Particle Tracking Model and Abstraction of Transport Processes Rev 00, ICN 00

MDL-NBS-HS-000020

January 2004

1. PURPOSE 
The purpose of this Model Report is to document the abstraction model being used in Total 
System Performance Assessment (TSPA) model calculations for radionuclide transport in the 
unsaturated zone (UZ). The particle-tracking method of simulating radionuclide transport is 
incorporated into the Finite Element Heat and Mass Model (FEHM) computer code. This Model 
Report outlines the assumptions, design, and testing of a model for calculating radionuclide 
transport in the UZ at Yucca Mountain. In addition, methods for determining and inputting 
transport parameters are outlined for use in the TSPA analyses. Concurrently, process-level flow 
model calculations are being documented in another Analysis Model Report (AMR) for the UZ 
(BSC 2003 [163228]). Three-dimensional (3-D), dual-permeability flow fields generated to 
characterize UZ flow (documented in BSC 2003 [163045]; DTN: LB03023DSSCP9I.001 
[163044]) are converted to make them compatible with the FEHM code, which in this 
abstraction model is used to simulate radionuclide transport using a particle-tracking method that 
is described in this report. This Model Report establishes the numerical method and 
demonstrates the use of the model that is intended to represent UZ transport in the TSPA. 
Capability of the UZ barrier for retarding the transport is demonstrated in this Model Report, and 
by the underlying process model (BSC 2003 [163228]). 
This Model Report is a revision of an AMR. The original work was documented as a scientific 
analysis (ANL-NBS-HS-000026 REV00, CRWMS M&O 2000 [141418]), whereas the current 
report is a Model Report (MDL-NBS-HS-000020 REV00). The technical scope, content, and 
management of this Model Report are described in the planning document Technical Work Plan 
(TWP) for: Performance Assessment Unsaturated Zone (BSC 2002 [160819], Section 1.11, 
Work Package (WP) AUZM07). Deviations from the TWP are noted within the text of this 
Model Report, as appropriate. 
Note that Section 7.3.3 provides information used to formulate the technical justification the 
abstraction model properly implements the active fracture model with matrix diffusion. 
The particle-tracking technique presented in this Model Report, called the Residence Time 
Transfer Function (RTTF) particle-tracking technique, uses a cell-based approach that sends 
particles from node to node on a finite difference or finite element grid, after keeping each 
particle at the cell for a prescribed period of time. To incorporate transport mechanisms such as 
dispersion and matrix diffusion, the residence time of a particle at a cell is computed using a 
transfer function that ensures that the correct distribution of residence times at the cell is 
reproduced. This procedure is computationally very efficient, enabling large-scale transport 
simulations of several million particles to be completed rapidly on modern workstations. This 
requirement was needed for complex, 3-D simulation involving the simulation of multiple 
radionuclides. Furthermore, since the cell-based approach uses directly mass flow rate 
information generated from a numerical fluid flow solution, complex, unstructured 
computational grids and the dual-permeability flow model formulation pose no additional 
complications. For the present application, the technique was adapted for use in unsaturated, 
dual-permeability transport simulations. For such systems, numerical techniques are required to 
allow accurate simulation of dual-permeability systems in which there is a vast disparity in the 
travel times depending on whether the transport is in the fractures or the matrix. This Model 
Report outlines the approach and defines the proper use of that approach. Furthermore, colloid- 
January 2004 13 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
facilitated radionuclide transport can be simulated, and complex source terms and decay 
chain/ingrowth capabilities have been included in the model. 
Like all numerical methods, the particle-tracking technique has limitations that must be 
considered when deciding whether its use is appropriate for a given application. The key 
physical and chemical assumptions are advection-dominated transport and linear, equilibrium 
sorption. Also, the accuracy of the method for dual-permeability flow systems was investigated 
in detail by performing comparisons to analytical solutions and alternate numerical methods, 
including the UZ transport process models documented in BSC 2003 [163228] and BSC 2003 
[163045] and testing of the FEHM code presented in the software documentation (FEHM V2.21, 
LANL 2003 [166306]). Given these results, this Model Report demonstrates that the particletracking 
model can be used in 3-D radionuclide transport simulations of the Yucca Mountain UZ 
as long as the limits on the model are recognized and parameters and inputs are chosen 
accordingly. Discussion of the limits and applicability are provided in this Model Report. Inputs 
used in the calculations presented are believed to be representative of those to be used in TSPA 
model calculations, but this contention must be verified explicitly when the actual parameters to 
be used in TSPA multiple realization simulations become available. 
January 2004 14 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
2. QUALITY ASSURANCE 
Development of this Model Report and the supporting modeling activities have been determined 
to be subject to the Office of Civilian Radioactive Waste Managements (OCRWM) quality 
assurance program as indicated in Technical Work Plan for: Performance Assessment 
Unsaturated Zone, TWP-NBS-HS-000003 REV 02 (BSC 2002 [160819], Section 8.2, WP 
AUZM07). Approved quality assurance procedures identified in the TWP (BSC 2002 [160819], 
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 
2002 [160819], Section 8.4, WP AUZM07) during the modeling and documentation activities. 
This Model Report discusses ambient radionuclide transport through hydrogeologic units below 
the repository, which constitute a natural barrier that is classified in the Q-List (BSC 2003 
[165179]) 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 results of this report are 
important to the demonstration of compliance with the postclosure performance objectives 
prescribed in 10 CFR 63.113 [156671]. The report contributes to the analysis data used to 
support performance assessment (PA); the conclusions do not directly impact engineered 
features important to preclosure safety, as defined in AP-2.22Q. 
January 2004 15 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
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16 MDL-NBS-HS-000020 REV 00 
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January 2004 Particle Tracking Model and Abstraction of Transport Processes 
3. USE OF SOFTWARE 
3.1 SOFTWARE TRACKED BY CONFIGURATION MANAGEMENT 
The computer codes used directly in this modeling activity are summarized in Table 3-1. The 
computer software code on which the UZ transport abstraction model is based is FEHM V2.21, 
(LANL 2003 [165741]). The qualification status of this and other software is indicated in the 
electronic Document Input Reference System (DIRS) database. All software was obtained from 
Software Configuration Management and is appropriate for the application. Qualified codes 
were used only within the range of validation as required by AP-SI.1Q, Software Management. 
Input and output files for this Model Report are located in data tracking numbers (DTN) and 
identified in the respective discussions in Section 6; the outputs are listed in Section 8.2. 
Software 
Title/Version (v) 
FEHM V2.21 
GoldSim V7.50.100 
ppptrk V1.0 
discrete_tf V1.1 
fehm2post V1.0 
Table 3-1. Qualified Software Used in this Report 
Code Usage 
Simulation of particle tracking validation runs 
Abstraction model simulations 
Abstraction model simulations 
Post-processing of particle breakthrough curve information 
Post-processing of discrete fracture model results to 
convert results to transfer functions 
Software 
Tracking 
Number 
(STN) 
10086-2.21-00 Generation of transfer function curve information using a 
discrete fracture model. 
10344- 
7.50.100-00 
11030-1.0-00 
11033-1.1-00 
11031-1.0-00 Executes multiple FEHM simulations along with pre- and 
post-processing runs. Used to execute the individual 
simulations and generation of transfer function curves 
used in the TSPA UZ transport abstraction model. 
17 
MDL-NBS-HS-000020 REV 00 
U0065 
DIRS 
165741 
161572 
165753 
165742 
165754 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
3.2 EXEMPT SOFTWARE 
Commercial, off-the-shelf software used in support of this Model Report is listed in Table 3-2. 
This software is exempt from the requirements of AP-SI.1Q. 
Software Name 
and Version (V) 
Software 
Tracking 
Number (STN) 
N/A Fortner Plot 
N/A Microsoft Excel 
Table 3-2. Exempt Software 
Description 
The commercial software, Fortner Plot, was used for 
plotting the results of breakthrough curve simulations. Only 
built-in standard functions in this software were used. No 
software routines or macros were used with this software to 
prepare this report. The output was visually checked for 
correctness. 
This standard spreadsheet package is used to perform 
simple spreadsheet calculations using built-in formulas and 
functions. 
Computer and 
Platform 
Identification 
SUN Workstation 
IBM PC, Window 
2000 operating 
system 
MDL-NBS-HS-000020 REV 00 18 
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January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
4. INPUTS 
4.1 DIRECT INPUT 
Data and parameters used in this Model Report as model inputs include: 
 Numerical Grid for the UZ transport model 
 UZ flow field for the prevailing climate 
 UZ rock properties 
- Porosity 
- Fracture spacing and aperture 
- Active Fracture Model (AFM) parameter  
- Fracture residual saturation 
- Rock density 
 UZ radionuclide transport parameters 
- Matrix diffusion coefficient 
- Radionuclide matrix adsorption coefficient 
- Colloid size distribution 
- Colloid size exclusion factor at fracture-matrix interface 
- Colloid filtration factor at Matrix Interface 
- Colloid concentration 
- Radionuclide adsorption coefficient kd onto colloid 
- Colloid retardation factor 
 Repository location 
4.1.1 Data 
The following data are used as inputs to FEHM for constructing the UZ transport model. 
January 2004 19 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
Data Source Data Name 
UZ flow model grid and nine base case flow 
fields. preqlA.ini, preqmA.ini, prequA.ini, 
monqla.ini, monqmA.ini, monqua.ini, glaqlA.ini, 
glaqmA.ini, glaquA.ini, fehmn.grid, and 
fehmn.stor 
Repository release bin location 
TOUGH2 element data 
Water saturation and permeability 
Table 4-1. Input Data 
Lawrence Berkeley National 
Laboratory site scale flow models 
NEVADA_SMT_percolation_BIN_ma. 
txt, which contains repository node 
location of the thermal model 
BSC 2003 [163045] UZ Flow Models 
and Submodels (MDL-NBS-HS- 
000006 REV01) 
BSC 2003 [163045] UZ Flow Models 
and Submodels (MDL-NBS-HS- 
000006 REV01) 
20 
In TSPA simulations, flow fields are pre-generated and saved for use in the UZ transport 
abstraction model to be used in TSPA analyses. At run time, FEHM reads in the pre-generated 
flow fields and uses them in transport simulations. The UZ flow model grid and flow field for 
the prevailing climate are used in this Model Report as input to FEHM to illustrate the set-up of 
UZ transport model. The effects of flow field uncertainty on TSPA are investigated through 
multiple realizations with different climate scenarios and corresponding flow fields. 
Repository location data are used to select repository nodes in the 3-D site scale model for 
releasing radionuclides into the UZ. There is no uncertainty related to this data. 
T2R3D 3-D site-scale transport results, developed using the dual-permeability (dual-k) model, 
are used for benchmarking for comparison with FEHM results. Uncertainty associated with those 
results is described in BSC (2003 [163228]). 
4.1.2 Parameters and Parameter Uncertainty 
The following parameters are inputs to the FEHM UZ transport model. The values of those 
parameters affect the strength of the transport mechanism those parameters are related to. The 
values of all the parameters vary from layer to layer, as do the distributions. More detailed 
information regarding parameter value and discussion of uncertainty can be found in Section 6 
where those parameters are discussed. 
MDL-NBS-HS-000020 REV 00 
U0065 
DTN 
LB0305TSPA18FF.001 
[165625] 
LL030610323122.029 
[164513] 
LB03023DSSCP9I.001 
[163044] 
LB03023DSSCP9I.001 
[163044] 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Parameter Name 
(Section 
discussed) 
Fracture 
dispersivity 
Section 6.5.2 
Matrix porosity 
Section 6.5.3 
Rock density 
Section 6.5.3 
Fracture porosity 
Section 6.5.7 
Fracture frequency 
Section 6.5.7 
Active fracture 
model parameters 
Section 6.5.6 
Fracture residual 
saturation 
Section 6.5.6 
Fracture spacing 
and aperture 
Section 6.5.7 
Colloid 
concentration 
distribution 
Section 6.5.12 
Radionuclide 
adsorption 
coefficient onto 
colloid 
Section 6.5.12 
Parameter Source 
BSC 2003 [162415] 
Saturated Zone In-Situ 
Testing (ANL-NBS-HS- 
000039 REV 00) 
BSC 2003 [160240] 
Calibrated Properties 
Model (MDL-NBS-HS- 
000003 REV01) 
BSC 2003 [161773] 
Analysis of Hydrologic 
Properties Data (MDLNBS-
HS-000014 
REV00) 
BSC 2003 [161773] 
Analysis of Hydrologic 
Properties Data (MDLNBS-
HS-000014 
REV00) 
BSC 2003 [161773] 
Analysis of Hydrologic 
Properties Data (MDLNBS-
HS-000014 
REV00) 
BSC 2003 [163045] 
UZ Flow Models and 
Submodels (MDL-NBSHS-
000006 REV01) 
BSC 2003 [160240] 
Calibrated Properties 
Model (MDL-NBS-HS- 
000003 REV01) 
BSC 2003 [161773] 
Analysis of Hydrologic 
Properties Data (MDLNBS-
HS-000014 
REV00) 
BSC 2003 [161620] 
Waste Form and Indrift 
Colloids-Associated 
Radionuclide 
Concentrations: 
Abstract and Summary 
(MDL-EBS-PA-000004 
REV 00) 
BSC 2003 [161620] 
Waste Form and Indrift 
Colloids-Associated 
Radionuclide 
Concentrations: 
Abstract and Summary 
(MDL-EBS-PA-000004 
REV 00) 
Table 4-2. Input Parameters 
DTN 
(Table 6.3-10 of BSC 2003 
[162415]) 
LB0305TSPA18FF.001 
[165625] 
LB0210THRMLPRP.001 
[160799] 
LB0205REVUZPRP.001 
[159525] 
LB0207REVUZPRP.001 
[159526] 
LB0205REVUZPRP.001 
[159525] 
LB0207REVUZPRP.001 
[159526] 
LB0305TSPA18FF.001 
[165625] 
LB0302UZDSCPUI.002 
[161787] 
LB0205REVUZPRP.001 
[159525] 
LB0207REVUZPRP.001 
[159526] 
SN0306T0504103.005 
[164132] 
SN0306T0504103.006 
[164131] 
MDL-NBS-HS-000020 REV 00 21 
Units Parameter 
Value(s) 
None Fixed Varies from 
layer to layer 
Single value kg/m3 Varies from 
layer to layer 
None Varies from 
layer to layer 
Varies from 
layer to layer 
None Varies from 
layer to layer 
and with 
infiltration 
scenario. 
Varies from 
layer to layer 
sampled 
Concentration 
will be 
sampled 
based on the 
given 
distribution 
U0065 
Distribution (or 
single value if fixed) 
10 m Fixed value 
 distribution. Layers 
are grouped together 
based on similar rock 
properties 
1/m Log-normal 
distribution 
Fixed value for a 
specific infiltration 
0.01 None Fixed 
m Layers with similar 
rock properties are 
grouped together and 
the parameters are 
mg/l Cumulative 
distribution 
ml/g Uniform distribution 
parameter range 
depends on the type 
of radionuclides 
Values will be 
sampled 
based on the 
given 
distribution 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Parameter Name 
Colloid size 
distribution 
Section 6.5.11 
Colloid filtration 
factors 
Section 6.5.9 
Colloid size 
exclusion factors 
Section 6.5.10 
Fractions of colloid 
traveling 
unretarded 
Section 6.5.13 
Colloid retardation 
factor 
Section 6.5.13 
Matrix diffusion 
coefficient 
Section 6.5.5 
Matrix adsorption 
coefficient 
Section 6.5.4 
Table 4-2. Input Parameters (Continued) 
Parameter Source 
CRWMS M&O 2000 
[148384] 
Total System 
Performance 
Assessment Model for 
Site Recommendation. 
(MDL-WIS-PA-000002 
REV 00) 
CRWMS M&O 2000 
[148384] 
Total System 
Performance 
Assessment Model for 
Site Recommendation. 
(MDL-WIS-PA-000002 
REV 00) 
CRWMS M&O 2000 
[148384] 
Total System 
Performance 
Assessment Model for 
Site Recommendation. 
(MDL-WIS-PA-000002 
REV 00) 
BSC 2003 [162729] 
Saturated Zone Colloid 
Transport 
(ANL-NBS-HS-000031 
REV 01) 
BSC 2003 [162729] 
Saturated Zone Colloid 
Transport 
(ANL-NBS-HS-000031 
REV 01) 
BSC 2003 [164889] 
Drift-Scale 
Radionuclide Transport 
(MDL-NBS-HS-000016 
REV00) 
BSC 2003 [163228] 
Radionuclide Transport 
Models Under Ambient 
Conditions (MDL-NBSHS-
000008 REV 01) 
DTN 
LL000122051021.116 
[142973] 
LA0003MCG12213.002 
[147285] 
LA0003MCG12213.002 
[147285] 
LA0303HV831352.003 
[165624] 
LA0303HV831352.002 
[163558] 
LB03023DSSCP9I.001 
[163044] 
LA0003JC831362.001 
[149557] 
LA0302AM831341.002 
[162575] 
Rock properties (rock density, fracture porosity, spacing, aperture, AFM parameter , and 
fracture residual saturation) are used as inputs to the FEHM UZ transport model. The validity 
and uncertainty of those parameters are documented in the corresponding Model Reports 
(Analysis of Hydrologic Properties Data (BSC 2003 [161773]), Calibrated Properties Model 
(BSC 2003 [160240]), and UZ Flow Models and Submodels (BSC 2003 [163045])). In this 
Model Report, we use the mean values of those parameters to demonstrate the abstraction of the 
UZ transport model. The influence of parameter uncertainty on system performance will be 
studied in TSPA multiple realization runs. 
U0065 
Distribution (or 
single value if fixed) 
None Cumulative distribution 
Fixed values but varies 
with layers 
Fixed values but vary 
from layer to layer 
Fractions of colloids 
traveling unretarded 
are given. 
None Cumulative distribution 
Layers are grouped 
together based on 
similar rock properties 
and parameters are 
sampled for estimating 
matrix diffusion 
coefficient 
Distributions defined in 
DTN by rock type and 
MDL-NBS-HS-000020 REV 00 22 
Parameter 
Value(s) 
Parameter 
values are 
sampled at run 
time 
Probability of a 
particle being 
filtered at 
matrix 
interface. 
Varies from 
layer to layer 
Probability of a 
colloid being 
excluded at 
fracture-matrix 
interface. 
Varies from 
layer to layer 
Varies with 
travel time 
Sampled 
statistical 
values 
Sampled 
parameter 
values 
Parameter 
values are 
sampled based 
on the given 
distribution 
Units 
None 
None 
None 
m2/s 
mL/g 
radionuclide 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Radionuclide transport properties are used in FEHM for simulating the transport processes of 
radionuclides in the unsaturated fracture media from repository downward to the water table. 
Colloid size distribution, concentration, adsorption coefficient, size exclusion, filtration factors, 
and retardation factors are input parameters to FEHM for simulating colloid-facilitated 
radionuclide transport in fractured media. Those data are functions of colloid and rock properties 
and vary from layer to layer. 
The uncertainty and validity of each parameter are addressed in the corresponding documents 
listed in the parameter source column in Table 4.2 and are also discussed in the various 
subsections of Section 6.5 of this Model Report as indicated in the parameter name column of 
Table 4-2. 
4.2 CRITERIA 
Technical requirements to be satisfied by PA are based on 10 CFR 63.114 [156671] and 
identified in the Yucca Mountain Project Requirements Document (Canori and Leitner 2003 
[161770]). The acceptance criteria that will be used by the U.S. Nuclear Regulatory Commission 
(NRC) to determine whether the technical requirements have been met are identified in the 
Yucca Mountain Review Plan (YMRP), Final Report (NRC 2003 [163274]). The pertinent 
requirements and acceptance criteria for this Model Report are summarized in Table 4-3. 
Table 4-3. 
Criteria 1 to 5 for Radionuclide Transport 
in the Unsaturated Zone b 
Requirement 
Numbera 
PRD-002/T-016 
b 
Project Requirements and Yucca Mountain Review Plan, Final Report Acceptance Criteria 
Applicable to This Model Report 
Yucca Mountain Review Plan, Final 
Report Acceptance Criteria 10 CFR 63 Link 
10 CFR 63.114(a-c) 
[156671] 
10 CFR 63.115(b) 
[156671] 
23 
Requirement Titlea 
PRD-002/T-015 Requirements for 
Performance Assessment 
Requirements for Multiple 
Barriers 
NOTES: a from Canori and Leitner 2003 [161770] 
from NRC 2003 [163274], Section 2.2.1.3.7.3 
c from NRC 2003 [163274], Section 2.2.1.1.3 
description of their applicability to this Model Report: 
process-level model, (Section 6.3). 
MDL-NBS-HS-000020 REV 00 
Criteria 1 to 3 for System Description 
and Demonstration of Multiple Barriersc 
The acceptance criteria identified in Sections 2.2.1.3.7.3 and 2.2.1.1.3 of the Yucca Mountain 
Review Plan, Final Report (NRC 2003 [163274]) are given below, followed by a short 
Acceptance Criteria for: Radionuclide Transport in the Unsaturated Zone (NRC 2003 [163274], 
Section 2.2.1.3.7.3) 
 Acceptance Criterion 1, System Description and Model Integration are Adequate: 
TSPA adequately incorporates important physical phenomena and uses consistent 
and appropriate assumptions throughout the Radionuclide Transport in the UZ 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
The description of aspects of hydrology, geology, and physical phenomena, and 
couplings, that may affect radionuclide transport in the unsaturated zone, is 
adequate, (Sections 6.3 and 6.4). 
The abstraction of radionuclide transport in the unsaturated zone uses assumption, 
technical bases, data, and models that are appropriate and consistent with other 
related U.S. Department of Energy abstractions (Sections 5, 6.2, 6.3, 6.4, and 6.5). 
Boundary and initial conditions used in the abstraction of radionuclide transport in 
the unsaturated zone are propagated throughout its abstraction approaches. 
Sufficient data and technical bases for the inclusion of features, events, and 
processes, related to radionuclide transport in the unsaturated zone in the total 
system performance assessment abstraction, are provided in Section 6.2. 
 Acceptance Criterion 2: Data are Sufficient for Model Justification: 
Geological, hydrological and geochemical values used in the license application are 
adequately justified. Adequate descriptions of how the data were used, interpreted, 
and appropriately synthesized into the parameters are provided, (Section 6.4). 
Sufficient data have been collected to establish initial and boundary conditions for 
the process-level model of Radionuclide Transport in the UZ, (Section 6.5). 
 Acceptance Criterion 3: Data Uncertainty is Characterized and Propagated Through the 
Model Abstraction: 
Models use parameter values, assumed ranges, probability distributions, and/or 
bounding assumptions that are technically defensible and reasonably account for 
uncertainties and variabilities Section 6.5 documents the distributions and 
uncertainties of model parameters important for performance assessment. 
 Acceptance Criterion 4, Model Uncertainty is Characterized and Propagated Through 
the Model Abstraction: 
Alternative modeling approaches are considered, consistent with available data and 
current scientific understanding, (Sections 6.6 and 6.7). 
Conceptual model uncertainties are adequately defined and documented, (Sections 
6.7 and 7.1). 
Appropriate alternative modeling approaches are consistent with available data and 
current scientific knowledge, and appropriately consider the 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 distribution and ranges of fracture flow and transport properties in the 
UZ (Sections 6.6, 6.7, and 7.1). 
January 2004 24 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
 Acceptance Criterion 5, Model Abstraction Output is Supported by Objective 
Comparisons: 
The abstraction methods proposed for implementation in the TSPA-License 
Application (LA) are based on and consistent with output from detailed process 
level models, (Sections 6.4, 6.5, 7.1, 7.2, and 7.3). 
Well-documented procedures that have been accepted by the scientific community 
to construct and test the mathematical and numerical models are used to simulate 
Radionuclide Transport through the UZ, (Sections 6.1, 6.2, 6.3, 6.4, and 6.6). 
Sensitivity or bounding analyses are provided, (Sections 7.1 and 8.2). 
Acceptance Criteria for: System Description and Demonstration of Multiple Barriers, (NRC 
2003 [163274], Section 2.2.1.1.3). 
 Acceptance Criterion 1, Identification of Barriers is Adequate: 
The unsaturated zone below the repository is a natural barrier important to waste 
isolation. This Model Report addresses the ability of the UZ geological units below 
the repository to limit and delay the transport of radionuclides to the saturated zone 
(SZ) and provides a basis for evaluating the barrier capability, (Sections 6.3 and 
6.8). 
 Acceptance Criterion 2, Description of Barrier Capability to Isolate Waste is 
Acceptable: 
The capability of the identified barriers to limit and retard the transport of 
radionuclides is adequately identified and described, including changes during the 
compliance period. The uncertainty associated with barrier capabilities is 
adequately described, (Sections 6.5, 6.6, 6.7, and 6.8). 
 Acceptance Criterion 3, Technical Basis for Barrier Capability is Adequately Presented: 
The technical bases for this radionuclide transport abstraction are consistent with 
the technical basis for TSPA-LA. The technical basis for assertions of barrier 
capability is commensurate with the importance of the barriers capability and 
associated uncertainties, (Sections, 6.3, 6.4, 6.6, and 6.8). 
The criteria listed in Table 4-3 include some that were not listed in Table 3-1 of the TWP (BSC 
2002 [160819]), but they are appropriate for this Model Report. 
4.3 CODES AND STANDARDS 
No specific formally established codes or standards have been identified as applying to this 
modeling activity. 
January 2004 25 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
MDL-NBS-HS-000020 REV 00 
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26 
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January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
5. ASSUMPTIONS 
In this section, the assumptions taken to develop the UZ radionuclide transport abstraction model 
are outlined as the first step toward developing the computational and mathematical models 
needed in radionuclide transport calculations for the TSPA model. In Section 6.4, the 
mathematical basis for this algorithm is outlined, and theory is developed to incorporate the 
effects of sorption, dispersion, and matrix diffusion into this new particle-tracking framework. 
In the remainder of this section, the fundamental assumptions of the techniques itself and the 
specific implementation for the UZ transport abstraction model are listed and justified. 
Assumption 1: Fracture frequency and permeability are log-normally distributed. 
Rationale: These properties are quantities bounded at the low end by zero. 
Therefore, a log-normal distribution is a natural choice that can meet the 
measured means and standard deviations, and are constrained to be larger than 
zero. 
Confirmation Status: This assumption does not require verification. 
Where Used: Section 6.5.7 
Assumption 2: The Active Fracture Model (AFM) appropriately accounts for reduced 
fracture/matrix interaction. 
Rationale: The reduction in fracture/matrix contact area is a result of the active 
fracture unsaturated flow model. This reduction is justified on the basis of the 
desirability of maintaining consistency with the assumptions underlying the 
development of the flow fields developed for the UZ flow modeling effort. 
These assumptions are developed in Liu et al. (1998 [105729]). 
Confirmation Status: This assumption does not require verification. 
Where Used: Section 6.4.3 
Assumption 3: The influence of matrix diffusion in a dual-permeability system can be handled 
with a sub-grid-block model consisting of parallel flow in a discrete fracture and 
connected matrix. 
Rationale: Although the submodel consisting of a repeating system of parallel, 
equally spaced fractures and parallel flow in the fractures and matrix is an 
idealization, it captures one of the key features in the UZ system, namely the 
influence of radionuclide diffusion between fractures and matrix. Furthermore, 
the influence of sharp concentration gradients in the matrix is implicitly 
accounted for in the model by incorporating results from a Discrete Fracture 
Model (DFM) designed to handle these effects accurately. Therefore, systems 
with relatively small amounts of matrix diffusion can be simulated, in contrast 
to implementations of dual-permeability transport that represent the matrix with 
January 2004 27 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
a single grid block. In numerical modeling, this type of idealization, commonly 
referred to as upscaling, is a technique for capturing the essential features of a 
physical system, even though it is understood that the actual system contains 
geometric complexities not simulated in the model. For example, Assumption 1 
showed that the distribution of fracture spacings of mapped fractures is not 
uniform. However, the important spacing of interest for transport is the spacing 
of flowing fractures, which adds significant additional uncertainty. Given this 
situation, an appropriate assumption for the purpose of capturing the impact of 
matrix diffusion is to assume the model geometry of equally spaced flowing 
fractures. 
Confirmation Status: This assumption does not require verification. 
Where Used: Section 6.4.3 
Assumption 4: Radionuclide sorption can be approximated with a linear, equilibrium sorption 
model characterized by a single parameter, the distribution coefficient Kd. 
Rationale: It is well-known that the effective sorption coefficient in porous 
media is a function of many factors, including mineralogy, groundwater 
aqueous chemistry (including redox conditions), and heterogeneity at scales 
smaller than are considered in numerical models. Furthermore, the kinetics of 
the sorption reaction must be considered to ensure that the reactions are 
effectively at equilibrium. Despite these limitations, the Kd model is by far the 
most widely used sorption model in PA calculations due to its simplicity and 
ease of use. The factors listed above do not preclude the use of this model. 
However, they must be considered when establishing the parameter uncertainty 
distribution for Kd. As long as the range of sorption coefficients used in PA 
calculations takes into account uncertainties arising due to the factors listed 
here, then this assumption is valid for the intended use of this model. 
Confirmation Status: This assumption does not require verification. 
Where Used: Section 6.4.1, Eq. 6-2 
Assumption 5: Dispersion of both aqueous and colloidal species can be approximated as 
consisting only of longitudinal dispersion, characterized by a constant value of 
the dispersivity l 
. 
Rationale: When dispersivity is used to model solute spreading in porous 
media, it is introduced to capture variability in the flow velocity that exists at 
smaller scales than are modeled in the numerical grid. Large-scale spreading 
caused by features explicitly present in the flow simulation is captured directly, 
and are not considered to be dispersion in the sense being used here. Because 
the use of this model is to predict travel time distributions of radionuclides to 
the water table, longitudinal dispersion is potentially important to capture a 
dispersed solute front arriving at the water table. By contrast, transverse 
January 2004 28 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
dispersion, omitted in this model, will tend to allow mass to migrate short 
distances in the horizontal direction. However, it is unlikely that the small 
lateral spreading orthogonal to the direction of gravitation flow will 
significantly change the transit time to the water table. Therefore, transverse 
dispersion can be neglected. Finally, to a first approximation, this variability 
will act similarly on aqueous and colloidal components. Therefore, the same 
dispersivity should be used for both. 
Confirmation Status: This assumption does not require verification. 
Where Used: Section 6.4.2 
/ coll coll c 
Assumption 6: Radionuclide mass sorbs reversibly or irreversibly to non-diffusing colloids. 
The parameter used in the model to capture this behavior is the equilibrium 
C fluid , where 
fluid 
sorption parameter K = C C is the radionuclide 
concentration residing on the colloids (moles radionuclide on colloid per kg 
fluid), and C is the corresponding concentration in the fluid phase (moles 
aqueous radionuclide per kg fluid). The value of c K is assumed to be constant 
for a given radionuclide in each realization. 
Rationale: Most measurements of sorption onto bulk rock and colloids are 
interpreted using an equilibrium sorption model such as this one. For 
compatibility with the data collected on sorption, this assumption is adopted in 
the numerical model as well. For colloids thought to be truly irreversible, the 
model can be used with an extremely large value of Kc for that portion of the 
radionuclide inventory. This approach yields a radionuclide migration behavior 
which exhibits no matrix diffusion. 
Confirmation Status: This assumption does not require verification. 
Where Used: Section 6.4.5 
Assumption 7: Colloids undergo reversible filtration in the porous medium, with a colloid 
retardation factor of R . coll 
Rationale: To estimate retardation of colloids in the fracture continuum, field 
experiments at the C-wells complex near Yucca Mountain were examined, in 
which transport of microspheres was used as an analog for colloids. The 
microsphere breakthrough curves were fit to forward and reverse filtration rates 
(DTN: LA0002PR831231.003 [144462]). These rate constants were then used 
to calculate a retardation factor for colloid transport through saturated fractured 
rock (BSC 2003 [162729]; DTN: LA0303HV831352.002 [163558]). For 
compatibility with this analysis of field data, this assumption is adopted in the 
numerical model as well. 
Confirmation Status: This assumption does not require verification. 
January 2004 29 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Where Used: Section 6.4.5 
Assumption 8: Radionuclide releases at the location of the proposed repository can be 
represented stochastically by identifying regions on the basis of the predicted 
water flux through the medium, and placing particles randomly within this 
region to represent the release. 
Rationale: Water flux through the repository region is known to be a key 
factor controlling waste package degradation and waste mobilization. By 
partitioning the finite difference grid cells in the UZ model into groups based 
on flux, radionuclides will preferentially enter the system at locations where 
the flux is highest. This approach preserves this known relationship, and does 
not artificially introduce radionuclides into the model at locations where travel 
times are extremely long. 
Confirmation Status: This assumption does not require verification. 
Where Used: Section 6.5.15 
Assumption 9: For the purposes of computing radionuclide transport, flow through the UZ can 
be approximated assuming that the system (rock mass and flow conditions) has 
not been influenced by repository waste heat effects or drift shadow effects. 
Durable changes to the rock mass hydrologic properties are also assumed to be 
negligible. 
Rationale: It is known from numerical modeling that the flow conditions 
around the proposed repository will change due to thermohydrologic effects. 
These effects are expected to last for on the order of a few thousand years. As 
long as the radionuclide releases occur after the main part of this perturbation 
takes place, the system should have bounced back to its pre-wasteemplacement 
flow conditions. Regarding the potential for durable changes to 
the rock mass properties, a range of hydrologic flow conditions (in the form of 
different flow fields imported to the model) are assumed. It is assumed that 
this range will encompass the possibility of changes to the far-field rock 
conditions from repository waste heat. 
Confirmation Status: This assumption does not require verification. 
Where Used: Section 6.5.1 
Assumption 10: Climate changes can be considered in an approximate way by imparting an 
instantaneous jump from one steady state flow field to another, with a 
corresponding rise or fall in the water table representing the bottom of the UZ 
model. Shorter-term transients (wet and dry years, individual storm events, 
etc.) are assumed to be adequately captured with a model that assumes such 
transients can be averaged to obtain a long-term, effective steady state. 
January 2004 30 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Rationale: In simulations of system performance lasting 10,000 to 20,000 
years, long-term changes in climatic conditions are expected to change the UZ 
flow field from its present-day condition. In the Yucca Mountain UZ, we 
expect water travel times of hundreds to thousands of years through the entire 
system, although this process is obviously uncertain. Assuming that the jump 
from one steady state flow field to another occurs instantaneously is a 
reasonable approximation, given the uncertainties and our inability to observe 
this process directly. When the climate changes from drier to wetter, as we 
expect it will within the regulatory compliance period, velocities will 
immediately be greater and the flow path length to the water table will be 
shorter: imposing both of these changes immediately will ensure that our 
approach will not artificially delay the imposition of the more rapid transport 
conditions. Regarding short-term transients, it is thought that the relatively 
unfractured portions of the rock, such as the Paintbrush non-welded vitric tuff 
(PTn) will dampen such transients, allowing a long-term steady state model to 
be used. 
Confirmation Status: This assumption does not require verification. 
Where Used: Sections 6.4.8 and 6.4.9 
January 2004 31 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
INTENTIONALLY LEFT BLANK 
32 MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
6. MODEL DISCUSSION 
6.1 MODELING OBJECTIVES AND APPROACH 
This Model Report documents the abstraction of UZ transport model to be used in TSPA-LA 
simulations. The UZ transport model studies the movement of radionuclides released from the 
Engineered Barrier System (EBS) into the unsaturated fractured geological media downward to 
the water table. Radionuclide mass flux versus time exiting the UZ is transferred to the SZ model 
in the TSPA system model. 
Processes affecting radionuclide transport in the UZ include: advection, dispersion, fracturematrix 
interaction, adsorption, colloid-facilitated transport, climate change and water table rises, 
and radionuclide decay/ingrowth. The numerical representation of those processes are described 
in Section 6.4. 
To simulate radionuclide transport through the UZ, FEHM needs the following data and 
parameters as inputs: 
 Numerical grid 
 Pre-generated flow fields 
 Rock density 
 Fracture properties 
 Spacing, porosity, aperture, residual saturation, and factor  for Active Fracture Model 
(AFM) 
 Radionuclide transport properties 
 Dispersivity, adsorption coefficient, matrix diffusion coefficient, and fracture retardation 
factor 
 Colloid properties 
 Size exclusion factor, filtration factor, and retardation factor 
 Repository release bins and water table collect bins. 
The pre-generated flow fields are simulated in BSC 2003 [163228] and saved for TSPA-LA use. 
The use of pre-generated flow fields increases the efficiency of transport simulations. 
In TSPA runs, GoldSim (BSC 2003 [161572]) initiates a call to the FEHM external dynamic link 
library (dll) to start UZ transport simulations (Figure 6-1). GoldSim (BSC 2003 [161572]) 
passes the following data to FEHM through the interface: 
 Simulation time 
January 2004 33 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
 Flow fields to be used 
 Coordinates for early failed packages and number of repository sub-regions 
 Number of radionuclide species 
 Radionuclide mass release from EBS to UZ in each designated sub-region for each 
species. 
At the end of each FEHM UZ transport run, FEHM passes the simulated mass output at the water 
table back for input to SZ. 
Start of GoldSim 
Call WAPDEG.dll for 
waste package degration 
Exteral dll and Goldsim 
for waste form model 
GoldSim EBS transport 
Call FEHM.dll for UZ 
transport 
call SZ_CONVOLUTE.dll 
for SZ transport 
GoldSim Biosphere model 
no End of 
simulation? 
yes 
Stop 
Figure 6-1. Schematic of the GoldSim-FEHM Coupling 
34 MDL-NBS-HS-000020 REV 00 January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
6.2 FEATURES, EVENTS, AND PROCESSES INCLUDED IN THE MODEL 
The development of a comprehensive list of features, events, and processes (FEPs) potentially 
relevant to post-closure performance of the Yucca Mountain repository is an ongoing, iterative 
process based on site-specific information, design, and regulations. The approach for developing 
an initial list of FEPs, in support of TSPA-Site Recommendation (SR) (CRWMS M&O 2000 
[153246]), was documented in Freeze et al. (2001 [154365]). The initial FEP list contained 328 
FEPs, of which 176 were included in TSPA-SR models (CRWMS M&O 2000 [153246], Tables 
B-9 through B-17). To support TSPA-LA, the FEP list was re-evaluated in accordance with the 
Enhanced FEP Plan (BSC 2002 [158966], Section 3.2). 
The included FEP abstractions incorporated in the TSPA-LA model and relevant to this report, 
are specifically addressed in this Model Report (Table 6-1). The rationale for excluding a FEP 
from the TSPA-LA model is given in the UZ FEPs Scientific Analysis Report, Features, Events, 
and Processes in UZ Flow and Transport (BSC 2003 [164873]). 
Table 6-1 provides a list of FEPs that are specifically addressed in this Model Report. Details of 
the implementation of these FEPs in TSPA-LA are summarized in Section 6.4. As noted above, 
as the FEPs list was re-evaluated (BSC 2002 [158966], Section 3.2), the current FEPs are not the 
same as those listed in the TWP (BSC 2002 [160819]) 
Included FEPs for This Model Report and Their Disposition in TSPA-LA Table 6-1. 
Treatment of FEP in this Model report Section 
Where FEP 
is 
FEP Name FEP Number Addressed 
Summary of 
Disposition in 
TSPA-LA 
1.2.02.01.0A Fractures Sections Groundwater flow 
6.4.3, 6.5.1, 
6.5.7, and 
6.6.2 
Influence of fractures on radionuclide 
in the Yucca transport through UZ is investigated 
Mountain region through the dual permeability model 
and transport of (Section 6.4.3). Influence of fracture 
any released characteristics on UZ flow are included in 
radionuclides may the model report through using the pretake 
place along generated flow fields (Section 6.5.1. DTN: 
fractures. The rate LB0305TSPA18FF.001 [165625]). Factors 
of flow and the (fracture aperture, porosity, and 
extent of transport frequency. DTNs: 
in fractures are LB0205REVUZPRP.001 [159525] and 
influenced by LB0207REVUZPRP.001 [159526]) 
characteristics such affecting UZ radionuclide transport are 
as orientation, summarized in Section 6.5.7. 
aperture, asperity, Simulation results for the basecase model 
fracture length, runs are documented in Section 6.6.2. 
connectivity, and 
the nature of any 
linings or infills. 
Fracture porosity and frequency data 
distributions are an output of this Model 
Report (Output-DTN: 
LA0311BR831371.003) and will be 
statistically sampled during TSPA-LA 
multi-realization runs. 
January 2004 35 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) Table 6-1. 
FEP Name FEP Number 
1.2.02.02.0A Faults 
1.3.01.00.0A Climate 
change 
MDL-NBS-HS-000020 REV 00 
Section 
Where FEP 
is 
Addressed 
Summary of 
Disposition in 
TSPA-LA 
Section Numerous faults of 
6.5.1, 6.5.7 
and 6.6.2. 
various sizes have 
been noted in the 
Yucca Mountain 
Region and in the 
repository area in 
specific. Faults may [165625]) and the characteristics of 
represent an 
alteration of the 
rock permeability 
and continuity of 
the rock mass, 
alteration or shortcircuiting 
of the flow 
paths and flow 
distributions close 
to the repository, For this FEP, no direct data feed is 
and represent generated for TSPA-LA by this Model 
unexpected Report. 
pathways through 
the repository. 
Sections 
6.4.9 and 
6.6.2 
Climate change 
may affect the longterm 
performance 
of the repository. 
This includes the 
effects of long-term 
change in global 
climate (e.g., 
glacial/interglacial 
cycles) and shorter- 
term change in 
regional and local 
climate. Climate is 
typically 
characterized by 
temporal variations 
in precipitation and 
temperature. 
36 
U0065 
Treatment of FEP in this Model report 
Influence of faults on radionuclide 
transport is included through the use of 
dual permeability model, the use of pregenerated 
flow fields which included the 
effects of faults in the 3-D model (Section 
6.5.1, DTN: LB0305TSPA18FF.001 
fractures within the faults (Section 6.5.7). 
In TSPA-LA runs, the influence of faults is 
included through the use of fault 
properties and the pre-generated flow 
fields under different climate conditions as 
described in Sections 6.5.1 and 6.5.7. 
Simulation results that included faults in 
the UZ are documented in Section 6.6.2. 
Climate change is included in Section 
6.4.9. The effect of climate change on 
repository performance was studied by 
using pre-generated flow fields under 
different climates (DTN: 
LB0305TSPA18FF.001 [165625]). For 
TSPA-LA, the pre-generated flow fields 
are used by the FEHM model as 
described in Section 6.4.9. 
Simulations results under present day 
mean infiltration condition and those 
under the glacial mean infiltration 
condition are documented in Section 
6.6.2. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) Table 6-1. 
FEP Name FEP Number 
1.4.01.01.0A Climate 
modification 
increases 
recharge 
2.2.03.01 .0A Stratigraphy 
MDL-NBS-HS-000020 REV 00 
Section 
Where FEP 
is 
Addressed 
Sections 
6.5.1 and 
6.6.2 
Sections 
6.5.1. 
Summary of 
Disposition in 
TSPA-LA 
Climate 
modification 
(natural or artificial) 
causes an increase 
in recharge in the 
Yucca Mountain 
region. Increased 
recharge might 
lead to increased 
flux through the 
repository, perched 
water, or water 
table rise. 
Stratigraphic 
information is 
necessary 
information for the 
performance 
assessment. This 
information should 
include 
identification of the 
relevant rock units, 
soils and alluvium, 
and their thickness, 
lateral extents, and 
relationships to 
each other. Major 
discontinuities 
should be 
identified. 
37 
U0065 
Treatment of FEP in this Model report 
The effect of climate changes in the form 
of increased recharge is included through 
the use of pre-generated flow fields 
(Section 6.5.1 and DTN: 
LB0305TSPA18FF.001 l165625]). In 
multi-realization TSPA-LA runs, different 
climate patterns are applied and the effect 
of climate change is included through 
FEHMs use of pre-generated flow fields 
for the corresponding climates as 
described in Section 6.5.1. 
Simulation results for present day mean 
and glacial mean climates are shown in 
Section 6.6.2. Water table rise is 
incorporated by processing the flow fields 
assuming that the water table immediately 
rises due to climate change  see Section 
6.4.9 for details. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
The FEP is included through the use of 
pre-generated flow fields (DTN: 
LB0305TSPA18FF.001 [165625]). The 
flow fields are used by FEHM in TSPA-LA 
multi-realization runs as described in 
Section 6.5.1. 
For this FEP, No direct data feed is 
generated for TSPA-LA by this Model 
Report. 
More detailed information, on 
implementation of this FEP for TSPA-LA 
can be found in document: Development 
of Numerical Grids for UZ Flow and 
Transport Modeling (BSC 2003 [160109]). 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) Table 6-1. 
FEP Name FEP Number 
2.2.03.02.0A Rock 
properties of 
host rock and 
other units 
2.2.07.02.0A Unsaturated 
groundwater 
flow in the 
geosphere 
MDL-NBS-HS-000020 REV 00 
Section 
Where FEP 
is 
Addressed 
Sections 
6.5.3, 6.5.7, 
and 6.6.2. 
Section 
6.5.1 and 
6.6.2. 
Summary of 
Disposition in 
TSPA-LA 
Physical properties 
such as porosity 
and permeability of 
the relevant rock 
units, soils, and 
alluvium are 
necessary for the 
performance 
assessment. 
Possible 
heterogeneities in 
these properties 
should be 
considered. 
Questions 
concerning events 
and processes that 
may cause these 
physical properties 
to change over time 
are considered in 
other FEPs. 
Groundwater flow 
occurs in 
unsaturated rocks 
in most locations 
above the water 
table at Yucca 
Mountain, including 
at the location of 
the repository. See 
related FEPs for a 
discussion of 
specific issue 
related to 
unsaturated flow. 
38 
U0065 
Treatment of FEP in this Model report 
Rock properties of host rock and other 
units are included and used in the 
simulations of radionuclide transport 
through the UZ. Sections 6.5.3 and 6.5.7 
document the matrix porosity, rock 
density, fracture porosity, fracture 
spacing, and aperture data (DTN: 
LB0305TSPA18FF.001 [165625], 
LB0210THRMLPRP.001 [160799], 
LB0205REVUZPRP.001 [159525], and 
LB0207REVUZPRP.001 [159526]). 
Section 6.6.2 demonstrates the simulation 
results of radionuclide transport through 
the UZ using the mean rock properties. 
The generated distributions of fracture 
porosity and fracture frequency are an 
Output (DTN: LA0311BR831371.003) of 
the Model Report and will be used by 
TSPA-LA in multi-realization runs as 
described in Sections 6.5.3 and 6.5.7. 
Unsaturated groundwater flow in the UZ is 
the driving force for radionuclide transport 
through the UZ. This FEP is addressed 
through the use of pre-generated flow 
fields (Section 6.5.1, DTN: 
LB0305TSPA18FF.001 [165625]) for 
TSPA-LA multi-realization runs. The pregenerated 
flow fields are directly used by 
FEHM as described in Section 6.5.1. 
Simulation results of radionuclide 
transport through the UZ under present 
day mean and glacial mean infiltration 
conditions are documented in Section 
6.6.2. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) Table 6-1. 
FEP Name FEP Number 
2.2.07.04.0A Focusing of 
unsaturated 
flow (fingers, 
weeps) 
2.2.07.06.0A Episodic / 
pulse release 
from repository 
2.2.07.06.0B Long-term 
release of 
radionuclides 
from repository 
MDL-NBS-HS-000020 REV 00 
Section 
Where FEP 
is 
Addressed 
Section 
6.5.1 and 
6.6.2. 
Sections 
6.4.6, 6.4.7, 
6.4.8, and 
6.4.9. 
Sections 
6.4.6 and 
6.4.7 
Summary of 
Disposition in 
TSPA-LA 
Unsaturated flow 
can differentiate 
into zones of 
greater and lower 
saturation (fingers) 
that may persist as 
preferential flow 
paths. 
Heterogeneities in 
rock properties, 
including fractures 
and faults, may 
contribute to 
focusing. Focused 
flow may become 
locally saturated. 
Episodic or pulse 
release of 
radionuclides from 
the repository and 
radionuclide 
transport in the UZ 
may occur both 
because of 
episodic flow into 
the repository, and 
because of pulse 
releases from failed 
waste packages. 
The release of 
radionuclides from 
the repository may 
occur over a long 
period of time, as a 
result of the timing 
and magnitude of 
the waste 
packages and drip 
shield failures, 
waste form 
degradation, and 
radionuclide 
transport through 
the invert. 
39 
U0065 
Treatment of FEP in this Model report 
In the current model abstraction report, 
the effect of focusing unsaturated flow is 
included through the use of pre-generated 
flow fields (Section 6.5.1, DTN: 
LB0305TSPA18FF.001 [165625]) as 
described in Section 6.5.1. For TSPA-LA, 
the pre-generated flow fields are used 
directly by FEHM. 
For this FEP, no direct data feed is 
generated for TSPA by this Model Report. 
This FEP is more fully addressed in the 
Model Report UZ Flow Models and 
Submodels (BSC 2003 [163045]). 
The implementation of episodic/pulse 
release from repository is discussed in 
Sections 6.4.6 through 6.4.9. 
For TSPA-LA, episodic/pulse release from 
repository is implemented by passing 
radionuclide mass release from GoldSim 
to FEHM through the GoldSim-FEHM 
interface (Sections 6.4.6 and 6.4.7). 
Episodic/pulse release caused by climate 
change, addressed in Sections 6.4.8 and 
6.4.9 is implemented by switching from 
one flow field to a new flow field at time of 
climate change through FEHM-GoldSim 
interface. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
Long-term radionuclide release due to the 
failure of waste packages in the repository 
is addressed in Sections 6.4.6 and 6.4.7. 
For each TSPA-LA GoldSim-FEHM run, 
GoldSim passes radionuclide mass 
releases to FEHM and FEHM simulates 
the transport process through the UZ as 
described in Sections 6.4.6 and 6.4.7. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) Table 6-1. 
Section 
Where FEP 
is 
Addressed FEP Name FEP Number 
Summary of 
Disposition in 
TSPA-LA 
Section 
6.5.1 
2.2.07.07.0A Perched water 
develops 
Zones of perched 
water may develop 
above the water 
table. If these 
zones occur above 
the repository, they 
may affect UZ flow 
between the 
surface and the 
waste packages. If 
they develop below 
the repository, for 
example at the 
base of the 
Topopah Spring 
welded unit, they 
may affect flow 
pathways and 
radionuclide 
transport between 
the waste 
packages and the 
saturated zone. 
Section 
6.5.1 
2.2.07.08.0A Fracture flow 
in the UZ 
Fractures or other 
analogous 
channels act as 
conduits for fluids 
to move into the 
subsurface to 
interact with the 
repository and as 
conduits for fluids 
to leave the vicinity 
of the repository 
and be conducted 
to the SZ. Water 
may flow through 
only a portion of the 
fracture network, 
including flow 
through a restricted 
portion of a given 
fracture plane. 
40 MDL-NBS-HS-000020 REV 00 
U0065 
Treatment of FEP in this Model report 
This FEP is included through the use of 
pre-generated flow fields (DTN: 
LB0305TSPA18FF.001 [165625]). In 
TSPA-LA runs, pre-generated flow fields 
are used by FEHM and used in UZ 
transport simulations as described in 
Section 6.5.1. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
More detailed information on the 
treatment of fracture flow in UZ can be 
found in the Model Report, UZ Flow 
Models and Submodels (BSC 2003 
[163045]). 
In the unsaturated zone, fracture flow 
plays an important role in the transport of 
radionuclides. In TSPA-LA runs, the direct 
effect of fracture flow on radionuclide 
transport (advection) is included through 
FEHMs use of pre-generated flow fields 
(DTN: LB0305TSPA18FF.001 [165625]) 
in UZ transport simulations as described 
in Section 6.5.1. 
For this FEP, no direct data feed is 
generated for TSPA in this Model Report. 
More detailed information on the 
treatment of fracture flow in UZ can be 
found in the Model Report, UZ Flow 
Models and Submodels (BSC 2003 
[163045]). 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) Table 6-1. 
Section 
Where FEP 
is 
Addressed FEP Name FEP Number 
Summary of 
Disposition in 
TSPA-LA 
Section 
6.5.1 
2.2.07.09.0A Matrix 
imbibition in 
the UZ 
Water flowing in 
fractures or other 
channels in the 
unsaturated zone is 
imbibed into the 
surrounding matrix. 
This may occur 
during steady flow, 
episodic flow, or 
into matrix pores 
that have been 
dried out during the 
thermal period. 
2.2.07.15.0B Advection and Section 
dispersion in 
the UZ 
6.4.1, 6.4.2, 
6.6.2, and 
7.1.1. 
Advection and 
dispersion 
processes may 
affect contaminant 
transport in the UZ. 
41 MDL-NBS-HS-000020 REV 00 
U0065 
Treatment of FEP in this Model report 
For TSPA-LA runs, the pre-generated flow 
fields (DTN: LB0305TSPA18FF.001 
[165625]) are used by FEHM in UZ 
transport simulations as described in 
Section 6.5.1. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
More detailed information on the 
treatment of fracture flow in UZ can be 
found in the Model Report, UZ Flow 
Models and Submodels (BSC 2003 
[163045]). 
Radionuclide transport through the UZ by 
advection is simulated using the RTTF 
(Residence Time Transfer Function) 
method documented in Section 6.4.1. 
Dispersion is incorporated into the RTTF 
algorithm through the use of a transfer 
function based on an analytical solution to 
the advection-dispersion equation 
(Section 6.4.2). 
Simulation results involving advection and 
dispersion under different flow conditions 
are shown in Section 6.6.2 and 7.1.1. 
In TSPA LA runs, advection and 
dispersion is simulated through the use of 
FEHM RTTF model and the pregenerated 
flow fields as described in 
Sections 6.4.1 and 6.4.2. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-1. 
Section 
Where FEP 
is 
Addressed FEP Name FEP Number 
Summary of 
Disposition in 
TSPA-LA 
2.2.08.08.0B Matrix diffusion Section 
in the UZ 6.4.3, 6.5.5, 
6.6.2, 7.1.2, 
7.1.3, and 
Attachment 
III. 
Matrix diffusion is 
the process by 
which radionuclides 
and other species 
transported in the 
UZ by advective 
flow in fractures or 
other pathways 
move into the 
matrix of the 
porous rock by 
diffusion. Matrix 
diffusion can be a 
very efficient 
retarding 
mechanism, 
especially for 
strongly sorbed 
radionuclides due 
to the increase in 
rock surface 
accessible to 
sorption. 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) 
U0065 
Treatment of FEP in this Model report 
Migration of radionuclides from fast flow 
fracture into surrounding slow flow matrix 
blocks by diffusion could play an important 
role in delaying the transport process of 
radionuclides in fractures. In this report, 
the role of matrix diffusion is included 
through the development of the transfer 
function approach as described in Section 
6.4.3. 
Transfer function curves (Output-DTN: 
LA0311BR831229.001) generated in this 
Model Report are a direct feed to TSPALA 
and will be used by FEHM in 
simulating the effect of matrix diffusion on 
radionuclide transport in TSPA-LA runs as 
described in Sections 6.4.3 and 
Attachment III. 
One important factor affecting the strength 
of matrix diffusion is the matrix diffusion 
coefficient. In this report matrix diffusion 
coefficient is related to matrix water 
content and matrix effective permeability 
through the relationship developed by 
Reimus et al. (2002 [163008]). The 
distributions of matrix water content and 
matrix effective permeability are an output 
of this Model Report (Section 6.5.5, 
Output-DTN: LA0311BR831371.003) and 
are used by TSPA in multiple realization 
runs for randomly generating matrix 
diffusion coefficients. 
Simulation results involving matrix 
diffusion, which are not a direct data feed 
to TSPA-LA, are illustrated in Sections 
6.6.2, 7.7.2, and 7.7.3. 
42 MDL-NBS-HS-000020 REV 00 January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) Table 6-1. 
Section 
Where FEP 
is 
Addressed FEP Name FEP Number 
Summary of 
Disposition in 
TSPA-LA 
2.2.08.09.0B Sorption in the 
UZ 
Sections 5., 
6.4.3, 6.4.5, 
6.5.4, 6.5.8, 
and 6.6.2. 
Sorption of 
dissolved and 
colloidal 
radionuclides in the 
UZ can occur on 
the surfaces of both 
fractures and 
matrix in rock or 
soil along the 
transport path. 
Sorption may be 
reversible or 
irreversible, and it 
may occur as a 
linear or nonlinear 
process. Sorption 
kinetics and the 
availability of sites 
for sorption should 
be considered. 
Sorption is a 
function of the 
radioelement type, 
mineral type, and 
groundwater 
composition. 
43 MDL-NBS-HS-000020 REV 00 
U0065 
Treatment of FEP in this Model report 
Sorption in the UZ is treated as a linear 
process (Section 5, assumption 4). 
In the matrix, sorption is incorporated in 
the generation of transfer function curves 
and expressed as part of the defined 
dimensionless parameters (Section 6.4.3). 
For colloid facilitated radionuclide 
transport, radionuclide sorption onto 
colloids and its effect on transport is 
simulated through the colloid retardation 
factor, which is a function of radionuclide 
sorption coefficient onto colloids and the 
colloid retardation factor (Section 6.4.5). 
Radionuclide sorption coefficients used in 
the simulation of radionuclide transport in 
UZ are documented in Section 6.5.4 
(DTN: LA0302AM831341.002 [162575]). 
Colloid concentration and radionuclide 
sorption coefficients onto colloids are 
documented in Section 6.5.12 (DTN: 
SN0306T0504103.005 [164132] and 
SN0306T0504103.006 [164131]). 
Simulation results involving colloid 
transport are demonstrated in Section 
6.6.2. 
In TSPA-LA runs, sorption coefficients are 
sampled and fed into FEHM as described 
in the above mentioned sections. 
Sorption onto fracture surfaces is 
neglected because of few data available 
in supporting such a retardation 
mechanism in the UZ. Thus, a fracture 
surface retardation factor of 1 is set for 
use in TSPA-LA runs (Section 6.5.8.). 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) Table 6-1. 
FEP Name FEP Number 
2.2.08.10.0B Colloidal 
transport in the 
UZ 
2.2.11.03.0A Gas transport 
in geosphere 
MDL-NBS-HS-000020 REV 00 
Section 
Where FEP 
is 
Addressed 
Sections 
6.4.5, 6.5.9, 
6.5.10, 
6.5.11, 
6.5.12, 
6.5.13, and 
6.6.2 
6.4.7 
Summary of 
Disposition in 
TSPA-LA 
Radionuclides may The influence of colloid transport on 
be transported in radionuclide migration through the UZ is 
groundwater in the discussed in Section 6.4.5. Parameters 
UZ as colloidal that can impact colloid transport in the UZ 
species. Types of include colloid size (DTN: 
colloids include true LL000122051021.116 [142973]), colloid 
colloids, pseudo 
colloids, and 
microbial colloids. 
Gas released from 
the drifts and gas 
generated in the 
near-field rock will 
flow through 
fracture systems in 
the near field rock 
and in the 
geosphere. Certain 
gaseous or volatile 
radionuclides may 
be able to migrate 
through the far-field 
faster than the 
groundwater 
advection rate. 
44 
U0065 
Treatment of FEP in this Model report 
concentration (DTN: 
SN0306T0504103.005 [164132]), 
radionuclide sorption coefficient onto 
colloid (DTN: SN0306T0504103.006 
[164131]), and colloid retardation factors 
(DTN: LA0303HV831352.002 [163558]) 
are documented in Sections 6.5.9 through 
6.5.13. 
Simulation results involving colloids are 
documented in Section 6.6.2. 
In TSPA-LA runs, colloid facilitated 
radionuclide transport is investigated 
through the FEHM colloid transport model 
and variations of colloid transport 
parameters as described in the above 
mentioned sections. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
This FEP is included on the basis that all 
radionuclides in TSPA are released into 
the aqueous phase. This is expected to 
bound any dose effects of gas-phase 
release due to the large dilution of gasphase 
release in the atmosphere 
(Features, Events, and Processes in UZ 
Flow and Transport, BSC 2003 [164873]). 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Included FEPs for This Model Report and Their Disposition in TSPA-LA (Continued) Table 6-1. 
Section 
Where FEP 
is 
Addressed FEP Name FEP Number 
Summary of 
Disposition in 
TSPA-LA 
3.1.01.01.0A Radioactive 
decay and 
Sections 
6.4.4, 
6.5.14, and ingrowth 
6.6.2 
Radioactivity is the 
spontaneous 
disintegration of an 
unstable atomic 
nucleus that results 
in the emission of 
subatomic 
particles. 
Radioactive 
isotopes are known 
as radionuclides. 
Radioactive decay 
of the fuel in the 
repository changes 
the radionuclide 
content in the fuel 
with time and 
generates heat. 
Radionuclide 
quantities in the 
system at any time 
are the result of the 
radioactive decay 
and the growth of 
daughter products 
as a consequence 
of that decay (i.e., 
ingrowth). Over a 
10,000-year 
performance 
period, these 
processes will 
produce daughter 
products that need 
to be considered in 
order to adequately 
evaluate the 
release and 
transport of 
radionuclides to the 
accessible 
environment. 
45 MDL-NBS-HS-000020 REV 00 
U0065 
Treatment of FEP in this Model report 
In this report, decay and ingrowth are 
simulated through the development of an 
effective integration algorithm (Section 
6.4.4). This algorithm can handle multiple 
species decay and ingrowth processes. 
Radionuclide half lives and daughter 
products considered in the UZ transport 
abstraction model are documented in 
Section 6.5.14. 
Simulation results involving radionuclide 
decay/ingrowth processes are illustrated 
in Section 6.6.2. 
In TSPA-LA runs, 36 species of 
radionuclides are simulated through the 
UZ using the FEHM decay/ingrowth model 
over a specified time period as described 
in the above mentioned sections in this 
Model Report. 
For this FEP, no direct data feed is 
generated for TSPA-LA by this Model 
Report. 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
6.3 THE UZ TRANSPORT ABSTRACTION MODEL 
The UZ transport component of the total system model tracks the movement of radionuclides 
released from the EBS down to the water table (Figure 6-2). 
Figure 6-2. Schematic of Water Movement and Radionuclide Transport through the UZ 
46 MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
The top boundary of the UZ flow model is the ground surface, with prescribed infiltration rates, 
and the bottom boundary is the water table. The side boundaries are no flow. 
The UZ flow fields are pregenerated and saved for use by FEHM. During TSPA simulation 
runs, the FEHM dll reads in the pregenerated flow fields and then carries out transport 
simulations. The impact of climate change is investigated by using the UZ flow fields 
corresponding to different climate scenarios. The FEHM-compatible flow field files developed 
for the TSPA-LA model are in DTN: LB0305TSPA18FF.001 [165625]. 
The UZ transport model is based on the dual permeability formulation for fluid flow, with 
additional transport considerations to incorporate the influence of sorption and fracture-matrix 
interactions on radionuclide transport. The influence of spatial variability is included through a 
3-D model that incorporates the appropriate geometry and geology. 
For the UZ transport model, radionuclides are released the repository where failed waste 
packages release radionuclides into the system. Any radionuclide that reaches the water table is 
removed from the UZ transport system and put into the SZ system. 
Once a radionuclide particle is released from the EBS into UZ, the particle is carried by water 
traveling through the fractured media downward to the water table. The following transport 
mechanisms can affect the movement of a radionuclide particle and are considered in the UZ 
transport model: 
 Advection 
 Dispersion 
 Adsorption 
 Fracture-matrix interaction including matrix diffusion 
 Colloid-facilitated transport 
 Radioactive decay/ingrowth 
 Climate change and water table rise. 
Implementation of the above transport mechanisms inside FEHM are described in Section 6.4 of 
this Model Report. The abstraction model is designed to facilitate parameter uncertainty 
analyses in TSPA. This is done by running multiple realizations with different parameter values 
based on parameter distributions. 
Performing multiple realizations (numbering in the hundreds) for such a complex system 
requires that the software used for simulating radionuclide transport in the system be efficient 
while also being able to handle complex physical and chemical processes with sufficient 
accuracy. FEHM (Zyvoloski et al. 1997 [100615]) was selected for simulating radionuclide 
transport in the system because of the efficiency of the particle tracking method and its ability to 
handle advection, dispersion, sorption, matrix-diffusion, and multiple-species radionuclide 
decay/ingrowth in the system. 
January 2004 47 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
6.4 THE NUMERICAL REPRESENTATION OF THE UZ TRANSPORT MODEL 
This section outlines the development of the general transport methods used for the Residence 
Time/Transfer Function (RTTF) particle-tracking model and issues specific to the use of this 
model to simulate radionuclide transport for the Yucca Mountain UZ. 
Prediction of solute transport is a critical element of many groundwater flow studies, including 
contaminant transport and the movement of dissolved species in solution. Modeling efforts 
typically are motivated by the need to predict the movement of a pollutant or dissolved chemical 
in the subsurface to answer practical questions concerning the rate and direction of contaminant 
movement and the predicted concentration in solution. In a typical solute transport simulation, a 
dissolved chemical is introduced into a steady-state or time-varying flow field, and the fate of the 
chemical is tracked while undergoing physical and chemical processes such as advection, 
dispersion, chemical and biological reaction, or diffusion into dead-end pore space. Often, a 
concentration front is established that must be tracked accurately. In addition, many field 
investigations employ natural or introduced tracers to study the flow and transport system. 
These studies also require models to simulate the movement of dissolved species. 
Traditional solutions to the advection-dispersion (AD) equation, such as those used in most 
finite-element or finite-difference flow and transport codes, are versatile and allow the 
simultaneous solution of multiple interacting species. One drawback of a finite-difference or 
finite-element solution to the AD equation is that significant numerical dispersion may arise in 
the portion of a computational domain occupied by a front of rapidly varying concentration. 
Reducing the numerical dispersion requires either increased grid resolution or higher-order 
approximation methods, both of which may lead to prohibitive computational costs. Numerical 
dispersion is identical in character to actual dispersion, so it is difficult to separate numerical 
from actual dispersion in complex transport simulations. 
Approaches to cope with this problem include front-tracking algorithms with multiple grids 
(e.g., Yeh 1990 [101501]; Wolfsberg and Freyberg 1994 [101498]), the method of characteristics 
(e.g., Chiang et al. 1989 [101384]), hybrid Eulerian-Lagrangian solution techniques (Neuman 
1984 [101463]), and particle-tracking techniques (e.g., Tompson and Gelhar 1990 [101490]). 
Front-tracking algorithms solve the AD equation in integrated form on a numerical grid while 
tailoring the mesh to increase the resolution of the calculation at fronts. In contrast, an Eulerian- 
Lagrangian technique casts the AD equation using the total derivative, so that the advection 
portion of transport can be solved accurately using particle-tracking techniques or the method of 
characteristics, while the dispersion component of transport is solved on a finite-difference or 
finite-element grid using standard techniques. 
Particle-tracking transport models take a fundamentally different approach. The trajectory of 
individual molecules or packets of fluid containing molecules are tracked through the model 
domain. When the fluid path lines are the model result of interest (Pollack 1988 [101466]; Lu 
1994 [101413]), a relatively small number of particles can be used to trace the streamlines. 
Particle tracking is also used to simulate solute transport, such as the migration of a contaminant 
plume (Akindunni et al. 1995 [101378]) or the prediction of breakthrough curves in interwell 
tracer experiments (Johnson et al. 1994 [101400]). For these applications, a relatively large 
number of such particles must be used to obtain accurate solutions to the transport problem. 
January 2004 48 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Particle tracking has also been used to solve the advective portion of complex reactive transport 
models that simulate chemical reactions among multiple species (Fabriol et al. 1993 [101387]). 
In a typical particle-tracking algorithm, a particle is sent to a new position assuming that the 
magnitude and direction of the velocity vector are constant during a time step. If small enough 
time steps are taken, particle pathways can be tracked accurately. Dispersion is treated as a 
random process that diverts the particle a random distance from its dispersion-free, deterministic 
path. In these so-called random walk models (e.g., Kinzelbach 1988 [101402]), dispersion is 
usually calculated stochastically subject to a Gaussian model to reproduce the specified 
dispersion coefficient. The technique has also been extended by employing non-Gaussian 
random walk functions to represent scale-dependent dispersion (Scheibe and Cole 1994 
[101477]). Linear equilibrium sorption can be handled through the use of a retardation factor to 
correct the magnitude of the particle velocity. 
A crucial component of most random-walk particle-tracking algorithms developed to date is the 
need to accurately estimate the velocity at every position in the model domain. In the context of 
a finite-difference or finite-element numerical code, this means that velocities at positions other 
than the node points of the fluid flow grid must be computed using an interpolation scheme. 
Many studies have proposed and studied the accuracy of different interpolation schemes, 
including methods developed for regular, two- or three-dimensional finite difference grids 
(Schafer-Perini and Wilson 1991 [101476]; Zheng 1993 [101502]), for two- and threedimensional 
finite-element grids (Cordes and Kinzelbach 1992 [101385]), and for codes that 
employ the boundary element method for computing fluid flow (Latinopoulos and Katsifarakis 
1991 [101408]). Special techniques have been developed to handle complexities such as point 
fluid sources and sinks and abrupt changes in the conductivity of the medium (Zheng 1994 
[101503]). 
Unfortunately, many of the velocity interpolation schemes used in conventional particle-tracking 
techniques are computationally intensive, thus limiting the number of particles that can 
practically be used. Another drawback to traditional particle-tracking approaches is that spatial 
and temporal discretization often results in numerical inaccuracy in the fluid flow solution upon 
which velocity determinations are based. Thus, precise and time-consuming velocity 
interpolation schemes may not be justified in finite-difference or finite-element models. Finally, 
and most important for the simulation of transport in the UZ at Yucca Mountain, 
dual-permeability models employ overlapping continua to represent fracture and matrix flow 
(Zyvoloski et al. 1992 [101026]; Zimmerman et al. 1993 [100614]). To develop a streamlinebased 
particle-tracking method for dual-permeability models, velocity interpolations on each 
continuum would have to be coupled to a transfer term that allows particles to move from one 
medium to the other. This additional complexity, along with the inherent approximations 
associated with the dual-permeability method itself, may make precise velocity interpolation 
calculations of limited validity. 
In this model, a particle-tracking technique is employed that can be used for transient, 
multi-dimensional finite-difference or finite-element codes. The algorithm is designed for 
computing solute concentration fields quickly and easily with structured or unstructured 
numerical grids of arbitrary complexity. Both continuum and dual-permeability formulations 
can be simulated. This flexibility is accomplished by extending the cell-based strategy of 
January 2004 49 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Desbarats 1990 [101386] for mapping out the path of the particle. In this method, the calculation 
of an exact pathline is replaced with a cell-to-cell migration of the particle. The mass flux 
from cell to cell is used directly, and no velocity interpolations are required. Since numerical 
solutions for fluid flow are typically mass-conservative (though not necessarily accurate) the 
particle-tracking method automatically conserves mass. 
6.4.1 Basic Methods 
The particle-tracking method developed in the present study views the fluid flow computational 
domain as an interconnected network of fluid storage volumes. Particles travel only from cell to 
cell, requiring no greater resolution of the particle pathways. In this sense, the method is similar 
to the node-to-node routing method of Desbarats (1990 [101386], p. 156). This simple starting 
point has been extended to include many different transport submodels and complex flow 
domains. Even though some aspects of the development that follows would appear to be 
applicable for steady-state, single-porosity flow fields, the extensions to the method for treating 
transient flow systems and dual-porosity model formulations are discussed in Section 6.4.3. The 
two steps in the particle-tracking approach are: 1) determine the time a particle spends in a given 
cell; and 2) determine which cell the particle travels to next. These two steps are detailed below. 
The residence time for a particle in a cell is governed by a transfer function describing the 
probability of the particle spending a given length of time in the cell. Thus, this particle-tracking 
approach is called the RTTF method. The schematic plots shown in Figures 6-3 and 6-4 
illustrate the basis of the RTTF approach. For a cumulative probability distribution function of 
particle residence times, the residence time of a particle in a cell is computed by generating a 
random number between 0 and 1 to determine the corresponding residence time from the 
distribution function. In the simplest case, advective transport through the cell, there is only one 
possible travel time through the cell, and the function illustrated in Figure 6-4 is the Heaviside 
function. However, dispersion and diffusion give rise to a distribution of travel times through the 
cell that must be reproduced in order to simulate these mechanisms. In this example, the 
advection-dispersion (AD) equation was used to generate the RTTF curve, but other transport 
mechanisms can be incorporated as well, as demonstrated below. 
Figure 6-3. Schematic of the Cell-Based Particle-tracking Technique 
50 MDL-NBS-HS-000020 REV 00 January 2004 Particle Tracking Model and Abstraction of Transport Processes 
R  , and R is given by 
 
