensionless mass FdfD := . fA0 +. Aj sin( jp  bd) 
flux into the fracture at the drift wall on 
j = 1 
invert side of boundary 
- 5 
=-9.745 10
FdfD 
Partial sum for verification of FdfD 
8 
CheckFdfD := .fA+ A sin( jp  bd)
0 . j
j = 1
- 6
CheckFdfD =-1.204 10 
j
max 
-
FdmD := (1bd)A-. A sin( jp  bd) Eq. (6-42) from main 
0j
j = 1
FdmD 
- 3 FdmD is the total dimensionless mass 
=-4.309 10 
flux into the matrix at the drift wall on 
invert side of boundary 
Partial sum for verification of FdmD 
8 
CheckFdmD := (1bd)A- A sin( jp  bd)
- 0 . j
j = 1
- 3
CheckFdmD =-4.405 10 
FdfD Dimensionless flux ratio on 
= 0.02211 
invert side of boundary
FdmD + FdfD 
MDL-NBS-HS-000016 REV 01 J-6 September 2004 

Drift-Scale Radionuclide Transport 
NOTE: The output of the calculation, which is the dimensionless flux ratio given 
above, is not affected by the evaluations from this point forward; these are 
presented to provide background information on the character of the solution. 
jEq. (6-40) from main 
max 
Cdi 
:= A0 ymd +. A cos . jp  xdi 
.tanh ( jp  ymd) Cdi are the dimensionless
j 
j = 1 
.. concentrations at the 
invert-rock interface 
CP i
() := 1 + CdCP(i) is the plotting variable for the unnormalized 
i 
dimensionless concentration 
XP i
() := xdXP(i) is the plotting variable for the 
i 
dimensionless distance 
Plot of the unnormalized dimensionless concentration 
(C/Cm) at the solution points for the Fourier coefficients 
0 0.2 0.4 0.6 0.8 
0.98 
0.9805 
0.981 
0.9815 
0.982 
0.9825 
()CP i
XP i
() 
MDL-NBS-HS-000016 REV 01 J-7 September 2004 

Drift-Scale Radionuclide Transport 
Behavior of local dimensionless mass flux at drift wall 
:=
qCi 
qdi 

.
.
+ 1
Cdi 
.
.
Local dimensionless mass flux in rock 
at drift wall 
qCP(i) is the plotting variable for the 
qCP i
() - := qCi 
negative of the local dimensionless advective 
mass flux in the rock at drift wall 
XP i
() := xd
i
XP(i) is the plotting variable for the 
dimensionless distance along the 
drift wall 
Plot of negative of local dimensionless flux at the 
solution points for the Fourier coefficients 
0 0.2 0.4 0.6 0.8 
0.003922 
0.003924 
0.003926 
0.003928 
0.00393 
()qCP i
XP i
() 
Output-DTN: LB0307FMRADTRN.001 
MDL-NBS-HS-000016 REV 01 J-8 September 2004 

Drift-Scale Radionuclide Transport 
Comparison of radionuclide flux in invert and rock at the drift wall at points not 
fixed in solution for the Fourier coefficients 
:= 40000
kmax 
k is the reference number for coordinates along the 
k 0 kmax..:= drift wall not fixed in the solution for the Fourier 
coefficients 
xdk 
:= k 
kmax 
xdk are the coordinates along the drift wall not fixed in the 
solution for the Fourier coefficients 
0.5 Pem
(

Pefe
..
)
xdk 
.
.
+ 1
.
.
:=
qdk 
Pefe
+
-
F
.
.
-
bd
F-
.
.
bd
-
.
.

xdk 
j
max 
(
)
jp  ymd

.
Dimensionless local flux in 
.
.
.
.
:=
Cdk 
A0 ymd

A 
jp  xdk 


tanh
+

cos
j 
rock at drift wall 
1
j
= 
:=
qCk 
qdk 

+ 1
Cdk 
.
.
.
.
j
max 
.
Dimensionless local flux in 
invert at drift wall 
.
.
.
.
dCdk 
A

