Conceptual Model and Numerical Approaches for Unsaturated Zone Flow and Transport Rev 01, ICN 00
MDL-NBS-HS-000005

September 2004 

1. PURPOSE 
The purpose of this model report is to document the conceptual and numerical models used for 
modeling unsaturated zone (UZ) fluid (water and air) flow and solute transport processes. This 
work was planned in Technical Work Plan for: Unsaturated Zone Flow Model and Analysis 
Report Integration (BSC 2004 [DIRS 169654], Sections 1.2.5, 2.1.1, 2.1.2 and 2.2.1). The 
conceptual and numerical modeling approaches described in this report are mainly used for 
models of UZ flow and transport in fractured, unsaturated rock under ambient conditions. 
Developments of these models are documented in the following model reports: 
 
UZ Flow Model and Submodels 
 
Radionuclide Transport Models under Ambient Conditions. 
Conceptual models for flow and transport in unsaturated, fractured media are discussed in terms 
of their applicability to the UZ at Yucca Mountain. The rationale for selecting the conceptual 
models used for modeling of UZ flow and transport is documented. Numerical approaches for 
incorporating these conceptual models are evaluated in terms of their representation of the 
selected conceptual models and computational efficiency; and the rationales for selecting the 
numerical approaches used for modeling of UZ flow and transport are discussed. 
This report also documents activities to validate the active fracture model (AFM) based on 
experimental observations and theoretical developments. The AFM is a conceptual model that 
describes the fracture-matrix interaction in the UZ of Yucca Mountain. These validation 
activities are documented in Section 7 of this report regarding use of an independent line of 
evidence to provide additional confidence in the use of the AFM in the UZ models. The AFM 
has been used in UZ flow and transport models under both ambient and thermally disturbed 
conditions. Developments of these models are documented in the following model reports: 
 
UZ Flow Model and Submodels 
 
Radionuclide Transport Models under Ambient Conditions 
 
Particle Tracking Model and Abstraction of Transport Processes 
 
Drift Scale Radionuclide Transport 
 
Mountain-Scale Coupled Processes (TH/THC/THM) 
 
Drift-Scale THC Seepage Model 
 
Multiscale Thermohydrologic Model 
 
Drift-Scale Coupled Processes (DST and TH Seepage) Models 
 
Drift Scale THM Model 
The model validation activities reported in this report were planned in the TWPs (BSC 2004 
[DIRS 169654], Section 2.2.1; BSC 2002 [DIRS 160819], Section I-1-3) and there was a 
deviation from the TWPs in this report. The currently available data from the 
large-infiltration-plot test at Alcove 8/Niche three have not been used for model validation 
because they are not suitable for validating the AFM. The currently available data were obtained 
under testing conditions corresponding to high fracture saturations. In this case, simulation 
results are not sensitive to the AFM parameters. 

Caveats and limitations include use of the van Genuchten relation for the active fracture 
continuum, use of porous-medium equivalence for describing flow and transport in fracture 
networks, and the assumption of steady-state liquid flow in the UZ. More discussions on these 
caveats and limitations are presented in Section 6 of this report. 

2. QUALITY ASSURANCE 
Development of this model report and the supporting modeling activities have been determined 
to be subject to the requirements in Quality Assurance Requirements and Description 
(DOE 2004 [DIRS 171539]). Approved quality assurance (QA) procedures identified in the 
technical work plan (TWP) (BSC 2004 [DIRS 169654], Section 4) have been used to conduct 
and document the activities described in this model report. The TWP also identifies the methods 
used to control the electronic management of data (BSC 2004 [DIRS 169654], Section 8.4) 
during the modeling and documentation activities. 
This model report describes the conceptual model of flow and transport in the UZ and the 
numerical approaches for its implementation. The UZ is part of the natural barrier classified in 
the Q-List (BSC 2004 [DIRS 168361]) as Safety Category, because of the barriers importance 
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 63.114 [DIRS 156605]. The report 
contributes to performance assessment; the conclusions do not directly impact engineered 
features important to preclosure safety, as defined in AP-2.22Q. 

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3. USE OF SOFTWARE 
The software programs used in this study are listed in Table 3-1. These are appropriate for the 
intended application and were used only within the range of validation. They were obtained 
from Software Configuration Management, and qualified under LP-SI.11Q-BSC, Software 
Management. 
Table 3-1. Qualified Software Used in This Report 
Software Name Version 
Software 
Tracking 
Number (STN) Platform Operating System 
DIRS Reference 
Number 
TOUGH2 1.4 10007-1.4-01 SUN ULTRASPARC, SUNOS 5.5.1, OSF1 LBNL 2000 
DEC ALPHA V4.0, OSF1 V5.1 [DIRS 146496] 
T2R3D 1.4 10006-1.4-00 SUN, DEC ALPHA, UNIX, WINDOWS LBNL 1999 
PC 95/98/NT 4.0 [DIRS 146654] 
infil2grid 1.7 10077-1.7-00 PC, DEC ALPHA DOS V4.00.1111, LBNL 2002 
OSF1 V4.0 [DIRS 154793] 
DIRS = Document Input Reference System; STN=software tracking number 
Standard Excel spreadsheets and display graphics programs (Excel 97 SR-1 and Tecplot V7.0) 
were also used but are not subject to software QA requirements. All information needed to 
reproduce the work using these standard software programs is included in this report, with 
references specified. 

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4. INPUTS 
4.1 DIRECT INPUT 
This report describes conceptual models and numerical approaches for UZ flow and transport. 
No data from the Technical Data Management System (TDMS) are used as direct input in this 
report, and no output data tracking numbers were used as direct input by the downstream 
technical products. Data used for model validation are presented in Section 7. 
4.2 CRITERIA 
The general requirements to be satisfied by the total system performance assessment (TSPA) are 
stated in 10 CFR 63.114 [DIRS 156605]. Technical requirements to be satisfied by the TSPA 
are identified in the Yucca Mountain Project Requirements Document (Canori and Leitner 2003 
[DIRS 166275]). The acceptance criteria that will be used by the Nuclear Regulatory 
Commission (NRC) to determine whether the technical requirements have been met are 
identified in Yucca Mountain Review Plan, Final Report (YMRP) (NRC 2003 [DIRS 163274]). 
The pertinent requirements and criteria for this report are summarized in Table 4-1. 
Table 4-1. Project Requirements and Acceptance Criteria Applicable to This Analysis Report 
Requirement 
YMRP Acceptance 
Numbera 
Requirement Titlea 
10 CFR 63 Link 
Criteriab 
Requirements for Performance 
10 CFR 63.114 (a)-(c) 
2.2.1.3.6.3, criteria 1 to 4 
PRD 002/T-015 
Assessment 
and (e)-(g) 
2.2.1.3.7.3, criteria 1 to 5 
a 
b 
Canori and Leitner (2003 [DIRS 166275]) 
NRC (2003 [DIRS 163274]). 
The acceptance criteria identified in Sections 2.2.1.3.6.3 and 2.2.1.3.7.3 of the YMRP 
(NRC 2003 [DIRS 163274]) are included below. In cases where subsidiary criteria are listed in 
the YMRP for a given criterion, only the subsidiary criteria addressed by this scientific analysis 
are listed below. Explanation of how this report meets the acceptance criteria below is given in 
Section 8.3. 
Note that the acceptance criteria in Table 4-1 are different from those identified in the TWP 
(BSC 2004 [DIRS169654], Table 3-1). After the TWP was completed, the applicability of 
acceptance criteria for the report are reevaluated and additional criteria applicable to this report 
are identified and included in Table 4-1. 
Acceptance Criteria from Section 2.2.1.3.6, Flow Paths in the Unsaturated Zone. 
Acceptance Criterion 1, System Description and Model Integration Are Adequate. 
(1) 
Total system performance assessment adequately incorporates, or bounds, 
important design features, physical phenomena, and couplings, and uses consistent 
and appropriate assumptions throughout the flow paths in the unsaturated zone 
abstraction process. Couplings include thermal-hydrologic-mechanical-chemical 
effects as appropriate; 

(2) 
The aspects of geology, hydrology, geochemistry, physical phenomena, and 
couplings that may affect flow paths in the unsaturated zone are adequately 
considered. Conditions and assumptions in the abstraction of flow paths in the 
unsaturated zone are readily identified and consistent with the body of data presented 
in the description; 
(3) 
The abstraction of flow paths in the unsaturated zone uses assumptions, technical 
bases, data, and models that are appropriate and consistent with other related U.S. 
Department of Energy abstractions. For example, the assumptions used for flow 
paths in the unsaturated zone are consistent with the abstractions of quality and 
chemistry of water contacting waste packages and waste forms, climate and 
infiltration, and flow paths in the saturated zone (Sections 2.2.1.3.3, 2.2.1.3.5 and 
2.2.1.3.8 of the Yucca Mountain Review Plan, respectively). The descriptions and 
technical bases are transparent and traceable to site and design data. 
(4) 
The bases and justification for modeling assumptions and approximations of 
radionuclide transport in the unsaturated zone are consistent with those used in model 
abstractions for flow paths in the unsaturated zone and thermal-hydrologic-
mechanical-chemical effects; 
(9) 
Guidance in NUREG-1297 (Altman et al. 1988 [DIRS 103597]) and 
NUREG-1298 (Altman et al. 1988 [DIRS 103750]), or other acceptable approaches 
for peer review and data qualification is followed. 
Acceptance Criterion 2: Data Are Sufficient for Model Justification. 
(6) 
Accepted and well-documented procedures are used to construct and calibrate 
numerical models; 
(7) 
Reasonably complete process-level conceptual and mathematical models are used 
in the analyses. In particular: (i) mathematical models are provided that are 
consistent with conceptual models and site characteristics; and (ii) the robustness of 
results from different mathematical models is compared; 
Acceptance Criterion 3: Data Uncertainty is Characterized and Propagated Through the 
Model Abstraction. 
(1) 
Models use parameter values, assumed ranges, probability distributions, and 
bounding assumptions that are technically defensible, reasonably account for 
uncertainties and variabilities, and do not result in an under-representation of the risk 
estimate; 
(6) 
Uncertainties in the characteristics of the natural system and engineered materials 
are considered. 

Acceptance Criterion 4, Model Uncertainty is Characterized and Propagated Through the 
Model Abstraction. 
(1) 
Alternative modeling approaches of features, events, and processes, consistent 
with available data and current scientific understanding, are investigated. The results 
and limitations are appropriately considered in the abstraction; 
(3) 
Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog 
information and process-level modeling studies; and the treatment of conceptual 
model uncertainty does not result in an under-representation of the risk estimate; 
Acceptance Criteria from Section 2.2.1.3.7, Radionuclide Transport in the Unsaturated 
Zone). 
Acceptance Criterion 1: System Description and Model Integration Are Adequate. 
(1) 
Total system performance assessment adequately incorporates important design 
features, physical phenomena, and couplings, and uses consistent and appropriate 
assumptions throughout the radionuclide transport in the unsaturated zone abstraction 
process; 
(2) 
The description of the aspects of hydrology, geology, geochemistry, design 
features, physical phenomena, and couplings, that may affect radionuclide transport 
in the unsaturated zone, is adequate. For example, the description includes changes in 
transport properties in the unsaturated zone, from water-rock interaction. Conditions 
and assumptions in the total system performance assessment abstraction of 
radionuclide transport in the unsaturated zone are readily identified, and consistent 
with the body of data presented in the description; 
(3) 
The abstraction of radionuclide transport in the unsaturated zone uses 
assumptions, technical bases, data, and models that are appropriate and consistent 
with other related U.S. Department of Energy abstractions. For example, the 
assumptions used for radionuclide transport in the unsaturated zone are consistent 
with the abstractions of radionuclide release rates and solubility limits and flow paths 
in the unsaturated zone (Sections 2.2.1.3.4 and 2.2.1.3.6 of the Yucca Mountain 
Review Plan). The descriptions and technical bases provide transparent and traceable 
support for the abstraction of radionuclide transport in the unsaturated zone; 
(5) 
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; and 
(6) 
Guidance in NUREG-1297 (Altman et al. 1988 [DIRS 103597]) and 
NUREG-1298 (Altman et al. 1988 [DIRS 103750]), or other acceptable approaches 
for peer review and data qualification is followed. 

Acceptance Criterion 3: Data Uncertainty is Characterized and Propagated Through the 
Model Abstraction. 
(1) Models use parameter values, assumed ranges, probability distributions, and 
bounding assumptions that are technically defensible, reasonably account for 
uncertainties and variabilities, and do not result in an under-representation of the risk 
estimate; 
Acceptance Criterion 4: Model Uncertainty is Characterized and Propagated Through the 
Model Abstraction. 
(1) 
Alternative modeling approaches of features, events, and processes are considered 
and are consistent with available data and current scientific understanding, and the 
results and limitations are appropriately considered in the abstraction; 
(2) 
Conceptual model uncertainties are adequately defined and documented, and 
effects on conclusions regarding performance are properly assessed. 
(3) 
Consideration of conceptual model uncertainty is consistent with available site 
characterization data, laboratory experiments, field measurements, natural analog 
information and process-level modeling studies; and the treatment of conceptual 
model uncertainty does not result in an under-representation of the risk estimate; and 
(4) 
Appropriate alternative modeling approaches are consistent with available data 
and current scientific knowledge, and appropriately consider their results and 
limitations, using tests and analyses that are sensitive to the processes modeled. For 
example, for radionuclide transport through fractures, the U.S. Department of Energy 
adequately considers alternative modeling approaches, to develop its understanding of 
fracture distributions and ranges of fracture flow and transport properties in the 
unsaturated zone. 
4.3 CODES, STANDARDS, AND REGULATIONS 
No codes or standards, other than those identified in the Project Requirements Documents 
(Canori and Leitner 2003 [DIRS 166275], Table 2-3) and determined to be applicable in 
Table 4-1, were used in this model report. 

5. ASSUMPTIONS 
The UZ is a complex hydrogeological system involving a number of important processes relating 
to fluid flow and solute transport. The assumptions made to develop conceptual model and 
numerical approaches for these processes are presented in Section 6. This report does not 
include assumptions used in the absence of direct confirming data or evidence to perform the 
model activity. Per AP-SIII.10Q, Models, only the latter assumptions need to be presented in 
this section. 

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6. MODEL DISCUSSION
This section discusses the conceptual model and numerical approaches used to describe flow and 
transport processes in the UZ. These processes are closely related to the hydrogeologic features 
of the UZ, which consists of heterogeneous volcanic rocks. These rocks have been welded and 
fractured to varying degrees, and are divided into hydrogeologic units (Montazer and Wilson 
1984 [DIRS 100161], pp. 920) based roughly on the degree of welding. Beginning from the 
land surface, they are the Tiva Canyon welded (TCw), the Paintbrush nonwelded (PTn), the 
Topopah Spring welded (TSw), the Calico Hills nonwelded (CHn), and the Crater Flat 
undifferentiated hydrogeologic units (Figure 6-1). The welded units typically have low matrix 
porosities and high fracture densities, whereas the nonwelded units have relatively high matrix 
porosities and low fracture densities (Montazer and Wilson 1984 [DIRS 100161], pp. 8-9). 
Water in the UZ moving downward through these units is considered to be partitioned between 
fractures (fracture flow) and the rock matrix (matrix flow), as described subsequently in this 
model report. 
The conceptual model of flow and transport processes is a framework to explain these processes 
in the UZ. The current conceptual model is based, to a great extent, on the ideas originally 
presented by Montazer and Wilson (1984 [DIRS 100161], pp. 36-49), and has been developed 
through the evaluation of collected data and the results of modeling studies. A detailed 
discussion of the conceptual model is presented in Sections 6.1 and 6.2. Different numerical 
approaches are available for modeling flow and transport in unsaturated fractured rocks. 
Section 6.3 briefly reviews the numerical approaches and provides an assessment of these 
approaches based on the conceptual model and other practical considerations. The AFM is also 
documented in this section and validated in Section 7. 
This report addresses the features, events, and processes (FEPs) listed in Table 6-1 that were 
taken from the license application FEP List (DTN: MO0407SEPFEPLA.000 [DIRS 170760]). 
The selected FEPs are those associated with the subject matter of this report. The 
cross-reference for each FEP to the relevant sections of this report is also given in Table 6-1. 
Note that in addition to FEPs in Table 6-1, the FEP Diffusion in the UZ (FEP number 
2.2.08.05.0A) is also identified in the TWP (BSC 2004 [169654], Table 2.1.5-1). This FEP is 
not included in this report because the general diffusion process in the UZ is not the key element 
of the conceptual model for UZ flow and transport. 
Table 6-1. FEPs Addressed in This Model Report 
FEP No. FEP Name Relevant Sections of this Report 
2.2.07.02.0A Unsaturated groundwater flow in 
geosphere 
Sections 6.1 and 7 
2.2.07.04.0A Focusing of unsaturated flow 
(fingers, weeps) 
Sections 6.1.7, 6.3.7 and 7 
2.2.07.08.0A Fracture flow in the UZ Section 6.1 
2.2.08.08.0B Matrix diffusion in the UZ Section 6.2.2 
2.2.08.09.0B Sorption in the UZ Section 6.2.3 
2.2.08.10.0B Colloidal transport in the UZ Section 6.2.4 

Figure 6-1. A Simplified Schematic Showing Conceptualized Water Flow through Yucca Mountain 
NOTE: The blue and red colors on the land surface approximately correspond to high and low infiltration rates, 
respectively, while the other colors approximately correspond to infiltration rates in between. 
6.1 CONCEPTUAL MODEL OF FLOW 
This subsection documents the conceptual model of flow used for modeling transport and flow 
within the UZ at Yucca Mountain. The conceptual model is presented by addressing important 
flow issues and processes. 
6.1.1 Infiltration 
Infiltration process refers to the penetration of liquid water (from precipitation) through the 
ground surface and to a depth where it can no longer be withdrawn by evaporation or 
transpiration by plants. Percolation process refers to vertical and lateral flow of liquid water 
within the UZ. Infiltration is the ultimate source of percolation flux at the repository horizon and 
provides the water for flow and transport mechanisms that may move radionuclides from the 
repository to the water table. Infiltration is spatially and temporally variable because of the 
nature of the storm events that supply precipitation (Hevesi et al. 1994 [DIRS 125315]) and 
variation in soil cover and topography. Infiltration is believed to be high on sideslopes and 
ridgetops where bedrock crops are exposed, and fracture flow in the bedrock is able to move 
moisture away from zones of active evaporation (Flint et al. 1994 [DIRS 103135]). 

Significant precipitation (and infiltration) occurs only every few years (Flint et al. 1996 
[DIRS 100147], pp. 4650). In these years, the amount of infiltration still varies greatly, 
depending on storm amplitudes, durations, or frequencies. In very wet years, infiltration pulses 
may infiltrate into Yucca Mountain during a relatively short time period. A more detailed 
discussion of infiltration at Yucca Mountain is documented in a report describing simulation of 
net infiltration for modern and potential future climates (BSC 2004 [DIRS 170007]). 
6.1.2. Fracture and Matrix Flow Component 
This subsection describes fracture and matrix flow component in various geologic layers 
(including the TCw, PTn, TSw and CHn) in the UZ. 
As a result of the relatively high density of interconnected fractures and low matrix 
permeabilities in the TCw, infiltration pulses are expected to move rapidly through the fracture 
system with little attenuation (Bodvarsson et al. 1999 [DIRS 120055], p. 10). This is partially 
supported by pneumatic sensors in the TCw showing little attenuation of the barometric signal in 
monitoring boreholes compared with the barometric signal observed at the land surface 
(Rousseau et al. 1999 [DIRS 102097], p. 89). In this unit, the gas flow paths are considered to be 
similar to those of liquid water. 
Once the unsaturated flow leaves the TCw and enters the PTn, totally different processes are 
evident. Because the PTn has relatively high matrix permeabilities and porosities, and low 
fracture densities, the predominant fracture flow in the TCw is expected to convert to dominant 
matrix flow within the PTn. The measured properties for the PTn and other units are 
documented in BSC (2004 [DIRS 170038], Tables 7 and 8). Pneumatic data are consistent with 
the notion that fracturing within the PTn is limited; the pneumatic signal is propagated 
predominantly through the high-storage matrix, leading to significant attenuation (Ahlers et al. 
1999 [DIRS 109715], p. 49). Similarly, much of the water flow occurs in the relatively 
high-porosity matrix in this unit. As a result, the PTn greatly attenuates infiltration pulses such 
that liquid-water flow below the PTn is approximately in steady state. This interpretation is 
consistent with the results of a modeling study by Wang and Narasimhan (1993 
[DIRS 106793], pp. 354-361). 
The dominance of matrix flow in the PTn unit and the attenuation effects are supported by field 
tests conducted in the same unit. Salve et al. (2003 [DIRS 164470]) performed water release 
tests along a fault within the PTn unit. Water was released under constant-head conditions from 
a 0.3-m interval within a borehole that crosses the fault. A total of 193 L of water during seven 
distinct events was released over two weeks between October 21, 1998, and November 5, 1998. 
Between November 30, 1999, and December 2, 1999, an additional 136 L of water were 
introduced into the same interval during three distinct events lasting 4 to 7 hours (Salve et al. 
2003 [DIRS 164470]). It was observed that during the first release test, the wetting front 
advanced slowly as a result of significant matrix imbibition. It was also found that water that 
imbibed into the matrix was retained for periods extending to at least a few months for the given 
test conditions. Based on these observations and considering that water release rates used in the 
tests were much larger than water percolation rates under ambient conditions, it is concluded that 
the dry porous PTn matrix is capable of attenuating episodic percolation fluxes in localized areas 

(such as around faults) where fast flow would otherwise be expected to dominate (Salve et al. 
2003 [DIRS 164470], p. 282). 
In an early conceptual model of Yucca Mountain, Montazer and Wilson (1984 [DIRS 100161], 
pp. 45-48) indicated that significant lateral flow occurs within the PTn unit. The contrast in 
hydraulic properties at internal layer contacts within the PTn could cause lateral flow. 
Additionally, the transient flow of water from the TCw unit to the PTn unit promotes air 
entrapment, which could further reduce the vertical liquid flux into the PTn. Montazer and 
Wilson (1984 [DIRS 100161], p. 47) also showed that vertical heterogeneities within the PTn 
unit may result in a much larger effective permeability of the unit in the direction of dip, 
compared with the effective permeability in the direction normal to the bedding plane. They 
argued that the combination of this factor and capillary barrier effects might introduce 
considerable lateral flow within the unit. A fine grid simulation reported by Wu et al. 
(2002 [DIRS 161058]) favors the existence of lateral flow within the PTn resulting from 
capillary barrier effects. This conceptual model was further supported by the fact that the site-
scale UZ flow model, considering lateral flow mechanisms within the PTn, better matches the 
observed chloride data within the UZ [UZ Flow Models and Submodels (BSC 2004 
[DIRS 169861], Section 6.5.2)], as shown in Figure 6-2. 
Figure 6-2. Comparison Between Observed and Simulated Chloride Concentration Distribution for 
Borehole USW SD-9 
Source: BSC 2004 [DIRS 169861], Figure 6.5-3. 
NOTE: The simulations were performed with the site-scale UZ flow model with and without lateral flow mechanism in 
the PTn. Some simulation results were removed from the original figure. 