Figure 6-4. Schematic of the RTTF Technique for Determining Particle Residence Time in a Cell. The 
time axis represents the probabilistically determined residence time of a particle in the cell. 
If a large number of particles pass through the cell, the cumulative residence time distribution of 
particles in the cell will be reproduced. Particle-tracking models of single-fracture transport 
(Yamashita and Kimura 1990 [101499]) have employed this approach to simulate fracture 
transport with diffusion into the rock matrix. From the solution of the flow field in a numerical 
model, the mass of fluid in the computational cell and the mass flow rate to or from each 
adjacent cell is computed. In the simplest case, the residence time of a particle in a cell,  , is 
given by 
fl 
fl part 
part 
M fl (Eq. 6-1) fl part m& out 
January 2004 
where M is the fluid mass in the cell and the summation term in the denominator refers to the 
outlet fluid mass flow rates from the cell to adjacent cells. In the absence of dispersion or other 
transport mechanisms, the transfer function describing the distribution of particle residence times 
is a Heaviside function (unit step function) that is unity at the fluid residence time fl , because 
for this simple case, all particles entering the cell will possess this residence time. Equilibrium, 
linear sorption is included by correcting the particle residence time by a retardation factor R . 
Thus,  
 =
bKd (Eq. 6-2) 
fl 


51 
= 
MDL-NBS-HS-000020 REV 00 
U0065 
=  
R = 1+
U0065 Particle Tracking Model and Abstraction of Transport Processes 
where 
d K is the equilibrium sorption coefficient (ml fluid/g rock) 
b  is the bulk rock density (g rock/ml total) 
fl  is the volumetric water content (ml fluid/ml total) 
Once again, in the absence of other transport processes, the transfer function is a Heaviside 
function. Note that the method is applicable for either liquid or gas phase transport, so the 
generic term gfluidh is used in the definition above. However, in this Model Report, only liquid 
phase transport is simulated. 
Before discussing more complex transfer functions for the RTTF method, the method for 
determining which cell a particle travels to after completing its stay at a given cell is discussed. 
The approach that is consistent with the RTTF method is that the probability of traveling to a 
neighboring cell is proportional to the mass flow rate to that cell. Only outflows are included in 
this calculation; the probability of traveling to an adjacent node is 0 if fluid flows from that node 
to the current node. A uniform random number from zero to one is used to make the decision of 
which node to travel to. In summary, the particle-tracking algorithm is: 1) compute the 
residence time of a particle at a cell using the RTTF method; and 2) at the end of its stay, send 
the particle to an adjacent cell randomly, with the probability of traveling to a given cell 
proportional to the mass flow rate to that cell. 
6.4.2 Dispersion 
Transport processes such as dispersion can be incorporated into the RTTF particle-tracking 
algorithm through the use of transfer functions. For dispersion, within a computational cell, the 
equation for one-dimensional, axial dispersion is applied. The solution desired is the 
concentration-time breakthrough curve at the outlet of the one-dimensional (1-D) model for a 
unit step change in inlet concentration. This solution represents the cumulative distribution of 
travel times for transport with dispersion, which is what is desired for the transfer function. The 
transport equation and boundary conditions for the 1-D, advective-dispersion equation are (from 
Eq. 9.9 of Freeze and Cherry 1979 [101173]): 
2 
= (Eq. 6-3) R Deff 2 
C
t 
C
z 
C 
z 
(Eq. 6-4) C 
 
( , ) = t z 
) , 0 ( t 
0 = t 
= , C (Eq. 6-5) C 0 
.  
 

0 = z 
0 C(z  ,t) = , z   (Eq. 6-6) 
 
 
0 , 
52 January 2004 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
where 
C is the concentration (moles/kg fluid) 
0 C is the injection concentration (moles/kg fluid) 
h is the flow velocity (m/s) 
D is the effective dispersion coefficient (m2/s), given by D eff 
dispersivity of the medium (m). 
Here the molecular diffusion coefficient is ignored, since in general it is much smaller than the 
flow dispersion component of D . A non-dimensional version of Equation 6-3 can be obtained eff 
z L C /C C = 
) 
z by the following transformations: / , and , 0 
path length. The solution to Equations 6-3 to 6-6 is obtained after manipulation of Freeze and 
Cherry (1979 [101173], p. 391, Equation 9.5), yielding: 
Pe . (1 t.) = + erfc C ) 
1
2 t. 2 . .

. 
. .
.
. 
. .
.
. 
Peg 
Pe = 
obtained from Freeze and Cherry by substituting the definitions of Pe and t. into the 
corresponding terms of the Freeze and Cherry equation and performing the needed algebra. 
The use of this solution in the RTTF particle-tracking method requires that the transport problem 
be advection-dominated, such that during the time spent in a computational cell, solute would not 
tend to spread a significant distance away from that cell. Then, the approximate use of a 
distribution of times within a single cell will be adequate. Quantitatively, the criterion for 
applicability is based on the grid Peclet number 
length scale of the computational cell. Note that in contrast to conventional numerical solutions 
of the advective-dispersion equation, coarse spatial discretization is helpful for satisfying this 
criterion. Of course, the mesh spacing must still be small enough to provide an accurate flow 
solution. Highly dispersive transport invalidates the assumptions of the RTTF particle-tracking 
technique. When dispersion coefficients are large, accurate solutions to the advective-dispersion 
equation are easily obtained by conventional finite-difference or finite-element techniques, so 
these techniques should be used instead under these circumstances. 
For multi-dimensional flow systems, the dispersion model developed for 1-D systems can be 
extended to include dispersion coefficient values aligned with the coordinate axes. For this case, 
the flow direction is determined by the vector drawn from the nodal position of the previous cell 
to the current cell, and the dispersivity for this flow direction is computed from the equation for 
an ellipsoid: 
h 
= . \ / x , where .x is the characteristic 
= ) 
ePeerfc 
53 
. .. 
. 
where Pe is the Peclet number (dimensionless), 
MDL-NBS-HS-000020 REV 00 
U0065 
= \v , where \ is the eff 
R L / t t. , where L is the flow 
Pe(1 .) t (Eq. 6-7) 
2 
h = 
. ... 
. .
. 
Deff = 
+ 
t. 
L / L / \. This solution was 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
L  
2 2 2 2 2 2 + .y / .x /  z y x + .z /  
where L now represents the distance from the previous cell to the current cell, x . , y . , and z . 
are the distances from one grid point to the other in the three coordinate directions, and 
and z  are the longitudinal dispersivities in the three coordinate directions. The RTTF particletracking 
technique cannot be simply formulated with a longitudinal and transverse dispersion 
coefficient model, with the tensor aligned with the flow direction, because the flow rates between 
cells are defined rather than the actual flow velocity at a position. For a dispersion model 
aligned with the flow direction, a random-walk particle-tracking method such as that of Tompson 
and Gelhar (1990 [101490]), also implemented in the SZ particle-tracking algorithm of FEHM, 
or a conventional finite-element or finite-difference solution to the AD equation, such as the 
reactive transport solution module in FEHM, should be used instead. 
6.4.3 Fracture-Matrix Interaction Submodel 
= 
MDL-NBS-HS-000020 REV 00 