jp  A

jp  xdk 
:=
+

cos
0 
j 
j
=
1 
MDL-NBS-HS-000016 REV 01 J-9 September 2004 

Drift-Scale Radionuclide Transport 
qCP(k) is a plotting variable for the 
() - := qCk 
negative of the local dimensionless 
qCP k
advective flux in the rock matrix plus the 
diffusive flux in the fracture at drift wall 
dCP(k) is a plotting variables for the 
dCP k
() - := dCdk negative of the local dimensionless 
diffusive flux in the invert at drift wall 
XP k
() := xdk 
XP(k) is a plotting variable for 
dimensionless distance 
Comparison plot of flux in the invert and rock at the 
drift wall over the entire domain 
0.8 
0.6 
dCP k
() 
0.4
qCP k
() 
0.2 
0 
0.2 
0 0.2 0.4 0.6 0.8 
XP k
() 
Output-DTN: LB0307FMRADTRN.001 
MDL-NBS-HS-000016 REV 01 J-10 September 2004 

Drift-Scale Radionuclide Transport 
Comparison plot of flux in the invert and rock at the 
drift wall over region near fracture 
0.8 
0.6 
dCP k
() 
0.4
qCP k
() 
0.2 
0 
0.2 
0 0.02 0.04 0.06 0.08 
XP k
() 
Output-DTN: LB0307FMRADTRN.001 
MDL-NBS-HS-000016 REV 01 J-11 September 2004 

Drift-Scale Radionuclide Transport 
Comparison plot of flux in the invert and rock at the 
drift wall - fracture close-up 
0.8 
0.6 
dCP k
() 
0.4
qCP k
() 
0.2 
0 
0.2 
0 0.002 0.004 0.006 0.008 
XP k
() 
Output-DTN: LB0307FMRADTRN.001 
MDL-NBS-HS-000016 REV 01 J-12 September 2004 

Drift-Scale Radionuclide Transport 
fak is the series expansion of the flux 
function 
qdk is the flux function 
Comparison of boundary condition results (drift wall) at intermediate x-
coordinates to those used in the solution for the discrete transform 
coefficients 
tanh 
()Eq.6-34 from main 
jp  
qdk 
+ 1
xdk 
cos 
bd 
) 
bd 
j
A
j
A 
Pefe 
. 
j 
qd1 
- = 1
:=
qdk 
fa
k 
:=
.
.
. 
.
. 
..
)

jp  ymd
(

- 
.
.
.
. 
-
.
. 
F-
.
. 
-
xdk 
.
.
F 
.
. 
.
. 


jp  xdk 
.
.

F(j1
-

+
..
j() 1ymdqdk 

-
-
Pefe
..
)

-
0.5 Pem
(

+ 
.
. 

F

.
. 
..
. 
MDL-NBS-HS-000016 REV 01 J-13 
September 2004 

Drift-Scale Radionuclide Transport 
XP k
() := xdk 
XP(k) is a plotting variable for the dimensionless distance 
() := qdk
QP k QP(k) is a plotting variable for the flux function 
FAP k
() := fak FAP(k) is a plotting variable for series representation of the flux 
function 
Comparison of boundary condition results (drift wall) at intermediate x-coordinates to 
those used in the solution for the discrete transform coefficients over the entire domain. 
0 0.2 0.4 0.6 0.81 
0.8 
0.6 
0.4 
0.2 
0 
() 
() 
QP kFAP k
XP k
() 
Output-DTN: LB0307FMRADTRN.001 
MDL-NBS-HS-000016 REV 01 J-14 September 2004 

Drift-Scale Radionuclide Transport 
Comparison of boundary condition results (drift wall) at intermediate x-coordinates to 
those used in the solution for the discrete transform coefficients over a region near the 
fracture. 
0 0.02 0.04 0.06 0.081 
0.8 
0.6 
0.4 
0.2 
0 
() 
() 
QP kFAP k
XP k
() 
Output-DTN: LB0307FMRADTRN.001 
MDL-NBS-HS-000016 REV 01 J-15 September 2004 

Drift-Scale Radionuclide Transport 
Comparison of boundary condition results (drift wall) at intermediate x-coordinates to 
those used in the solution for the discrete transform coefficients - fracture close-up. 
0 0.002 0.004 0.006 0.0081 
0.8 
0.6 
0.4 
0.2 
0 
() 
() 
QP kFAP k
XP k
() 
Output-DTN: LB0307FMRADTRN.001 
MDL-NBS-HS-000016 REV 01 J-16 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX K 
SUPPLEMENTARY DERIVATIONS
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
SUPPLEMENTARY DERIVATIONS 
This appendix provides additional information pertaining to Section 6.4.5 of the main text and 
Appendices A, D, and I. 
The derivation of Equation 6-50 in the main text, starting from Equation 6-49, 
2
.
.
m
1
1
...
.
...
.
1
..
. 
..
.
S 
S
-
1
-
2 
fna 
m 
fna 
F
= 
(Eq. 6-49) 
2
.
.
m
1
1
...
.
...
.
1
..
. 
..
.
S 
S
-
1
-
2 
fn 
m 
fn 
1and expanding the numerator for small mS fma using the following first-order Taylor series 
expansion: 
1 
1x
(
)
m