Because of its high fracture density and low matrix permeability, water flow in the TSw (below 
the PTn) is considered to be primarily through the fractures. Assuming a unit hydraulic gradient, 
the matrix percolation rate will be the same as the matrix hydraulic conductivity. Using matrix 
saturated hydraulic conductivities determined from permeabilities measured in core samples 
from the TSw, the calculated matrix percolation rate is a small fraction of the average infiltration 
rate currently estimated (Pruess et al. 1999 [DIRS 117112], p. 283). Therefore, the remainder of 
the flow must be distributed in the fracture network. Calcite-coating data show that most of the 
deposition is found within the fractures in the welded units (Paces et al. 1998 [DIRS 107408], 
p. 37), supporting the hypothesis that fracture water flow is a major flow mechanism within 
TSw. The calcite coating is a signature of liquid-water flow history. Carbon-14 (14C) ages of the 
perched water bodies below the TSw unit ranges from 3,500 to 11,000 years (Yang et al. 1996 
[DIRS 100194], p. 34), again suggesting a fracture-dominated flow within the TSw. The water 
travel times from the ground surface to the perched water zone are much longer for the liquid 
water flowing in the matrix (Bandurraga and Bodvarsson 1999 [DIRS 103949], p. 40, Table 3). 
Because of the small matrix permeabilities, the perched water bodies would be expected to have 
much older ages if they result from matrix water flow within the TSw unit. 
The occurrence of perched water bodies, reported from a number of boreholes at the lower 
portion of the TSw and the upper portion of the CHn (Wu et al. 1999 [DIRS 117167], 
pp. 159-163), indicates that the layers of the TSw basal vitrophyre and the CHn serve as barriers 
to vertical flow and cause lateral flow. The main hydrogeologic units below the repository are 
the CHn and Crater Flat undifferentiated hydrogeologic units. Both of these units have vitric and 
zeolitic components that differ by the degree of hydrothermal alteration (Flint 1998 
[DIRS 100033], pp. 29-33). The zeolitic rocks have low matrix permeabilities and some 
fracture permeability, and therefore a relatively small amount of water may flow through the 
zeolitic units, with most of the water flowing laterally in perched water bodies and then vertically 
down faults (Figure 6-1). On the other hand, similar to the PTn unit, the vitric units have 
relatively high matrix porosity and permeability, and, therefore, mostly porous-medium flow 
predominates. Fracture flow is believed to be limited in these units. 
6.1.3 Fracture-Matrix Interaction 
The transfer of water between fractures and the rock matrix, denoted by fracture-matrix 
interaction, is likely to be limited within welded units at Yucca Mountain (Bodvarsson et al. 
1999 [DIRS 120055], p. 13). The chloride concentration data indicate that perched water was 
recharged mainly from fracture water, with a small degree of interaction with matrix water 
(Yang et al. 1996 [DIRS 100194], p. 55). Studies by Ho (1997 [DIRS 100584], pp. 401-412) 
evaluate methods of incorporating the conceptual model of fracture-matrix interaction into a 
dual-permeability model. He shows that the calibration with observed matrix saturation and 
water-potential data is improved using techniques that reduce the fracture-matrix interaction 
significantly. 
The limited fracture-matrix interaction at the Yucca Mountain site is consistent with many other 
independent laboratory tests as well as theoretical and numerical studies. In a number of 
laboratory experiments, Glass et al. (1996 [DIRS 139237], pp. 67) demonstrated that 
gravity-driven fingering flow is a common flow mechanism in individual fractures. This 
mechanism can reduce the wetted area in a single fracture to fractions as low as 0.01 to 0.001 of 

the total fracture area. However, most of their studies were conducted in analogue fractures 
without interaction with the matrix. Imbibition in the matrix can increase wetted areas of 
fingering flow patterns in individual fractures, as shown in a numerical study of Abdel-Salam 
and Chrysikopoulos (1996 [DIRS 132960], pp. 15371538). In their study, they investigated 
unsaturated flow in a quasi-three-dimensional fracture-matrix system (with spatially variable 
apertures accounting for matrix imbibition). They showed that fingering flow occurs in a 
fracture, but matrix imbibition will reduce the degree of fingering. Therefore, while fingering 
flow in individual fractures is an important mechanism for reducing fracture-matrix interaction, 
its effects may not be as significant as shown in individual fracture experiments that do not 
incorporate matrix imbibition. 
In a theoretical study, Wang and Narasimhan (1993 [DIRS 106793], pp. 329335) indicated that 
the wetted area in a fracture under unsaturated flow conditions is generally smaller than the 
geometric interface area between fractures and matrix, even when fingering flow does not occur. 
This results from the assumption that liquid water in an unsaturated fracture occurs as saturated 
segments that cover a portion of the fracture-matrix interface area. On the other hand, in a recent 
laboratory experiment study, Tokunaga and Wan (1997 [DIRS 139195]) demonstrated that water 
film flow could be important in unsaturated fractures. However, note that in their experiments, 
water film flow becomes important only when the matrix is nearly saturated and water flow 
occurs from matrix to fractures, as indicated by the conditions of their experiment. Therefore, at 
this point, we can hypothesize that liquid water generally exists as saturated segments around 
contact points in unsaturated fractures. The distribution of liquid water in this form will reduce 
the fracture-matrix interaction (as compared to the case in which the whole geometric interface 
area is considered to contribute to flow and transport between fractures and matrix). 
Liu et al. (1998 [DIRS 105729], p. 2645) suggested that in unsaturated, fractured rocks, fingering 
flow occurs at both a single fracture scale and a connected fracture-network scale (Figure 6-3). 
This is supported in a study of Kwicklis and Healy (1993 [DIRS 100587], pp. 40974099). They 
used numerical simulations to investigate liquid water flow in a simple, unsaturated fracture 
network and found that a large portion of the connected fracture network played no role in 
conducting the flow when the fractures do not have uniform apertures. The fingering flow at a 
network scale has important effects on large-scale flow and transport, and significantly 
contributes to the reduction of fracture-matrix interaction. 
Studies also showed that fracture coating might have important effects on fracture-matrix 
interaction. Thoma et al. (1992 [DIRS 139189]) performed experiments on actual coated and 
uncoated tuff fractures and observed that the low-permeability coatings inhibited matrix 
imbibition considerably. In contrast, fracture coatings may in some cases increase the 
fracture-matrix interaction when microfractures develop in the coatings (Sharp et al. 1996 
[DIRS 139240], p. 1331). Therefore, fracture coating may or may not result in fracture-matrix 
interaction reduction. Coating effects are not considered in modeling flow and transport in the 
UZ at Yucca Mountain. 

Figure 6-3. A Simplified Schematic for Water Flow in Fractures Characterized by Fingering Flow at 
Different Scales 
Although several mechanisms exist for limiting fracture-matrix interaction in the UZ, as 
discussed above, fingering flow at a fracture network scale is considered to be the key 
mechanism (Liu et al. 1998 [DIRS 105729]; Glass et al. 1996 [DIRS 139237], pp. 6-7). The 
AFM based on this mechanism (Liu et al. 1998 [DIRS 105729]) is used for modeling 
fracture-matrix interaction. This model is documented in Section 6.3 of this report. 
6.1.4 Perched Water 
Perched water is the groundwater in saturated zones that is above or not directly connected to the 
static water table (Freeze and Cherry 1979 [DIRS 101173], p. 45), and may occur when large 
permeability differences exist between geologic units. Perched water zones at Yucca Mountain 
were reported from a number of boreholes at the lower portion of the TSw and the upper portion 
of the CHn. The field tests indicated that perched water zones with very different water volumes 

exist at Yucca Mountain (Bodvarsson et al. 1999 [DIRS 120055], p. 14; Wu et al. 1999 
[DIRS 117167]). 
The presence of perched water has important implications for the travel times and flow paths of 
water through the UZ at Yucca Mountain (Figure 6-4). First, perched water 14C data indicates 
that apparent age estimates of perched water bodies range from approximately 3,500 to 
11,000 years (Yang et al. 1996 [DIRS 100194], p. 34), suggesting dominant fracture flow in the 
TSw unit (Section 6.1.2). Second, the occurrence of perched water bodies indicates that the 
layers of the TSw basal vitrophyre and the CHn serve as barriers to vertical flow and cause 
lateral flow. Portions of the Calico Hills formation have been extensively altered to zeolites, 
creating the perched water bodies observed within this unit (Bodvarsson et al. 1999 
[DIRS 120055], pp. 14-15). 
Figure 6-4. A Simplified Schematic for Flow Patterns within and near a Perched Water Body 
Characterized by Strong Lateral Flow within the Perched Water Body and the Associated 
Fault-Dominated Flow 

6.1.5 Effects of Major Faults 
Numerous strike-slip and normal faults with varying amounts of displacement exist at Yucca 
Mountain. It is important to understand how major faults affect the flow processes in the UZ at 
Yucca Mountain. 
A fault can act as a fast-flow conduit for vertical liquid-water flow. In this case, transient 
liquid-water flow may occur within the fault as a result of temporally variable infiltration. Note 
that major faults cut through the PTn, and the damping effect of the PTn is significantly reduced. 
However, if occurring, this transient flow along the major faults is expected to carry only a small 
amount of water and may not be a significant liquid-flow mechanism for the UZ at Yucca 
Mountain, as will be discussed in Section 6.1.7. It is reasonable to assume that recharge through 
alluvial channels and the associated faults and other potential fast pathways above the repository 
is minimal compared to the overall recharge flux. Note that faults intercepting the perched water 
bodies below the repository, however, can correspond to significant vertical liquid-water flow 
(see Figure 6-4). 
A fault can also act as a barrier for lateral liquid-water flow. Where a fault zone is highly 
fractured, the corresponding coarse openings will create a capillary barrier for lateral flow. 
Alternatively, a fault can displace the surrounding geologic units, such that a unit with low 
permeability faces one with relatively high permeability in a fault zone. In this case, the fault 
will act as a permeability barrier to the lateral flow within the units with relatively high 
permeability. Montazer and Wilson (1984 [DIRS 100161], p. 20) conceptualized that 
permeability would vary along faults, with higher permeability in the brittle, welded units and 
lower permeability in the nonwelded units where gouge or sealing material may be produced. 
Whereas a fault sealed with gouge or other fine-grained material would have much higher 
capillary suction, it will also have low permeability, retarding the movement of liquid water. 
In summary, because lateral flow is hypothesized to be insignificant above the repository and 
significant focusing infiltration near faults may not occur (Section 6.1.7), faults conduct only a 
small amount of water and are not considered to contribute significantly to the large-scale 
percolation pattern from the surface to the repository level. Below the repository, 
low-permeability layers in the CHn channel some flow to faults acting as conduits to the water 
table. 
6.1.6 Transient Flow 
Flow in the UZ is time dependent or transient, mainly resulting from the temporal variation in 
the infiltration flux at the surface. The temporal variation of the infiltration may be 
approximated as occurring over short intervals characterized by changes in weather, resulting in 
episodic transient flows, or over much longer time periods corresponding to climate change. 
However, as discussed in Section 6.1.2, the PTn greatly attenuates episodic infiltration pulses 
such that liquid-water flow below the PTn is considered to be approximately in steady state. 
This is supported by the modeling study of Wang and Narasimhan (1993 [DIRS 106793], 
pp. 354-361). The attenuation is a result of matrix flow in the PTn and the relatively large 
storage that mainly results from the relatively low matrix saturation in this unit. On the other 
hand, longer-term climate change has a more pronounced influence on flow pattern within the 

mountain than episodic infiltration, and ultimately impacts the entire flow field in the UZ 
(DOE 1998 [DIRS 100550], pp. 3-115 and 3-116). However, previous modeling studies suggest 
that use of steady-state flow fields is a good approximation for modeling radionuclide transport 
in the UZ associated with climate changes (DOE 1998 [DIRS 100550], p. 3-116). The reason for 
this is that the change in flow in the fractures, which dominates the flux in most hydrogeologic 
units, responds relatively quickly to a change in infiltration (DOE 1998 [DIRS 100550], 
p. 3-116). Thus, it is reasonable to assume flow to be in steady state for modeling liquid-water 
flow in the UZ. 
It is expected that flow through isolated fast flow paths that by-pass the PTn unit may exhibit a 
strong transient character for the lack of a significant attenuation mechanism. However, these 
isolated flow paths are believed to carry only a small amount of water. More discussions of this 
issue are given in the next subsection. 
6.1.7 Focusing Flow and Fast Flow Paths 
Flow focusing refers to the occurrence of a significant amount of water flowing through a very 
small area and/or zone. Depending on geological conditions and the magnitude of the flux, flow 
focusing leading to fast flow pathways across the PTn may occur. A number of samples 
obtained from the Exploratory Studies Facility (ESF) arguably show bombpulse signatures of 
Cl-36 (BSC 2004 [DIRS 170004], Section 6.14). (Note that the UZ flow model captures the 
fast-flow component associated with bombpulse signatures of Cl-36 (BSC 2004 
[DIRS 169861], Appendix H) in order to be conservative.) They are generally associated with 
localized fault structures that cut through the PTn, and these pathways are likely responsible for 
the presence of bombpulse signatures of Cl-36 within the TSw at the repository horizon. 
However, for the following reasons, these fast and transient flow paths actually carry only a 
small amount of water: (1) bombpulse signatures were arguably found in only a few locations 
in the ESF (BSC 2004 [DIRS 170004], Section 6.14.2), (2) these discrete fast paths are not 
associated with large catchment areas involving large volumes of infiltrating water, and 
(3) bombpulse tracers (e.g., Cl-36, and C-14) are not detected in perched water. 
The above arguments support a conceptual model that focused flow does not significantly occur 
above the TSw layer. The potential for flow focusing below the PTn unit has been demonstrated 
using numerical studies (based on the heterogeneous continuum approach) by Bodvarsson et al. 
(2003 [DIRS 163443]). Along the line of thinking of Bodvarsson et al. (2003 [DIRS 163443]), 
Liu et al. (1998 [DIRS 105729]) and Glass et al. (1996 [DIRS 139237]), the following 
conceptual model of unsaturated flow focusing (Figure 6-5) is suggested. In this conceptual 
model, infiltration is dispersed in the near surface and also in the low effective permeability PTn 
layer. From there, water begins to be focused in the TSw layer and continues into fewer discrete 
flow pathways on through the Calico Hills vitric and Calico Hills zeolitic layers. These discrete 
flow pathways, which likely occur in fractures as in Figure 6-3, then deliver percolating water to 
the groundwater. Whereas this focused flow pattern below the PTn unit has a critical impact on 
the percolation distribution above the repository and radionuclide transport from the repository to 
water table, details of this focused flow pattern is not well understood. 
While focused flow occurs in the TSw and below, the distribution of focused flow paths is 
relatively uniform, and focused flow paths are not limited to major faults, as supported by spatial 

uniformity of many related field observations (Bodvarsson et al. 1999 [DIRS 120055], p. 13). 
For example, average measured matrix saturations suggest relatively uniform values for most of 
the units, and in situ water potential measurements also show little variability within the TSw for 
different boreholes. It was also observed that temperatures within the TSw unit are fairly 
uniform (Bodvarsson et al. 1999 [DIRS 120055], p. 13). 
Figure 6-5. A Simplified Schematic Showing Conceptual Model of Unsaturated Zone Flow Focusing in 
Yucca Mountain 
NOTE: Blue zones correspond to saturated zone and perched water bodies. Axes units are meters and PP 
represents hydrogeologic units PP1 through PP4 that are part of the CHn (BSC 2004 [DIRS 169855], 
Table 6-5). 
6.1.8 Gas Flow Process 
Gas (air) flow at Yucca Mountain mainly depends on the characteristics of fracture networks. 
The fractures are generally much more permeable than the matrix because of both their larger 
absolute permeability and lower liquid saturation. In the welded units, this is particularly true, 
but in the PTn, the permeability of the fracture continuum is closer to that of the matrix 
continuum, because of lower liquid saturation and larger pore sizes in the PTn matrix. Little data 
exist on gas flow below the bottom of the TSw, though high liquid saturation and low 
permeability likely will significantly reduce gas flow. 
The ambient gas-flow processes occurring at Yucca Mountain include barometric pumping, 
wind, and density-driven flow. Barometric pumping is the response of subsurface pneumatic 
pressure to changes in atmospheric pressure. Because this is a transient process, both the 

permeability and storage of the media affect the subsurface response. In the welded units, this 
translates into little change in the pneumatic pressure signal with depth (Rousseau et al. 1999 
[DIRS 102097], pp. 89-97). The PTn, however, attenuates and lags the pressure signal. Ahlers 
et al. (1999 [DIRS 109715], p. 58) showed a strong correlation between the PTn thickness and 
pneumatic response below the PTn. They also showed that faults are fast pathways for gas flow 
but affect subsurface response only at a relatively local scale (Ahlers et al. 1999 [DIRS 109715], 
pp. 47 and 59-66). 
Gas flow occurs under ambient conditions as a result of density- and wind-driven processes 
(Weeks 1987 [DIRS 100612]). Density-driven flow occurs in the area of low elevation and is a 
consequence of the differences between the density of dry air in the atmosphere and wet air in 
the mountain. The wet air is lighter and rises in response to the pressure exerted by the heavier 
dry air, causing flow within the mountain from the lower elevations toward the crest. 
Wind-driven flow occurs because of the higher pressure exerted on the windward side of the 
mountain and the lower pressure in the lee of the crest. Thus, wind-driven flow will also 
promote flow toward the crest. Measurement of air-flow in an open borehole near the crest of 
Yucca Mountain shows that density- and wind-driven flow occurs mainly in the TCw 
(Thorstenson et al. 1990 [DIRS 100831], p. 262). 
6.1.9 Summary and Further Discussions 
Based on the discussions of flow issues and processes in the UZ (Sections 6.1.1 through 6.1.8), a 
conceptual model of flow in the UZ is constructed. Infiltration is mainly characterized by high 
spatial and temporal variabilities. Infiltration pulses move rapidly through the fractures in the 
TCw unit with little attenuation by the matrix. Because of the expected attenuation effects of the 
PTn unit, the liquid-water flow processes below this unit are considered to be approximately in 
steady state, under ambient conditions. Considerable lateral flow in the PTn occurs, and fracture 
liquid-water flow is dominant in welded units and matrix flow in nonwelded units. 
Fracture-matrix interaction in the welded units is limited. The existence of perched water bodies 
introduces three-dimensional lateral flow within the UZ. Major faults do not act as flow paths to 
significantly alter the percolation pattern from the surface to the repository level. Below the 
repository, low-permeability layers in the CHn may channel some flow to faults that can act as 
conduits to the water table. 
It is instructive to compare the current conceptual model of flow in the UZ with other conceptual 
models published in the literature. Since the mid-1980s, the prevailing view of the UZ at Yucca 
Mountain has been that, under ambient conditions, water flow mainly occurs through the rock 
matrix even in the welded, densely fractured TSw unit (Wang and Narasimhan 1993 
[DIRS 106793], pp. 327-339; Peters and Klavetter 1988 [DIRS 100604]; Nitao and Buscheck 
1991 [DIRS 102860]). Based on capillary theory, it was believed that under unsaturated 
conditions, liquid water would essentially be excluded from fractures because of strong 
capillarity in the matrix. However, with more and more data available for characterizing the site, 
it has become evident that unsaturated flow in the welded units is primarily through the fractures, 
as discussed in Section 6.1.2 of this report. 
While the current conceptual model is based to a great extent on the model originally presented 
by Montazer and Wilson (1984 [DIRS 100161], pp. 3649), the major differences between these 

two models are the roles of the structural features, or faults, in conducting liquid water through 
the UZ. Montazer and Wilson (1984 [DIRS 100161], pp. 5051) hypothesized that the 
combination of dipping beds, permeability layering, and capillary-barrier effects results in 
significant lateral flow within the PTn toward the bounding structural features. Most of the 
infiltrated water is transmitted downward to the water table along structural features (Montazer 
and Wilson 1984 [DIRS 100161], p. 51). As discussed in Sections 6.1.2, 6.1.5 and 6.1.7, more 
recent studies indicate that faults are not likely to act as flow paths to significantly alter the flow 
pattern above the repository level in the UZ. 
In a recent study, Pruess (1999 [DIRS 104250]) proposed a conceptual model for flow in the UZ. 
While the details of his conceptual model can be found in Pruess (1999 [DIRS 104250]), key 
elements of the model can be summarized as follows (Pruess 1999 [DIRS 104250], p. 1041): 
1. 
Most of the water flow in thick UZs of fractured rock proceeds by way of episodic, 
transient, and localized flow through fractures. 
2. 
Liquid-water flow can remain localized even in the presence of dispersive effects that 
would tend to cause lateral spreading. 
3. 
Several mechanisms combine to severely reduce the effects of matrix imbibition. 
While both the model of Pruess (1999 [DIRS 104250]) and the current conceptual model 
consider the fracture-matrix interaction to be limited in the UZ, and only a portion of fractures to 
be active in conducting liquid water, they are different in their description of time-dependent 
character of fracture flow. Pruess hypothesizes that fracture flow paths in unsaturated, fractured 
rocks are transient (Pruess 1999 [DIRS 104250], p. 1041). As discussed in Sections 6.1.2, 6.1.6, 
and 6.1.7, the current conceptual model hypothesizes that liquid-water flow below the PTn unit 
is approximately in steady state. 
6.2 CONCEPTUAL MODEL OF TRANSPORT 
This subsection documents the conceptual model used for modeling transport within the UZ of 
Yucca Mountain. The conceptual model is presented by addressing important transport issues 
and processes. Note that transport is closely tied to flow processes, because water is the 
principal medium in which solutes are transported through the UZ. 
6.2.1 Advective Transport 
Advective transport (advection) refers to the movement of dissolved or colloidal materials within 
the bulk flow of fluid (Fetter 1993 [DIRS 102009], p. 47). Transport is strongly related to liquid 
water flow through advection, and advective transport pathways coincide with flow pathways 
discussed in Section 6.1. In welded units, advection through fractures is expected to dominate 
transport behavior, mainly because liquid water largely flows through fracture networks in these 
units. Advection is also an important mechanism for transport between fractures and matrix, 
especially at interfaces between nonwelded and welded units. At these interfaces, transitions 
occur between dominant fracture flow and dominant matrix flow. Liquid-water flow paths 
below the repository are critical to potential radionuclide transport resulting from advection. 
Perched water results in lateral transport of the radionuclides. Dominant fracture flow in the 

