Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media Rev 00, ICN 00

ANL-NBS-HS-000022

July 2000

1 PURPOSE 
The purpose of this dispersion analysis is to provide estimates of the transverse and longitudinal 
dispersion that may occur at the sub-gridblock scale within the saturated zone (SZ) site-scale 
model. This analysis explicitly applies only to that part of the SZ flow path that is located within 
the fractured Tertiary volcanic rocks in the SZ down-gradient from beneath the potential 
repository. The amount of dispersion is characterized by values of dispersivity for each of the 
three principal directions. Estimates of dispersivity derived from this analysis are compared to 
estimates of dispersivities derived from the analytical solutions; these estimates can be used 
directly, or with modification, in performance assessment calculations. This analysis is designed 
to use existing modeling and analysis results as the basis for heterogeneous models of fracture 
permeability at the sub gridblock scale. The scope of this modeling exercise includes site scale 
model gridblocks containing both background fracture permeability and enhanced 
permeability: those dominated by large, throughgoing high permeability features. Two different 
source geometries are used: point and distributed planar. 
This analysis is governed by the CRWMS M&O "Analysis/Model Report (AMR) Work 
Direction and Planning Document" for, Geostatistical and Heterogeneity Analysis for the SZ 
Flow and Transport Model (McKenna, 1999). The work presented in this AMR comprises a 
component of the SZ Process Model Report (PMR). 
2 QUALITY ASSURANCE 
The activities documented in this Analysis/Model Report (AMR) were evaluated in accordance 
with QAP 2-0, Conduct of Activities, and were determined to be subject to the requirements of 
the U.S. DOE Office of Civilian Radioactive Waste Management (OCRWM) Quality Assurance 
Requirements and Description DOE/RW-0333P (QARD) (DOE 1998). This evaluation is 
documented in CRWMS M&O 1999a, b, Wemheuer, 1999 (activity evaluation for Work 
Package #WP1401213SM1). This AMR has been prepared in accordance with procedures 
identified in CRWMSM&O "Analysis and Modeling Report (AMR) Work Direction and 
Planning Document for Geostatistical and Heterogeneity Analysis for the SZ Flow and Transport 
Model (McKenna, 1999) and with procedure AP-3.10Q Analyses and Models. 
3 COMPUTER SOFTWARE AND MODEL USAGE 
It has been determined that AP-SI.1Q applies to the software routines used in this work. 
3.1 INDUSTRY STANDARD SOFTWARE 
The following industry standard software was used in this analysis and documentation: 
EXCEL 97-SR-1

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 10 of 60 
Used for spreadsheet calculations and calculation of basic statistics on the output of the 
calc_D_old and calc_cdf routines described below. 
SigmaPlot 4.0 
Used for plotting and visualization of analysis results from calc_D_old (described below) in 
figures shown in this report. 
3.2 PERMEABILITY MODELING 
The background permeability models are created with the indicator geostatistical simulation 
routine sisim. The enhanced permeability models are created by combining the background 
permeability models with the results of the ellip2 routine. Two different sets of UNIX shells are 
used to run the codes that build the permeability models and then accomplish post processing. 
One set is used for the background permeability models and one set for the enhanced 
permeability models. These shells are discussed below. 
3.2.1 Geostatistical Simulations 
The routine sisim (version 2.0) was used to create the background fracture permeability models. 
This routine is included as part of the Geostatistical Software Library (GSLIB) (Deutsch and 
Journel, 1998). This subroutine is discussed in the Section 6.1.2.1, and the source code for this 
subroutine is listed in Attachment 4. A Pentium personal computer was used to run the sisim 
code. 
The routine modgeom (version 1.0) is used to change the random number seed after each call to 
the sisim or ellip2 routines. The seed is decremented by a constant value as set in the code. For 
the work reported herein, the seed is decremented by four each time modgeom is called. 
3.2.2 Object Simulations 
The routine ellip2_MC (version 1.0) was used to create the disk shaped objects that are combined 
with the background fracture permeability models to create the enhanced permeability models. 
ellip2_MC is an extension of the GSLIB routine ellipsim. The feature added for this work is the 
ability to draw object orientations from a Gaussian distribution. The original ellipsim routine can 
only produce features with a constant orientation. The ellip2_MC subroutine is discussed in 
Section 6.1.2.2, and the source code for this subroutine is listed in Attachment 5. ellip2_MC was 
run on a Sun UltraSparc UNIX workstation. 
The enhanced fracture permeability models are created by combining the background 
permeability models with the disk-shaped objects created in ellip2_MC. Combining the two sets 
of simulation results is accomplished with the routine combine (version 1.0). This routine sets the 
log10 permeability to a constant value of 11.0 within each of the disk-shaped objects and writes 
out the log10 permeability field as an ascii file in GeoEAS format. This subroutine is discussed 
in Section 6.1.2.2, and the source code for this subroutine is listed in Attachment 6. combine was 
run on a SUN UltraSparc workstation.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 11 of 60 
3.2.3 Validation Checks 
Several postprocessing checks are made in an attempt to validate the fracture permeability 
models. These checks include the cumulative distribution function (cdf) and the mean spacing 
between high permeability features. These checks are made using the calc_cdf (version1.0) and 
gamfil (version 1.0) routines respectively. The use of these subroutines is discussed in Section 
6.1.3.2, and the source code for both subroutines is listed in Attachments 7 and 9 respectively. 
3.2.4 Reformatting 
The output files from either sisim or combine are reformatted to the input format required by 
FEHM by using the routine gs2fehm (version 1.0). This subroutine is discussed in section 
6.1.3.2, and the source code for this subroutines is listed in Attachment 8. 
3.3 FLOW MODELING 
The code FEHM Version 2.00 (Software tracking number 10031-2.00-00) (Zyvoloski et al. 
1997a; 1997b). was obtained from the Software Congifuration Management and is used to solve 
for a steady state flow solution on the heterogeneous fields created with the sgsim and ellip2_MC 
codes. Solving for a steady-state solution is an appropriate use of FEHM and is within the range 
of FEHM. Different Unix shells, run_50_back.ksh and run_50_feat.ksh are used to run the flow 
model codes and do the particle tracking on the background permeability realizations and the 
enhanced permeability model realizations respectively. These shells are discussed in Section 
6.2.2. The source codes of run_50_back.ksh and run_50_feat.ksh are listed in Attachment 11 
and 12 respectively. 
The intrinsic macro flxo is activated within FEHM for these flow solutions. The flxo macro 
writes the internodal flux between each pair of selected nodes within the model. The maximum 
number of node pairs that can be written to the output file ( het_flow.out) is 500 
The UNIX directories containing the files necessary for the flow and particle tracking as well as 
the calculation of the dispersivities are written to the same CD-ROM that contains the 
attachments as electronic files. Memory limitations do not allow for all flow and particle 
tracking output files to be retained. Therefore, these directories contain example input and 
output files for the flow and particle tracking solutions created with FEHM. The directory path 
for these files on the CD-ROM is: /AMR/FEHM/ for the flow solutions. FEHM is run on a Sun 
UltraSparc workstation to produce the flow solutions. 
3.4 PARTICLE TRACKING 
The code FEHM Version 2.00 (Software tracking number 10031-2.00-00)is used to determine 
the streamlines (particle tracks) using the steady-state flow solution created in the previous step. 
There are two different particle-tracking routines within FEHM. This study uses the FEHM sptr 
macro for particle tracking. The sptr macro is an intrinsic macro within FEHM.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 12 of 60 
The flux weighted particle release locations for the planar source are determined with the 
routine cr8sptr (version 1.0).. This routine reads in the output of the flxo macro in FEHM 
(het_flow.out) and determines the flux weighted starting locations for the particles along the 
plane. The output of the cr8sptr routine is the file sptr.dat. FEHM uses the sptr.dat file as an 
input file to define the particle starting locations for the intrinsic sptr macro. The cr8sptr 
subroutine is discussed in Section 6.2.2, and the source code for this subroutine is listed as 
Attachment 13. 
The flux weighted particle release locations for the point source are determined with the routine 
cr8sptr_cell (version 1.0). This routine is a variation of cr8sptr used for the planar source. Input 
and output from this routine are the het_flow.out and sptr.dat files respectively. This subroutine 
is discussed in the section 6.2.2, and the source code for this subroutine is listed as Attachment 
14. 
The directory path for the particle tracking runs on the CD-ROM is: /AMR/FEHM/track/. 
Example input and output files for the particle tracking are contained there. The particle tracking 
is run on a Sun UltraSparc UNIX workstation. 
3.5 DISPERSION CALCULATIONS 
The dispersion calculations are done with the routine calc_D_old (version 1.0). The source code 
for this subroutine is listed as Attachment 15. The routine takes the het_flow.sptr2 output file 
from FEHM as input and calculates the longitudinal and transverse dispersivities at each 
collection plane. The old in the title of this routine refers to the current form of the output 
from FEHM contained in het_flow.sptr2. A new output format (new) in a developmental 
version of FEHM was also examined for these calculations, but due to excessive output, was not 
used for the final runs. 
Output from calc_D_old is written to four different files: disper_L.out, disper_X.out, 
disper_Z.out and debug.out. These contain dispersivity values for the three principal directions 
and the number of particles that reached each collection plane. These files are written as ascii 
files with nine values, corresponding to each of the nine collection planes written on each line. 
The new values for each realization are appended to the bottom of the existing file, such that at 
the completion of the run_50_back.ksh and run_50_feat.ksh shells, each of these files has a total 
of 50 lines. 
The dispersion calculations were run on a Sun UltraSparc UNIX workstation. The directory path 
for the dispersion calculations on the CD-ROM is: /AMR/FEHM/track/ and results of the 
dispersion calculations are stored in: /AMR/FEHM/track/RESULTS/ 
4 INPUTS 
4.1 DATA AND PARAMETERS 
No data were obtained from the TDMS for this AMR. All corroborative information necessary 
for the creation of the models in this AMR is derived from references. These references are cited

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 13 of 60 
in the appropriate places in the text. A list of these three references and the corroborative 
information obtained from them is shown in Table 1 
Table 1. Input Information Sources 
Data Set Data Description Ascession Number 
Fracture Length 
(Sweetkind and Williams-Stroud, 
1996) 
Fracture Length Distributions 
TIC: 239254 
Fracture Orientation 
(Sweetkind and Williams-Stroud, 
1996) 
Fracture Orientation Distributions 
TIC: 239254 
Fracture Permeability 
(CRWMS M&O, 1998a) 
Fracture Permeability Distributions 
MOL.19981008.0008 
Feature Spacing 
(CRWMS M&O, 1999c) 
Feature Spacing Distributions 
Pending 
4.2 CRITERIA 
There are no criteria at this time. This AMR complies with the DOE interim guidance (Dyer 
1999). Subparts of the interim guidance that apply to this analysis or modeling activity are those 
pertaining to the characterization of the Yucca Mountain site (Subpart B, Section 15), the 
compilation of information regarding hydrology of the site in support of the License Application 
(Subpart B, Section 21(c)(1)(ii)), and the definition of hydrologic parameters and conceptual 
models used in performance assessment (Subpart E, Section 114(a)). 
4.3 CODES AND STANDARDS 
There are currently no applicable codes or standards that pertain to this analysis. 
5 ASSUMPTIONS 
There are several significant assumptions made in this study regarding the representation of 
fracture permeability within a numerical flow model. 
5.1 EFFECTIVE CONTINUUM REPRESENTATION 
Numerical modeling of fracture properties is done in one of two ways: discrete fracture models 
or effective continuum models. The effective continuum model used in this study is a stochastic 
continuum model as multiple realizations of the permeability field are created. As used in this 
report, these terms apply solely to the permeability model and do not imply any connotations for 
the transport model. The transport used in this study is only streamline particle tracking in a 
single-porosity medium. Discrete fracture models represent each fracture as a distinct object 
within the modeling domain. While the discrete fracture approach retains the discrete nature of 
the observed fractures within the resulting model, the computational burden of calculating a flow 
solution on a discrete fracture model becomes extremely large for even a relatively simple 
fracture model. For this reason, and the fact that the Yucca Mountain Project does not have a 
qualified discrete fracture modeling software package, the effective continuum representation of 
fracture permeability is used in this study.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 14 of 60 
The main assumption inherent in using the effective continuum approach is that the permeability 
field arising from the discrete fractures can be accurately represented by a numerical model 
composed of continuum gridblocks. Under the continuum approach, the fractures do not appear 
as discrete entities, but rather they contribute to an effective permeability at each gridblock. The 
resulting models do not exhibit discrete fractures, but rather areas of higher and lower 
permeability. In order to retain as much of the discrete fracture behavior as possible, the 
numerical gridblocks are kept to a minimum size. For the work here, the gridblocks are 4 x 4 x 2 
meters. This gridblock size is not inconsistent with the estimated widths of the fracture zones 
observed at Yucca Mountain (CRWMS M&O, 1999c). This assumption is used in Section 6.1 
(see paragraphs 1 and 2) and also throughout Section 6.1.2. This assumption does not require 
further confirmation. 
5.2 BOUNDARY CONDITIONS 
In this study, tracer transport is analyzed within a single site-scale model numerical gridblock 
that is 500 x 500 x 50 meters. This gridblock is part of a larger model and the boundary 
conditions for this gridblock within the site-scale model would be constant fluxes into and out of 
the neighboring gridblocks. However, for this study on a single site-scale gridblock, the 
boundary conditions are set to fixed head values on the two ends of the domain and to no-flow 
boundaries on the sides of the model domain. The head difference across the model domain is 
based on the average value of the gradient along the direction of the most likely flowpath in the 
SZ site-scale model. This gradient is 2.9x10-04 and is within the range of gradients presented by 
Luckey, et al. 1996, p. 27). The inherent assumption here is that these imposed boundary 
conditions do not adversely affect the dispersion calculations. This assumption is not explicitly 
restated in Section 6, but is used in Section 6.2.2. This assumption does not require further 
confirmation. 
5.3 SOURCE SIZE 
The spatial distribution of the potential radionuclide plume within the unsaturated zone is a 
complex function of the local saturation, the canister failure history and the heterogeneous 
properties of the fracture system. This uncertainty in the unsaturated zone source history and 
transport properties leads to uncertainty in the shape of the potential radionuclide plume within 
the saturated zone. With regards to source size, it is assumed that each of two different 
conceptual models is a valid representation of the source geometry. The first conceptual model 
of the source is that used in the recent Total System Performance Assessment-Viability 
Assessment (TSPA-VA) and the second model is considered to be the most conservative case. 
The first conceptual model is that of planar source geometry. This model is adapted from the 
streamtube model of the contaminant plume employed in TSPA-VA (CRWMS M&O, 1998a, p. 
8-40 and Figure 8-22) in which the radionuclides enter the saturated zone in one of six different 
streamtubes from the unsaturated zone. Each streamtube was associated with a different zone of 
the repository footprint (CRWMS M&O, 1998a, p. 8-40). The planar source implementation in 
this study assumes that the source zone is 400 meters wide by 10 meters high and is centered 
within the model domain. Because this study employs a heterogeneous representation of the 
permeability field, the particle release points are not uniformly distributed (the perfectly mixed