1
-
mx 
where 
x
=
S 
m 
fma
-
Substitute this into the numerator of Equation 6-49 gives, 
2
.
.
1
1
...
.
...
.
S 
mS
..
. 
11
-
-
2 
fna
...
m 
fma 
F
= 
(Eq. K-1) 
2
.
.
m
1
1 
-
...
.
...
. 
..
. 
1
..
.
S 
S
1
-
2 
fn 
m 
fn 
Reducing the numerator gives, 
1 
2
+
22
S m 
m 
fna
F
= 
(Eq. K-2) 
2
.
.
m
1
1 
-
...
.
1
...
. 
..
. 
1
..
.
S
-
S
2 
fn 
m 
fn 
MDL-NBS-HS-000016 REV 01 K-1 September 2004 

Drift-Scale Radionuclide Transport 
Rearranging to solve for Sfma gives, 
4+ m 1 .. 1 . m . 2 
m
2m = FS 2 . 1-. 1- S fn 
.
.. ..
(Eq. K-3)
S 
fna 2 fn . ..
m 
. 
or 
2m 
4+ m
. 1 .
.. F . .. 1 . m . 2 . 
2
= ..
. m 
. S fn . 1-.. 1 - Sm . .. (Eq. 6-50) 
S 
fna 2 . fn .. 
. . ... 
. . ...
. 
Equations (A-1) and (A-2) in Appendix A are derived as follows: 
Let Y be log-normal with mean Y and standard deviation sY and X is normal with mean X and 
standard deviation sX; also X = ln(Y) or Y = eX . 
First, find eX and e2 X , or equivalently, Y and Y 2. 
2 
2
8 X -( X - X )s X 
X 2 X 
e =.ee 2s X dX = e 
+ 
2 (Eq. K-4) 
8 - 2sp X 
2
s X 
X

+ 
or =e 2 (Eq. K-5)
Y 
and 
2 
8 2 X ( X - ) 
2 X 22 X + 2s X
e =.2 
e 
sp Xe 
- 
2s XX 
dX = e 2 (Eq XI-6) 
8 - 
2
22 X
and because s Y = e - eX , then, 
22 2
22 X +s X s X 2 s X
s
Y = e ( e - 1)=
( e - 1) (Eq. K-7)
Y 
Rearranging Equation (K-7) and solving for sX gives, 
2
. 
.
s
X = 1 ln +
s Y .
. (Eq. A-2)
. 2 .

. Y . 
MDL-NBS-HS-000016 REV 01 K-2 September 2004 

Drift-Scale Radionuclide Transport 
Rearranging Equation (K-5) and using Equation (A-2) to solve for X gives, 
=
1 
Y 
.
Y 
.
. 
. 
s 
 
ln()
XY

-
1ln 
2 .
.
. 
. 
2 
2
+
(Eq. A-1) 
The derivation of equations (D-4), (D-5), (I-4), and (I-5) from Abramowitz and Stegun (1972 
[DIRS 103280], Equation 26.1.33) is shown here: 
= a 
=
(Eq. K-8)
mean
b
+
a 
ab
variance = 2
s
(Eq. K-9)
=
a
+
(
)
(
)
b 1
2
b
+
+
a 
Solve equation (K-8) for b 
Also note from equation (K-8) that 
b
.
1
. 
.
. 


-
(Eq. K-10)
a
=
.
.
a 
 
=
b 
(Eq. K-11)
+
a 
Substitute equations (K-10) and (K-11) into equation (K-9) to give 
.
. 
.
. 


-
1
2
a
.
. 
. 
=s
2 
(Eq. K-12)
2
.
.
. 
.
. 
+
1
a 
a 
.
.
.
.

.
. 
) 
 
Simplifying equation (K-12) gives 
(
1 
a
-

s
2

(Eq. K-13)
=
.
.
+
1
.
.
.
.
 