zeolitic components of the CHn provides relatively short travel times for transport to the water 
table, whereas the dominant matrix flow in the vitric components provides much longer travel 
times. 
6.2.2 Matrix Diffusion and Potential Scale-Dependency of Effective Matrix Diffusion 
Coefficient 
Matrix diffusion refers to solute transport from fracture networks into the surrounding matrix 
blocks resulting from molecular diffusion (Neretnieks 1993 [DIRS 123099], pp. 4748). Mass 
transfer between fractures and the tuff matrix plays an important role in transport within the UZ. 
Because flow velocity in the matrix is much slower than in fractures, transfer of radionuclides 
from fractures to the matrix can significantly retard the overall transport of radionuclides from 
the repository to the water table. The transfer can result from advection, dispersion, and 
diffusion processes. Where fracture flow is dominant, the advection from fractures to the matrix 
is not important, because only a relatively small amount of water flows into the matrix, with the 
rest flowing through fractures. In this case, matrix diffusion is a major mechanism for mass 
transfer between fractures and the matrix. On the other hand, the diffusion process in the matrix 
is more important than dispersion due to the slow pore velocity in the matrix. Therefore, 
diffusion is probably the most important physical process in the matrix, contributing to the 
retardation of radionuclide transport when fracture flow is dominant. 
The effective matrix diffusion coefficient (molecular diffusion coefficient in free water 
multiplied by matrix tortuosity) is a key parameter for describing matrix diffusion. Matrix 
diffusion coefficient values measured from small rock samples in the laboratory are generally 
used for modeling field-scale solute transport in fractured rock (e.g., Moridis et al. 2003 
[DIRS 161902]). Recently, several research groups have independently found that effective 
matrix-diffusion coefficients much larger than laboratory measurements are needed to match 
field-scale tracer-test data (Shapiro 2001 [DIRS 162132]; Neretnieks 2002 [DIRS 162140]; Liu 
et al. 2003 [DIRS 162470]; BSC 2004 [DIRS 169861], Section 7.6). 
Effective matrix-diffusion-coefficient values have been estimated from a number of field test 
sites characterized by different rock types. To compile these values (corresponding to different 
tracers) as a function of the test scale, a matrix-diffusion-coefficient ratio, RD, is defined as an 
effective coefficient value (estimated from field data) divided by a local value from laboratory 
measurements. It is an indicator of scale dependency that is expected to exist when RD is a 
function of the test scale. 
Figure 6-6 shows the relationship between values for RD, determined from a number of sites by 
different research groups (Maloszewski and Zuber 1993 [DIRS 101460]; Jardine et al. 1999 
[DIRS 169950]; Becker and Shapiro 2000 [DIRS 169947]; Callahan et al. 2000 [DIRS 156648]; 
Shapiro 2001 [DIRS 162132]; Neretnieks 2002 [DIRS 162140]; Liu et al. 2003 [DIRS 162470]; 
BSC 2004 [DIRS 169861], Section 7.6), and the corresponding test scales. Jardine et al. (1999 
[DIRS 169950]) performed and analyzed a carefully designed tracer test in fractured shale 
bedrock. They were able to obtain breakthrough curves from wells with different distances to 
the source. However, the same parameters were used to match all the breakthrough curves for a 
given tracer. As indicated in their Figure 9, the breakthrough curves from wells about 6 m from 
the source are reasonably matched, but the curve from the well 17 m from the source is not. A 

larger effective matrix-diffusion-coefficient value seems to be needed to match the data from the 
latter well, an indication of a possible increase in the coefficient with scale. Therefore, in 
Figure 6-6, the fitted effective matrix diffusion is considered to correspond to a test scale of 6 m 
only. Note that, as indicated by Jardine et al. (1999 [DIRS 169950]), their intentions were not to 
rigorously model all of the processes contributing to solute transport in the system, but, rather, to 
test the importance of matrix diffusion. 
104 
103 
102 
10
-1 
100 101 102 103 104 
101 
RD 
() 
(2003a) 
(2003b) 
(
(
(2000) 
(1999) 
(
Callahan et al. 2000Liu et al. 
Liu et al. 
Neretnieks 2002) 
Shapiro 2001) 
Becker and Shapiro 
Jardine et al. 
Maloszewski and Zuber 1993) 
100 
10
-1 
Test Scale (m) 
Source: Liu et al. 2004 [DIRS 169948], Figure 1. 
Figure 6-6. Effective Matrix Diffusion Coefficient as a Function of Test Scale. RD Refers to the Effective 
Coefficient Value (Estimated from Field Data) Divided by the Corresponding Local Value 
Neretnieks (2002 [DIRS 162140]) reported matches to tracer test data collected from the sp 
site with a test scale of 5 m and found a need for a factor 30 times larger for the fracture-matrix 
interface area (or effective matrix-diffusion coefficient) than expected. The increase in 
fracture-matrix interface area is equivalent to the increase in effective diffusion coefficient (for a 
given interface area in a model). He also indicated that nine other research groups had also 
independently evaluated the tracer test data from the site using different modeling approaches. 
Nearly all the groups found the need for a factor 30-50 times larger effective fracture-matrix 
interface area (or effective matrix-diffusion coefficient) than expected. In Figure 6-6, a 
representative RD value of 40 is used for the sp test site. 
Liu et al. (2003 [DIRS 162470]) and BSC (2004 [DIRS 169861], Section 7.6) presented model 
analyses of two different field test data, collected in the UZ of Yucca Mountain. Unlike studies 
reported by other researchers mentioned in this subsection, Liu et al. (2003 [DIRS 162470]) and 
BSC (2004 [DIRS 169681], Section 7.6) matched both the flow field (characterized by water 
travel time and/or seepage into subsurface openings) and tracer breakthrough curves. They 
reported that increased fracture-matrix interface areas (or effective matrix diffusion coefficients) 

were needed for both tests. The data of Callahan et al. (2000 [DIRS 156648]) were also 
collected for the rock matrix in the UZ of Yucca Mountain. 
Becker and Shapiro (2000 [DIRS 169947]) and Shapiro (2001 [DIRS 162132]) reported analyses 
of tracer test data from fractured crystalline rock at the Mirror Lake site. Becker and Shapiro 
(2000 [DIRS 169947]) showed that laboratory measurement of the effective diffusion coefficient 
should be replaced by the coefficient in free water (corresponding to RD = 3,333) to match the 
bromide data in their Test C with a test scale of about 36 m. However, they were not able to 
match all the breakthrough curves for different tracers, and argued that advective transport 
processes contribute to this discrepancy. An alternative explanation may be that a simple model 
used by those authors cannot capture all the importance processes (such as effects of subsurface 
heterogeneity), even when matrix diffusion is a dominant process. Nevertheless, the value of 
RD = 3,333 is included in Figure 6-6. Shapiro (2001 [DIRS 162132]) found that 3-5 orders of 
magnitude greater than the estimates of the matrix-diffusion coefficient from laboratory 
experiments were needed to match the tracer data observed at a kilometer scale. His analysis 
probably provides the first estimate for kilometer-scale effective diffusion coefficient. A 
representative value of Shapiro (2001 [DIRS 162132]) for RD (1.0E+4) is used in Figure 6-6. 
Figure 6-6 also includes analyses results of Maloszewski and Zuber (1993 [DIRS 101460]) for 
three different sites. 
Although some uncertainties exist, the data shown in Figure 6-6 seem to strongly suggest that the 
effective matrix diffusion coefficient, like permeability and dispersivity, increases with test scale. 
A number of researchers have attempted to explain why the effective coefficient determined 
from field data is larger than the corresponding laboratory value (Shapiro 2001 [DIRS 162132]; 
Neretnieks 2002 [DIRS 162140]; Liu et al. 2003 [DIRS 162470]; BSC 2004 [DIRS 169681], 
Section 7.6). 
Shapiro (2001 [DIRS 162132]) suggested that kilometer-scale effective matrix diffusion is not 
a diffusive process, but actually an advective process between high and low permeability zones, 
resulting in a significantly large effective diffusion coefficient. While this may be a plausible 
explanation, further confirmation is still needed. For example, Liu et al. (2003 [DIRS 162470]; 
BSC 2004 [DIRS 169861], Section 7.6) used a dual-permeability model involving both fast flow 
in fractures and slow flow in the matrix (as well as the advective transport between the two) and 
still found the need to use increased effective diffusion coefficients for matching the tracer test 
data. Neretnieks (2002 [DIRS 162140]) argued that existence of fracture in-filling creates 
relatively large areas for solute to diffuse into rock matrix, which, together with the process of 
diffusion into stagnant water, contributes to the need for increasing the effective diffusion 
coefficient to match the data. Wu et al. (2001 [DIRS 156399]) and Liu et al. (2003 
[DIRS 162470]) indicated that the existence of many small-scale fractures (which considerably 
increase the fracture-matrix interface area, but are not considered in numerical models) may be 
the major reason for the relatively large effective diffusion coefficient calculated from field data. 
While these suggested mechanisms seem to be reasonable for field-scale solute transport in 
fractured rock, they cannot be directly used to explain why the effective diffusion coefficient 
increases with test scale because they are not able to relate the effective matrix diffusion 
coefficient to the corresponding test scale. 

Liu et al. (2004 [DIRS 169948]) proposed a fractal-based explanation for the scale-dependent 
behavior of the effective diffusion coefficient. Considering that both fracture roughness and 
fracture-network geometry can be characterized by fractals, Liu et al. (2004 [DIRS 169948]) 
hypothesize that a solute travel path within a fracture network is fractal, rather than a straight line 
(as assumed in common numerical or analytic models). Based on this hypothesis, Liu et al. (2004 
[DIRS 169948]) were able to show that RD is a power function of test scale and increases with 
test scale. 
Although the potential scale-dependency and the preliminary explanation of Liu et al. (2004 
[DIRS 169948]) need to be confirmed by more investigations, the use of core-scale matrix 
diffusion coefficients in the site-scale UZ transport models likely underestimates radionuclide 
transport time in the UZ, as discussed above, and therefore the corresponding simulation results 
for radionuclide transport processes are likely to be conservative in terms of estimating 
performance of the repository. 
6.2.3 Fracture and Matrix Sorption 
Sorption is an important process involved in reactive transport. Sorption refers to a combination 
of chemical interactions between dissolved solutes and the solid phases (immobile rock matrix or 
colloids) (Fetter 1993 [DIRS 102009], p. 117). The strength of the sorptive behavior is a 
function of chemical element, the rock type involved in the interaction, and the geochemical 
conditions of the water contacting the rock (Domenico and Schwartz 1990 [DIRS 100569], 
pp. 440443). Sorption, for example, can act to retard the movement of radionuclides in the 
groundwater. Reactive chemicals, which are strongly sorbed to rock matrix, are relatively 
immobile. On the other hand, sorptive interactions may enhance solute transport if the aqueous 
species sorbs to colloids (Fetter 1993 [DIRS 102009], pp. 149-150). (Colloid-facilitated 
transport will be discussed in Section 6.2.4.) Generally, sorption is a reversible process; 
however, in some cases, sorption can be irreversible, as will be discussed in the next section. 
The importance of sorption in the different rock types is not only a function of the sorptive 
strength, but also the degree of contact that solutes have with the rock matrix during transport 
through the UZ. Zeolitic tuff generally has a larger sorptive strength than vitric tuff, but has a 
relatively small matrix flow component because of its low matrix permeability (DOE 1998 
[DIRS 100550], p. 3-118). Sorption in the zeolitic tuff, thus, may not be able to effectively 
retard solute transport, along with small molecular diffusion coefficients corresponding to 
insignificant matrix diffusion. 
The surfaces of fractures, often lined with minerals differing from the bulk of the rock matrix, 
may be capable of sorbing many of the radionuclides that may be released from the potential 
repository (Triay et al. 1997 [DIRS 100422], p. 173). However, characterizing distributions of 
the fracture-lining minerals and sorptive interactions with these minerals has been limited. Also, 
the fracture minerals have a relatively small volume and surface area relative to the bulk rock 
matrix. For these reasons, a conservative assumption in modeling radionuclide transport is that 
no sorptive interaction with fracture surfaces occurs, and that sorptive interactions are only 
possible for radionuclides in matrix blocks. 
Numerous rock-water chemical interactions may influence radionuclide transport. Sorption, 
representing the combination of these interactions, is characterized by a sorption or 

distribution coefficient (Kd). In general, for a given radionuclide and rock type, this coefficient 
is not a constant, but depends on the temporally and spatially varied chemical composition of 
both the aqueous and solid phases (Domenico and Schwartz 1990 [DIRS 100569], pp. 442-443), 
the latter affecting underlying interactions. As a conservative approach to model radionuclide 
transport through the UZ, a minimum bound for Kd can be used. The minimum Kd represents the 
smallest reasonable ratio of radionuclides attached to the solid phase versus dissolved in the 
aqueous phase. 
6.2.4 Colloid-Facilitated Transport 
Radionuclide transport in the UZ at Yucca Mountain may be facilitated by colloidal transport 
processes. Colloids are particles that are small enough to become suspended (and thus 
transportable) in a liquid (Fetter 1993 [DIRS 102009], p. 149), and can interact with 
radionuclides through sorption mechanisms. Unlike sorption of radionuclides to the rock matrix, 
however, radionuclides sorbed on colloids are potentially mobile. Therefore, colloids can 
facilitate radionuclide transport through the UZ at a faster rate than the aqueous phase alone 
(de Marsily 1986 [DIRS 100439], pp. 270-271). Another form of colloidal radionuclides occurs 
when the radionuclide is an integral component of the colloid structure. In this case, the 
radionuclide is irreversibly bound to the colloid (DOE 1998 [DIRS 100550], p. 3-105). 
The colloid-facilitated transport is controlled by several processes, including advection of 
colloids, matrix diffusion and dispersion of colloids, sorption of radionuclides on colloids, 
radioactive decay of radionuclides, and filtration of colloid particles. Advective radionuclide 
transport paths coincide with liquid-water flow paths below the repository. The advective 
transport through fractures is enhanced by reduced matrix diffusion and matrix sorption. Colloid 
particles themselves are not expected to experience any significant matrix diffusion because of 
the very low diffusion coefficients associated with colloids. Colloids may not be able to move 
through some of the rock matrix, particularly the welded and zeolitic rock types, because of the 
large colloid size relative to the matrix pore size. However, movement through the more 
permeable nonwelded vitric rock in the Calico Hills may be possible. The restriction of matrix 
particle size on movement of colloid particles is described as a filtration process (de Marsily 
1986 [DIRS 100439], pp. 271-272). Filtration of colloids generally means the retention of 
colloids moving with the suspending fluids in pores, channels, and fracture apertures that are too 
small or dry to allow passage of the colloids. Obviously, the colloid-facilitated transport 
becomes a more important transport mechanism for radionuclides that strongly sorb onto the 
solid phase. 
6.2.5 Other Transport Issues and Processes 
Radioactive decay is a process that affects the concentration of radionuclides during transport 
through the UZ. For simple decay, radionuclide concentration decreases exponentially with time 
(de Marsily 1986 [DIRS 100439], p. 265), creating stable decay products. Chain-decay adds 
another layer of complexity because of the growth of new radionuclides created from the decay 
of a parent radionuclide. One aspect of potential significance with respect to chain-decay is that 
daughter products may have significantly different sorption behavior than the parent 
radionuclide, and, therefore, exhibit different transport behavior. 

Dispersion is a transport mechanism caused by localized variations in flow velocity (de Marsily 
1986 [DIRS 100439], pp. 234235 and 244). However, it is not expected to play an important 
role in the UZ transport. An important reason that dispersion is secondary is the explicitly 
modeled variations in transport velocity caused by the fracture-matrix system. (See 
Section 6.3.6.3 for further discussion.) In the rock matrix, dispersion is also considered to be 
minor compared with diffusion because of the low pore velocity in the matrix. Dispersive flux is 
proportional to pore velocity (de Marsily 1986 [DIRS 100439], pp. 236-238). 
The presence of perched water may serve as a mechanism to dilute liquid-phase solute 
concentrations in the UZ. In the TSw unit above perched water, solutes are expected to be carried 
primarily by many flow channels within active fractures (see Section 6.1.3 and Figure 6-3). 
Once they arrive at perched water zones, these solutes may mix with perched water, resulting in 
a decrease in chemical concentrations. The degree of dilution depends on the residence time of 
the solutes in the perched water; longer residence time corresponds to a larger degree of mixing 
within the perched water and therefore a larger degree of dilution. The relevant observations and 
modeling studies suggest that a large degree of mixing occurs in the perched water zones 
(Sonnenthal and Bodvarsson 1999 [DIRS 117127], pp. 118 and 151). Sonnenthal and 
Bodvarsson (1999 [DIRS 117127], p. 118) observed that chloride concentrations in water 
samples collected during hydraulic tests in the perched water bodies are not very variable 
because the water is probably well-mixed. Their modeling exercise also showed that perched 
water compositions are best matched by a mixture of Pleistocene age water with variable 
amounts of modern water (Sonnenthal and Bodvarsson 1999 [DIRS 117127], p. 151). 
6.2.6 Summary and Further Discussions 
Based on the discussions of transport issues and processes for the UZ (Sections 6.2.1 through 
6.2.5), a conceptual model of transport in the UZ can be summarized as follows: (1) advective 
transport pathways coincide with flow pathways; (2) matrix diffusion is a major mechanism for 
mass transfer between fractures and matrix, and is expected to contribute to the retardation of 
radionuclide transport when fracture flow is dominant; and (3) sorption may retard the 
movement of radionuclides in the UZ, but this retardation is limited by reduced fracture-matrix 
interfacial area resulting from fingering flow in fractures. However, sorptive interactions may 
enhance radionuclide transport if the aqueous species sorbs to colloids that are subsequently 
transported through the UZ. Dispersion is not expected to be a major transport mechanism in the 
UZ. 
Because flow is a major driving force for transport, the conceptual model of transport in the UZ 
is closely tied to the conceptual model of flow. Alternative conceptual models of flow give rise 
to different transport behavior from that discussed above. If the liquid-water flow primarily 
occurs in the matrixas hypothesized by Wang and Narasimhan (1993 [DIRS 106793], 
pp. 327-339), Peters and Klavetter (1988 [DIRS 100604]) and Nitao and Buscheck (1991 
[DIRS 102860])matrix diffusion will be insignificant for UZ transport, and colloid-facilitated 
transport may not need to be considered, given that it mainly occurs in fractures. In contrast, if 
most liquid-water flows through structural features (Montazar and Wilson 1984 [DIRS 100161], 
p. 51) or very sparse flow paths (Pruess 1999 [DIRS 104250]), transport will be primarily 
determined by flow in fractures, and the effects of the matrix, such as matrix diffusion and 
matrix sorption, become insignificant. However, as discussed in Section 6.1.9 of this report, 

liquid-water flow in the UZ is considered more likely to be consistent with the current 
conceptual model of flow rather than either totally matrix- or fracture-dominated. In the current 
conceptual model, dominated fracture flow (that is not characterized by very sparse flow paths) 
occurs in the welded units (Section 6.1.9). In this case, matrix diffusion is important for 
radionuclide transport in the welded units (Section 6.2.2). 
6.3 NUMERICAL APPROACHES 
This section briefly reviews the currently available numerical approaches that can be used for 
modeling flow and transport in unsaturated fractured rocks, followed by a discussion of the 
appropriateness of these approaches for use in the UZ flow and transport model and other 
relevant issues. 
6.3.1 Available Numerical Schemes 
A variety of numerical approaches have been proposed in the literature to deal with flow and 
transport processes in fractured media at the field scale. When classified according to the 
manner in which fracture networks are treated in the model structure, the approaches fall into one 
of three groups: continuum approaches, discrete fracture-network approaches, and other 
approaches. Excellent reviews on these approaches, which have been developed and used in 
different fields (including oil-reservoir engineering, groundwater hydrology, geothermal 
engineering, and soil physics), can be found in Bear et al. (1993 [DIRS 116773], pp. 267320 
and 396-428) and the National Research Council (1996 [DIRS 139151], pp. 307394). This 
section does not intend to give a comprehensive review of all the approaches, but will rather 
focus on those that can be used for unsaturated, fractured rock. 
6.3.1.1 Continuum Approaches 
6.3.1.1.1 Basic Physical and Numerical Principles 
In continuum approaches, fractures are considered to be sufficiently ubiquitous and distributed in 
such a manner that they can be described statistically in a meaningful way (Bear et al. 1993 
[DIRS 116773], pp. 395396). The role of individual fractures in fractured media is considered 
to be similar to that of individual pores in porous media. Therefore, one can describe average 
fracture properties as macroscopic, and those associated with individual fractures as microscopic. 
Theoretically, the macroscopic scale is related to the so-called representative elementary volume 
(REV) (Bear et al. 1993 [DIRS 116773], pp. 3-10). A physical property value at a point in the 
fracture or matrix continuum is defined as that averaged over the corresponding REV. When the 
continuum approaches are valid, the size of a REV must be much larger than the scale of 
microscopic heterogeneity and much smaller than the scale of whole flow and/or transport 
domain. 
In continuum approaches, connected fractures and rock matrix are viewed as two or more 
overlapping, interacting continua. In other words, at a point, two or more continua are 
considered to co-exist. In this case, the continuum mechanics formulations, such as those used 
for porous media, can be used to describe flow and transport in each continuum. Coupling of 
processes between different continua is determined by interaction mechanisms at a subgrid scale. 