54 
The numerical implementation of this technique requires the determination of the dimensionless 
time t. in Equation 6-7 for a randomly determined value of the dimensionless concentration C )
. 
This determination is accomplished numerically in the particle-tracking code by fitting Equation 
6-7 at selected values of Pe between 1 and 1000 using a piecewise continuous series of straight 
lines spanning the entire range of values. Then, the value of t. at an arbitrary value of Pe is 
computed by linear interpolation between values determined at the Peclet numbers that bracket 
the actual value. This technique, involving a simple search for the correct type curves, followed 
by the calculation of two values of t. and an interpolation, is much more computationally 
efficient (about a factor of two in cpu time) and robust than an iterative approach to the exact 
solution using Newtons method. Solutions of adequate accuracy (less than 1% RMS error: see 
LANL 2003 [166306], Verification and Validation (V&V) Report, tests titled Tests of Cell- 
Based Particle Tracking Model) are easily obtained using this linear-interpolation method. This 
error is trivial compared to the uncertainties being propagated through the model. Therefore, this 
implementation is adequate for the purposes of the model. 
In a dual-permeability system, the transfer of solute mass between fractures and matrix can occur 
via advection, where fluid movement carries solute from one medium to the other, and matrix 
diffusion, where molecular diffusion transports mass. Matrix diffusion has been recognized as 
an important transport mechanism in fractured porous media (e.g., Neretnieks 1980 [101148]; 
Robinson 1994 [101154]). For many hydrologic flow systems, fluid flow is dominated by 
fractures because of the orders-of-magnitude larger permeabilities in the fractures compared to 
the surrounding rock matrix. However, even when fluid in the matrix is completely stagnant, 
solute can migrate into the matrix via molecular diffusion, resulting in a physical retardation of 
solute compared to pure fracture transport. This effect has recently been demonstrated on the 
laboratory scale by Reimus (1995 [101474]) and on the field scale both by Maloszewski and 
Zuber (1991 [146957]) and in the SZ at Yucca Mountain by Reimus et al. (1999 [126243]). In 
the UZ at Yucca Mountain, dual-permeability models allow fluid to migrate in both the fractures 
and the matrix. An additional process that allows solute to transport between the continua is 
x  , y  , 
January 2004 
U0065 
(Eq. 6-8) U0065 Particle Tracking Model and Abstraction of Transport Processes 
molecular diffusion. The distribution of travel times through such a system is a complex 
function of the relative velocities in the two media, the advective flux between the media, the 
spacing between flowing fractures, matrix diffusion coefficients, and sorption. In this section, 
we describe the submodel developed to obtain transfer functions suitable for use in 
dual-permeability systems. 
For transport in a dual-permeability system at the field scale, it is important to recognize that the 
flow model consists of one matrix grid cell for each fracture cell. However, important processes 
associated with flow and transport occur at scales smaller than those considered in the mountainscale 
UZ model, particularly in the immediate region of the matrix adjacent to each flowing 
fracture. Therefore, the incorporation of fracture-matrix interactions into the model is in essence 
an upscaling problem. The goal of this development is to utilize a suitable idealized system that 
captures, at the small scale, important transport processes, and allows this small-scale behavior to 
be simply upscaled for inclusion in the large-scale model. As we will demonstrate, this upscaling 
method will allow us to test alternate conceptual models for the fracture/matrix (f/m) interaction 
model for transport. 
To accomplish the upscaling within the particle tracking transport model, we continue to use the 
transfer function approach, constructing an idealized transport model at the small scale that 
allows the transfer functions to be tabulated. In a dual-permeability system, transport behavior is 
vastly different depending on whether solute starts in the fracture or in the matrix. Therefore, the 
transfer function method is adapted in the UZ transport model to accommodate dual-permeability 
behavior. The approach consists of using transfer functions to determine both the residence time 
in a cell, and to determine whether the particle enters the next cell in the fractures or the matrix. 
In this way, the combined fracture and matrix system will be treated as a unified medium in 
which there is a distribution of travel times depending on whether the particle enters the cells in 
the fracture versus the matrix. The transfer functions themselves (described below and in 
Attachment III) are computed based on an idealized f/m transport model with parallel flow in the 
fractures and matrix. The steps of the algorithm are as follows (note that the algorithm starts 
with a known particle location , either in the fracture or matrix continuum): 
Step 1. Determine probabilistically whether the particle should move to the other medium due to 
advective flux to that medium 
Step 2. Determine probabilistically whether the particle will leave this cell via the current 
medium or the other medium 
Step 3. Use the conditional transfer function to determine probabilistically the residence time of 
the particle 
Step 4. Determine probabilistically using the relative total flux to adjacent nodes which cell the 
particle moves to next (whether it starts in the fracture or matrix continuum in the next cell has 
been determined previously in Step 2). 
This approach handles the combined fracture and matrix continua as a single porous medium 
through which mass travels, and apportions the particles to each continuum according to the 
diffusive and advective fluxes defined by the flow field and the transport parameters. In the 
January 2004 55 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
most general case, the dual-permeability flow model at the mountain scale prescribes a net flow 
through the fracture continuum, a net flow through the matrix continuum, and a fracture to 
matrix (or matrix to fracture) fluid flux. To implement this algorithm and allow the transfer 
function to be computed readily, Step 1 takes the fracture-matrix advective flux term and applies 
it immediately when the particle enters the cell. Then, after potentially shifting the particle from 
one medium to the other via advection (with no increase to the travel time), the subsequent 
transfer functions are based on parallel flow in the two continua with no flux between the 
continua. This approach, which amounts to a form of upwinding of the fracture-matrix fluid flux 
term, simplifies the transfer function process by eliminating the need for an additional variable, 
the fracture-matrix advective flux, in the construction of the transfer function curves. Instead, 
we assign a probability p of the particle transferring to the other medium (Step 1) as fm 
0 = if the fracture-matrix flux term fm f is into the medium in which the p fm 
particle already resides, or 
= f /( f p fm fm fm f ) , where fin is the total flux into the continuum in which the + in 
particle currently resides. 
Step 2 accounts for the fact that there is a finite probability that, due to matrix diffusion, the 
particle will leave the cell through the other medium regardless of where it starts. In the transfer 
function approach, we introduce solute mass in the model system (the 2-D Discrete Fracture 
Model [2DFM]) in either the fracture fluid or the matrix fluid. For the general case of water flow 
through both the fracture and matrix, mass leaves the DFM via either medium. Therefore, 
conditional transfer functions must be generated to obtain the probabilities in Step 2. That is, for 
mass injected with the fracture fluid entering the discrete fracture submodel, there is a 
breakthrough curve for mass leaving the model via the fracture fluid, and a similar breakthrough 
curve for mass leaving via the matrix fluid. Similarly, there are two breakthrough curves for 
mass injected with the matrix fluid. The plateau values attained for a given transfer function 
curve represents the probability of leaving via a particular medium in Step 2. In other words, the 
probability of a particle leaving via a given continuum equals the steady state solute mass flux 
(the plateau of the transfer function curve) divided by the total mass flux through the DFM. This 
step provides a way to assign probabilities for moving particles between the media via diffusion 
in a system in which water flows through both continua. 
Once Step 2 is completed using the steady state solute mass flux derived from the conditional 
transfer functions, we now know which transfer function to apply to obtain the residence time for 
Step 3. This part of the method is identical to that described previously, which is to generate a 
random number between 0 and 1 and determine the particle residence time from the transfer 
function. 
Finally, Step 4 routes the particle to the appropriate connecting cell in the finite volume domain, 
as described earlier. If the particle is determined to enter an adjoining cell via the fracture 
continuum, then the internodal fluxes associated with the fractures are used to define the 
probabilities of traveling to each connected fracture cell. Similarly, for transport to an adjoining 
matrix cell, matrix fluxes are used. 
MDL-NBS-HS-000020 REV 00 January 2004 56 Particle Tracking Model and Abstraction of Transport Processes 
The process employed in this model to obtain the transfer functions for the dual permeability 
transport submodel consists of a series of numerical simulations on the idealized model system 
shown in Figure 6-5. Because each grid block in the mountain-scale model possesses different 
hydrologic and transport parameters, a procedure for deriving a non-dimensional form of the 
submodel is required to make the method practical. Attachment III presents the derivation of the 
non-dimensional model, and presents the method for generating the transfer function curves. In 
summary, there are three non-dimensional groups that, if specified, fully capture the range of 
behavior of the submodel: 
D is the effective diffusion coefficient, In these equations, f n and m n are the fluid travel times 
in the fracture and matrix, respectively, f R and m R are the retardation factors in the fracture and 
matrix, respectively, B is the half-spacing between flowing fractures, b is the fracture halfaperture, 
and cf and cm are the volumetric water contents of the fracture and matrix, 
respectively. For a given parameter vector ( 1 p , p ) , there is a unique set of conditional 
transfer function curves of the form C. 
versus t. , where C. is the normalized breakthrough curve 
for the non-dimensional time t. given by 
n
n
t 
f R nf 
MDL-NBS-HS-000020 REV 00 
f m 
1 
D n Rf 
2R B m 
D m m = 
f 
p = 
p2
3 
m 
m 
p = 
t. = 
f c n 
bB cf 
Rf (Eq. 6-11) 
Rm
p , 
(Eq. 6-12) 
57 
U0065 
(Eq. 6-9) 
(Eq. 6-10) 
3 2 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
x 
z 
m f 
f f 
b 
B 
f m 
d K
Dm 
3 2 1 
Figure 6-5. Schematic of the Fracture Transport Submodel 
The set of conditional transfer function curves consists of a total of four normalized curves for 
each ) ( p , p , p : mass input in fracture, output in fracture; mass input in fracture, output in 
matrix; mass input in matrix, output in fracture; and mass input in matrix, output in matrix. This 
capability for sampling conditional transfer functions associated with the fracture-matrix 
interaction dual permeability submodel of the UZ transport abstraction model has been 
implemented and documented in FEHM V2.21 (LANL 2003 [165741]). For details on the 
generation of the transfer function curves and other important implementation details, see 
Attachment III. 
The final issue associated with implementing the transfer function approach is the means by 
which the idealized model of Figure 6-5 is simulated. In this abstraction model, we implement 
58 MDL-NBS-HS-000020 REV 00 January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
two Alternate Conceptual Models (ACMs) to simulate different types of fracture/matrix (f/m) 
interaction conceptualizations. In the first ACM, called the DFM formulation, a two-dimensional 
numerical grid is used with fine discretization in the matrix close to the fracture. This allows 
sharp gradients in concentration close to the fracture to be captured. The second ACM, called the 
dual-k formulation, uses a numerical grid with one finite volume cell that is paired with each 
fracture grid cell. This type of discretization is identical to that used in the dual-k transport 
formulation of the T2R3D process model. It could be argued that the DFM formulation more 
accurately captures the small-scale transport processes. However, the dual-k formulation has the 
advantage of consistency with the model formulation on which the flow simulations are based. 
Furthermore, as a practical matter, the 3-D process model uses a dual-k formulation for transport, 
so for benchmarking purposes the dual-k approach is more likely to yield comparable results. 
The advantage of the transfer function approach used in the particle tracking abstraction model is 
that both conceptualizations can be implemented easily by using either the DFM or dual-k model 
grid to generate the transfer function curves. Then, when running the abstraction model, the user 
selects one or the other set of transfer function curves, and all other input remains the same. 
Additional details on the behavior of these two f/m interaction submodels are presented in 
Attachment III. 
6.4.4 Multiple Radionuclides With Decay/Ingrowth 
The FEHM code (Zyvoloski et al. 1997 [100615]) allows particles to decay with or without the 
production of the daughter product. For multiple species with decay chains, the code uses the 
approach outlined below to determine the number of decayed particles, and the code performs 
the bookkeeping needed to keep track of the locations and numbers of each type of radionuclide. 
These multiple species can each have their own transport parameters such as sorption and 
diffusion coefficients. 
For decay-ingrowth simulations with time-dependent release of tracer particles, the 
computational burden increases dramatically with the number of particles in the field. For 
example, the decay-ingrowth calculation for species i decaying into species j at a decay rate  is: 
i N 
N { } 1 . exp[ ] . ( ) t . t (Eq. 6-13) j = m 
m 1 
= 
where Nj is the number of particles of species j decayed from species i, Ni is the number of 
particles of species i, and tm is the time at which the m th particle is injected into the system. If 
500,000 particles of species i are injected into the system, then at each time step, the number of 
mathematical operations for ingrowth calculations alone are around 2.5 million. For a simulation 
time period of 1 million years, the typical calculation requires about 100 time steps. Therefore, 
the total number of operations for ingrowth calculations will reach 0.25 billion. Therefore, for 
site-scale simulations, the use of Equation 6-13 would be extremely inefficient. 
To reduce the computational burden in simulations, the decay-ingrowth calculation in Equation 
6-13 is approximated with an integral by assuming that particles are injected into the system 
uniformly in time domain. Multiplying both sides of Equation 6-13 by .t, the average injection 
time interval between particles, and approximating Equation 6-13 with respect to m t t . : 
January 2004 59 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
1 2 1 2 1 N j . 
 . . . 
. . . 
where  = 1 1 t . tNi 
( )  .  + . .  . . exp [ ] exp( ) ( ) .t (Eq. 6-14) 
, t and 2 = 1 t is the time at which particle injection starts, Ni t is the time of 
the Nth injected particle, and t is the time at which the decay-ingrowth calculation is carried out. 
The use of Equation 6-14 reduces the number of operations within one time step from millions of 
operations to just 10, which greatly increases the speed of simulations. Validity of this approach 
is demonstrated in Figure 6-6. 
3  4  2  
January 2004 60 
t . 
The accuracy of the integral approach depends on the number of particles and their release 
history. In general, the use of a greater number of particles increases the accuracy. With respect 
to release, for the same number of particles, a simulation with a constant release rate will exhibit 
less error than a time-varying release such as a shorter pulse. If the release rate changes with 
time, the release period is divided into segments so that within each segment the release rate can 
be treated as a constant. 
Validity of this approach was demonstrated in detail in LANL (2003 [166306]). A FEHM test 
run from the cited document is summarized in this report to demonstrate the capability of FEHM 
decay-ingrowth model. Simulation results from the FEHM particle tracking model with decay 
and ingrowth were verified against results from a semi-analytical solutions for a 4 species chain 
decay-ingrowth model, CHAIN (van Genuchten 1985 [146961]) The method of comparison for 
the run is a visual comparison of the plotted results. 
For all comparisons of FEHM with the semi-analytical solution for decay-ingrowth simulations, 
a flow system was developed with the following attributes LANL (2003 [166306]): 
. Saturated steady state flow in a 1-D system 
. Porosity of 0.3 
. Average pore-water velocity was 1.05192x10-4 m/year 
. Solute with constant injection concentration of 1.0 mol/l released from 0 to 5,000 years 
at origin x=0. Breakthrough data were collected at x=1 m down stream. 
. FEHM grid resolution: 0.005 m 
. Longitudinal dispersivity of 0.005 m. 
In the test case, a pseudo sequential decay chain is simulated with species 1 , with 
half lives for species 1 through species 4 of 10,000, 3,000, 10,000, and 4,000 years, respectively. 
The transport process was dominated by advection and dispersion only with a grid Peclet number 
of 1.0. In the FEHM simulations, the 5,000 year release period was divided into 50 segments so 
that each segment corresponding to 100 years. Within each segment, 10,000 particles were 
injected into the system uniformly over the 100 year period for species 1. There was no source 
release for the other species, which are generated by the decay-ingrowth model. The retardation 
factors for species 1 through species 4 were 1.0, 1.0, 1.9, and 1.001, respectively. 
MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
The FEHM and CHAIN breakthrough curves are plotted in Figure 6-6. In general, good 
agreement was observed between FEHM and CHAIN curves. Combined with the suite of 
validation runs documented in Section 7 of this Model Report, this simulation demonstrates that 
the particle tracking model accurately handles decay chains and, thus, is suitable for use in 
simulating multiple radionuclides in the UZ transport model. 
8000 
6000 
4000 
2000
0 
0 
Figure 6-6. Comparison of Software CHAIN and FEHM Transport Results for a Case with a 4-Member 
Decay-Ingrowth CHAIN and a Retardation Factor of 1.9 for Species 3. Peclet Number = 1.0 
eff 
where D is the same as for an aqueous solute and Rcoll is the colloid retardation factor. The 
governing equation for the corresponding dissolved contaminant moving in fractures with 
interactions with matrix blocks but without decay can be derived from Equation (1) of Sudicky 
and Frind (1982 [105043]) and re-written as: 
t 
Rf 
(used for comparative purposes only; taken from Fig. 59 of LANL 2003 [166306]). 
6.4.5 Colloid Transport 
For colloid-facilitated transport, the transport equations for matrix diffusion, with either the 
semi-infinite or finite fracture spacings, can be simply revised. Given the assumptions listed in 
Section 5, the expression for transport for contaminant on colloids is analogous to Eq. 6-3 earlier 
(from Eq. 9.9 of Freeze and Cherry 1979 [101173]): 
MDL-NBS-HS-000020 REV 00 
2C C coll coll Ccoll .  (Eq. 6-15) Rcoll Deff 
2C q (Eq. 6-15a) 2 b z 
January 2004 
Concentration (Number of particles) 
U0065 
1 
2 
3 
4 
CHAIN solution: 
Species 1 
Species 2 
Species 3 
Species 4 
FEHM solution 
5000 25000 20000 15000 10000 
Time (years) 
.  
 
Deff 
= 
C = . 
z 
C
z  
 
t 
z 2 
 
 
61 Particle Tracking Model and Abstraction of Transport Processes 
where Rf is the retardation factor of the dissolved contaminant, b is half of the fracture aperture, 
and q (mass per time per unit area) is the mass exchange rate through fracture-matrix interface. 
Combining Equations 6-15 and 6-15a, and making use of the relation K = Ccoll / C : 
R + K Rcoll c f = Deff K 
C
t c 
coll 
 
.
.
b 
1+ 
coll 
coll 
. .
.
. 
This equation can be recognized as being analogous to the matrix diffusion model of Sudicky 
and Frind (1982 [105043], Eq. 1), with the exception of a different term preceding the time 
derivative and a modified denominator of the term involving diffusive flux q . Mathematically, 
this implies that the transport equation for matrix diffusion can be revised to include colloid 
facilitated transport by replacing the half-aperture b by 
f 
MDL-NBS-HS-000020 REV 00 
= (1 
And the retardation factor in the fracture by 
R coll = f , 
These relationships are built into the FEHM particle-tracking code, so that the additional terms 
c K and Rcoll are provided as inputs. Note that to simulate a radionuclide irreversibly attached to 
colloids, one should set a large value of c K (say, 1.e20) so that the radionuclide essentially 
travels without diffusion. Then, either a retarded or unretarded colloidally bound radionuclide is 
simulated by setting R to a number greater than or equal to 1. 
In addition to the transport of radionuclides bound to colloids, there are several mechanisms 
related to the migration of the colloids themselves that can be simulated in the model. Above, 
the reversible retardation factor for colloid migration R was introduced. In addition, the 
model parameterization provides a means for accounting for colloid size and surface charge 
effects. When the colloid size and/or surface properties preclude their transport into a porous 
medium, size exclusion and/or filtration can occur. In the particle-tracking module, models have 
been implemented for these processes. For advective flow from fracture to matrix in the dualpermeability 
model, a size-exclusion model is implemented whereby colloids can remain in the 
fracture in proportions greater than the relative flow rate entering the matrix. A size exclusion 
parameter 1 f  is defined such that the probability of particles entering the matrix due to 
advective transport is multiplied by this factor. Therefore, complete exclusion from the matrix is 
obtained by setting coll 0 = , whereas aqueous solute behavior is retained by setting 1 = . 
Filtration, resulting in complete immobilization of the particle, can also be simulated at specified 
interfaces within either the fracture or matrix continua. To invoke this mechanism, a filtration 
factor filt f at an interface (the finite element connections between two specified zones in an 
FEHM simulation) is defined. If a particle is slated to pass from one zone to the other via 
q 2C 
K ) b(1 
C
z z 2
c 
. 
coll 
 