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 15 of 60 
scenario used in TSPA-VA) but are distributed proportional to the groundwater flux through the 
400 x 10 meter plane. 
The second conceptual model of the source is that of a point release. This source model 
corresponds to a single canister release in the unsaturated zone or, in the most conservative case, 
strong channeling (focusing) of flow within the unsaturated zone from a number of canister 
releases. It is assumed that under this scenario the potential radionuclide plume enters the 
saturated zone as a spatially compact source and therefore, under this scenario, all of the particle 
release points are within a single numerical gridblock. The gridblock chosen for the particle 
release points is that with the highest groundwater flux that also lies within the 400 x 10 meter 
plane used as the planar source. This choice produces the most conservative estimates of plume 
spreading. 
The assumed source geometries are based on the current understanding of UZ-SZ transport 
coupling, and the second of these two assumed geometries represents the most conservative case 
for this coupling. The two different source sizes are employed in Section 6.2.2. This assumption 
does not require further confirmation. 
5.4 GEOSTATISTICAL REPRESENTATION 
It is assumed that geostatistical simulation can be used to adequately model the fracture lengths 
and the spacings between flowing intervals. This assumption is tested against the resulting 
models in Section 6.1.4. For this work, exponential variogram models are employed with the 
effective range set to be three times the desired feature, or spacing, length. By definition, for the 
exponential model, the effective range is three times the integral scale, and the integral scale is 
equal to the mean feature length (Deutsch and Journel, 1998, p. 25). This assumption is 
employed in Sections 6.1.4, 6.1.2.1 and 6.1.2.2. This assumption does not require further 
confirmation 
5.5 ORIENTATION OF GROUNDWATER GRADIENT 
In this study, it is assumed that the higher permeability features created by the fracture patterns 
control the direction of groundwater flow (i.e., the hydraulic gradient is aligned with the 
principal direction of the permeability anisotropy ellipse). This assumption is supported by 
observations of the principal fracture orientation being generally north-south (Sweetkind and 
Williams-Stroud, 1996, p. 52) and the hydraulic gradient south of the repository to also be 
oriented in a north-south direction (see Luckey, et al. 1996). This assumption is used in Section 
6.2.1, paragraph 1. This assumption does not require further confirmation. 
5.6 CALCULATION OF DISPERSIVITY 
The analytical solution used here to compare to the numerical results is based on the assumption 
that the solute plume can be described by a Gaussian distribution of concentration in the three 
principal directions. This assumption does not hold up in the numerical results presented here 
and the differences are discussed in Section 6.2.3. This portion of the assumption underlies the 
analytical solution of equations 1, 2, 3 and 4 in Section 6.2.1.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 16 of 60 
For the calculations done here, the Gaussian assumption is also invoked to describe the 
distribution of log transformed travel times for calculation of the dispersivities. This assumption 
is made primarily to use the log-transform as a smoothing technique to decrease the effects of 
statistical outliers in the time or displacement distributions. Examination of the log transformed 
travel times showed the Gaussian distribution to be an adequate approximation. Also, by using a 
large number of particles (4000) the deviations from the Gaussian distribution are limited. This 
portion of the assumption is used in Equations 5, 6a and 6b in Section 6.2.1. This assumption 
does not require further confirmation. 
5.7 FRACTURE FLOW 
For the models contructed here, it is assumed tha the longer length fractures dominate the flow 
sytstem and especiallly the relatively faster flow paths within the fractured rocks. This 
assumption is based on observations of rapid pressure responses in outlying wells during the Chole 
testing (Geldon et al., 1997) This assumption is also based on providing the most 
conservative (fastest) estimates of groundwater transport. Simple geometry shows that the larger 
fractures are better connected across the domain. If these fractures are also assigned relatively 
higher permeability values, flow will be faster than in the less connected and lower permeability 
fractures. This assumption is used in Section 6.1.2.1. This assumption does not require further 
confirmation. 
6 ANALYSIS 
6.1 REPRESENTATION OF FRACTURE PERMEABILITY 
The purpose of this portion of the modeling exercise is to create stochastic images of the fracture 
permeability within a 500 x 500 x 50 meter domain. These fracture permeability fields are used 
as input to a groundwater flow and particle tracking exercise being conducted to better define the 
amounts of dispersion at the sub gridblock scale for the Yucca Mountain Site Characterization 
Project (YMP) SZ site-scale model. The fracture permeability fields are unconditioned in the 
sense that there are no point measurements of permeability that must be reproduced within each 
realization. However, there are specific univariate distributions of fracture attributes observed on 
discrete fractures, as well as prevailing conceptual models that must be represented in the final 
fracture permeability models. This analysis explicitly applies only to that part of the SZ flow 
path that is located within the fractured Tertiary volcanic rocks in the SZ down-gradient from 
beneath the potential repository. It is proposed that the heterogeneous fields created through the 
techniques outlined in this report provide a meaningful representation of the uncertainty in 
particle tracking results arising from uncertainty in the spatial distribution of the fracture 
permeability. 
In contrast to discrete fracture models, which represent fractures as discrete objects within an 
impermeable matrix, an alternative technique for representing fracture permeability within a 
groundwater flow model is the stochastic continuum model (SCM). Stochastic continuum

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 17 of 60 
models have been proposed as a means of representing the spatially heterogeneous nature of 
fracture permeability at the scale of continuum gridblocks (see Hsieh, 1998, pp. 336-338). In 
general, the discrete behavior of individual fractures is represented by an average property over a 
representative elementary volume (REV). The SCM approach has been used previously to 
model fracture systems at experimental facilities for nuclear waste programs in the U.S. (see 
Altman et al. 1996) and in Sweden (Follin and Thunvik, 1994; Tsang et al. 1996). In these 
studies, geostatistical simulation algorithms were used to model continuum properties of discrete 
fracture systems at the scale of numerical flow and transport model gridblocks (1s to 10s of 
meters). The geostatistical realizations of these properties were then used as input to flow and 
transport models to predict the advective travel time of particles through the heterogeneous 
systems. The current project also employs a SCM approach to modeling fracture permeability. 
Two techniques for creation of fracture permeability models are described. These techniques 
have been used to populate the three-dimensional model domain representative of a single 
gridblock within the site-scale saturated zone (SZ) model. The background pattern of grid-block 
transmissivity across the three-dimensional domain is defined using an indicator geostatistical 
simulation process. This spatial simulation algorithm populates the domain with a continuous 
distribution of log10 fracture permeability having specified ranges of spatial correlation. The 
distribution is non-parametric such that at predefined points on the cumulative distribution, the 
amount and anisotropy of the spatial correlation can be varied. This variability allows the higher 
permeability portion of the distribution to have an anisotropic and preferentially aligned 
orientation such as that observed in fractures and flowing features at Yucca Mountain. 
Additionally, some larger features that may dominate the flow and transport for a region of the 
saturated zone are simulated using a boolean simulation algorithm. The features produced by the 
boolean simulation are added to the background permeability pattern modeled by the indicator 
geostatistical simulations to produce the enhanced models of permeability. 
6.1.1 Available Data 
The available data, listed in table 1 of Section 4.1, exist as both direct measurements of fracture 
permeability at the Yucca Mountain site as well as observations of discrete fractures made on 
outcrops and in the Exploratory Studies Facility (ESF). Two conceptual models of fracture 
permeability are developed (Section 6.1.2) from the interpretations of hydraulic testing done in 
both the saturated and unsaturated (air testing) zones as well as from observations of the 
fractures made in boreholes and on outcrops and within the ESF. The various sources of data are 
reviewed below. 
6.1.1.1 Permeability Testing 
The dominant mechanism for water movement in the fractured volcanic rocks at Yucca 
Mountain is believed to be fracture flow, and consequently the origin, characteristics and 
occurrence of fractures have been the subject of several studies (Sonnenthal, et al. 1997; 
Sweetkind and Williams-Stroud, 1996). Hydraulic tests have been conducted using a variety of 
test methods and interpretive models. Single-well, double-packer tests have been conducted 
throughout the aquifer, and multi-well interference tests have been conducted in a number of the

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 18 of 60 
identified flowing intervals (CRWMS M&O, 1998a, Figure 8-27). The log permeability 
histograms (Figure 1) of these tests overlap, suggesting that some of the single-well test results 
represent the more conductive flowing intervals (CRWMS M&O, 1998a; Figure 8-27). The 
natural-log variance of the data set in Figure 1 is 9.46 The minimum log permeability of the 
multi-well tests suggests that the log permeability threshold for flowing features is approximately 
12.2 m2. All the permeability data shown in Figure 1 yields an empirical cumulative distribution 
(cdf) typical of a weakly bimodal distribution (Figure 2), similar to that used in the UZ studies of 
Tsang (1997). 
A specific set of tests has been conducted at the C-well complex southeast of the proposed 
repository. Interpretations of these tests and borehole televiewer logs by Geldon (1996) indicate 
that the highly transmissive zones are due to discrete zones of enhanced fracturing. Hydraulic 
testing at the C-well complex has also indicated the presence of large-scale (up to several 
kilometers) high-permeability features. In the vicinity of the C-well complex, these features are 
associated with observed faults (Geldon et al. 1997) 
6.1.1.2 Borehole Flowmeter Testing 
A number of studies in fractured rock aquifers have shown that groundwater flow does not occur 
uniformly within all fractures, but instead often occurs in just a small fraction of the available 
fractures (see Hsieh, 1998, pp.348-350; Tsang, et al. 1996). More generally, the aquifer material 
may contain many different types of deformation structures: fractures, joints, shear zones, etc. 
that may be formed by different genetic processes (e.g., cooling or tectonic deformation). Given 
the various genetic histories, these different structures are often referred to using the general term 
features. The features that conduct the largest volume of groundwater are of most importance 
for groundwater transport. These features are often referred to as flowing features, flowing 
intervals, or water conducting features. 
A recent analysis of fracture and flowing feature data (CRWMS M&O, 1999c) provides 
information on the spacing between flowing features and fractures. Borehole flowmeter surveys 
indicate that discrete intervals of the aquifer have flow rates that are noticeably greater than the 
remainder of the aquifer. The spacing and thickness of these flowing intervals were analyzed 
(CRWMS M&O, 1999c), and it was found that the dip-corrected geometric mean flowing 
interval spacing is 19.7 m (Figure 3). It should be noted that there is no direct measurement of 
the length, width, structure or origin of the flowing features that create these flowing intervals. 
Only the spacing between these features is measured. 
6.1.1.3 Fracture Observations 
Mapping studies in boreholes, and the ESF suggest a dense, well-connected set of fractures, with 
approximately 89% of the fractures in the range of 0.3 to 3m in length, and approximately 1% 
between 10 to 34m. Fracture spacings tend to be on the same order as fracture lengths, i.e., 
fractures of 10m length tend to be spaced 10m apart. Geometrically, this suggests that the 
fractures are well-connected over a range of length scales, contributing to a scale-dependent 
permeability (Sonnenthal et al. 1997, p 7-26 and p 7-34).

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 19 of 60 
Figure 1. Histogram of permeability measurements made in the middle volcanic aquifer including the 
distribution (solid line) derived from an expert elicitation (CRWMS M&O, 1998b). The dotted and dashed 
lines are the log-normal distributions fit to the single-hole and multi-hole data respectively (CRWMS M&O, 
1998a). This histogram is shown as a cumulative distribution function in Figure 2 (obtained from CRWMS 
M&O, 1998a) 
Single-Hole 
Multi-Hole 
PDF Experts 
Log10 (Permeability in m2) 
No. of Observations 
Probability 
0.0 
0.1 
0.2 
0.3 
0.4 
0.5 
0 
10 
20 
30 
40
-20 -18 -16 -14 -12 -10 -8

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 20 of 60 
Figure 2. Cumulative distribution of observed log10 permeability measurements (CRWMS M&O, 1998a) 
as shown in Figure 1 and the model used to describe the cumulative distribution within the geostatistical 
simulation algorithm. 
The fractures appear to be of two origins, each with specific geometries and spacings. The first 
fracture type is cooling joints, which tend to be relatively smooth, subvertical fractures of 
approximately 4m length, oriented north-south, with a high proportion of blind terminations 
(Sonnenthal et al. 1997; Tsang, 1997). The second type of fracture is tectonic, induced by rock 
stress. These fractures have a wide range of lengths from the microscopic to many tens of 
meters. Tectonic fractures also tend to be subvertical and oriented north-south, as result of the 
reactivation of cooling joints. Borehole data and line surveys indicate that, after correcting for 
dip, the geometric mean fracture spacing is 0.25m for all fractures (Table 6; CRWMS M&O, 
1999c). 
Sweetkind and Williams-Stroud (1996) conducted a synthesis of the fracture data available at 
Yucca Mountain. The results of this synthesis can be used to help constrain the models of 
fracture permeability created in this work. Specifically, information regarding fracture length 
and the variability in fracture orientation can be gained from the work of Sweetkind and 
Williams-Stroud (1996) and used directly in the creation of the feature-based enhanced 
conceptual model of fracture permeability as discussed below. 
Log10 Permeability (m2) 
-20 -18 -16 -14 -12 -10 -8 
Cumulative Frequency 
0.0 
0.2 
0.4 
0.6 
0.8 
1.0 
Observed Data 
Model

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 21 of 60 
Figure 3. Distribution of the spacing between flowing features. Note that the X-axis is log scaled. 
Obtained from CRWMS M&O (1999c). 
Fracture length observations made by Sweetkind and Williams-Stroud (1996) were obtained on 
both surface outcrops and along a scanline in the ESF. The observations of surface length are 
truncated on both the short and long ends of the distribution. The truncation on the short end is 
necessary to make the mapping practical and the truncation on the long end is due to the finite 
extent of the outcrop exposure. Fracture mapping of the surface exposures employed a minimum 
trace length (truncation length) of 1.5 meters and the maximum observable length was 
approximately 15 meters. Given these constraints, the distributions of fracture length for the 
different outcrops appear to be either exponential or power-law (Sweetkind and Williams-Stroud, 
1996, page 52 and Figure 21). Fracture mapping conducted within the ESF was done up to 
station 18+00 (north ramp). For this portion of the ESF, the detailed line survey was mapped 
with a truncation length of 0.30 meters. An additional high-resolution map along 60 meters of 
the ESF was completed with a truncation length 0.15 meters. The results of these two ESF 
fracture mappings, using considerably lower truncation lengths than were used on the outcrop 
surveys, also show the fracture lengths to be either exponentially or power-law distributed 
(Sweetkind and Williams-Stroud, 1996, p. 52 and Figure 22). 
1 10 100 1000 
Corrected Flowing Interval Spacing Data (m) 
0 
0.05 
0.1 
0.15 
0.2 
0.25 
Relative Frequency