Depending on the number of continua and methodologies used to treat fracture-matrix 
interaction, continuum approaches can be further classified as effective-continuum, 
dual-continua, and multiple interacting continua (MINC) approaches. 
6.3.1.1.2 Effective Continuum Approach 
In the effective continuum method (ECM) approach, fractures and rock matrix are replaced with 
a single effective continuum (Figure 6-7(a)). In the traditional ECM (Pruess and Tsang 1994 
[DIRS 117451], pp. 4749), nonzero liquid saturation in the fracture does not occur until the 
matrix is fully saturated, which occurs at the so-called threshold saturation. Composite 
characteristic curves are constructed which embody matrix behavior when the saturation of the 
effective continuum is less than the threshold saturation, and fracture behavior when the 
saturation is larger than the threshold saturation. In the modified ECM (Wu et al. 1999 
[DIRS 117161], p. 194), the concept of threshold saturation is not invoked. Instead, liquid 
saturation is partitioned into the matrix and fracture in accordance with the principle of local 
thermodynamic equilibrium, which requires capillary pressure in the matrix and fracture 
components of a gridblock to be equal. Thus, in the generalized ECM formulation, fracture flow 
occurs at all saturations, although small fracture flow is computed at low saturations. In each 
gridblock, ECM also assumes that water in the fractures and matrix have the same chemical 
concentration and temperature. 
The ECM approach provides a substantial simplification for describing flow and transport in 
fractured porous media, and is computationally efficient in handling a large model grid. 
However, the assumptions on which ECM is based may break down when long times are needed 
to reach local equilibrium condition between the fracture and matrix continua. This is especially 
true for a very tight and low-permeability rock matrix with rapid fracture flow (Wu et al. 1999 
[DIRS 117161], p. 195). 
M22 
M21 
M23 
M12 
M11 
M13 
M32 
M31 
M33 
M42 
M41 
M43 
M52 
M51 
M53 
F1 M1 
F2 M2 
F3 M3 
F4 M4 
F5 M5 
F1 M1 
F2 M2 
F3 M3 
F4 M4 
F5 M5 
F1 
F2 
F3 
F4 
F5 
F1 
F2 
F3 
F4 
F5 
Figure 6-7. Schematic Diagram of One-Dimensional Column of Gridblock, Modeled as (a) ECM, 
(a) (b) (c) (d) 
(b) Dual-Porosity with One Matrix Gridblock, (c) Dual-Permeability with One Matrix 
Gridblock per Fracture Gridblock, and (d) MINC with Three Matrix Gridblocks per Fracture 
Gridblock 

6.3.1.1.3 Dual-Continua Approaches 
In dual-continua approaches, fractures and matrix are treated as two separate, yet interacting 
continua, and each gridblock is subdivided into one fracture block and one matrix block 
(Figure 6-7). The fracture-matrix flow and transport are approximated as quasi-steady. This 
treatment is the numerical equivalent of the Warren and Root (1963 [DIRS 100611]) 
formulation. If global flow occurs only between fracture gridblocks, the approach is known as a 
dual-porosity approach, because fractures alone control large-scale fluid flow and the matrix 
only contributes an additional storage term. If global flow occurs within both fracture and matrix 
continua, the scheme is known as a dual-permeability approach (Doughty 1999 [DIRS 135997], 
p. 76). 
Compared to ECM, dual-continua approaches can more accurately predict flow and transport, 
because nonequilibrium is allowed between fracture and matrix continua. The dual-porosity 
approach is valid only when matrix flow is not important. When both fracture flow and matrix 
flow are important, the dual-permeability scheme is more accurate. On the other hand, since 
only one matrix block is used for each gridblock and a quasi-steady fracture-matrix flow 
assumption is employed, gradients of matrix capillary pressures, temperature, and concentration 
near a fracture-matrix interface may be poorly predicted using dual-continua schemes. This is 
especially true during a rapid, transient flow or transport period in a system with large size and 
low-permeability matrix blocks. Therefore, the dual-continua approach could give rise to poor 
solutions to fracture-matrix flow for rapid, transient flow and transport. Under steady-state 
conditions, however, the gradients near the matrix surface become minimal, and the approaches 
are expected to produce acceptable solutions. 
6.3.1.1.4 Multiple Interacting Continua Approach 
As indicated previously, dual-continua approaches could give rise to poor solutions to 
fracture-matrix flow for rapid, transient flow and transport. A more general and rigorous 
approach, MINC, was developed by Pruess and Narasimhan (1985 [DIRS 101707]) to overcome 
this limitation. Specifically, MINC is based on the notion that changes in fluid pressures, 
temperature, and phase compositions will propagate rapidly through the fracture system, while 
invading the tight matrix blocks slowly. Therefore, changes in matrix conditions will be locally 
controlled by the distance from the fractures. In the MINC, all fractures are lumped into 
Continuum #1; all matrix materials within a certain (small) distance from the fractures are 
lumped into Continuum #2; matrix materials at larger distance from the fractures become 
Continuum #3; and so on. Therefore, the MINC approach can be considered a generalization of 
the dual-continua approach. 
Compared with dual-continua approaches, the MINC approach can more accurately predict flow 
and transport in fractured media, but has larger computational requirements in both central 
processing unit times and storage space. 
6.3.1.2 Discrete Fracture-Network Approaches 
Discrete fracture-network approaches are based on an assumption that flow and transport 
behavior can be predicted from knowledge of the fracture geometry and data on hydraulic 
properties of individual fractures (National Research Council 1996 [DIRS 139151], p. 332). 

These approaches involve computational generation of synthetic fracture networks and 
subsequent modeling of flow and transport in each individual fracture. These approaches have 
been extensively used for single-phase flow and transport, with deterministic, stochastic, 
artificial, or site-specific fracture networks in two or three dimensions (National Research 
Council 1996 [DIRS 139151], pp. 333-350). Recently, the same approaches have also been 
applied to unsaturated conditions (e.g., Kwicklis and Healy 1993 [DIRS 100587]; Liu et al. 2002 
[DIRS 160230]). 
While discrete fracture-network approaches are useful as tools for concept evaluation or 
model-based process studies, they have several limitations. First, the approaches require 
geometric parameters that may strongly impact flow and transport, such as fracture apertures and 
conductivity, but typically cannot be well constrained from field observations (Pruess et al. 1999 
[DIRS 117112], p. 308). Second, it is difficult to separate the conductive fracture geometry from 
the nonconductive fracture geometry (National Research Council 1996 [DIRS 139151], p. 350). 
Third, flow and transport models based on these approaches can be complex and computationally 
intensive for realistic fracture densities (National Research Council 1996 [DIRS 139151], 
p. 350). Fourth, so far, the studies based on discrete fracture-network approaches have rarely 
considered fracture-matrix interaction because of computational complexity (Pruess et al. 1999 
[DIRS 117112], p. 308). Fracture-matrix interaction has important effects on flow and transport 
in unsaturated fractured rocks. 
6.3.2 Assessment of Numerical Approaches 
Several basic numerical approaches for unsaturated, fractured porous media have been briefly 
reviewed, and the advantages and limitations of these approaches have also been discussed. It 
needs to be indicated that several other numerical approaches are also available in the literature 
(e.g., Clemo and Smith 1997 [DIRS 139105], pp. 17631765). These additional approaches, 
however, can be considered as variations and/or combinations of the basic approaches mentioned 
above. The appropriateness of the currently available numerical approaches for the UZ flow and 
transport model depends on several important factors, including flow and transport behavior at 
the Yucca Mountain site, scale of the problem, data availability, and computational feasibility. 
The overall flow and transport behavior in the UZ at Yucca Mountain may be characterized by 
two important features. The first feature is the existence of relatively uniform flow and 
transport along fractures (Section 6.1.7) which makes continuum approaches a reasonable choice 
for the UZ model. The second feature is the coexistence of matrix-dominant flow and transport 
in nonwelded units and fracture-dominant flow and transport in welded units. This feature can 
be easily handled by continuum approaches, but not by other approaches such as a 
fracture-network model. For example, as previously indicated, studies based on discrete 
fracture-network approaches have rarely considered fracture-matrix interaction because of 
computational complexity (Pruess et al. 1999 [DIRS 117112], p. 308). Consideration of this 
feature is important for correctly simulating flow and transport processes in the UZ of Yucca 
Mountain. 
Scale of the problem is an important factor for assessing the appropriateness of numerical 
schemes for the UZ flow and transport model. Because continuum approaches are relatively 
simple and straightforward to implement, they are preferred for most applications that are 

encountered in practice (National Research Council 1996 [DIRS 139151], p. 331). There are 
estimated to be on the order of 109 fractures at Yucca Mountain (Doughty 1999 [DIRS 135997], 
p. 77). It is practically impossible to construct and calibrate a discrete fracture network site-scale 
model with so many fractures, considering the data availability and computational feasibility. 
Based on the above considerations, continuum approaches have been considered to be 
appropriate for use in the UZ flow and transport model. As a compromise between accuracy and 
feasibility, the dual-permeability method has become the main modeling approach currently used 
in the UZ model to simulate water flow, heat transfer, and chemical transport. 
6.3.3 Consistency Between Continuum-Approach-Based Simulation Results and Field 
Observations 
As discussed in Section 6.3.2, the continuum approach has been used for modeling flow and 
transport in the UZ. Recently, efforts have also been made to evaluate the performance of the 
continuum approach (e.g., Liu et al. 2003 [DIRS 162470]; BSC 2004 [DIRS 169861], 
Section 7.6). Given the complexity of the flow and transport processes in the unsaturated 
fractured rock, a direct comparison between numerical simulations (based on the continuum 
approach) and field experimental observations would be a useful and relatively simply way to 
evaluate the validity of the approach (Liu et al. 2003 [DIRS 162470], Section 1). 
Field-scale experiment data of flow and transport through unsaturated fractured rock, obtained 
under controlled conditions, are very limited. However, two field-scale experiments (referred to 
as Alcove 1 test and Alcove 8/Niche 3 test, respectively) of this kind were recently conducted in 
the UZ. The Alcove 1 test site is located near the North Portal of the ESF (Liu et al. 2003 
[DIRS 162470]). Alcove 1 was constructed for collecting seepage water originating from a 
controlled application of surface infiltration. The alcove is about 5.5 m high and 5.8 m wide, and 
about 20 m below the ground surface. Rocks between the ground surface and the alcove are 
intensely fractured and within the TCw unit. A bulkhead was installed in order to isolate the 
alcove from the ESF. The bulkhead was intended to raise the relative humidity in the alcove and 
reduce evaporation from the wall of the alcove. Maintaining relative humidity allows the 
determination of the wetting front arrival from the observation of dripping from the alcove 
ceiling and walls. During the infiltration test, water was applied at the ground surface directly 
over the end of the alcove. The size of the infiltration plot was 7.9 m  10.6 m. During the late 
stage of the Alcove 1 test, a tracer, bromide, was introduced into the infiltrating water. Seepage 
into the alcove was collected as a function of time. Tracer concentrations were obtained by 
analyzing the seepage water. 
Infiltration and tracer transport tests were also conducted at the cross-over test site, where 
Alcove 8 in the enhanced characterization of the repository block (ECRB) cross-drift is about 
20 m directly above Niche 3 in the ESF main drift (BSC 2004 [DIRS 170004], Section 6.12). 
The test site is located in the upper lithophysal and middle nonlithophysal subunits of the TSw 
unit. The upper lithophysal subunit contains lithophysal cavities. Liquid water without and with 
tracers was released sequentially along a fault (line-release) and from a large 3 m  4 m plot 
(areal release) on the floor of Alcove 8. Water release locations are different for line-release and 
areal release. The test along the fault was conducted before the large plot test. Seepage rate and 
tracer concentration data were collected from Niche 3. 

Comparisons between simulation results and field observations from these two tests are used to 
evaluate the continuum approach used in the site-scale UZ flow model. A three-dimensional 
submodel for the Alcove 8/Niche 3 test site was developed, and both model calibration and 
prediction analyses were performed (BSC 2004 [DIRS 169861], Section 7.6). Infiltration rate, 
seepage rate, and tracer concentration data from the tests were used to corroborate model 
simulations. It was found that the field observations are well represented by the modeling 
results. For example, Figure 6-8 shows a comparison between simulated and observed seepage 
rate as a function of time. A similar model evaluation approach is also used for Alcove 1 tests. 
Again, modeling results are found to be consistent with field observations (e.g., Figure 6-9). 
These comparisons demonstrate that a continuum-approach-based model is able to capture 
important features of the unsaturated flow and transport processes in the UZ. 
Figure 6-8. Comparison Between Simulated Seepage Rates as a Function of Time and Field 
Observations Collected from Alcove 8/Niche 3 Tests 
Source: BSC 2004 [DIRS 169861], Figure 7.6-8. 

Figure 6-9. Comparison Between Simulated Seepage Rates as a Function of Time and Field 
Observations Collected from Alcove 1 Tests 
Source: Liu et al. 2003 [DIRS 162470], Figure 4. 
6.3.4 Treatment of Heterogeneity 
Heterogeneities exist at different scales within both fracture and matrix continua in the UZ. 
Treatment of subsurface heterogeneity is important for modeling flow and transport processes. 
A geology-based deterministic approach, in which an entire model layer is assigned uniform 
properties, is used mainly for representing subsurface heterogeneity. 
The key justification for the above approach is that the overall behavior of site-scale flow and 
transport processes is determined mainly by relatively large-scale heterogeneities associated with 
the geologic stratification and tectonic features (e.g., faults) of the mountain. Within the same 
geologic unit, hydrologic properties are relatively uniformly distributed because of the intrastrata 
homogenization induced by tuff depositional environments. This justification is also consistent 
with a field observation that matrix saturation distribution is relatively uniform within a given 
geologic unit (Flint 1998 [DIRS 100033], pp. 24 to 30). Displacement of strata along faults can 
result in units with different hydrologic properties being placed against each other across the 
fault, resulting in lateral heterogeneities within the UZ. 
Zhou et al. (2003 [DIRS 162133]) recently demonstrated the validity of this approach in dealing 
with subsurface heterogeneity. They used a two-dimensional vertical cross section in the east 
west direction through Borehole USW UZ-14 to investigate the effect of multiscale 
heterogeneity on unsaturated flow and transport within the UZ. Specifically, they generated and 
used random fields of three selected properties: matrix permeability, km; matrix van Genuchten 
parameter, am; and fracture permeability, kf (Zhou et al. 2003 [DIRS 162133], Figure 13). For 
comparison, they employed different sets of rock property distributions in three cases. In these 

cases, mean rock properties for a given geological layer are the same. In Case A, the layered 
approach mentioned above was used. In Case B, stochastically generated kf variability was 
considered within a geological layer. In Case C, variabilities of all the selected rock properties 
were included, with the variabilities determined from the measured hydrologic properties. Thus, 
Case A only considers large-scale heterogeneity, while Cases B and C include small-scale 
heterogeneity within a geological unit. 
Figure 6-10 shows comparisons of vertical water fluxes within the matrix and fractures along the 
repository zone for the three cases. Although relatively large differences exist for the water flux 
in the matrix, distributions of water fluxes in fractures are very similar for these three cases. 
Because the matrix flux corresponds to only a small percentage of total water flux, the 
three cases essentially provide similar water flow fields at the site scale. Zhou et al. (2003 
[DIRS 162133], Figure 17) also compared simulated results for tracer transport from the 
repository to water table, and again found that the results are similar for the three cases. In 
summary, the study of Zhou et al. (2003 [DIRS 162133]) demonstrates that heterogeneities 
within each geological unit have only a minor effect on the site-scale flow processes. 
Figure 6-10. Comparison of Simulated Matrix and Fracture Flux (m/s) at the Repository Horizon in Cases 
A, B, and C 
Source: Zhou et al. 2003 [DIRS 162133], Figure 16. 

6.3.5 van Genuchten Relations for Modeling Unsaturated Flow in Fractures 
In the dual-continua approach, porous-medium equivalence has been used for describing water 
flow in the fracture continuum (National Research Council 1996 [DIRS 139151], p. 380). 
Specifically, Darcys law is used to determine water flux within the fracture continuum, and 
constitutive relations between relative permeability, capillary pressure, and saturation 
(van Genuchten 1980 [DIRS 100610]) are employed for modeling unsaturated water flow in 
fractures. The van Genuchten (1980 [DIRS 100610]) relations are given by 
n ]- m
Se = [1+aP
c 
(Eq. 6-1) 
1/ mm ]2
kr =Se [1- (1- Se ) (Eq. 6-2) 
where Pc is the capillary pressure; kr is the relative permeability; a, n, and m are empirical fitting 
parameters with m equal to 1  1/n; and Se is the effective saturation given by 
S - Sr
=
Se Ss - Sr (Eq. 6-3) 
where S is the water saturation, Sr is the residual saturation, and Ss is the satiated saturation. The 
parameter m is an index of pore size distribution. 
Although van Genuchten (1980 [DIRS 100610]) relations have been widely used in porous 
media, their usefulness for fractures has not been fully established. To evaluate these relations, 
Liu and Bodvarsson (2001 [DIRS 160110]) performed numerical experiments for 
two-dimensional fracture networks. Figure 6-11 shows one of the fracture networks generated 
from fracture data collected in the UZ of Yucca Mountain. 
Source: Liu and Bodvarsson 2001 [DIRS 160110], Figure 1b. 
Figure 6-11. A Computationally Generated Fracture Network 

The effective constitutive relations for fractures were determined by numerical simulations of 
steady-state unsaturated flow in fracture networks (Liu and Bodvarsson 2001 [DIRS 160110]). 
The rock matrix is treated as being impermeable for purposes of focusing on the fracture 
continuum. Different parameters (including aperture and van Genuchten parameters) were 
assigned to different groups of individual fractures. Liu and Bodvarsson (2001 [DIRS 160110]) 
imposed the same capillary pressures at the top and bottom boundaries of a fracture network and 
nonflow conditions at the side boundaries. The capillary pressures at the top and bottom 
boundaries were considered to be effective capillary pressures of the fracture network. Because 
the effective capillary pressure gradient is zero in the vertical direction (resulting from the same 
pressure values used as the top and bottom boundary conditions), the average vertical flux should 
(according to Darcys law) be the same as the hydraulic conductivity of the corresponding 
fracture network. The network is considered to be a fracture continuum within the context of the 
dual continua approach. For a number of different uniform capillary pressures at the boundaries, 
the corresponding values of volumetric saturation and hydraulic conductivity (or relative 
permeability) can be obtained for a fracture network, resulting in the desired constitutive 
relations. This computational procedure is similar to laboratory procedures to determine 
constitutive relations for porous media. The relative permeability is determined from the ratio of 
the unsaturated conductivity to the saturated conductivity (Liu and Bodvarsson 2001 
[DIRS 160110]). 
Some evaluation results of Liu and Bodvarsson (2001 [DIRS 160110]) are given in Figures 6-12 
and 6-13. These figures also show the results for BrooksCorey relations (Brooks and Corey 
1966 [DIRS 119392]), which can be expressed by 
-.
= 
Pc /Pd
Se 
(Eq. 6-4) 
2 
= Se 
(3+ )kr . (Eq. 6-5) 
where Pd is known as the air entry pressure and . is a dimensionless index of pore size 
distribution. If Pd is approximated by 1/a , the BrooksCoreys capillary pressure-saturation 
relation is equivalent to that of the van Genuchten model with (van Genuchten 1980 
[DIRS 100610]; Wang and Narasimhan 1993 [DIRS 106793]) 
.= n - 1 (Eq. 6-6) 
This relation allows use of the van Genuchten parameter n to estimate relative permeability using 
the Brooks-Corey model that has been employed in this study to minimize the number of 
property parameters. 
Figure 6-12 shows fairly good fits between the van Genuchten (1980 [DIRS 100610]) capillary 
pressure-effective saturation relations and the simulated retention curve, except for high 
saturations, for the fracture network in Figure 6-11. 

Figure 6-12. Fit of the van Genuchten Model to the Simulated Capillary PressureEffective Saturation 
Relations 
Source: Liu and Bodvarsson 2001 [DIRS 160110], Figure 2a. 
Figure 6-13. Comparison between Simulated Relative PermeabilityEffective Saturation Relations. The 
Curves Predicted Using the van Genuchten (VG) Relations, the BrooksCorey (BC) 
Relations, and a New Relation (Equation 6-10) with the m Values Determined from 
Figure 6-12. 
Source: Liu and Bodvarsson 2001 [DIRS 160110], Figure 3a. 

