Estimating Large-Scale Fracture Permeability of ... Wu et al. Vodose Zone... · lic conductivity many orders of magnitude higher than infiltration rates. Under such conditions, slight

Estimating Large-Scale Fracture Permeability of Unsaturated Rock Using BarometricPressure Data

Yu-Shu Wu, Keni Zhang,* and Hui-Hai Liu

ABSTRACTWe present a three-dimensional modeling study of gas flow in the

unsaturated fractured rock of Yucca Mountain. Our objective was toestimate large-scale fracture permeability, using the changes in subsur-face pneumatic pressure in response to barometric pressure changes atthe land surface. We incorporate the field-measured pneumatic datainto a multiphase flow model for describing the coupled processes ofliquid and gas flow under ambient geothermal conditions. Comparisonof field-measured pneumatic data with model-predicted gas pressuresis found to be a powerful technique for estimating the fracture perme-ability of the unsaturated fractured rock, which is otherwise extremelydifficult to determine in field studies with large scales of interest.In addition, this study demonstrates that the multidimensional floweffect on estimated permeability values is significant and should be in-cluded when determining fracture permeability in heterogeneous frac-tured media.

DURING THE PAST TWO DECADES, as the proposed site ofa geological repository for storing high-level radio-

active waste, the unsaturated zone (UZ) of the highlyheterogeneous, fractured tuffs at Yucca Mountain,Nevada has been extensively investigated. Driven bythe need to conduct long-term performance assessmentof the repository, many site characterization studies havebeen performed, and various types of data have beencollected. Because of the large temporal and spatialscales involved, it has been recognized that the develop-ment and use of numerical models are necessary to makequantitative evaluations and long-term predictions offlow and transport processes in the UZ under futureclimates. This need has motivated a continual researcheffort to develop and apply large mountain-scale flowand transport models (e.g., Wu et al., 1999, 2002) forfuture repository performance analysis. Thus, most sitecharacterization investigations have been conducted (i)to understand unsaturated flow and transport processesin the UZ and (ii) to estimate various hydrological pa-rameters required for model input and predictions (e.g.,Rousseau et al., 1999; Wu et al., 2003).Even with the significant progress made in character-

izing the Yucca Mountain UZ system since the 1980s,the complexity in both site geological conditions andphysical processes has challenged quantitative charac-terizationefforts. Inparticular, determining theappropri-ate model input parameters on the temporal and spatialscales relevant to understanding the nuclear waste dis-

posal system and assessing the repository performanceremains a very difficult task. In a continual researcheffort, many core samples have been taken from bore-holes, tunnels, and outcrops for different hydrogeologicalunits or layers. These samples have been very useful formaking laboratory determinations of rock-matrix hydro-logical properties. However, resolving how to properlyestimate fracture flow properties at large spatial scales isstill a challenging task. This is because fracture flowproperties, such as fracture permeability, are relatedto flow processes occurring at the large spatial scales(10|100 m) required as input for model predictions.These large-scale model parameters for fractures aregenerally more difficult to measure at the site than thosefor the rock matrix.

Estimation of large-scale flow parameters for the un-saturated rock at Yucca Mountain relies primarily oninverse modeling studies, which incorporate field- andlaboratory-measured moisture data to obtain parametersets (e.g., Bandurraga and Bodvarsson, 1999; Ghezzeheiand Liu, 2004). However, past studies using inversemod-eling have concluded that fracture flow properties arenot very sensitive to measured moisture data from coresamples of the site. For example, measured liquid-saturation and water-potential data for the rock matrix(although very useful for determining matrix properties)do not provide much information about fracture proper-ties. This is because under ambient conditions associatedwith low infiltration and arid climates, fractures containlittle moisture (i.e., they are “dry”). At the same time, asshown in field tests, the fracture system is well connectedand highly permeable, with a saturated fracture hydrau-lic conductivity many orders of magnitude higher thaninfiltration rates. Under such conditions, slight changesin moisture conditions, caused by the ambient infiltra-tion, have little impact on fracture flow responses. Onthe other hand, the dry, large pore space in fracturesmakes almost entire fracture apertures available for gasflow. Therefore, pneumatic signals and data from airinjection tests at the Yucca Mountain site are found tobe more sensitive to fracture flow properties and havebeen used as the main data source for determining frac-ture flow parameters (e.g., Ahlers et al., 1999).