 
K R 
1+ Kc 
 

K )b (Eq. 6-17) 
f 
+
R + 
+ 
(Eq. 6-18) 
coll 
. 
c 
62 
U0065 
c 
(Eq. 6-16) 
c 
fcoll 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
) is the filt f - 1 filt f is the probability the particle continues moving, ( advective transport, 
probability that it is irreversibly removed by filtration). 
When using the filtration option, a word of caution is warranted. Colloid simulations are 
typically used to provide a mechanism for radionuclides to travel in the water bound to colloids. 
Filtration renders the colloids immobile, which, in reality, only renders the radionuclide 
immobile if it is irreversibly bound to the colloid. When the radionuclide is only weakly sorbed 
to the colloid, the filtration option will artificially remove radionuclide mass from the system, 
resulting in a non-conservative simulation. Therefore, the filtration option should only be 
invoked for irreversibly bound radionuclides or when simulating colloid tracer experiments. The 
reversible model, using R to delay the migration, should be used instead for colloid-facilitated coll 
transport of radionuclides. 
6.4.6 Particle Sources and Sinks 
There are two methods for introducing particles into the flow system: particles are (1) either 
injected with the source fluid entering the model domain or (2) released at a particular cell or set 
of cells. The first method is used to track source fluid as it passes through the system. The 
number of particles entering with the source fluid at each cell is proportional to the source flow 
rate at that cell, which is equivalent to injecting fluid with a constant solute concentration. For 
Method 2, an arbitrary number of particles are released at each specified cell, regardless of the 
source flow rate. In the present application, Method 2 is used to input particles, which are used 
to represent radionuclide mass into the system at the repository level. 
Within Method 2, there are various ways to input a time-varying source of particles. For 
stand-alone simulations, the particles are inserted at a constant rate for a specified duration. 
There is also an option, used when the FEHM code is coupled with GoldSim (BSC 2003 
[161572]), to input a time-varying and spatially varying source mass flux into the model. The 
details of the method for accepting complex sources of multiple radionuclides from the EBS 
model are discussed in the next section. 
When fluid exits the model domain at a sink, the model treats this flow as another outlet flow 
from the cell. The decision of whether the particle leaves the system or travels to an adjacent 
cell is then made on a probabilistic basis, just as though the fluid sink were another connected 
cell. Thus, the complexities discussed by Zheng (1994 [101503]) for handling a so-called weak 
sink are avoided in the RTTF particle-tracking model. 
6.4.7 EBS Random Release Model for Radionuclide Source Terms 
If waste packages containing high level radionuclide material in the repository eventually fail 
due to corrosion, the process will almost certainly be variable in both space and time. At early 
times, a few packages may fail, releasing radionuclides into the UZ. At later times, a greater 
number of packages may fail. In Viability Assessment calculations (DOE 1998 [100547], 
Figure 4-10), releases from the EBS to UZ were spread over the entire repository sub-regions. 
Such treatment of the EBS release could result in significant artificial dilution of the UZ 
transport source term. In reality, waste packages may not fail uniformly in space and time. 
Rather, a few waste packages may fail at early times, while others may fail gradually over longer 
January 2004 63 MDL-NBS-HS-000020 REV 00  Locate the M_fine early failed package nodes in repository sub-regions based on given 
failed package coordinates. If no node matches a given coordinate, then select the 
nearest node to the given coordinate. Note that in the current version of the TSPA 
model, the M_fine user option is not used. However, because it is still in the code, the 
GoldSim (BSC 2003 [161572]) calling program passes M_fine = 0 to FEHM. 
From FEHM particle-tracking subroutine part_track, subroutine getrip is called to determine the 
particle release locations. First, the subroutine obtains information passed by GoldSim (BSC 
2003 [161572]) in an input 1-D array called in[ ]. The structure of the in[ ] array is shown in 
Figure 6-7. 
time 
flow field index 
parameter index 
M_fine, # of early 
List # of failed 
packages in each 
sub-region (N_large) 
Number of species or 
the product of number 
of species and N_large 
U0065 Particle Tracking Model and Abstraction of Transport Processes 
time periods. An EBS random release model was developed in FEHM to allow the model to 
simulate early failed packages and time- and spatially variable radionuclide releases. 
To begin, a repository is defined consisting of N_large sub-regions. Each sub-region contains 
certain number of waste packages. Initially, M_fine packages fail at locations designated by 
package x-y locations (x,y). The M_fine failed packages release radionuclides at a mass flow 
rate of M_flux_i, where i is the ith failed package. 
With time, packages fail in the sub-regions of the repository. At each time step, there are a 
certain number of failed packages in each sub-region i. The mass flux released from those 
packages is denoted as N_large_flux for the ith sub-region. In this model, the release nodes in the 
numerical grid for the failed packages are randomly selected from the available repository nodes 
within that sub-region to mimic the failure process of the waste packages. The mass release of 
M_fine packages is separated from those of the other failed packages. 
To simulate the impact of the EBS random release on system performance at the Yucca 
Mountain site, the FEHM EBS random release model was developed to perform the following 
tasks: 
 Randomly select the failed package nodes in the designated sub-region i. 
 Release particle into the selected fracture or matrix nodes based on the fracture flow 
fraction data passed from EBS. 
For a species, a particle can be released into a fracture node or a matrix node. The probability of 
the particle being released into the fracture node is proportional to the fracture fractional flow 
data from EBS. At run time, a random number is generated for each particle, if the random 
number is smaller than the fracture fractional flow data, then the particle will be released into the 
selected fracture node. Otherwise, the particle will be injected into the matrix node 
corresponding to the selected fracture node. 
Mass release for each species during the current 
time step. Values are passed first for the early 
failed packages for all species from the first 
Optional input. 
default value: 1. 
Fracture fractional 
flow data for each 
species (N_large x 
#_of_species) 
January 2004 64 MDL-NBS-HS-000020 REV 00 
failed packages 
(x,y) coordinates of 
early failed packages 
(M_fine) 
N_la rge, # of 
repository sub-regions 
Mass input flag. 
0: no mass input 
1: there is mass input 
# of in put buffers, 
M_fine+N_large 
# of output buffers 
releasing node to the M_fine th node. Then, from 
the first sub-region to the N_large th sub-region 
(M_fine+N_large) x number_of_species
U0065 Particle Tracking Model and Abstraction of Transport Processes 
Figure 6-7. The Structure of the in [ ] Array Passed to FEHM from GoldSim 
The algorithm used in FEHM EBS random release model is summarized in Figure 6-8, the flow 
chart of the EBS random release model. 
Starting with the M_fine early failed packages, getrip extracts the (x,y) coordinates of the early 
failed packages and loops through each repository sub-region node to select the one that is 
closest to the given coordinates. To prevent a node being selected more than once for two or 
more given coordinates, getrip checks the selected nodes for overlapping. If overlapping is 
found, getrip prints out error messages to the error file fehmn.err, then stops the program. 
When the selection of M_fine nodes is complete, getrip extracts the number of failed packages in 
each sub-region for the N_large sub-regions. The number of failed packages at the current time 
step is compared with the values at the previous time step to determine the number of newly 
failed packages, N_newly_failed, within the current time step in each sub-region. Then, getrip 
randomly selects N_newly_failed nodes within the corresponding sub-region. The selected 
failed nodes are stored in the memory for use in releasing radionuclides and are removed from 
the base of available repository nodes. If the number of failed packages is larger than the 
number of nodes in a sub-region, then radionuclide will be released from all nodes within the 
sub-region. Once all nodes of failed packages are determined, getrip allocates the number of 
released particles proportionally to the mass flux values of each failed package. Then, 
subroutine setmptr is called to inject particles into the system for each species. 
When the locations/coordinates of M_fine early failed packages are unknown, the user can 
simulate the effect of early failed packages on UZ transport by passing the number of early failed 
packages in the N_large sub-regions to FEHM. FEHM then randomly selects the locations of the 
early failed packages and releases particles into the UZ as described in the paragraph above. 
Using this option, the user will pass M_fine=0 to FEHM and omit the coordinates of the early 
failed packages (the 5th data block in Figure 6-7 is not needed). 
To investigate the influence of matrix diffusion on UZ transport behavior, a radionuclide can be 
released from either a fracture node or a matrix node. The probability of the particle to be 
released from a fracture node is proportional to the fracture fractional flow data passed from 
GoldSim to FEHM in the input array in[ ] (Figure 6-7). At run time, a random number is 
generated, when the generated random number is smaller than the given fracture fraction flow, 
the particle is released from a selected fracture node. Otherwise, the particle is released through 
a selected matrix node. 
In the case of radionuclide release as gas phase and transport through geosphere, TSPA treats the 
released mass as aqueous phase. This is expected to bound any dose effects of gas-phase release 
due to the large dilution of gas-phase release in the atmosphere (Features, Events, and Processes 
in UZ Flow and Transport, BSC 2003 [164873]) 
65 MDL-NBS-HS-000020 REV 00 January 2004 Particle Tracking Model and Abstraction of Transport Processes 
within part track subroutine 
call subroutine getrip to get mass and node 
release information passed by GoldSim 
Yes 
mass input = 0 From 
GoldSim? 
No 
get the M_fine group coordinates and select nodes 
that have the shortest distance to the given 
coordinates 
is a node selected twice 
due to similar coordinate 
values
No 
randomly select N_newly_failed nodes in each subregion 
for radionuclide release 
in each sub-region, sum the mass flux of M_fine 
group with N_large group, then set number of 
particles released based on mass fraction of the 
M_fine group and N_large group, respectively 
call subroutine to release particles from the 
selected nodes into the system 
back to calling subroutine part_track 
Figure 6-8. Flow Chart of EBS Random Release Model 
6.4.8 Transient Fluid Flow 
When the RTTF particle-tracking method is implemented for a time-varying fluid flow system, 
the approach is somewhat more complex but still tractable. Consider a numerical simulation in 
which a discrete time step is taken at time t and a new fluid flow field is computed. In this 
model, the new fluid flow time t + .t is treated as an intermediate time at which the tnew = 
particle-tracking calculation must stop. The time is intermediate because if the flow field is at 
steady state, there is no reason to stop at any time before the end of the simulation except to 
record particle information for output or processing purposes. The fate of all particles is tracked 
from time t to time t assuming that the flow field is constant over this time interval. When new 
the simulation reaches t , the position (cell number) of the particle is recorded, along with its new 
fractional time remaining at the cell and the randomly generated y-coordinate of the transfer 
function used for that particle in the cell. When the new fluid flow solution is established, the 
remaining residence time for a particle is determined from the following steps: 
1. Compute a new fluid residence time f . 
2. Using the y-coordinate of the transfer function previously computed and the new 
transfer function, calculate a new particle residence time. 
MDL-NBS-HS-000020 REV 00 66 
Yes 
Stop, print out error 
message 
U0065 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
3. Multiply this time by the fractional time remaining in the cell to obtain the remaining 
time in the cell. 
This method approximates the behavior in a transient system, while reducing to the behavior that 
would be obtained in an unchanging flow field had the calculation not been forced to stop at the 
intermediate time. 
Another transient effect that must be considered is that the sum of the outlet mass flow rates 
m& out in Equation 6-1 does not necessarily equal the sum of the inlet mass flow rates. When 
there is net fluid flow into a cell, the particle-tracking algorithm uses the sum of the inlet flow 
rates in Equation 6-1, whereas Equation 6-1 itself is used when there is net outflow from a cell. 
Finally, with respect to the transfer function methodology outlined in Section 6.4.3, when the 
climate changes, the code redefines the parameters in Equations 6-9, 6-10, and 6-11, and uses 
these parameters and the new flow field to continue the transport simulation. 
6.4.9 Climate Change and Water Table Rise 
One important factor that could affect the performance of the repository is future climate 
changes. As it is difficult and time consuming to simulate the transition of flow fields from one 
climate to another, in TSPA several pre-generated flow fields are used to represent the 
corresponding climates. These flow fields are developed in BSC 2003 [163045], and are 
converted to FEHM-compatible flow fields in DTN: LB0305TSPA18FF.001 [165625]. This 
approach treats flow in the system as a sequence of steady states (CRWMS M&O 2000 
[153246], Section 3.2.3.1). For TSPA simulations, those pre-generated flow fields are read in by 
FEHM at run time and whenever the GoldSim (BSC 2003 [161572]) model signals to FEHM 
that the climate is changing. From that point until the climate changes again, the flow field is 
assumed to be steady. Section 6.4.8 details the numerical approach for handling varying flow 
fields. 
It is expected that the water table will be higher in future climates (CRWMS M&O [153246], 
Section 3.7.2). One issue related to climate change is water table rise. In the UZ transport model 
abstraction, water table is switched instantaneously from one climate to another when climate 
changes. Any radionuclides (in the form of particles in the particle tracking model) below the 
new water table are immediately removed from the UZ and sent to SZ. This approach is 
conservative as both the flow field and water table are immediately switched to the wetter 
climate at time of climate change, which not only accelerates the movement of radionuclides in 
the system but also tends to result in instantaneous pulses of radionuclides into the SZ. 
To set the water table elevation to a higher value than that used for the development of the flow 
fields in DTN: LB0305TSPA18FF.001 [165625], the flow field files must be post-processed 
using the software WTRISE (LBNL 2003 [163453]). This has not been done in this abstraction 
model because the calculations presented are being compared to process model results that 
assumed the present-day water table for the future climate modeling. For TSPA-LA model 
calculations, this processing step has been performed for all flow fields of future, wetter 
climates. The use of WTRISE requires the specification of a water table elevation under the 
future climate scenarios. The code adjusts the flow field for all grid blocks beneath this elevation 
to force particles to immediately leave when reaching any of these grid blocks. Therefore, an 
January 2004 67 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
elevation for the higher water table must be selected. Forester et al. (1999 [109425], p. 56) 
suggests that site data are consistent with past water table elevations up to 120 m higher than 
present day elevations. Because the water table is not flat, a nominal elevation for the presentday 
water table must be selected and the future water table must then be based on that selection. 
For the typical water table elevation under present day conditions beneath the repository of 730 
m (BSC 2003 [162649], Section 6.4.5.1), a rise of 120 m results in an elevation of 850 m. As a 
comparison, note that BSC 2003 [162649], Section 6.4.5.1 performed an analysis in which the 
water table was assumed to be 100 m higher than present-day, but processed the water table to 
parallel the present-day water table at all locations. Figure 6.4-8 of BSC 2003 [162649] shows 
that for the future water table analysis used to investigate the impact on SZ processes, the 850 m 
elevation contours passes through the repository footprint. Therefore, choosing an elevation of 
850 m for processing the UZ flow fields for the future climate cases is consistent with available 
site data, and is consistent with SZ studies. Furthermore, since there is no site data or numerical 
modeling available to form a basis for selecting different water table elevations for the various 
future climate states, the 850 m elevation should be used for all future climate flow fields. With 
respect to UZ transport to the water table, this approximation should be conservative because a 
reasonable maximum elevation, resulting in a minimum for the UZ flow path length, is used for 
all future climates. The flow fields processed to incorporate the higher water table for the future, 
wetter climates are available in DTN: LB0312TSPA06FF.001 [166671]. 
6.4.10 Interface With GoldSim 
The interface between GoldSim and FEHM establishes a protocol for defining the radionuclide 
sources to the UZ transport model (provided by GoldSim (BSC 2003 [161572]), the definition of 
a particular flow field for FEHM to use, and exit mass fluxes of radionuclides from the UZ 
model (from FEHM to GoldSim based on the particle-tracking simulation). This protocol is 
quite flexible, allowing an arbitrary number of source regions, radionuclides, exit regions, and 
flow fields to be defined and passed between GoldSim and FEHM through the FEHM subroutine 
call statement. Figure 6-9 shows a simplified flow chart of the GoldSim-FEHM coupling. 
During a GoldSim simulation, FEHM cedes control of the time step to GoldSim. At each time, 
GoldSim provides a flag defining the flow field and the mass flux inputs of radionuclides. By 
changing the flow field during a simulation, the model can simulate the impact of a 
climate-induced change in the UZ system. When this occurs, FEHM reads in the new flow field 
and proceeds with the transport simulation (see Section 6.4.8). Since each flow field is a steady 
state flow field, the implicit assumption is a quasi-steady one, that is, the system establishes a 
new steady state rapidly in comparison to transport velocities through the UZ. At the end of each 
time step, FEHM passes back to GoldSim the exiting mass flux values from the UZ model. 
January 2004 68 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
EBS release GoldSim initiate calls to FEHM DLL 
to start UZ transport simulations 
FEHM receives control parameters 
and mass release data from 
GoldSim through the interface 
Call subroutines to initialize 
variables and prepare data based on 
control parameters passed by 
GoldSim 
Call FEHM particle tracking to 
initiate UZ radionuclide transport 
simulations 
EBS mass release == 0? 
no 
Release radionuclides into UZ from 
the repository 
Start particle tracking to simulate the 
transport of radionuclide in UZ 
Calculate radionuclide mass 
reaching the water table during the 
current time step and pass the 
results back to GoldSim 
Figure 6-9. Schematic Flow Chart of GoldSim-FEHM Coupling 
69 
6.5 TRANSPORT MODEL INPUTS 
The top boundary of the transport model is the repository where radionuclides are released from 
the EBS into the system. The strength of the source release varies with time and depends on the 
failure rate of the waste packages. 
At the bottom boundary (the water table), radionuclides are removed from the UZ system and 
become the source term for the SZ model. 
The side boundaries of the transport model are no-flow boundaries. 
The initial condition of the transport model is set to a concentration of zero for all radionuclides. 
MDL-NBS-HS-000020 REV 00 
U0065 
GoldSim initiate calls to 
SZ_CONVOLUTE for SZ 
transport simulations 
yes 
FEHM domain 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Strength of the different transport mechanisms depends on the values of their corresponding 
parameters that are inputs to the transport model. Parameters read in by FEHM as input to the 
transport model include 
 Dispersivity (m) 
 Matrix porosity and rock density (kg/m3) 
 Matrix adsorption coefficient (mL/g) 
 Matrix diffusion coefficient (m2/sec) 
 Fracture residual saturation and fracture gamma parameters (unitless) 
 Fracture porosity, fracture spacing (m), and fracture aperture (m) 
 Fracture surface retardation factor (unitless) 
 Colloid size distribution, colloid Kc, colloid Rc, and colloid filtration factor 
 Radionuclide half lives (years) and daughter products. 
For layers above the repository, placeholder values for these transport parameters are used in the 
input files for the model, but these values are not germane to the model results because 
radionuclide particles do not pass through these units. Beyond the above transport parameters, at 
run time, FEHM also reads in the pre-generated flow fields and property zone data. Those data 
are inputs from UZ flow model to the transport model. 
The sub-sections below give a more detailed discussion about each parameter. 
6.5.1 Pre-generated Flow Fields 
In TSPA runs, a total of 9 base case flow fields corresponding to 9 climate scenarios, present day 
[low, mean, and high], glacial transition [low, mean, and high], and monsoon [low, mean, and 
high], are pre-generated and fed into FEHM. 
The flow fields are based on the dual permeability/dual porosity model formulation that allows 
water flow in both fractures and the corresponding matrix blocks. A total of 120,711 physical 
nodes are used to discretize the Yucca Mountain Project site. For the dual permeability/dual 
porosity model, at any physical node, there is a fracture node and a corresponding matrix node. 
Thus, the flow model has a total of 241,422 flow nodes (DTN: LB0305TSPA18FF.001 
[165625]). 
The UZ flow model is characterized by potential lateral flow in the PTn unit, the occurrence of 
perched water within low-permeability zeolites in the CHn or the densely welded basal 
vitrophyre of the TSw unit, and the effects of faults on the UZ flow system (BSC 2003 
[163045]). 
In TSPA-LA runs, all the 9 base case flow fields will be used in the corresponding climates. The 
name of the flow fields and corresponding files are listed in Table 4-1. 
6.5.2 Dispersivity 
Yucca Mountain site-scale flow models have indicated that flow in the fractured rock system is 
dominated by fast fracture flow (CRWMS M&O 2000 [134732], Section 6.2.2, Figure 8). In 
January 2004 70 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
such a system, radionuclide transport is primarily advection dominated, and the influence of 
dispersion on radionuclide transport is not important (CRWMS M&O 2000 [148384], 
Section 6.3.6). 
There are few data available on dispersivity distributions at Yucca Mountain site. (Neuman 
1990 [101464]) showed that field dispersivity varied with the scale of study. Field tracer tests at 
the C-holes at Yucca Mountain also showed that on a 100 m scale, field dispersivity had a range 
of approximately 3 to 63 m (BSC 2003 [162415], Table 6.3-10). 
In past simulations (CRWMS M&O 2000 [148384], Section 6.3.6), the dispersivity values of all 
units had a value of 20 m. 
Sensitivity studies from TSPA-SR, using flow conditions and dispersivity values representative 
of the UZ at Yucca Mountain, showed that transport of radionuclides is not sensitive to 
variations in dispersivities within the UZ. Use of a dispersivity greater than 20 m does not show 
any significant effect on radionuclide peak concentration or arrival time (CRWMS M&O 2000 
[148384], Section 6.3.6, Figures 6-156 and 6-157). 
In TSPA-LA, the fracture dispersivity is set at 10 m. This is toward the lower end of the value 
from field studies (BSC 2003 [162415], Table 6.3-10). Although the impact of dispersivity 
should be very small, the value chosen should be conservative, as higher dispersivity tends to 
spread the radionuclide plume and reduce the peak value. While it can be argued that for a 
decaying species, higher dispersivity can allow a greater fraction of the mass to arrive 
downstream before decaying, the point here is that in comparison to diffusion and large scale 
heterogeneities, dispersivity effects have a very small influence on the breakthrough curves. 
Input Name 
Fracture 
dispersivity 
Table 6-2. Dispersivity Used in UZ Transport Model 
Input Description 
MDL-NBS-HS-000020 REV 00 
Input to FEHM for simulating 
dispersion effect Saturated Zone In-Situ Testing. 
Because the dual permeability abstraction model treats the combined fracture-matrix system as a 
unified continuum, this dispersivity applies to the medium as a whole. Therefore, the model does 
not distinguish between fracture dispersivity and matrix dispersivity. 
6.5.3 Matrix Porosity and Rock Density 
Matrix porosity is used to calculate the matrix pore volume associated with each matrix block. 
The pore volume data are then multiplied by the corresponding water saturation data to 
determine the fluid volume in a cell. 
Matrix porosity and rock density values combined with rock adsorption coefficient and water 
saturation are used for calculating matrix retardation factors used in simulating the adsorption 
effect on radionuclide transport. 
71 
Value (units) Input Sources 
BSC 2003 [162415], Table 6.3-10 
U0065 
10 m 
Type of 
Uncertainty 
Fixed value 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Values of matrix porosity are from the Technical Data Management System (TDMS) 
(DTN: LB0305TSPA18FF.001[165625]) and listed in Table 6-3. 
Table 6-3. Matrix Porosities Used in the Transport Model 
Matrix 
Porosity 
Matrix 
Layer Type of Uncertainty Input Source Input Description 
LB0305TSPA18FF.001 Fixed values for each layer 
but varies from layer to layer [165625] 
tcwm1 2.41E-01 Matrix porosity values 
tcwm2 8.80E-02 is used in determining 
matrix pore volume, 
simulating matrix 
diffusion effect, and 
calculating matrix 
Eighteen 3-D Site Scale UZ 
Flow Fields Converted from 
TOUGH2 to T2FEHM 
format. TOUGH2 file: 
glaq_uA.dat 
tcwm3 2.00E-01 
ptnm1 3.87E-01 
ptnm2 4.38E-01 
ptnm3 2.54E-01 adsorption coefficient 
ptnm4 4.11E-01 
ptnm5 4.99E-01 
ptnm6 4.92E-01 
tswm1 5.40E-02 
tswm2 1.57E-01 
tswm3 1.55E-01 
tswm4 1.11E-01 
tswm5 1.31E-01 
tswm6 1.03E-01 
tswm7 1.03E-01 
tswm8 4.30E-02 
tswmv 2.29E-01 
tswmz 2.75E-01 
ch1mv 3.31E-01 
ch2mv 3.46E-01 
ch3mv 3.46E-01 
ch4mv 3.46E-01 
ch5mv 3.46E-01 
ch6mv 3.31E-01 
ch1mz 2.85E-01 
ch2mz 3.22E-01 
ch3mz 3.22E-01 
ch4mz 3.22E-01 
ch5mz 3.22E-01 
ch6mz 2.71E-01 
pp4mz 3.21E-01 
pp3md 3.18E-01 
pp2md 2.21E-01 
January 2004 72 MDL-NBS-HS-000020 REV 00 tr2mz 2.34E-01 
U0065 
Type of Uncertainty 
Particle Tracking Model and Abstraction of Transport Processes 
Table 6-3. Matrix Porosities Used of the Transport Model (Continued) 
Matrix 
Porosity 
Matrix 
Layer 
pp1mz 2.97E-01 
bf3md 1.75E-01 
bf2mz 2.34E-01 
tr3md 1.75E-01 
pcm38 4.30E-02 
pcm39 2.75E-01 
pcm1z 2.85E-01 
pcm2z 3.22E-01 
pcm5z 3.22E-01 
pcm6z 2.71E-01 
pcm4p 3.21E-01 
Input Source Input Description 
Rock density values are from the TDMS (DTN: LB0210THRMLPRP.001 [160799]) and are 
listed in Table 6-4 below. 
Rock 
Density 
Matrix Layer (kg/m3) 
tcwm1 2514. Rock density data are 
used by FEHM in the tcwm2 2514. 
calculation of matrix 
adsorption coefficient tcwm3 2274. 
ptnm1 2288. 
ptnm2 2288. 
ptnm3 2288. 
ptnm4 2288. 
ptnm5 2288. 
ptnm6 2283. 
tswm1 2274 
tswm2 2514. 
tswm3 2358. 
tswm4 2466. 
tswm5 2325. 
tswm6 2473. 
tswm7 2473. 
tswm8/pcm38 2274. 
2274. tswm9/pcm39/t 
swmv/tswmz 
ch1mv 2288. 
ch2mv 2256. 
ch3mv 2256. 
ch4mv 2256. 
Table 6-4. Matrix Rock Density Values 
Type of Uncertainty Input Source Input Description 
LB0210THRMLPRP.001 Fixed values for each 
layer but varies from 
[160799] layer to layer 
Thermal Properties of 
UZ Model Layers: Data 
Summary 
MDL-NBS-HS-000020 REV 00 January 2004 73 Particle Tracking Model and Abstraction of Transport Processes 
(kg/m3) Matrix Layer 
ch1mz/pcm1z 2288. 
ch5mz/pcm5z 2256. 
ch6mz/pcm6z 2256. 
pp4mz/pcm4p 2103. 
Table 6-4. Matrix Rock Density Values (Continued) 
Rock Density 
Input Description 
ch6mv 2256 
ch3mz 2256. 
ch4mz 2256. 
pp3md 2103 
pp2md 2385. 
pp1mz 2038. 
bf3md 2106. 
bf2mz 2012. 
tr3md 2371. 
tr2mz 2224 
Input Source 
ch5mv 2256. 
ch2mz/pcm2z 2256. 
Type of Uncertainty 
January 2004 
Fault Zone Rock Density Data 
tcw 2394 
ptn 2286 
tsw 2368 
chn 2198 
MDL-NBS-HS-000020 REV 00 
6.5.4 Matrix Adsorption Coefficient (mL/g) 
Dissolved radionuclide waste traveling through the matrix can be retarded due to adsorption on 
to the surface of the porous matrix material. In TSPA-LA runs, the linear adsorption model is 
used to describe the partitioning of radionuclides between the solute and the matrix through the 
UZ system. Matrix adsorption coefficients can be read in by FEHM at run time. The values are 
then used to calculate matrix rock retardation factors of different radionuclides. The validity of 
the linear equilibrium assumption (Section 5, assumption 4) and the derivation of adsorption 
coefficient distributions based on laboratory experiment data are documented in Model Report, 
Radionuclide Transport Models Under Ambient Conditions (BSC 2003 [163228]). 
The strength of matrix adsorption depends on the properties of the rock material and the 
radionuclides. Matrix adsorption coefficients for different rock types (zeolitic, devitrified, and 
vitric) are taken from the TDMS (DTN: LA0302AM831341.002 [162575]). Values of the 
adsorption coefficient are divided into three groups based on rock type (e.g., devitrified, vitric, 
and zeolitic). Table 6-5 lists the statistical distribution of matrix adsorption coefficient for 
different radionuclide types. 
To address the influence of adsorption coefficient uncertainty on system performance, the matrix 
adsorption coefficients of each species are pre-sampled for each rock type (based on the listed 
74 
U0065
Particle Tracking Model and Abstraction of Transport Processes 
distribution values in Table 6-5) for each TSPA realization. For a discussion on the method of 
correlating sorption coefficients to one another in the stochastic sampling of parameters, see 
Input Description 
Coefficients describing 
distribution (Kd: mL/g) 
The matrix 
adsorption 
coefficient data are 
read in at run time 
by FEHM for 
simulating the 
effect of matrix 
adsorption on 
radionuclide 
transport. 
(100., 0.5) (200., 1.0) 
range= 100 - 1000 
range= 100 - 2000 
(400., 0.5) (1000., 1.0) 
range= 1000  20,000 
range= 1000  20,000 
range= 1000  20,000 
(Kd value, probability) (425., 0) 
(5,000., 0.5) (20,000., 1.0) 
range = 1 - 15 
(2., 0.5) (100., 1.0) 
range = 50 - 2000 
range = 10 - 70 
range = 0 - 50 
range = 1000 - 5000 
range = 100 - 1000 
range = 50 - 600 
range = 1000 - 30,000 mL/g 
range = 1000 - 10,000 mL/g 
range = 1000 - 10,000 mL/g 
Attachment II of BSC (2003 [163228]). 
Table 6-5. Sorption-Coefficient Distributions for Unsaturated Zone Units 
Type of 
Species Rock Type Uncertainty 
U 
Np 
Pu 
Am 
Pa 
Cs 
Sr 
Ra 
Th 
DTN: LA0302AM831341.002 [162575] 
Zeolitic Cumulative (Kd value, probability) (0, 0) 
(0.5, 0.5) (30., 1.0) 
Devitrified Cumulative (Kd value, probability) (0, 0) 
(0.2, 0.5) (4., 1.0) 
Vitric Cumulative (Kd value, probability) (0, 0) 
(0.2, 0.5) (3., 1.0) 
Zeolitic Cumulative (Kd value, probability) (0, 0) 
(0.5, 0.5) (6., 1.0) 
Devitrified Cumulative (Kd value, probability) (0, 0) 
(0.5, 0.5) (6., 1.0) 
Vitric Cumulative (Kd value, probability) (0, 0) 
(1.0, 0.5) (3., 1.0) 
Zeolitic Cumulative (Kd value, probability) (10., 0) 
(100., 0.5) (200., 1.0) 
Devitrified Cumulative (Kd value, probability) (10., 0) 
(70., 0.5) (200., 1.0) 
Cumulative (Kd value, probability) (10., 0) Vitric 
Cumulative (Kd value, probability) (100., 0) 
Zeolitic Uniform 
Devitrified Uniform 
Vitric 
Cumulative 
Zeolitic Uniform 
Devitrified Uniform 
Vitric Uniform 
Zeolitic 
Devitrified Uniform 
Vitric Cumulative (Kd value, probability) (0., 0) 
Uniform 
Zeolitic Uniform 
Devitrified Uniform 
Vitric Uniform 
Zeolitic Uniform 
Devitrified Uniform 
Vitric Uniform 
Zeolitic Uniform 
Devitrified Uniform 
Vitric 
MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 75 Particle Tracking Model and Abstraction of Transport Processes 
6.5.5 Matrix Diffusion Coefficient (m2/sec) 
It has been shown that matrix diffusion combined with matrix adsorption can play an important 
role in slowing the movement of radionuclides in fractured rocks (Sudicky and Frind 1982 
[105043]). 
A matrix diffusion coefficient is used in FEHM for simulating the effect of matrix diffusion on 
radionuclide transport in the fractured media. Values of matrix diffusion coefficient affect the 
strength of fracture-matrix interaction due to diffusion of radionuclides. 
In the Radionuclide Transport Process Model documented in BSC 2003 [163228], the diffusive 
flux is defined in terms of the concentration gradient and the effective diffusion coefficient, 
which is the product of the free diffusion coefficient and the tortuosity. BSC 2003 [163228] 
show, based on work by Grathwohl (2000 [141512]) that it is a reasonable approximation to set 
tortuosity equal to the matrix porosity. The abstraction model calls for the effective diffusion 
coefficient as a direct parameter input, rather than separately defining tortuosity and free 
diffusion coefficient. In the development below, correlations between effective diffusion 
coefficient, water content, and matrix permeability are proposed based on available experimental 
data. The end result of this development is a range of effective diffusion coefficients that in 
effect capture the uncertainty in the mechanisms associated with diffusion through tortuous pore 
spaces. Therefore, even though the tortuosity is not a direct model input, its impact on matrix 
diffusion, and the correlation between diffusion and matrix porosity, is implicitly captured in the 
abstraction model. 
In current TSPA simulations, unsaturated matrix diffusion coefficients are based on the 
correlation between matrix diffusion, porosity, and saturated permeability developed for the SZ 
(Reimus et al. 2002 [163008]). To adapt the relationship for the UZ, the porosity is replaced 
with water content and the permeability is replaced with effective permeability. The equation is 
re-written as 
+ log 38 . 1 = . 49 . 3 m 
where Dm is the matrix diffusion coefficient in cm2/s, m is the matrix water content, and km is 
the effective permeability to water in m2. 
The data from Reimus et al. (2002 [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 [149557] would provide a better 
representation of the uncertainty in matrix diffusion. To capture this with the correlation given 
by Reimus et al. (2002 [163008]), consider the following transformation: 
( ) D 
X = log 
Dm
0 D 
. .. 
. 
76 MDL-NBS-HS-000020 REV 00 
U0065 
+ (Eq. 6-19) 0.165log m m 
 . 
. 
(k ) 
(Eq. 6-20) 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
where D0 is the limiting upper value for Dm. This value is given in DTN: LA0003JC831362.001 
[149557] as 10-9 m2/s. The average for X is 
 log (D ) log(D ) (Eq. 6-21) X 
The mean for Y is taken to be 
= 
= ln 
m 
Y 
such that the mean for the Reimus correlation is unchanged by the transformation to a lognormal 
distribution. In this case, note that x is the median of X, not the mean. Distribution parameters 
may be obtained by setting log( ) D to be the log of the geometric mean of the mean values in 
DTN: LA0003JC831362.001 [149557] and then adjust the standard deviation for Y such that it 
covers the range of values represented by cations and anions in DTN: LA0003JC831362.001 
[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 [149557], as shown in 
Figure 6-10. 
where the second term on the right hand side is the mean of log( D ). 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. 6-22) 
(  ) (Eq. 6-23) 
0 - 
77 MDL-NBS-HS-000020 REV 00 
U0065 
m 
m 
X 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
1.00E-09 
1.00E-10 
1.00E-11 
1.00E-12
0.000 
Figure 6-10. Cumulative Probability for Matrix Diffusion Under Saturated Conditions 
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 low distribution may be computed 
based on the Reimus correlation (Reimus et al. 2002 [163008]) by assigning the mean using the 
5th percentile water content and effective matrix permeability and a high distribution based on 
the 95th percentile of values of these quantities. The results are shown in Figure 6-11. 
MDL-NBS-HS-000020 REV 00 January 2004 78 
Diffusion Coefficient m2/s 
U0065 
distribution for anions 
distribution for cations 
primary distribution 
Cumulative Probability for Matrix Diffusion 
1.000 0.800 0.600 0.400 0.200 
Cumulative Probability 
Output DTN: LA0311BR831371.003 Particle Tracking Model and Abstraction of Transport Processes 
1.00E-09 
1.00E-10 
1.00E-11 
1.00E-12 
0.200 0.100 0.000 
Figure 6-11. Comparison of Cation/Anion Distributions with Reimus High/low Distributions for 
Unsaturated Conditions 
Figure 6-11 shows that most of the matrix diffusion coefficients estimated using Equation 6-19 
will fall within the range of the Reimus low and Reimus high curves. The data used to 
develop the distributions in DTN: LA0003JC831362.001 [149557] were from diffusion 
measurements under saturated conditions. Therefore, the generally lower values represented by 
the Reimus distributions are expected. The comparison with measured diffusion coefficients for 
tritium, technetium, and carbon is given in Figure 6-12. Again, the correlations for the UZ are 
lower than the measured values, which were all performed under saturated conditions. 
The groups of model units for sampling matrix diffusion shown in Table 6-6 were selected based 
on similarity in properties of porosity, permeability, and water content. Distributions for the 
water content and (log) effective permeability to water for each group are derived from the 9 
flow fields used for TSPA calculations (Source: BSC 2003 [163045]; 
DTN: LB03023DSSCP9I.001 [163044]). 
The influence of matrix diffusion coefficient uncertainty on radionuclide transport is investigated 
by independently sampling water content and permeability for each rock group (Table 6-6). The 
water content and (log) effective permeability are independently sampled from these cumulative 
distributions. A matrix diffusion coefficient is then computed from equation Equation 6-19. 
MDL-NBS-HS-000020 REV 00 January 2004 79 
Diffusion Coefficient m2/s 
U0065 
distribution for anions 
distribution for cations 
Reimus low 
Reimus high 
Cumulative Probability for Matrix Diffusion 
1.000 0.900 0.800 0.700 0.600 0.500 0.400 0.300 
Cumulative Probability 
Output DTN: LA0311BR831371.003 1 bf2mz, ch1mz, 2.06E-01 8.41E-02 5.33E-01 6.81E-03 -1.62E+01 5.50E-01 1.33E-10 
ch[1,2,3,4,5, 6]mv, 
tswmv, tswmz, , 
pp3Md, pp2Md, 
pp1Mz, pp4Mz, 
2 ch[2,3,4,5,6]mz, 3.00E-01 5.12E-02 5.78E-01 7.73E-02 -1.83E+01 4.20E-01 8.10E-11 
pcm[1,2,5,6]mz, 
3 tswm[3,4,5,6,7,8], 1.12E-01 3.43E-02 3.19E-01 7.75E-5 -1.89E+01 4.62E-01 3.47E-11 
Output DTN: LA0311BR831371.003 
Dm Standard Mean Log calculated Deviation Effective using listed 
Permeability Permeability mean values Log Effective 
(m2) and Eq. 6-19 
U0065 
(m2/s) 
Particle Tracking Model and Abstraction of Transport Processes 
1.00E-09 
1.00E-10 
1.00E-11 
1.00E-12
0.000 0.200 
Diffusion Coefficient m2/s 
Figure 6-12. Comparison of the Distributions With Diffusion Data 
Table 6-6. Distribution of Water Content and Effective Permeability 
Unit Mean Water 
Content (-) 
bf3Md, tr3Md 
pcm39, pcm4p, 
pcM38 
0.800 0.600 0.400 
Cumulative Probability 
Maximum Minimum 
Water 
Standard 
Deviation 
Water Water 
Content Content Content 
Group 
Index 
DTN: LA0311BR831371.003 
NOTE: A Beta distribution was used for the matrix water content, and a lognormal distribution was used for the 
matrix effective permeability. 
MDL-NBS-HS-000020 REV 00 
Cumulative Probability for Matrix Diffusion 
distribution for anions 
distribution for cations 
Reimus low 
Reimus high 
Reimus tritium data 
Reimus technetium data 
Reimus carbon data 
1.000 
(m2) 
January 2004 80 U0065 Particle Tracking Model and Abstraction of Transport Processes 
In all TSPA simulations, colloid matrix diffusion (diffusion of a colloid from the fracture to the 
matrix) is neglected because of lack of data and because diffusion coefficients for colloidal 
particles are expected to be small. This is conservative with respect to the dose rates calculated 
by the TSPA model. 
6.5.6 Fracture Residual Saturation and Active Fracture Model Gamma Parameters 
(Unitless) 
Fracture residual saturation and fracture  parameter values are used by FEHM to calculate the 
fracture spacing based on the Active Fracture Model (Liu et al. 1998 [105729]). 
In TSPA-LA, a constant fracture residual saturation of 0.01 is used for all layers 
(DTN: LB0302UZDSCPUI.002 [161787]). Currently, there are no data from Yucca Mountain 
that could be used to assess the uncertainty in residual fracture saturation. 
Input Name 
Fracture 
residual 
saturation 
Table 6-7. Fracture Residual Saturation Values 
Input Source 
LB0302UZDSCPUI.002 
[161787] 
Input Description 
Fracture residual saturation is 
used to calculate active 
fracture spacing 
81 
Type of Uncertainty 
Fixed value. The 
fracture residual 
saturation is constant 
over all layers and does 
not change with climate 
Values of fracture  parameter vary with infiltration rates in each rock layer. Tables 6-8 through 
6-10 list the fracture  parameter values used in TSPA-LA for different infiltration scenarios 
(DTN: LB0305TSPA18FF.001 [165625]). 
The influence of  parameter uncertainty on radionuclide transport is investigated using 
sensitivity analyses in Section 7.3.3. 
January 2004 
Input Value 
0.01 
MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-8. Fracture  Parameter for Lower-Bound Infiltration Scenario 
Rock Input 
Layer Fracture  Description 
Rock 
Layer Fracture  
tcwf1 0.4834 ch1fz 0.2759 This value is 
Tcwf2 0.4834 ch2fz 0.2759 read in by FEHM 
and used in 
tcwf3 0.4834 ch3fz 0.2759 calculating 
ptnf1 0.1032E-01 ch4fz 0.2759 fracture spacing 
values based on 
the active 
fracture model. 
ptnf2 0.1032E-01 ch5fz 0.2759 
ptnf3 0.1032E-01 ch6fz 0.2759 
ptnf4 0.1032E-01 pp4fz 0.2759 
ptnf5 0.1032E-01 pp3fd 0.2476 
ptnf6 0.1032E-01 pp2fd 0.2476 
tswf1 0.3741E-01 Pp1fz 0.2776 
tswf2 0.5284 bf3fd 0.2476 
tswf3 0.5284 bf2fz 0.2759 
tswf4 0.4764 tr3fd 0.2476 
tswf5 0.4764 tr2fz 0.2759 
tswf6 0.4764 pcf38 0.00 
tswf7 0.4764 pcf39 0.00 
tswf8 0.4764 Pc1fz 0.00 
tswfz 0.2759 Pc2fz 0.00 
tswfv 0.2500 Pc5fz 0.00 
ch1fv 0.2500 Pc6fz 0.00 
ch2fv 0.2500 pc4fp 0.00 
ch3fv 0.2500 tcwff (fault) 0.4000 
ch4fv 0.2500 ptnff (fault) 0.1138 
ch5fv 0.2500 tswff (fault) 0.3000 
ch6fv 0.2500 chnff (fault) 0.3000 
82 MDL-NBS-HS-000020 REV 00 
U0065 
Type of 
Uncertainty 
Input 
Source 
LB0305TSP 
A18FF.001 
Fixed value 
for each 
layer but 
varies from 
layer to 
layer. The 
values also 
depends on 
climate. 
[165625] 
Eighteen 3- 
D Site Scale 
UZ Flow 
Fields 
Converted 
from 
TOUGH2 to 
T2FEHM 
format. 
File : 
glaq_lA.dat. 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-9. Fracture  Parameter for Mean Infiltration Scenario 
Rock Layer Fracture  Fracture  Input 
Description 
Rock 
Layer 
Tcwf2 0.5866 ch2fz 0.3704 
tcwf1 0.5866 ch1fz 0.3704 This value is 
read in by 
tcwf3 0.5866 ch3fz FEHM and 
0.3704 used in 
ptnf1 0.9051E-01 ch4fz 0.3704 calculating 
fracture 
spacing 
values based 
0.3704 on the active 
fracture 
model. 
ptnf2 0.9051E-01 ch5fz 0.3704 
ptnf3 0.9051E-01 ch6fz 0.3704 
ptnf4 0.9051E-01 pp4fz 
ptnf5 0.9051E-01 pp3fd 0.1989 
ptnf6 0.9051E-01 pp2fd 0.1989 
tswf1 0.1289 pp1fz 0.3704 
tswf2 0.6000 bf3fd 0.1989 
tswf3 0.6000 bf2fz 0.3704 
tswf4 0.5686 tr3fd 0.1989 
tswf5 0.5686 tr2fz 0.3704 
tswf6 0.5686 pcf38 0.00 
tswf7 0.5686 pcf39 0.00 
tswf8 0.5686 pcf1z 0.00 
tswfz 0.3704 pcf2z 0.00 
tswfv 0.2500 pcf5z 0.00 
ch1fv 0.2500 pcf6z 0.00 
ch2fv 0.2500 pcf4p 0.00 
ch3fv 0.2500 tcwff (fault) 0.4000 
ch4fv 0.2500 ptnff (fault) 0.1138 
ch5fv 0.2500 tswff (fault) 0.3000 
ch6fv 0.2500 chnff (fault) 0.3000 
83 MDL-NBS-HS-000020 REV 00 
U0065 
Type of 
Uncertainty 
Input 
Source 
LB0305TSP 
A18FF.001 
Fixed value for 
each layer but 
varies from 
layer to layer. 
The values 
also depends 
on climate. 
[165625] 
Eighteen 3- 
D Site Scale 
UZ Flow 
Fields 
Converted 
from 
TOUGH2 to 
T2FEHM 
format. 
File : 
glaq_mA.dat 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-10. Fracture  Parameter for Upper-Bound Infiltration Scenario 
Rock Layer Fracture  Rock Layer Fracture  Type of 
Uncertainty 
Input 
Description 
Input 
Source 
0.5000 tcwf1 ch1fz 0.5000 This value is 
read in by 
LB0305TSP 
A18FF.001 Tcwf2 0.5000 ch2fz 0.5000 
FEHM and 
tcwf3 0.5000 ch3fz 0.5000 used in 
ptnf1 0.8319E-01 ch4fz 0.5000 calculating 
Fixed value 
for each 
layer but 
varies from 
layer to 
layer. The ptnf2 0.8319E-01 ch5fz 0.5000 fracture 
spacing values also 
depend on 
climate. 
ptnf3 0.8319E-01 ch6fz 0.5000 values based 
ptnf4 0.8319E-01 pp4fz 0.5000 on the active 
ptnf5 0.8319E-01 pp3fd 0.5000 fracture 
model. 
[165625] 
Eighteen 3- 
D Site Scale 
UZ Flow 
Fields 
Converted 
from 
TOUGH2 to 
T2FEHM 
format. File : 
glaq_uA.dat. 
ptnf6 0.8319E-01 pp2fd 0.5000 
tswf1 0.1000 pp1fz 0.5000 
tswf2 0.5606 bf3fd 0.5000 
tswf3 0.5606 bf2fz 0.5000 
tswf4 0.5700 tr3fd 0.5000 
tswf5 0.5700 tr2fz 0.5000 
tswf6 0.5700 pcf38 0.0000 
tswf7 0.5700 pcf39 0.0000 
tswf8 0.5700 pcf1z 0.0000 
tswfz 0.5000 pcf2z 0.0000 
tswfv 0.2500 pcf5z 0.0000 
ch1fv 0.2500 pcf6z 0.0000 
ch2fv 0.2500 pcf4p 0.0000 
ch3fv 0.2500 tcwff (fault) 0.4000 
ch4fv 0.2500 ptnff (fault) 0.1138 
ch5fv 0.2500 tswff (fault) 0.3000 
ch6fv 0.2500 chnff (fault) 0.3000 
6.5.7 Fracture Porosity, Fracture Spacing (M), and Fracture Aperture (M) 
Fracture porosity is used in FEHM to calculate the fracture pore volume of the corresponding 
fracture node block for determining the resident time of radionuclides within each fracture cell. 
Fracture spacing and aperture data are used by FEHM in estimating the effect of matrix diffusion 
on radionuclide transport. In the abstraction model, aperture and spacing based on geometric 
considerations are adjusted before use in the transport calculations to conform to the assumptions 
of the AFM of Liu et al. (1998 [105729]). This section describes the geometric parameters. For a 
discussion of how the model implements the AFM for transport, see Attachment III, Section III- 
5. 
The fracture porosity and fracture spacing data are sampled to address the uncertainty of fracture 
properties on radionuclide transport in TSPA calculations. The data sets 
(DTN: LB0205REVUZPRP.001 [159525] and DTN: LB0207REVUZPRP.001 [159526]) list 
fracture spacing data in terms of fracture frequency, defined as the inverse of fracture spacing. 
84 MDL-NBS-HS-000020 REV 00 January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Thus, the fracture frequency is first sampled, and the inverse of the sampled data are taken to 
derive sampled fracture spacing data. 
Table 6-11 lists the uncalibrated fracture porosity and frequency data based on field information. 
Among them, data for the fault zone are from DTN: LB0207REVUZPRP.001 [159526]. Those 
are the uncalibrated properties as developed in BSC 2003 [160240]. However, fracture porosity 
and frequency data are not subject to adjustment in the calibration in BSC 2003 [160240], 
therefore, these properties are carried forward into the calibrated property set without 
modification. 
Among the listed geological rock layers only those that below the repository could affect the 
transport of radionuclides downward toward the water table are sampled. Rock layers below the 
repository are grouped together based on similarity in the fracture porosity and frequency 
characteristics. The 9 groups identified are shown in Table 6-12. For groups with multiple units 
having different parameter values, an arithmetic average value is used for the group. There is 
only one standard deviation for fracture porosity, so the other groups are assigned a fracture 
porosity standard deviation such that the ratio of the standard deviation to the mean is constant 
for all the groups. Group 9 (tswf3) has its own standard deviation for fracture frequency, which 
is used. For the other groups, the standard deviation is set equal to 0.831 times the mean. This is 
based on the relationship between fracture frequency and the standard deviation of fracture 
frequency found for model units above the proposed repository (see Figure 6-13). In this way, 
the mean and standard deviation for each parameter in each group was computed. 
As porosity must lie within the finite range of 0 to 1, a beta distribution with these bounds is 
suitable for studying the influence of porosity uncertainty on radionuclide transport, Table 6-13 
lists the distribution data for fracture porosity. 
January 2004 85 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-11. Fracture Porosity and Frequency Data 
f  f 
(1/m) 
Type of 
Uncertainty Input Source Input Description Std. Rock Layer 
LB0205REVU 
ZPRP.001 
As porosity 
must fall in 
the range of 0 
and 1, a beta 
distribution is 
suitable to 
[159525] 
Fault zone 
fracture 
porosity data 
Data are 
uncalibrated. 
However, the describe the 
uncertainty of 
the porosity 
values. 
are from 
LB0207REVU 
ZPRP.001 
[159526] 
data are not subject 
to adjustment in 
f 
tcwf1 2.4E-2 - 0.92 0.94 
f  is the fracture 
tcwf2 1.7E-2 - 1.91 2.09 porosity and f is 
tcwf3 1.3E-2 - 2.79 1.43 fracture frequency. 
ptnf1 9.2E-3 - 0.67 0.92 
ptnf2 1.0E-2 - 0.46 - 
ptnf3 2.1E-3 - 0.57 - fracture porosity and 
ptnf4 1.0E-2 - 0.46 0.45 fracture frequency 
ptnf5 5.5E-3 - 0.52 0.6 
ptnf6 3.1E-3 - 0.97 0.84 calibration; 
tswf1 5.0E-3 - 2.17 2.37 therefore, those 
tswf2 8.3E-3 - 1.12 1.09 properties are 
carried forward into 
tswf3 5.8E-3 - 0.81 1.03 the calibrated 
tswf4 8.5E-3 2.50E-03 4.32 3.42 property set without 
tswf5 9.6E-3 - 3.16 - modification. 
tswf6 1.3E-2 - 4.02 - 
tswf7 1.3E-2 - 4.02 - 
tswf8/pcf38 1.1E-2 - 4.36 - 
tswf9/pcf39/ 4.3E-3 - 0.96 - 
tswfz/tswfv 
ch1fv 6.1E-4 - 0.10 - 
ch2fv 7.7E-4 - 0.14 - 
ch3fv 7.7E-4 - 0.14 - 
ch4fv 7.7E-4 - 0.14 - 
ch5fv 7.7E-4 - 0.14 - 
ch6fv 7.7E-4 - 0.14 - 
ch1fz/pcf1z 1.6E-4 - 0.04 - 
ch2fz/pcf2z 3.7E-4 - 0.14 - 
ch3fz 3.7E-4 - 0.14 - 
ch4fz 3.7E-4 - 0.14 - 
ch5fz/pcf5z 3.7E-4 - 0.14 - 
ch6fz/pcf6z 1.6E-4 - 0.04 - 
pp4f/pcf4p 3.7E-4 - 0.14 - 
pp3f 9.7E-4 - 0.20 - 
pp2f 9.7E-4 - 0.20 - 
pp1f 3.7E-4 - 0.14 - 
bf3f 9.7E-4 - 0.20 - 
bf2f 3.7E-4 - 0.14 - 
tr3f 9.7E-4 - 0.20 - 
tr2f 3.7E-4 - 0.14 - 
tcw fault 2.9E-2 1.90 - 
ptn fault 1.1E-2 0.54 - 
tsw fault 2.5E-2 1.70 - 
chn fault 1.0E-3 0.13 - 
- 
- 
- 
- 
January 2004 86 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-12. Grouping of Rock Layers Below the Repository 
Group Units Porosity Frequency (m-1) 
1 chnf 1.0E-03 0.13 
2 tswf 2.5E-02 1.7 
3 0.14 
4 
5 
6 
7 tswf9/pcf39/ 4.3E-3 0.96 
tswfz/tswfv 
8 
9 tswf3 5.8E-3 0.81 
Source DTNs: LB0205REVUZPRP.001 [159525] and 
LB0207REVUZPRP.001 [159526] 
MDL-NBS-HS-000020 REV 00 
U0065 
ch[2,3,4,5]fz 3.7E-4 
pc[2,5]fz 3.7E-4 0.14 
pp4fz/pcf4p 3.7E-4 0.14 
pp1fz 3.7E-4 0.14 
bf2fz 3.7E-4 0.14 
tr2fz 3.7E-4 0.14 
pp3fd 9.7E-4 0.20 
pp2fd 9.7E-4 0.20 
bf3fd 9.7E-4 0.20 
tr3fd 9.7E-4 0.20 
ch1fz/pcf1z 1.6E-4 0.04 
ch6fz/pcf6z 1.6E-4 0.04 
ch1fv 6.1E-4 0.10 
0.14 ch[2,3,4,5,6]fv 7.7E-4 
tswf4 8.5E-3 4.32 
tswf5 9.6E-3 3.16 
tswf[3,6,7] 1.3E-2 4.02 
tswf8/pcf38 1.1E-2 4.36 
January 2004 87 Particle Tracking Model and Abstraction of Transport Processes 
4 
3.5
3 
2.5
2 
1.5
1 
0.5
0 
1.00 0.00 
Fracture Frequency (1/m) 
Figure 6-13. Relationship between Fracture Frequency and Standard Deviation 
Given that fracture frequency can theoretically span values from zero to infinity, the lognormal 
distribution is suitable. The mean and standard deviation for ln( ) f are given in terms of the 
mean and standard deviation for f by the following relationships from Hogg and Craig (1978 
[163236], pp. 180 and 432): 
MDL-NBS-HS-000020 REV 00 
2f 
(Eq. 6-24) 1 ln ln( f f ) 
1 ln 
2 2f 
2 
(Eq. 6-25) ln 1 f
2f 
ln( f ) 
January 2004 
Equations I-1, I-2, and XI-4 through XI-7. Values for 
.
. .
.
. 
+ 
88 
g = 
mln( ) f 
Standard Deviation of 
Fracture Frequency (1/m) 
For further information on this derivation, see Attachments I and XI of BSC 2003 [164889], 
and m are given in Table 6-13. 
g . .
. 
m . 
+
 g . . m . 
gln( f ) 
U0065 
Fracture Frequency 
Data 
Linear regression to 
data 
y = 0.831x 
R2 = 0.783 
Fracture Frequency 
5.00 4.00 3.00 2.00 
Output DTN: LA0311BR831371.003 
. .