MDL-NBS-HS-000016 REV 01 K-3 September 2004 

Drift-Scale Radionuclide Transport 
Solving equation (K-13) for a gives 
.(1 -)-1..
a= 
.. 
s2 (Eq. D-4 and I-4) 
and substituting equation (D-4) for a in equation (K-10) gives 
b=(1 -).(1 -)-1..
. (Eq. D-5 and I-5)
.. 
s2
MDL-NBS-HS-000016 REV 01 K-4 September 2004 

Drift-Scale Radionuclide Transport 
APPENDIX L 
DEMONSTRATION OF EQUIVALENCE OF THE DISCRETE TRANSFORM 
SOLUTION AND FOURIER SERIES SOLUTION 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
MDL-NBS-HS-000016 REV 01 September 2004 

Drift-Scale Radionuclide Transport 
DEMONSTRATION OF EQUIVALENCE OF THE DISCRETE TRANSFORM 
SOLUTION AND FOURIER SERIES SOLUTION 
This appendix provides additional information pertaining to Section 6.4.3 of the main text. 
Summary from Sections 6.4.2 and 6.4.3 
The steady-state diffusion equation and four boundary conditions to be solved are given by 
equations (6-24) through (6-28) of the main text: 
( , 2. ddd xCdy ) = 0 (Eq. 6-24) 
Cd (xd ,0)= 0 (Eq. 6-25) 
. 
. 
d 
d 
x 
C(,0 dy ) = 0 (Eq. 6-26) 
.Cd 
.xd 
1, yd( )= 0 (Eq. 6-27) 
. 
. 
d 
d 
y 
C( ,dx mdy ) = dq ( dx ) (( ,dd xC mdy ) )1+ (Eq. 6-28) 
A solution that satisfies Equation 6-24 and the boundary conditions, Equations 6-25 to 6-27 is 
8 
Cd (xd , y )= y B +.Bj cos( jpx )sinh( jpy ) (Eq. 6-33) 
d 0 d dd 
j =1 
which may be verified by direct substitution. 
Substituting Equation 6-33 into Equation 6-28 gives 
8 
A0 (1- q ()y )+.A cos(jpx )[jp- q (x )tanh(jpy )]= q ()(Eq. 6-34)
dxdmd j d dd mddxd 
j=1 
or 
8 
.M ij Aj = q (Eq. 6-35) 
di 
j=0
MDL-NBS-HS-000016 REV 01 L-1 September 2004 

Drift-Scale Radionuclide Transport 
where 
Mi0=( 1 - q ( x ) y ) (Eq. 6-36) 
d di md 
M 
ij =cos( jp x )[ jp- q ( x ) tanh( jp y )] for i> 0 (Eq. 6-37) 
di ddi md 
q =q ( x ) (Eq. 6-38) 
di ddi 
Aj =Bj cosh( jp y ) (Eq. 6-39) 
md 
The transformation from Bj to Aj is introduced to eliminate numerical difficulties in the 
evaluation of cosh( j p ymd ) and sinh ( j p ymd ) for large j. 
Explanation of Discrete Transform Solution Method 
If a solution for Aj can be found that satisfies equation (6-35) at all points in the domain of the 
problem, then, in combination with equation (6-39) and equation (6-33) we have the exact 
solution to equations (6-24) through (6-28). Therefore, equation (6-35) represents a linear 
system of equations for Aj that can produce the exact solution in the limit as j .8 . An 
approximate solution may be derived by solving for Aj at a finite number of points and this 
solution converges as j increases. 
Demonstration of Equivalence with Fourier Series 
A test of the discrete transform solution method is given here for a problem in which the 
standard Fourier solution is also available. In this test, an analytical form for the concentration at 
the invert-rock boundary was assumed. That is, starting with equations (6-24) through (6-27), 
we then specify the concentration at the invert-rock interface, replacing the flux boundary 
condition in equation (6-28) with a concentration boundary condition. With this type of 
boundary condition, the solution may be obtained using standard Fourier methods. This solution 
was then substituted into equation (6-28) to derive a form for q( x ) that is consistent with the 
dd 
assumed concentration boundary condition. Therefore, we now have the identical problem with 
a flux-type boundary condition as given in equation (6-28). A series of values for q() were
d xd 
then generated from the standard Fourier solution and used as input to the discrete transform 
solution method to solve equations (6-24) through (6-28). The resulting Fourier coefficients may 
be compared with those generated from the standard Fourier solution, and the concentration 
distribution at the invert-rock boundary may be compared with the assumed concentration 
distribution. The following presents the details of this comparison. 
Given equations (6-33) and (6-39), we have, 
8 
Cd ( xd , y )= y A +. Aj cos( jpx ) tanh( jp y ) (Eq. 6-40) 
dm 0 dm ddm 
j= 1 
MDL-NBS-HS-000016 REV 01 L-2 September 2004 