Airfloworgas (amixtureof air andwater vapor)move-ment through the unsaturated zone is driven by changesin barometric pressure, temperature-induced density dif-ferences, wind effects, and topography (Rousseau et al.,1999; Weeks, 1987). Changes in barometric pressure atthe land surface between day and night or seasonally

Earth Sciences Division, Lawrence Berkeley National Lab., 1 Cyclo-tron Rd., Berkeley, CA 94720. Received 20 Jan. 2006. *Correspond-ing author ([email protected]).

Published in Vadose Zone Journal 5:1129–1142 (2006).Original Researchdoi:10.2136/vzj2006.0015ª Soil Science Society of America677 S. Segoe Rd., Madison, WI 53711 USA

Abbreviations: CFu, Crater Flat undifferentiated unit; CHn, CalicoHills nonwelded unit; ESF, Exploratory Studies Facility; PTn, Paint-brush Tuff nonwelded unit; TCw, Tiva Canyon welded unit; TSw,Topopah Spring welded unit; UZ, unsaturated zone.

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result in corresponding changes in pneumatic pressuresat different depths inside the UZ. For example, substan-tial airflow was observed in two wells drilled at YuccaMountain, showing air exchange between the subsur-face and the atmosphere, with flow into the wells duringwinter and out of the wells during summer (Weeks, 1987).The process is controlled by geothermal gradients ordensity differences. Subsurface pneumatic responses tosurface barometric pressure fluctuations reflect the oc-currence of gas flow through highly permeable subsur-face fractures or permeable porous media. With moreflow resistance at deeper depth for downward gas flowfrom the ground surface, subsurface pressure signals areamplitude-attenuated and time-lagged relative to the sur-face pressure signals. Therefore, naturally occurring gas-pressure variations provide a good indication of howwell the formation is able to transmit gas flow, a measurethen used to derive fracture permeability.A number of studies in the literature use gas flow data

or barometric pressure cycles in characterizing the vadosezone. Among the early research efforts, Weeks (1978)presented a systematic study (including a model formu-lation and numerical code as well as field testing results)for determining vertical permeability to air in a layeredunsaturated zone. In 1987, he further provides a concep-tual model and site-specific analysis of gas flow in theYucca Mountain UZ caused by topographic effects.In the literature, there are several types of gas flow

data sources used in characterizing unsaturated porousmedia. The first type is the measurement of naturally oc-curring barometric pressure fluctuations on the surfaceand in the subsurface (e.g., Ahlers et al., 1999; Neeper,2002). The second approach, called the air-injection per-meability test (air-k test), involves the injection of airinto boreholes or wells and monitoring of gas pressureor gas flux changes at and near injectors (LeCain, 1999;Illman and Neuman, 2000, 2001, 2003; Vesselinov et al.,2001a, 2001b; Illman and Tartakovsky, 2005; Illman,2005). Both types of data have been applied to charac-terizing the Yucca Mountain site, with the air-k testsextremely valuable for calculating fracture permeabilitywithin a small-scale (|1 m) spatial domain (Huang et al.,1999). In addition, Unger et al. (2004) reported on anindirect approach of using radon gas concentration data,measured in an underground tunnel at Yucca Mountain,to estimate large-scale fracture properties. It should bementioned, however, that the application of subsurfacepneumatic responses to surface barometric signals is inmost cases limited to one-dimensional vertical flow sce-narios (Weeks, 1987; Ahlers et al., 1999; Neeper, 2002).In particular, existing studies are suitable primarily forhandling homogeneous or horizontal layered unsaturatedformations only.We describe a comprehensive modeling effort to esti-

mate large-scale fracture permeability using pneumaticdata measured from boreholes of the Yucca MountainUZ. Our modeling approach, built on the current three-dimensional (three-dimensional) mountain-scale UZflow model (Wu et al., 2003, 2004), incorporates pneu-matic data into a modeling analysis of two-phase liquidand gas flow under ambient geothermal conditions. The

gas flow modeling studies are performed under present-day infiltration conditions using the site-specific geo-logical model and characterization data. Calibration ofmodel-predicted gas pressures against field-measuredpneumatic data leads to a methodology for estimatingfracture permeability in the unsaturated fractured rock,an important parameter that would otherwise be diffi-cult to determine at large scales (Ahlers et al., 1999).