Figure 6-13 shows comparisons between the simulated relative permeabilityeffective saturation 
relations and curves predicted using the van Genuchten model and the Brooks-Corey model, with 
the m values obtained from curve fitting in Figure 6-12. The predicted relative permeability 
values are consistently smaller than the simulated ones for a given saturation, while the 
Brooks-Corey model gives better results than the van Genuchten model. This may result from 
the different representations of pore geometry and their applications to fractures. First, the 
Brooks-Corey (Brooks and Corey 1966 [DIRS 119392]) relative permeabilitysaturation relation 
was derived from a model, in which pores are represented by a group of parallel capillary tubes 
with different radii, whereas the van Genuchten relation is based on the more complicated 
pore-geometry model of Mualem (1976 [DIRS 100599]). The Brooks-Corey model representing 
pores with a group of parallel capillary tubes may be more consistent with the unsaturated flow 
in a fracture network characterized by a number of major flow paths in the vertical direction 
(Kwicklis and Healy 1993 [DIRS 100587]). Second, because of the difference between fracture 
network geometry and pore space geometry, tortuosities of flow paths in a fracture network are 
considerably different from those in a porous medium. Because pore sizes in a porous medium 
are generally much smaller than fracture apertures, unsaturated flow in a fracture network is 
mainly gravity-driven (Liu et al. 1998 [DIRS 105729]), especially for a large fracture water 
saturation and, consequently, the capillary force is generally much stronger in a porous medium. 
The latter is expected to result in more tortuous flow paths around solid particles (through pores) 
in a porous medium. The following expression for tortuosity factor t was assumed in deriving 
Equation 6-5 (Brooks and Corey 1966 [DIRS 119392]). 
t= 2 
eS (Eq. 6-7) 
If t is assumed to be its maximum value of 1, Equation 6-5 will become 
rk= )21( 
.+ 
eS (Eq. 6-8) 
Both the Brooks-Corey and van Genuchten models reasonably predict the simulated relative 
permeabilitysaturation relations for small water saturations (e.g., less than 0.10 in Figure 6-13). 
This may be because capillary force becomes important at low saturations, resulting in similar 
unsaturated flow behavior in both a porous media and a fracture network. These two models are, 
thus, approximately valid for modeling water flow in the Yucca Mountain UZ under ambient 
conditions, which generally involve very low fracture saturations as a result of low infiltration 
rates in that region. However, under disturbed conditions, the thermal-hydrologic response of 
the unsaturated rocks to the decay heat of nuclear wastes can give rise to relatively high fracture 
saturations around the repository. The van Genuchten and Brooks-Corey models may lead to 
considerable error in modeling flow processes under these conditions. To improve the accuracy 
of the Brooks-Corey model in predicting the relative permeability-effective saturation relation 
for a fracture network, Liu and Bodvarsson (2001 [DIRS 160110]) modify the tortuosity 
expression (Equation 6-7) for the Brooks-Corey model to 
t= Se 
2(1- Se 3/4) 
(Eq. 6-9) 

Compared with Equation 6-7, the above equation gives tortuosity factor values that are closer to 
1 for large saturations and essentially the same as those calculated from Equation 6-7 for low 
saturations. Although Equation 6-9, like the expressions for tortuosity factor used in both the 
Brooks-Corey and the van Genuchten models, is empirical, it is consistent with the previous 
discussion. Following Brooks and Corey (1966 [DIRS 119392]), and using Equation 6-9 leads 
to 
k
r 
=
S
e 
(3
-
2
Se 
3/4
+
2/ )
.
=
S
e 
(3
-
2
Se 
3/4
+
2 
n 1
-
) 
(Eq. 6-10) 
Improved matches between the simulated relative permeabilitysaturation relations and those 
calculated with Equation 6-10 are shown in Figure 6-13. Therefore, the new simulated 
constitutive relations can be represented by a combination of van Genuchtens capillary 
pressureeffective saturation relation and the modified Brooks-Corey relative 
permeability-effective saturation relation. 
In summary, the results of Liu and Bodvarsson (2001 [DIRS 160110]) indicate that the van 
Genuchten (1980 [DIRS 100610]) relations are valid for modeling water flow in the Yucca 
Mountain UZ under the ambient conditions that generally involve very low fracture saturations 
resulting from low infiltration rates in that region. 
6.3.6 Special Issues for Flow and Transport Modeling 
6.3.6.1 Gas Flow 
Gas (air) flow behavior is different from that of liquid water. No data are available to 
characterize gas relative permeability in the UZ of Yucca Mountain. It is reasonable to expect 
phase interference to reduce the mobility of the gas phase in both the matrix and the fractures. 
Indirect evidence of the reduction for gas flow between fractures and the matrix is found in 
pneumatic pressure data measured in the ESF (Rousseau et al. 1999 [DIRS 102097], pp. 77-110). 
These data show insignificant attenuation and lag of the pneumatic signal through the TSw, 
which can only occur in the presence of high permeability and/or low porosity. The very high 
gas saturation in the fractures indicates that the relative permeability of the gas phase in the 
fractures is also high. The effective porosity for the gas-phase system can be reduced by 
decreasing the mobility (or saturation) of the gas phase in the matrix, which provides a 
substantial portion of the gas-phase storage in the TSw. The widely used Brooks-Corey 
relationship for gas relative permeability, krg , is suitable for this problem and is given by 
(Brooks and Corey 1966 [DIRS 119392], p. 71) 
1 -
S
e 
... 
..
+
2 
(Eq. 6-11) 
2
...
(
1
rg
-
S
e
)
k
=
where . is a pore-size distribution parameter and Se is effective saturation given by 
Equation 6-3. For the van Genuchten relationship, which is used to describe liquid relative 
permeability and water potential, pore-size distribution is determined from liquid desaturation 
data. The van Genuchten pore-size distribution parameters n and m can be related to the 
MDL-NBS-HS-000005 REV 01 6-32 September 2004 

Brooks-Corey ., as shown in Equation 6-6 (van Genuchten 1980 [DIRS 100610], p. 895). 
Substituting m=1-1/n into Equation 6-6 gives 
.= m 
1 - m (Eq. 6-12) 
Substituting Equation 6-12 into Equation 6-11 gives 
2-m .
2 .-
k
rg =(1- Se ).1 Se m 
.. (Eq. 6-13) 
Equation 6-13 is used to describe the gas relative permeability in the fractures and matrix, and 
uses the same m as the liquid relative-permeability and water-potential relationships. 
6.3.6.2 Particle-Tracking Algorithm for Chemical Transport 
In general, there are two kinds of numerical algorithms for modeling chemical transport in the 
subsurface. One is the conventional algorithm based on finite-difference and/or finite-element 
methods. Another is the particle-tracking algorithm. In a particle-tracking algorithm, chemical 
mass is divided into a large number of particles. Chemical transport is simulated by calculating 
particle movement, which is determined by velocity fields, dispersion/diffusion coefficients, and 
fracture-matrix interaction formulations. Compared with the conventional approaches, particle 
tracking has the following two advantages. First, it can significantly reduce or eliminate 
numerical dispersion. Numerical dispersion is a common numerical problem for coarse grid 
simulations of chemical transport problems. It artificially smears concentration fronts in 
simulations. Second, the particle-tracking algorithms can be computationally more efficient. 
However, one shortcoming of particle-tracking algorithms is that they can only be used for 
chemical transport with simple chemical reactions like linear adsorption and decay. The above 
considerations suggest that particle-tracking algorithms are appropriate for modeling chemical 
transport with simple reactions, and conventional algorithms are appropriate for transport with 
complex reactions. Note that both particle tracking and conventional algorithms should yield 
similar simulation results for transport with simple reactions when numerical dispersion is 
insignificant. 
6.3.6.3 Dispersion in Fractures 
Although it is generally recognized that dispersion in a fractured medium is physically different 
from dispersion in a porous medium, the porous medium form of the dispersion tensor is 
generally used for lack of a more appropriate expression (Bear et al. 1993 
[DIRS 116773], p. 419). As discussed in Section 6.2.5, the dispersion may not be a major 
transport mechanism for the UZ of Yucca Mountain. It physically makes sense, because for a 
dual-continua system, chemical transport is mainly determined by the largest heterogeneity, the 
difference in properties between the matrix and fracture continua. In this case, heterogeneity in 
each continuum, resulting in the corresponding macroscopic dispersion process, becomes 
secondary. Therefore, a more accurate description of the fracture dispersion may not 
significantly improve the accuracy of transport simulations. This is supported by a tracer 
transport simulation study on the ESF Alcove 1 test (Liu et al. 2003 [DIRS 162470]). The 

Alcove 1 modeling study shows that the simulation results are sensitive to matrix diffusion, but 
not to dispersion in the fracture continuum. 
6.3.6.4 Use of the Dual-Continua Approach for Modeling Radionuclide Transport 
Since radionuclide transport is a transient process, the use of the dual-continua approach may 
result in some modeling errors for chemical transfer between fractures and the matrix. This is 
particular true when the chemical transfer occurs only within a portion of matrix close to the 
fracture-matrix interfaces. Generally, the dual-continua approach may underestimate the 
chemical concentration gradient at the fracture-matrix interface, and, therefore, may 
underestimate chemical transfer from fractures to matrix under certain conditions. This is 
supported by the modeling study of Doughty (1999 [DIRS 135997], pp. 94-95), showing that the 
dual-continua approach yields shorter travel times than the MINC approach. Since the matrix 
transport processes correspond to relatively long travel times to the water table compared with 
those in fractures, the dual-continua approach is expected to give conservative predictions of 
radionuclide transport in the UZ. This point is further confirmed in BSC (2004 [DIRS 164500], 
Section 6.19), which reported that the simulated breakthrough time for tracer transport from the 
repository to water table are significantly longer for the MINC model than that for the 
dual-continua model. 
6.3.7 Active Fracture Model 
In a dual-continua approach, the treatment of fracture-matrix interaction is important for accurate 
modeling of flow and transport because flow and transport behaviors in fractures and the matrix 
are very different. This subsection discusses the AFM used in the UZ Flow and Transport 
Model. The validation of the AFM will be presented in Section 7. 
6.3.7.1 Active Fracture Concept 
Although a number of mechanisms exist for limiting fracture-matrix interaction (Section 6.1.3), 
fingering flow at a fracture network scale is considered to be a key mechanism, and more 
important than that at a single fracture scale. We expect that for unsaturated fractured rock, the 
water-flow pattern should be characterized by significant preferential (fingering) flow at a 
fracture-network scale, because of a combination of the large nonlinearity involved in an 
unsaturated system and heterogeneities of fracture structure at different scales (Liu et al. 1998 
[DIRS 105729]). The active fracture concept is based on the reasoning that as a result of 
fingering flow, only a portion of fractures in a connected, unsaturated fracture network 
contribute to liquid water flow, while others are simply by-passed. The portions of the 
connected fractures that actively conduct water are called active fractures. It is hypothesized 
that the number of active fractures in the UZ of Yucca Mountain is small compared to the total 
number of connected fractures. With this in mind, active fractures, rather than total connected 
fractures, must be used in numerical models. It is further hypothesized that the number of active 
fractures within a gridblock is large, such that a continuum approach is still valid for describing 
fracture flow. These hypotheses are consistent with the consideration that flowing fractures in 
the UZ are many and highly dispersed. 
To use the active fracture concept to model flow and transport in fractures, we treat active 
fractures as a portion of the homogeneous fracture continuum for a given gridblock. 

It is important to note differences between the AFM and the conventional, 
capillary-equilibrium-based, fracture water distribution model. The latter assumes that liquid 
water occupies fractures with small apertures first, and then fractures with relatively large 
apertures as water potential (or water saturation) increases. In contrast, the AFM presumes 
gravity-dominated, nonequilibrium, preferential liquid water flow in fractures, which is expected 
to be similar to fingering flow in unsaturated porous media. A liquid finger can by-pass a large 
portion of a porous medium, which does not necessarily correspond to large pores. It is also 
consistent with the numerical study results of Kwicklis and Healy (1993 [DIRS 100587], 
pp. 40974099), showing that distribution of liquid water in a connected fracture network is not 
necessarily determined by fracture apertures. 
Flow and transport conditions, and fractured rock properties should determine the fraction of 
active fractures in a connected fracture network, fa. An expression for fa must satisfy the 
following conditions: all connected fractures are active (fa = 1) if the system is fully liquid 
saturated; all fractures are inactive (fa = 0) if the system is at residual saturation; and fa should be 
related to water flux in fractures. More fractures are considered to be conducive for a larger 
water flux (Liu et al. 1998 [DIRS 105729], pp. 26352636). The water flux in fractures is also 
considered to be mainly dependent on fracture saturation because fracture water flow is 
gravity-dominated. A simple expression for fa (Liu et al. 1998 [DIRS 105729], pp. 26352636) 
that meets these conditions and includes one parameter only is a power function of effective 
water saturation in connected fractures, Se : 
ae
f =S . 
(Eq. 6-14) 
where . is a positive constant depending on properties of the corresponding fracture network, 
and the effective water saturation in connected fractures is given by 
eS = 
r 
rf 
S 
SS 
- 
- 
1 (Eq.6-15) 
where Sf is the water saturation of all connected fractures and Sr is the residual fracture 
saturation. Equation 6-14 is used to determine the fraction of active fractures because it is 
mathematically simple. As discussed below, Equation 6-15 allows us to treat all the 
ramifications of the active fracture hypothesis (modified fracture capillarity, relative 
permeability, and fracture-matrix interaction reduction) in an integrated manner. As indicated in 
Section 7.2, this equation is also consistent with fractal flow patterns often observed in 
unsaturated flow systems. 

6.3.7.2 Constitutive Relations 
Note that only the active fracture continuum, a portion of the total fracture continuum, 
contributes to flow and transport in fractures and fracture-matrix interaction. Therefore, fracture 
hydraulic properties should be defined for active fractures. The effective water saturation of 
active fractures, Sae , is related to the effective water saturation in connected fractures, Se, by (Liu 
et al. 1998 [DIRS 105729], p. 2636) 
e
S= S = S 1-.
ae e
fa (Eq. 6-16) 
Because Sae is less than or equal to one, . should be less than or equal to one. The effective 
water saturation of active fractures is related to the actual water saturation in active fractures, Sa, 
by (Liu et al. 1998 [DIRS 105729], p. 2636) 
S - S
ar
S = 
ae 
1- Sr (Eq. 6-17) 
If all connected fractures are considered to be active in conducting water, the water capillary 
pressure for the fracture continuum may be described by the well-known van Genuchten (V-G) 
relation (Equation 6-1). In the AFM, however, the V-G capillary pressure relation is considered 
to be relevant for the active fracture continuum rather than for the whole fracture continuum. 
The capillary pressure for active fractures is determined by replacing Se in Equation 6-1 with Sae 
and rearranging to give 
1
S P ) = [S - 1/ m - 1]1/ n = 1[S (.- 1)/ m - 1]1/ n (Eq. 6-18) 
(
ceae e
aa 
Equation 6-18 rather than 6-1 should be used in flow simulations in the fracture continuum. 
Figure 6-14 shows fracture capillary pressure curves for several . values. For a given effective 
water saturation in connected fractures, a larger . value corresponds to a larger effective water 
saturation in active fractures, and, therefore, to a lower absolute value for capillary pressure. 
The liquid-phase relative permeability for the active fracture continuum, kar, is directly 
determined by the effective water saturation of active fractures (Figure 6-14). However, as only 
a portion of the fractures are active, the relative permeability of the entire fracture continuum, kr , 
should be the relative permeability of active fractures multiplied by fa, or (Liu et al. 1998 
[DIRS 105729], p. 2636). 
k =k f = S . k (Eq.6-19)
r aar e ar 
where kar can be given by the following V-G permeability relation (Liu et al. 1998 
[DIRS 105729], p. 2636): 
1/ m }m ]2 (1-. )/2[1- 1{ - S (1-. )/ m }m ]2
Sk =
1/2[1- 1{ - S = S (Eq.6-20)
arae aee e 

Combining Equations 6-16 and 6-20 yields 
(1-.)/ m }m ]2
k =S (1+.)/2[1- 1{ - S (Eq. 6-21) 
re e 
10-1 
100 
101 
102 
m = 0.5 
0.5 
0.9 
.- Pc x a  
= 0 (V-G relation) 
0.0 0.2 0.4 0.6 0.8 1.0 
S 
e 
Source: Liu et al. 1998 [DIRS 105729], Figure 2. 
Figure 6-14. Capillary Pressure Curves of Fracture Continuum for . = 0, 0.5 and 0.9 
Relative permeability (kr) curves are shown in Figure 6-15 for several .values. In general, the 
relative permeability (kr) is affected by . in a complicated manner for a given Se. A larger . 
value, resulting in a higher effective water saturation in active fractures (Sae), gives rise to a 
larger value of kar. On the other hand, a larger . value corresponds to a smaller value of fa. 
Because the former effect is dominant, a larger . value gives a larger relative permeability for a 
given effective water saturation of the fracture continuum, as indicated in Figure 6-15. 

10-9 
10-8 
10-7 
10-6 
10-5 
10-4 
10-3 
10-2 
10-1 
100 
0.5 
0.9 
k r 
.m=0.5 
= 0 (V-G relation) 
Figure 6-15. Relative Permeability Curves of Fracture Continuum for . = 0, 0.5 and 0.9 
0.2 0.4 0.6 0.8 1.0 
S e 
Source: Liu et al. 1998 [DIRS 105729], Figure 3. 
In the AFM, a term called the fracture-matrix interface-area reduction factor (R) accounts for 
three features of fingering flow that reduce fracture-matrix interaction. First, the average 
interface area between mobile water (saturated liquid water segments) in an active fracture and 
the surrounding matrix is smaller than the geometric interface area. Second, the number of 
active fractures is smaller than that of connected fractures. Conventionally, all the connected 
fractures were considered to contribute to fracture-matrix interaction. Third, average active 
fracture spacing is much larger than that for connected fractures. Under the quasi-steady-state 
condition, flow and transport between fractures and surrounding matrix is inversely proportional 
to the corresponding fracture spacing. Based on these considerations and Equation 6-14, Liu 
et al. (1998 [DIRS 105729], pp. 26362638) derived an approximate expression for the reduction 
factor: 
R. S 1+. (Eq. 6-22) 
e 
Note that the AFM uses a combination of the volume-averaged continuum method and a simple 
filter to deal with fracture flow and transport. Inactive fractures are filtered out in modeling 
fracture-matrix interaction, flow, and transport in the fracture continuum. Note that use of the 
filtering method adds a capability to continuum approaches for capturing dispersed fingering 
flow at a subgrid scale. This addresses a major limitation of continuum approaches, which was 

considered to be their inability to represent subgrid-scale fingering flow (Glass et al. 1996 
[DIRS 139237], p. 7). 
Note that the . factor may be interpreted as a measure of the activity of connected fractures. 
Generally speaking, a smaller . value corresponds to a larger number of active fractures in a 
connected fracture network. For example, .= 0 results in fa = 1 in Equation 6-14, corresponding 
to all connected fractures being active. On the other hand, .= 1 corresponds to zero fracture 
capillary pressure (Equation 6-18), indicating that all active fractures are saturated. In the latter 
case, the fraction of active fractures is very small for small percolation fluxes because relatively 
high fracture permeabilities measured at Yucca Mountain allow most of the water to flow 
through only a few fractures. The . value cannot be determined by laboratory measurements of 
fractured core samples, because . represents an inherently large-scale process. Instead, it must 
be inferred through inverse modeling using the site-scale UZ model and field-scale data collected 
at Yucca Mountain (Liu et al. 1998 [DIRS 105729], p. 2638). Note that preferential (fingering) 
flow in unsaturated fractures is captured by the AFM-based continuum approach even when a 
coarse numerical grid is used. For an extreme example, the fracture pore velocity simulated with 
the AFM (for a . value of 0.8) is about 10-4 m/s (in the TSw unit) (Liu et al. 1998 
[DIRS 105729], Figure 12), or 3,153.6 m/yr. This velocity corresponds to very fast preferential 
flow paths. (It should be emphasized that this velocity is not realistic for the UZ, and only used 
for demonstrating the capability of the AFM in capturing a large range of fast flow behavior.) 
6.4 MODEL UNCERTAINTY 
The objective of this report is to document the conceptual model and numerical approaches for 
UZ flow and transport under ambient conditions. These models have been developed mainly 
based on the geologic setting of the UZ and a variety of data collected from the UZ, in addition 
to theoretical and numerical studies conducted in the last two decades (Sections 6.1 to 6.3). 
However, these models are simplifications and/or approximations of the real-world system and 
subject to uncertainties. 
Flow focusing . While the conceptual model for UZ flow has been supported by many field 
observations (as discussed in this report), some conceptual aspects related to focused flow at 
different scales are not fully understood. The flow focusing mechanism has been partially 
considered by the use of the AFM in site-scale models. The AFM considers only a portion of 
fractures in a connected, unsaturated fracture network to contribute to liquid water flow, while 
others are simply bypassed. The AFM has been implemented in the UZ flow and transport 
models (BSC 2004 [DIRS 169861]; BSC 2004 [DIRS 164500]). 
Flow paths below the repository . Flow paths below the repository are critical for 
radionuclide transport from the repository to water table. Because the data available for 
characterizing these flow paths and the associated rock properties are very limited, the current 
conceptual model for flow below the repository (Section 6.1.2) is subject to uncertainty. 
However, the good matches between chloride and strontium data in samples below the repository 
and simulation results from the site-scale UZ flow model (BSC 2004 [DIRS 169861], Section 7) 
indicate that the UZ flow model (based on the current conceptual model) essentially captures 
important flow paths below the repository. 

The continuum approach . The UZ flow model is based on the continuum approach (that 
conceptualizes a fracture network as a continuum), as discussed in Section 6.3. The continuum 
approach is a practical approach for dealing with a large-scale, average UZ flow process, and it is 
generally supported by the consistency between continuum-approach-based model results and 
field observations (Section 6.3.3). However, it is uncertain that the continuum approach is 
adequate for capturing effects of highly localized (or focused) flow paths. 
The AFM . The AFM is a key element of UZ flow and transport model (BSC 2004 
[DIRS 169861]; BSC 2004 [DIRS 164500]). The validity of the AFM is presented in Section 7. 
The AFM-based simulation results are shown to be consistent with the relevant field 
observations and the AFM itself is also theoretically related to fractal flow patterns often 
observed in unsaturated systems (Section 7). However, it is uncertain that the AFM adequately 
captures the complex flow behavior in the unsaturated fractures. 
A sensitivity study of the AFM parameter on flow and transport simulations is presented in BSC 
(2004 [DIRS 169861], Section 6.8). The study shows that values for the AFM parameter that are 
used in the current UZ flow and transport models likely underestimate radionuclide travel times 
from the repository to water table. Therefore, the current UZ flow and transport models (based 
on these parameter values) are conservative. 
van Genuchten relations . UZ flow and transport models use van Genuchten (1980 
[DIRS 100610]) relationships developed especially for porous media for describing unsaturated 
flow in fractures. Liu and Bodvarsson (2001 [DIRS 160110]) reported that van Genuchten (1980 
[DIRS 100610]) relationships may be valid for low water saturations in the fracture continuum 
(corresponding to the ambient conditions), but underestimate fracture relative permeability for a 
large range of relatively high water saturations. 