. ( ) g 
=
Particle Tracking Model and Abstraction of Transport Processes 
Table 6-13. Fracture Porosity and Frequency Distribution Data 
Group Units 
1 chnf 1.0E-03 3.09E-04 1.26E-01 1.05E-01 
2 tswf 2.5E-02 7.25E-03 1.75E+00 1.45E+00 
3 
4 
ch[2,3,4,5]fz 
pcf[2,5]z 
pp4fz 
pp1fz 
bf2fz 
tr2fz 
pp3fd 
pp2fd 
bf3fd 
tr3fd 
5 ch1fz/pcf1z 1.6E-4 4.71E-05 4.00E-02 3.32E-02 
ch6fz/pcf6z 
6 ch[1,2,3,4,5,6]fv 6.9E-4 2.03E-04 1.20E-01 9.96E-02 
7 tswf9/pcf39 4.3E-3 1.26E-03 9.60E-01 7.97E-01 
8 
/tswfv/tswfz 
Tswf[4,5] 
tswf[6,7] 
tswf8/pcf38 
9 tswf3 5.8E-3 1.71E-03 8.10E-01 1.03E+00 
DTN: LA0311BR831371.003 
In TSPA-LA calculations, the fracture porosity and fracture frequency are sampled 
independently. The basis for this approximation is that there is only a very weak correlation 
between fracture porosity and frequency (Figure 6-14). Therefore, correlating these two 
parameters is not warranted. 
f 
-2.42E+00 7.24E-01 7.94E-03 
2.11E-01 7.24E-01 1.43E-02 
-2.31E+00 7.24E-01 2.64E-03 
-1.96E+00 7.24E-01 4.85E-03 
-3.57E+00 7.24E-01 4.00E-03 
-2.47E+00 7.24E-01 5.75E-03 
-3.87E-01 7.24E-01 4.48E-03 
1.03E+00 7.24E-01 2.64E-03 
-6.92E-01 9.81E-01 7.16E-03 
f  
MDL-NBS-HS-000020 REV 00 
Porosity (-) 
Beta Distribution 
min = 0; max = 1 
Std 
Fracture Frequency 
(m-1) 
Mean Std Mean 
3.7E-4 1.09E-04 1.40E-01 1.16E-01 
9.7E-4 2.85E-04 2.00E-01 1.66E-01 
1.05E-02 3.10E-03 3.97E+00 3.29E+00 
89 
U0065 
Fracture Frequency (m-1) Aperture (m) 
2b Lognormal Distribution 
derived from 
Eq. 6-26: 
2b = 
Mean Std 
For ln (f) For ln (f) 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
5.00E+00 
4.50E+00 
4.00E+00 
3.50E+00 
3.00E+00 
2.50E+00 
2.00E+00 
1.50E+00 
1.00E+00 
5.00E-01 
0.00E+00 
0.00E+ 1.00E- 2.00E- 3.00E- 4.00E- 
02 02 02 02 
f 
where b 2 is the fracture aperture (m), f is the fracture frequency (m-1), and f 
is the fracture 
porosity (-). Fracture frequency is the inverse of the fracture spacing. 
6.5.8 Fracture Surface Retardation Factor (Unitless) 
Because few data are available on fracture surface retardation factors, no fracture surface 
retardation is simulated in the TSPA model. In current TSPA simulations, all the fracture 
surface retardation factors are set to 1.0 (no fracture surface retardation) to be conservative. 
Values of fracture surface retardation factors are included in FEHM input data file and are read 
in at run time. 
Figure 6-14. Relationship between Fracture Porosity and Frequency 
The sampled fracture porosity and frequency data are used in deriving the fracture spacing and 
aperture based on the following relationship: 
MDL-NBS-HS-000020 REV 00 
b) 2 ( = f 
90 
(Eq. 6-26) 
Fracture Frequency vs Porosity 
Fracture Porosity (-) 
y = 85.797x + 0.4827 
R2 = 0.2634 
Fracture data 
Linear regression of 
data 
Fracture Frequency (1/m) 
00 
U0065 
Output DTN: LA0311BR831371.003 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-14. Fracture Surface Retardation Factor 
Fracture Surface 
Retardation Factor 
Rock 
Layers 
Type of 
Uncertainty Input Source Input Description 
Fixed value 1.0 All layers CRWMS M&O 2000 
[148384] 
Parameter used to simulate the effect 
of fracture surface retardation on 
radionuclide transport. 
6.5.9 Colloid Filtration at Matrix Interface 
Matrix pore size distribution combined with colloid size distribution is used in FEHM for 
determining colloid filtration at the interfaces between matrix units. Each time step, at a matrix 
unit interface FEHM compares a colloids size against the sampled pore size of the matrix unit it 
is entering. If the colloid size is bigger than the pore size, then the colloid cannot enter the 
matrix and is removed from the simulation (permanently filtered). In TSPA simulations the 
cumulative probabilities for colloid transport between one matrix unit and another are taken from 
DTN: LA0003MCG12213.002 [147285] and listed in Table 6-15 (only colloid size data beneath 
the repository level are listed). In FEHM the matrix pore size data are sampled based on the 
cumulative colloid transport probability data in Table 6-15 and the sampled data are used in 
simulating colloid filtration at matrix interfaces. 
Table 6-15. Cumulative Probabilities for Colloid Transport at Matrix Interfaces 
Colloid Size (nm) 
Units 2000 1000 450 200 100 50 6 
TMN/TSW4 1.00 0.92 0.87 0.81 0.71 0.55 0.31 
TLL /TSW5 1.00 0.80 0.79 0.70 0.61 0.51 0.19 
TM2/TSW6 1.00 0.94 0.90 0.82 0.65 0.51 0.21 
TMN1/TSW7 1.00 0.99 0.99 0.99 0.93 0.68 0.36 
PV3 /TSW8 1.00 0.98 0.96 0.94 0.90 0.89 0.68 
PV2/TSW9 1.00 0.72 0.57 0.47 0.39 0.35 0.22 
BT1a/CH1 1.00 0.91 0.89 0.87 0.85 0.83 0.53 
CHV 1.00 0.58 0.49 0.43 0.39 0.36 0.07 
CHZ 1.00 0.79 0.76 0.73 0.68 0.56 0.30 
BT/CH6 1.00 0.95 0.94 0.92 0.92 0.85 0.40 
PP1 1.00 0.79 0.68 0.63 0.57 0.48 0.21 
PP2 1.00 0.91 0.86 0.81 0.65 0.53 0.22 
PP3 1.00 0.49 0.34 0.26 0.21 0.16 0.07 
PP4 1.00 0.99 0.99 0.98 0.98 0.96 0.32 
BF2 1.00 0.98 0.97 0.96 0.96 0.83 0.25 
BF3 1.00 0.97 0.94 0.83 0.74 0.66 0.14 
Data are used by FEHM in combination with colloid size distribution data for simulating the 
effect of colloid filtration at matrix interface. 
Input 
Description 
DTN: LA0003MCG12213.002 [147285]. Input Source 
Fixed values. Type of 
Uncertainty 
January 2004 91 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
6.5.10 Colloid Size Exclusion 
Due to flow exchange between fractures and the corresponding matrix block, colloids may be 
carried into matrix from fractures by advection. The amount of colloids that can enter into 
matrix depends on the size of the colloids and the size of the matrix pores. At the fracture-matrix 
interface, when a colloids size is larger than the matrix pore size, this colloid will stay in the 
fracture. On the other hand, when a particle size is smaller than the matrix pore size, the colloid 
will enter into the matrix through advection. The colloid size exclusion effect in the current 
FEHM model is simulated with a size exclusion factor fc based on the percentage of the pores 
that are greater than the expected colloid size of 100 nm (DTN: LA0003MCG12213.002 
[147285]). Table 6-16 lists the values used in FEHM. There is no site-specific transport data 
available to validate this aspect of the colloid transport model. The incorporation of this feature 
is intended to avoid a non-physical situation in which colloids are allowed to enter the matrix 
even when they are larger than the typical pore size. This aspect of the model is conservative, in 
that it will tend to exclude some colloids from the slower moving matrix fluid and keep them in 
the fractures. 
Rock Units 
Table 6-16. Colloid Size Exclusion Factor Used in FEHM 
Input Description 
Parameters are used by LA0003MCG12213.002 
FEHM for simulating the [147285] 
effect of colloid size 
exclusion on 
radionuclide transport at 
the fracture-matrix 
interface. 
TMN (TSW4) 0.29 
TLL (TSW5) 0.39 
TM2 (TSW6) 0.35 
TMN1 (TSW7) 0.07 
PV3 (TSW8) 0.10 
PV2 (TSW9) 0.61 
BT1a (CH1) 0.15 
CHV 0.61 
CHZ 0.27 
BT (CH6) 0.08 
PP4 0.02 
PP3 0.79 
PP2 0.35 
PP1 0.43 
BF3 0.26 
BF2 0.04 
6.5.11 Colloid Size Distribution 
92 
Size Exclusion 
Factor 
effects at matrix unit interfaces. 
MDL-NBS-HS-000020 REV 00 
Input Source 
A colloid size distribution is used by FEHM to get the interpolated colloid size of each colloid 
particle. The colloid size information is then combined with pore size data to simulate filtration 
The colloid size range of 6 nm to 450 nm is based on CRWMS M&O (2001 [154071], 
Section 6.3); DTN: LL000122051021.116 [142973]. However, because a specific distribution 
was not available, the following distribution (Table 6-17) was chosen (not developed) to be 
Type of Uncertainty 
Fixed value. In 
TSPA-LA simulations, 
a random number 
generator is used to 
determine the 
probability of a colloid 
entering into matrix 
from the corresponding 
fractures. 
January 2004 
U0065
Particle Tracking Model and Abstraction of Transport Processes 
consistent with Figure 23 of CRWMS M&O (2001 [154071]); DTN: LA0007MCG12213.001 
[153251]. 
The same colloid size distribution data are used in this abstraction model. FEHM data files 
contain the colloid size input data under the macro size. 
Colloid 
Size (nm) 
Table 6-17. Colloid Size Distribution 
Input Description Input Source 
LL000122051021.116 
[142973] 
Cumulative 
Probability 
6 0.2 
1 0 Colloid size distribution 
data are used in 
simulating colloid 
50 0.4 filtration effect at matrix 
100 0.6 interface. 
200 0.8 
450 1.0 
6.5.12 Colloid Concentration and Colloid Kc 
assigned for Kc (see Table 6-18). 
The colloid equilibrium sorption parameter Kc is defined as Kc=Ccoll/Cfluid, where Ccoll is the 
radionuclide concentration residing on colloids and Cfluid is the radionuclide concentration in 
fluid. Colloid Kc is used in FEHM as an input parameter for calculating the retardation factors 
for colloid facilitated radionuclide transport in the media. 
Radionuclide sorption to colloids can be categorized into reversible and irreversible categories. 
When sorption to colloids is treated as an irreversible process, a very large number (1.0E20) is 
Type of Uncertainty 
FEHM read in the cumulative 
distribution data at run time. 
Random colloid size data are 
generated on the fly to address 
the effect of colloid size 
uncertainty on filtration. 
Irreversible 
Colloids 
Irreversible 
colloids 
Table 6-18. Kc for Irreversible Colloid 
Input Description 
93 
irreversible. 
Input Source Kc 
1.0E20 Simulating the effect of A large value that ensures the 
irreversible sorption to colloid. adsorption process to colloids be 
NOTE: This input value is not data: rather it is a recommended input value to allow irreversible sorption to colloids to 
be simulated in the abstraction model. 
For reversible radionuclide sorption to colloids, the Kc values are calculated by multiplying the 
adsorption coefficient, Kd, of radionuclide to colloid by colloid concentrations in the water. 
Field data and laboratory experiments have shown that colloid concentration in groundwater can 
vary several order of magnitudes and is also a function of ionic strength and groundwater pH 
(BSC 2003 [161620]; DTN: SN0306T0504103.005 [164132]). To address the uncertainty of 
colloid concentration on colloid facilitated radionuclide transport, in TSPA-LA, the colloid 
concentration is sampled at run time and provided to FEHM for the calculation of reversible 
colloid Kc. Table 6-19 lists the distribution of colloid concentration used in TSPA-LA. 
MDL-NBS-HS-000020 REV 00 
U0065 
Type of 
Uncertainty 
Fixed value 
January 2004 U0065 
Type of Uncertainty Input Source 
The cumulative distribution 
data listed in this table will 
be used to generated 
random colloid 
concentrations at TSPA-LA 
run time to address the 
influence of colloid 
concentration uncertainty of 
radionuclide transport. 
Particle Tracking Model and Abstraction of Transport Processes 
Table 6-19. Colloid Concentration Distribution 
Cumulative 
Probability Input Description 
Colloid 
Concentration 
(mg/l) 
50 0.001 to 0.1 
75 0.1 to 1.0 Section 6.3.2.2.2, 
Figure 31, and 90 1.0 to 10 
Ionic strength less than BSC 2003 [161620], 
0.05. Data are used in 
the estimation of 
reversible colloid Kc. 
98 10 to 50 
100 50 to 200 
Table 6. 
SN0306T0504103.005 
[164132] 
1.E-6 100 Ionic strength >= 0.05 
NOTE: The probability of occurrence values listed in the source Table 6 are summed up to generate the 
cumulative probability in this table. 
The strength of radionuclide adsorption onto colloid is determined by the adsorption coefficient 
Kd. In TSPA-LA, the following Kd distribution is used (Table 6-20). Among them, Kd ranges 
and distributions for Th and Pa are assumed to be those of Am primarily because of limited data 
on Th and Pa (BSC 2003 [161620]; DTN: SN0306T0504103.006 [164131]). 
Table 6-20. Radionuclide Adsorption Coefficient (mL/g) Onto Colloids 
Input Source Input Description 
Type of 
Radionuclide Colloid Values (-) Uncertainty 
Pu BSC 2003 [161620], Parameters are 
used in the 
calculation of colloid 
Am Kc values by FEHM. 
Section 6.3.2.3.1, 
Table 7, and 
Section 6.5.3, Table 15. 
SN0306T0504103.006 
Th [164131] 
Pa 
Cs 
Iron-(hydr)oxide 104 to 106 Uniform 
Smectite 103 to 106 Uniform 
Iron-(hydr)oxide 105 to 107 Uniform 
Smectite 104 to 107 Uniform 
Iron-(hydr)oxide 105 to 107 Uniform 
Smectite 104 to 107 Uniform 
Iron-(hydr)oxide 105 to 107 Uniform 
Smectite 104 to 107 Uniform 
Iron-(hydr)oxide 101 to 103 Uniform 
Smectite 102 to 104 Uniform 
In TSPA-LA calculations, to reflect the influence of reversible colloid facilitated radionuclide 
transport on system performance, colloid Kd values d K ,coll are sampled at run time and used in 
coll 
the calculation of Kc. The sampled radionuclide adsorption coefficients are then multiplied by 
the colloid concentration C to calculate the colloid Kc values: 
coll c d , C K = K coll (Eq 6-27) 
6.5.13 Fractions of Colloids Traveling Unretarded and Colloid Retardation Factor 
Colloid retardation factor, Rc, is used in FEHM to study the impact of colloid retardation in the 
fractured media on irreversibly sorbed radionuclide transport. Field experiments have shown 
that a small percentage of colloids transport through the groundwater system essentially without 
January 2004 94 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
retardation (BSC 2003 [162729]). The fractions of unretarded colloids have been developed 
based on field data and are listed in Table 6-21. 
This table, derived in BSC 2003 [162729], postulates that the fraction of colloids escaping 
retardation due to physical and chemical processes is a function of the residence time of the 
colloid: progressively fewer colloids migrate unretarded with time. This poses a difficulty in 
simulating transport for the unretarded colloids  the travel times are not known a priori. 
Therefore, it is recommended that the fraction be chosen for a travel time that can be reasonably 
expected to be conservative, such as 100 yr in the UZ. If simulations suggest that a different 
residence time is more representative, then this time should be changed, and a new unretarded 
fraction should be selected from Table 6-21. It should be noted that this aspect of the colloid 
transport model is relatively uncertain, so parameter sensitivity studies are advisable if it is 
determined that a colloidal radionuclide may be important to performance. 
Colloids traveling unretarded will be given a retardation factor of 1. 
Travel Time 
(Years) 
Table 6-21. Fractions of Colloids Traveling Unretarded 
Input Source 
LA0303HV831352.003 
[165624] 
Input Description 
1 0.011 This parameter is used in BSC 2003 [162729] 
determining fractions of 
colloids traveling 
unretarded in the UZ. 
5 0.005702 
10 0.004297 
20 0.003238 
30 0.002744 
40 0.00244 
50 0.002227 
75 0.001888 
100 0.001678 
300 0.001072 
600 0.000808 
1000 0.000656 
2000 0.000494 
5000 0.00034 
95 
Fraction of 
Colloids Unretarded 
10000 0.000256 
MDL-NBS-HS-000020 REV 00 
Type of 
Uncertainty 
Fixed value 
For colloids that are delayed relative to a conservative species, the retardation of colloids in 
groundwater system depends on colloid type; colloid size; groundwater PH, Eh, and ionic 
strength; and rock properties, etc. Field (C-wells complex near Yucca Mountain and Nevada 
Test Site) and laboratory experiments were carried out under saturated conditions to estimate 
colloid retardation factors (BSC 2003 [162729]). As there is no data are available on colloid 
retardation factors in the UZ, the distribution of retardation factors from the SZ are used to 
represent colloid retardation through unsaturated fractures. Table 6-22 lists the cumulative 
distribution data of colloid retardation factors. 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-22. Colloid Retardation Factors 
Type of Uncertainty Input Source 
Cumulative 
Probability Input Description 
Colloid 
Retardation 
Factor 
BSC 2003 [162729] 
LA0303HV831352.002 
[163558] 
10 0.240831 Colloid retardation factor 
12 0.268609 is used by FEHM in 
simulation the effects of 
14 0.296387 
A cumulative distribution 
is used to describe the 
distribution of colloid 
retardation factor. In 
TSPA-LA, the colloid 
retardation factor will be 
colloid retardation in 
14 0.324165 fractured rock on colloid 
facilitated radionuclide 
transport. sampled at runtime and 
used by FEHM in TSPA 
calculations. 
20 0.351942 
20 0.37972 
21 0.435276 
22 0.463053 
24 0.490831 
30 0.518609 
32 0.546387 
40 0.574165 
40 0.601942 
40 0.62972 
46 0.657498 
50 0.685276 
50 0.713053 
53 0.740831 
60 0.768609 
60 0.796387 
200 0.835276 
280 0.890831 
410 0.918609 
600 0.972232 
800 1 
In TSPA-LA calculations, to investigate the uncertainty of colloid retardation factors on 
radionuclide transport, colloid retardation factors are sampled for each realization at run time 
based on the given cumulative distribution in Table 6-22. 
6.5.14 Radionuclide Half Lives (Years) and Daughter Products 
FEHM needs the radionuclide half life and daughter products information to simulate the 
influence of radionuclide decay and ingrowth on system performance. The radionuclide half life 
and daughter products for the following species are used in FEHM as input parameters (see 
Table 6-23). 
January 2004 96 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-23. Radionuclide Half-Life and Daughter Products used in TSPA 
Input Description 
Daughter 
Radionuclide Half-Life (yr) Product 
C14 5.715E+03 Radionuclide half-lives Parrington et al. 1996 
and daughter products. [103896] Cs135 2.3E6 
Those data will be used 
Cs137 3.007E+1 by FEHM in 
I129 1.57E+7 radionuclide decay and 
Sr90 2.878E+1 ingrowth calculations. 
Tc99 2.13E+5 
Am243 7.37E+3 Pu239 
Pu239 2.410E+4 U235 
U235 7.04E+8 Pa231 
Pa231 3.28E+04 
Am241 4.327E+2 Np237 
Np237 2.14E+06 U233 
U233 1.592E+5 Th229 
Th229 7.3E+3 
Pu240 6.56E+3 U236 
U236 2.342E+7 Th232 
Th232 1.40E+10 
U232 6.98E+1 
Pu242 3.75E+5 U238 
Pu238 8.77E+1 U234 
U238 4.47E+9 U234 
U234 2.46E+5 Th230 
Th230 7.54E+4 Ra226 
Ra226 1.599E+3 
Irreversible and reversible colloid facilitated 
radionuclide has the same half-life and daughter 
products as corresponding dissolved species. 
Pu242 3.75E+5 
Pu240 6.56E+3 
Pu239 2.410E+4 
Pu238 8.77E+1 
Am243 7.37E+3 
Am241 4.327E+2 
6.5.15 Repository Radionuclide Release Bins 
Radionuclides will be released from nodes corresponding to the repository location. These nodes 
were grouped into bins (zones) that shared common infiltration ranges, to be compatible with a 
conceptual model for radionuclide release in which releases are a strong function of the 
percolation rates at the repository horizon. This would help to categorize release points 
according to high or low percolation rates. Five bins were chosen based on the cumulative 
probability of percolation for the glacial climate period. The glacial period was selected to 
perform this binning because the majority of the simulation is performed under this climate state. 
The definition of the 5 bins is listed in Table 6-24. 
97 MDL-NBS-HS-000020 REV 00 
U0065 
Type of 
Uncertainty Input Source 
Fixed values 
DTN: N/A accepted data 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Bin 3 Bin 1 
Range of Cumulative 
Probability 
Table 6-24. Definition of Repository Release Bins 
0.30  0.70 0  0.05 
0.73  6.71 
Bin 2 
0.05  0.30 
98 
0.70  0.95 
6.71  11.77 11.77  21.22 21.22  38.48 38.48  76.67 
Bin 5 
0.95  1.00 
January 2004 
Range of Percolation Glacial 
Climate (mm/year) 
NOTE Binning data are from BSC 2001 [158204], Attachment VIII, Binning Calculations. 
Node coordinates within each bin are given in the multiscale thermohydrological model 
(DTN: LL030610323122.029 [164513]). As the grid resolution of the thermohydrological 
model is much finer (file: NEVADA_SMT_percolation_BIN_ma.txt. 
DTN: LL030610323122.029 [164513]) than the site scale FEHM transport model, the node 
coordinates of the thermohydrological model are mapped onto the FEHM grid to derive the 
corresponding FEHM nodes. 
The mapping was done using FEHM V2.21 (LANL 2003 [165741]) and Microsoft Excel. The 
SMT (Smeared-sources Mountain-scale Thermal model) node coordinates from the 
thermohydrological model were read in by FEHM using the zone macro. FEHM did a search 
to find the closest node to a given SMT coordinate. Once FEHM nodes corresponding to the 
given SMT coordinates are found, Excel was used to get the frequency of FEHM node within 
each bin (data to be submitted). The following rules are applied during the mapping using Excel. 
 As the FEHM grid is coarser than the thermohydrological model grid, it is possible that 
some nodes in the thermohydrological model within different bins may map onto a 
single FEHM node in the corresponding bins. In this case, the FEHM node with the 
most frequent appearance prevails. For example, FEHM 36189 appeared two times in 
bin 1 and four times in bin 4. Based on the rule, FEHM node 36189 was assigned to 
bin4. 
 When a FEHM node appeared equal number of times in different bins, this node will be 
assigned to the highest bin number to be conservative. For example, FEHM node 39316 
appeared three times in bin2 and bin3, respectively. Thus, node 39316 was assigned to 
bin3. 
A file containing a listing of these bins and the associated nodes was created and named 
repository_bins. The bin data are incorporated into FEHM zone files in TSPA simulations and 
used to release radionuclides from the repository. 
Figures 6-15 and 6-16 are plots showing the location of SMT repository release nodes and the 
transformed FEHM repository release nodes, respectively. It is clear that the transformed FEHM 
release nodes corresponding to the SMT release nodes closely. But, because of the much coarser 
FEHM grid and the lack of a one-to-one transformation from one grid to the other, the FEHM 
repository release nodes does not capture the detail depicted in the SMT grid. Nevertheless, the 
transformation is sufficient for the purposes of depicting the role of percolation variability on 
radionuclide releases and transport. 
MDL-NBS-HS-000020 REV 00 
U0065 
Bin 4 Particle Tracking Model and Abstraction of Transport Processes 
237000 
236500 
236000 
235500 
235000 
234500 
234000 
233500 
233000 
232500 
232000 
231500 
170000 169500 
Figure 6-15. 
MDL-NBS-HS-000020 REV 00 
Northing (m) 
171500 171000 170500 
Easting (m) 
SMT Repository Release Nodes. 
99 
U0065 
repo_zone_1 
repo_zone_2 
repo_zone_3 
repo_zone_4 
repo_zone_5 
172500 172000 
Output-DTN: LA0311BR831371.003 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
237000 
236500 
236000 
235500 
235000 
234500 
234000 
233500 
233000 
232500 
232000 
231500 
169500 
Figure 6-16. FEHM Repository Release Nodes Transformed Based on SMT Release Nodes (Shown in 
Figure 6-15). 
6.5.16 Radionuclide Collecting Bins at UZ/SZ Interface 
For the UZ/SZ interface, all nodes at (or below) the highest potential water table elevation of 850 
m in the UZ model were grouped into four regions (or bins). The purpose of this process is for 
increased resolution to be captured in the TSPA model with respect to the arrival location and its 
impact on travel times in the SZ. Radionuclide mass reaching the water table in one location may 
have a different SZ travel path and travel time than mass arriving at some other location. The 
collecting bins are the means by which this potentially significant feature of the system can be 
quantified. The total radionuclide mass flow rate in each of these four bins will be focused at a 
random point (within each of the four bins) in the SZ model to reduce the effects of artificial 
dilution between the model interfaces. The four regions (Figure 6-17) are defined by an eastwest 
boundary at a Universal Transverse Mercator (UTM) easting coordinate of 548500 and a 
north-south boundary at a UTM northing coordinate at 4078630 m (BSC 2003 [164870], 
Table 6-8). 
MDL-NBS-HS-000020 REV 00 January 2004 100 
Northing (m) 
U0065 
repo_zone_1 
repo_zone_2 
repo_zone_3 
repo_zone_4 
repo_zone_5 
172500 172000 171500 171000 170500 170000 
Easting (m) 
Output-DTN: LA0311BR831371.003 U0065 Particle Tracking Model and Abstraction of Transport Processes 
All nodes at or beneath the water table in the UZ model were grouped into one of the four 
regions based on data listed in Table 6-8 in BSC 2003 [164870]. The FEHM water table 
collecting bins are larger than the SZ source release bins defined in Figure 6-17 to ensure that no 
particles fall outside of the four SZ release zone and go uncounted. The FEHM water table 
collecting bin nodes were extracted from the ELEME data from TOUGH2 site scale flow model 
package (DTN: LB0323DSSCP9I.001 [163044]). This data contains the cell name and 
coordinates for each node in the site scale UZ flow model. As the UZ transport model uses the 
Nevada State Plan (NSP) coordinates, the given UTM coordinates are converted into NSP 
coordinates during the extraction of the water table collect bins. The extraction was done in an 
Excel spreadsheet through several conditional if statements (See Attachment II for detail). The 
four collecting bins in FEHM are named 701, 702, 703, and 704, containing SZ source release 
regions 1, 2, 3, and 4, respectively. Among them, zone 701 contains all nodes beneath the water 
table with a UTM easting coordinate less than 548500 m (NSP: 171189.79 m) and a UTM 
northing coordinate greater than 4078630 m (NSP: 233459.87m); zone 702 contains all water 
table nodes with a UTM easting coordinate greater than 548500 m (NSP: 171189.79 m) and a 
UTM northing coordinate greater than 4078630 m (NSP: 233459.87m); zone 703 contains all 
water table nodes with a UTM easting coordinate less than 548500 m (NSP: 171189.79 m) and a 
UTM northing coordinate less than 4078630 m (NSP: 233459.87m); and zone 704 contains 
water table nodes with a UTM easting coordinate greater than 548500 m (NSP: 171189.79 m) 
and a UTM northing coordinate less than 4078630 m (NSP: 233459.87m). 
Nodes contained in each of the collection bins were stored in file wt.zone and defined in the 
corresponding FEHM zone file. Once a particle reaches the water table, the particle is removed 
from the system. Inside FEHM, the code records mass leaving the system within each bin/zone 
(FEHM V2.21 Users Manual, LANL 2003 [165741]). As climate change can cause water table 
rise or fall, the defined collection bins/zones contain all nodes between the lowest and the highest 
water tables, up to an elevation of 850 m (see Section 6.4.9 for details). Note that for the 
simulations in this Model Report, the present day water table is used for all simulation results to 
maintain consistency and allow comparison to the process model simulation results. 
At the end of each simulation time step, FEHM collects the total radionuclide mass leaving each 
water table collection bin/zone and then passes the data to GoldSim (BSC 2003 [161572]) for 
use as input for SZ transport simulations. 
6.6 BASE-CASE MODEL 
In this Model Report, we set our base case as a case using mean radionuclide transport 
parameters and present day mean infiltration. The results from this run will not be used by 
TSPA. This simulation activity illustrates the possible transport behavior of radionuclides within 
the UZ under the conditions of present day mean infiltration condition and mean transport 
parameter values. In TSPA-LA, the abstracted model will be used with different parameter 
combinations to study the uncertainty of parameters and flow fields on radionuclide transport 
through the UZ and its impacts on system performance. 
January 2004 101 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
6.6.1 Overview 
The simulation was carried out using FEHM V2.21 (LANL 2003 [165741]). Data used in this 
simulation are the mean parameter values listed in Section 6.5 Transport Model Inputs. The flow 
field used in this simulation was for present day mean infiltration. 
The objective of this run is to study the movement of radionuclides released from EBS into 
unsaturated fractured geological media downward to the water table as stated in Section 6.1 
Model Objectives. 
A total of 36 species (Table 6-25) were simulated to study the transport of radionuclides. 
4082000 
4081000 
2 
4080000 1 
m ) 
n g (
4079000 
4078000 
N o rt 
hi 
MT
U 
4077000 
4076000 
3 4 
4075000 
546000 547000 548000 549000 550000 551000 
UTM Easting (m) 
Source: BSC 2003 [164870], Figure 6-26 
Figure 6-17. Source Regions for Radionuclide Release in the SZ Transport Abstraction Model. Dashed 
lines represent the boundaries of the SZ release regions and the solid lines represent the 
January 2004 
boundary of the repository release region. 
6.6.2 Base-Case Model Results 
Figure 6-18 shows the normalized cumulative breakthrough curves at water table for the 
36 species simulated under the present-day mean infiltration condition. Note that for the colloid 
simulations, colloid filtration at matrix interfaces (Section 6.5.9) was not included in these 
calculations. The process model does not have this particular feature, so it was decided that, in 
order to make comparison with the process model results simpler, the calculations presented here 
should omit this process as well. However, this mechanism should be included in the TSPA-LA 
102 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
model. The simulation results reveal that irreversible fast colloids (curves labeled If239, If241, 
If242, and If243) which are not affected by matrix diffusion and retardation have the shortest 
breakthrough times and the greatest breakthrough quantities. Within a time period of less than 
100 years, over 50 percent of the irreversible fast colloids traveled through the UZ. 
Irreversible slow colloids which undergo retardation move more slowly than their corresponding 
fast colloids but faster than their corresponding dissolved species. The travel time of the 
irreversible slow colloids depends on their retardation factor. In TSPA-LA simulations, the 
retardation factors of the slow colloids will be sampled and its impact on system performance 
will be evaluated. 
1.8 
1.7 
1.6 
1.5 
1.4 
1.3 
1.2 
1.1 
1.0 
0.9 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
0.1 
0.0
1.E-01 1.E+00 
Cs135 C14 
If239 Ic239 
Ic240 Pu240 
If238 Ic238 
NOTE: These results are for comparison purposes only. Actual radionuclide mass flux reaching the water table will 
depend on release rates and locations, and will be simulated in the TSPA model. 
Figure 6-18. Base Case Model Normalized Breakthrough Curve for 36 Radionuclide Species, Presentday 
Mean Infiltration Scenario 
MDL-NBS-HS-000020 REV 00 January 2004 103 
Normalized Cumulative Breakthrough 
U0065 
1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 
Time (year) 
Pu239 If243 Ic243 Am243 Tc99 Sr90 I129 Cs137 
Th229 U233 Np237 If241 Ic241 Am241 Pa231 U235 
Pu238 If242 Ic242 Pu242 U232 Th232 U236 If240 
Ra226 Th230 U234 U238 
Output-DTN: LA0311BR831371.003 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Dissolved species have the longest breakthrough time among the three transport mechanism 
(irreversible fast colloids, irreversible slow colloids, and dissolved species) due to matrix 
diffusion and matrix adsorption. The results show that for non-sorbing species, like Tc-99 and 
I-129, about 20 percent of the mass travels through fast flow paths and arrives at the water table 
in less than 100 years. The remainder of the mass traveled at much lower velocities due to matrix 
diffusion. Dissolved species with moderate matrix adsorption, like the isotopes of Uranium, 
travel more slowly through the UZ than the non-sorbing species Tc-99 and I-129. Within the first 
100 years under the present-day mean infiltration conditions, only about 5% percent of the total 
U-233 mass passed through the UZ. U-234 exhibits a relatively fast transport process with 
higher mass output than the other dissolved Uranium radionuclides because it is produced by the 
decay of a colloid facilitated species (Pu-238). Strongly sorbing species like Pu-242 (median Kd 
of 100 mL/g in Zeolitic, 70 mL/g in Devitrified, and 100 mL/g in vitric layers) exhibit transport 
of less than 15% of the input through the UZ within the 20,000 year period. The most strongly 
sorbing species such as Th-230 (mean Kd of 15500mL/g in Zeolitic, 5500 mL/g in Devitrified, 
and 5500mL/g in vitric layers) do not break through the UZ within the 20,000 year period. 
Finally, note that U-234 and Np-237 have normalized cumulative breakthrough values greater 
than 1 at 20,000 year due to the decay of Pu-238 (Pu238, If238, and Ic238) and Am241 (Am241, 
If241, and Ic241), respectively. 
For comparison, a case was also run under the wetter glacial mean infiltration condition to 
investigate the influence of higher infiltration on radionuclide transport through the UZ. 
Figure 6-19 shows the normalized cumulative breakthrough curves of the same 36 species with 
the same rock and transport properties as for the present day mean infiltration case. As before, 
normalized cumulative breakthrough values for some Uranium species (U-234, U-235, and U- 
236) and Np-237 are larger than 1 due to decay of Pu and Am (Am-241, If241, and Ic241, 
respectively). Under the glacial mean infiltration condition, all species travel much faster and 
arrive at the water table earlier. A comparison of Figures 6-18 and 6-19 reveals that significantly 
more Tc-99 breaks through at the water table under the glacial infiltration condition, which 
indicates increased fast flow in fractures and more modest matrix diffusion effects. The same is 
true for Np-237, which diffuses and sorbs to the matrix rock. This comparison shows that fast 
water flow under wetter infiltration conditions can reduce the effect of matrix diffusion and 
transport radionuclides through the UZ within the simulation time period of 20,000 years. 
January 2004 104 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
2.0 
1.9 
1.8 
1.7 
1.6 
1.5 
1.4 
1.3 
1.2 
1.1 
1.0 
0.9 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
0.1 
0.0
1.E-01 1.E+00 
Cs135 C14 
If239 Ic239 
Ic240 Pu240 
If238 Ic238 
NOTE: These results are for comparison purposes only. Actual radionuclide mass flux reaching the water table will 
depend on release rates and locations, and will be simulated in the TSPA model. 
Figure 6-19. Base Case Model Normalized a Breakthrough Curve for 36 Radionuclide Species, Glacial 
Mean Infiltration Scenario 
With regard to colloid transport, the simulation results show that current conceptualizations 
suggest that colloids can play an important role in accelerating the transport of radionuclides in 
the UZ, especially the irreversible fast colloids. Of course, if the quantity of irreversible fast 
colloids is low, the impact on dose would not be expected to be important. In TSPA-LA 
calculations, a conservative percentage of irreversible fast colloids will be selected to study its 
impact on dose. For irreversible slow colloids, the retardation factor should be sampled to 
investigate parameter uncertainty on system performance. 
Matrix diffusion and matrix adsorption can play an important role in retarding the movement of 
dissolved radionuclides and could significantly impact dose predictions. The strength of 
fracture-matrix interaction due to matrix diffusion and adsorption depends on matrix diffusion 
coefficient, matrix adsorption coefficient, fracture spacing, and fracture aperture. In TSPA-LA 
calculations, those parameters will be sampled based on uncertainty distributions, and the impact 
MDL-NBS-HS-000020 REV 00 January 2004 105 
Normalized Cumulative Breakthrough 
U0065 
1.E+05 1.E+04 1.E+03 1.E+02 1.E+01 
Time (year) 
Pu239 If243 Ic243 Am243 Tc99 Sr90 I129 Cs137 
Th229 U233 Np237 If241 Ic241 Am241 Pa231 U235 
Pu238 If242 Ic242 Pu242 U232 Th232 U236 If240 
Ra226 Th230 U234 U238 
Output-DTN: LA0311BR831371.003 U0065 Particle Tracking Model and Abstraction of Transport Processes 
on system performance of these uncertainties will be quantified. Another important factor that 
controls the transport process is infiltration rate. The impact of climate changes on system 
performance will be investigated using different flow fields developed in BSC 2003 [163045] 
and DTN: LB0305TSPA18FF.001 [165625]. These flow fields have different amounts of 
fracture and matrix flow, and water table elevation changes will also be included (see Section 
6.4.9). Based on the results presented here, under the wetter climate conditions, radionuclide 
transport velocities will increase during the wetter climates due to increased infiltration and 
greater fracture flow. 
January 2004 106 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-25. Radionuclides Simulated in Base Case Run 
Decay 
Species Half-Life (days) Ingrowth Species_Name 
1 2.09E+06 Simple decay C14 
2 8.4E+08 Simple decay Cs135 
3 1.10E+04 Simple decay Cs137 
4 5.73E+09 Simple decay I129 
5 1.05E+04 Simple decay Sr90 
6 7.78E+07 Simple decay Tc99 
7 2.69E+06 10 Am243 
8 2.69E+06 11 Ic243 
9 2.69E+06 12 If243 
10 8.80E+06 13 Pu239 
11 8.80E+06 13 1c239 
12 8.80E+06 13 if239 
13 2.57E+11 14 U235 
14 1.20E+07 Simple decay Pa231 
15 1.58E+05 18 Am241 
16 1.58E+05 18 ic241 
17 1.58E+05 18 if241 
18 7.82E+08 19 Np237 
19 5.81E+07 20 U233 
20 2.7E+06 Simple decay Th229 
21 2.40E+06 24 Pu240 
22 2.40E+06 24 ic240 
23 2.40E+06 24 if240 
24 8.55E+09 25 U236 
25 5.11E+12 Simple decay Th232 
26 2.55E+04 Simple decay U232 
27 1.37E+08 33 Pu242 
28 1.37E+08 33 ic242 
29 1.37E+08 33 if242 
30 3.20E+04 34 Pu238 
31 3.20E+04 34 ic238 
32 3.20E+04 34 if238 
33 1.63E+12 34 U238 
34 8.99E+07 35 U234 
35 2.75E+07 36 Th230 
36 5.84E+05 Simple decay Ra226 
Source: BSC (2002 [160059]) 
NOTE: Half-life data are from Table 6-23. The 3rd column shows the species index 
the radionuclide decays into. Species with a name starting as icxxx 
represents irreversible colloids traveling retarded. Species with a name 
starting as ifxxx represents irreversible colloids traveling unretarded. 
January 2004 107 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
6.7 EVALUATION OF ALTERNATIVE MODELS AND MODEL UNCERTAINTY 
Geological, hydrological, and geochemical data have been used to support parameters, used in 
conceptual models, process-level models, and alternative conceptual models, considered in the 
abstraction of radionuclide transport in the UZ. These traceable, well-documented data have 
been used to support the technical bases for FEPs that have been included in the abstraction of 
radionuclide transport in the UZ (Table 6-1). As discussed in the Radionuclide Transport Process 
Model (BSC 2003 [163228]) on which this abstraction model is based, analysis demonstrates 
that the associated burden in implementing complex alternative conceptual or processes models 
is not commensurate to the benefit in reducing uncertainty in model predictions. Therefore a 
conservative model approach has been used to address conceptual model or processes 
uncertainty (Table 6-26). The selected conceptual model of radionuclide transport in the UZ is 
conservative, and supported by available data and current scientific understanding. 
BSC (2003 [163228]) discusses alternative conceptual radionuclide transport models involving: 
a) Different representations of the matrix-fracture system - multiple interactive continua, 
(MINC) versus dual-permeability (dual-k) systems. 
b) Different conceptual methods of describing the transport problem (Particle tracking 
versus conventional representation in control-volume finite element codes). 
In the MINC method, the steep gradients at the matrix fracture surface are resolved by including 
additional grids in the matrix in an appropriate number of nested shells. This is based on the 
concept that rapid changes at the fracturematrix interface will propagate rapidly through the 
fracture system, while invading the tight matrix comparatively slowly (steep gradient to the 
inside of matrix block). The MINC behavior results in later breakthrough times (as the enhanced 
fracture/matrix interaction allows for increased diffusion), longer contact times, and more 
effective sorption (in sorbing media/solute systems). In BSC (2003 [163228]), the MINC model 
response (using both T2R3D V1.4 (LBNL 1999 [146654]) and TOUGH2 V1.11 MEOS9nTV1.0 
(LBNL 1999 [113943]) codes) was compared to UZ transport models employing a particletracking
based numerical method (DCPT V2.0; LBNL 2003 [154342]). The results of those 
simulations are presented in the Validation section of the present Model Report (Figure 7-7). The 
result with the MINC grid conforms to expectations, resulting in later breakthrough times, when 
matrix diffusion is significant. However, despite its conceptual appeal, the application of the 
MINC concept to the 3-D UZ site-scale model would incur a large computational burden because 
it necessitates replacement of the single matrix block in the current dual permeability system 
with several MINC sub-domains. The validation conducted in Section 7 shows that the FEHM 
particle-tracking code replicates behavior similar to that of the MINC model when transfer 
functions developed using a Discrete Fracture Model (DFM) are used. By contrast, when 
transfer functions are developed with a dual-k formulation, behavior similar to that of the dual-k 
process model are obtained. Therefore, these alternate conceptual models can both be examined 
at the total-system level using the UZ transport abstraction model. 
Table 6-26 gives a summary of alternative conceptual models and processes, and the 
recommended disposition for the TSPA transport abstraction. 
January 2004 108 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-26. Summary of Alternative Conceptual Model Processes and their Dispositions for TSPA 
Alternative Conceptual 
Model 
MINC model of UZ matrix, 
alternative to single matrix 
dual permeability model 
Finite difference numerical 
models EOS9nT, T2R3D, 
and DCPT particle tracking, 
alternative to FEHM particle (T2R3D) or multiple 
tracking Radionuclides 
(EOS9nT). 
Lateral flow diversion in UZ 
above repository, 
alternative to no PTn lateral 
diversion model flow fields 
No Radionuclide release 
into faults, alternative to 
radionuclide release into all 
repository level nodes 
including faults. 
Include drift shadow, a 
capillary diversion, 
alternative to no drift 
shadow effects 
Perched water permeability 
barrier zones below the 
repository, alternative to no 
perched water permeability 
barrier (continuous and 
well-connected fractures) 
MDL-NBS-HS-000020 REV 00 
Key Assumptions 
More accurately models 
concentration gradient 
at fracture-matrix 
interface, resulting in a 
more accurate model of 
matrix diffusion 
Provide a basis for 
modeling coupled flow 
and transport of single 
Lateral flow in the PTn 
will divert percolating 
water to the faults and 
reduce percolation flux 
at repository. 
High fault permeability No significant effects on 
leads to fast advective overall transport to water 
transport of radionuclide table even for Non-sorbing 
directly released into 
Faults to top of TSw 
and to water table. 
Capillary diversion even 
under ambient 
conditions may result in 
low fracture saturation 
below the drift (drift 
shadow) that may 
persist for years 
Perched water will delay Continuous well connected 
and dilute radionuclide 
concentration and 
reduce advective 
transport 
Summary of Subsystem 
Evaluation 
Results in later breakthrough 
times when matrix 
diffusion is significant for 
long lived radionuclides. 
MINC models not directly 
handled by particle tracking 
codes. 
Used primarily to provide 
validated models of UZ 
transport processes that 
form the basis for the 
abstraction models. These 
are calibrated against a 
variety of experimental and 
analytical models. 
Used in UZ flow model to 
provide evaluation of the 
impact of lateral flow on UZ 
flux. The steady state flow 
fields provide basis for 
transport simulations. 
tracers, except for Np and 
Pu (which already has a 
high t10). There is no effect 
on t50, because lateral 
diversion redirects advective 
flow to faults and other fast 
flow pathways 
Drift shadow may develop 
and remain only under low 
infiltration. Seepage through transport in the UZ 
fractures may be significant 
after climate change 
fractures are used to model 
transport processes using 
the particle tracking method. perched water is a 
The flow fields from the UZ conservative treatment. 
account for perched water 
effects. 
109 
U0065 
Recommend TSPA 
Evaluation 
MINC not directly used in 
TSPA because of large 
computation burden, but 
FEHM particle tracking 
transport abstraction model 
reproduces the results 
predicted by MINC and 
discrete fracture models. 
Large computational 
burden limits use for 
multiple realizations that 
can provide uncertainty 
estimates. FEHM particle 
tracking transport 
abstraction model can 
reproduce the results 
predicted by dual-k models 
by using transfer functions 
developed using a dual-k 
formulation. 
The base case flow fields 
used provide a basis. 
Lateral diversion is not 
significant at infiltrations > 
1mm/year and may be 
important only at lower 
bounds of infiltration ranges 
or in areas with low 
infiltration. 
Conservative estimate of 
transport times, but has 
substantial effect on 
radionuclide arrival at top of 
CHn (TSw39). TSPA 
models should consider no 
release into faults by 
limiting the nodes into 
which radionuclides are 
released. 
Ignoring drift shadow is a 
conservative assumption of 
Perched water may only be 
present in the northern part 
of the repository. Ignoring 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-26. Summary of Alternative Conceptual Model Processes and their Dispositions for TSPA 
(Continued) 
Key Assumptions 
Vaporization due to 
repository heat will 
maintain the drift dry for 
several hundreds to a 
few thousand years. 
THC and THM effects 
may alter flow and 
transport properties of 
UZ rocks 
Summary of Subsystem 
Evaluation 
TH, THC, and THM effects Ignoring TH, THC THM 
are insignificant after change effects is a conservative 
to Glacial climate, the period assumptions 
during which transport 
processes are dominant, 
following release of 
radionuclides by corrosion 
processes. 
6.8 DESCRIPTION OF BARRIER CAPABILITY 
The unsaturated zone units below the repository are barriers that delay and limit radionuclide 
movement to the water table due to a variety of natural processes influenced by local 
hydrological, the intrinsic characteristics of the rocks, and by the repository design. A full 
treatment of the barrier capability is presented in BSC (2003 [163228]); a condensed summary is 
given below. The major large-scale processes included in this TSPA abstraction model are: 
1. The limited and low rate of flow of water through the unsaturated zone, which limits 
the rate at which radionuclides can move by advection out of the repository: included 
through the use of UZ model flow and transport properties and steady state flow fields. 
2. Sorption, which chemically binds radionuclides to minerals in the rock matrix and on 
fracture walls: included by explicit modeling of sorption processes. (Section 6.5.4) 
3. Matrix diffusion, which physically traps and delays radionuclides within the rock 
matrix: included by explicit modeling of molecular and colloidal diffusion in the 
abstraction of transport. (Section 6.5.5) 
Other processes that operate at a more local scale also contribute to UZ ability to limit water 
movement and radionuclide transport. Examples include the diversion of flowing water around 
drift openings in the UZ by capillary suction and the dry-out of the region surrounding repository 
drifts by heat associated with emplacement waste. These processes are beyond the scope of this 
Model Report, which treats only Mountain-scale radionuclide transport. 
On the other hand, colloidal transport of radionuclides has the potential to offset the 
effectiveness of both sorption and matrix diffusion by providing a mechanism for transport of 
radionuclides that have very low solubility limits. Radionuclides can be transported as intrinsic 
(true) colloids (fine particles 1 to 10,000 nm) of elemental particles e.g., Plutonium. They can 
also be transported as pseudo colloids i.e., bound to naturally occurring fine particles. The size 
of the colloids determines their ability to be excluded or filtered by matrix pores, and transported 
by fracture advection and dispersion processes. The effect of colloidal transport is discussed in 
110 
Alternative Conceptual 
Model 
Include TH, THC, and THM 
effects on UZ on flow and 
transport 
Source: BSC 2003 [163045] 
(Section 6.5.1) 
MDL-NBS-HS-000020 REV 00 
Recommend TSPA 
Evaluation 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
BSC (2003 [163228]) and is accounted for in this TSPA abstraction of UZ transport (Sections 
6.5.9 to 6.5.13). 
6.8.1 Analyses of Barrier Capability 
99 
The breakthrough times provide a quantitative assessment of the ability of the UZ to delay 
(retard) the transport of radionuclides to the accessible environment. An example set of 
calculations from the UZ Transport Process Model (BSC 2003 [163228]) is reproduced in Tables 
6-27, 6-28, and 6-29, for aqueous and colloidal radionuclide species. The sorption and diffusion 
parameters used in these simulations are given in Tables 6.5-1 and 6.6-1 of BSC 2003 [163228]. 
The t10 (time for 10% arrival) and t50 (time for 50% arrival) values for solute and colloidal 
transport, are presented for representative radionuclides, and combinations of three climate 
states, three infiltration cases, and the two release scenarios (instantaneous and continuous). At 
repository closure, short lived radionuclides such as strontium-90 and cesium-137 will be 
reduced to a small fraction of their initial inventory long before they could be transported 
through the UZ. For long lived radionuclides, models provide a means for assessing the 
effectiveness of the UZ to delay and retard (by slow advection, sorption and diffusion) their 
transport through the UZ. For strongly sorbing radionuclides like plutonium-239, the rate of 
movement is retarded so much that there is virtually no breakthrough before 10,000 years for the 
mean infiltration case. For weakly sorbing radionuclides such as neptunium-237, radionuclide 
transport is retarded for at least 1,000 years. For the long-lived non-sorbing radionuclides like 
Tc, the rate of transport is dictated by matrix diffusion and advective transport. However, even 
these require 3,000 to 4,000 years to move through the unsaturated zone (BSC 2003 [163228]). 
January 2004 111 MDL-NBS-HS-000020 REV 00 U0065 
T50 (Years) T10 (Years) T50 (Years) 
Particle Tracking Model and Abstraction of Transport Processes 
Table 6-27. Radionuclide Travel Times in Years to the Water Table for Instantaneous Release 
Climate/ Present-Day Monsoon Glacial 
Infiltration 
T50 (Years) Radionuclide Case T10 (Years) T10 (Years) 
241Am Lower - - - - - - 
Mean - - - - - - 
Upper 12 - 3 - 1 - 
237Np Lower 33,800 >1,000,000 15 6,160 185 34,400 
Mean 410 25,400 8 2,120 4 1,070 
Upper 4 1,600 2 714 1 336 
231Pa Lower - - - - - - 
Mean - - - - - - 
Upper 13 - 4 - 2 - 
239Pu Lower - - 86,000 - - - 
Mean - - 10,400 - 3,710 - 
Upper 1,530 - 4 - 2 - 
226Ra Lower - - - - - - 
Mean - - - - - - 
Upper - - - - 3 - 
90Sr Lower - - - - - - 
Mean - - - - - - 
Upper - - - - 3 - 
99 
229
Tc Lower 13,900 >1,000,000 22 1,310 102 8,140 
Mean 83 6,640 9 417 6 164 
Upper 6 230 2 92 1 42 
Th Lower - - - - - - 
Mean - - - - - - 
Upper - - 4 - 2 - 
233U Lower 65,200 >1,000,000 103 6,730 549 36,900 
Mean 433 29,100 34 2,130 16 893 
Upper 12 1,120 3 458 2 208 
235U Lower 55,300 >1,000,000 101 6,480 540 32,600 
Mean 430 26,500 34 2,080 15 882 
Upper 12 1,100 3 450 2 206 
135Cs Lower >1,000,000 >1,000,000 22,400 >1,000,000 150,000 >1,000,000 
Mean 52,500 >1,000,000 4,690 309,000 2,460 120,000 
Upper 2,170 71,200 753 24,500 305 990 
DTN: LB0307MR0060R1.007 [164752] 
Source: BSC 2003 [163228] 
NOTE: Symbol - indicates breakthrough at this relative arrival (i.e. either 10% or 50%) was never achieved in 
simulations. 
January 2004 112 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
Table 6-28. Radionuclide Travel Times in Years to the Water Table for Continuous Release 
Case 
(Mean Infiltration/Present-Day 
Climate) 
Three-Parents 
239Pu-Chain 
241Am-Chain 
DTN: LB0307MR0060R1.007 [164752] 
Source: BSC 2003 [163228] 
NOTES: (a) Corresponds to the sum of the chain members. Symbol - indicates breakthrough at this relative 
arrival (i.e. either 10% or 50%) was never achieved in simulations. 
Table 6-29. Colloid Travel Times in Years to the Water Table for Continuous Release 
Case 
(Mean Infiltration/Present- 
Day Climate) 
1 
(no declogging, in which 
colloids, once filtered, do 
not detach from the 
pore/fracture walls) 
2 
(strong kinetic declogging, 
providing an estimate of 
maximum colloidal transport) 
3 
(weak kinetic declogging, 
approaching equilibrium 
filtration behavior) 
4 
(same as Case 2, but the 
fractures have the same 
colloidal transport properties 
as the corresponding matrix; 
provides an estimate of the 
importance of fractures in the 
transport of colloids) 
DTN: LB0307MR0060R1.007 [164752] 
Source: BSC 2003 [163228] 
NOTES: (a) Corresponds to the sum of the chain members. Symbol - indicates breakthrough at this relative 
arrival (i.e. either 10% or 50%) was never achieved in simulations. 
Species 
99Tc 74 3,901 
237Np 781 22,940 
235Pu - - 
239Pu+235U+231Pa 
241Am+237Np+233U+229Th 1,027(a) 23,450(a) 
Colloid Size 
(nm) 
450 4.35 - 
200 4.39 - 
100 4.53 - 
6 - - 
450 4.35 - 
200 4.39 - 
100 4.53 - 
6 - - 
450 4.35 - 
200 4.39 - 
100 4.52 - 
6 - - 
450 32.4 243 
200 27.8 251 
100 27.6 - 
6 - - 
MDL-NBS-HS-000020 REV 00 
U0065 
t10 (years) t50 (years) 
(a)6,419 (a)33,660 
t50 (years) t10 (years) 
January 2004 113 U0065 Particle Tracking Model and Abstraction of Transport Processes 
6.8.2 Summary of Barrier Capability 
The radionuclide transport processes model (BSC 2003 [163228]) demonstrates that even under 
the conservative approach in the 3-D site-scale models, the UZ of Yucca Mountain is an 
effective barrier to the transport of the strongly sorbing radionuclides (90Sr, 226Ra, 229Th, 241Am, 
221Pa and 239Pu). The variably sorbing 135Cs (strongly on zeolites, much less on other rocks), the 
mildly sorbing 233U, 235U, 237Np, and the nonsorbing 99Tc arrive at the water table at times that 
are fractions of their respective half-lives. However, this is not necessarily an indication of a 
breached or ineffective UZ barrier, but can be a direct consequence of the conceptual model of 
UZ flow and of the conservative approach taken to model transport. Eliminating potential 
sources from the vicinity of the fault fractures appears to have a small effect on transport and 
arrivals at the water table. For instantaneous release, the breakthrough curves show a small 
increase in t10, but t50 is practically unchanged. 
Figures 6-20 and 6-21 are plots of normalized cumulative breakthrough curves for the same 11 
species listed in Table 6-27, which were simulated using the base-case abstraction model in this 
Model Report. A comparison between the base-case results of this Model Report (Figures 6-20 
and 6-21) and results from the process model (Table 6-27) reveals similar behavior for 
radionuclide transport through the UZ. The abstraction model shows that for the base-case 
model it takes the colloids far less time to travel through the UZ than the corresponding 
dissolved species. Due to matrix diffusion, the transport process for even non-sorbing species, 
like Tc-99, are retarded. Under the present day mean infiltration condition, only about 10 
percent of the total mass travels through the UZ within the first 40 years. By 6000 years, about 
50 percent of the Tc-99 arrives at the water table. Under the high-glacial infiltration scenario, 
where the matrix diffusion effect is reduced by the fast flow in the fractures, ten percent of the 
Tc-99 travels through the UZ in the first 5 years, and 50 percent arrives at the water table within 
slightly greater than 100 years. These travel times are qualitatively similar to those for the 
process model presented in Table 6-27. The weakly adsorbed Np-237 had a relatively higher 
breakthrough value than Tc-99 due to the decay of Am-241 traveling in the form of dissolved 
species (Am-241), colloids with irreversible sorption but retardation (Ic241), and colloids 
traveling unretarded (If241). Species with short half-life (Sr-90 and Am-241) did not appear 
within the 10,000 year period. Clearly, these results are similar to the conclusions reached in 
BSC (2003 [163228]), providing further confirmation that the abstraction model is in substantial 
agreement with the process model. 
The abstraction model results indicate that the UZ can act as an effective barrier to transport of 
the dissolved radionuclide species because of matrix diffusion and adsorption. Fast fracture flow 
in the UZ can weaken the UZ barriers capability by reducing the effectiveness of matrix 
diffusion. Given the current model assumptions, the UZ system is a weak barrier for the fraction 
of the radionuclide inventory that travels via colloid facilitated radionuclide transport, especially 
under the high-infiltration scenarios. Ultimately, the quality of the barrier with respect to 
colloids will depend on the quantity of colloids in groundwater, the adsorption coefficient, 
matrix diffusion coefficient, and geological properties of rock layers. Monte Carlo simulations 
to address the uncertainty of transport process on system performance are intended to be 
implemented in the TSPA model. 
January 2004 114 MDL-NBS-HS-000020 REV 00 1.4 
Particle Tracking Model and Abstraction of Transport Processes 
1.3 
1.2 
1.1 
1.0 
0.9 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
0.1 
0.0
1.E-01 
NOTE: Ic239 and If239 are colloid species of Pu-239, and Ic241 and If241 are colloid species of Am-241. 
Figure 6-20. Normalized Cumulative Breakthrough Curves of the 11 Radionuclides Under Present Day 
Mean Infiltration Condition. Also shown are four breakthrough curves of colloidal forms of 
Time (year) 
Ic239 
Ra226 
Normalized Cumulative Breakthrough 
1.E+00 
Tc99 Sr90 Cs135 
U233 Np237 If241 
Pu-239 and Am-241. 
If241 
Ic239 
Tc99 
1.E+02 1.E+01 
Pu239 
Th229 
MDL-NBS-HS-000020 REV 00 115 
If239 
1.E+03 
U235 If239 
Np237 
U235 
U233 
Ic241 
Cs135 
Pu239 
1.E+04 
Am241 Pa231 
U0065 
1.E+05 
Ic241 
Output DTN: LA0311BR831371.003 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
NOTE: Ic239 and If239 are colloid species of Pu-239, and Ic241 and If241 are colloid species of Am-241. 
Figure 6-21. Normalized Cumulative Breakthrough Curves of the 11 Species Radionuclides Under Glacial 
Mean Infiltration Condition. Also shown are four breakthrough curves of colloidal forms of 
Time (year) 
Ic239 
Ra226 
Normalized Cumulative Breakthrough 
If241 
1.E+00 
1.9 
1.8 
1.7 
1.6 
1.5 
1.4 
1.3 
1.2 
1.1 
1.0 
0.9 
0.8 
0.7 
0.6 
0.5 
0.4 
0.3 
0.2 
0.1 
0.0
1.E-01 
Tc99 Sr90 Cs135 
U233 Np237 If241 
Pu-239 and Am-241. 
Ic23 
Tc99 
U233 
1.E+02 1.E+01 
Pu239 
Th229 
MDL-NBS-HS-000020 REV 00 116 
If239 
Ic241
Cs135 
1.E+03 
U235 If239 
Np237 
U235 
Pu239 
1.E+04 
Am241 Pa231 
U0065 
1.E+05 
Ic241 
Output DTN: LA0311BR831371.003 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
7. VALIDATION 
Criteria for validation of this abstraction model have been developed in Technical Work Plan 
(TWP) for: Performance Assessment Unsaturated Zone (BSC 2002 [160819], Section I-2, Work 
Package [WP] AUZM07) and discussed in general terms in Section 4.2, Acceptance Criterion 5. 
In essence, validation of this abstraction model consists of a series of visual comparisons of 
model results with both simple models and a full process model of the UZ. The specific 
comparisons mentioned in the TWP (BSC 2002 [160819], Section I-2-2-1) are in effect satisfied 
in this Validation by performing comparisons equivalent to the ones cited in the TWP. For 
example, the requirement of a comparison to the solution of Sudicky and Frind (1982 [105043]) 
is satisfied by the comparison to the Discrete Fracture Model (DFM) in Section 7.1.1 below, and 
the requirement to compare to DCPT V2.0 (LBNL 2002 [154342]) is satisfied in the 
comparisons to the process model in Sections 7.2 and 7.3. These simulations are designed to 
summarize and augment the code verification checks that have been performed and documented 
in the qualification of FEHM V2.21 (see V&V documentation of this code: LANL 2003 
[166306]), as well as the individual tests reported in other sections of this Model Report (for 
example, the decay-chain example of Section 6.4.4). Tests in the V&V documentation but not 
reproduced here include additional tests for dispersion and matrix diffusion. Validation runs 
under the more complex situations of interest to TSPA, namely 2-D and 3-D model domains for 
which process model simulations are available, are also carried out in this report. 
Three classes of comparisons are made in this Validation section. The first, presented in 
Section 7.1, is a series of comparisons of the particle tracking model and a DFM. This 
comparison focuses on the ability of the model to adequately capture transport in a dualpermeability 
system under a variety of parameterizations. The series of tests is designed to 
demonstrate the validity of the underlying particle tracking method on a simple system. 
Simulations for this suite of runs can be thought of as representing the behavior of transport 
through an individual layer containing a small number of cells with uniform transport properties. 
Second, complexity is increased by comparing the particle tracking model with simulations in a 
2-D cross sectional model. For comparison purposes, results are available on this cross section 
from Model Report BSC 2003 [163228] (DTN: LB03093RADTRNS.002 [166071]) assuming 
both a dual-k and a MINC formulation to capture fracture-matrix interactions. We show that the 
conceptual model for the fracture/matrix (f/m) interactions has an impact on the predicted 
behavior, especially for the fastest traveling portion of the solute. By using different transfer 
function representations (the dual-k and discrete fracture conceptual models) we test the ability 
of the model to replicate the behavior of the process models employing similar 
conceptualizations (dual-k and MINC, respectively). Finally, the third class of comparisons uses 
the full 3-D transport model being used in TSPA-LA, thereby representing the full complexity of 
the UZ in terms of heterogeneities in fluid flow conditions and properties. The radionuclide 
Tc-99 is released at the repository horizon, and the breakthrough at the water table is recorded 
and compared to results from T2R3D, documented in BSC 2003 [163228] (DTN: 
LB0307MR0060R1.007 [164752]). Results are available at the process model level only for the 
dual-k f/m interaction conceptualization, so direct comparisons to the particle tracking model are 
made for the dual-k transfer functions. We then perform a sensitivity analysis to show the effect 
of employing the DFM conceptualization in the particle tracking model, as well as some 
January 2004 117 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
qualitative tests of the implementation of the Active Fracture Model (AFM) in this abstraction 
model. 
7.1 COMPARISONS WITH DISCRETE FRACTURE MODEL 
A DFM, in which transport in a dual-permeability medium is simulated directly, is an excellent 
test case of the computationally simpler transport model employed in the UZ abstraction model. 
In the most general case, water moves in both media, as well as between the media, and solute 
communicates between the media as it moves through the system via molecular diffusion and 
advection. First, a test case for the advective movement between the fracture and matrix in such 
a system is presented. Then, we focus attention on parallel flow and transport in the two media, 
with solute introduced into either the fracture or the matrix. To investigate the ability of the 
model to span a range of hydrologic conditions, a fracture-dominated flow situation (essentially 
100% fracture flow) and a case with a 60/40 f/m flow split are used for testing. Figure 6-5 
represents the model system simulated with a DFM. Transport between the media occurs via 
molecular diffusion, so that the breakthrough curve at the outlet of such a model is a function of 
the relative and absolute velocities, and the degree of diffusive communication of solute between 
the media. Geometric, flow, and transport parameters, listed in Table 7-1 for this suite of tests, 
are selected to be representative of transport conditions in the UZ at Yucca Mountain, but do not 
constitute an actual model of the system, merely a testing setup to enable comparisons to be 
made. Therefore, data sources for these values are not required. 
For this entire set of simulations, a 2-D DFM with these parameters was simulated using FEHM 
V2.21 (LANL 2003 [165741]) in a manner similar to that used to generate the transfer functions 
(see Attachment III), and the resulting breakthrough curves at the outlet were processed using the 
software routine discrete_tf V1.1 (LANL 2003 [165742]). For the simulations using the particle 
tracking model, a simple one-dimensional pathway is constructed consisting of ten 
dual-permeability cells (twenty total). The flow conditions (water contents, volumes, flow rates, 
m  
f f 
m f 
D m
d K 
Table 7-1. Parameter Values for Discrete Fracture Model Test Suite 
Parameter Symbol Case 2 (Sect. 7.1.2) 
118 MDL-NBS-HS-000020 REV 00 
300 Flow Path length (m) 
0.5 Fracture Half-Spacing (m) 
0.5e-3 Fracture Half-Aperture (m) 
Fracture Saturation (unitless) 
Matrix Water Content (unitless) 
Fracture water flux (kg/s) 1.583e-5 (99% of total) 
1.583e-7 (1% of total) Matrix water flux (kg/s) 
Diffusion Coefficient (m2/s) 1.e-30, 1.e-12, 1.e-11, 
1.e-10, 1.e-9 
0 Matrix sorption coefficient (mL/g) 
Value 
L 
CASE 3 (Sect. 7.1.3) 
300 
0.5 
0.5e-3 
0.2 0.2 
0.4 0.4 
9.49e-6 (60% of total) 
6.336e-6 (40% of total) 
1.e-30, 1.e-12, 1.e-11, 
1.e-10, 1.e-9 
0 or 5 
January 2004 
U0065 
B 
b 
f  U0065 Particle Tracking Model and Abstraction of Transport Processes 
etc.) were built into an FEHM restart flow field file by hand. These conditions, along with the 
grid files and the main FEHM input file, are read directly into the code and the transport particle 
tracking solution is obtained for the input flow field. This process was chosen to make this test 
as similar as possible to the way the code is to be used in TSPA calculations, in which flow fields 
are read in directly and transport is computed. Results are then post-processed using software 
routine ppptrk V1.0 (LANL 2003 [165753]). 
7.1.1 Test of Advective Transport Between Continua 
In this initial test case (CASE 1), we examine a situation with parallel flow in the two media, but 
with 90% fracture flux, 10% matrix flux for the first half of the flow path, transitioning abruptly 
to 60% fracture flux, 40% matrix flux for the second half of the path. Other geometric and 
storage parameters are the same as those listed in Table 7-1. Solute mass is input into the 
fracture. By turning off diffusion (which is tested separately in runs discussed later), it is trivial 
to determine the arrival times that the particle tracking code should produce. The early arrival 
represents mass that stays in the fracture, and later arrival represents the fracture transport for 
half of the path, and matrix transport for the remainder. In the results plotted in Figure 7-1, the 
vertical lines are the theoretical arrival times that the code should reproduce, and the horizontal 
line (at 2/3, or 0.67) is the theoretically determined proportion of mass that should take the 
fracture pathways all the way through the model. The particle tracking code reproduces the 
theoretical behavior for advective movement between the media, thereby confirming that the 
code correctly routes particles on the basis of advective flow between the fracture and matrix 
continua. The two simulation curves in the figure are: a simulation with the diffusion model 
turned off completely, and a simulation with the diffusion model invoked, but the diffusion 
coefficient set to a low value. Despite the fact that both means for performing the simulation 
yield acceptable results, it is advisable to completely turn off the diffusion model if the intention 
is to model a solute with no diffusion. Nevertheless, this result indicates that if diffusion 
coefficient is set low, the model yields the correct behavior. 
January 2004 119 MDL-NBS-HS-000020 REV 00 Diffusion model 
Advection only 
Normalized breakthrough 
U0065 Particle Tracking Model and Abstraction of Transport Processes 
1.0 
t=0.042 yr 
0.8 
plateau=0.667 
0.6 
0.4 
0.2 
t=74.96 yr 
0.0 
1e-02 1e-01 1e+00 1e+01 1e+02 1e+03 
Time, years 
Output DTN: LA0311BR831371.001 
Figure 7-1. Particle Tracking Abstraction Model Behavior for Advective Transport Between the Fracture 
and Matrix Continua: No Diffusion or Sorption, Solute Injected into the Fracture, Compared 
January 2004 120 
to Theoretical Results 
7.1.2 Comparisons with Diffusion for Fracture-Dominated Flow 
Figure 7-2 (Case 2) shows the results of simulations representative of fracture-dominated flow, 
with 99% of the flow occurring in the fracture. Solute is introduced into the fracture, and the 
breakthrough at the end of the model is simulated. The simulations show that over the range 
from fracture-dominated transport (D=1.e-30 m2/s) to conditions corresponding to complete 
diffusive interchange between the two media (D=1.e-9 m2/s), the particle tracking model 
provides very close agreement with the DFM of the same system. Although it is tempting to 
assume that the model is simply reproducing the same curve that was provided as input in the 
form of a transfer function, this is not the case. In the particle tracking model, the code executes 
a transfer function operation for each of the ten cells of the flow path. Each cell has a fracture 
travel time of one-tenth the total, meaning that the code correctly seeks the appropriate transfer 
function for that cell, and then predicts the overall breakthrough curve for a pathway consisting 
of multiple nodes. Deviations between the particle tracking model and the discrete fracture 
solution are due to the fact that the exact transfer functions for the test case are not available, and 
the model must find the curve with parameters closest to the desired values. This approach is 
therefore approximate, and relies on the code being supplied a family of transfer functions that 
covers the range of parameters encountered in a given simulation. Despite this limitation, this 
test demonstrates that the basic process for determining the travel times of individual particles 
MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
through a series of connected cells is properly implemented. It also demonstrates the ability of 
the model to simulate the behavior for an important end-member condition, that of fracturedominated 
flow. 
Nonsorbing, D = 1.e-9, 1.e-10, 1.e-11, 1.e-12, 1.e-30 m 
Solute Injection into Fracture 
1.0 
0.8 
0.6 
0.4 
Black - Particle Tracking; Red - Discrete Fracture Model 
D = 1.e-20
1.e-12 
1.e-11 
1.e-10 
1.e-9 
0.2 
0.1 1 
0.0
0.01 
Time, years 
Figure 7-2. Comparison of Discrete Fracture Model and Particle Tracking Abstraction Model: 
Non-Sorbing Solute Injected into the Fracture, for Different Values of Diffusion Coefficient, 
121 January 2004 
f f = 0.99 
7.1.3 Comparisons with Diffusion and Sorption for Intermediate Flow Case 
Figure 7-3 (Case 3) compares the DFM and the particle tracking model for the case of more 
evenly divided flow in the two media (60/40 f/m flow split). Different diffusion coefficients are 
used, spanning the range from fracture-dominated transport to a diffusive regime in which the 
system is essentially behaving as a single continuum. The particle tracking model replicates the 
behavior adequately over the entire range of parameters. At the lower diffusion coefficients (1.e- 
11 and 1.e-12 m2/s), there is a slight distortion in the breakthrough curve of the particle tracking 
model at later times caused by the process by which particles are probabilistically shifted from 
one medium to the other due to the diffusive process. This is explained as follows. Consider the 
case in which a particle that enters a cell via the fracture is instructed by the algorithm to leave 
that cell via the matrix. This can occur in a low-diffusion regime for some of the solute mass. 
When the particle is placed in the matrix in the next cell, it is implicitly assumed to be randomly 
placed along the width of the matrix. In reality, for low diffusion, solute mass will reside 
preferentially near the fracture, so that the assumption of it being randomly placed along the 
MDL-NBS-HS-000020 REV 00 
Normalized Concentration 
U0065 
10 
100 
Output DTN: LA0311BR831371.001 Particle Tracking Model and Abstraction of Transport Processes 
matrix width is somewhat in error. This results in somewhat longer travel times for mass that 
shifts from fracture to matrix. The result is a tendency to predict longer travel times than is 
expected from a DFM. Despite this error, the initial breakthrough is captured very well, and the 
overall trends of the DFM are reproduced. At higher diffusion coefficients, this problem does not 
occur because the assumption of randomly distributed solute mass along the matrix width is a 
good one. Therefore, the important end-member of single-continuum behavior, with 
breakthrough times controlled by the matrix storage volume, is reproduced as well. Finally, this 
phenomenon is less pronounced for the fracture-dominated flow case of the previous section 
because fewer particles leave via the matrix for the case of low matrix flow. Although this error 
is reasonably small compared to the robust fashion in which the model captures the transport 
behavior over orders of magnitude ranges in diffusion coefficient, and the error is fairly small for 
either fracture-dominated flow or highly diffusive transport, we perform additional tests at the 
end of this section to investigate the nature of this error and document its magnitude. 
Nonsorbing, D = 1.e-9, 1.e-10, 1.e-11, 1.e-12, 1.e-30 m 
Solute Injection into Fracture 
1.0 
0.8 
0.6 
0.4 
0.2 
Black - Particle Tracking; Red - Discrete Fracture Model 
D = 1.e-30 
1.e-12 
1.e-11 
1.e-10 
1.e-9 
0.1 10 1 
0.0
0.01 
Time, years 
Figure 7-3. Comparison of Discrete Fracture Model and Particle Tracking Abstraction Model: 
Non-Sorbing Solute Injected into the Fracture, for Different Values of Diffusion Coefficient, 
122 
5 = cc/g. d K
January 2004 
f f = 0.6 
Figure 7-4 shows a set of breakthrough curves for Case 2 with a sorbing solute of 
Similar behavior is observed, with longer travel times caused by sorption of the mass that 
diffuses into the matrix. Similar to the nonsorbing solute comparisons, these comparisons 
MDL-NBS-HS-000020 REV 00 
Normalized Concentration 
U0065 
100
Output DTN: LA0311BR831371.001 U0065 Particle Tracking Model and Abstraction of Transport Processes 
illustrate that the model adequately captures the impact of sorption on the matrix rock. 
Differences similar to those observed in the non-sorbing cases are present, but the particle 
tracking model replicates the fracture-matrix interactions in the dual permeability model over a 
broad range of diffusion coefficients with sorption included. Further verification of the correct 
implementation of the model for sorption is shown in Figures 7-5 and 7-6, which show the 
comparisons to the discrete fracture model for high values of d K . At a diffusion coefficient of 
d K in the model are 1.e-11 (Figure 7-5) or 1.e-10 (Figure 7-6), the application of high values of 
shown to reproduce the expected behavior for the discrete fracture model. 
Next, Figure 7-7 replicates the conditions of the nonsorbing simulations, except that the solute 
mass is introduced into the matrix. Very important features of the transport behavior predicted by 
the DFM are replicated quite closely in these runs. The generally longer travel times are due to 
the introduction of mass into the slower moving matrix flow. The nature of these results in terms 
of first arrivals and mean behavior can be understood as follows. When diffusion is finite but 
relatively low, the small portion of the solute introduced close to the fracture can diffuse into the 
fracture and travel rapidly to the outlet, yielding a leading edge of the breakthrough curve at 
short times. This important aspect of the behavior for releases into the matrix is reproduced very 
accurately by the particle tracking code, as evidenced by the comparison to the DFM. This 
leading edge is not present for higher diffusion coefficients because mass diffuses readily 
between the continua, making the probability of rapid transport along the entire length of the 
model negligibly small. However, the rise in the breakthrough curve representing the bulk of the 
mass arrival occurs earlier for the high-diffusion case. This can be understood by recognizing 
that when diffusion is large enough to allow migration of solute over distances comparable to B , 
the system becomes essentially a composite medium with an effective flow rate equal to the sum 
of the fracture and matrix fluxes. By contrast, at low diffusion coefficients, travel times through 
the matrix are governed by the matrix flux, which in this example is only 40% of the total. 
Hence, arrival times for the matrix release case and low diffusion is later than for the highdiffusion 
case. 
Of note in these comparisons is that the particle tracking model reproduces these features quite 
well, with the following caveats. At later arrival times, the particle tracking and discrete fracture 
models diverge somewhat, with particle tracking breakthroughs occurring somewhat earlier than 
the DFM breakthrough. The explanation described when explaining the differences for fracture 
releases applies in reverse for solute releases into the matrix. Nevertheless, the particle tracking 
simulations compare well overall with the DFM results, capturing the key features and the travel 
times for matrix releases. This comparison provides important assurance that the mass that enters 
the UZ transport model via EBS diffusive releases into the matrix will be properly simulated. 
January 2004 123 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
1.0 
0.8 
0.6 
0.4 
0.2 
0.0
0.1 
Figure 7-4. Comparison of Discrete Fracture Model and Particle Tracking Abstraction Model: Sorbing 
Solute Injected into the Fracture, for Different Values of Diffusion Coefficient 
U0065 
Output DTN: LA0311BR831371.001 
Normalized Concentration 
MDL-NBS-HS-000020 REV 00 
Sorbing, K = 5, D = 1.e-10, 1.e-11, 1.e-12 m d 
Solute Injection into Fracture 
Black - Particle Tracking; Red - Discrete Fracture Model 
Diffusion Coeff. 
1.e-10 
1.e-11 
1.e-12 
1000 10 100 1 
Time, years 
January 2004 124 Particle Tracking Model and Abstraction of Transport Processes 
Sorbing, K = 0 to 10000, D = 1.e-11 m d 
Solute Injection into Fracture 
Black - Particle Tracking; Red - Discrete Fracture Model 
1.0 
0.8 
0.6 
1000 
K =0 mL/g d 0.4 5 50 
10000 
0.2 
0.0
1e-01 1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 1e+07 
Time, years 
U0065 
Output DTN: LA0311BR831371.001 
Figure 7-5. Comparison of Discrete Fracture Model and Particle Tracking Abstraction Model: Solute 
Injected into the Fracture, for Different Values of Sorption Coefficient. D = 1.e-11. m 
Normalized Concentration 
January 2004 125 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
Sorbing, various K , D = 1.e-10 m d 
Solute Injection into Fracture 
Black - Particle Tracking; Red - Discrete Fracture Model 
1.0 
0.8 K = 5 cc/g d 
1000 
0.6 
0.4 
0.2 
0.0
1e-01 1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 1e+07 
Time, years 
U0065 
Output DTN: LA0311BR831371.001 
Figure 7-6. Comparison of Discrete Fracture Model and Particle Tracking Abstraction Model: Solute 
Injected into the Fracture, for Different Values of Sorption Coefficient. D = 1.e-10. m 
January 2004 126 MDL-NBS-HS-000020 REV 00 
Normalized Concentration
Particle Tracking Model and Abstraction of Transport Processes 
Figure 7-7. Comparison of Discrete Fracture Model and Particle Tracking Abstraction Model: 