Drift-Scale Radionuclide Transport 
Assume the following form for the concentration distribution at the invert-rock interface: 
Cd (xd , y )=K1 +K 2 [1 -exp(-x K )] (Eq. L-1)
dm 3 d 
where K1, K 2 , and K3 are constants. 
For the Fourier cosine series, 
.aj cos() (Eq. L-2)
C
d (xd , y )= a0 +
8 
jx
dm 2 j=1 
where x =pxd . 
Fourier coefficients are obtained using the orthogonality properties of the cosine function, 
2
p. . 
p
a0 = ..K1 +K 2 .1 -exp ..
-K3 x ..
..
..
dx (Eq. L-3) 
0 . . .p ... 
2 p. ..-K3 ... 
dx jx (Eq. L-4)
p
aj = ..K1 +K 2 .1 -exp. x ...cos()
0 . . .p ... 
giving the following results for the Fourier Coefficients: 
=2K1 +2K 2 -2 
KK 
32 [1 -exp(-K )] (Eq. L-5)
a
03 
2 
K 
aj =
-2K K 3 [1 -exp(-K )cos(jp)] (Eq. L-6) 
32 + j 2p23 
Comparing Equations 6-40 and L-2 we find, 
a0 
=y A dm (Eq. L-7)
20 
aj =Aj tanh(jpy ) (Eq. L-8)
dm 
Therefore, 
A0 =K1 + K 2 - K 2 [1 -exp(-K )] (Eq. L-9) 
3
y
dmydm y K dm 
3 
Aj =
-2K K 3 [1 -exp(-K )cos(jp)] 
(Eq. L-10)
23 
2 22
K3 + j p tanh(jpy )
dm 
MDL-NBS-HS-000016 REV 01 L-3 September 2004 

Drift-Scale Radionuclide Transport 
and expressions for Bj are derived using Equation 6-39 in combination with L-9 and L-10. 
Substituting for Bj into equation (6-33) gives, 
1 d 2 d - 2 d
Cd (xd , y )=y K + y K y K [1 - exp(- K )]
d 
y y K 3 
dm ydm 3 dm 
8 2K K 3 [1 - exp(- K )cos( jp)] cos( jpxd )sinh( jpy ) 
(Eq. L-11) 
23
-. 2 
22 d 
j =1 K3 + j p sinh( jpy )
dm 
and 
.C (xd , y ) K1 + K 2
d =- K 2 [1 - exp(- K )]
.y ydm ydm y K 3 
d 3 dm 
8 2K K 3 ( jp)[1 - exp(- K )cos( jp)] 
cos( jpxd )cosh( jpy ) 
(Eq. L-12) 
23
-. 2 
22 d 
j =1 K3 + j p sinh( jpy )
dm 
Evaluating Equations L-11 and L-12 at yd =y gives
dm 
Cd (xd , y )= K + K2 - K2 [1- exp(- K )]
K
dm 1 
33 
(Eq. L-13)
8 
2
-. 2K K 3 [1- exp(- K )cos( jp)]cos( jpxd ) 
j=1 K32 + j 2p23 
and 
.x C d , y ) K1 + K2
dm =
(- K2 [1- exp(- K )]
.yd ydm ydm y K dm 
3 
3 
8 2K K 3 ( jp)[1- exp(- K )cos( jp)]cos( jpxd ) 
(Eq. L-14) 
23
-. 2 
22 
j=1 K3 + j p tanh( jpy )
dm 
From equation (6-28) 
.C (xd , y )
dm 
d 
d xd (Eq. L-15)
q()= 
Cd (xd 
. 
, 
yy )+ 1
dm 
Substituting Equations L-13 and L-14 into Equation L-15 allows for the evaluation of q (x ) .
dd 
MDL-NBS-HS-000016 REV 01 L-4 September 2004 