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 22 of 60 
Orientations of fractures were observed within the non-lithophysal zone of the TSw (Sweetkind 
and Williams-Stroud, 1996). These orientations show a mainly northeast orientation with a steep 
dip to the west (Sweetkind and Williams-Stroud, 1996, Figure 17). Other orientations describing 
a significant proportion of the measured fractures are north and north-northwest. 
6.1.2 Conceptual Models 
Two conceptual models of fracture permeability have been constructed in this analysis. The first 
model is referred to as the background model and the second model is the enhanced model. 
It is noted that the enhanced model is an extension of the background model. The background 
model is created solely with indicator geostatistical simulation to produce a series of high 
permeability features with the same orientation, anisotropy and length characteristics. This 
background model is based on a conceptualization of a single set of fractures as observed at 
Yucca Mountain. This model of fracture permeability is created such that the long-axis of the 
anisotropic permeability ellipse is aligned parallel to the imposed hydraulic gradient used in the 
flow and particle tracking model (Section 6.2). This modeling decision is made based on the 
assumption (Section 5.3) that the overall fracture permeability resulting from these high 
permeability features controls the direction of groundwater flow. Additionally, at Yucca 
Mountain, the primary fracture orientation is approximately north-south, and for the area south 
of the repository, this orientation is roughly parallel to the hydraulic gradient (see CRWMS 
M&O, 1998a, Figure 8-21). 
The enhanced model uses the initial permeability structure created for the background model and 
then overlays a set of discrete features onto the existing background model. These discrete 
features represent the large features observed in the field, and the larger unobserved features 
inherent in the suggested power-law distribution of fracture lengths, that may control the local 
flow patterns. Examples of such features are the high permeability connections observed 
between the C-well complex and boreholes USW H-4 and UE-25 WT#14 (Geldon et al. 1997, 
Table 9, p Hydraulic Tests-37). 
The middle volcanic aquifer consists of welded tuffs that include all or parts of the Prow Pass, 
Bullfrog and Tram formations of the Crater Flat Group (CRWMS M&O, 1998a, Table 8-11). 
This work is based on data for the middle volcanic aquifer and the conceptual models of fracture 
permeability are also created for the middle volcanic aquifer. However, these models are valid 
interpretations of any moderately to densely welded tuff in the saturated zone at Yucca 
Mountain. This interpretation is supported by results (CRWMS M&O, 1999c, Tables 8 and 9) 
that show the spacing of flowing features is not a function of the specific rock type or 
hydrogeologic unit. 
6.1.2.1 Background Permeability Model 
The field observations and lithology of the middle volcanic aquifer indicate a medium dominated 
by fracture flow with strong anisotropy (major axis aligned north-south) and subvertical dip 
directions. The fracturing appears to be sufficiently dense and interconnected that it exhibits a 
weakly scale-dependent behavior, similar to a stochastic continuum. Relatively large flowing

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 23 of 60 
features have been identified, and hydraulic tests define a bimodal distribution of the log 
permeability for the flowing features and the intervening rock. For the purposes of continuum 
modeling, these characteristics suggest simulating the middle volcanic aquifer as an anisotropic 
permeability field, with separate classes of spatial continuity to represent the flowing features 
and the surrounding rock, respectively. 
One method of geostatistical simulation, the indicator approach, is well adapted to such a 
bimodal simulation. The indicator approach uses the empirical cdf of the data to develop a 
discrete, nonparametric estimate of the true cdf of the simulated medium. Each cutoff level of 
the input discrete cdf has a separate spatial correlation function represented by a variogram, 
whose range represents the continuity of features at that cutoff level. For a preferentially 
fractured media, the major axis of variogram anisotropy corresponds to the fracture plane. This 
study uses the sisim (version 2.0) routine, from the GSLIB package (Deutsch and Journel, 1998) 
to create the background fields of log10 permeability. 
The input discrete cdf for log permeability is simply inferred from the pooled single-well and 
multiwell hydraulic test data (Figure 1). Cutoff values are chosen from the empirical cdf (Figure 
2) to both realistically represent the observed data and create numerically stable simulations. 
The minimum of log10 permeability is 18.2 m2, and the maximum is 10.0 m2. The minimum 
log10 permeability of the multi-well hydraulic tests, 12.2 m2, is used as a cutoff value in the 
discrete cdf and denotes the threshold between background and feature permeability. 
Variogram models for each cutoff are inferred based on the conceptual model. In the ideal case, 
experimental variograms of the hydraulic test data could be used to infer variogram models, but 
there are too few tests to allow such direct inference. Furthermore, the relationship between 
discrete fracture characteristics and permeability are not well understood. As an indirect 
approach, this study uses the observed fracture lengths and flowing interval spacings to set 
variogram ranges, using the relationship that the integral scale of the exponential variogram 
model is equal to the average length of simulated features. 
For cutoffs below the critical value of 12.2 log10 m2, flow is assumed (see Section 5.7) to be 
dominated by the permeability resulting from the majority of fractures, whose length is 3 to 4 m 
or less (Sweetkind and Williams-Stroud, 1996). Thus in the plane of the fracture, the assumed 
variogram integral scale is 4 m (ie., an exponential variogram with effective range of 12 m). The 
thickness of such fractures (in the X-direction) is on the order of millimeters, suggesting that 
adjacent blocks of a finite element should not be correlated. This will be achieved if the 
effective range perpendicular to the fracture plane is less than the target grid scale of 4 m. Thus, 
below 12.2 log10 m2, all cutoffs will have an exponential variogram with 3:12:12 m (X,Y,Z) 
effective ranges in the east:north:vertical directions. The thresholds and the variogram 
parameters for the permeability model are shown in Table 2. 
The permeabilities above 12.2 log10 m2 are assumed to represent the flowing features. The 
lengths of these features are unmeasured, but, conservatively , it can be argued that they are 
comprised of higher permeability fractures, and as such, are planar features oriented north-south 
(Y-direction) with subvertical dips, with spacing approximately equal to length. This study uses 
an integral scale of 20m in the plane of the flowing features (i.e., an exponential model with

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 24 of 60 
effective range of 60m). This integral-scale length is based on the interpretation of an 
exponential or power-law distribution to define the fracture lengths (Sweetkind and Williams- 
Stroud, 1996, p. 52 and Figure 21). Although distributions were not fit to the observed data, the 
choice of a 20 meter integral scale corresponds to the upper limit of these suggested distributions 
based on the data shown in Figure 21 of Sweetkind and Williams-Stroud (1996). The thickness 
of the measured flowing features is 8.3m, corresponding to an exponential variogram with an 
effective range of 25m perpendicular to the plane of the flowing feature. That is, the 
permeabilities 12.2 log10 m2 and above will have an exponential variogram with 25:60:60 m 
effective ranges in the east:north:vertical directions. Three views of an example background 
fracture permeability realization are shown in Figures 4 and 5. 
One limitation of the indicator method is that the frequency and size of features are related 
through the variogram, and thus the variogram range perpendicular to the plane of the flowing 
features may require calibration. This study thus calibrates the east-west variogram range for 
cutoffs of 12.2 log10 m2 and above by post-simulation audits of the permeability fields to verify 
that the flowing interval spacing is similar to that observed in the field. 
Table 2. Parameters describing the indicator variogram models used to build the background fracture 
permeability simulations. An exponential model is specified for all variograms. 
Threshold 
Permeability 
(log10 (m2)) 
cdf value at 
Threshold 
Nugget Sill Effective Range 
(Y-dir.) (meters) 
Anisotropy 
(X:Y:Z) 
-18.2 0.00 NA Minimum NA NA 
-15.7 0.06 0.0 0.056 12 3:12:12 
-15 0.18 0.0 0.148 12 3:12:12 
-14.5 0.30 0.0 0.210 12 3:12:12 
-13.7 0.50 0.0 0.250 12 3:12:12 
-13 0.65 0.0 0.228 12 3:12:12 
-12.2 0.75 0.0 0.182 60 25:60:60 
-11.8 0.85 0.0 0.131 60 25:60:60 
-11.6 0.92 0.0 0.074 60 25:60:60 
-10 1.00 NA Maximum NA NA

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 25 of 60 
Figure 4. Example realization of the background fracture permeability conceptual model. The color 
legend indicates log10 permeability in m2. 
0 
100 
200 
300 
400 
500 
Easting 
400 
300 
200 
100 
0 
Northing 
-16 
-15 
-14 
-13 
-12 
-11 
(m) (m)

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 26 of 60 
Figure 5. Two images of a horizontal slice (layer 12) through the example background fracture 
permeability model. The upper image shows the full distribution of log10 permeability (m2). The lower 
image shows the locations of those features with log10 permeability greater than or equal to 12.2 m2. 
0.0 100.0 200.0 300.0 400.0 500.0 
0.0 
100.0 
200.0 
300.0 
400.0 
500.0 
Easting (m) 
Northing (m) 
-16 
-15 
-14 
-13 
-12 
-11 
0.0 100.0 200.0 300.0 400.0 500.0 
0.0 
100.0 
200.0 
300.0 
400.0 
500.0 
Easting (m) 
Northing (m)

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 27 of 60 
6.1.2.2 Enhanced Permeability Model 
Boolean simulation is defined as the superimposition of independent (non-interacting) random 
objects at random locations within the simulation domain (Schmitt and Beucher, 1997, p. 201). 
In contrast to true geostatistical models, the boolean model relies on complete spatial 
independence. In the context of fracture permeability modeling, boolean models can be used to 
place high permeability features at random locations within a domain. The random placement of 
these objects is derived from the often-used conceptualization of fracture locations as a spatial 
Poisson process. The shapes of these features need not be random and, for the case of fracture 
modeling, are often considered to be disks with radii and orientations drawn from specified 
distributions. 
In this current analysis, the boolean models are created with the code ellip2_MC (version 1.0). 
This code is an extension of the ellipsim code developed by Deutsch and Journel (1998) and 
allows the random placement of disks with radii drawn from user specified distributions 
including both exponential and power-law models. The orientations of the disks are also drawn 
from user specified distributions. The distributions for the orientations are either normal or 
triangular. 
For this exercise, the effect of a small number of domain spanning features is examined by 
simulating disks with a length that is equal to or larger than the domain length. The centers of 
the disks can lie outside the simulation domain such that only portions of the disks appear within 
the domain (see left front corner of Figure 6). The orientation of these features is drawn from a 
normal distribution with a mean orientation of 0 degrees (North) and a standard deviation of 15 
degrees. The boolean simulation is constrained to comprise a total of two percent of the 
simulation domain. 
The resulting boolean simulations are combined with the background fracture permeability 
simulations using the routine combine. This combination is done by simply mapping the disks 
onto the background permeability simulation. The mapping is done such that the permeability 
assigned to the disk is retained at all points within the disk, regardless of the background 
permeability at that location. A constant log10 permeability of 11 is assigned to the disks. This 
permeability corresponds, approximately, to the 95th percentile of the measured permeability 
values as shown in Figure 2. A resulting combination of indicator geostatistical and boolean 
models is shown in Figure 7.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 28 of 60 
Figure 6. Example of large-scale features created using boolean simulation. These features are assigned 
a constant log10 permeability of 11.0 m2 and combined with an indicator geostatistical simulation such 
as that shown in Figure 4 to produce the final feature model of fracture permeability. 
Figure 7. Example realization of the feature-based conceptual model of fracture permeability. This model 
is created by combining the geostatistical simulation of background permeability in Figure 4 and the 
boolean simulation of features in Figure 6. 
50 
25
0 
Elevation (m) 
0 
100 
200 
300 
400 
500 
Easting (m) 
500 
400 
300 
200 
100 
0 
Northing (m) -16 
-15 
-14 
-13 
-12 
-11 
50 
25
0 
Elevation (m) 
0 
100 
200 
300 
400 
500 
Easting (m) 
500 
400 
300 
200 
100 
0 
Northing (m)

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 29 of 60 
6.1.3 Implementation Issues 
The size and discretization of the permeability model domain are set to be coincident with that of 
the FEHM flow and transport model. Several post-processing checks on the heterogeneous 
models are conducted prior to using them as input to the flow and particle-tracking model. 
6.1.3.1 Simulation Domain 
The models of fracture permeability are created within a three-dimensional domain that is 
representative of a single gridblock (element) within the saturated-zone site-scale model. The 
dimensions of the domain are 500 x 500 x 50 meters. The size of this domain is near that of the 
finest resolution gridblock within the SZ site-scale model. For this study of the effects of sub 
gridblock heterogeneity on flow and transport parameters, the domain is discretized into 4 x 4 x 
2 meter gridblocks. The number of elements in the X, Y and Z directions is 125, 125 and 25 
respectively for a total of 390,625 elements. Due to the node-based structure of FEHM, the final 
dimensions of the flow model domain are actually 496.0 x 496.0 x 48.0 meters. This level of 
discretization within the domain represents a compromise between trying to capture the finescale 
heterogeneity resulting from variations in the permeability and connectivity of individual 
discrete fractures and still being able to run the multiple flow and transport models using FEHM 
in a reasonable time frame. This is the same discretization and domain size shown in the figures 
of this report. 
6.1.3.2 Numerical Implementation 
A number of steps using different routines are required to complete the permeability modeling 
process. These steps are described below. 
The background permeability models are created using the GSLIB routine sisim. These models 
are created on a Pentium PC and then transferred to the NWMP UNIX network via ftp. A total 
of 50 realizations of the background permeability are created using sisim. The output files from 
sisim are named as: sisim.#.out, where # is the realization number. To facilitate efficient file 
transfer, these realizations are created in batches of 10 (each input file creates 10 realizations and 
stores them in the same output file). Electronic copies of the five input files are included on the 
CD-ROM accompanying this report. The directory containing the input and output files for the 
background permeability models is on the CD-ROM as: /AMR/SISIM/SET1/ 
The enhanced permeability models are created by running the UNIX shell file cr8_50_feat.ksh. 
These calculations are done on a Sun UltraSparc UNIX workstation. A listing of this shell file is 
included as Attachment 3. This shell file does the following: 
 uncompresses the corresponding background permeability realization and copies it to the file 
sisim.out in its current directory (/AMR/SISIM/SET1/ on the CD-ROM)

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 30 of 60 
 runs the routine ellip2_MC routine to create a domain containing several discrete disk-shaped 
features. The input file for this routine is named ellip2.par. The output files from ellip2_MC 
are named ellip2.out and they are used as input to the routine combine. The routine 
ellip2_MC also creates a debugging file with the naming convention: ellip2.*.dbg, where the 
* indicates the realization number. 
 combines the background permeability model with the disk shaped features using the routine 
combine. The inputs to combine are the sisim.out and ellip2.out files discussed above. The 
output files from combine are named combine.out and used as input to the gs2fehm and 
gamfil routines. 
 checks the spacing of high permeability features (those with log10 permeability greater than 
12.2 m2) using the routine gamfil. The input into gamfil is the combine.out file. The output 
from gamfil is named gam.*.res where the * indicates the realization number. All of the 
gam.*.res files are combined together using the UNIX cat command to create the 
gam_all.res file. This file is the source of the distributions shown in Figures 8 and 9. The 
source code for the gamfil routine is Attachment 9. 
 creates a new input file (ellip2.par) for the ellip2_MC routine by changing the random 
number generator seed in the old input file. This change of seed is accomplished by running 
the routine modgeom. The source for the modgeom routine is listed as Attachment 10. 
The above steps are done in a loop over all 50 realizations. Note that the feature spacing is also 
checked on the background permeability models in the same way as described above for the 
enhanced permeability models. The shell file to accomplish checking of the background 
permeability feature spacing is run_50.ksh in the directory: /AMR/SISIM/SET1/ on the CDROM. 
The source code for this shell is in Attachment 2. 
6.1.4 Model Validation 
Model validation is completed to check the reproduction of the measured data (permeability 
distribution and feature spacing) in the resulting permeability files. Additionally, the 
reproduction of the assumed correlation lengths (variogram models) in the resulting permeability 
models are also checked. 
The criteria used in the validation are: 
1) On average, the cdfs of the permeability realizations must match the cdf of the input 
permeability data. The quantitative criterion used here is to check the mean cdf value 
across all 50 realizations at each of the 8 threshold values. The mean threshold value 
from the 50 realizations must be within +/- 10% of the input threshold value. 
2) The mean high permeability feature spacing is calculated for each of the 50 
realizations and compared to the distribution of flowing interval spacings in Figure 3. 
The validation criterion is that the distribution of mean spacings must fall within the 
distribution of observed spacings as shown in Figure 3. 
3) The variograms are calculated across each realization and are compared to the input 
variogram model. Unlike the permeability distribution and the feature spacing