Non-Sorbing Solute Injected into the Matrix, for Different Values of Diffusion Coefficient 
To further explore the discrepancies for cases with relatively even distribution of flow in the two 
media, we examine a series of tests in which the number of grid cells in the path are varied. 
These tests were performed for D=1.e-11 m2/s, no sorption, and solute introduced in the fracture. 
Figure 7-8 compares the breakthrough curves for different numbers of cells with the DFM 
results. In all cases the overall flow path characteristics are the same, but the discretization is 
varied. For one cell, the discrete fracture model is replicated virtually exactly, because in this 
case we truly are reproducing a DFM result that was used to generate the transfer function itself. 
This curve merely shows that for a single cell, the code finds the correct transfer function and the 
stochastic particle tracking method is implemented properly. As the number of cells in the path is 
increased to five or ten, the moderate error observed previously appears. An important point to 
consider in assessing this grid error is the fact that when flow transitions at interfaces of 
contrasting hydrologic properties, major transitions in particles from one medium to the other 
due to advection are likely to occur. Therefore, this type of test really replicates the behavior of 
the model within a single hydrogeologic unit. Since the number of grid cells within a unit tends 
to be rather small, the error within a unit is also likely to be small, perhaps of the magnitude 
shown in the five-cell curve. 
MDL-NBS-HS-000020 REV 00 January 2004 127 
Time, years 
Output DTN: LA0311BR831371.001 
Normalized Concentration 
U0065 
Nonsorbing, D = 1.e-10, 1.e-11, 1.e-12 m 
Solute Injection into Matrix 
Black - Particle Tracking; Red - Discrete Fracture Model 
1.0 
0.8 
Diffusion Coeff. 
1.e-10 
1.e-11 
1.e-12 
0.6 
0.4 
0.2 
1000 100 10 1 
0.0
0.1 
Particle Tracking Model and Abstraction of Transport Processes 
Nonsorbing, D = 1.e-11 
1.0 
0.8 
Solute Injection into Fracture 
0.6 
Grid Resolution Test of Particle Tracking Algorithm 
X 
X 
X 
X 
X 
X 
X 
0.4 
0.2 
Discrete fracture model 
1 cell 
2 cells 
X 5 cells 
10 cells 
0.1 
X 
X 
X 
XXXXXXXXXX 
X 0.0
0.01 
Figure 7-8. Comparison of Discrete Fracture Model and Particle Tracking Abstraction Model: Sorbing 
Solute Injected into the Fracture, for Different Numbers of Grid Cells in the Flow Path. 
7.1.4 Summary of Validation Tests for a Discrete Fracture Model 
To summarize the results of this first validation test suite, the behavior of the particle tracking 
model agrees well with a DFM over a very broad range of transport conditions. The deviations 
that have been observed between the two models are very unlikely to influence TSPA model 
predictions, and the cause of these differences is well-understood. Furthermore, fracture-matrix 
advective transport has been demonstrated to be properly implemented, and the case of releases 
into the matrix is also shown to be properly implemented. Therefore these comparisons 
constitute an adequate demonstration of the effectiveness of the particle tracking model for 
capturing the fracture-matrix interactions that the model is designed to simulate. 
7.2 COMPARISON WITH THE DUAL-K AND MINC MODEL FORMULATIONS ON 
A TWO-DIMENSIONAL CROSS SECTION MODEL 
Multi-dimensional benchmarking simulations of the UZ transport system is the next step in the 
validation of the abstraction model. Of course, the system is too complex to enable comparison 
to analytical solutions. In fact, selecting a code to benchmark against is also difficult because all 
available codes formulate the transport problem somewhat differently. BSC (2003 [163228]) 
showed that these formulations, which constitute alternate conceptual models for transport, can 
produce significantly different results. These differences must be understood to appreciate the 
MDL-NBS-HS-000020 REV 00 128 January 2004 
Time, years 
Output DTN: LA0311BR831371.001 
Normalized Concentration 
m 
100 10 1 
U0065
U0065 Particle Tracking Model and Abstraction of Transport Processes 
differences in the benchmarking results, especially for a complex, multi-dimensional model. In 
this section, we benchmark the particle tracking abstraction model developed here to simulations 
of the system performed using T2R3D, documented in BSC (2003 [163228]). Two ACMs have 
been developed on the 2-D cross section model using T2R3D. The simulations called dual-k 
use a finite-volume dual-permeability model formulation in which the fracture-matrix diffusion 
term is governed by a simple gradient calculated as the difference in concentration between the 
media divided by a characteristic distance, on the order of the flowing fracture spacing. In 
addition, in BSC 2003 [163228] the MINC conceptual model employs a series of grid blocks in 
the matrix. The UZ abstraction model implemented in FEHM is capable of simulating either 
situation. In the conceptualization we term the DFM f/m interaction model, sharp concentration 
gradients are captured through use of a transfer function obtained using a DFM with fine 
discretization in the matrix, analogous to a MINC formulation. These are the transfer functions 
used in the comparisons to the DFM in Section 7.1. By contrast, a dual-k model can be used to 
generate transfer functions, and those results might be expected to resemble those of T2R3D 
when an analogous dual-k formulation is used. These comparisons are performed in this section. 
A final point on these conceptual models is that in all abstraction model cases, the flow field on 
which the transport model is run is a dual-k flow field because the particle tracking abstraction 
model was formulated with the dual-k flow assumption. Therefore, the transport runs with the 
DFM formulation for the f/m interaction submodel employ a finely discretized matrix block for 
transport, but a single matrix block for the flow field. This approach should enable sharp 
gradients likely to be present for solute transport to be captured in the model. 
Figure 7-9 plots the comparison results of the particle tracking model and the two ACMs 
simulated with T2R3D. For the FEHM runs, the 2-D flow fields compatible with FEHM were 
obtained from the TDMS (DTN: LB0310T2FEHMFF.001 [166060]). In all cases, particles are 
released uniformly across all nodes designated as repository nodes in the model. First, we 
examine the case of no diffusion. This comparison is performed to benchmark the particle 
tracking code in a mode in which particles are routed through the model with dispersion. There is 
excellent agreement between the particle tracking model and the dual-k, no-diffusion model 
using T2R3D. Slight differences may be attributable to subtle differences in model formulation, 
numerical errors for one or the other model, or due to the fact that one of the eleven nodes 
designated as a repository node in the T2R3D runs was omitted from the particle tracking runs 
because it was found to be located in the PTn. Even with these possible sources for the 
difference, the agreement provides confidence that particle routing and transit times are properly 
implemented. We also note that colloidal species will be simulated with no diffusion, so these 
results provide confidence in the transport predictions for colloid-facilitated radionuclides. 
January 2004 129 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
1.0 
0.8 
0.6 
0.4 
0.2 
0.0
1e-01 1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 
Figure 7-9. Comparison of Particle Tracking Model with Process Models for a 2-D, Mountain-scale 
Model: With and Without Diffusion, for Dual-k and DFM Formulations for the f/m Interaction 
130 January 2004 
Time, years 
T2R3D Simulations DTN: LB030932RADTRNS.002 [166071] 
Output DTN: LA0311BR831371.002 
Model. 
Before proceeding to the results with diffusion, a discussion of the MINC simulation with no 
diffusion is in order. Since transport runs without diffusion depend only on advective processes, 
it is apparent that the mismatch between the MINC, no diffusion and the dual-k simulations (both 
T2R3D and particle tracking) indicates that there are differences in the flow regime for the 
MINC model. The reasons for this difference stem from the fact that the numerical discretization 
of this model is different than that of the dual-k model. We raise this issue not to imply that one 
model is correct and the other is not, but rather to point out that because of differences in the 
flow regimes of the MINC and dual-k flow models, we do not necessarily expect the particle 
tracking runs, which input the dual-k flow field rather than the MINC flow field, to match the 
MINC results precisely. Nevertheless, we would expect similar breakthrough curve features to be 
predicted by the particle tracking and MINC models, when the former are computed with the 
DFM conceptual model transfer function curves. By contrast, diffusion in the dual-k transport 
model is expected to predict much earlier breakthrough of a portion of the solute mass. 
The simulations with diffusion in Figure 7-9 confirm this result. In this figure, various FEHM 
particle tracking simulations are benchmarked against simulations using a dual-k or MINC 
MDL-NBS-HS-000020 REV 00 
Normalized Breakthrough 
Process Model 
Dual-k, no diffusion 
Dual-k, diffusion 
MINC, no diffusion 
MINC, diffusion 
No diffusion 
U0065 
FEHM Abstraction Model 
No diffusion 
Dual-k 
DFM 
High diffusion 
Diffusion 
U0065 Particle Tracking Model and Abstraction of Transport Processes 
formulation for the 2-D cross section. The difference in predicted behavior between the two 
conceptual models is reflected in the FEHM simulations in a manner similar to that of the 
process models. Comparing the MINC and FEHM DFM conceptual model, first arrivals in both 
cases occur much later in time than the dual-k models. For comparison, a high-diffusion case is 
also presented to illustrate the upper limit of breakthrough times for this flow field. Regarding 
the dual-k models, the characteristic feature of early arrival of a significant portion of the mass at 
times similar to that of pure fracture transport is produced in both the process and abstraction 
models. The fraction of the mass arriving early is somewhat lower in the FEHM model than in 
the T2R3D model, but qualitatively, the dual-k transfer function curves yield behavior quite 
similar to the process model result using T2R3D. Also, both the process model and abstraction 
model results converge at longer travel times, regardless of the formulation of the f/m interaction 
model or the value of diffusion coefficient used. Finally, the high-diffusion FEHM simulation is 
shown to bracket the behavior of the breakthrough curves in the figure, with results that are very 
close to that of the MINC model. 
All of these indicators show that the abstraction model compares adequately with the process 
models, and properly accounts for the role of conceptual model uncertainty in the f/m interaction 
model. The relatively minor differences of the models employing the dual-k f/m conceptual 
model are probably attributable to subtle differences in model formulation and mathematical 
techniques for solving the transport problem. 
7.3 COMPARISON WITH T2R3D PROCESS MODEL FOR THE THREE 
DIMENSIONAL SYSTEM 
Full simulation of the 3-D UZ transport system is the last step in the validation of the abstraction 
model. In Section 7.2 we demonstrated on a system for which the dual-k and MINC f/m 
interaction model results were available for comparison, the FEHM particle tracking results can 
provide qualitatively similar behavior for these ACMs simply by choosing transfer functions 
developed for a given conceptualization. In this section, we benchmark the particle tracking 
abstraction model developed here to simulations of the system performed using T2R3D, 
documented in BSC (2003 [163228]). The T2R3D simulations use a finite-volume dualpermeability 
model formulation in which the fracture-matrix diffusion term is governed by a 
simple gradient calculated as the difference in concentration between the media divided by a 
characteristic distance, on the order of the flowing fracture spacing. No results are available 
using a MINC or other formulation that captures sharp gradients into the matrix. Therefore, our 
principle benchmarking simulations for FEHM will be those using the dual-k transfer functions. 
However, we also demonstrate that the code can effectively explore uncertainty associated with 
this conceptual model. 
7.3.1 Comparisons of FEHM and T2R3D for the Dual-k Conceptual Model 
In these comparisons, we restrict attention to a non-sorbing radionuclide Tc-99, since simulations 
in Section 7.1 above showed that sorption is handled appropriately. For all model runs using 
either FEHM or T2R3D, breakthrough at the water table is simulated for a release function 
consisting of a pulse of radionuclide introduced uniformly across the entire repository. The 
comparisons between the models are for the cumulative, normalized arrival time distributions at 
the water table. Of course, these release functions are not realistic representations of how the 
January 2004 131 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
actual engineered system will behave. Such a release function yields the distribution of travel 
times for the UZ as a whole for releases across the repository, and as such is a useful point of 
reference for how the UZ behaves, as well as being an appropriate benchmark for comparing the 
models. Parameters in the abstraction model are uncertain. For this comparison, values 
documented in BSC 2003 [163228] are used to perform this comparison, and the present-day 
climate flow fields are used to make the comparison throughout the entire simulation period. 
This approach allows us to test the model over a significant range of infiltration scenarios, those 
spanning the uncertainty range for infiltration rate using the three present-day flow fields derived 
in BSC 2003 [163045]. 
Figure 7-10 shows the cumulative travel time distributions through the UZ for Tc-99 for the two 
models for the three flow fields (lower, mean, and upper) developed to capture uncertainty in the 
present-day infiltration rates. The agreement between FEHM using the dual-k transfer functions 
and T2R3D is excellent, considering the vast range of infiltration conditions covered in these 
comparisons. For the lower infiltration scenario, the early arrival of a small fraction of the 
released mass, and the steepening breakthrough curve after 10,000 years, are observed in both 
models. The plateau at values between 0.4 and 0.5 at long times is due to radioactive decay of 
Tc-99. For the mean infiltration flow field, the agreement of the process and abstraction models 
is also excellent at all travel times. For the upper infiltration scenario, FEHM predicts a 
somewhat earlier arrival for the fastest moving solute, indicating a difference in the way the two 
models handle diffusion in rapid fracture flow. Nevertheless, in benchmarking exercises of such 
a complex model, differences are the norm. In this case, we consider the benchmarking results to 
be very successful, in that all significant features of the UZ transport system are captured with 
the abstraction model. 
January 2004 132 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
Figure 7-10. Comparison of Breakthrough Curves for Tc-99 for T2R3D and the UZ Transport Abstraction 
Model: Simulations for Different Present-Day Infiltration Rate Scenarios (Lower, Mean, and 
January 2004 133 
Time, years 
T2R3D Simulations: DTN: LB0307MR0060R1.007 [164752] 
Output DTN: LA0311BR831371.002 
Upper) 
7.3.2 Influence of Diffusion Coefficient and F/M Interaction ACM 
To amplify on the simulations presented in the previous section, in Figure 7-11 we bracket the 
behavior of the particle tracking model as a function of diffusion. This figure shows the behavior 
of the FEHM model over the complete range of diffusion coefficients, from no diffusion to a 
case in which diffusion is set so high that it effectively yields a composite medium behavior 
(D=1.e-8 m2/s). The envelope of behavior as a function of diffusion is quite large, whereas the 
behavior of T2R3D is reproduced when the same parameters and conceptual model for f/m 
interactions is selected. This result illustrates that the abstraction model yields reasonable results 
over a wide range of diffusion coefficient, one of the key parameter uncertainties in the TSPA 
model. Also shown in Figure 7-11 is the predicted behavior using the DFM formulation for the 
f/m interaction model. No process model results are available for comparison due to the 
computational limitations of simulating the full 3-D model using a MINC formulation. These 
limitations are not an issue for the abstraction model, which simply uses a different set of 
transfer functions as input. The results are reasonable, given our understanding of these models 
and the comparisons presented in Section 7.2 for the smaller 2-D cross section model. The main 
differences for these ACMs are at the earliest arrival times, where the dual-k model predicts 
much faster arrivals at the water table. For later travel times, the two curves track each other 
closely, showing that the results are insensitive to the conceptual model. Finally, all 
breakthrough curves with diffusion, including the high-diffusion case, converge at large travel 
MDL-NBS-HS-000020 REV 00 
0.0 
1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 
Tc-99 Normalized Breakthrough at the Water Table 
U0065 
Comparison of FEHM Particle Tracking to T2R3D 
Dual-k formulation, Black: FEHM, Red: T2R3D 
1.0 
Lower 
Mean 
Upper 
0.5 
Particle Tracking Model and Abstraction of Transport Processes 
times. This result is also reasonable, providing additional evidence for the correct functioning of 
the f/m interaction model. 
1.0
Comparison of FEHM Particle Tracking to T2R3D 
Tc-99: Impact of diffusion on FEHM Results 
T2R3D dual-k 
FEHM no diffusion 
FEHM dual-k 
FEHM DFM 
FEHM high diffusion 
0.5 
0.0 
1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 
Figure 7-11. Comparison of Breakthrough Curves for Tc-99 for T2R3D and the UZ Transport Abstraction 
Model: Mean Infiltration Scenario, Diffusion in FEHM Ranging from No Diffusion to High 
January 2004 134 
Time, years 
T2R3D Simulations: DTN: LB0307MR0060R1.007 [164752] 
Output DTN: LA0311BR831371.002 
Values. 
The influence of f/m conceptual model is explored more fully in Figure 7-12, a comparison, 
using only the FEHM particle tracking model, of the dual-k and DFM Alternative Conceptual 
Models (ACMs) for all of the flow scenarios. The choice of ACM is particularly sensitive for the 
upper infiltration scenario, whereas differences become progressively more subtle for the mean 
and lower infiltration scenarios, respectively. As the fluid velocity is reduced, the characteristic 
diffusional distance into the matrix increases. For this situation, the dual-k model becomes more 
like the DFM in the sense that concentration gradients in the latter are not nearly as steep. With 
respect to the abstraction model, we conclude that these comparisons have reasonable qualitative 
explanations. This result illustrates that the abstraction model can propagate conceptual model 
uncertainties for f/m interactions through the TSPA model. 
MDL-NBS-HS-000020 REV 00 
Tc-99 Normalized Breakthrough at the Water Table 
U0065 
Particle Tracking Model and Abstraction of Transport Processes 
Figure 7-12. Breakthrough curves for Tc-99 using the UZ Transport Abstraction Model to Investigate the 
Role f/m Interaction Conceptual Model: Simulations for Different Present-day Infiltration 
January 2004 
Rate Scenarios (Lower, Mean, and Upper) 
7.3.3 Tests of the Active Fracture Model Implementation 
The AFM has been identified in BSC 2003 [163228] and BSC 2003 [163045] as a model whose 
parameters are quite uncertain, and potentially this uncertainty may significantly influence UZ 
performance predictions. Therefore, it is important to demonstrate that the sensitivity explored in 
the process model work can be represented in the abstraction model. In this section we examine 
the impact of the gamma parameter in the AFM on the results. This set of simulations is intended 
to confirm that the AFM formulation in FEHM yields results similar to that of the process model, 
and to extend those results by performing the same analysis for the DFM model for f/m 
interactions. To be completely rigorous, one would need to regenerate flow fields using the 
alternate AFM model parameters because the AFM influences both flow and transport processes. 
However, process flow model results (BSC 2003 [163045], Section 6.8.1) have demonstrated 
that the AFM parameters have very little influence on the relevant flow model parameters for 
transport, namely the fluid saturations and flow rates in the fracture and matrix continua. 
Therefore, it is an excellent approximation to simply apply AFM parameter changes to the 
transport model using flow model results obtained from the base case flow simulation. Figure 7- 
13 illustrates the impact of lowering the gamma parameter in the same fashion as was done in 
Section 6.8.2 of BSC 2003 [163045]. Note the close qualitative similarity of the simulation 
results with that of Figure 6.8-3 of that report. Lowering the gamma parameter in the TSw in the 
same manner as in BSC (2003 [163045]) yields a trend toward longer arrival times for the 
MDL-NBS-HS-000020 REV 00 135 
0.0 
1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 
Time, years 
Output DTN: LA0311BR831371.002 
Tc-99 Normalized Breakthrough at the Water Table 
U0065 
Comparison of Dual-k and DFM Models 
Curves with symbols denote DFM models 
1.0 
Lower 
Mean 
Upper 
0.5 
Particle Tracking Model and Abstraction of Transport Processes 
earliest arriving solute. The curves converge at longer travel times. The fact that the lowering of 
gamma in additional units below the repository has no further effect indicates that the principle 
sensitivity is for the AFM parameters in the TSw. For the purposes of the abstraction model 
validation, this qualitative comparison to the results of BSC (2003 [163045], Figure 6.8-3) 
provides strong evidence that the implementation in FEHM with respect to the AFM replicates 
the behavior of the process model. 
NOTE: The colors, line types, and legend descriptors are chosen to facilitate a direct visual comparison to the 
simulation results presented in BSC 2003 [163045], Figure 6.8-3. 
Figure 7-13. Breakthrough Curves for Conservative Solute Using the UZ Transport Abstraction Model to 
Investigate the Role of AFM Parameter Gamma: Dual-k ACM, Simulation for Different 
January 2004 
Values of Gamma in Rock Units Beneath the Repository. 
Finally, Figure 7-14 shows a similar investigation of the role of AFM model parameters for the 
DFM conceptualization. Note that in comparison to the dual-k DFM, gamma has smaller 
influence on the transport behavior. This result is a consequence of the way in which the two 
ACMs simulate the early-time behavior of the breakthrough curves. When a more refined grid is 
used to resolve gradients in the matrix, the role of flowing fracture spacing and interface area is 
less important than for the case in which a single matrix grid block is used to represent diffusion. 
The implication of this conclusion is that AFM model parameters will have a relatively smaller 
influence on predicted UZ behavior for the DFM conceptualization. By contrast, a somewhat 
larger sensitivity to AFM gamma parameter is predicted for the dual-k conceptual model. These 
differences must be recognized when interpreting sensitivity studies involving the AFM and the 
MDL-NBS-HS-000020 REV 00 136 
Time, years 
T2R3D Simulations: DTN: LB0307MR0060R1.007 [164752] 
Output DTN: LA0311BR831371.002 
0.0 
1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 
Tc-99 Normalized Breakthrough at the Water Table 
U0065 
Impact of AFM Gamma Parameter 
Dual-k ACM 
1.0 
Base case 
lower gamma TSw only 
lower gamma below repository 
0.5 
Particle Tracking Model and Abstraction of Transport Processes 
f/m interaction models. In general, the diffusion coefficient itself, rather than the AFM model 
parameters, is a much more sensitive parameter controlling the UZ performance. 
NOTE: The colors, line types, and legend descriptors are chosen to facilitate a direct visual comparison to the 
simulation results presented in BSC 2003 [163045], Figure 6.8-3. 
Figure 7-14. Breakthrough Curves for Conservative Solute Using the UZ Transport Abstraction Model to 
Investigate the Role of AFM Parameter Gamma: DFM ACM, Simulation for Different Values 
January 2004 
of Gamma in Rock Units Beneath the Repository 
7.4 DISCUSSION OF VALIDATION ACTIVITIES 
The series of simulations presented in this section, along with additional simulations performed 
to test the performance of the model in the FEHM V&V documentation, provide assurance that 
the UZ transport system is adequately captured in the abstraction model that is the subject of this 
Model Report. Direct numerical comparisons with quantitative criteria would be inappropriate 
for these comparisons because the modeling approach is designed to capture the essential 
features of the transport behavior over an extremely broad range of conditions (flow rates, 
transport parameters, relative flow rates in the two media, and the conceptual model for f/m 
interactions). Furthermore, analytical solutions do not exist to perform the comparisons made in 
this study, so the issue of whether the model is correct is not answerable by simply comparing 
to another code. Rather, the sort of benchmarking performed in this section is designed to build 
confidence in the adequacy of the abstraction model through a series of comparisons designed to 
probe the key features of the model that will be exercised during its use in TSPA simulations. 
MDL-NBS-HS-000020 REV 00 137 
Time, years 
0.0 
1e+00 1e+01 1e+02 1e+03 1e+04 1e+05 1e+06 
Output DTN: LA0311BR831371.002 
Tc-99 Normalized Breakthrough at the Water Table 
U0065 
Impact of AFM Gamma Parameter 
Discrete Fracture ACM 
1.0 
Base case 
lower gamma below repository 
0.5 
U0065 Particle Tracking Model and Abstraction of Transport Processes 
Adequate visual comparisons for benchmarking against the DFM simulations illustrate that the 
algorithms have been implemented to handle upscaling of dual permeability transport processes, 
for low or high diffusion, sorbing or nonsorbing solutes, and fracture or matrix releases. 
Discrepancies between the particle tracking and discrete fracture models, though relatively small, 
were noted and additional investigations were conducted to explain and assess the differences. In 
this way the robustness of the model was demonstrated, and we conclude that TSPA simulations 
using the UZ transport abstraction model will be able to propagate uncertainties in the form of 
parameter distributions through the UZ portion of the TSPA model. After testing the model in a 
simple particle tracking setup, the complexities of the system were studied in two and three 
dimensions through comparisons to the T2R3D based process model. These results are also 
adequate. Good agreement was observed at a variety of infiltration scenarios and diffusion 
models and parameters. In addition, the abstraction model is set up to enable alternate conceptual 
models for f/m interaction through the use of a different set of transfer function curves. Finally, 
the implementation of the AFM in the abstraction model was shown to reproduce the qualitative 
features of the breakthrough curves documented in the process model reports on which this 
abstraction is based. Thus, the abstraction model has been compared in the full complexity of the 
UZ model, and found to be able to represent the system robustly and efficiently for the entire 
range of parameters and conceptual models required. On this basis we conclude that the UZ 
transport abstraction model is suitable for use in TSPA analyses. 
January 2004 138 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
8. CONCLUSIONS 
8.1 SUMMARY OF MODELING ACTIVITY 
The principle output from this Model Report is an abstraction model for radionuclide transport in 
the UZ. It is intended for this model to be used directly in the TSPA system model developed 
using GoldSim V7.50.100 (BSC 2003 [161572]). The code used to implement the model is 
FEHM V2.21 (LANL 2003 [165741]), in the form of a dynamic link library (dll) callable from 
GoldSim. Testing of the operation of the dll in a GoldSim model environment has been 
developed and tested elsewhere (V&V documentation of FEHM V2.21; LANL 2003 [166306]) 
and is not repeated here, except to discuss the data structure of the interface between GoldSim 
and the FEHM dll. 
This Model Report pulls together information and data from a variety of sources, creating a 
simulation model capable of efficiently computing the transport of multiple radionuclides 
through the UZ. Data sources are listed in Section 4.1, assumptions are discussed in detail in 
Section 5, and the mathematical formulation and assessment of parameter ranges and 
distributions are treated in Section 6. The main activity documented in this Model Report is the 
synthesis of data and models into a simulation tool. The model to be used in TSPA simulations 
consists of a code (FEHM V2.21, PC dll) and input files to the code that must be present to run 
the model within GoldSim. Table 8-2 lists the computer files required to run the base-case 
model, and a brief description of the purpose of each file. Fixed parameters have been inserted 
into the appropriate FEHM files. Parameter distributions given in Section 6.5 should be used to 
generate a table of parameters in a text file, which is read using FEHMs capability of reading in 
parameters from a separate file and inserting those parameters into the simulation at runtime (see 
the User Documentation for FEHM V2.21 for details). Thus, this set of files provides the 
template for the TSPA modelers to set up the UZ abstraction model in a multiple-realization 
GoldSim system model. The table of uncertain parameters itself is not generated in this Model 
Report: this needs to be done by TSPA system modelers to facilitate parameter correlations and 
to enable the exploration of parameter sensitivities to be studied systematically at the system 
level. Table 8-1 lists the UZ transport parameters which should be pre-sampled and assembled 
into a table and for FEHM to read at run time, in TSPA. 
This report is intended to fulfill some of the abstraction model acceptance criteria, listed in the 
Yucca Mountain Review Plan (YMRP), Final Report (NRC 2003 [163274]). Further discussion 
with respect to the YMRP criteria, and the sections where they are addressed, is provided in 
Section 4.2. 
January 2004 139 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
List of Uncertain Parameters to be Sampled in TSPA-LA Runs Table 8-1. 
Description Uncertain 
Parameters 
matrix adsorption 
coefficient (mL/g) 
matrix diffusion 
coefficient (m2/sec) 
Matrix adsorption coefficient will be pre-sampled to based on given distributions 
for dissolved species in Section 6.5.4, Table 6-5. 
Matrix water content and effective permeability will first be sampled based on 
given distribution in Section 6.5.5, Table 6-6. Then, the sampled water content 
and effective permeability are used in Eq. 6.19 for estimating matrix diffusion 
coefficients. 
If desired, fracture porosity, fracture frequency, and fracture aperture can be 
sampled based on given distribution in Table 6-13 and Eq. 6-26. 
fracture porosity, 
fracture frequency, 
and fracture aperture 
(m) 
colloid Kc Colloid concentration and colloid Kd are sampled based given distribution in 
Tables 6-19 and 6-20. The sampled colloid concentration and Kd are then used in 
Section 6.5.12, Eq. 6-27 for calculating colloid Kc. 
colloid Rc Colloid R 
8.2 MODEL OUTPUTS 
c is sampled based on given distribution in Section 6.5.13, Table 6-22. 
140 January 2004 
8.2.1 Developed Output 
Many of the model outputs (FEHM input files to be used by TSPA system modelers) are derived 
from results of process models or other studies. For a discussion of the uncertainties of those 
parameters, the reader is referred to the references cited in Table 8-1. For those outputs in 
Table 8-2 listed as being developed in this Model Report, the development of the parameter 
values is discussed in this Model Report. The table shows 2 primary output DTNs. In addition 
to the files listed in the table, there may be auxiliary files that the TSPA modeling group must 
develop and document to complete the process of incorporating the UZ transport abstraction 
model into GoldSim V7.50.100 (BSC 2003 [161572]). These files, which are the responsibility 
of the TSPA modeling group to create, may include files such as batch files to copy files at 
runtime from one filename to another. They will implement features that are documented in 
FEHM V2.21, and are discussed in the User Manual for the code. They will contain no data, so 
are not required to be documented in this Model Report. 
MDL-NBS-HS-000020 REV 00 
U0065
Particle Tracking Model and Abstraction of Transport Processes 
Table 8-2. 
Computer Files 
comprising the UZ 
Transport Process 
Model 
Files Developed in other Studies That Feed this Abstraction Model. 
fehmn.grid 
fehmn.stor 
fehmn.zone 
fehmn.zone2 
preqla.ini 
preqma.ini 
prequa.ini 
glaqla.ini 
glaqma.ini 
glaqua.ini 
monla.ini 
monma.ini 
monua.ini 
glaqlA_wtrise.ini 
glaqmA_wtrise.ini 
glaquA_wtrise.ini 
monlA_wtrise.ini 
monmA_wtrise.ini 
monuA_wtrise.ini 
Files Developed in this Model Report 
fehm_amr_base.rock Rock properties for all zones 
defined in fehm.zone  bulk rock 
density, heat capacity (placeholder, 
not used in the model), and 
porosity. File is part of the UZ 
transport process model. 
fehm_amr_base.dpdp Dual permeability model parameters 
fehm_amr_base.mptr 
. 
repo.zon.xls 
wt.zone 
fehm_la.zone2 
Computer Files Comprising the UZ Transport Process Model 
Data Tracking Number used to 
Develop 
Qualitative Description and 
Intended Use 
LB0305TSPA18FF.001 [165625] Numerical model grid files required 
for UZ transport abstraction model. 
LB0305TSPA18FF.001 [165625] 
LB0305TSPA18FF.001 [165625] 
LB0312TSPA06FF.001 [166671] 
File that indexes each grid node 
number to a hydrologic zone. Input 
zone list file for UZ transport 
abstraction model. Fehmn.zone2 
also contains repository zones. 
Steady state flow fields used to set 
the fluid flow rates in the UZ 
transport abstraction model. 
LB0305TSPA18FF.001 [165625] 
LB0210THRMLPRP.001 [160799] 
LB0205REVUZPRP.001 [159525] 
LB0207REVUZPRP.001 [159526]  fracture volume fraction, 
characteristic distance into the 
matrix between fractures. File is 
part of the UZ transport process 
model. 
All solute transport parameters for 
the multiple radionuclide 
simulations. File is part of the UZ 
transport process model. 
LA0302AM831341.002 [162575] 
LB0302UZDSCPUI.002 [161787] 
LB0305TSPA18FF.001 [165625] 
LL000122051021.116 [142973] 
SN0306T0504103.005 [164132] 
SN0306T0504103.006 [164131] 
LA0303HV831352.002 [163558] 
LL030610323122.029 [164513] 
LB03023DSSCP9I.001 [163044] 
LB0305TSPA18FF.001 [165625] 
repo.zone.xls and wt.zone 
Zone lists containing node numbers 
of repository nodes in each 
infiltration bin. Used in UZ transport 
abstraction model as part of 
radionuclide release model in 
GoldSim (BSC 2003 [161572]) 
system model. 
Zone lists containing node numbers 
of grid nodes in each collection 
node at the water table. 
Zone files containing node numbers 
in different rock layers and the 
repository and water table collection 
bins from repo.zone.xls and 
wt.zone. 
MDL-NBS-HS-000020 REV 00 141 
N/A 
N/A 
N/A 
U0065 
Product Output DTN 
LA0311BR831371.003 
LA0311BR831371.003 
LA0311BR831371.003 
LA0311BR831371.003 
LA0311BR831371.003 
LA0311BR831371.003 
January 2004 Particle Tracking Model and Abstraction of Transport Processes 
Qualitative Description and Intended 
Use 
Table 8-2. 
Computer Files 
comprising the UZ 
Transport Process 
matrix_ekwc.doc 
uz_tfcurves_nn_396 
0.in 
uz_tfcurves_dualk_n 
n_3960.in 
fehm_amr_base.dat 
Computer Files Comprising the UZ Transport Process Model (Continued) 
Model 
fracture_pf.doc File contains developed fracture porosity 
and frequency distribution data to be used 
in LA 
Matrix water content and effective 
permeability distributions developed for 
estimating matrix diffusion coefficient. 
Transfer function curves for implementing 
the RTTF particle tracking model for 
upscaling of fracture-matrix interaction 
process. 
All control parameters for the FEHM 
simulation. Used as main input file for UZ 
transport process model. 
8.2.2 Output Uncertainty 
MDL-NBS-HS-000020 REV 00 
The calculation of UZ transport uncertainties in the TSPA model will be performed and 
documented in the TSPA Model Report because the radionuclide source term is computed using 
the system model, of which the UZ transport abstraction model is a part. The goal of the present 
Model Report is to ensure that a computational tool is set up for TSPA to perform the simulation 
modeling, and that the uncertainties of parameters in the abstraction model are fully justified and 
documented. Those goals have been accomplished, in that the software and computer files 
needed to perform the modeling have been completed, allowing parameter and conceptual 
uncertainties in the UZ transport to be propagated through the TSPA model. 
The uncertainties associated with transport in the UZ have been documented in the Model Report 
for UZ transport (BSC 2003 [163228]), and have been summarized briefly in the present Model 
Report. Of note is that fact that both parameter and conceptual model uncertainty have been 
shown to be incorporated into this abstraction. The key ACMs discussed in BSC (2003 
[163228]) and Section 6.7 of this Model Report relate to the treatment of fracture-matrix 
interactions. Model validation simulations presented in Section 7 suggest strongly that the 
particle tracking formulation in the abstraction model developed in FEHM replicates the 
behavior of the process model, and does so in a computationally efficient manner. In addition, 
simulations using transfer function curves implemented with a dual-k or DFM conceptual model 
for f/m interactions were shown to yield reasonable results. Thus, both f/m interaction models 
could conceivably be investigated in TSPA simulations. However, due to the fact that Process 
Model validation activities were performed based on a dual-k model, the dual-k transfer 
functions (file uz_tfcurves_dualk_nn_3960.in) should be used in TSPA analyses. The transfer 
functions based on the DFM conceptual model (file uz_tfcurves_nn_3960.in), are provided 
because the DFM was required to test the implementation of the particle tracking model through 
comparison to other numerical models. The DFM representation, though perhaps a more 
physically realistic scenario for diffusion between the media, should only be used for code 
validation or sensitivity analyses unless a parallel validation effort of the Process Model using a 
DFM formulation is successfully carried out in the future. 
LA0311BR831371.003 
LA0311BR831371.003 
LA0311BR831229.001 
LA0311BR831371.003 
January 2004 
LB0205REVUZPRP.001 [159525] 
LB0207REVUZPRP.001 [159526] 
LB03023DSSCP9I.001 [163044] 
N/A, developed output 
N/A, developed output 
142 
U0065 
Product Output DTN Data Tracking Number used to 
Develop U0065 Particle Tracking Model and Abstraction of Transport Processes 
9. INPUTS AND REFERENCES 
The following is a list of the references cited in this document. Column 1 represents the unique 
six-digit numerical identifier (the Document Input Reference System [DIRS] number), which is 
placed in the text following the reference callout (e.g., BSC 2002 [160819]). The purpose of 
these numbers is to assist the reader in locating a specific reference in the DIRS database. 
Within the reference list, multiple sources by the same author (e.g., BSC 2002) are sorted 
alphabetically by title. 
9.1 DOCUMENTS CITED 
(Civilian Radioactive Waste Management System Management and Operations) 
101378 Akindunni, F.F.; Gillham, R.W.; Conant, B.; and Franz, T. 1995. Modeling of 
Contaminant Movement Near Pumping Wells: Saturated-Unsaturated Flow with 
Particle Tracking. Ground Water, 33, (2), 264-274. Worthington, Ohio: National 
Water Well Association. TIC: 226455. 
158204 BSC (Bechtel SAIC Company) 2001. Multiscale Thermohydrologic Model. ANLEBS-
MD-000049 REV 00 ICN 02. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: MOL.20020123.0279. 
160059 BSC (Bechtel SAIC Company) 2002. Radionuclide Screening. ANL-WIS-MD- 
000006 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
MOL.20020923.0177. 
160819 BSC (Bechtel SAIC Company) 2002. Technical Work Plan for: Performance 
Assessment Unsaturated Zone. TWP-NBS-HS-000003 REV 02. Las Vegas, Nevada: 
Bechtel SAIC Company. ACC: MOL.20030102.0108. 
158966 BSC (Bechtel SAIC Company) 2002. The Enhanced Plan for Features, Events, and 
Processes (FEPs) at Yucca Mountain. TDR-WIS-PA-000005 REV 00. Las Vegas, 
Nevada: Bechtel SAIC Company. ACC: MOL.20020417.0385. 
161773 BSC (Bechtel SAIC Company) 2003. Analysis of Hydrologic Properties Data. 
MDL-NBS-HS-000014 REV 00. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: DOC.20030404.0004. 
160240 BSC (Bechtel SAIC Company) 2003. Calibrated Properties Model. MDL-NBS-HS- 
000003 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
DOC.20030219.0001. 
160109 BSC (Bechtel SAIC Company) 2003. Development of Numerical Grids for UZ Flow 
and Transport Modeling. ANL-NBS-HS-000015 REV 01. Las Vegas, Nevada: 
Bechtel SAIC Company. ACC: DOC.20030404.0005. 
January 2004 143 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
164889 BSC (Bechtel SAIC Company) 2003. Drift-Scale Radionuclide Transport. MDLNBS-
HS-000016 REV 00. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
DOC.20030902.0009. 
164873 BSC (Bechtel SAIC Company) 2003. Features, Events, and Processes in UZ Flow 
and Transport. ANL-NBS-MD-000001 REV 02A. Las Vegas, Nevada: Bechtel 
SAIC Company. ACC: MOL.20031016.0004. 
165179 BSC (Bechtel SAIC Company) 2003. Q-List. TDR-MGR-RL-000005 REV 00. Las 
Vegas, Nevada: Bechtel SAIC Company. ACC: DOC.20030930.0002. 
163228 BSC (Bechtel SAIC Company) 2003. Radionuclide Transport Models Under 
Ambient Conditions. MDL-NBS-HS-000008 REV 01. Las Vegas, Nevada: Bechtel 
SAIC Company. ACC: DOC.20031201.0002. 
162729 BSC (Bechtel SAIC Company) 2003. Saturated Zone Colloid Transport. ANLNBS-
HS-000031 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
DOC.20030916.0008. 
162415 BSC (Bechtel SAIC Company) 2003. Saturated Zone In-Situ Testing. ANL-NBSHS-
000039 REV 00A. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
MOL.20030602.0291. 
162649 BSC (Bechtel SAIC Company) 2003. Site-Scale Saturated Zone Flow Model. MDLNBS-
HS-000011 REV 01A. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
MOL.20030626.0296. 
164870 BSC (Bechtel SAIC Company) 2003. SZ Flow and Transport Model Abstraction. 
MDL-NBS-HS-000021 REV 00. Las Vegas, Nevada: Bechtel SAIC Company. 
ACC: DOC.20030818.0007. 
163045 BSC (Bechtel SAIC Company) 2003. UZ Flow Models and Submodels. MDL-NBSHS-
000006 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
DOC.20030818.0002. 
161620 BSC (Bechtel SAIC Company) 2003. Waste Form and In-Drift Colloids-Associated 
Radionuclide Concentrations: Abstraction and Summary. MDL-EBS-PA-000004 
REV 00. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
DOC.20030626.0006. 
161770 Canori, G.F. and Leitner, M.M. 2003. Project Requirements Document. TER-MGRMD-
000001 REV 01. Las Vegas, Nevada: Bechtel SAIC Company. ACC: 
DOC.20030404.0003. 
101384 Chiang, C.Y.; Wheeler, M.F.; and Bedient, P.D. 1989. A Modified Method of 
Characteristics Technique and Mixed Finite Elements Method for Simulation of 
Groundwater Solute Transport. Water Resources Research, 25, (7), 1541-1549. 
Washington, D.C.: American Geophysical Union. TIC: 226452. 
January 2004 144 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
101385 Cordes, C. and Kinzelbach, W. 1992. Continuous Groundwater Velocity Fields and 
Path Lines in Linear, Bilinear, and Trilinear Finite Elements. Water Resources 
Research, 28, (11), 2903-2911. Washington, D.C.: American Geophysical Union. 
TIC: 226449. 
134732 CRWMS M&O 2000. Analysis of Base-Case Particle Tracking Results of the Base- 
Case Flow Fields (ID: U0160). ANL-NBS-HS-000024 REV 00. Las Vegas, 
Nevada: CRWMS M&O. ACC: MOL.20000207.0690. 
141418 CRWMS M&O 2000. Particle Tracking Model and Abstraction of Transport 
Processes. ANL-NBS-HS-000026 REV 00. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.20000502.0237. 
148384 CRWMS M&O 2000. Total System Performance Assessment (TSPA) Model for Site 
Recommendation. MDL-WIS-PA-000002 REV 00. Las Vegas, Nevada: CRWMS 
M&O. ACC: MOL.20001226.0003. 
153246 CRWMS M&O 2000. Total System Performance Assessment for the Site 
Recommendation. TDR-WIS-PA-000001 REV 00 ICN 01. Las Vegas, Nevada: 
CRWMS M&O. ACC: MOL.20001220.0045. 
154071 CRWMS M&O 2001. Colloid-Associated Radionuclide Concentration Limits: ANL. 
ANL-EBS-MD-000020 REV 00 ICN 01. Las Vegas, Nevada: CRWMS M&O. 
ACC: MOL.20010216.0003. 
101386 Desbarats, A.J. 1990. Macrodispersion in Sand-Shale Sequences. Water 
Resources Research, 26, (1), 153-163. Washington, D.C.: American Geophysical 
Union. TIC: 236576. 
100547 DOE (U.S. Department of Energy) 1998. Overview - Viability Assessment of a 
Repository at Yucca Mountain. DOE/RW-0508. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. ACC: 
MOL.19981007.0027. 
101387 Fabriol, R.; Sauty, J.P.; and Ouzounian, G. 1993. Coupling Geochemistry with a 
Particle Tracking Transport Model. Journal of Contamination Hydrology, 13, 117- 
129. New York, New York: Elsevier. TIC: 222395. 
109425 Forester, R.M.; Bradbury, J.P.; Carter, C.; Elvidge-Tuma, A.B.; Hemphill, M.L.; 
Lundstrom, S.C.; Mahan, S.A.; Marshall, B.D.; Neymark, L.A.; Paces, J.B.; Sharpe, 
S.E.; Whelan, J.F.; and Wigand, P.E. 1999. The Climatic and Hydrologic History of 
Southern Nevada During the Late Quaternary. Open-File Report 98-635. Denver, 
Colorado: U.S. Geological Survey. TIC: 245717. 
154365 Freeze, G.A.; Brodsky, N.S.; and Swift, P.N. 2001. The Development of Information 
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. 
January 2004 145 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
101173 Freeze, R.A. and Cherry, J.A. 1979. Groundwater. Englewood Cliffs, New Jersey: 
Prentice-Hall. TIC: 217571. 
141512 Grathwohl, P. 2000. Diffusion in Natural Porous Media: Contaminant Transport, 
Sorption/Desorption and Dissolution Kinetics. Boston, Massachusetts: Kluwer 
Academic Publishers. TIC: 247983. 
163236 Hogg, R.V. and Craig, A.T. 1978. Introduction to Mathematical Statistics. 4th 
Edition. New York, New York: Macmillan. TIC: 254311. 
101400 Johnson, J.A.; Ravi, V.; and Rumery, J.K. 1994. Estimation of Solute 
Concentrations Using the Pathline Counting Method. Ground Water, 32, (5), 719- 
726. Worthington, Ohio: National Water Well Association. TIC: 226453. 
101402 Kinzelbach, W. 1988. The Random Walk Method in Pollutant Transport Simulation. 
Groundwater Flow and Quality Modelling. Pages 227-245. Norwell, Massachusetts: 
D. Reidel Publishing Company. TIC: 224064. 
166306 LANL (Los Alamos National Laboratory) 2003. Validation Test Plan (VTP) for the 
FEHM Application Version 2.21. 10086-VTP-2.21-00. Los Alamos, [New Mexico]: 
Los Alamos National Laboratory. ACC: MOL.20031031.0264; 
MOL.20031031.0265. 
101408 Latinopoulos, P. and Katsifarakis, K. 1991. A Boundary Element and Particle 
Tracking Model for Advective Transport in Zoned Aquifers. Journal of Hydrology, 
124, 159-176. Amsterdam, The Netherlands: Elsevier. TIC: 226466. 
105729 Liu, H.H.; Doughty, C.; and Bodvarsson, G.S. 1998. An Active Fracture Model for 
Unsaturated Flow and Transport in Fractured Rocks. Water Resources Research, 
34, (10), 2633-2646. Washington, D.C.: American Geophysical Union. TIC: 
243012. 
101413 Lu, N. 1994. A Semianalytical Method of Path Line Computation for Transient 
Finite-Difference Groundwater Flow Models. Water Resources Research, 30, (8), 
2449-2459. Washington, D.C.: American Geophysical Union. TIC: 211997. 
146957 Maloszewski, P. and Zuber, A. 1991. Influence of Matrix Diffusion and Exchange 
Reactions on Radiocarbon Ages in Fissured Carbonate Aquifers. Water Resources 
Research, 27, (8), 1937-1945. Washington, D.C.: American Geophysical Union. 
TIC: 247494. 
101148 Neretnieks, I. 1980. Diffusion in the Rock Matrix: An Important Factor in 
Radionuclide Retardation. Journal of Geophysical Research, 85, (B8), 4379-4397. 
Washington, D.C.: American Geophysical Union. TIC: 221345. 
101463 Neuman, S.P. 1984. Adaptive Eulerian-Lagrangian Finite Element Method for 
Advection-Dispersion. International Journal for Numerical Methods in 
January 2004 146 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Engineering, 20, 321-337. New York, New York: John Wiley & Sons. TIC: 
226440. 
101464 Neuman, S.P. 1990. Universal Scaling of Hydraulic Conductivities and 
Dispersivities in Geologic Media. Water Resources Research, 26, (8), 1749-1758. 
Washington, D.C.: American Geophysical Union. TIC: 237977. 
163274 NRC (U.S. Nuclear Regulatory Commission) 2003. Yucca Mountain Review Plan, 
Final Report. NUREG-1804, Rev. 2. Washington, D.C.: U.S. Nuclear Regulatory 
Commission, Office of Nuclear Material Safety and Safeguards. TIC: 254568. 
103896 Parrington, J.R.; Knox, H.D.; Breneman, S.L.; Baum, E.M.; and Feiner, F. 1996. 
Nuclides and Isotopes, Chart of the Nuclides. 15th Edition. San Jose, California: 
General Electric Company and KAPL, Inc. TIC: 233705. 
101466 Pollock, D.W. 1988. Semianalytical Computation of Path Lines for Finite- 
Difference Models. Ground Water, 26, (6), 743-750. Worthington, Ohio: National 
Water Well Association. TIC: 226464. 
101474 Reimus, P.W. 1995. The Use of Synthetic Colloids in Tracer Transport Experiments 
in Saturated Rock Fractures. Ph.D. dissertation. LA-13004-T. Los Alamos, New 
Mexico: Los Alamos National Laboratory. TIC: 240694. 
126243 Reimus, P.W.; Adams, A.; Haga, M.J.; Humphrey, A.; Callahan, T.; Anghel, I.; and 
Counce, D. 1999. Results and Interpretation of Hydraulic and Tracer Testing in the 
Prow Pass Tuff at the C-Holes. Milestone SP32E7M4. Los Alamos, New Mexico: 
Los Alamos National Laboratory. TIC: 246377. 
163008 Reimus, P.W.; Ware, S.D.; Benedict, F.C.; Warren, R.G.; Humphrey, A.; Adams, A.; 
Wilson, B.; and Gonzales, D. 2002. Diffusive and Advective Transport of 
{superscript 3}H, {superscript 14}C, and {superscript 99}Tc in Saturated, Fractured 
Volcanic Rocks from Pahute Mesa, Nevada. LA-13891-MS. Los Alamos, New 
Mexico: Los Alamos National Laboratory. TIC: 253905. 
101154 Robinson, B.A. 1994. A Strategy for Validating a Conceptual Model for 
Radionuclide Migration in the Saturated Zone Beneath Yucca Mountain. 
Radioactive Waste Management and Environmental Restoration, 19, (1-3), 73-96. 
Yverdon, Switzerland: Harwood Academic Publishers. TIC: 222513. 
101476 Schafer-Perini, A.L. and Wilson, J.L. 1991. Efficient and Accurate Front Tracking 
for Two-Dimensional Groundwater Flow Models. Water Resources Research, 27, 
(7), 1471-1485. Washington, D.C.: American Geophysical Union. TIC: 226448. 
101477 Scheibe, T.D. and Cole, C.R. 1994. Non-Gaussian Particle Tracking: Application 
to Scaling of Transport Processes in Heterogeneous Porous Media. Water Resources 
Research, 30, (7), 2027-2039. Washington, D.C.: American Geophysical Union. 
TIC: 226446. 
January 2004 147 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
105043 Sudicky, E.A. and Frind, E.O. 1982. Contaminant Transport in Fractured Porous 
Media: Analytical Solutions for a System of Parallel Fractures. Water Resources 
Research, 18, (6), 1634-1642. Washington, D.C.: American Geophysical Union. 
TIC: 217475. 
101490 Tompson, A.F.B. and Gelhar, L.W. 1990. Numerical Simulation of Solute 
Transport in Three-Dimensional, Randomly Heterogeneous Porous Media. Water 
Resources Research, 26, (10), 2541-2562. Washington, D.C.: American 
Geophysical Union. TIC: 224902. 
146961 van Genuchten, M.T. 1985. Convective-Dispersive Transport of Solutes Involved in 
Sequential First-Order Decay Reactions. Computers in Geosciences, 11, (2), 129- 
147. New York, New York: Pergamon Press. TIC: 245188. 
166070 Wang, J.S. 2003. Scientific Notebooks Referenced in Model Report U0065, 
Particle Tracking Model and Abstraction of Transport Process, MDL-NBS-HS- 
000020 REV 00. Letter from J.S. Wang (BSC) to File, December 4, 2003, with 
attachment. ACC: MOL.20031208.0348. 
101498 Wolfsberg, A.V. and Freyberg, D.L. 1994. Efficient Simulation of Single Species 
and Multispecies Transport in Groundwater with Local Adaptive Grid Refinement. 
Water Resources Research, 30, (11), 2979-2991. Washington, D.C.: American 
Geophysical Union. TIC: 226450. 
101499 Yamashita, R. and Kimura, H. 1990. Particle-Tracking Technique for Nuclide 
Decay Chain Transport in Fractured Porous Media. Journal of Nuclear Science and 
Technology, 27, (11), 1041-1049. Tokyo, Japan: Nihon Genshryoku Gakkai. TIC: 
236573. 
101501 Yeh, G.T. 1990. A Lagrangian-Eulerian Method with Zoomable Hidden Fine-Mesh 
Approach to Solving Advective-Dispersion Equations. Water Resources Research, 
26, (6), 1133-1144. Washington, D.C.: American Geophysical Union. TIC: 
224067. 
101502 Zheng, C. 1993. Extension of the Method of Characteristics for Simulation of 
Solute Transport in Three Dimensions. Ground Water, 31, (3), 456-465. 
Worthington, Ohio: Water Well Publishing Company. TIC: 226465. 
101503 Zheng, C. 1994. Analysis of Particle Tracking Errors Associated with Spatial 
Discretization. Ground Water, 32, (5), 821-828. Dublin, Ohio: Water Well 
Publishing Company. TIC: 226463. 
100614 Zimmerman, R.W.; Chen, G.; Hadgu, T.; and Bodvarsson, G.S. 1993. A Numerical 
Dual-Porosity Model with Semianalytical Treatment of Fracture/Matrix Flow. 
Water Resources Research, 29, (7), 2127-2137. Washington, D.C.: American 
Geophysical Union. TIC: 236571. 
January 2004 148 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
101026 Zyvoloski, G.; Dash, Z.; and Kelkar, S. 1992. FEHMN 1.0: Finite Element Heat and 
Mass Transfer Code. LA-12062-MS, Rev. 1. Los Alamos, New Mexico: Los 
Alamos National Laboratory. ACC: NNA.19910625.0038. 
100615 Zyvoloski, G.A.; Robinson, B.A.; Dash, Z.V.; and Trease, L.L. 1997. Users Manual 
for the FEHM ApplicationA Finite-Element Heat- and Mass-Transfer Code. LA- 
13306-M. Los Alamos, New Mexico: Los Alamos National Laboratory. TIC: 
235999. 
Software Cited: 
161572 BSC (Bechtel SAIC Company) 2003. Software Code: GoldSim. V7.50.100. PC. 
10344-7.50.100-00. 
165742 LANL (Los Alamos National Laboratory) 2003. Software Code: discrete_tf. V1.1. 
SUN, SunOS 5.8; PC, Windows 2000 and Linux 7.1. 11033-1.1-00. 
165741 LANL (Los Alamos National Laboratory) 2003. Software Code: FEHM. V2.21. 
SUN, SunOS 5.8; PC, Windows 2000 and Linux 7.1. 10086-2.21-00. 
165754 LANL (Los Alamos National Laboratory) 2003. Software Code: fehm2post. V1.0. 
SUN, SunOS 5.8 and 5.7; PC, Windows 2000 and Redhat Linux 2.4.18. 11031-1.0- 
00. 
165753 LANL (Los Alamos National Laboratory) 2003. Software Code: ppptrk. V1.0. 
SUN, SunOS 5.8 and 5.7; PC, Windows 2000 and Linux 7.1. 11030-1.0-00. 
146654 LBNL (Lawrence Berkeley National Laboratory) 1999. Software Code: T2R3D. 
V1.4. FORTRAN 77, SUN, DEC/ALPHA. 10006-1.4-00. 
113943 LBNL (Lawrence Berkeley National Laboratory) 1999. Software Code: TOUGH2. 
V1.11 MEOS9nTV1.0. MAC, SUN, DEC/Alpha, PC. 10065-1.11MEOS9NTV1.0- 
00. 
154342 LBNL (Lawrence Berkeley National Laboratory) 2002. Software Code: DCPT. 
V2.0. PC, Windows. 10078-2.0-00. 
163453 LBNL (Lawrence Berkeley National Laboratory) 2003. Software Code: WTRISE. 
V2.0. PC/WINDOWS 2000/98; DEC ALPHA/OSF1 V5.1. 10537-2.0-00. 
9.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES 
156671 66 FR 55732. Disposal of High-Level Radioactive Wastes in a Proposed Geologic 
Repository at Yucca Mountain, NV. Final Rule 10 CFR Part 63. Readily available. 
AP-2.22Q, REV 1, ICN 0. 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. 
January 2004 149 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
AP-SI.1Q, REV 5 ICN 2. Software Management. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. ACC: DOC.20030902.0003. 
9.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER 
144462 LA0002PR831231.003. Probabilities from C-Wells Microsphere Data. Submittal 
date: 02/17/2000. 
149557 LA0003JC831362.001. Preliminary Matrix Diffusion Coefficients for Yucca 
Mountain Tuffs. Submittal date: 4/10/2000. 
147285 LA0003MCG12213.002. Cumulative Probabilities for Colloid Transport Between 
One Matrix and Another Calculated from Interpolation of Pore Volume Data from 
Yucca Mountain Hydrologic (Stratigraphic) Samples. Submittal date: 03/10/2000. 
153251 LA0007MCG12213.001. Colloid Size Distribution. Submittal date: 07/31/2000. 
162575 LA0302AM831341.002. Unsaturated Zone Distribution Coefficients (KDS) for U, 
NP, PU, AM, PA, CS, SR, RA, and TH. Submittal date: 02/04/2003. 
163558 LA0303HV831352.002. Colloid Retardation Factors for the Saturated Zone 
Fractured Volcanics. Submittal date: 03/31/2003. 
165624 LA0303HV831352.003. Fraction of Colloids that Travel Unretarded. Submittal 
date: 03/31/2003. 
159525 LB0205REVUZPRP.001. Fracture Properties for UZ Model Layers Developed from 
Field Data. Submittal date: 05/14/2002. 
159526 LB0207REVUZPRP.001. Revised UZ Fault Zone Fracture Properties. Submittal 
date: 07/03/2002. 
160799 LB0210THRMLPRP.001. Thermal Properties of UZ Model Layers: Data Summary. 
Submittal date: 10/25/2002. 
163044 LB03023DSSCP9I.001. 3-D Site Scale UZ Flow Field Simulations for 9 Infiltration 
Scenarios. Submittal date: 02/28/2003. 
161787 LB0302UZDSCPUI.002. Drift-Scale Calibrated Property Sets: Upper Infiltration 
Data Summary. Submittal date: 02/05/2003. 
165625 LB0305TSPA18FF.001. Eighteen 3-D Site Scale UZ Flow Fields Converted from 
TOUGH2 to T2FEHM Format. Submittal date: 05/09/2003. 
164752 LB0307MR0060R1.007. Ambient Radionuclide Transport - TSPA Deliverable 
Extractions. Submittal date: 07/19/2003. 
166071 LB03093RADTRNS.002. Three Way Transport Model Comparison: Data 
Summaries. Submittal date: 09/24/2003. 
January 2004 150 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
166060 LB0310T2FEHMFF.001. 1-D and 2-D Site Scale UZ Flow Fields Converted from 
TOUGH2 to T2FEHM Format. Submittal date: 10/20/2003. 
166671 LB0312TSPA06FF.001. Six Flow Fields with Raised Water Tables. Submittal date: 
12/23/2003. 
142973 LL000122051021.116. Summary of Analyses of Glass Dissolution Filtrates. 
Submittal date: 01/27/2000. 
164513 LL030610323122.029. Multiscale Thermohydrologic Model Output to TSPA and 
WAPDEG for the Mean Infiltration Case. Submittal date: 06/27/2003. 
164132 SN0306T0504103.005. Revised Groundwater Colloid Mass Concentration 
Parameters for TSPA (Total System Performance Assessment). Submittal date: 
06/30/2003. 
164131 SN0306T0504103.006. Revised Sorption Partition Coefficients (KD Values) for 
Selected Radionuclides Modeled in the TSPA (Total System Performance 
Assessment). Submittal date: 06/30/2003. 
9.4 OUTPUT DATA, LISTED BY DATA TRACKING NUMBER 
LA0311BR831229.001. UZ Transport Abstraction Model, Transfer Function Calculation Files. 
Submittal date: 11/17/2003. 
LA0311BR831371.001. UZ Transport Abstraction Model, Validation Simulations for the 
Discrete Fracture Comparison Problem. Submittal date: 11/202003. 
LA0311BR831371.002. UZ Transport Abstraction Model, Validation Simulations for the 
Comparison to T2R3D. Submittal date: 11/202003. 
LA0311BR831371.003. UZ Transport Abstraction Model, Transport Parameters and Base Case 
Simulation Results. Submittal date: 11/25 /2003. 
January 2004 151 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
INTENTIONALLY LEFT BLANK 
152 MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
ATTACHMENT I 
DERIVATION OF THE DISTRIBUTION OF WATER CONTENT AND EFFECTIVE 
PERMEABILITY FOR SAMPLING MATRIX DIFFUSION COEFFICIENT 
January 2004 I-1 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
INTENTIONALLY LEFT BLANK 
I-2 MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
ATTACHMENT I 
DERIVATION OF THE DISTRIBUTION OF WATER CONTENT AND EFFECTIVE 
PERMEABILITY FOR SAMPLING MATRIX DIFFUSION COEFFICIENT 
Matrix diffusion is linked through the correlation given by Reimus et al. 2002 [163008] to 
porosity and permeability. For unsaturated conditions, this relationship is extended to water 
content and effective permeability. This is done in segments from the output file from rows 
61001-122000, 122001-184000, and 184001-245506, and repeated for each of the nine flow 
fields. Rows 1-61000 are not needed because none of these cells lie within the repository 
footprint. 
Starting with the flow output for file for saturation and relative permeability discussed earlier, 
the file is first sorted on column T to sort out the cells not in the repository footprint. This 
approximation is made to simplify the procedure, and is a reasonable approach since, for the 
most part, transport is vertically downward. After sorting the matrix data is copied into a new 
file. The rock types in column K are compared with the rock types that exist in or beneath the 
proposed repository horizon. This is done using the following formulas: 
Urn = IF(Krn=bf3Md,1,IF(Krn=tr3Md,1,0)) 
Vrn = IF(Krn=pp2Md,2,IF(Krn=pp1Mz,2,IF(Krn=pp4Mz,2,0))) 
Wrn = 
IF(Krn=ch2Mz,3,IF(Krn=ch3Mz,3,IF(Krn=ch4Mz,3,IF(Krn=ch5Mz,3,IF(Krn=ch6Mz 
,3,0))))) 
Xrn = 
IF(Krn=pcM1z,3,IF(Krn=pcM2z,3,IF(Krn=pcM39,3,IF(Krn=pcM4p,3,IF(Krn=pcM5z, 
3,IF(Krn=pcM6z,3,0)))))) 
Yrn = IF(Krn=ch2Mv,4,IF(Krn=ch3Mv,4,IF(Krn=ch4Mv,4,IF(Krn=ch5Mv,4,0)))) 
Zrn = IF(Krn=tswMv,5,IF(Krn=ch1Mv,5,IF(Krn=ch6Mv,5,IF(Krn=pp3Md,5,0)))) 
AArn = IF(Krn=tswMz,6,IF(Krn=ch1Mz,6,IF(Krn=bf2Mz,6,0))) 
ABrn = IF(Krn=tswM8,7,IF(Krn=pcM38,7,0)) 
ACrn = IF(Krn=tswM4,8,IF(Krn=tswM6,8,IF(Krn=tswM7,8,0))) 
ADrn = IF(Krn=tswM3,9,IF(Krn=tswM5,9,0)) 
AErn = SUM(U1:AD1) 
January 2004 I-3 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
The sum of the columns in column AE identifies, by number, the rock group from 1 to 9. Here is 
a table of the rock groups: 
Hydrogeologic Units Rock Group 
pp2Md, pp1Mz, pp4Mz 
ch2Mz, ch3Mz, ch4Mz, ch5Mz, ch6Mz, pcM1z, pcM2z, pcM39, pcM4p, pcM5z, pcM6z 
ch2Mv, ch3Mv, ch4Mv, ch5Mv 
tswMv, ch1Mv, ch6Mv, pp3Md 
tswMz, ch1Mz, bf2Mz 
1 bf3Md, tr3Md 
2 
3 
4 
5 
6 
7 tswM8, pcM38 
8 tswM4, tswM6, tswM7 
9 tswM3, tswM5 
The groupings are based on similarities in porosity and permeability, as shown here: 
Porosity Model Unit Permeability m2 Rock Group 
bf3Md 0.175 3.55E-14 1 
pp2Md 0.221 1.7E-15 2 
pp1Mz 0.297 2.57E-15 2 
pp4Mz 0.321 1.02E-15 2 
ch6Mz 0.271 8.2E-19 3 
pcM39 0.275 6.2E-18 3 
pcM1z 0.285 9.3E-20 3 
pcM2z 0.322 2.4E-18 3 
ch5Mz 0.322 5.2E-18 3 
ch4Mz 0.322 5.2E-18 3 
ch3Mz 0.322 5.2E-18 3 
ch2Mz 0.322 5.2E-18 3 
ch5Mv 0.346 4.9E-11 4 
ch4Mv 0.346 4.9E-11 4 
ch3Mv 0.346 4.9E-11 4 
ch2Mv 0.346 4.9E-11 4 
tswMv 0.229 2.24E-13 5 
pp3Md 0.318 1.26E-13 5 
ch1Mv 0.331 1.39E-12 5 
tswMz 0.275 3.5E-17 6 
ch1Mz 0.285 3.5E-17 6 
pcM38 0.043 3E-19 7 
tswM8 0.043 7.4E-18 7 
tswM7 0.103 7.41E-19 8 
tswM6 0.103 7.41E-19 8 
tswM4 0.111 2.96E-19 8 
tswM5 0.131 8.55E-18 9 
tswM3 0.155 2.39E-179 9 
January 2004 I-4 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
The rock type identification files are stored as 
gt upper rock type identification 61001-122000.xls 
gt upper rock type identification 122001-184000.xls 
gt upper rock type identification 184001-245506.xls 
gt mean rock type identification 61001-122000.xls 
gt mean rock type identification 122001-184000.xls 
gt mean rock type identification 184001-245506.xls 
gt lower rock type identification 61001-122000.xls 
gt lower rock type identification 122001-184000.xls 
gt lower rock type identification 184001-245506.xls 
ms upper rock type identification 61001-122000.xls 
ms upper rock type identification 122001-184000.xls 
ms upper rock type identification 184001-245506.xls 
ms mean rock type identification 61001-122000.xls 
ms mean rock type identification 122001-184000.xls 
ms mean rock type identification 184001-245506.xls 
ms lower rock type identification 61001-122000.xls 
ms lower rock type identification 122001-184000.xls 
ms lower rock type identification 184001-245506.xls 
pd upper rock type identification 61001-122000.xls 
pd upper rock type identification 122001-184000.xls 
pd upper rock type identification 184001-245506.xls 
pd mean rock type identification 61001-122000.xls 
pd mean rock type identification 122001-184000.xls 
pd mean rock type identification 184001-245506.xls 
pd lower rock type identification 61001-122000.xls 
pd lower rock type identification 122001-184000.xls 
pd lower rock type identification 184001-245506.xls 
Columns U through AD are deleted and the file is sorted on column U (Rock Type) in 
descending order. Those with rock type 0 are deleted. 
These files are saved as 
gt upper sort by rock type 61001-122000.xls 
gt upper sort by rock type 122001-184000.xls 
gt upper sort by rock type 184001-245506.xls 
January 2004 I-5 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
gt mean sort by rock type 61001-122000.xls 
gt mean sort by rock type 122001-184000.xls 
gt mean sort by rock type 184001-245506.xls 
gt lower sort by rock type 61001-122000.xls 
gt lower sort by rock type 122001-184000.xls 
gt lower sort by rock type 184001-245506.xls 
ms upper sort by rock type 61001-122000.xls 
ms upper sort by rock type 122001-184000.xls 
ms upper sort by rock type 184001-245506.xls 
ms mean sort by rock type 61001-122000.xls 
ms mean sort by rock type 122001-184000.xls 
ms mean sort by rock type 184001-245506.xls 
ms lower sort by rock type 61001-122000.xls 
ms lower sort by rock type 122001-184000.xls 
ms lower sort by rock type 184001-245506.xls 
pd upper sort by rock type 61001-122000.xls 
pd upper sort by rock type 122001-184000.xls 
pd upper sort by rock type 184001-245506.xls 
pd mean sort by rock type 61001-122000.xls 
pd mean sort by rock type 122001-184000.xls 
pd mean sort by rock type 184001-245506.xls 
pd lower sort by rock type 61001-122000.xls 
pd lower sort by rock type 122001-184000.xls 
pd lower sort by rock type 184001-245506.xls 
The results for each climate scenario are compiled into a single file and ordered by column V in 
descending order. The files are stored as: 
gt upper composite by rock type.xls 
gt mean composite by rock type.xls 
gt lower composite by rock type.xls 
ms upper composite by rock type.xls 
ms mean composite by rock type.xls 
ms lower composite by rock type.xls 
pd upper composite by rock type.xls 
pd mean composite by rock type.xls 
pd lower composite by rock type.xls 
MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 I-6 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Similarities between rock groups 1, 2, 4, 5, and 6 led to making this a single group. The same 
was also found for groups 7, 8, and 9. This reduces the groupings to 3 composite groups: 
1, 2, 4, 5, and 6 
3 
7, 8, and 9 
The first analysis, for the glacial-transition upper climate scenario, was conducted on the 
individual rock groups 1-9. Porosity was randomly sampled because the flow fields and 
resulting saturations and effective permeabilities are independent of porosity under steady-flow 
conditions. Porosity sampling was conducted for each model unit according to the mean and 
standard deviation for the model unit and a minimum and maximum of 9 and 1, respectively, 
using a beta distribution. The sampling methodology is described on pages 55 through 59 of 
Wang (2003 [166070], SN-LBNL-SCI-236-V1). Once the sampled porosities were generated on 
separate worksheets in the same file, the porosities were copied and pasted into column T on the 
main worksheet. Water content for each cell is generated by multiplying column D by column T 
as follows: 
Urn = Drn*Trn 
After generating the water content for each model unit, the combined units were assembled and 
the main worksheet was ordered by rock type (descending order) and secondarily by cell name 
(ascending order). 
Statistics for the water content and effective permeability were assembled from the data based on 
a volume-weighted average. The cell volumes are given in column L. The total sum of cell 
volumes are computed as follows: 
X1 = SUM(L1:Lre) 
Where re stands for the last row of data on the worksheet. The statistics for water content are 
derived from the following: 
Yrn = Urn*Lrn/W$1 
Zrn = ((Urn-Z$1)^2)*Lrn/W$1 
AA1 = SUM(X1:Xre) 
AB1 = SQRT(SUM(Y1:Yre)) 
AC1 = MAX(U1:Ure) 
AD1 = MIN(U1:Ure) 
where Yrn and Zrn are the sums to determine the volume weighted mean and variance of the 
water content. AA1 is then the mean water content, AB1 is the standard deviation of water 
content, AC1 is the maximum water content, and AD1 is the minimum water content. 
January 2004 I-7 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
Statistics for the effective permeability are based on a log-normal distribution. The statistics are 
derived through the following formulas: 
AFrn = LOG(Frn*Srn)*Lrn/W$1 
AGrn = ((LOG(Frn*Srn)-AG$1)^2)*Lrn/W$1 
AH1 = SUM(AF1:AFre) 
AI1 = SQRT(SUM(A1:AGre)) 
Where AFrn and AGrn are the sums to determine the volume weighted mean and variance of the 
logarithm of the effective permeability. AH1 is then the mean of the logarithm of the effective 
permeability and AI1 is the standard deviation of the logarithm of the effective permeability. 
This was carried out for each of the nine flow fields. The files containing the results are stored 
as: 
gt upper group 6-5-4-2-1 diffusion parameters.xls 
gt upper group 3 diffusion parameters.xls 
gt upper group 9-8-7 diffusion parameters.xls 
gt mean group 6-5-4-2-1 diffusion parameters.xls 
gt mean group 3 diffusion parameters.xls 
gt mean group 9-8-7 diffusion parameters.xls 
gt lower group 6-5-4-2-1 diffusion parameters.xls 
gt lower group 3 diffusion parameters.xls 
gt lower group 9-8-7 diffusion parameters.xls 
ms upper group 6-5-4-2-1 diffusion parameters.xls 
ms upper group 3 diffusion parameters.xls 
ms upper group 9-8-7 diffusion parameters.xls 
ms mean group 6-5-4-2-1 diffusion parameters.xls 
ms mean group 3 diffusion parameters.xls 
ms mean group 9-8-7 diffusion parameters.xls 
ms lower group 6-5-4-2-1 diffusion parameters.xls 
January 2004 I-8 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
ms lower group 3 diffusion parameters.xls 
ms lower group 9-8-7 diffusion parameters.xls 
ps upper group 6-5-4-2-1 diffusion parameters.xls 
ps upper group 3 diffusion parameters.xls 
ps upper group 9-8-7 diffusion parameters.xls 
ps mean group 6-5-4-2-1 diffusion parameters.xls 
ps mean group 3 diffusion parameters.xls 
ps mean group 9-8-7 diffusion parameters.xls 
ps lower group 6-5-4-2-1 diffusion parameters.xls 
ps lower group 3 diffusion parameters.xls 
ps lower group 9-8-7 diffusion parameters.xls 
Summary files for each climate were created. These are stored as: 
Summary of matrix diffusion for glacial-transition climate.xls 
Summary of matrix diffusion for monsoon climate.xls 
Summary of matrix diffusion for present day climate.xls 
Averages were conducted across the climate/infiltration scenarios to create categories based on 
rock type only. Simple arithmetic averages of the results from each climate infiltration scenario 
were computed for the mean and variance of water content and logarithm of the effective 
permeability. Composite Distributions for all climate scenarios segregated only by the higher 
level rock groupings (6-5-4-2-1, 3, 9-8-7) are given in the following file: 
Matrix diffusion summary with averages by rock type.xls 
And a summary file with only the results is given in: 
Matrix diffusion - summary values only.xls 
January 2004 I-9 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
INTENTIONALLY LEFT BLANK 
I-10 MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
ATTACHMENT II 
DERIVATION OF WATER TABLE COLLECTING BINS 
II-1 MDL-NBS-HS-000020 REV 00 January 2004 Particle Tracking Model and Abstraction of Transport Processes 
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II-2 MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
ATTACHMENT II 
DERIVATION OF WATER TABLE COLLECTING BINS 
The water table bins were calculated starting with the ELEME data from TOUGH2 available in 
DTN: LB03023DSSCP9I.001 [163044]. This data contains the cell name and coordinates for 
each node in the site-scale UZ flow model. Because the number of elements is 245506, the file 
is split into 4 groups as follows such that the data fits onto an excel worksheet: 
Group A 
1-62000.xls 
62001-124000.xls 
124001-186000.xls 
186001-245506.xls 
The BT cells in the UZ flow model comprise the bottom boundary of the model at the presentday 
water table. These are cells in the file 186001-245506.xls from row 57465 to row 59506. 
The BT cell coordinates were put into columns I, J, and K of the following files: 
Group B 
1-62000 with exact WT picks.xls 
62001-124000 with exact WT picks.xls 
124001-186000 with exact WT picks.xls 
186001-245506 with exact WT picks.xls 
Columns L and M were generated using the following relationship: 
Lrn = Ern&Frn 
Mrn = Irn&Jrn 
where the rn subscripts stand for row number. The character strings in columns L and M 
represent, respectively, a unique x-y coordinate character for the grid nodes and for the BT 
cells. Each grid node was then checked for a match with a BT cell. The index for the match 
was recorded in Column N, 
Nrn = MATCH(Lrn,M$1:M$end,0) 
where M$end represents the last occupied cell in column M. 
The index in column N is then used to extract the local water table elevation in column H as 
follows: 
Hrn = INDEX(K:K,Nrn) 
In roughly 10% of the cells, no match was found, in which case a value of #N/A was returned. 
To evaluate a value of the local water table for these cells, columns A through H were copied 
into a second worksheet in the files listed above. A column was inserted into column A for a 
sequential number for each cell. Therefore, the local water table resided in column I. The 
January 2004 II-3 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
worksheet was sorted on column I to group the cells without local water table values. The cells 
without local water table values were copied into the following file: 
Stragglers.xls 
Cells without local water table values were found for each of the following cell ranges: 
1-62000 
62001-124000 
186001-245506 
and these cells were kept on separate worksheets in the Straggles.xls file. 
To identify an appropriate local water table elevation for these cells, the following file was 
developed: 
WT identification for stragglers.xls 
Columns A, B, and C, from row 3 to row 4086 contain the coordinates of the BT cells. Up to 
250 x-y coordinates for cells without an exact water table value were put in rows 1 and 2, 
columns D through IS. Then the square of the distance between each cell and each BT cell 
was computed for each x-y coordinate as follows: 
COLrn = (COL$1-$Arn)^2+(COL$2-$Brn)^2 
where COL represents a column label and rn the row number. Each column represents the x-y 
distance from a cell without an exact local water table value to each of the BT cells. The 
minimum distance was determined in row 4087 using the following formula: 
COL4087 = MIN(COL3:COL4086) 
The index of the BT cell associated with the minimum distance was determined in row 4088 as 
follows: 
COL4088 = MATCH(COL4087,COL3:COL4086,0) 
And the water table elevation associated with the index is determined in row 4089 as follows: 
COL4089 = INDEX($C3:$C4086,COL4088) 
These water table elevations were included in the third worksheet of the Group B files. 
Files 62001-124000 wt bins.xls, 124001-186000 wt bins.xls, and 186001-245506 wt bins.xls 
contain the extracted water table collection cells in TOUGH2 columns using conditional if 
statements and the definition of the collection bin boundary data. 
January 2004 II-4 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
File 62001-124000 wt bins with fehm nodes .xls, 124001-186000 wt bins with fehm 
nodes.xls, and 124001-186000 wt bins with fehm nodes.xls contain extracted collection bin 
nodes in FEHM grid format. 
The final extracted water table collection bins are stored in file collect_zone which only contains 
the fracture nodes as required by FEHM. 
All the files used in the extraction of water table collection bins are included in zip file wtbin.zip. 
The file names are listed below. 
January 2004 II-5 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
INTENTIONALLY LEFT BLANK 
II-6 MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
ATTACHMENT III 
DERIVATION OF FRACTURE-MATRIX INTERACTION SUBMODEL AND 
GENERATION OF TRANSFER FUNCTIONS 
January 2004 III-1 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
INTENTIONALLY LEFT BLANK 
III-2 MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
ATTACHMENT III 
DERIVATION OF FRACTURE-MATRIX INTERACTION SUBMODEL AND 
GENERATION OF TRANSFER FUNCTIONS 
III-1. DERIVATION OF FRACTURE-MATRIX INTERACTION SUBMODEL 
The governing equations required for the fracture-matrix interaction submodel is a solute 
transport system in a domain consisting of parallel flow in a fracture and adjacent matrix, with 
fracture-matrix solute interaction via molecular diffusion in the rock matrix. This model is 
therefore an extension of the model of Sudicky and Frind 1982 [105043], which assumed the 
water in the matrix is stagnant. For simplicity, longitudinal dispersion is not considered in either 
medium, advection is considered only in the z direction, and diffusion is considered only normal 
to the flow direction. The rationales for these simplifications are as follows. With regard to 
longitudinal dispersion, this submodel is intended only to capture the impact of diffusion because 
dispersion is captured separately in the particle tracking algorithm. Likewise, the advection from 
fracture to matrix (or the reverse) is implemented in the particle tracking algorithm separately. 
Therefore, the remaining processes to be included as part of the transfer functions are advection 
and diffusion in the z-direction only. 
We begin with a derivation of the transport equation for the fracture. A variant of this equation 
with longitudinal dispersion and decay was presented by Sudicky and Frind (1982 [105043], Eq. 
1). We rederive the equation from first principles to demonstrate the means by which terms in 
the dimensionless groups must be altered to include the effects of the Active Fracture Model 
(AFM). Taking a control volume in the fracture of width b (half of the full aperture), depth d , 
and length z . , we write the following terms of the transient solute mass balance (units of each 
of these terms are solute mass per time): 
(C . C ) 
Accumulation: bd.z  R prev (Eq. III-1) f f 
where prev f  is the volumetric water 
content in the fracture, and 
z z 
Cm 
.t 
C represents the concentration at the previous time step, 
f R is the fracture retardation factor. 
Advection: bdV (C .C ) (Eq. III-2) z 
(Eq. III-3) Diffusion into Matrix: m .z d  Dm 
+ .z 
where Vz is the Darcy velocity in the fracture, equal to volumetric flow rate divided by the total 
cross sectional area in the fracture. 
x=b 
m 
x 
where D is the effective diffusion coefficient in the matrix and m is the matrix volumetric 
water content. These terms form the overall solute mass balance equation: 
III-3 January 2004 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
(C .Cprev ) 
bd z Rf f 
Dividing by 
V /  V = f z f 
f R
.t 
, and taking the limit as z . and t . go to 0, we obtain: 
C 
f 
R 
bd.z  , making use of the relation for the fracture interstitial pore-water velocity 
x 
(Eq. III-5) 
(Eq. III-6) 
t 
Note also that we have adopted the subscript f on the concentration to denote the fracture. 
Given the assumptions listed at the beginning of this derivation, the differential equation 
governing transport in the matrix is: 
m 
t 
C 
. =
m
m 
m V is the interstitial pore-water velocity in matrix, and Dm is the matrix retardation factor. where 
The initial and boundary conditions for the system are: 
0C (z,0) = (Eq. III-7) 
0C (x, z,0) = (Eq. III-8) 
) C (b, z,t) = C (z,t (Eq. III-11) 