Drift-Scale Radionuclide Transport 
Letting K1 - = 02. 0 , K 2 = 0025. 0 , and K3 = 10 , the concentration profile (Equation L-1) and 
Fourier representation of that concentration profile (Equation L-13) using 101 Fourier 
coefficients is plotted in Figure L-1 (note that Cd ranges from 1 to 0 and Cd + 1 is plotted): 
0 1 
Xd 
l 
iCd+1 and Fourier Representation of Cd+1 
0.98 
0.9805 
0.981 
0.9815 
0.982 
0.9825 
0.983 
0.2 0.4 0.6 0.8 1.2 
Cd+1OriginaFourier Representaton 
Output-DTN: LB0307FMRADTRN.001. 
Figure L-1. Assumed Concentration Profile and its Fourier Representation 
As expected, the Fourier decomposition may be used to reconstruct the function. 
Using Equation L-15 to generate values of qd, the discrete transform solution method was used to 
solve Equations 24 through 28. For this test case, 128 discrete transform coefficients were used 
in solution of Equation 6-35 for Aj . Fourier coefficients determined in Equations L-9 and L-10 
are compared with the coefficients determined from the discrete transform solution method 
concentration as shown in Figure L-2. 
MDL-NBS-HS-000016 REV 01 L-5 September 2004 

Drift-Scale Radionuclide Transport 
Comparison of Fourier Coefficients
Fourier Coefficient 
0.000E+00
-1.000E-04
-2.000E-04
-3.000E-04
-4.000E-04
-5.000E-04
ilStandard Fourer 
Series 
DT Soution Method 
0 50 100 150 
Fourier Coefficient Index 
Output-DTN: LB0307FMRADTRN.001. 
Figure L-2. Assumed Concentration Profile and its Fourier Representation 
This shows that the original Fourier coefficients are closely approximated by the coefficients 
determined using the discrete transform solution method for the same problem. The coefficient 
for A0 is not shown in this figure so that the scale of the figure may more clearly show the 
comparison for the remaining coefficients. For the original Fourier coefficients, A0 = -0.004437 
as compared with 0.004441 for the discrete transform solution method. 
The discrete transform solution method was also used to determine the concentration at the 
invert-rock interface. The comparison between this concentration and the original concentration 
shown above is shown in Figure L-3. 
MDL-NBS-HS-000016 REV 01 L-6 September 2004 

Drift-Scale Radionuclide Transport 
0 1 
Xd 
l 
lComparison of Original Cd+1 
with Profile from DT Solution Method 
0.98 
0.9805 
0.981 
0.9815 
0.982 
0.9825 
0.983 
0.2 0.4 0.6 0.8 1.2 
Cd+1OriginaDT soution method 
Output-DTN: LB0307FMRADTRN.001. 
Figure L-3. Comparison of Assumed Profile and Computed Profile using DT Method 
The root-mean-square relative error between the concentration curves is 1.3 x 10-5. Therefore, 
the discrete transform solution method for Equations 24 through 28 results in a concentration 
distribution that is essentially identical with the original concentration distribution. 
Excel Calculations for Fourier Solution 
Equation L-13 is computed in excel using the following: 
For the first Fourier coefficient (evaluated in cell B2), Equation L-9 in Excel is: 
B2=0.25*($CY$1+$CZ$1-($CZ$1/$DA$1)*(1-EXP(-$DA$1))) 
Where K1, K2, and K3 (see Equation L-1) are constants in cells CY1, CZ1, and DA1, 
respectively.
The remaining Fourier coefficients, in cells C2 through CX2, are computed from Equation L-10, 
which in Excel is: 
COL2=(-2*$CZ$1*$DA$1/($DA$1^2+COL$1^2*PI()^2))*(1-EXP(-
$DA$1)*COS(COL$1*PI()))/TANH(COL$1*PI()*4) 
MDL-NBS-HS-000016 REV 01 L-7 September 2004 