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 31 of 60 
distribution there are no direct observations of the variogram; the validation can only 
be made against the assumed variogram models used as input. The validation 
criterion is that the shape of the model variogram be reproduced within the extent 
possible given the ergodic hypothesis constraints as discussed below. 
6.1.4.1 cdf Reproduction 
The reproduction of the measured distribution of permeability used as input to the fracture 
permeability models (Figures 1 and 2) is checked. This check is made by determining the value 
of the cdf at each of the eight thresholds defined in Table 1 for each of the 50 realizations for 
both conceptual models of fracture permeability. The results of these calculations are shown in 
Table 3 and Table 4. 
Table 3. Results of 50 realizations of the background permeability model compared to the input 
distribution at eight permeability thresholds. 
Threshold 
Log10 (m2) 
Input cdf Mean cdf Minimum cdf Maximum cdf 
-15.7 0.06 0.060 0.056 0.063 
-15 0.18 0.178 0.173 0.183 
-14.5 0.30 0.295 0.289 0.301 
-13.7 0.50 0.481 0.472 0.488 
-13 0.65 0.616 0.606 0.625 
-12.2 0.75 0.822 0.810 0.834 
-11.8 0.85 0.888 0.879 0.896 
-11.6 0.92 0.938 0.931 0.947 
Table 4. Results of 50 realizations for the enhanced conceptual model compared to the input distribution 
at eight permeability thresholds. 
Threshold 
Log10 (m2) 
Input cdf Mean cdf Minimum cdf Maximum cdf 
-15.7 0.06 0.059 0.054 0.062 
-15 0.18 0.174 0.168 0.179 
-14.5 0.30 0.287 0.281 0.294 
-13.7 0.50 0.470 0.461 0.478 
-13 0.65 0.600 0.588 0.612 
-12.2 0.75 0.802 0.783 0.816 
-11.8 0.85 0.865 0.854 0.878 
-11.6 0.92 0.914 0.904 0.927 
In general, the resulting background and enhanced permeability models reproduce the measured 
distributions of permeability. The resulting models do overpredict and underpredict some of the 
threshold cdf values; however, these discrepancies are always within 10% or less of the input 
values. The resulting models are deemed to be adequate representations of the input 
permeability cdf. 
6.1.4.2 High Permeability Feature Spacing 
The resulting realizations of enhanced fracture permeability were checked to determine the 
spacing of high permeability features. A randomly located transect was drawn through each 
simulated field parallel to the X-axis (Easting axis in Figures 4 to 7). Along each transect, the 
simulated permeability values were compared against the assumed lower limit of permeability

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 32 of 60 
for the flowing features (-12.2 log10 m2). If a simulated permeability exceeds that threshold, 
then the sampling routine counts that value as a flowing feature and continues on to the next 
simulated value. Contiguous values exceeding the flowing feature minimum are counted as a 
single flowing feature, and the statistics for the spacings and widths of such features are 
accumulated for each transect. Results of the spacing and width calculations are presented in 
Figure 8 and 9 as distributions calculated across all 50 realizations. 
Results of the transect sampling shown in the upper images of Figures 8 and 9 can be directly 
compared with the distribution of spacings between flowing features in Figure 3. Examination 
of Figures 8 and 9 shows that the geostatistical realizations produce average feature spacings that 
are within the distribution of measured feature spacings. These models are deemed to be valid 
representations of the observed feature spacing. 
The available data on flowing features do not indicate the width of these features. They could 
represent single discrete fractures or enhanced flow within fracture zones. The continuum model 
representation of these features is limited to a minimum feature width equal to that of the 
numerical gridblocks (4.0 meters). The distributions in the lower images of Figures 8 and 9 
show that on average the mean feature width is approximately five meters. These mean values 
can be interpreted as every fourth feature being two gridblocks wide (8 meters) with the 
remainder of the features being one gridblock (4 meters) in width. 
6.1.4.3 Variogram Reproduction 
Reproduction of the input variogram models is checked across the ensemble of realizations 
created for the background fracture permeability model. This validation step is conducted by 
calculating the variogram on each realization in the three principal directions (X,Y,Z) and 
comparing the results to the input variogram model. The variogram values calculated across the 
ensemble of realizations for any specific separation distance (or lag) will form a distribution. For 
the majority of the lag spacings, this distribution should capture the specified input model. 
The checks on the reproduction of the specified variogram model in the resulting permeability 
fields are shown in Figures 10, 11 and 12. Variograms are checked at two of the eight 
thresholds: threshold 3 at 14.5 log10 m2 and threshold 6 at 12.2 log10 m2. Variogram 
reproduction is excellent at the lower threshold (upper images, Figures 10, 11 and 12). The 
variograms at threshold 6 show the distinct effect of the finite domain size.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 33 of 60 
Figure 8. Distributions of high permeability feature spacing (upper image) and feature width (lower image) 
for the background fracture permeability models. The values shown are the mean values from one 
sampling transect for each of the 50 realizations. The heavy dashed line indicates the mean value of the 
distribution and the thin dashed line indicates the median value of the distribution (overlapping in these 
plots). 
1.0 10.0 100.0 1000.0 
0.0 
0.05 
0.10 
0.15 
0.20 
Mean Feature Spacing (m) 
Relative Frequency 
1.0 10.0 100.0 
0.0 
0.05 
0.10 
0.15 
0.20 
Mean Feature Width (m) 
Relative Frequency

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 34 of 60 
Figure 9. Distributions of high permeability feature spacing (upper image) and feature width (lower image) 
for the enhanced permeability models. The values shown are the mean values from one sampling 
transect for each of the 50 realizations. The heavy dashed line indicates the mean value of the 
distribution and the thin dashed line indicates the median value of the distribution (overlapping in the 
upper plot). 
1.0 10.0 100.0 1000.0 
0.0 
0.05 
0.10 
0.15 
0.20 
0.25 
Mean Feature Spacing (m) 
Relative Frequency 
1.0 10.0 100.0 
0.0 
0.05 
0.10 
0.15 
0.20 
0.25 
Mean Feature Width (m) 
Relative Frequency

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 35 of 60 
Figure 10. Results of east-west (X-direction) variograms calculated on all 50 realizations of the 
background fracture permeability model and compared to the input variogram model. The upper image 
shows the results for the 14.5 log10 m2 permeability threshold and the lower image shows the results for 
the 12.2 log10 m2 permeability threshold. The gray zones in both images indicate the range of variability 
in the variance of the realizations. 
Legend
Variance 
Model 
Minimum 
Maximum 
Mean 
0.0 10.0 20.0 30.0 40.0 50.0 
0.00 
0.05 
0.10 
0.15 
0.20 
0.25 
Distance (meters) 
Indicator Semi Variance 
Legend
Variance 
Model 
Minimum 
Maximum 
Mean 
0.0 20.0 40.0 60.0 80.0 100.0 
0.00 
0.05 
0.10 
0.15 
0.20 
Distance (meters) 
Indicator Semi Variance

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 36 of 60 
Figure 11. Results of north-south (Y-direction) variograms calculated on all 50 realizations of the 
background fracture permeability model and compared to the input variogram model. The upper image 
shows the results for the 14.5 log10 m2 permeability threshold and the lower image shows the results for 
the 12.2 log10 m2 permeability threshold. The gray zones in both images indicate the range of variability 
in the variance of the realizations. 
Legend
Variance 
Model 
Minimum 
Maximum 
Mean 
0.0 10.0 20.0 30.0 40.0 50.0 
0.00 
0.05 
0.10 
0.15 
0.20 
0.25 
Distance (meters) 
Indicator Semi Variance 
Legend
Variance 
Model 
Minimum 
Maximum 
Mean 
0.0 20.0 40.0 60.0 80.0 100.0 
0.00 
0.05 
0.10 
0.15 
0.20 
Distance (meters) 
Indicator Semi Variance

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 37 of 60 
Figure 12. Results of vertical (Z-direction) variograms calculated on all 50 realizations of the background 
permeability model and compared to the input variogram model. The upper image shows the results for 
the 14.5 log10 m2 permeability threshold and the lower image shows the results for the 12.2 log10 m2 
permeability threshold. The gray zones in both images indicate the range of variability in the variance of 
the realizations. 
Legend
Variance 
Model 
Minimum 
Maximum 
Mean 
0.0 10.0 20.0 30.0 40.0 50.0 
0.00 
0.05 
0.10 
0.15 
0.20 
0.25 
Distance (meters) 
Indicator Semi Variance 
Legend
Variance 
Model 
Minimum 
Maximum lag variance 
Mean 
0.0 10.0 20.0 30.0 40.0 50.0 
0.00 
0.05 
0.10 
0.15 
0.20 
Distance (meters) 
Indicator Semi Variance

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 38 of 60 
Central to the theory underlying geostatistics is the ergodic hypothesis that allows the 
replacement of a spatial variable within a single unbounded domain by an average of the same 
variable over an ensemble of realizations (see Zhan, 1999, p. 113). In practical terms, the finite 
domain over which the ensemble of realizations are created needs to be roughly 10 correlation 
lengths or greater in each dimension to achieve accurate variogram reproduction. For the case 
considered here, the variograms at threshold 3 are reproduced accurately because the correlation 
lengths are all small enough (3:12:12 meters in the X, Y and Z directions) relative to the domain 
size (500 x 500 x 50 meters). The variogram ranges for threshold 12 are: 25:60:60. This 
violation of the ergodic hypothesis lowers the overall indicator variance of the simulated 
permeability fields and causes the variograms to fall below the input model (lower images, 
Figures 10, 11 and 12). The shape of the model variograms is preserved in the resulting 
realizations, but the sill (total variance) is less than that of the data set due to limitations imposed 
by the ergodic hypothesis. The shape of the input variogram model is maintained, albeit at a 
lower variance, thus these realizations are considered to be valid representations of the input 
geostatistical model. 
The implication of this lower sill value at the 12.2 m2 threshold is that the variability in the 
modeled permeability distribution at the higher permeability values is not as large as in the input 
data set (Figures 1 and 2). However, this decrease in variance is only slight as shown by the 
close reproduction of the input cdf by the models in the lower rows of Tables 3 and 4. 
Therefore, these lower sill values will have negligible effects on the dispersivity calculations. 
6.2 CALCULATION OF DISPERSIVITIES 
Dispersion in groundwater transport systems can be defined as the occurrence and evolution of a 
transition zone between two domains of the fluid phase with different compositions. This 
definition does not imply any specific process through which this transition zone comes into 
being, nor does it imply a specific scale for this transition zone. Dispersivity is the rate of 
change of the second moment of the contaminant plume. Dispersivity is generally calculated 
along the principal axes of the flow system. Along each principal axis, the dispersivity, with 
units of length, can be considered as a characteristic length of the transition zone between the 
two domains of the fluid phase. 
6.2.1 Approach 
For the calculation of the transverse dispersivities, the approach of Wen and Gomez-Hernandez 
(1998, pp. 144-145) is followed. Wen and Gomez-Hernandez (1998) examined two-dimensional 
transport in heterogeneous fields with particle tracking. This approach is outlined and expanded 
to the three-dimensional case below. 
This work represents the solute plume by a finite set of particles tracked along streamlines. In 
this situation, the dispersivities are given in terms of the change in second moments, X11, X22, 
X33, of the particle trajectories with respect to time (after Wen and Gomez-Hernandez, 1998):

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 39 of 60 
dt 
dX 
U 
t 
dt 
dX 
U 
t 
dt 
dX 
U 
t 
V
H
L 
33 
22 
11 
2
1 
) ( 
2
1 
) ( 
2
1 
) ( 
=
= 
= 
a
a
a 
Where t is time, U is the mean particle velocity, aL is the longitudinal dispersivity, aH is the 
horizontal transverse dispersivity and aV is the vertical transverse dispersivity. Equations 1a and 
1b are taken directly from Wen and Gomez-Hernandez (1998, p. 133). Equation 1c is the same 
as 1a and 1b, but written for the third (Z) dimension. 
Apparent macrodispersivities are those determined from a single measurement of the particle 
trajectories at time t. These macrodispersivites are given, for an instantaneous injection 
boundary condition, as (after Wen and Gomez-Hernandez, 1998, p. 133): 
Ut
t X 
t 
Ut
t X 
t 
Ut
t X 
t 
V
H
L 
2 
) ( 
) ( 
2 
) ( 
) ( 
2 
) ( 
) ( 
33 
22 
11 
=
= 
= 
a
a
a 
Several stochastic theories defining macrodispersion have been developed (e.g., Dagan, 1988; 
Gelhar and Axness, 1983). For transport in a three-dimensional field with a flux weighted 
source boundary condition, Dagan (1988, eqns 24 and 38) gives the following expressions for the 
second moments of the plume as a function of normalized time: 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
.. 
. .. 
. + + - + - = = 
.. 
. 
.. 
. 
. .. 
. 
. .. 
. 
.. 
. .. 
. + - + - - = 
- 
- 
' 
2 3 3 
2 2 
33 22 
' 
2 3 
2 2 
11 
' 
1 
'
4 
'
4 
'
4 
' 
1 
3
1 
2 ) ' ( ) ' ( 
' 
1 
1 
'
8 
'
8 
' 
4 
3
8 
' 2 ) ' ( 
t 
Y 
t 
Y 
e 
t t t t t 
t X t X 
e 
t t t t 
t t X 
. s 
. s 
(Eq. 1a) 
(Eq. 1b) 
(Eq. 1c) 
(Eq. 2a) 
(Eq. 2b) 
(Eq. 2c) 
(Eq. 3) 
(Eq. 4)