7. VALIDATION 
This section documents activities to validate the AFM and the corresponding model validation 
results. 
7.1 MODEL VALIDATION ACTIVITIES 
The AFM has been used in UZ flow and transport models. The AFM is a modification of the 
traditional dual-continua model that specifies a constitutive relationship for unsaturated flow in 
fractures. This modification is motivated by field observations showing that under unsaturated 
conditions, not all fractures in a connected fracture network actually carry water flow (Liu et al. 
1998 [DIRS 105729]). The AFM has been reviewed and published by Liu et al. (1998 
[DIRS 105729]), and several papers (e.g., Houseworth et al. 2003 [DIRS 164394]; Liu et al. 
2003 [DIRS 162470]; Zhou et al. 2003 [DIRS 162133]; Xu et al. 2003 [DIRS 162124]) 
describing simulation results based on the AFM have been published in the Journal of 
Contaminant Hydrology, a peer-reviewed international journal publishing scientific articles 
pertaining to the contamination of groundwater. Section 7.2 shows that the AFM is 
approximately consistent with a fractal-distribution behavior for liquid water (characterized by a 
fractal dimension) in a fracture network. The fractal flow behavior has been often reported in the 
literature for unsaturated flow and multiphase flow systems. The fractal analysis is used to 
analyze the fracture coating data from UZ, indicating that the UZ may also exhibit fractal flow 
behavior. This consistency provides an important theoretical foundation for the AFM. 
Section 7.3 demonstrates that the AFM also captures behavior of film flow that has been 
regarded as a potentially important mechanism for water flow in unsaturated fractures (e.g., 
Tokunaga and Wan 1997 [DIRS 139195]; Tokunaga et al. 2000 [DIRS 152914]), which further 
supports the usefulness of the AFM. The validation of the AFM with field observations from the 
Yucca Mountain UZ, including fracture coating data and carbon-14 data, is documented in 
Section 7.4. 
The criteria of model validation are given in the TWP (BSC 2004 [DIRS 169654], Section 2.2.1; 
BSC 2002 [DIRS 160819], Section I-1-3). The AFM is an element of the TSPA for the license 
application component model of UZ flow. As stated in the TWP (BSC 2004 [DIRS 169654], 
Section 2.2.1), models supporting that TSPA for the license application component require 
Level I validation. The criteria for model validation using carbon-14 data and fracture coating 
data are: (a) that simulated water travel times are sensitive to AFM parameters and within the 
range of measured data for the TSw unit; and (b) that the simulated active portion of the fractures 
is similar to the percentage of fractures with mineral coatings; or (c) that other factors, not 
directly related to the AFM, can explain any significant disparity between simulations and the 
observed results. 
The model validation criteria mentioned above allow for evaluating the AFM by showing 
whether model results based on the AFM are consistent with different field observations 
simultaneously when the relevant results are sensitive to the AFM parameters. Because 
carbon-14 data and fracture coating data are signatures of past flow and transport processes in 
the UZ, these data provide important insight into the flow and transport processes under ambient 
conditions and are directly related to the intended use of the AFM. Consistency of the AFM with 
these field observations (and the fractal flow behavior often observed in unsaturated systems) is 

able to demonstrate that the AFM is sufficiently accurate for its intended use (for modeling UZ 
flow and transport) given the uncertainties represented in the UZ flow and transport models that 
implement the AFM. As shown in Section 7.4, the criteria ((a) and (b)) are met for the suitable 
AFM parameter values. 
In numerical simulations reported in this section, codes TOUGH2 V1.4 (LBNL 2000 
[DIRS 146496]) and T2R3D V1.4 (LBNL 1999 [DIRS 146654]) are used because they have 
been comprehensively tested and widely used for modeling UZ flow and transport. 
The model validation activities documented in Sections 7.2 and 7.4 were published by Liu et al. 
(2003 [DIRS 166106]) in Vadose Zone Journal, a leading scientific journal for vadose zone 
hydrology. The film-flow model (Section 7.3) was published by Liu (2004 [DIRS 170129]) in 
Hydrogeology Journal, the official Journal of the International Association of Hydrogeologists. 
Both of these two journals are peer-reviewed scientific journals. 
The key scientific notebooks and the data tracking numbers (DTNs) of the specific input data 
sets for the model validation activities in this section are presented in Tables 7-1 and 7-2, 
respectively. 
Table 7-1. Scientific Notebooks 
LBNL Scientific Notebook ID M&O Scientific Notebook ID Relevant Pages Citation 
YMP-LBNL-HHL-GZ-1 SN-LBNL-SCI-227-V1 8-19,21-54,70-71,73-84, Wang 2003 
87 [DIRS 161654] 
YMP-LBNL-YSW-3 SN-LBNL-SCI-199-V1 92-99 Wang 2003 
[DIRS 161654] 
LBNL= Lawrence Berkeley National Laboratory; M&O=management and operating contractor; YMP=Yucca 
Mountain Project 
Table 7-2. Data Tracking Numbers for Input Data Used 
Data Description DTN 
1-D site-scale calibrated properties: supporting files LB02091DSSCP3I.001 [DIRS 161292] 
1-D Calibrated hydrologic properties for UZ model: Data LB02091DSSCP3I.002 [DIRS 161433] 
Summary 
Supporting files of calibrated hydrologic properties for UZ LB0208UZDSCPMI.001 [DIRS 161285] 
model: Mean Infiltration 
Yucca Mountain Project borehole locations MO9906GPS98410.000 [DIRS 109059] 
Diffusion of sorbing and non-sorbing radionuclides LA000000000034.002 [DIRS 148603] 
Infiltration maps for Three Infiltration Scenarios GS000308311221.005 [DIRS 147613] 
3-D UZ numerical grid LB03023DKMGRID.001 [DIRS 162354] 
Line Survey information from ESF Obtained to Estimate GS980308315215.008 [DIRS 107355] 
Secondary Mineral Abundance 
Fracture Properties for UZ Model Layer LB0205REVUZPRP.001 [DIRS 159525] 
Chemical & Isotopic Composition of Pore Water and Gas GS961108312271.002 [DIRS 121708] 
Carbon 13 and Carbon 14 Abundance in Water and Gas MO0012CARB1314.000 [DIRS 153398] 
1-D=one-dimensional; 3-D= three-dimensional; DTN=data tracking number; ESF=Exploratory Studies Facility; 
UZ=unsaturated zone 
MDL-NBS-HS-000005 REV 01 7-2 September 2004 

Finally, AP-SIII.10Q and AP-2.27Q also require documentation of decisions or activities that are 
implemented to generate confidence in the model during model development, including the 
following: 
(1) Selection of input parameters and/or input data, and a discussion of how the selection 
process builds confidence in the model [AP-SIII.10Q 5.3.2(b)(1) and AP-2.27Q 
Attachment 3 Level I (a)] 
Because the AFM is a conceptual model describing fracture-matrix interaction, its development 
does not involve input parameter values or input data (See Section 6.3.7). 
(2) Description of calibration activities, and/or initial boundary condition runs, and/or run 
convergences and a discussion of how the activity or activities build confidence in the 
model. Inclusion of a discussion of impacts of any non-convergence runs. 
[AP-SIII.10Q 5.3.2(b)(2) and AP-2.27Q Attachment 3 Level 1 (e)] 
Because the AFM is a conceptual model describing fracture-matrix interaction, its development 
does not involve calibration activities and/or the use of initial boundary conditions (See 
Section 6.3.7). 
(3) Discussion of the impacts of uncertainties to model results. [AP-SIII.10Q 5.3.2(b)(3) 
and AP-2.27Q Attachment 3 Level 1 (d) and (f)] 
Because the AFM is not a process model, its development does not generate numerical model 
results (See Section 6.3.7). 
(4) Formulation of defensible assumptions and simplifications. [AP-2.27Q Attachment 3 
Level I (b)] 
As discussed in Section 6.3.7, the development of the AFM is based on assumptions and 
simplifications accepted in the scientific community. The AFM was published in a 
peer-reviewed, highly regarded scientific journal Water Resources Research (Liu et al. 1998 
[DIRS 105729]) 
(5) Consistency with physical principles, such as conservation of mass, energy, and 
momentum. [AP-2.27Q Attachment 3 Level I (c)] 
As discussed in Section 6.3.7, the development of the AFM is consistent with fingering flow in 
unsaturated fractures. 
7.2 CONSISTENCY BETWEEN AFM AND FRACTAL FLOW BEHAVIOR IN 
UNSATURATED SYSTEMS 
7.2.1 Evidence of Fractal Flow-Patterns in Unsaturated or Multiphase Flow Systems 
Fractals have been shown to be a common language for describing many different natural 
phenomena (Mandelbrot 1983 [DIRS 160848]). A vast literature exists for discussing the validity 
of the fractal concept in a great number of fields. Many recent studies show that complex flow 

patterns in unsaturated or multiphase flow systems can be described by fractals. For example, 
viscous fingering in porous media has been experimentally shown to be fractal (Feder 1988 
[DIRS 160844], Chapter 4). (The problem of viscous fingering in porous media is of 
central importance in oil recovery.) Flury and Flhler (1995 [DIRS 160845]) fitted a 
diffusion-limited-aggregation (DLA) model for solute transport in one of three field plots under 
unsaturated conditions, and then predicted solute transport reasonably well for the other two. A 
detailed description of DLA is given in Flury and Flhler (1995 [DIRS 160845]). The DLA 
generates fractal patterns (Feder 1988 [DIRS 160844], pp. 5356). Persson et al. (2001 
[DIRS 160840]) further confirms the finding of Flury and Flhler (1995 [DIRS 160845]) by 
showing that flow patterns resulting from an unsaturated field site resemble fractals. Glass (1993 
[DIRS 160751]) demonstrated that unsaturated flow patterns in individual fractures can be 
reasonably modeled by a percolation-based model. Percolation-based models generate fractal 
patterns (Feder 1988 [DIRS 160844], Section 7.8; Stauffer and Aharony 2001 [DIRS 160846], 
Section 6.6). 
Although detailed experimental studies of unsaturated flow patterns in natural fracture networks 
are still lacking in the literature, unsaturated flow patterns in a fracture network are expected to 
be (at least approximately) fractal also. This expectation is supported by fracture coating data 
from the UZ of Yucca Mountain. As will be discussed in Section 7.4, fracture coating is 
generally a signature of water flow paths. Detailed line survey data for coated fracture is 
available from DTN: GS980308315215.008 [DIRS 107355]. Since the middle nonlithophysal 
(Tptpmn) unit (corresponding to UZ model layer tsw34) has the largest number of survey 
intervals, data from this unit are analyzed using the box counting method that will be discussed 
in Section 7.2.2. The locations of the coated fractures along the survey line form a set of points 
in a one-dimensional space. For a given box size (length of a segment) l, there are 30/l small 
boxes (or segments) for a given survey interval that is 30 m long. N in this subsection denotes 
total numbers of boxes that cover at least one location of the coated fractures (along the survey 
line) for all the survey intervals. The determination of N as a function of l is given in 
Appendix B. Figure 7-1 shows that the observed N values as a function of l can be fitted by a 
power function with a power of 0.5 that corresponds to a fractal dimension of 0.5 for the set of 
points. A more detailed discussion of fractal dimension will be given in Section 7.2.2. This 
indicates that the analysis result from coated fractures is consistent with a fractal flow pattern in 
the corresponding fracture network. Note that for a given spatial pattern, fractal dimensions are 
different for different Euclidean dimensions of a space. The curve fitting is performed using 
Tecplot. 

150 
25 
50 
75 
N 
100 
125 
10 20 30 4050 
l(m) 
Source: DTN: GS9803083152115 [DIRS107355]. 
Figure 7-1. Relation Between N and l (Appendix B). The Data Points Correspond to Observed Values for 
the Tptpmn Unit 
7.2.2 Fractal Dimension 
A fractal pattern is characterized by the fractal dimension (df ) that is generally noninteger and 
less than the corresponding Euclidean dimension of a space, D . Among the different definitions 
for fractal dimension (Feder 1988 [DIRS 160844], Section 2.3), the most straightforward 
definition is based on box counting. In this case, the fractal dimension is determined from the 
following equation by counting the number (N ) of boxes (e.g., square and cubic for 
two-dimensional and three-dimensional problems, respectively), needed to cover a spatial 
pattern, as a function of the box size (l ) (Feder 1988 [DIRS 160844], pp. 1415): 
l N )
(
=
...
L
l 
...
df 
(Eq. 7-1) 
where L refers to the size of whole spatial domain under consideration. Figure 7-2 shows a 
box-counting procedure for a spatial pattern with df = 1.6 in a two-dimensional domain with size 
L (Yamamoto et al. 1993 [DIRS 160843], Figure 3). 
MDL-NBS-HS-000005 REV 01 7-5 September 2004 

= ... > . . .. 
? . . .." @ . . ..& 
)6 !. 
Figure 7-2. Schematic Showing Demonstration of Box Counting Procedure for Several Box Sizes, with 
the Shaded Areas Containing Saturation and Active Flow 
Obviously, if a spatial pattern is uniformly distributed in space, the fractal dimension will be 
identical to the corresponding Euclidean dimension. In this case, the box number, N*, and the 
box size l have the following relation 
D 
N *(l)
=
...
L
l 
... 
(Eq. 7-2) 
7.2.3 Consistency of the AFM and a Fractal Flow Pattern 
Consider Figure 7-2 to be a gridblock containing a fracture network and the corresponding flow 
pattern in the fracture network to be fractal. Only a portion of the medium within a gridblock 
contributes to water flow (Figure 7-2). This is conceptually consistent with the AFM (Liu et al. 
1998 [DIRS 105729]). Note that in Figure 7-2, a box is shaded if it covers one or more fractures 
(or fracture segments) that conduct water. For simplicity, further consider that fractures are 
randomly distributed in space and thus the dimension for water saturation distribution is the 
corresponding Euclidean dimension when all the connected fractures actively conduct water. 

Combining Equations 7-1 and 7-2 gives 
l N 
( )]1/ df
=
)]1/ D
N (l
*
[ 
[ 
(Eq. 7-3) 
The average water saturation (S) for the whole gridblock (Figure 7-2) is determined as 
V
S 
(Eq. 7-4) 
=
lDfN *(l) 
where V is the total water volume (excluding residual water) in fractures within the gridblock 
(Figure 7-2), and f is fracture porosity. Similarly, the average water saturation (Sb) for shaded 
boxes with a size of l is given as 
V
S 
(Eq. 7-5) 
=
b 
l D l N )
(
f 
From Figure 7-2, it is obvious that there exists a box size l1 < L satisfying: 
V
1 (Eq. 7-6) 
=
l1 
Df
Based on Equations 7-3 to 7-6, the average saturation for shaded boxes with a size of l1, Sb1, can 
be expressed by 
df 
S
b1
=
S
D 
(Eq. 7-7) 
Because a fractal is similar at different scales, the procedure for deriving Equation 7-7 from a 
grid-block with size L can be applied to shaded boxes with a smaller size l1. In this case, for a 
given box size smaller than l1, the number of shaded boxes will be an averaged number for those 
within the relatively large shaded boxes with a size of l1. Again, one can find a box size l2 < l1 to 
obtain a saturation relation: 
2
=
S
....
df 
D
.
df
...
D
S
b
2
=
(
S
b1
) 
(Eq. 7-8) 
The procedure to obtain Equation 7-8 can be continued until it reaches an iteration level n* at 
which all the shaded boxes with a size of ln cover active fractures only. The resultant average 
saturation for these shaded boxes is 
n* 
df
...
...
S
bn 
=
(S )
.
D
. 
(Eq. 7-9) 

By definition of active fractures, Sbn should be equivalent to the effective saturation of active 
fractures. It is remarkable that Equation 7-9 is similar to Equation 6-15, obtained from a key 
hypothesis of the AFM that the fraction of active fractures in an unsaturated fracture network is a 
power function of the average effective saturation of the network. Comparing these two 
equations yields: 
.= 1 -
.
.
. dDf 
.
.
. n* 
(Eq. 7-10) 
Equation 7-10 provides the first theoretical relation between the parameter . and the fractal 
dimension for a fractal flow system, while . was initially developed as an empirical parameter 
(Liu et al. 1998 [DIRS 105729]). Therefore, the AFM essentially captures fractal flow behavior 
at the subgridblock scale (df < D), whereas traditional continuum approaches assume a uniform 
flow pattern (or effective-saturation distribution) at that scale (corresponding to df = D or . = 0). 
In other words, the AFM can be used for simulating fractal flow behavior in an unsaturated 
fracture network that cannot be handled by the traditional continuum approach. 
Equation 7-10 implies that in the fractal flow model, . is not a constant, but a function of 
saturation, because both iteration level n* and df may be dependent on water saturation for a 
given fracture network. However, a constant . is a reasonable treatment at least for a limited 
range of water saturations (or flow conditions), which is the case for the Yucca Mountain UZ 
where fracture saturation is typically less than 10 percent under ambient conditions. This is 
because . will not change significantly for a limited range of saturation. It is not totally clear how 
. depends on the other hydraulic parameters for a large range of water saturations. Experimental 
evidence suggests that . is a weak function of saturation (at least for porous media), which will 
be discussed below. It is obvious from the derivation of Equation 7-10 that the fractal flow 
concept and Equation 7-10 can be applied to porous media also, as long as fingering flow 
patterns in them are fractals. Therefore, results from porous media can be used to conceptually 
evaluate the relation between . and water saturation for unsaturated fracture networks. 
Based on laboratory experimental observations collected by applying water at the top of the 
corresponding porous media, Wang et al. (1998 [DIRS 155770], pp. 21882189) reported a 
relation between flow conditions and a parameter, F, defined as the ratio of horizontal 
cross-sectional area occupied by fingers to the total cross-sectional area. F corresponds to fa, 
defined as the portion of active fractures in a fracture network (Liu et al. 1998 [DIRS 105729]). 
Wang et al. (1998 [DIRS 155770], pp. 21882189) related F to the ratio of average water flux 
through the whole cross-sectional area, q, to saturated hydraulic conductivity of the porous 
medium, Ks, by 
. q . 1/ 2 
F .. 
.. 
. Ks . (Eq. 7-11) 

for q/Ks = 0.4  1.0. By definition, the average water flux within fingers (qF) can be related to q 
by 
q
qF =
F (Eq. 7-12) 
and the average water saturation of fingers, SF, can be related to the average water saturation for 
the whole cross-section area, Se, by 
SF =Se 
F (Eq. 7-13) 
It is expected that flow within a gravitational finger is gravity dominated. In this case: 
qF =kr = SF 
*
Ks (Eq. 7-14) 
Equation 7-14 uses the Brooks-Corey (Brooks and Corey 1964 [DIRS 156915]) model for 
describing relative permeability (kr)saturation relationship. * is a constant. Combining 
Equations 7-11 to 7-14 yields 
* 
F= (Se )1+* 
(Eq. 7-15) 
Comparing the above equation with Equation 6-14 gives 
 * 
.=
1 +* (Eq. 7-16) 
Therefore, . is a constant under certain conditions in porous media. Consequently, it is expected 
that . should be a weak function of saturation for unsaturated fracture networks if fingering flow 
patterns in a porous medium are considered to be an analogue of flow patterns in the networks. 
Equation 7-16 cannot be directly used for estimating .values for fracture networks (in the AFM) 
because detailed flow mechanisms are different for unsaturated fractured rock and porous media. 
It also needs to be emphasized that Equation 7-16 is valid for porous media under a condition of 
q/Ks = 0.4 1.0 (Wang et al. 1998 [DIRS 155770], pp. 21882189). The relation between .and 
other hydraulic properties has not been established for a fracture network. 
7.3 COMPARISON WITH A FILMFLOW MODEL 
Film flow on fracture surfaces may be an important mechanism for fast flow in unsaturated 
fractured rocks (Tokunaga and Wan 1997 [DIRS 139195]), although the importance of the film 
flow in the UZ is still an issue of debate (Pruess 1999 [DIRS 104250]). As an alternative 
conceptual model for unsaturated flow in fractures, a model assuming pure film flow within 
unsaturated fractures is developed to compare with the AFM. The major objective of this 

comparison is to demonstrate that fast flow behavior caused by film flow is already essentially 
captured by the current version of the AFM. 
7.3.1 Film-Flow Model 
Tokunaga et al. (2000 [DIRS 152914], pp. 17431744) both conceptually and experimentally 
demonstrated similarities between film flow on rough fracture surfaces and unsaturated flow in 
porous media. They also found that measured film thickness-potential relation data could be 
fitted very well by a power function, which may be related to unsaturated flow in porous media 
with fractal pore-size distributions (Tokunaga et al. 2000 [DIRS 152914], p. 1743). 
Constitutive relationships for porous media with fractal pore-size distributions have been 
extensively studied. The most commonly used constitutive-relationship model for these porous 
media is the Brooks-Corey model, although this model was not initially developed based on 
fractal concepts (Brooks and Corey 1964 [DIRS 156915]). The Brooks-Corey model can be 
formulated as follows (Liu and Bodvarsson 2001 [DIRS 160110]) 
-.
= 
Pc /Pd
Se 
(Eq. 7-17a) 
2 
=t Se 
(1+ )kr . (Eq. 7-17b) 
t= Se 
2 
(Eq. 7-17c) 
where Pc is the capillary pressure, Pd is the air entry pressure, . is a dimensionless index of pore 
size distribution, kr is the relative permeability, t is the tortuosity factor, and Se is the effective 
saturation. Note that Equation 7-17a is valid when absolute values of Pc are larger that the 
absolute value of Pd. 
Film flow is closely related to fracture surface roughness, which has also been studied 
extensively (National Research Council 1996 [DIRS 139151]). It has been found that the surface 
topographies for fractures could be represented in terms of fractal geometry. Although an 
equivalent pore-size distribution for a fracture surface has not been defined, it is conceptually 
reasonable to hypothesize (based on the conception of Tokunaga et al. (2000 [DIRS 152914], 
p. 1743)) that film flow on a fractal fracture surface is similar to an unsaturated water flow 
process in a porous medium with fractal pore-size distribution. Based on this hypothesis, the 
Brooks-Corey model can be adopted to develop a constitutive-relationship model for film flow. 
Considering average film thickness, f , and film transmissivity, T, to be analogues of effective 
water saturation and hydraulic conductivity (Brooks and Corey 1964 [DIRS 156915]), 
respectively, for a porous medium, one can obtain 
-.
f
Pc
= 
fref 
Pref 
(Eq. 7-18a) 

2
1 
T= .. 
f . (. *+ + )
. 
. 
T 
. 
ref . fref .. 
(Eq. 7-18b) 
. *
t.f (Eq. 7-18c) 
where fref and Tref are average film thickness and film transmissivity, respectively, for a 
reference capillary pressure Pref , and . * is an empirical constant. Upper limits for f and T, 
unlike their counterparts for porous media, cannot be defined for unbounded fracture surfaces 
(Tokunaga et al. 2000 [DIRS 152914]). Here, . is considered to be a parameter characterizing 
the geometry of the fracture surface. Since film flow is essentially two-dimensional and 
pore-scale water flow in a porous medium is essentially three-dimensional, different tortuosity 
factors are expected for the two different cases. 
Experimental observations of Tokunaga and Wan (1997 [DIRS 139195]) and Tokunaga et al. 
(2000 [DIRS 152914]) are used to verify the proposed constitutive-relationship model for film 
flow. Specifically, we examine whether Equation 7-18 can match the data. Note that the two 
data sets used here are measured for very different fracture surfaces, corresponding to a natural 
fracture surface of Bishop Tuff (Tokunaga and Wan 1997 [DIRS 139195], p. 1298) and an 
artificially roughened surface (Tokunaga et al. 2000 [DIRS 152914], p. 1740). Comparisons 
with these two data sets provide a unique opportunity to examine the validity (or robustness) of 
the proposed model under different conditions. 
Tokunaga et al. (2000 [DIRS 152914], p. 1743, Figure 6) showed that the measured film 
thicknesspotential relation data could be fitted by a power function corresponding to . = 0.37 
in Equation 7-18a. The curve fitting is performed using Tecplot for all the relevant figures in 
this subsection. Figure 7-3 shows a match of Equation 7-18b with the surface 
transmissivity-film thickness relation (Appendix A of this report) of Tokunaga et al. (2000 
[DIRS 152914]), which was derived from their measurements, indicating that the relation can be 
represented by a power function with a power value of 6.91. Using . = 0.37 and the power value 
of 6.91, we obtain . * = 0.50 from Equation 7-18b. Figure 7-4 shows matches of 
Equations 7-18a and 7-18b with the data of Tokunaga and Wan (1997 [DIRS 139195]), again 
indicating that the data are very well represented by power functions. The resultant . and . * 
values are 1.36 and -1, respectively. Different . values are obtained for the two data sets, 
because of the differences between the corresponding fracture surfaces, as previously mentioned. 
Considerably different . * values are also obtained for the two surfaces as a potential result of 
different ranges of average film thickness involved in the two data sets (Figures 7-3 and 7-4). 
Further examination of the relation from Tokunaga et al. (2000 [DIRS 152914]) (Figure 7-3) 
seems to indicate that it can be more accurately represented by different power functions for 
different thickness ranges. For example, Figure 7-5 shows a match of Equation 7-18b to the data 
of Tokunaga et al. (2000 [DIRS 152914]) that exclude measurements below the thickness of 2 
 m, as compared with the match in Figure 7-3. The resultant power value is 5.67, corresponding 
to . * = -0.74 (based on Equation 78b and . = 0.37 given by Tokunaga et al. (2000 
[DIRS 152914])). This is generally consistent with . * = -1 for the data of Tokunaga and Wan 
(1997 [DIRS 139195]) (Figure 7-4), considering that their data involve larger values of average 
film thickness than those reported by Tokunaga et al. (2000 [DIRS 152914]). 