Drift-Scale Radionuclide Transport 
where COL is a generic designation for the column label. 
The concentration at a given location is computed using Equation L-13. The cells B3 through 
B130 contain the dimensionless coordinate, xd. Cells Crn through CXrn (where rn lies between 3 
and 130) are the elements of the summation in Equation L-13 for each location, xd, not including 
the common factor in the summation that is independent of the summation index. The Excel 
formula for the series elements is: 
COLrn=(1-EXP(-
$DA$1)*COS(COL$1*PI()))*COS(COL$1*PI()*$Brn)/($DA$1^2+COL$1^2*PI()^2) 
where rn is a generic designation for row number. A portion of the results using these formulas 
is shown in Table L-1. See Wang (2003 [DIRS 163234], SN-LBNL-SCI-236-V1, p. 75) and 
DTN: LB0307FMRADTRN.001 for the complete output. 
Table L-1. Fourier Coefficients and Calculation of Concentration Profile 
A B C D E F G 
1 j 0 1 2 3 4 5 
2 Fourier Coefficients -0.004437497 -0.00046 -0.000358462 -0.00026 -0.00019 -0.00014 
3 Dimensionless 
coordinate, Xd 
0 0.009102 0.007169243 0.005296 0.003877 0.002884 
4 0.0078125 0.009099 0.007160607 0.005282 0.003858 0.002862 
5 0.015625 0.009091 0.007134721 0.005239 0.003803 0.002798 
6 0.0234375 0.009077 0.007091646 0.005167 0.00371 0.002691 
7 0.03125 0.009058 0.007031488 0.005068 0.003582 0.002544 
Output-DTN: LB0307FMRADTRN.001 
The summation is carried out in cells CY3 through CY130 using the following formula: 
CYrn=SUM(Crn:CXrn) 
The common factor is multiplied by the summation results in cells CYrn and the constant in 
Equation L-13 is added. This is performed in CZ3 through CZ130 using the following formula: 
CZrn=$CY$1+$CZ$1-($CZ$1/$DA$1)*(1-EXP(-$DA$1))-2*$CZ$1*$DA$1*CYrn 
The value of Cd+1 is given by the values in CZrn plus 1 in column DB. 
The calculation of Equation L-14 is also performed in Excel. This is done using a similar 
structure as for the series expression for Equation L-13 discussed above. Cells B135 through 
B262 contain the values of the dimensionless coordinate, xd. Cells Crn through CXrn (where rn 
lies between 135 and 262) are the elements of the summation in Equation L-14 for each location, 
xd, not including the common factor in the summation that is independent of the summation 
index. The Excel formula for the series elements is: 
MDL-NBS-HS-000016 REV 01 L-8 September 2004 

Drift-Scale Radionuclide Transport 
COLrn=(COL$134*PI())*(1-EXP(-
$DA$1)*COS(COL$134*PI()))*COS(COL$134*PI()*$Brn)/(($DA$1^2+COL$134^2*PI()^2)* 
TANH(COL$134*PI()*4)) 
A portion of the results using these formulas is shown in Table L-2. See Wang (2003 
[DIRS 163234], SN-LBNL-SCI-236-V1, p. 75) and DTN: LB0307FMRADTRN.001 for the 
complete output. 
Table L-2. Calculation of Concentration Derivative with Respect to yd 
134 j 1 2 3 4 5 
135 Dimensionless 
coordinate, Xd 
0 0.028595 0.045045679 0.049915 0.048721 0.045304 
136 0.0078125 0.028587 0.04499142 0.049779 0.048486 0.044963 
137 0.015625 0.028561 0.044828772 0.049374 0.047785 0.043946 
138 0.0234375 0.028518 0.044558128 0.048702 0.046623 0.042268 
139 0.03125 0.028457 0.044180139 0.047765 0.045012 0.039954 
Output-DTN: LB0307FMRADTRN.001 
The summation is carried out in cells CY135 through CY262 using the following formula: 
CYrn=SUM(Drn:CYrn) 
The common factor is multiplied by the summation results in cells CYrn and the constant in 
Equation L-14 is added. This is performed in CZ135 through CZ262 using the following 
formula:
CZrn=0.25*$CY$1+0.25*$CZ$1-(0.25*$CZ$1/$DA$1)*(1-EXP(-$DA$1))-
2*$CZ$1*$DA$1*CYrn 
The dimensionless flux (qd) profile is then computed from Equation L-15 using the following 
Excel formula: 
DBrn=CZrn/DB(rn-132) 
which gives the dimensionless flux at each coordinate xd. 
Mathcad Calculations for the Discrete Transform Method. 
The discrete transform calculation discussed above was performed using Mathcad and is given 
on the following pages: 
MDL-NBS-HS-000016 REV 01 L-9 September 2004 