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 40 of 60 
where sY
2 is the variance of the lnK field with isotropic spatial correlation of integral length . 
(practical range = 3.), and t= X/. is the dimensionless time, or displacement. Combining 
Equations 2 a,b and c with Equations 3 and 4 gives expressions for the macrodispersivities as a 
function of time. 
Using the analytical solutions of Dagan (1988), both longitudinal and transverse dispersivity are 
calculated for a range of t. These results are shown in Figure 13 for natural log transformed 
permeability variances of 1.0 and 9.46. These values of variance are the upper limit considered 
in the development of the theory and the variance of the saturated zone permeability data shown 
in Figure 1, respectively. The longitudinal dispersivity is seen to rise to an asymptotic value 
after a travel distance of several tens of correlation lengths (longitudinal correlation length = 20 
m in this study). The two transverse dispersivities (i.e., horizontal and vertical) are equal in 
magnitude and initially increase in value and then decrease asymptotically to zero at infinite 
time. 
For the numerical modeling done in this study, the longitudinal and transverse dispersivities are 
calculated from the particle travel times and the transverse displacements of the particles. The 
transverse displacements are determined from the starting locations to the point where each 
particle crosses a collection plane downstream of the source location oriented normal to the 
mean flow direction. For this model setup and a flux-weighted, instantaneous injection of 
particles, Kreft and Zuber (1978) present an analytical solution for the longitudinal dispersivity: 
2 
) ( 
) ( 
2 . .. 
. 
. .. 
. 
= 
x m 
x x 
t
t 
L 
s 
a (Eq. 5) 
where mt(x) and st(x) are the mean and standard deviation of the travel times at travel distance of 
x. Other researchers (Desbarats and Srivastava, 1991; Moreno and Tsang, 1994) have found that 
the longitudinal dispersivity calculated using Equation 5 can fluctuate considerably from one 
realization to the next. These fluctuations have been attributed to outliers in the travel time 
distribution. Even with a flux weighted particle source term, there are some particles that travel 
through very low permeability material and take an excessively long time to reach the collection 
plane. These outliers give the travel time distribution an extremely long tail and lead to spurious 
values of the dispersivity. 
The problem of long time outliers in the calculation of the longitudinal dispersivity is handled 
here by using the log transform of the travel times. The mean and standard deviation of the log 
time distribution are determined and then converted back to raw space. Statistics based on the 
log values of the travel times are much less sensitive to outliers than are those calculated with the 
raw travel times. Inherent in this log transform filtering of the distribution is the assumption 
(first paragraph of Section 5.6) that the travel time distribution can be approximated as a lognormal 
distribution. Other researchers (Khaleel, 1994; Wen and Gomez-Hernandez, 1998) have 
succesfully applied this log transform approach to the determination of longitudinal dispersivity 
and we follow those examples in this work. The expressions for the mean and standard deviation 
of the travel time distribution are now determined as:

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 41 of 60 
] 1 )) ( )[exp( ( ) ( 
] 2 / ) ( ) ( exp[ ) ( 
2 
ln 
2 2 
2 
ln ln 
- = 
+ = 
x x m x 
x x m x m 
t t t 
t t t 
s s 
s 
where mln t(x) and s2
ln t(x) are the mean and variance of the natural log travel times at a travel 
distance x. 
The transverse dispersivities are calculated as: 
x
x 
x 
x
x 
x 
V
H 
2 
) ( 
) ( 
2 
) ( 
) ( 
33 
22 
. 
a 
. a 
=
= 
where .22(x) and .33(x) are the variances of the differences between the transverse particle 
travel position at travel distance x and the initial traverse coordinate at the source location for the 
transverse X (horizontal) and Z (vertical) positions respectively. These variances are used to 
approximate the transverse second-order spatial moments, X22 and X33, presented in equations 2b 
and 2c. This approximation has been used successfully to evaluate transverse dispersion in 
previous studies (Follin and Thunvik, 1994; Wen and Gomez-Hernandez, 1998). 
This section has presented an approach for the derivation of longitudinal and transverse 
dispersivities from the results of particle tracking simulations. This approach is based on the 
analytical solutions of Dagan (1988) and the assumption (second paragraph of Section 5.6) that a 
Gaussian distribution in each of the three principal directions can describe the solute plume. The 
growth of the second moment of the plume in the transverse directions is difficult to derive from 
the particle tracking results, especially in a strongly heterogeneous medium. Therefore, the 
variances of the transverse displacements of the particles are used as a proxy for the transverse 
second moments of the plume. The permeability fields used here differ from those specified in 
the development of the analytical solutions in that the natural log variance is higher than 1.0 at 
9.46 and that the fields are not ergodic nor isotropic. Differences between analytical results and 
numerical results are compared at the end of this report. 
(Eq. 6a) 
(Eq. 6b) 
(Eq. 7a) 
(Eq. 7b)

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 42 of 60 
Figure 13. Longitudinal (upper image) and transverse (lower image) dispersivity as a function of travel 
distance as calculated using the analytical solutions in Equations 2a and 2b along with Equations 3 and 4. 
The two lines correspond to the variances assigned to the theoretical limit of applicability (ln variance = 
1.0) and the Yucca Mountain Project data (ln variance = 9.46). 
Travel Distance (meters) 
0 200 400 600 800 1000 
Transverse Dispersivity (meters) 
0
1
2
3
4
5
6
7 
ln Variance 1.0 
ln Variance 9.46 
Travel Distance (meters) 
0 200 400 600 800 1000 
Longitudinal Dispersivity (meters) 
0 
20 
40 
60 
80 
100 
120 
140 
160 
180 
200 
ln Variance = 1.0 
ln Variance = 9.46

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 43 of 60 
6.2.2 Numerical Implementation 
Longitudinal and transverse dispersivities are calculated using Equations 5 (along with 6a and 
6b) and 7a and 7b above. Input to these equations are the travel distances, the mean and standard 
deviation of the travel time distribution and the variances of the differences between transverse 
starting and arrival positions. These travel time and location statistics are determined by 
modeling streamlines through the heterogeneous fields. The modeling process is outlined as: 
 A heterogeneous permeability field is selected and converted from the GSLIB format to the 
FEHM format using the code gs2fehm. The permeability field is the output of either the 
sisim or combine routine depending on whether it is a background or an enhanced 
permeability model respectively. 
 A steady-state flow solution is obtained using FEHM (version 2.00) and the flxo macro 
within FEHM is activated to write out internodal fluxes within a 100 x 5 gridblock plane of 
the flow model. 
 The output of the flxo macro (het_flow.out) is used as input to the code cr8sptr or 
cr8sptr_cell. These two codes generate the FEHM sptr macro for the flux weighted source 
and the single grid block source respectively. This code reads in the internodal fluxes in 
flxo.out and determines the starting locations for the particles using a flux-weighted scheme. 
The flux weighting determines the number of particles to go into each cell. Within each cell, 
the particles are given random starting locations. The output of cr8sptr or cr8sptr_cell is the 
sptr macro for FEHM saved in the sptr.dat file. 
 A second FEHM run is done for the particle tracks. The sptr macro contained in sptr.dat is 
used for the particle starting locations. A single time step within FEHM is used and the 
solution from the previous FEHM run, stored in the het_flow.fin file, is copied to the initial 
conditions file, het_flow.ini, for this second run. 
 The FEHM output file het_flow.sptr2 contains the times and locations of all the particles as 
they move through the three-dimensional domain. This file is used as input to the code 
calc_D_old that calculates the longitudinal and transverse dispersivities. There are four 
outputs from calc_D_old: disper_L.out, disper_X.out, disper_Z.out and debug.out. The 
disper files contain the longitudinal (L) and transverse (X and Z) dispersivities as calcuated 
in calc_D_old using Equations 5 and 7a and 7b above. The dispersivities are calculated for 9 
different travel distances and each column in the output files of calc_D_old is for a different 
travel distance (increasing distance from leftmost to rightmost column). 
These five steps as listed in the bullets above are repeated for each realization of the permeability 
field. For the calculations presented below, 50 realizations are completed for both the 
background permeability and the enhanced models. The 50 runs are completed by using the 
UNIX K-shell scripts run_50_back.ksh and run_50_feat.ksh. Output files written by calc_D_old 
are appended for each realization such that at the end of the 50 runs, each dispersivity output has 
50 lines of 9 columns each.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 44 of 60 
For the final analyses, the output files from calc_D_old are transferred to a PC via ftp and each 
file is read into Excel. Within Excel, the mean and median of each column are calculated. These 
values are the mean and median value of the dispersivity calculated across all 50 realizations for 
each of the nine travel distances. Graphs of the median dispersivity as a function of travel 
distance are shown in the Results section below. 
The number of particles required for accurate dispersivity calculations is not known a priori. 
The number used here was 4000 particles. This number was chosen by considering a number 
small enough to run in a reasonable time and also create output files of a manageable size 
(approximately 100MB), yet large enough to provide accurate results. The accuracy of the 
results were checked by selecting one permeability realization and running the dispersion 
calculations with the same flow solution, but with increasing numbers of particles for each 
calculation. For the realization examined, the calculated dispersivity became relatively stable 
when more than 2000 particles were used. Some variation in the number of particles necessary 
will occur from one realization to another, so 4000 particles were used to ensure that stable 
values of dispersivity would be calculated on all realizations. 
6.2.3 Results 
Longitudinal, aL, transverse horizontal, aH, and transverse vertical dispersivities, aV, were 
determined on both the background and the enhanced fracture permeability models. For each 
fracture permeability model a total of 50 realizations were created and the particle tracking was 
completed using two different source terms: point and plane. The point source term begins 
all particles within the same numerical gridblock. The chosen gridblock is the one with the 
highest groundwater flux within the central region of the flow model at the same Y coordinate 
(20.0 meters downgradient of the upper fixed head boundary) as the plane source. The plane 
source, as described previously, assigns the particles in a flux weighted manner to the gridblocks 
within the central 400 x 10 m of the flow model at a location 20 meters downstream of the upper 
fixed head boundary. For either source term, the particles within any single gridblock are 
distributed randomly. 
Table 5. Travel distances for the dispersivity calculations. The relative distances are calculated as: 
(absolute travel distance ) /., where . is set to the model input value of 20.0 meters. 
Collection Plane Absolute Travel Distance 
(meters) 
Relative Travel Distance 
(Number of correlation lengths) 
1 20.0 1.0 
2 40.0 2.0 
3 80.0 4.0 
4 120.0 6.0 
5 180.0 9.0 
6 240.0 12.0 
7 300.0 15.0 
8 380.0 19.0 
9 460.0 23.0

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 45 of 60 
For each directional dispersivity, the results are shown as an X-Y plot of dispersivity in meters as 
a function of absolute travel distance. The dispersivity shown in each plot is the median value 
determined across the 50 realizations. Travel distance is defined as the distance from the source 
to the collection plane. A total of 9 different collection planes were used at different distances 
downstream of the source. These distances are shown as both absolute and relative values in 
Table 5. 
6.2.3.1 Longitudinal Dispersivity 
Longitudinal dispersivity is calculated from the coefficient of variation of the travel time 
distribution as measured at each collection plane (Equation 5). The numerical results for the two 
different conceptual models and the two different source terms are shown in Figure 14. 
Figure 14. Longitudinal dispersivity as a function of travel distance for both the background and enhanced 
permeability models with both point and plane particle sources. 
The most notable aspect of Figure 14 is the extreme values of dispersivity that occur with the 
enhanced permeability model and the plane source. These values are approximately an order of 
magnitude higher than the values for the background model with either source geometry or for 
the same enhanced model with the point source. Also, these values are considerably larger than 
the travel distance. Examination of the results from individual realizations shows that the 
calculated dispersivities vary drastically from one realization to the next. The distribution of 
dispersivity values across all 50 realizations exhibits a slightly multimodal behavior. 
Travel Distance (meters) 
0 100 200 300 400 500 
Longitudinal Dispersivity (meters) 
0 
500 
1000 
1500 
2000 
2500 
3000 
3500 
Background, Point Source 
Enhanced, Point Source 
Background, Plane Source 
Enhanced, Plane Source

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 46 of 60 
These extreme results are interpreted as being due to some realizations producing a strongly 
bimodal distribution of traveltimes while others do not. Two examples of high permeability 
features are shown below (Figure 15) as support for this interpretation. The two feature 
realizations in Figure 15 produce very similar longitudinal dispersivity values at 460 meter travel 
distance for the point source: realization 10 (upper image) produces a dispersivity of 233 meters 
while realization 7 (lower image) produces a dispersivity of 163 meters. However, with the 
planar source geometry, realization 10 (upper image) produces a longitudinal dispersivity of 392 
meters while realization 7 (lower image) produces a value of 5,890 meters. 
In light of the images in Figure 15 and visual examination of other realizations, those realizations 
with high permeability features that can capture a significant fraction of the particles along the 
flowpath will have larger dispersivities than those that do not. The high permeability feature 
geometry that is best suited for capturing the flowpaths is a feature that has an oblique 
orientation to the principal flow direction. Features that are completely, or close to, parallel with 
the principal flow direction will not cause such a bimodal distribution of travel times. The lower 
image of Figure 15 shows a prime example of a high permeability feature that will capture all 
particles starting in between the two large features, but not capture particles starting outside of 
these two features. 
For the point source geometry, the high permeability features create channels of high flux and all 
of the particles are assigned starting locations within that channel. Dispersivities for the point 
source geometry are considerably smaller than those calculated for the planar source geometries. 
The results in Figure 14 also show decidedly non-Gaussian behavior in that dispersivity is 
highest at short travel distances and then asymptotically decreases to a final value at large travel 
distances. Compare this behavior to the analytical solution graphed in Figure 13 that shows a 
gradual rise in longitudinal dispersivity to an asymptotic value at large travel distance. Rather 
than spreading as a plume in which the longitudinal concentration profile could be described by a 
Gaussian distribution, as the analytical solution assumes, the travel times are much more variable 
at shorter travel distances. This high dispersivity at short distances is due to the fracture 
permeability models creating large spatial variability in groundwater flux across a plane normal 
to the mean flow direction. In flow through the fracture permeability models exhibiting high 
variability in log permeability, flux is partitioned into discrete zones much more so than in the 
lower variance Gaussian based permeability models inherent in the analytical solutions. This 
partitioning of flux into discrete zones creates large variability in groundwater travel times at 
short distances resulting in large calculated values of dispersivity. As the travel distance 
increases, the flowpaths get channeled into relatively higher permeability flowzones and the 
travel times become more homogeneous. 
The longitudinal dispersivity results obtained in this numerical study can be compared to results 
obtained from modeling tracer experiments at the C-wells complex. Three different sets of 
results have been obtained from tracer tests done between the same boreholes UE-25C #2 and 
UE-25C #3 (see Fahy, 1997; Geldon, et al. 1997). The straight-line distance between the 
boreholes is roughly 30 meters and dispersivity values of 1.9 to 2.6 meters (Geldon et al. 1997) 
2.4 to 2.6 meters (Fahy, 1997) have been interpreted from matches to the observed tracer data.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 47 of 60 
These tracer-test derived values indicate longitudinal dispersivities on the order of 3.7 to 8.7 
percent of the travel distance. 
In terms of absolute values and percentage of travel distance, the longitudinal dispersivities 
derived from the tracer tests are all less than the values derived from this numerical study. A 
reason for this difference may be that transport between the two C wells is thought to occur in 
only 2 or 3 discrete fracture pathways, while flow in the numerical studies presented here occurs 
throughout the fracture network. Another difference between the tracer test results and the result 
in this study is that the flow field for the tracer tests is radially convergent flow, while the 
numerical models use a uniform flow field. It is possible that the different flow fields also 
account for the differences in dispersivity values between the studies; however, analysis of these 
effects is beyond the scope of this study.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 48 of 60 
Figure 15. High permeability features in two example enhanced permeability model realizations that 
produce drastically different longitudinal dispersivity values. Particle tracking on realization 10 (upper 
image) produces a longitudinal dispersivity of 392 meters. Particle tracking on realization 7 (lower image) 
produces a longitudinal dispersivity of 5890 meters. The arrow indicates flow direction. 
50 
25
0 
Elevation (m) 
0 
100 
200 
300 
400 
500 
Easting (m) 
500 
400 
300 
200 
100 
0 
Northing (m) 
50 
25
0 
Elevation (m) 
0 
100 
200 
300 
400 
500 
Easting (m) 
500 
400 
300 
200 
100 
0 
Northing (m)