This study represents a continuation of the work byAhlers et al. (1999) to characterize large-scale fracturepermeability in the YuccaMountain UZ. However, eventhough the methodology in this study is similar to that ofAhlers et al. (1999), there are significant differencesbetween the two studies and their results. Specifically,the current study is focused on estimating large-scalefracture permeability through three-dimensional mod-eling studies, while previous investigations (Ahlers et al.,1999) consisted primarily of one- and two-dimensionalmodel results, as well as some three-dimensional mod-eling efforts with limited spatial and temporal scale. Themain objective ofAhlers’ studywas to develop amethod-ology for characterizing subsurface pneumatic responsesat the Yucca Mountain. Our study differed in that it wasbased on (i) the updated geological framework model,(ii) the current hydrological UZ flow conceptual model,(iii) the newly designed three-dimensional numericalgrid model, and (iv) the updated fracture and matrixproperties. More specifically, gas flow within the YuccaMountain UZ is shown to be a three-dimensional phe-nomenon in this study. In general, model dimensionalityhas a significant influence on model-estimated perme-ability values, and multidimensional flow effects shouldbe accounted for when simulating gas flow in heteroge-neous fractured media.

HYDROGEOLOGICAL SETTING,PNEUMATIC DATA, ANDCONCEPTUAL MODEL

The geological setting (implemented in the three-dimensional pneumatic model of this study) for describ-ing the Yucca Mountain hydrogeological condition isbased on the current site-scale UZ flow and transportmodel (Wu et al., 2003), which is in turn built on a geo-logical framework model (BSC, 2004a) for Yucca Moun-tain. This section briefly discusses the geological model,the measured pneumatic data, and the gas flow concep-tual model used in this modeling study.

Geological ModelFigure 1 shows a typical vertical west–east cross sec-

tion in the proximity of the repository, where the UZ isbetween 500 and 700 m thick and overlies a relativelyflat water table. Geologically, Yucca Mountain is a struc-turally complex system of Tertiary volcanic, layered, an-isotropic, and fractured volcanic rocks (Scott and Bonk,1984). These volcanic formations consist of alternatinglayers of welded and nonwelded ash flow and air-falltuffs. The primary geological formations, from the landsurface downward, are the Tiva Canyon, Yucca Moun-

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1130 VADOSE ZONE J., VOL. 5, NOVEMBER 2006

tain, Pah Canyon, and Topopah Spring tuffs of thePaintbrush Group. Underlying these are the Calico HillsFormation and the Prow Pass, Bullfrog, and Tram tuffsof the Crater Flat Group (Buesch et al., 1995).For hydrological investigations, the UZ geologic for-

mations have been categorized into several hydrogeo-logical units based primarily on their degree of welding(Montazer and Wilson, 1984). These units are classifiedas the Tiva Canyon welded (TCw) hydrogeological unit;the PaintbrushTuff nonwelded unit (PTn), consisting pri-marily of the Yucca Mountain and Pah Canyon beddedtuffs; the Topopah Spring welded (TSw) unit; the CalicoHills nonwelded (CHn) unit; and the Crater Flat undif-ferentiated (CFu) unit. Table 1 lists the geological unitsand layers for different hydrogeological units and the as-sociated grid-layer information for the numerical model.These hydrogeological units and layers are generallythree-dimensionally distributed and vary significantly inthickness and slope across the model domain, as shownin Fig. 2.

Pneumatic DataAs part of the Yucca Mountain site characterization

effort, several deep boreholes instrumented in the UZare continuously monitored to record changes in pneu-matic pressure at different depths (Rousseau et al.,1999). Gas pressures are also measured at the land sur-face, which is referenced to atmospheric pressure at the

time measurements in boreholes are taken. Measure-ments in subsurface boreholes are conducted throughisolated pressure transducers or pressure monitoring ports.Monitoring points in these pneumatic monitoring bore-holes are distributed primarily along the shallow TCw,PTn, and TSw units, and a few of the boreholes havemonitoring points below the bottom of the TSw.

Pneumatic pressure data have been collected by USGSscientists at a number of boreholes, includingUZ-1, UZ#4,UZ#5, NRG-6, NRG-7a, SD-7, SD-9, SD-12, and UZ-7a,with most of the measurements performed in 1995 and1996. Locations of these boreholes are shown in Fig. 2.Available gas pressure data cover time periods rangingfrom slightly less than 6 mo up to 1 yr. The longer-periodrecords include downhole pressure measurements thatcover most of the annual barometric pressure cycle, alarge portion of which was not or insignificantly dis-turbed by interference from construction of the under-ground tunnels. Boreholes UZ-1, NRG-6, NRG-7a, UZ#4,and UZ#5 were instrumented with downhole pressuretransducers that measure absolute pneumatic pressure.Detailed discussion of the field measurements and testmethods of gas-pressure pneumatic data can be found inRousseau et al. (1999).