Theoretically, .* should be positive because a tortuosity factor should be smaller than one 
(Brooks and Corey 1964 [DIRS 156915]). The negative .* value results from the empirical 
nature of Equations 7-17 and 7-18. A similar situation was also reported for several different 
unsaturated porous media (Schaap and Leij 2000 [DIRS 160841]). Based on the above analyses, 
.* = -1 seems to be reasonable for film flow with an average film thickness larger than 2 m. In 
summary, while the proposed model may need to be further evaluated using more data sets, the 
excellent agreement between calculation results and experimental observations of Tokunaga and 
Wan (1997 [DIRS 139195]) and Tokunaga et al. (2000 [DIRS 152914]) supports the usefulness 
of the model for describing film flow in unsaturated fractures. 
10
-11 
10
-12 
10
-13 
10
-14 
10
-15 
Surface Transmissivity (m2/s) 
1 2 345 
Average Film Thickness (micrometer) 
NOTE: Squares correspond to the surface transmissivity-film thickness relation (Appendix A) obtained from Figure 9 
of Tokunaga et al. (2000 [DIRS 152914]). 
Figure 7-3. Match of Equation 7-18b to Surface Transmissivity-Film Thickness Measurements 

(a) 
100 101 102 103 
100 
101 
102 
()Average Film Thickness micrometer
-Capillary Potential (Pa) 
(b) 
Surface Transmissivity (m2/s)
10
-8 
10
-9 
10
-10 
10
-11 
100 101 102 103 
-Capillary Potential (Pa) 
NOTE: Squares correspond to the measurements (Appendix A). (a) potential measurements given in Figure 7 of 
Tokunaga and Wan (1997 [DIRS 139195]); (b) potential measurements given in Figure 6 of Tokunaga and 
Wan (1997 [DIRS 139195]). 
Figure 7-4. Matches of Equation 7-18 to (a) Film Thickness and (b) Surface Transmissivity-Film 
Thickness 

10
-12 
10
-13 
10
-14 
10
-15 
10
-16 
1 2 345 
Average Film Thickness (micrometer) 
NOTE: Squares correspond to the surface transmissivity-film thickness relation (Appendix A) obtained from Figure 9 
of Tokunaga et al. (2000 [DIRS 152914]) that exclude points below the thickness of 2  m, as compared with 
the match in Figure 9. 
Figure 7-5. Match of Equation 7-18b to Surface TransmissivityFilm Thickness Measurements 
Assuming that film flow only occurs in unsaturated fractures, the fractures would become 
saturated when the average film thickness is equal to half the average aperture. In this case, the 
air entry value Pd for fractures can be used as the reference capillary pressure. As a result, film 
thickness ratio and transmissivity ratio in Equation 7-18 are equivalent to the effective saturation 
(Se) and relative permeability (kr), respectively, for fractures. Equation 7-18 with . = -1 is then 
rewritten as 
-.
Pc
=
Se Pd 
(Eq. 7-19a) 
kr =Se 
2/ . 
(Eq. 7-19b) 
Note that for the same . value, the ratio of relative permeability from the Brooks-Corey model 
(Equation 7-17) to that from Equation 7-19b is Se3, indicating that Equation 7-19b predicts much 
higher kr value than the Brooks-Corey model at low saturations. That also explains why film 
flow corresponds to fast flow in unsaturated fractures. Equation 7-19 can be used to describe 
film flow within the context of the continuum approach, if all fractures are assumed to be 
hydraulically the same within a gridblock. Note that effects of variability in fracture aperture are 
not considered in Equation 7-19. This issue may need further investigation in the future if film 
flow is determined to be a key flow mechanism. 
10
-11 
Surface Transmissivity (m2/s) 

7.3.2 Model Comparison 
This section provides a simple comparison between the film-flow model (Equation 7-19) and the 
AFM. In welded units, water mainly percolates through fractures (Liu et al. 1998 
[DIRS 105729], Figure 7-6). For a given infiltration flux, pore velocity within fractures in a 
welded unit is proportional to the relative permeability, divided by the effective saturation, 
because fracture flow is gravity dominant (Liu et al. 1998 [DIRS 105729]). Therefore, for a 
given relative permeability, it will be determined whether the effective saturation predicted by 
the film model, using parameters derived from observations by Tokunaga and Wan (1997 
[DIRS 139195]) and Tokunaga et al. (2000 [DIRS 152914]), is approximately within the range 
of saturations calculated by the AFM for a range of .values. If it is the case, pore velocity 
determined from the film-flow model should be approximately within the range of pore velocity 
predicted by the AFM. In other words, the fast flow behavior caused by fracture film flow is 
captured by the AFM. 
10
-7 
10
-8 
10-6 
10-5 
10-4 
10-3 
llambda=0.37 
ambda=1.36 
gamma = 0 
0.4 
0.8 
1.0 
0.2 0.4 0.6 0.8 1 
Se 
Source: From experimental results of Tokunaga and Wan (1997 [DIRS 139195]) and Tokunaga et al. (2000 
[DIRS 152914]). 
Figure 7-6. Comparison Between Relative Permeability-Saturation Relations Calculated Using the AFM 
with m = 0.633 (DTN: LB0205REVUZPRP.001 [DIRS 159525]) for Several . Values (Solid 
Red Lines) and Relations Calculated from the Film-Flow Model with . Values (Dashed Lines) 
10
100 
-1 
10
-2 
Relative permeability

Figure 7-6 shows a comparison between relative permeability-saturation relations calculated with 
the AFM and the film-flow model. For . = 0.37, even the AFM with .= 0 (i.e., all connected 
fractures are active) can predict larger pore velocity at low saturations compared to the film-flow 
model. For . = 1.36, the relative permeability-saturation relation given by the film-flow model 
is consistent with the AFM with a .value between 0.8 and 1.0. Therefore, fast flow predicted by 
the film-flow model with parameters obtained from observations by Tokunaga and Wan (1997 
[DIRS 139195]) and Tokunaga et al. (2000 [DIRS 152914]) can be captured by the AFM with 
different .values. This largely results from the capability of the AFM to capture a large range of 
flow behaviors. 
Although a typical . value for the UZ is not available, .should be bounded by the values used in 
Figure 7-6. This is based on the observation that water flow processes in the UZ described by the 
AFM are bounded by . values between 0 and 0.8. As indicated by Liu et al. (1998 
[DIRS 105729]), field observations support the concept that not all connected fractures are active 
in the UZ (. >0). On the other hand, Liu et al. (1998 [DIRS 105729], Figure 11) also showed that 
pore velocity within fractures in welded units is on the order of 1.0E-4 m/s (or 3154 m/year) for 
.=0.8. No evidence supports such a high pore velocity in the UZ. As a result, if film flow were 
indeed important in the UZ, the corresponding relative permeability-saturation relation would be 
bound by the relations for the two . values shown in Figure 7-6. Consequently, the above 
comparison is likely valid for the Yucca Mountain UZ. 
Note also that derivation of Equation 7-19 implies a uniform film flow in all fractures. This is 
supported by the widespread nature of the film flow observed from small-scale laboratory 
experiments (Tokunaga and Wan 1997 [DIRS 139195]; Tokunaga et al. 2000 [DIRS 152914]). 
This uniform film-flow generally results in a much larger degree of matrix diffusion (resulting 
from a larger fracture-matrix interfacial area) than with the AFM, and therefore a larger degree 
of retardation for radionuclide transport in the UZ, even when pore velocity is the same for the 
two models. All these considerations support the idea that AFM does not overestimate the 
performance of the UZ, even if film flow were the main mechanism for fracture flow in the UZ. 
7.4 EVALUATION OF THE AFM WITH CARBON-14 AND MINERAL COATING 
DATA 
Carbon-14 and fracture coating data are used for evaluating the AFM. They contain useful 
information regarding water flow and fracture-matrix interaction in the UZ under ambient 
conditions. It is especially of interest to examine if the AFM can represent two different data 
sets for a similar range of the AFM parameter ., which is an indication of whether the AFM is 
able to capture the large-scale UZ flow behavior. This model evaluation activity is documented 
in Scientific Notebooks (Wang 2003 [DIRS 161654], SN-LBNL-SCI-227-V1, pp. 819, 2154, 
7071, 7384; SN-LBNL-SCI-199-V1, pp. 9299). 
7.4.1 Model Validation with Carbon-14 Data 
Carbon-14 data were collected from perched water, pore water, and gas samples from the Yucca 
Mountain UZ (BSC 2002 [DIRS 160247], Section 6.6.4). Pore-water carbon-14 data from 
various boreholes at Yucca Mountain were affected by contamination from atmospheric 14CO2 
during drilling, which may result in apparently younger residence times (Yang 2002 

[DIRS 160839], Section 4.1.2; BSC 2002 [DIRS 160247], Section 6.6.4.2). Carbon-14 data 
from gas samples are considered to be most representative of in situ conditions (Yang 2002 
[DIRS 160839], Section 4.1.2). Gas samples were collected from different kinds of boreholes, 
including open surface-based boreholes and instrumented surface boreholes. The data from the 
latter boreholes (USW SD-12 and USW UZ-1) are the most reliable indicators of in situ 
conditions (BSC 2002 [DIRS 160247], Section 6.6.4.3). Carbon-14 residence ages (BSC 2002 
[DIRS 160247], Table 20) calculated using the data from these two boreholes are used for 
validating the AFM. Water travel times from the ground surface to the perched water bodies are 
dominated by PTn where flow occurs mainly in the rock matrix and is, thus, insensitive to the 
AFM parameters (Wang 2003 [DIRS 161654], SN-LBNL-SCI-227-V1, pp. 4950). Therefore, 
carbon-14 data collected from perched water are not used for validating the AFM. 
Gas-phase Carbon-14 ages (DTN: GS961108312271.002 [DIRS 121708] for Borehole USW 
SD-12 and DTN: MO0012CARB1314.000 [DIRS 153398] for Borehole USW UZ-1) are 
interpreted to be representative of ages of the in situ pore water. The rationale for this 
interpretation is provided by Yang (2002 [DIRS 160839], Section 4.1.2). This interpretation 
presumes rapid exchange of gas-phase CO2 (in hours to days) with dissolved CO2 and (HCO3-) in 
pore water. Furthermore, the amount of C in an aqueous-phase pore water relative to C in the 
CO2 gas-phase reservoir is a hundred times greater. Consequently, the aqueous phase will 
dominate the gaseous phase when exchange occurs, indicating the reasonableness of the 
interpretation (Yang 2002 [DIRS 160839], Section 4.1.2). 
One-dimensional numerical models are developed for Boreholes USW SD-12 and USW UZ-1. 
Numerical grids for these models are taken from DTN: LB02091DSSCP3I.001 [DIRS 161292]. 
The measurement elevations are determined from collar elevations of the boreholes 
(DTN: MO9906GPS98410.000 [DIRS 109059]) and depth information given in the DTNs in the 
above paragraph. The calibrated rock properties for present-day, mean infiltration maps are used 
except for the . values (DTN: LB02091DSSCP3I.002 [DIRS 161433]). The value of the AFM 
parameter . for model layers (tsw32 to tsw38) is varied for different simulations to check the 
sensitivity of this parameter to simulated water travel times. The top boundary condition 
corresponds to the present-day infiltration rate for flow simulations and a constant tracer 
concentration for transport simulations. Initial conditions for solute transport include 
zero concentration within the fractured rocks. Previous studies indicate that dispersion processes 
have an insignificant effect on overall solute transport behavior in unsaturated fractured 
rocks (Liu et al. 2003 [DIRS 162470]), and therefore they are ignored here. An 
effective-diffusion-coefficient value of 1.97E-10 m2/s is employed in this study and equal to the 
average value of measured coefficients for tritiated water (DTN: LA000000000034.002 
[DIRS 148603]; TOUGH2 V1.4 (LBNL 2000 [DIRS 146496]); and T2R3D V1.4 (LBNL 1999 
[DIRS 146654]) codes are used for simulating steady-state water flow and tracer transport 
processes. (The input and output files associated with these software items are described in 
Scientific Notebook (Wang 2003 [DIRS 161654], SN-LBNL-SCI-227-V1, pp. 819, 2154, 
70-71, and 7384) and submitted to TDMS under Output DTNs: LB0212C14INFIL.001 and 
LB0212AFPGAMMA.001.) Simulated water travel times (or ages) for the rock matrix are 
compared with carbon-14 ages. A simulated water travel time at a given location is defined as 
the time when the matrix concentration reaches 50 percent of the top-boundary concentration. It 
represents the average travel time for water particles from the ground surface to the location. 

Figure 7-7 shows simulated water travel times (ages) for different .values of UZ Model layers 
tsw32 to tsw38. The considerable sensitivity of simulated results to .indicates that carbon-14 
data are useful for validating the AFM and for constraining the . values for the TSw unit. For . 
values less than 0.4, simulated results approximately match the observations. A larger .value 
generally corresponds to a larger travel time for the matrix because of a smaller degree of matrix 
diffusion, resulting from a smaller fracture-matrix interfacial area available for mass transport 
between fractures and the matrix. 
Simulated water travel times change sharply at an elevation of about 1,100 m for two boreholes 
(Figure 7-7). This is because the upper portion of the TSw unit has relatively small fracture 
density values and, thus, corresponds to a smaller degree of matrix diffusion for a given . value 
(DTN: LB0205REVUZPRP.001 [DIRS 159525]). For the Borehole USW UZ-1, the simulated 
water travel time is generally longer than the observation for a given elevation. This may be a 
result of subsurface heterogeneity, which gives larger fracture densities (resulting in a larger 
degree of matrix diffusion) at the borehole location than what are used in the numerical model. 
Layer-averaged fracture properties are used in the UZ Model (Section 6.3.4). Also note that 
unlike the case for USW SD-12, the simulation result for .=0 provides the best match to the data 
for USW UZ-1. This may again result from the spatial variability. Like many other hydraulic 
properties (e.g., permeability), . is spatially variable. Nevertheless, .= 0.4 gives the reasonable 
matches to the data from the two boreholes simultaneously. 
In summary, a comparison between simulated water travel times and observed carbon-14 ages 
indicates that the AFM with . values less than 0.4 (for UZ model layers tsw32-tsw38) can 
reasonably represent the data. The comparison satisfies the model validation criterion that 
simulated water travel times are sensitive to the AFM parameters and within the range of 
measured data for the TSw unit (Section 7.1). 

(a) 
PTn 
TSw 
CHn 
gamma=0 
gamma=0.1 
gamma=0.2 
gamma=0.3 
gamma=0.4 
gamma=0.5 
gamma=0.6 
800 
1000 
1200 
1400 
Elevation(m) 
UZ-1 
Measured 
100 1000 10000 100000 1000000 
Age(Yrs) 
(b) 
Elevation(m) 
1300 
1200 
1100 
1000 
900 
800 
PTn 
TSw 
SD-12 
TCw 
CHn 
Measured 
gamma=0 
gamma=0.1 
gamma=0.2 
gamma=0.3 
gamma=0.4 
gamma=0.5 
gamma=0.6 
100 1000 10000 100000 1000000 
Age(Yrs) 
Source: Wang (2003 [DIRS 161654], SN-LBNL-SCI-227-V1, p. 87). 
Output DTN: LB0212C14INFIL.002 (files: C14_UZ-1_age.doc and C14_SD-12_age.doc). 
Figure 7-7. Comparisons Between Simulated Water Travel Times (Ages) for Rock Matrix at Boreholes (a) 
USW UZ-1 and (b) USW SD-12, as well as the Corresponding Carbon-14 Ages for Several . 
Values 

7.4.2 Model Validation with Mineral Coating Data 
The process of UZ mineral deposition is initiated during infiltration. Here, meteoric water 
interacts with materials in the soil, after which a portion may then enter the bedrock fracture 
network. Fracture coating is generally a signature of water flow paths. Therefore, the coating 
data are useful for validating the AFM describing water flow in fractures. 
Fracture coating data were collected in the ESF (DTN: GS980308315215.008 [DIRS 107355]). 
Observed spatial distribution of fractures with coatings is used to estimate the portion of active 
fractures in the UZ. For a given survey interval along ESF, a frequency of coated fractures can 
be estimated for a geologic unit, based on the total number of coated fractures. The ratio of 
coated-fracture frequency to total fracture frequency (DTN: LB0205REVUZPRP.001 
[DIRS 159525]) will provide an estimate of the portion of active fracture for the given geologic 
unit (Wang 2003 [DIRS 161654], SN-LBNL-SCI-227-V1, pp. 7071). The estimated average 
portion of the active fractures for the TSw is 7.2 percent. The abundance of mineral coating 
(coating volume divided by total rock volume), divided by the corresponding fracture porosity, 
gives another estimate of the portion of the active fractures in the UZ under ambient conditions. 
Abundance data for all intervals in welded tuffs have an arithmetic mean of 0.084 percent 
(BSC 2002 [DIRS 160247], Section 6.10.1.1), while a typical fracture porosity is 1 percent 
(DTN: LB0205REVUZPRP.001 [DIRS 159525]). Therefore, an estimate of the average portion 
of active fractures for welded units is %084.0%1 = 8.4 percent, close to the estimate determined 
from the frequency of coated fractures. Note that fracture coatings may not precisely represent 
active flow paths in the UZ and some flow paths may not have coatings (Liu et al. 1998 
[DIRS 105729]). Nevertheless, these values at least give a rough estimate of lower limits for the 
portion of active fractures in the UZ  about 10 percent. 
Mineral growth rate data imply that the UZ fracture network has maintained a large degree of 
hydrologic stability over time, and fracture flow paths in the deep UZ are buffered from 
climate-induced variations in precipitation and infiltration (BSC 2002 [DIRS 160247], 
Section 6.10.3.9). If the AFM actually represents water flow processes in the UZ, modeling 
results based on the AFM should be consistent with this important observation. 
To check the consistency of the AFM against the coating data, a one-dimensional model for 
Borehole USW SD-12 is used. The model is the same as that described in Sections 6.3.7 and 
7.2.1. USW SD-12 is chosen because it is located near the middle of the ESF, where coating 
data were collected. Two infiltration rates, present data mean infiltration rate and glacial 
maximum infiltration rate, are used for simulations. Again, uniform . distributions within model 
layers tsw32 to tsw38 are employed. The latter infiltration rate is about five times as large as the 
former rate and represents the maximum infiltration rate in past climates. 
Figure 7-8 shows the simulated average portion of active fractures, fa, for the relevant model 
layers (tsw32 to tsw38) as a function of infiltration rate and .. The average portion is calculated 
from Equation 6-14 using the average effective saturation for model layers tsw32 to tsw38. The 
calculated fa values range about 10 percent for . values close to 0.4, which are similar to those 
used for matching the carbon-14 data. For the same range of . values, the calculated fa values do 
not change significantly for the two infiltration rates (Figure 7-8), which is consistent with the 

observation of flow-path stability over time. The present day mean infiltration rate 
is obtained from file GENER_m_rad_200 in DTN: LB0208UZDSCPMI.001 
[DIRS 161285]. The glacial maximum infiltration rate is determined using software routine 
infil2grid V1.7 (LBNL 2002 [DIRS 154793]) based on infiltration maps (BSC 2004 
[DIRS 170007]; DTN: GS000308311221.005 [DIRS 147613]) and UZ numerical grid 
(DTN: LB03023DKMGRID.001 [DIRS 162354]; Wang 2003 [DIRS 161654], SN-LBNL-SCI-
199-V1, pp. 9299; SN-LBNL-SCI-227-V1, pp. 89). The determined glacial maximum 
infiltration rate is 17.3108 mm/year (Wang 2003 [DIRS 161654], SN-LBNL-SCI-227-V1, p. 8). 
The simulation results satisfy the model validation criterion that simulated active portion of 
fractures is similar to the percentage of fractures with mineral coating (Section 7.1). 
fa (active fracture portion)
1.0E+1 
1.0E+0 
1.0E-1 
1.0E-2 
1.0E-3 
1.0E-4 
Present day mean infiltration rate 
Glacial maximum infiltration rate 
0.00 0.20 0.40 0.60 0.80 1.00 
Gamma 
Output DTN: LB0212AFPGAMMA.002 (files: gamma_analysis.doc, FA_GA_GU.dat, and FA_GA_PM.dat). 
Figure 7-8. Simulated Average Portion of Active Fracture for the Relevant Model Layers (tsw32 to tsw38) 
as a Function of Infiltration Rate and . 
In summary, the simulation results based on the AFM are consistent with both carbon-14 data 
and fracture coating data, for a similar range of . values. This result, together with the 
consistency of the AFM with fractal flow patterns and film-flow behavior (Sections 7.2 and 7.3, 
respectively), support the usefulness of the AFM. 
7.5 VALIDATION SUMMARY 
The AFM has been validated by applying acceptance criteria based on an evaluation of the 
models relative importance to the potential performance of the repository system. All the 
validation requirements defined in TWP-MGR-HS-000001 REV 00 (BSC 2004 [DIRS 169654], 
Section 2.2.1) have been fulfilled, including corroboration of model results with experimental 
data (Section 7.4), publications in refereed professional journals (Section 7.1), and corroboration 

with alternative conceptual models (Sections 7.2 and 7.3). Confidence building during model 
development was obtained by publishing the AFM in Water Resources Research (Liu et al. 1998 
[105729]). The model development activities and post-development validation activities 
described establish the scientific bases for the AFM. Based on these activities (that satisfy the 
model validation criteria), the AFM is considered to be sufficiently accurate and adequate for the 
intended purpose, and to the level of confidence required by the models relative importance to 
the potential performance of the repository system. 