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 49 of 60 
Figure 16. Expanded view of Figure 14 showing longitudinal dispersivity as a function of travel distance 
for the background permeability models with both point and plane particle sources, and the enhanced 
permeability model with a point source. 
Figure 16 shows the lower three plots in Figure 14 using an expanded vertical scale. From 
Figure 16, it is possible to see that the asymptotic values of longitudinal dispersivity for these 
combinations of permeability model and source geometry all fall within the 110 to 180 meter 
range. These dispersivities are roughly 24 to 39 % of the travel distance. From the results in 
Figure 16, it is unclear whether or not the longitudinal dispersivities have truly reached an 
asymptotic macrodispersivity. The results for the two different source geometries in the 
background permeability models appear to have reached an asymptote; however, the 
dispersivities calculated with the enhanced permeability model appear still be rising after 460 
meters of travel. 
Results of the longitudinal dispersivity calculations also show that once the large-scale features 
are added into the permeability models, these features completely alter the behavior of the 
particle transport through the domain. Figure 17 shows cross-plots of the longitudinal 
dispersivity calculated with the enhanced permeability model as a function of the same 
dispersivity calculated with the background permeability model. For both the planar- and pointsource 
geometry, there is no correlation between the results obtained on the background 
permeability model and those obtained with the enhanced model. These results indicate that the 
nature of the transport process changes completely with the addition of large-scale highpermeability 
features. 
Travel Distance (meters) 
0 100 200 300 400 500 
Longitudinal Dispersivity (meters) 
0 
100 
200 
300 
400 
500 
600 
700 
Background, Point Source 
Enhanced, Point Source 
Background, Plane Source

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 50 of 60 
Figure 17. Scatterplots showing the longitudinal dispersivity value calculated at a 460 meter travel 
distance with the enhanced permeability models as a function of the value calculated with the background 
model. The upper image shows the point source results and the lower image shows the planar source 
results. 
Background Model 
Longitudinal Dispersivity (meters) 
0 200 400 600 800 1000 1200 
Enhanced Model 
Longitudinal Dispersivity (meters) 
0 
200 
400 
600 
800 
Background Model 
Longitudinal Dispersivity (meters) 
0 50 100 150 200 250 300 350 400 450 500 
Enhanced Model 
Longitudinal Dispersivity (meters) 
0 
1000 
2000 
3000 
4000 
5000 
6000 
7000

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 51 of 60 
6.2.3.2 Horizontal Transverse Dispersivity 
Horizontal transverse dispersivity is calculated from the variance of the horizontal displacements 
of the particles as measured at each collection plane (Equation 7a). The results for the two 
different conceptual models and the two different source terms are shown in Figure 18. 
Figure 18. Horizontal transverse dispersivity as a function of travel distance for both the background and 
enhanced permeability models with both point and planar particle sources. 
Similar to the results for longitudinal dispersivity shown in Figures 14 and 16, the results for 
horizontal transverse dispersivity in Figure 18 show that the largest values of dispersivity occur 
within the enhanced fracture permeability model when planar source geometry is assumed. 
Similar to the longitudinal dispersivity results, the planar source allows the particle to sample 
almost all possible flowpaths. When this source is coupled with an enhanced permeability 
model, the possibility of preferential channels developing with significantly different transverse 
flow directions is increased. Recall, that the large scale features have variable orientations about 
the main flow direction. As an example, consider the field shown in the lower image of Figure 
15. While translation in the directions normal to the average flow direction does not cause 
transverse dispersion by itself, the translations created by the converging features shown in the 
lower image of Figure 15 will certainly enhance transverse variability in flow paths. 
The theoretical behavior for transverse dispersivity is that of a rapid rise to a peak value within a 
few correlation lengths of travel distance and then a gradual decrease to a dispersivity value of 
Travel Distance (meters) 
0 100 200 300 400 500 
Horizontal Dispersivity (meters) 
0.0 
0.5 
1.0 
1.5 
2.0 
2.5 
3.0 
3.5 
4.0 
Background, Point Source 
Enhanced, Point Source 
Background, Plane Source 
Enhanced, Plane Source

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 52 of 60 
zero. The planar source geometry in the background permeability model shown in Figure 18 
reproduces the macroscopic dispersivity behavior predicted by theory (Equation 7a, compare to 
results in the lower image of Figure 13). It is difficult to determine whether or not results from 
the planar source geometry in the background permeability model have reached an asymptotic 
value or are still gradually decreasing (Figure 18). The final values of horizontal transverse 
dispersivity range from approximately 0.6 to 3.0 meters, or approximately 0.1 to 0.6 % of the 
travel distance. 
6.2.3.3 Vertical Transverse Dispersivity 
Vertical transverse dispersivity is calculated from the variance of the vertical displacements of 
the particles as measured at each collection plane (Equation 7b). The results for the two different 
conceptual models and the two different source terms are shown in Figure 19. 
Figure 19. Vertical transverse dispersivity as a function of travel distance for both the background and 
enhanced permeability models with both point and planar particle sources. 
The vertical dispersivity values shown in Figure 19 demonstrate results that are different from 
the longitudinal and horizontal values shown above in Figures 14 and 18. For the vertical 
dispersivity calculations, the background permeability model, not the enhanced model, produces 
the largest values of dispersivity. Additionally, all combinations of conceptual model and source 
geometry converge to the same final dispersivity value of approximately 0.2 meters at a travel 
distance of 460 meters. 
The final value of transverse vertical dispersivity at the 460 meter travel distance (approximately 
0.2 meters) is an order of magnitude smaller than that predicted by the analytical solution 
Travel Distance (meters) 
0 100 200 300 400 500 
Vertical Dispersivity (meters) 
0.0 
0.5 
1.0 
1.5 
Background, Point Source 
Enhanced, Point Source 
Background, Plane Source 
Enhanced, Plane Source

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 53 of 60 
(Equations 2c and 4). This result is due to the size of the domain used in the numerical models. 
The vertical dimension of the flow domain is 50 meters or about 2 to 3 vertical correlation 
lengths (see Figure 12). The analytical solutions assume an infinite unbounded domain. In 
practical terms, this means a domain of at least 10 to 20 correlation lengths at a minimum. While 
this relative size constraint is met in the longitudinal and horizontal transverse directions, it is 
certainly not met in the vertical transverse direction and thus the calculated dispersivity values 
are considerably smaller than those predicted by the analytical solution. 
6.3 COMPARISON TO ANALYTICAL SOLUTIONS 
Two important conclusions are noted from a comparison of the analytical solutions to the 
numerical results presented here: 1) with the exception of one of the longitudinal dispersivity 
cases, the numerical results show dispersivity values that are similar to results derived from the 
analytical solutions. 2) while the dispersivity values at 460 meter travel distance are similar 
between analytical and numerical solutions, the values at shorter distances may be considerably 
different. Tables 6, 7 and 8 show the values of dispersivity calculated both numerically and 
analytically for the 460-meter travel distance. Note the lower values of vertical transverse 
dispersivity in the numerical results relative to the analytical results as discussed above. 
Table 6. Calculated longitudinal dispersivity values at 460 meter travel distance. For the numerical 
results, the median value across 50 realizations is given. 
Longitudinal Dispersivity Calculation Dispersivity after 460 meter travel distance 
(meters) 
Analytical (ln s2 = 9.46) 169 
Background, Point source 115 
Enhanced Point Source 140 
Background, Planar source 175 
Enhanced Planar Source 2380 
Table 7. Calculated horizontal transverse dispersivity values at 460 meter travel distance. For the 
numerical results, the median value across 50 realizations is given. 
Horizontal Transverse Dispersivity Calculation Dispersivity after 460 meter travel distance 
(meters) 
Analytical (ln s 2 = 9.46) 2.4 
Background, Point source 0.6 
Enhanced Point Source 0.6 
Background, Planar source 0.9 
Enhanced Planar Source 3.0 
Table 8. Calculated vertical transverse dispersivity values at 460 meter travel distance. For the 
numerical results, the median value across 50 realizations is given. 
Vertical Transverse Dispersivity Calculation Dispersivity after 460 meter travel distance 
(meters) 
Analytical (ln s 2 = 9.46) 2.4 
Background, Point source 0.2 
Enhanced Point Source 0.2 
Background, Planar source 0.2 
Enhanced Planar Source 0.2

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 54 of 60 
7 CONCLUSIONS 
Fracture data available from Yucca Mountain are used as input to create multiple effectivecontinuum 
realizations of two different conceptual models of fracture permeability. Both 
conceptual models are consistent with the available observations. The fracture permeability 
realizations honor the input cumulative distribution function and also reproduce the specified 
models of spatial correlation within the constraints imposed on the modeling by the finite size 
domain. Additionally, the spacing between high permeability features matches the spacing of 
flowing intervals measured at Yucca Mountain using borehole flow meters. 
These realizations are used as input to a groundwater flow model and the results of the flow 
model are used as the basis for streamline particle tracking. The temporal moments of the 
particle travel times at nine different collection planes downstream of the source area are used to 
determine the longitudinal dispersivity. The second moment of the transverse particle 
displacements is used to determine the horizontal and vertical transverse dispersivity values. 
These results are compared to results obtained with an analytical solution based on stochastic 
theory of groundwater transport. 
Results of this dispersivity study show: 
 Flow in highly heterogeneous fractured media is not dispersive in the classical sense of 
stochastic theory; rather the fracture permeability pattern leads to channelized flow. Solute 
plumes will not exist as elliptical bodies, but instead the solute will move as a ribbon along 
preferential pathways of relatively higher permeability. 
 In spite of the above conclusion, the analytical expressions for longitudinal and transverse 
dispersivity developed by Dagan (1988) do an adequate job of predicting the 
macrodispersivity after 460 meters, or roughly 23 correlation lengths, of travel distance. This 
result appears to be a case of the wrong physics giving the correct answers. With the 
exception of the vertical transverse dispersivity calculations, the numerical results suggest 
extremely non-Gaussian behavior at early times (short travel distances) which is contrary to 
the basis of the analytical solutions. The notable exception to this conclusion of correct 
results from the analytical solutions is the case of the longitudinal dispersivity calculated 
with the enhanced permeability model and a planar (distributed) source. 
 Large-scale, high-permeability features can dominate the solute transport behavior of the 
saturated zone. In the presence of continuous high-permeability features, using either a point 
or a distributed planar flux weighted source term, the background fracture permeability 
pattern has no relation to the transport results. 
 In general, the dispersivity values have not reached a final asymptotic value after 460 meters 
of travel distance (23 correlation lengths). The final values for the enhanced permeability 
model with the planar source appear to be the furthest from an asymptote after 460 meters 
for both the longitudinal and transverse dispersivity. The background model with the planar 
source gives the highest values of vertical transverse dispersivity.

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 55 of 60 
7.1 RECOMMENDATIONS TO SITE CHARACTERIZATION 
Based on the conclusions presented above, several recommendations are made (to the site 
characterization team: Natural Environment Program Operations) regarding further 
characterization of the fractured rock portion of the saturated zone: 
 High permeability features control solute transport within fractured rocks. The locations, 
orientations, lengths and connectivity of these features needs to be defined. It may be 
possible to map some of these features deterministically using geophysical or drilling 
techniques; however many of these features will be too hard to detect. The majority of the 
additional information will most likely be statistical in nature. That information can be very 
useful in defining conceptual models upon which performance assessment (PA) can base 
abstractions. 
 The information on the frequency of flowing features obtained from borehole flowmeters is 
extremely useful in characterizing the fractured saturated zone. Flowmeter logging should be 
conducted in as many wells as possible. 
7.2 RECOMMENDATIONS TO PERFORMANCE ASSESSMENT 
Based on the conclusions presented above, several recommendations are made to the 
performance assessment team regarding transport in the saturated zone: 
 Due to the channeling nature of the flow system, one-dimensional transport modeling along 
streamlines (the current approach to PA transport modeling) is strongly recommended. 
 The conceptual model of large streamtubes of perfectly mixed solute concentrations existing 
for considerable length along the saturated zone transport pathway, such as was used in the 
TSPA-VA, is unrealistic. However, it may still be possible to abstract the saturated zone 
transport model using these types of streamtubes. 
 The estimates of transverse dispersivities provided by the expert elicitation panel (CRWMS 
M&O, 1998b) are in general agreement with the results reported in this work. The results 
presented here do not extend to PA length scales, but all indications suggest that minimal 
transverse dispersion will occur along the transport pathway. In the vertical dimension, the 
water table will act upon a shallow plume as a no flow boundary and constrain the possible 
amount of vertical transverse dispersion. 
7.3 UNCERTAINTIES/RESTRICTIONS 
There are several additional pieces of knowledge that, if obtained, could further the results 
presented here. Without this additional knowledge, there are some uncertainties in the results as 
discussed below: 
 Critical examination of the role of multiple fracture sets on the amount of transverse 
dispersivity. In this work, with the exception of the features in the enhanced model, all

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 56 of 60 
fractures were oriented parallel to flow. Larger amounts of horizontal transverse dispersion 
may occur if there are multiple fracture sets oriented obliquely to the principal flow 
directions. Implementing this conceptual model in a continuum numerical model may prove 
difficult. 
 Doing a similar study using a discrete fracture network model could check the validity of the 
continuum model assumption employed herein. 
 The fractured rocks represent only a fraction of the saturated zone transport pathway. A 
dispersion study similar to the one presented here should be performed on the alluvial section 
of the saturated zone. The recent data coming out of the Nye County wells could be used in 
such a study. 
8 REFERENCES 
8.1 DOCUMENTS CITED: 
Altman, S.J.; Arnold, B.W.; Barnard, R.W.; Barr, G.E.; Ho, C.K.; McKenna, S.A.; and Eaton, 
R.R. 1996. Flow Calculations for Yucca Mountain Groundwater Travel Time (GWTT-95). 
SAND96-0819. Albuquerque, New Mexico: Sandia National Laboratories. ACC: 
MOL.19961209.0152. 
CRWMS M&O 1998a. "Saturated Zone Flow and Transport." Chapter 8 of Total System 
Performance Assessment-Viability Assessment (TSPA-VA) Analyses Technical Basis Document. 
B00000000-01717-4301-00008 REV 01. Las Vegas, Nevada: CRWMS M&O. ACC: 
MOL.19981008.0008. 
CRWMS M&O 1998b. Saturated Zone Flow and Transport Expert Elicitation Project. 
Deliverable Number SL5X4AM3. Las Vegas, Nevada: CRWMS M&O. ACC: 
MOL.19980825.0008. 
CRWMS M&O 1999a. M&O Site Investigations. Activity Evaluation, January 23, 1999. Las 
Vegas, Nevada: CRWMS M&O. ACC: MOL.19990317.0330. 
CRWMS M&O 1999b. M&O Site Investigations. Activity Evaluation, September 28, 1999. 
Las Vegas, Nevada: CRWMS M&O. ACC: MOL.19990928.0224. 
CRWMS M&O 1999c. Probability Distribution for Flow Interval Spacing. ANL-NBS-MD- 
000003. Las Vegas, Nevada: CRWMS M&O. Submit to RPC URN-0183 
Dagan, G. 1988. "Time-Dependent Macrodispersion for Solute Transport in Anisotropic 
Heterogeneous Aquifers." Water Resources Research, 24, (9), 1491-1500. Washington, D.C.: 
American Geophysical Union. TIC: 245369. 