x 
(0,t) = C 
(x,0,t) = Co (Eq. III-10) 
( , ,t z B ) 
f 
Cm 
f o C , and Co,m for the fracture and matrix, respectively, are nonzero if mass is Here the terms 
being introduced into that medium, and 0 if mass is being introduced in the other medium. 
Non-dimensionalization of these equations can be accomplished by introducing the following 
dimensionless variables: 
x 
C. 
C.
m 
=
m 
Cf 
Cm 
Cm 
.  
f 
MDL-NBS-HS-000020 REV 00 
U0065 
Cm (Eq. III-4) ( D bdV C C z d m m z z z z 
x=b 
Cf m m 
f 
.  
x=b 
. = 
V 
) + 
D C 
b 
. +
m 
x 
Cm 
z 
m D
f 
. 
m 
f
V 

 
f 
z 
(Eq. III-9) 
(Eq. III-12) 
f 
+ 
2C
2
/ 
. m 
, f o 
m ,
0 = 
C /C (Eq. III-13) o 
C (Eq. III-14) o 
=
=
III-4 January 2004 Particle Tracking Model and Abstraction of Transport Processes 
where L is the length of the flow path. Eq. III-19 uses the definition of n = L /V ; a 
corresponding relation is also used for the matrix fluid travel time ( n = 
because the equations are nondimensionalized with respect to travel times through the fracture 
and matrix, the physical dimensions of the flow path, including the length, is unimportant to the 
final implementation in the code. Next, we substitute Eqs. III-15 to III-19 into Eq. III-7 and III- 
8, which yields 
n 
=
D n c m m 
bB f 
m 
c
. 2C
. 2 x 
)= C z, . ( . t. (Eq. III-24) 
= 1
C b B z t ) . , . , / ( . 
= 
1 C t ) . , 0 ( . = (or 0 if injection is into the matrix) 
(or 0 if injection is into the fracture) 
= 0
f
0 (Eq. III-25) z t ) . , . , 1 ( 
The end result is that Eqs. III-20 and III-21 illustrate that a when non-dimensional form of the 
model equations are produced, the system is fully characterized by three dimensionless 
parameters (Eq. 6-9 to 6-11 of the main document): 
.x. 
1 
D n 
.Cm 
. 
.
2R 
p = 
The boundary and initial conditions (Eqs. III-3 to III-8) are transformed to 
0C z ) 0 , . ( . (Eq. III-20) 
.
.
m 
B 
III-5 MDL-NBS-HS-000020 REV 00 
.C.
f 
. 
t = . 
C. 
z.
f 
. 
m 
.t 
.
m 
. 
.C
t 
f 
. 
C x t ) . , 0 , . ( .
m 
. = 
B 
m 
U0065 
z. = z / L (Eq. III-15) 
x.
= x / B (Eq. III-16) 
t Vf (Eq. III-17) t
Rf L f Rf 
f f 
L /V ). Note that m m 
. f f Cm (Eq. III-18) 
.x . 
. 
x=b / B 
. 
+
f R R f f m . (Eq. III-19) 
.
n
n .C
z. Rm m m
f 
m 
(Eq. III-22) 
(Eq. III-23) 
. 
(Eq. III-21) 
(Eq. III-26) 
= 
C x z ) 0 , . , . ( . 
f 
= 
D n Rf 
2Rm 
January 2004 U0065 Particle Tracking Model and Abstraction of Transport Processes 
m f Dm   
(Eq. III-27) 2 bB f 
f Rf 
p = 
3 p = (Eq. III-28) 
mRm 
where the retardation factor 
3 2 