Drift-Scale Radionuclide Transport 
Solution Method Test Case 
Values used for calculation 
ydm : = 4.00 ydm is the dimensionless invert thickness 
j:= 127 jmax+1 is the number of Fourier coefficients 
max 
Distance coordinate along drift wall 
i := 0.. ji is reference number for the coordinates along the drift wall 
max 
j := 0.. jj is the reference number for the Fourier coefficients 
max
i
:=
xdi jxdi is the dimensionless distance along the drift wall 
max 
Sample values for verification of xdi 
xd0 
= 0 xd1 
= 7.874 10- 3 xd2 
= 0.016 ..... xd126 
= 0.992 xd127 
= 1 
Solution for Fourier coefficients 
qd := qd is input from the 
Fourier solution, 
represented by the 
icon, and calculated 
from Equation L-15. 
qdi is the dimensionless 
water flux profile at the 
invert-rock interface DTN: LB0307FMRADTRN.001 
MDL-NBS-HS-000016 REV 01 L-10 September 2004 

Drift-Scale Radionuclide Transport 
Sample values for verification of qd 
- 3 - 3 
qd0 
- = 0.06qd1 
- = 0.041qd2 
- = 0.023.... qd126 
=-4.107 10 qd127 
=-4.026 10 
-j - ( j
Mij:= F(). 1 - ymdqdi 
.+F(j1)cos . jp  xdi 
.. jp  - qdi 
tanh ymdp). 
,. 
. ... . 
Mi,j is the coefficient 
matrix for A 
Sample values for verification of Mi,j 
M,= 1.242 M= 3.202 .... M0 126 = 395.901 M= 399.043
0001, 0 127 
, , 
= 1.166 M11= 3.182 , - = 395.761M1 127 - = 399.024
, 
M10, .... M1 126 , 
= 1.09 M21= 3.16 ,= 395.379 M2 127 = 399.005 
, 
M20, .... M2 126 , 
. . 
. = 141.293 .
M64 64 
. ,
.
= 1.016 M126 1 - = 3.145.... , - = 395.724 = 398.986
M126 0 , M126 126 M126 127 
, , 
= 1.016 M127 1 - = 3.146.... ,= 395.845 - = 398.986
M127 0 , M127 126 M127 127 
, , 
- 1
A := M qd A is the vector of 
Fourier coefficients 
Verification of matrix solution for Fourier coefficients, A. 
CheckA is a vector of the residuals for M*A-qd 
CheckA := M A - qd
 
MDL-NBS-HS-000016 REV 01 L-11 September 2004 

Drift-Scale Radionuclide Transport 
Plot of residuals for M*A-qd 
1 .10 14
5 .10 15
CheckAi 
0 
5 .10 15
0 50 100 150
i
j
max 
Cdi are the dimensionless
Cdi 
:= A0 ymd +. A cos . jp  xdi 
.tanh ( jp  ymd)
j 
.. concentrations at the
j = 1
invert-rock interface 
CP i
() := 1 + CdCP(i) is the plotting variable for the unnormalized 
i
dimensionless concentration 
XP i
() := xdXP(i) is the plotting variable for the 
i
dimensionless distance 
MDL-NBS-HS-000016 REV 01 L-12 September 2004 

Drift-Scale Radionuclide Transport 
Plot of the unnormalized dimensionless concentration 
(C/Cm) at the solution points for the Fourier coefficients 
0 0.2 0.4 0.6 0.8 
0.98 
0.9805 
0.981 
0.9815 
0.982 
0.9825 
()CP i
XP i
() 
Output-DTN: LB0307FMRADTRN.001 
MDL-NBS-HS-000016 REV 01 L-13 September 2004 

Drift-Scale Radionuclide Transport 
Behavior of local dimensionless mass flux at drift wall 
:=
qCi 
qdi 

.
.
+ 1
Cdi 
.
.
Local dimensionless mass flux in rock 
at drift wall 
qCP(i) is the plotting variable for the 
qCP i
() - := qCi 
negative of the local dimensionless advective 
mass flux in the rock at drift wall 
XP i
() := xd
i
XP(i) is the plotting variable for the 
dimensionless distance along the 
drift wall 
Plot of negative of local dimensionless flux at the 
solution points for the Fourier coefficients 
0 0.2 0.4 0.6 0.80 
0.02 
0.04 
0.06 
0.08 
()qCP i
XP i
() 
Output-DTN: LB0307FMRADTRN.001. 
MDL-NBS-HS-000016 REV 01 L-14 September 2004