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 57 of 60 
Desbarats, A.J. and Srivastava, R.M. 1991. "Geostatistical Characterization of Groundwater 
Flow Parameters in a Simulated Aquifer." Water Resources Research, 27, (5), 687-698. 
Washington, D.C.: American Geophysical Union. TIC: 245375. 
Deutsch, C.V. and Journel, A.G. 1998. GSLIB Geostatistical Software Library and User's 
Guide, 2nd Edition. New York, New York: Oxford University Press. TIC: 240101. 
DOE (U.S. Department of Energy) 1998. Quality Assurance Requirements and Description. 
DOE/RW-0333P, Rev. 8. Washington, D.C.: U.S. Department of Energy, Office of Civilian 
Radioactive Waste Management. ACC: MOL.19980601.0022. 
Dyer, J.R. 1999. "Revised Interim Guidance Pending Issuance of New U.S. Nuclear Regulatory 
Commission (NRC) Regulations (Revision 01, July 22, 1999), for Yucca Mountain, Nevada." 
Letter from Dr. J.R. Dyer (DOE/YMSCO) to Dr. D.R. Wilkins (CRWMS M&O), September 3, 
1999, OL&RC:SB-1714, with enclosure, "Interim Guidance Pending Issuance of New NRC 
Regulations for Yucca Mountain (Revision 01)." ACC: MOL.19990910.0079. 
Fahy, M.F. 1997. "Dual-Porosity Analysis of Conservative Tracer Testing in Saturated 
Volcanic Rocks at Yucca Mountain in Nye County, Nevada." International Journal of Rock 
Mechanics and Mining Sciences, 34, (3-4), 486. Amsterdam, The Netherlands: Elsevier Science 
Ltd. TIC: 237601. 
Follin, S. and Thunvik, R. 1994. "On the Use of Continuum Approximations for Regional 
Modeling of Groundwater Flow Through Crystalline Rocks." Advances in Water Resources, 17, 
133-145. New York, New York: Elsevier Science. TIC: 245366. 
Geldon, A.L. 1996. Results and Interpretation of Preliminary Aquifer Tests in Boreholes UE- 
25c #1, UE-25c #2, and UE-25c #3, Yucca Mountain, Nye County, Nevada. Water-Resources 
Investigations Report 94-4177. Denver, Colorado: U.S. Geological Survey. ACC: 
MOL.19980724.0389. 
Geldon, A.L.; Umari, A.M.A.; Fahy, M.F.; Earle, J.D.; Gemmell, J.M.; and Darnell, J. 1997. 
Results of Hydraulic and Conservative Tracer Tests in Miocene Tuffaceous Rocks at the C-Hole 
Complex, 1995 to 1997, Yucca Mountain, Nye County, Nevada. Milestone SP23PM3. Denver, 
Colorado: U.S. Geological Survey. ACC: MOL.19980122.0412. 
Gelhar, L.W. and Axness, C.L. 1983. "Three-Dimensional Stochastic Analysis of 
Macrodispersion in Aquifers." Water Resources Research, 19, (1), 161-180. Washington, D.C.: 
American Geophysical Union. TIC: 222815. 
Hsieh, P.A. 1998. "Scale Effects in Fluid Flow Through Fractured Geologic Media." Chapter 
12 of Scale Dependence and Scale Invariance in Hydrology. Sposito, G., ed. 335-353. New 
York, New York: Cambridge University Press. TIC: 245367. 
Khaleel, R. 1994. "Scale and Directional Dependence of Macrodispersivities in Colonnade 
Networks." Water Resources Research, 30, (12), 3337-3355. Washington, D.C.: American

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 58 of 60 
Geophysical Union. TIC: 245376. 
Kreft, A. and Zuber, A. 1978. "On the Physical Meaning of the Dispersion Equation and Its 
Solutions for Different Initial and Boundary Conditions." Chemical Engineering Science, 33, 
(11), 1471-1480. New York, New York: Pergamon Press. TIC: 245365. 
Luckey, R.R.; Tucci, P.; Faunt, C.C.; Ervin, E.M.; Steinkampf, W.C.; D'Agnese, F.A.; and 
Patterson, G.L. 1996. Status of Understanding of the Saturated-Zone Ground-Water Flow 
System at Yucca Mountain, Nevada, as of 1995. Water-Resources Investigations Report 96- 
4077. Denver, Colorado: U.S. Geological Survey. ACC: MOL.19970513.0209. 
McKenna, S. 1999. Analysis and Modeling Report (AMR) Work Direction and Planning 
Document for Geostatistical and Heterogeneity Analysis for the SZ Flow and Transport Model, 
Saturated Zone Flow and Transport PMR. 14012031M3. Las Vegas, NV: CRWMS M&O. 
ACC: MOL.19990707.0298. 
Moreno, L. and Tsang, C.F. 1994. "Flow Channeling in Strongly Heterogeneous Porous 
Media: A Numerical Study ." Water Resources Research, 30, (5), 1421-1430. Washington, 
D.C.: American Geophysical Union. TIC: 222363. 
Schmitt, M. and Beucher, H. 1997. "On the Inference of the Boolean Model." Geostatistics 
Wollongong 1996, International Geostatistics Congress, Wollongong, Australia, September 
1996. Pages 200-210. Dordrecht, The Netherlands: Kluwer Academic. TIC: 245400. 
Sonnenthal, E.L.; Ahlers, C.F.; and Bodvarsson, G.S. 1997. "Fracture and Fault Properties for 
the UZ Site-Scale Flow Model." Chapter 7 of The Site-Scale Unsaturated Zone Model of Yucca 
Mountain, Nevada, for the Viability Assessment. Bodvarsson, G.S.; Bandurraga, T.M.; and Wu, 
Y.S., eds. LBNL-40376. Berkeley, California: Lawrence Berkeley National Laboratory. 
ACC: MOL.19971014.0232. 
Sweetkind, D.S. and Williams-Stroud, S.C. 1996. Characteristics of Fractures at Yucca 
Mountain, Nevada: Synthesis Report. Administrative Report. Denver, Colorado: U.S. 
Geological Survey. ACC: MOL.19961213.0181. 
Tsang, C-F. 1997. Drift Scale Heterogeneous Permeability Field Conditioned to Field Data. 
Milestone SP331BM4. Berkeley, California: Lawrence Berkeley National Laboratory. ACC: 
MOL.19971125.0915. 
Tsang, Y.W.; Tsang, C.F.; and Hale, F.V. 1996. "Tracer Transport in an Stochastic Continuum 
Model of Fractured Media." Water Resources Research, 32, (10), 3077-3092. Washington, 
D.C.: American Geophysical Union. TIC: 245377. 
Wen, X-H. and Gomez-Hernandez, J.J. 1998. "Numerical Modeling of Macrodispersion in 
Heterogeneous Media: A Comparison of Multi-Guassian and Non-Multi-Guassian Models." 
Journal of Contaminant Hydrology, 30, 129-156. Amsterdam, The Netherlands: Elsevier

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 59 of 60 
Science. TIC: 245368. 
YMP (Yucca Mountain Project) 1997. Q-List. YMP/90-55Q, Rev. 4. Las Vegas, Nevada: 
Yucca Mountain Site Characterization Office. ACC: MOL.19970714.0474. 
Zhan, H. 1999. "On the Ergodicity Hypothesis in Heterogeneous Formations." Mathematical 
Geology, 31, (1), 113-134. New York, New York: Plenum Publishing. TIC: 245383. 
Zyvoloski, G.A.; Robinson, B.A.; Dash, Z.V.; and Trease, L.L. 1997. Summary of Models and 
Methods for the FEHM Application - A Finite Element Heat- and Mass-Transfer Code. LA- 
13307-MS. Los Alamos, New Mexico: Los Alamos National Laboratory. TIC: 235587. 
Zyvoloski, G.A.; Robinson, B.A.; Dash, Z.V.; and Trease, L.L. 1997. User's Manual for the 
FEHM Application - A Finite-Element Heat- and Mass-Transfer Code. LA-13306-M. Los 
Alamos, New Mexico: Los Alamos National Laboratory. TIC: 235999. 
8.2 CODES, STANDARDS, REGULATIONS AND PROCEDURES 
AP-3.10Q, Rev. 2 , ICN 0 (C). Analyses and Models. Washington, D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste Management. ACC: MOL.20000217.0246 
QAP-2-0, Rev. 5. Conduct of Activities. Las Vegas, Nevada: CRWMS M&O. ACC: 
MOL.19980826.0209 
9 ATTACHMENTS 
The majority of the attachments are source listings for routines and shells. With the exception of 
Attachment 1, all attachments are included as electronic files. In most cases, the source file has 
the same name as the routine or shell with a *.doc extension. In some cases, the routine is made 
up of separate source and include files. For these routines, all files are listed as Attachment 
#@, where the # refers to the attachment number and the @ is the sub-attachment identifier. 
ATTACHMENT 1 OCRWM Document Input Reference Sheet 
ATTACHMENT 2 Listing of the run_50.ksh UNIX shell 
ATTACHMENT 3 Listing of the cr8_50_feat.ksh UNIX shell 
ATTACHMENT 4 Listing of the sisim FORTRAN Routine 
Attachment 4a acorni.doc 
Attachment 4b beyond.doc 
Attachment 4c chknam.doc 
Attachment 4d cova_3.doc 
Attachment 4e getindex.doc 
Attachment 4f ksol.doc

Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media 
ANL-NBS-HS-000022 Rev 00 07/14/2000 60 of 60 
Attachment 4g locate.doc 
Attachment 4h ordrel.doc 
Attachment 4i picksupr.doc 
Attachment 4j powint.doc 
Attachment 4k setrot.doc 
Attachment 4l setsupr.doc 
Attachment 4m sisim.doc 
Attachment 4n sortem.doc 
Attachment 4o sqdist.doc 
Attachment 4p srchsupr.doc 
ATTACHMENT 5 Listing of the ellip2_MC FORTRAN Routine 
Attachment 5a acorni.doc 
Attachment 5b chknam.doc 
Attachment 5c ellip2_MC.doc 
Attachment 5d expon.doc 
Attachment 5e gcum.doc 
Attachment 5f setrot.doc 
Attachment 5g sqdist.doc 
ATTACHMENT 6 Listing of the combine.c Routine 
ATTACHMENT 7 Listing of the calc_cdf.c Routine 
ATTACHMENT 8 Listing of the gs2fehm.c Routine 
ATTACHMENT 9 Listing of the gamfil FORTRAN Routine 
Attachment 9a CHKNAM.doc 
Attachment 9b GAMFIL1.doc 
Attachment 9c RAND.doc 
Attachment 9d gamfil.inc.doc 
ATTACHMENT 10 Listing of the modgeom.c Routine 
ATTACHMENT 11 Listing of the run_50_feat.ksh UNIX shell 
ATTACHMENT 12 Listing of the run_50_back.ksh UNIX shell 
ATTACHMENT 13 Listing of the cr8sptr.c Routine 
ATTACHMENT 14 Listing of the cr8sptr_cell.c Routine 
ATTACHMENT 15 Listing of the calc_D_old.c Routine

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
2a 
1 
64 FR (Federal Register) 8640. Disposal of 
High-Level Radioactive Waste in a Proposed 
Radiologic Repository at Yucca Mountain. 
Proposed rule 10 CFR 63. Readily available. 
Referen 
ce Only 
Rules regulating the disposal of 
high-level waste in the United 
States 
N/A N/A N/A N/A 
2 Altman, S.J.; Arnold, B.W.; Barnard, R.W.; 
Barr, G.E.; Ho, C.K.; McKenna, S.A.; and 
Eaton, R.R. 1996. Flow Calculations for 
Yucca Mountain Groundwater Travel Time 
(GWTT-95). SAND96-0819. Albuquerque, 
New Mexico: Sandia National Laboratories. 
ACC: MOL.19961209.0152. 
Pages 
47-65 
Referen 
ce Only 
GWTT-95 report cited as an 
example of stochastic continuum 
modeling 
N/A N/A N/A N/A 
3 CRWMS M&O. 1998a. Total System 
Performance Assessment  Viability 
Assessment (TSPA-VA) Analyses Technical 
Basis Document. Chapter 8 Saturated Zone 
Flow and Transport. B00000000-01717- 
4301-00008 Rev 01. Las Vegas, Nevada: 
CRWMS M&O. ACC: MOL.19981008.0008. 
DTN: SNT05082597001.003 
Figure 8- 
27 
Referen 
ce Only 
Section 
4, Inputs 
and 
Section 
6, 
Analysis 
Citing distribution of 
permeabilities measured in the 
saturated zone 
N/A N/A N/A N/A 
4 CRWMS M&O. 1998b. Saturated Zone Flow 
and Transport Expert Elicitation Project. 
SL5X4AM3. Las Vegas, Nevada: CRWMS 
M&O. ACC: MOL.19980825.008. 
Referen 
ce Only 
Results of expert elicitation used 
as a basis for dispersion values 
in TSPA-VA document 
N/A N/A N/A N/A 
5 CRWMS M&O 1999a. Activity Evaluation of 
M&O Site Investigations. Las Vegas, 
Nevada: CRWMS M&O. ACC: 
MOL.19990317.0330. 
Referen 
ce Only 
Yucca Mountain Site 
Characterization Procedure 
N/A N/A N/A N/A

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
6 CRWMS M&O 1999b. Activity Evaluation of 
M&O Site Investigations. Las Vegas, 
Nevada: CRWMS M&O. ACC: MOL. 
19990928.0224 
Referen 
ce Only 
Yucca Mountain Site 
Characterization Procedure 
N/A N/A N/A N/A 
7 CRWMS M&O 1999c. Probability 
Distribution for Flowing Interval Spacing. 
ANL-NBS-MD-000003. Las Vegas, Nevada: 
CRWMS M&O ACC: Pending, DTN: 
SN990&T0571599.001. 
Figure 11 Referen 
ce Only 
Section 
4, Inputs 
and 
Section 
6, 
Analysis 
Citing distribution of spacings 
between flowing features 
N/A N/A N/A N/A 
8 Dagan, G. 1988. Time-Dependent 
Macrodispersion for Solute Transport in 
Anistropic Heterogeneous Aquifers. Water 
Resources Research, 24 (9), 1491-1500. 
Washington, D.C.: American Geophysical 
Union. TIC: 245369. 
Referen 
ce Only 
Journal article presenting 
stochastic-analytical solution for 
dispersion in heterogeneous 
aquifers 
N/A N/A N/A N/A 
9 Desbarats, A.J. and Srivastava, R.M. 1991. 
Geostatistical Characterization of 
Groundwater Flow Parameters in a Simulated 
Aquifer. Water Resources Research, 27 (5), 
687-698. Washington, D.C.: American 
Geophysical Union. TIC: 245375. 
Referen 
ce Only 
Numerical study of dispersion in 
two-dimensional heterogeneous 
aquifer 
N/A N/A N/A N/A 
10 Deutsch, C.V. and Journel, A.G. 1998. 
GSLIB: Geostatistical Software Library and 
Users Guide. 2nd Edition. New York, New 
York: Oxford University Press. TIC: 224174. 
Pages 
175-180, 
182-183 
Referen 
ce Only 
User's manual for some of the 
software routines used in this 
analysis 
N/A N/A N/A N/A