 
m R is related to the sorption coefficient d K using Eq. 6-2. This 
derivation shows that a series of transfer function curves generated based on a model with 
parallel flow in the fractures and matrix can capture the range of behavior of the UZ transport 
fracture-matrix interaction submodel as long as the curves span the ranges of the parameters in 
p , the vector ( 1 p , p ) . The documentation for the FEHM V2.21 (LANL 2003 [165741]) 
contains information on the formatting of the input files to invoke this portion of the particle 
tracking transport model. 
III-2. GENERATION OF TRANSFER FUNCTIONS 
This section describes the process for generating the transfer function curves. This is 
accomplished through a numerical solution of the model domain depicted in Figure 6-5. As 
described in Section 6.4.3, both a Discrete Fracture Model (DFM) and a dual-k model 
conceptualization is implemented as part of the abstraction. For the DFM, a 2-D DFM was set up 
to perform transport simulations using the advection-dispersion module of FEHM V2.21 (LANL 
2003 [165741]). The model consists of a regular grid domain consisting of regular spacing of 6 
m in the z direction (51 grid points in this direction for a total length of 300 m), and increasing 
grid spacing into the matrix in the x direction, starting with the first column of nodes of width 
equal to that of a fracture (22 grid points in this direction). In the model simulations, fracture 
properties are given to the nodes of the first column, and the remaining nodes are given matrix 
properties. To ensure that parallel flow occurs in the fracture and matrix in the z direction, a flow 
permeability barrier is established between the fracture and matrix. Furthermore, for injection 
into the matrix, water is input and output from the boundary nodes in proportion to the volume of 
that cell. This model design ensures that flow streamlines remain completely in the z direction. 
Finally, note that although the transfer functions being used are for unsaturated transport, there is 
no requirement that this submodel use unsaturated flow to generate them, as long as the water 
content values are known. Therefore, for simplicity, these simulations were performed for 
saturated flow conditions, with the fracture and matrix porosities used instead of water contents. 
For the dual-k model, a simple grid was constructed with identical spacings in the x direction, 
but only one matrix cell in the y direction. Aside from the different grid, cell numbering, and 
application of boundary conditions, the process for generating the breakthrough curves and 
transfer functions is the same for the dual-k model. Furthermore, the use of these curves in an 
FEHM particle tracking simulation is completely transparent, requiring only a choice of which 
transfer function file to use. 
In the simulations to generate the transfer functions, parameter 3 p is varied systematically from 
fracture-dominated to matrix-dominated flow by varying the relative water flux values in the 
fractures and matrix. Ranges of other parameter values consistent with the span of those 
parameters required for the UZ transport model are also selected. Table III-1 lists the variations 
III-6 January 2004 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
of each parameter that were used in the formulation of the transfer function curves. Note that for 
the sorption coefficient Kd, the fact that the range of values only goes to 100 does not imply that 
the model is incapable of accurately simulating transport behavior for higher values of Kd. In 
Section III-4 below, a procedure for normalizing the transfer function curves is described 
whereby higher values of Kd are properly handled. This procedure allows the code to cover 
arbitrarily large values of Kd without the need to include transfer function curves that extend to 
such large values. 
p , 3 2 
A four-dimensional matrix of parameters were established with the parameter values listed in the 
table, and the transfer function curves for each were computed, for a total of 11x12x3x10=3960 
values of the parameter vector ( 1 p , p ) . 
+ 
Table III-1. 
f /( 
Parameter 
) f f m f F = f f 
D m 
3 
List of parameter values used to compute transfer function curves 
# of 
values List of values 
0.01, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.99 11 
12 1.e-8, 3.e-9, 1.e-9, 3.e-10, 1.e-10, 3.e-11, 1.e-11, 3.e-12, 
1.e-12, 3.e-13, 1.e-13, 1.e-20 
0.01, 0.1, 0.5 3 
0., 0.3, 0.5, 1., 3., 5., 10., 30., 50., 100. 10 
3960 p , p ) in excel spreadsheet parameter runs.xls 3 2 ( 1 p , 
January 2004 III-7 
f  
d K 
Total: 11x12x3x10 
Note: Kd range of 0-100 does not mean that the model is limited to Kd values of 100 or less. See Section III-4 for 
details on the normalization procedure for handling higher values of Kd. 
Two runs of the model are performed for each parameter set: one where solute mass is injected 
in the fracture, and another where mass is injected in the matrix. The list of parameter values 
p , p ) are given in the Excel spreadsheet parameter runs 3960.xls, along with the 2 ( 1 p , 
underlying fehm input parameters for each simulation. The code fehm2post V1.0 (LANL 2003 
[165754]) was used to execute the multiple realizations and to post-process the results to obtain 
the transfer functions. The post-processing itself (executed by fehm2post) was performed using 
the software discrete_tf V1.1 (LANL 2003 [165742]). The resulting output from these runs is 
then concatenated by hand and the appropriate header information inserted by hand to conform 
to the input required by FEHM. The file called uz_tfcurves_nn_3960.in is the transfer function 
file for the DFM formulation, whereas the corresponding file for the dual-k formulation is 
uz_tfcurves_dualk_nn_3960.in. These files, along with the excel spreadsheet mentioned above, 
and the control files required for execution of these runs is available as DTN: 
LA0311BR831229.001. 
III-3. DISCUSSION OF FRACTURE-MATRIX SUBMODEL BEHAVIOR 
In this section we explore the behavior of the fracture-matrix submodel for the two alternate 
formulations, DFM and dual-k. In contrast to the discrete fracture based transfer function model, 
the dual-k formulation has a single matrix block for each fracture block. All other aspects of the 
MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
parameterization are kept the same. Figures III-1 and III-2 compare the DFM and dual-k 
transport models for a flow situation consisting of 60% fracture flow, 40% matrix flow, over a 
range of diffusion coefficients given in Table III-2. Breakthrough curves from the fracture are 
presented for solute injection into the fracture at the inlet. Also shown are vertical, dotted red 
lines representing the limiting behavior expected for fracture transport and no diffusion 
(dimensionless time of 1) and composite medium behavior for the case of infinitely large 
diffusion. Composite medium behavior is attained when the time for diffusion across the model 
domain B is of that same order or smaller than transport time along the flow path. Under these 
conditions, the travel time through the system reduces to 
R mm m mf Rf  = (III-29) comp fm f f 
where 
and 
comp 
+
+ 
f m and mm are the fluid masses in a cell for the fracture and matrix, respectively, and f f 
m f are the fluid mass fluxes for the fracture and matrix, respectively. Intuitively, Eq. III-29 
is derived by picturing a solute molecule traveling with fluid of total flux given by the 
denominator, with total storage volume (including sorption sites) given by the numerator. The 
time  is an important characteristic time for this system, and serves as a reference for 
understanding the behavior and deriving the detailed method for using transfer function, 
described in the next section. 
Diffusion coefficients used in simulations 
Curve Label Diffusion Coefficient (m2/s) 
a 1.e-8 
b 1.e-10 
c 1.e-11 
d 1.e-12 
e 1.e-13 
f 1.e-20 
III-8 
Table III-2. 
MDL-NBS-HS-000020 REV 00 
U0065 
January 2004 Injection in Fracture, Breakthrough in Fracture 
DFM Conceptual Model 
e 
d 0.6 
0.4 c 
0.2 b 
a 
0.0
1e-01 1e+03 1e+01 
1e+05 
Output DTN: LA0311BR831229.001 
t/Rf f 
Figure III-1. Transfer Function Computed for the Discrete Fracture Model Formulation: Solute Injection 
in Fracture, Breakthrough in Fracture, Diffusion Coefficients Given in Table III-2 
January 2004 III-9 MDL-NBS-HS-000020 REV 00 
Normalized Mass Flux 
U0065 Particle Tracking Model and Abstraction of Transport Processes 
1.0 
f 
0.8
Injection in Fracture, Breakthrough in Fracture 
Dual-k Conceptual Model 
0.6 
c 
0.4 
f 0.2 b e 
a 
0.0
1e-01 1e+05 1e+03 1e+01 
t/Rff 
Output DTN: LA0311BR831229.001 
Figure III-2. Transfer Function Computed for the Dual-k Model Formulation: Solute Injection in Fracture, 
Breakthrough in Fracture, Diffusion Coefficients Given in Table III-2 
For each model, the behavior at the extremes of low and high diffusion are similar. For 
negligible diffusion, travel times approach a dimensionless time of 1, and the normalized mass 
flux attains a plateau at 1, which is to say that all mass injected in the fracture leaves via the 
fracture. By contrast, at high diffusion, travel times approach  , and the plateau of comp 
normalized mass flux approaches a value of f F (0.6 in this example), meaning that at this 
extreme, the probability of mass in the fracture leaving via the fracture equals the fraction of the 
total flow traveling through the fracture. It is at the intermediate values of diffusion coefficient 
that the two models diverge. Specifically, the dual-k formulation tends to predict early 
breakthrough due to rapid transport through the fracture for a significant portion of the mass, 
compared to the DFM formulation, for which smooth breakthrough curves at progressively 
January 2004 III-10 MDL-NBS-HS-000020 REV 00 
Normalized Mass Flux 
U0065 Particle Tracking Model and Abstraction of Transport Processes 
1.0 
d 
0.8
U0065 Particle Tracking Model and Abstraction of Transport Processes 
longer travel times are predicted for increasing diffusion coefficients. This means that the dual-k 
formulation ought to predict earlier breakthrough for the first-arriving mass if the parameter 
ranges of our model are in this intermediate range. Conversely, the models should be similar 
behavior for high diffusion or low diffusion. 
III-4. ADDITIONAL IMPLEMENTATION CONSIDERATIONS 
In this section we address some additional details concerning the implementation of the transfer 
function methodology. These considerations concern the nondimensionalization of the transfer 
function curves, and the method by which the model handles cases in which some parameters are 
selected that fall at or outside the range of values assumed when generating the transfer function 
curves. 
comp 
In Figures III-1 and III-2, we demonstrated that, in addition to the fracture travel time f R f used 
to nondimensionalize time in the transfer function curves, the composite travel time  is a 
natural parameter for bracketing the behavior of the f/m interaction submodel. Time in the 
f R f , which contains no information relevant to the 
. To make the method more robust, we have comp 
transfer functions supplied to FEHM is t / 
extreme of long travel times, which approach  
found that an improved nondimensionalization for time can be made as follows: 
f f t = (Eq. III-30) 
. R f f comp 
Assuming, as is the case for the UZ transport model, that  R  , Eq. III-26 normalizes f f comp 
 
t / 
the breakthrough times to values in the approximate range of 0 and 1 in Figures III-1 and III-2. 
Because FEHM reads in time values of f R f , we need a means for converting these to 
dimensionless times given by Eq. III-30. This is done by first dividing the top and bottom of Eq. 
III-30 by f R f : 
t / R  .1 f f 
 / f f comp 
The FEHM input time t / f R f minus 1 is the numerator, so we simply need to determine a 
p , p ) that can be used to express the 3 relation involving the dimensionless parameters ( 1 p , 
denominator. For this we first recognize the following relation (obtained from simple algebra 
from Eqs. III-26 to III-28: 
f 
>> 
(Eq.III-31) 
(Eq. III-32) = 
b  
t = 
p2 3 p 
p1 
R  .1
2
B m 
m f 
 . 
. 
 
.
.
. .. 
. 
f 
t . R  
. .
.
. 
b  and B m  are proportional to the fluid mass in the fracture Alternatively, recognizing that 
and matrix, respectively, then this expression reduces to: 
III-11 January 2004 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
p 3 fm (Eq. III-33) 2
p
p
1 f f 
An equivalent expression using the definition f ) is f f /( m f f f + 
(Eq. III-34) F = f 
2 1 p3 
comp Returning to the definition of  
manipulations: 
R m R m f m m f m m m 3 2 2 
= 
F =
p
p 1
p + 
(Eq. III-29), we perform the following algebraic 
F R ) =   = R F R F R ) ( 1 ( ) 1 ( comp f f f m m f f f f f f 
R
R 
p p 
p 
p
p 
 
f f 
f
f m f f f f 1 1 
 = 
 
comp 
 
m / f f 
+ 
(Eq. III-35) 
As a guide to this series of steps, we use Eqs. III-30, III-33, and III-28, along with the definitions 
F f /( f f ) , m / f , and R  . Finally, the denominator / 1 
=
f f f m m f f f f m 
2 
 
Rf / 
+
3 
p p3 
=
m
1 
+
comp 
2 1 

2 
=
3 
 
p + 
The important point here is that the transformation of Eq. III-31 can be made by subtracting 1 
from the input dimensionless time and dividing by the expression in Eq. III-36. This operation is 
performed by FEHM upon reading in the transfer function curves. Then, after the normalized 
time for a particle t is obtained in the particle tracking algorithm, Eq. III-30 is used to back out 
the dimensional value of time of the particle. By using this approach, we are taking advantage of 
the self-similarity of the family of curves such as those in Figures III-1 or III-2. That is, even if 
p , the parameters ( 1 p , p ) at a given location in the model are not exactly those used to 
generate the transfer function, the use of the times f R f and comp from the model at a given 
grid cell provide a means for scaling the transfer function accordingly. Also, because we 
generate a relatively large number of transfer function curves (3960), it is likely that in most 
instances a curve fairly close to the parameters used in the transfer function will be found. 
Despite the effectiveness of this method, we have found that there are a few cases for which 
special consideration needed to be made. This is because of the extraordinarily wide range of 
parameter values required to be covered in the TSPA model. As a result, the way in which the 
model handles some of the extreme values of certain parameters is through the use of special 
rules designed to achieve accuracy. These methods, described below, all call for the adjustment 
+
+ 
+ 
in Eq. III-33 is obtained through further algebra and the use of Eq. III-34: 
MDL-NBS-HS-000020 REV 00 
. 
p (1. p ) 
(Eq. III-36) 
January 2004 
=
f  . = 
III-12 U0065 Particle Tracking Model and Abstraction of Transport Processes 
at a given location in the model so as to yield the 3 2 p , of one or more of the parameters ( 1 p , p ) 
desired behavior. Details are given below. 
Low Diffusion Coefficient: It is often desirable to lower the diffusion coefficient to extremely low 
values to examine this end-member case. Furthermore, colloids are low-diffusion species that 
require accuracy at low values of D . The most fool-proof way to do this is to not use the m 
1 p and 2 p , so in the search algorithm we need to account for the fact that below a 
transfer function model all, but instead to simply route the particles through the model with 
advection and dispersion only. However, if this option is not chosen, we still require that the 
model perform properly at the low end of diffusion. The diffusion coefficient only affects 
parameters 
minimum value of D (10-18 m2/s in the code), the precise values of these parameters are not m 
3 p , 1 p 
2 p , are assigned values that were actually used in the generation of the low- diffusion 
1 p and 2 p , are deimportant. 
To ensure that the search algorithm locates a curve with the correct value of 
and 
transfer function curves (see Table III-1), so that during the search, 
emphasized and 
that the code finds the portion of the parameter space with the correct values for 
3 p is in essence the only parameter considered. In doing so, we are ensuring 
3 p . If this is not 
done, the least squares method for selecting the correct transfer function curve can sometimes 
compensate for the extreme parameters chosen by selecting an undesirable part of the parameter 
space. With the approach just described, the method is forced to select a low-diffusion regime 
while obtaining the correct ratio of travel times in the fracture and matrix. 
High Matrix Sorption: Similar to the case just described, an extremely large value of m R beyond 
the range used in the transfer functions causes problems for the search algorithm. When 
searching for the closest transfer function, the uncorrected method compensates for a large 
by selecting a fracture-dominated flow case to attain as low a value of 
the calculation of 
m R 
3 p as possible. Similarly, 
1 p is also affected. Thus, to correct for this case, the maximum value of m R 
. In 
used in the transfer function curve generation (1000) is used as an upper limit when searching for 
the correct transfer function curve. However, note that this does not mean that the matrix 
retardation is limited to that value in the particle tracking travel time calculation. Recall that the 
transfer function curves themselves are normalized using Eq. III-30, which includes comp 
contrast to the determination of the closest transfer function curve, the actual value of 
in computing  
m R is used 
, which results in a determination of travel time that is scaled by the actual comp 
sorption set in the matrix. Thus the correction is applied only to find an appropriate transfer 
function curve, and the method for nondimensionalizing those curves ensures that an 
appropriately large travel time is reproduced for the case of high matrix sorption. 
Fracture-Dominated Flow: The parameterization of the transfer function curves is based on a 
model that has some flow both the fracture and matrix. When the flow is fracture dominated 
( 9 > 0.9), the details of the actual fraction of flow should be unimportant, since advective f F 
, the algorithm for finding the transfer function will inappropriately attempt to select 
transport in the matrix should be negligible. However, without correction for cases where 
f F 99 . 0 > 
January 2004 III-13 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
curves with high m R to compensate for the fact that transfer functions with extremely large f F 
are not included. To correct for this problem, the code makes use of the following rearranged 
form of Eq. III-30: 
F ) 1 ( . f 1 (Eq. III-37) 3 
p
p2 Ff 
, the code uses 0.99 and the values of When 99 f F > 0. 1 p and 2 p to compute 3 p for the 
purposes of selecting the transfer function curve. This assures that a fracture-dominated transfer 
function is chosen with appropriate values for the other diffusion and sorption parameters. 
Matrix-Dominated Flow: For this extreme, it is desirable to bypass the transfer function method 
altogether, since the travel time is trivially found to be m R m . Allowing the transfer function 
algorithm to be used for this case causes problems because the normalization procedure 
implicitly assumes that the matrix travel time is longer than the fracture travel time. To cover the 
special case of essentially no flow in the fracture, the travel time is assigned a value of  , comp 
which reduces to m R m under these conditions. 
III-5. ADAPTING THE ACTIVE FRACTURE MODEL FOR TRANSPORT 
The AFM of Liu et al. (1998 [105729]) is formulated on the basis that only a fraction of the 
fractures flow. This requires that adjustments be applied to the interface area and the mean 
spacing between flowing fractures. These adjusted parameters can then be used in the transport 
model calculations. Examining the individual terms of the mass balance for the fracture derived 
in Section III-1, the accumulation term (Eq. III-1) is unchanged by the AFM, because it is based 
on the storage volume in the fracture, as well as sorption parameters. Storage volumes in the 
dual-k flow fields are fully defined by the fracture volume fractions and the fluid saturations in 
the fracture continuum. Fluid saturations are model output from the flow simulations, and no 
further correction for transport is required for the accumulation term. Likewise, the Darcy 
velocity in the advection term (Eq. III-2) is fully defined by the flux through the fracture 
continuum, so no AFM corrections are required for advection either. The diffusion term (Eq. III- 
Cm 3) consists of a flux  times an interfacial area, which on geometrical grounds for mDm x x=b 
the simple geometry of our transfer function model is z d. . This interfacial area term, according 
to the AFM, should be reduced to account for the fact that not all fractures are flowing. Liu et al. 
(1998 [105729], Eq. 12), gives the following reduction factor for correcting the advective flux 
term (note: nomenclature from Liu et al. 1998 [105729] is used in this equation): 
nf a , Afm a , = R (Eq. III-38) d 
da Afm nf 
 . 
. 
 
.
.
. .. 
. 
p = 
. .
.
. 
Although Liu et al. (1998 [105729]) refers to R as the F-M interface area reduction factor, it is 
clear from their derivation that the term represents the ratio of the fluxes for the uncorrected and 
 
.
.
. .
.
. 
III-14 January 2004 MDL-NBS-HS-000020 REV 00 U0065 Particle Tracking Model and Abstraction of Transport Processes 
corrected cases, correcting for both the interface area and the transport length scale associated 
with the distance between the flowing fractures (the third term on the right hand side of this 
equation). Therefore, in the FEHM simulations, AFM-based adjustments should be applied to 
both the interface area and the spacing B . The term d / is the adjustment to the fracture a d 
spacing, and is accounted for by adjusting the spacing B in the FEHM transport simulations 
using the following relation (Liu et al. 1998 [105729], Eq. 17): 
S  (Eq. III-39) e 
d 
da 
Thus, the geometric spacing is divided by e S  to obtain the spacing between flowing fractures. 
The interface-area portion of the adjustment consists of the first two terms on the right hand side 
of Eq. III-38, the first to account for the reduction in wetted area within an individual fracture, 
and the second to account for the reduction in area associated with a smaller number of wetted 
fractures. This term can be related to the AFM parameters using Eqs. 13 and 14 of Liu et al. 1998 
[105729]: 
 .  1 , nf a Afm a , = S = S (Eq. III-40) Se e e nf Afm 
 
.
.
. .
.
. 
. .
.
. 
To implement this area reduction term in FEHM, we divide the geometrically defined aperture b 
by e S . The adjustment to b is for convenience, and actually arises from the need to adjust the 
interface area in the fracture transport equation. These adjustment factors have been incorporated 
into FEHM so that for given AFM model parameters, B and b , input as geometrically defined 
parameters, are converted to hydrologic parameters for use in the transfer function methodology. 
= 
 
.
. 
III-15 January 2004 MDL-NBS-HS-000020 REV 00 Particle Tracking Model and Abstraction of Transport Processes 
INTENTIONALLY LEFT BLANK 
III-16 MDL-NBS-HS-000020 REV 00 
U0065 
January 2004