8. CONCLUSIONS 
8.1 CONCEPTUAL MODEL AND NUMERICAL APPROACHES 
A variety of flow and transport processes occur in the UZ of Yucca Mountain. The conceptual 
model and numerical modeling approaches used for modeling these processes are summarized in 
this report. 
Flow processes are considered to be characterized by the following attributes (Section 6.1). The 
percolation processes below this unit are considered to be approximately in steady state under 
ambient conditions because of the expected attenuation effects of the PTn unit. Fracture 
liquid-water flow is dominant in the welded units and matrix flow in the nonwelded units. 
Fracture-matrix interaction in the welded units is limited. The existence of perched water bodies 
introduces three-dimensional lateral flow within the UZ. 
Solute transport within the UZ of Yucca Mountain is closely tied to the conceptual model of flow 
(Section 6.2). Advective transport pathways coincide with flow pathways. Matrix diffusion is a 
major mechanism for mass transfer between fractures and the matrix, and contributes to the 
retardation of radionuclide transport when fracture flow is dominant. Sorption can also act to 
retard the movement of radionuclides in the UZ: radionuclides and reactive chemicals, which 
are strongly sorbed to rock matrix, are relatively immobile. On the other hand, sorptive 
interactions may enhance radionuclide transport if the aqueous species sorbs to colloids. 
Dispersion is not expected to be a major transport mechanism in the UZ. In addition, perched 
water bodies may dilute solute and radionuclide plumes. 
Several basic numerical approaches are available for modeling flow and transport in unsaturated, 
fractured rock. Based on flow and transport behavior in the UZ of Yucca Mountain, the scale of 
the problem, data availability, and computational feasibility, the dual-permeability approach is 
considered the most appropriate approach for modeling flow and transport processes 
(Section 6.3). Relevant issues, such as the comparison between conventional approaches and 
particle-tracking methods for modeling transport processes, are also addressed. 
This report also discusses model uncertainties related to understanding of focused flow at 
different scales, use of the continuum approach for dealing with UZ flow and transport 
processes, and the validity of the van Genuchten relationships and the AFM for describing 
unsaturated flow in fractures (Section 6.4). 
8.2 MODEL VALIDATION 
This report documents activities to validate the AFM and the corresponding model validation 
results (Section 7). The AFM is evaluated based on (fractal) flow patterns in unsaturated 
systems, the consistency with different types of field observations, and a comparison with an 
alternative (film-flow) model. The AFM is shown to be consistent with fractal distributions of 
flow patterns that have been often observed from unsaturated or multiphase flow systems 
(porous media). Simulation results based on the AFM, with a similar range of AFM-parameter 
values, match both the carbon-14 ages and fracture coating data collected from the UZ. 
Furthermore, a simple comparison between the AFM and the film-flow model, an alternative 
model, shows that the AFM would capture the fast flow behavior of water film if film flow were 

the major mechanism for fracture flow. All these support the usefulness of the AFM in 
describing flow and transport processes in the UZ. The model validation results were 
submitted to TDMS under DTNs: LB0212C14INFIL.001, LB0212C14INFIL.002, 
LB0212AFMGAMMA.001, and LB0212AFPGAMMA.002. 
8.3 HOW THE ACCEPTANCE CRITERIA ARE ADDRESSED 
The following information describes how this model report addresses the acceptance criteria in 
the YMRP (NRC 2003 [DIRS 163274], Sections 2.2.1.3.6.3 and 2.2.1.3.7.3). Only those 
acceptance criteria that are applicable to this report (see Section 4.2) are discussed. In most 
cases, the applicable acceptance criteria are not addressed solely by this report; rather, the 
acceptance criteria are fully addressed when this report is considered in conjunction with other 
analysis and model reports that describe flow and transport in the unsaturated zone. 
Acceptance Criteria from Section 2.2.1.3.6, Flow Paths in the Unsaturated Zone. 
Acceptance Criterion 1, System Description and Model Integration Are Adequate. 
Subcriterion (1) The model described in this report adequately incorporates physical 
phenomena related to UZ flow including the various mechanisms involved in 
fracture-matrix interaction, perched water, major faults, transient flow, and focused 
flow (discussed in Sections 6.1.3, 6.1.4, 6.1.5, 6.1.6, and 6.1.7, respectively). The 
model described in this report is used by UZ flow and transport models that support 
TSPA. 
Subcriterion (2) An adequate and detailed discussion of water flow paths and the 
associated processes is presented in Section 6.1. This discussion includes 
consideration of effects of rock properties, infiltration, major faults, perched water, 
flow focusing and fracture-matrix interaction on the UZ flow paths. Conditions and 
assumptions related to these processes are identified in the subsection discussing each 
and are consistently throughout the model development (Sections 6.1 and 6.3). 
Subcriterion (3) The assumptions, technical bases, and models described in 
Sections 6.1, 6.2 and 6.3 are appropriate and consistent with other Yucca Mountain 
related abstractions regarding flow in the UZ and flow in the saturated zone. The 
descriptions and technical bases are transparent and traceable to site data through a 
discussion of the geologic features of Yucca Mountain (Sections 6.1 and 6.2). 
Subcriterion (4) The bases and justification presented in Section 6 support the 
conclusion in Section 8 that fracture liquid-water flow is dominant in welded units 
and matrix flow, in nonwelded units. These approximations are employed in the 
numerical approaches described in Section 6.3 to represent radionuclide transport in 
the unsaturated zone and are consistent with the models and approaches in related 
abstracts. 
Subcriterion (9) This report was developed in accordance with the QARD, which 
commits to NUREGs 1297 (Altman et al. 1988 [DIRS 103597]) and 1298 (Altman 
et al. 1998 [DIRS 103750]). Moreover, compliance with the DOE procedures, which 
are designed to ensure compliance with the QARD, is verified by audits by QA and 

other oversight activities. Accordingly, the guidance in NUREGs 1297 and 1298 has 
been followed as appropriate. 
Acceptance Criterion 2: Data Are Sufficient for Model Justification. 
Subcriterion (6) Approved QA procedures identified in the TWP (BSC 2004 
[DIRS 169654], Section 4) have been used to conduct and document the activities 
described in this model report. 
Subcriterion (7) The relatively uniform distribution of fracture flow paths at Yucca 
Mountain makes the continuum approach a reasonable choice for the UZ model as 
noted in Section 6.3.2. The continuum model adopted reflects a robust, complete 
mathematical model reflecting the most appropriate choices from a number of 
approaches suggested in the literature (Section 6.3.2). Approaches considered have 
been developed and used in different fields (including oil-reservoir engineering, 
groundwater hydrology, geothermal engineering and soil physics). Model validity 
was demonstrated by comparison of model simulations with field-scale results for the 
Alcove 8/Niche 3 test site (Section 6.3.3) where it was found that the field 
observations are well represented by the modeling results. 
Acceptance Criterion 3: Data Uncertainty is Characterized and Propagated Through the 
Model Abstraction. 
Subcriterion (1) The assumptions implicit in the model developed in this report are 
consistent with those for similar models in other applications (Sections 6.1 through 
6.3). They reasonably account for uncertainties and variabilities by choice of the most 
appropriate model from a number of possibilities (Section 6.3) and, due to the 
conservative nature of the dual-continua model, do not result in an 
under-representation of the risk. 
Subcriterion (6) Uncertainties and heterogeneity of the UZ are considered by 
adopting a geology-based deterministic approach, in which an entire model layer is 
assigned uniform properties. This approach is used mainly for representing 
subsurface heterogeneity because overall behavior of site-scale flow and transport 
processes is determined mainly by relatively large-scale heterogeneities associated 
with the geologic stratification and faults (Section 6.3.4). 
Acceptance Criterion 4, Model Uncertainty is Characterized and Propagated Through the 
Model Abstraction. 
Subcriterion (1) A number of alternate modeling approaches are considered in 
Section 6.3.1 and assessed in Section 6.3.2. The approaches fall into one of three 
groups: continuum approaches, discrete fracture-network approaches, and other 
approaches that can be considered as variations and/or combinations of the other two 
approaches. An extensive review of literature on each approach with a discussion of 
the limitations of each is presented in Section 6.3.2. A geology-based deterministic 
approach, in which an entire model layer is assigned uniform properties, is used 
mainly for representing subsurface heterogeneity because overall behavior of 

site-scale flow and transport processes is determined mainly by relatively large-scale 
heterogeneities associated with the geologic stratification and faults (Section 6.3.4). 
Subcriterion (3) The conceptual model uncertainties were discussed in Section 6.4. 
Model validation in Section 7 provides comparisons between the AFM and alternate 
models and physical data (14C and mineral coating). Results of these comparisons 
indicate that the model matches the physical data and other models within expected 
limits. These results support the conclusion that the AFM is considered the 
appropriate approach for modeling flow and transport processes in the UZ 
(Section 8.1). 
Acceptance Criteria from Section 2.2.1.3.7, Radionuclide Transport in the Unsaturated 
Zone). 
Acceptance Criterion 1: System Description and Model Integration Are Adequate. 
Subcriterion (1) The model described in this report adequately incorporates important 
physical phenomena related to UZ transport including the various advective transport, 
matrix diffusion, fracture and matrix sorption, colloid-facilitated transport, and other 
transport issues (discussed in Sections 6.2.1, 6.2.2, 6.2.3, 6.2.4, and 6.2.5, 
respectively). Assumptions that are consistent with other abstracts and appropriate for 
the physical phenomena expected in the UZ are applied throughout the report 
(especially in Section 6). 
Subcriterion (2) The detailed discussion of radionuclide transport processes is 
presented in Section 6.2. This discussion includes effects of advection, matrix 
diffusion, sorption and colloid-facilitated transport on radionuclide transport behavior 
in the UZ. These conditions and assumptions are consistent with other documents 
supporting UZ transport (Section 6). 
Subcriterion (3) This report uses assumptions, technical bases, data, and models that 
are appropriate and consistent with other related abstractions for flow and transport in 
the UZ. Related abstractions that use this model are the UZ flow model, model for 
radionuclide transport under ambient conditions, and particle tracking model for UZ. 
The descriptions and technical bases for the continuum model chosen provide 
transparent and traceable support for the TSPA abstraction through extensive 
literature cites and discussion (Sections 6.1 through 6.3). 
Subcriterion (5) Sufficient technical bases have been presented in Sections 6.2 and 7 
to support the extent to which FEPs have been addressed. These include the 
discussions of matrix diffusion (Section 6.2.2), fracture and matrix sorption 
(Section 6.2.3), and colloid-facilitated transport (Section 6.2.4). 
Subcriterion (6) This report was developed in accordance with the QARD, which 
commits to NUREGs 1297 and 1298. Moreover, compliance with the DOE 
procedures, which are designed to ensure compliance with the QARD, is verified by 
audits by QA and other oversight activities. Accordingly, the guidance in NUREGs 
1297 and 1298 has been followed as appropriate. 

Acceptance Criterion 3: Data Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
Subcriterion (1) The assumptions implicit in the model developed in this report are 
consistent with those for similar models in other applications (Sections 6.1 through 
6.3). They reasonably account for uncertainties and variabilities by choice of the best 
model from a number of possibilities (Section 6.3) and, due to the conservative nature 
of the dual-continua model, do not result in an under-representation of the risk. 
Acceptance Criterion 4: Model Uncertainty Is Characterized and Propagated Through the 
Model Abstraction. 
Subcriterion (1) A number of alternate modeling approaches suggested in current 
scientific literature are considered in Section 6.3.1 and assessed in Section 6.3.2. An 
extensive review of literature on each approach with a discussion of the limitations of 
each is presented in Section 6.3.2. 
Subcriterion (2) The model uncertainties are addressed in Section 6.4. 
Subcriterion (3) The conceptual model uncertainties were discussed in Section 6.4. 
Model validation in Section 7 provides comparisons between the AFM and alternate 
models and physical data (14C and mineral coating). Results of these comparisons 
indicate that the model matches the physical data and other models within expected 
limits. These results support the conclusion that the AFM is considered the 
appropriate approach for modeling flow and transport processes in the UZ 
(Section 8.1). 
Subcriterion (4) Appropriate alternative modeling approaches from current scientific 
literature have been investigated as discussed in Section 6.3. Validation using two 
alternative models: 1) Fractal flow in unsaturated systems (Section 7.2) and, 2) a 
film-flow model (Section 7.3) concludes that the AFM-based continuum model 
adopted does not overestimate the performance of the UZ for the conditions 
applicable to the other models. 

INTENTIONALLY LEFT BLANK

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for the Yucca Mountain Site Characterization Project. Eckhardt, R.C., ed. 
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Analysis of Hydrologic Properties Data, MDL-NBS-HS-000014 REV 00 
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Wu, Y.S.; Haukwa, C.; and Bodvarsson, G.S. 1999. A Site-Scale Model for Fluid 117161 
and Heat Flow in the Unsaturated Zone of Yucca Mountain, Nevada. Journal of 
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Calcite Precipitation and Evaluation of Infiltration Fluxes in Unsaturated Fractured 
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Fractures and Its Modeling Using Cascade Process. Scale Effects in Rock Masses, 
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Yang, I.C. 2002. Percolation Flux and Transport Velocity in the Unsaturated Zone, 160839 
Yucca Mountain, Nevada. Applied Geochemistry, 17, ([6]), 807-817. [New York, 
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Yang, I.C.; Rattray, G.W.; and Yu, P. 1996. Interpretation of Chemical and Isotopic 100194 
Data from Boreholes in the Unsaturated Zone at Yucca Mountain, Nevada. 
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Zhou, Q.; Liu, H-H.; Bodvarsson, G.S.; and Oldenburg, C.M. 2003. Flow and 162133 
Transport in Unsaturated Fractured Rock: Effects of Multiscale Heterogeneity of 
Hydrogeologic Properties. Journal of Contaminant Hydrology, 60, ([1-2]), 1-30. 
New York, New York: Elsevier. TIC: 253978. 
9.2 CODES, STANDARDS, REGULATIONS, AND PROCEDURES 
10 CFR 63. Energy: Disposal of High-Level Radioactive Wastes in a Geologic 156605 
Repository at Yucca Mountain, Nevada. Readily available. 
AP-2.22Q, Rev. 1, ICN 1. Classification Analyses and Maintenance of the Q-List. 
Washington, D.C.: U.S. Department of Energy, Office of Civilian Radioactive 
Waste Management. ACC: DOC.20040714.0002. 
AP-2.27Q, Rev. 1, ICN 4. Planning for Science Activities. Washington, D.C.: 
U.S. Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040610.0006. 
AP-SIII.10Q, Rev. 2, ICN 7. Models. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. ACC: 
DOC.20040920.00002. 
LP-SI.11Q-BSC, Rev. 0, ICN 0. Software Management. Washington, D.C.: U.S. 
Department of Energy, Office of Civilian Radioactive Waste Management. 
ACC: DOC.20040225.0007. 
9.3 SOURCE DATA, LISTED BY DATA TRACKING NUMBER 
GS000308311221.005. Net Infiltration Modeling Results for 3 Climate Scenarios for 147613 
FY99. Submittal date: 03/01/2000. 

GS961108312271.002. Chemical and Isotopic Composition of Pore Water and Pore 121708 
Gas, 199496, from Boreholes USW UZ-1, USW UZ-14, UE-25 UZ#16, 
USW NRG-6, USW NRG-7A, USW SD-7, USW SD-9, ESF-AL#3-RBT#1, and 
ESF-AL#3-RBT#4, and ESF Rubble. Submittal date: 12/04/1996. 
GS980308315215.008. Line Survey Information from the Exploratory Studies 107355 
Facility Obtained to Estimate Secondary Mineral Abundance. Submittal 
date: 03/24/1998. 
LA000000000034.002. Diffusion of Sorbing and Non-Sorbing Radionuclides. 148603 
Submittal date: 06/22/1993. 
LB0205REVUZPRP.001. Fracture Properties for UZ Model Layers Developed from 159525 
Field Data. Submittal date: 05/14/2002. 
LB0208UZDSCPMI.001. Drift-Scale Calibrated Property Sets: Mean Infiltration 161285 
Supporting Files. Submittal date: 08/27/2002. 
LB02091DSSCP3I.001. 1-D Site Scale Calibrated Properties: Supporting Files. 161292 
Submittal date: 09/18/2002. 
LB02091DSSCP3I.002. 1-D Site Scale Calibrated Properties: Data Summary. 161433 
Submittal date: 09/18/2002. 
LB03023DKMGRID.001. UZ 3-D Site Scale Model Grids. Submittal 162354 
date: 02/26/2003. 
MO0012CARB1314.000. Water - Carbon 13 and Carbon 14 Abundance. Submittal 153398 
date: 12/01/2000. 
MO0407SEPFEPLA.000. LA FEP List. Submittal date: 07/20/2004. 170760 
MO9906GPS98410.000. Yucca Mountain Project Borehole Locations. Submittal 109059 
date: 06/23/1999. 
9.4 OUTPUT DATA, LISTED BY DATA TRACKING NUMBER 
LB0212C14INFIL.001. 1-D Simulation and Sensititvity Analyses of Groundwater 
Age by Matching to C14 Age Data: 1. Supporting Files. Submittal date: 
12/19/2002. 
LB0212C14INFIL.002. 1-D Simulation and Sensititvity Analyses of Groundwater 
Age by Matching to C14 Age Data: 2. Data Summaries. Submittal date: 
12/19/2002. 
LB0212AFPGAMMA.001. Active Fracture Parameter Analysis: 1. Supporting 
Files. Submittal date: 12/23/2002. 

LB0212AFPGAMMA.002. Active Fracture Parameter Analysis: 2. Data 
Summaries. Submittal date: 12/23/2002. 
9.5 SOFTWARE CITED 
LBNL (Lawrence Berkeley National Laboratory) 1999. Software Code: T2R3D. 146654 
V1.4. FORTRAN 77, SUN, DEC/ALPHA. 10006-1.4-00. 
LBNL (Lawrence Berkeley National Laboratory) 2000. Software Code: TOUGH2. 146496 
V1.4. Sun Workstation and DEC/ALPHA. 10007-1.4-01. 
LBNL (Lawrence Berkeley National Laboratory) 2002. Software Code: infil2grid. 154793 
V1.7. DEC-Alpha, PC. 10077-1.7-00. 

APPENDIX A 
DATA POINT VALUES IN FIGURES 7-3 AND 7-4 

Data point values in Figure 7-3 (estimated from Figure 9 of Tokunaga et al. (2000 
[DIRS 152914])): 
Average film thickness (m) Surface transmissivity (m2/s) 
1.2 2.5E-16 
1.5 1.0E-14 
2.0 1.5E-13 
2.5 7.0E-13 
3.0 2.0E-12 
3.5 7.0E-12 
4.0 1.0E-11 
5.0 2.5E-11 
Data point values in Figure 7-4 (a) (estimated from Figure 7 of Tokunaga and Wan (1997 
[DIRS 139195])): 
Capillary potential (Pa) Average film thickness (m) 
-310 1.0 
-215 2.0 
-165 3.0 
-118 5.0 
-93 7.0 
-70 8.0 
-45 20.0 
-30 30.0 
-14 70.0 

Data point values in Figure 7-4 (b) (estimated from Figure 6 of Tokunaga and Wan (1997 
[DIRS 139195])): 
Capillary pressure (Pa) Surface transmissivity (m2/s) 
-250 8.0E-11 
-200 1.5E-10 
-150 3.5E-10 
-100 8.0E-10 
-50 3.5E-9 
-12 4.0E-8 

APPENDIX B 
DATA POINT VALUES IN FIGURE 7-1

Coating data from DTN: GS980308315215.008 [DIRS 107355] are used to determine the data 
point values. Since Tptpmn unit has the largest number of survey intervals, data from this unit 
are analyzed using the box counting method. There are 29 survey intervals (30 m long) for this 
unit that include coated fractures. The total number of coated fractures is 134. The locations of 
the coated fractures along the survey line form a set of points in a one-dimensional space. For a 
given box size (length of a segment) l, there are 30/l small boxes (or segments) for a given 
survey interval. N denotes total numbers of boxes that cover at least one location of the coated 
fractures (along the survey line) for all the survey intervals. The determined N values as a 
function of l are given as follows: 
N l (m) 
102 3 
91 3.75 
83 5. 
81 6. 
68 7.5 
63 10 
50 15 
29 30 

INTENTIONALLY LEFT BLANK