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
11 DOE (U.S. Department of Energy) 1998. 
Quality Assurance and Requirements 
Description. DOE/RW-0333P, REV 8. 
Washington D.C.: U.S. Department of 
Energy, Office of Civilian Radioactive Waste 
Management. ACC: MOL.19980601.0022. 
Referen 
ce Only 
OCRWM Quality Assurance and 
Description 
N/A N/A N/A N/A 
12 Dyer, J. R. 1999. "Revised Interim Guidance 
Pending Issuance of New U. S. Nuclear 
Regulatory Commission (NRC) Regulations 
(Revision 01, July 22, 1999), for Yucca 
Mountain, Nevada." Letter from J. R. Dyer 
(DOE) to D. R. Wilkins (CRWMS M&O), 
September 9, 1999, OL&RC:SB-1714, with 
enclosure, "Interim Guidance Pending 
Issuance of New U. S. Nuclear Regulatory 
Commission (NRC) Regulations (Revision 
01)" . ACC: MOL.19990910.0079. 
Referen 
ce Only 
Interim guidance for work on 
Yucca Mountain Site 
Characterization Project 
N/A N/A N/A N/A 
13 Follin, S. and Thunvik, R. 1994. On the Use 
of Continuum Approximations for Regional 
Modeling of Groundwater Flow Through 
Crystalline Rocks. Advances in Water 
Resources, 17 (3), 133-145. Southampton, 
U.K.: C.M.L. Publications; New York, New 
York: Springer-Verlag. TIC: 245366. 
Referen 
ce Only 
Example of stochastic continuum 
modeling in heterogeneous 
aquifers and example of 
numerical calculation of 
transverse dispersivity 
N/A N/A N/A N/A 
14 Geldon, A.L. 1996. Results and 
Interpretation of Preliminary Aquifer Tests in 
Boreholes, UE-25c #1, UE-25c #2, and UE- 
25c #3, Yucca Mountain, Nye County, 
Nevada. Water-Resources Investigations 
Report 94-4177. Denver, Colorado: U.S. 
Geological Survey. ACC: 
MOL.19980724.0389. 
Referen 
ce Only 
Results and interpretation of 
aquifer testing completed at Choles. 
N/A N/A N/A N/A

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
15 Geldon, A.L.; Umari, A.M.A.; Fahy, M.F.; 
Earle, J.D.; Gemmell, J.M.; and Darnell, J. 
1997. Results of Hydraulic and Conservative 
Tracer Tests in Miocene Tuffaceous Rocks at 
the C-Hole Complex, 1995 to 1997, Yucca 
Mountain, Nye County, Nevada. SP23PM3. 
Las Vegas, Nevada: U.S. Geological Survey, 
Yucca Mountain Project Branch. ACC: 
MOL.19980122.0412. 
Table 9, 
p. 
Hydrauli 
c Tests- 
37 
Referen 
ce Only 
Results and interpretation of 
aquifer and tracer testing 
completed at C-holes. 
N/A N/A N/A N/A 
16 Gelhar, L.W. and Axness, C.L., 1983, Three- 
Dimensional Stochastic Analysis of 
Macrodispersion in Aquifers, Water 
Resources Research, 19(1), pp. 161-180, 
Washington, D.C.: American Geophysical 
Union. TIC 222815. 
Referen 
ce Only 
Stochastic analytical solution for 
dispersion in heterogeneous 
aquifers. 
N/A N/A N/A N/A 
17 Hsieh, P.A. 1998. Scale Effects in Fluid 
Flow Through Fractured Geologic Media. 
Scale Dependence and Scale Invariance in 
Hydrology. Pages 335-353. Editor: Sposito, 
G. Cambridge, United Kingdom; New York, 
New York: Cambridge University Press. TIC: 
245367. 
Referen 
ce Only 
Review article on fractured rock 
hydrology. 
N/A N/A N/A N/A 
18 Khaleel, R. 1994. Scale and Directional 
Dependence of Macrodispersivities in 
Colonnade Networks. Water Resources 
Research, 30 (12), 3337-3355. Washington, 
D.C.: American Geophysical Union. TIC: 
245376. 
Referen 
ce Only 
Numerical study on dispersion in 
fractured rocks. Example of the 
log transform as a means of 
decreasing the significance of 
outliers in travel time distribution. 
N/A N/A N/A N/A

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
19 Kreft, A. and Zuber, A. 1978. On the 
Physical Meaning of the Dispersion Equation 
and Its Solutions for Different Initial and 
Boundary Conditions. Chemical Engineering 
Science, 33 (11), 1471-1480. Oxford, United 
Kingdom; New York, New York: Pergamon 
Press. TIC: 245365. 
Referen 
ce Only 
Analytical solution for longitudinal 
dispersion in aquifer. 
N/A N/A N/A N/A 
20 Luckey, R.R.; Tucci, P.; Faunt, C.C.; Ervin, 
E.M.; Steinkampf, W.C.; DAgnese, F.A.; and 
PattersonG.L. 1996. Status of 
Understanding of the Saturated-Zone 
Groundwater Flow System at Yucca 
Mountain, Nevada as of 1995. Water 
Resources Investigations Report 96-4077. 
Denver, Colorado: U.S. Geological Survey. 
TIC: 227084. 
Referen 
ce Only 
Summary status report on 
saturated zone hydrology at 
Yucca Mountain. 
N/A N/A N/A N/A 
21 Moreno, L. and Tsang, C-F. 1994. Flow 
Channeling in Strongly Heterogeneous 
Porous Media: A Numerical Study. Water 
Resources Research, 30 (5), 1421-1430. 
Washington, D.C.: American Geophysical 
Union. TIC: 222363. 
Referen 
ce Only 
Numerical study of dispersion in 
highly heterogeneous rock. 
N/A N/A N/A N/A 
22 Schmitt, M. and Beucher, H. 1997. On the 
Inference of the Boolean Model. 
Geostatistics Wollongong 96, International 
Geostatistics Congress, Wollongong, 
Australia, September 1996, 200-210. Baafi, 
E.Y. and Schofield, N.A., eds. Boston, 
Massachusetts: Kluwer Academic. TIC: 
245400. 
Referen 
ce Only 
Conference proceeding article on 
the inference of Boolean models. 
N/A N/A N/A N/A

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
23 Sonnenthal, E.L.; Ahlers, C.F.; and 
Bodvarsson, G.S. 1997. Chapter 7: 
Fracture and Fault Properties for the UZ Site- 
Scale Flow Model. The Site-Scale 
Unsaturated Zone Model of Yucca Mountain, 
Nevada, for the Viability Assessment. LBNL- 
40376, 7-1 : 7-34. Bodvarsson, G.S.; 
Bandurraga, T.M.; and Wu, Y.S., eds. 
Berkeley, California: Lawrence Berkeley 
National Laboratory. ACC: 
MOL.19971014.0232. 
Referen 
ce Only 
Summary of fracture information 
completed for the Site-Scale 
unsaturated zone model. 
N/A N/A N/A N/A 
24 Sweetkind, D.S. and Williams-Stroud, S.C. 
1996. Characteristics of Fractures at Yucca 
Mountain, Nevada: Synthesis Report. 
Denver, Colorado: U.S. Geological Survey. 
TIC: 239254. DTN:GS960808314222.003 
Page 52 
and 
Figures 
21 and 
22 
Referen 
ce Only 
Section 
4, Inputs 
and 
Section 
6, 
Analysis 
Citing distribution of mapped 
fracture lengths. 
N/A N/A N/A N/A 
25 Sweetkind, D.S. and Williams-Stroud, S.C. 
1996. Characteristics of Fractures at Yucca 
Mountain, Nevada: Synthesis Report. 
Denver, Colorado: U.S. Geological Survey. 
TIC: 239254. 
Figure 17 Referen 
ce Only 
Section 
4, Inputs 
and 
Section 
6, 
Analysis 
Citing distribution of measured 
fracture orientations. 
N/A N/A N/A N/A 
26 Tsang, C.F. 1997. Drift-Scale 
Heterogeneous Permeability Field 
Conditioned to Field Data. Milestone 
SP331BM4. Berkeley, California: Lawrence 
Berkeley National Laboratory. ACC: 
MOL.19971125.0911. Corrected by ACC: 
MOL.19990622.0022. 
Referen 
ce Only 
Initial report on modeling of 
fracture permeability based on 
air testing in unsaturated zone. 
N/A N/A N/A N/A

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
27 Tsang, Y.W.; Tsang, C.F.; Hale, F.V.; and 
Dverstorp, B. 1996. Tracer Transport in a 
Stochastic Continuum Model of Fractured 
Media. Water Resources Research, 32 (10), 
3077-3092. Washington, D.C.: American 
Geophysical Union. TIC: 245377. 
Referen 
ce Only 
Journal article giving an example 
of a stochastic continuum model 
used for tracer transport. 
N/A N/A N/A N/A 
28 Wen, X-H. and Gomez-Hernandez, J.J. 
1998. Numerical Modeling of 
Macrodispersion in Heterogeneous Media: A 
Comparison of Multi-Gaussian and Non-Multi- 
Gaussian Models. Journal of Contaminant 
Hydrology, 30 (1-2), 129-156. Amsterdam, 
The Netherlands; New York, New York: 
Elsevier Science B.V. TIC: 245368. 
Referen 
ce Only 
Journal article describing the 
numerical modeling of solute 
transport in two-dimensional 
heterogeneous media. Example 
of numerical technique used to 
calculate transverse dispersivity. 
N/A N/A N/A N/A 
30 YMP (Yucca Mountain Project) 1997. Q-List. 
YMP/90-5Q. Las Vegas, Nevada: Yucca 
Mountain Site Characterization Office. ACC: 
MOL.19970714.0474. 
Referen 
ce Only 
Yucca Mountain Site 
Characterization Project listing of 
Q data and documents 
N/A N/A N/A N/A 
31 Zhan, H. 1999. On the Ergodicity 
Hypothesis in Heterogeneous Formations. 
Mathematical Geology, 31 (1), 113-134. New 
York, New York: Plenum. TIC: 245383. 
Referen 
ce Only 
Journal article defining the limits 
of the ergodic hypothesis 
N/A N/A N/A N/A 
32 Zyvoloski, G.A., Robinson, B.A., Dash, Z.V. 
and Trease, L.L., 1997a, Users Manual 
for the FEHM Application-A Finite- 
Element Heat and Mass-Transfer Code, 
LANL Report LA-13306-M. Los Alamos, 
New Mexico, Los Alamos National 
Laboratory. TIC: 2359999. 
Referen 
ce Only 
User's manual for the FEHM 
code 
N/A N/A N/A N/A

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
33 Zyvoloski, G.A., Robinson, B.A., Dash, Z.V. 
and Trease, L.L., 1997b, Summary of the 
Models and Methods for the FEHM 
Application-A Finite-Element Heat and 
Mass-Transfer Code, LANL Report LA- 
13307-MS. Los Alamos, New Mexico, 
Los Alamos National Laboratory. TIC 
235587. 
Referen 
ce Only 
Background information for the 
FEHM code. 
N/A N/A N/A N/A 
32 Software Code: run_50.ksh. STN: 
PENDING. 
Entire TBV- 
3537 
UNIX shell to check feature 
spacing of back ground 
permeability models. TBV 
indicates pending documentation 
of verification of routine. 
1.0 X 
33 Software Code: cr8_50_feat.ksh. STN: 
PENDING. 
Entire TBV- 
3538 
UNIX shell to create enhanced 
perm models. TBV indicates 
pending documentation of 
verification of routine. 
1.0 X 
34 Software Code: sisim. STN: PENDING. Entire TBV- 
3539 
FORTRAN routine to create 
indicator geostatical simulation of 
permeability. TBV indicates 
pending documentation of 
verification of routine. 
1.0 X 
35 Software Code: ellip2_MC. STN: 
PENDING. 
Entire TBV- 
3540 
FORTRAN Routine to create 
high permeability features for 
enhances model. TBV indicates 
pending documentation of 
verification of routine. 
1.0 X 
36 Software Code: combine.c. STN: 
PENDING. 
Entire TBV- 
3541 
Preprocessing C routine to 
combine the background perm 
models and high permeability 
features into the final enhanced 
permeability model. TBV 
indicates pending documentation 
of verification of routine. 
1.0 X

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
37 Software Code: calc_cdf.c. STN: 
PENDING. 
Entire TBV- 
3542 
Postprocessing C Routine to 
check the cdf of the permeability 
model at each indicator 
threshold. TBV indicates pending 
documentation of verification of 
routine. 
1.0 X 
38 Software Code: gs2fehm.c. STN: 
PENDING. 
Entire TBV- 
3543 
Preprocessing C routine to 
reformat the permeability models 
from GSLIB to FEHM formate 
routine. TBV indicates pending 
documentation of verification of 
routine. 
1.0 X 
39 Software Code: gamfil. STN: PENDING. Entire TBV- 
3544 
Postprocessing FORTRAN 
Routine to check the feature 
spacing in the permeability 
models. TBV indicates pending 
documentation of verification of 
routine. 
1.0 X 
40 Software Code: modgeom.c. STN: 
PENDING. 
Entire TBV- 
3545 
Preprocessing routine to change 
the random seed in the 
ellips_MC input files. TBV 
indicates pending documentation 
of verification of routine. 
1.0 X 
41 Software Code: run_50_feat.ksh. STN: 
PENDING. 
Entire TBV- 
3546 
UNIX shell to run the flow, 
particle tracking and dispersion 
calculations 50 times on the 
enhanced permeability models. 
TBV indicates pending 
documentation of verification of 
routine. 
1.0 X 
42 Software Code: run_50_back.ksh. STN: 
PENDING. 
Entire TBV- 
3547 
UNIX shell to run the flow, 
particle tracking and dispersion 
calculations 50 times on the 
background permeability models. 
TBV indicates pending 
documentation of verification of 
routine. 
1.0 X

AP-3.15Q.1 Rev. 06/30/1999 
OFFICE OF CIVILIAN RADIOACTIVE WASTE MANAGEMENT 
DOCUMENT INPUT REFERENCE SHEET 
1. Document Identifier No./Rev.: Change: Title: 
ANL-NBS-HS-000022 00 Modeling Sub Gridblock Scale Dispersion in Three-Dimensional Heterogeneous Fractured Media (S0015) 
Input Document 8. TBV Due To 
2. Technical Product Input Source Title and 
Identifier(s) with Version 
3. Section 4. Input 
Status 
5. Section 
Used in 
6. Input Description 7. TBV/TBD 
Priority 
Unqual. From Uncontrolled 
Source 
Unconfirmed 
43 Software Code: cr8sptr.c. STN: PENDING. Entire TBV- 
3548 
Preprocessing 
C Routine to create flux weighted 
input file for FEHM sptr macro. 
TBV indicates pending 
documentation of verification of 
routine. 
1.0 X 
44 Software Code: cr8sptr_cell.c. STN: 
PENDING. 
Entire TBV- 
3549 
Preprocessing C Routine to 
create single cell input file for 
FEHM sptr macro. TBV indicates 
pending documentation of 
verification of routine. 
1.0 X 
45 Software Code: calc_D_old.c. STN: 
PENDING. 
Entire TBV- 
3550 
C Routine to calculate 
longitudinal and transverse 
dispersivities. TBV indicates 
pending documentation of 
verification of routine. 
1.0 X