Figure 3 presents typical pneumatic pressure recordsfor instrument stations in the monitored Borehole NRG-7a. Figure 3 indicates that sensors in the TCw recordlittle to no amplitude attenuation or phase lag comparedwith the surface barometric signals. Results from spec-

Fig. 1. Schematic showing typical vertical profiles of hydrogeological layers and units, as well as the conceptualized barometric pressure signalswithin a typical east–west cross section of the unsaturated zone flow model domain (see Fig. 2 for the cross-section location).

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tral analyses of in situ pneumatic pressure responses tothe synoptic pressure variations indicate that the phaselags range from a few hours to several tens of hours atdifferent depths (Rousseau et al., 1999). As shown inFig. 3, sensors in the PTn unit record increasing attenua-tion and lag with increasing depth. In most boreholes,sensors in the TSw unit monitor a similar amount ofattenuation and a practically indistinguishable lag overthe entire vertical interval of the TSw, because of thehigh density of fractures within the TSw unit. Horizon-tally within the TSw, the observed attenuation variesand appears to depend on the thickness of the overlyingPTn (Ahlers et al., 1999).

The gas pressure signal consists of multiple compo-nents, including daily, seasonal, and annual changes as

Table 1. Lithostratigraphy and correlations of model grid layerand hydrogeological unit used in the three-dimensional pneu-matic model.

Major UnitLithostratigraphicNomenclature

Model GridLayer

Tiva Canyon Tpcr tcw11welded (TCw)

Tpcp tcw12

TpcLD

Tpcpv3 tcw13

Tpcpv2

Paintbrush Tpcpv1 ptn21nonwelded (PTn)

Tpbt4 ptn22

Tpy (Yucca)

ptn23

ptn24

Tpbt3

Tpp (Pah) ptn25

Tpbt2 ptn26

Tptrv3

Tptrv2

Topopah Spring Tptrv1 tsw31welded (TSw)

Tptrn

tsw32

Tptrl, Tptf tsw33

Tptpul, RHHtop

Tptpmn tsw34

Tptpll tsw35

Tptpln tsw36

tsw37

Tptpv3 tsw38

Tptpv2 tsw39 (vit, zeo)

Calico Hills Tptpv1 ch1 (vit, zeo)nonwelded (CHn)

Tpbt1

Tac (Calico) ch2 (vit, zeo)

ch3 (vit, zeo)

ch4 (vit, zeo)

ch5 (vit, zeo)

Tacbt (Calicobt) ch6 (vit, zeo)

Tcpuv (Prowuv) pp4

Tcpuc (Prowuc) pp3

Tcpmd (Prowmd) pp2

Tcplc (Prowlc)

Tcplv (Prowlv) pp1

Tcpbt (Prowbt)

Tcbuv (Bullfroguv)

Crater Flat Tcbuc (Bullfroguc) bf3undifferentiated (CFu)

Tcbmd (Bullfrogmd)

Tcblc (Bullfroglc)

Major UnitLithostratigraphicNomenclature

Model GridLayer

Tcblv (Bullfroglv) bf2

Tcbbt (Bullfrogbt)

Tctuv (Tramuv)

Tctuc (Tramuc) tr3

Tctmd (Trammd)

Tctlc (Tramlc)

Tctlv (Tramlv) tr2

Tctbt (Trambt) and below

Table 1. Continued.

Nevad aCoordinate E-W (m)

Nev

ada

Coo

rdin

ate

N-S

(m

)

170000 172000 174000230000

231000

232000

233000

234000

235000

236000

NRG-7A

WT-18

NRG-6

SD-7

SD-12

UZ-7a

Sol

itari

oC

anyo

nF

ault

Gho

stD

anc e

Fau

lt

Imbr

ica t

eF

ault

Drillhole

Wash

Fault

PaganyW

ashFault

SeverWash

Fault

UZ#5

H-5

UZ#4

UZ-14/1

H-4

SD-9

Borehole

Cross-sectionFault

Fig. 2. Plan view of the three-dimensional model domain, showingmodel boundary, horizontal grid layer, major fault locations, andselected borehole locations.

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well as the interference from each other. Seasonal com-ponents of the annual barometric pressure cycle arecharacterized by high-frequency, large-amplitude synoptic-pressure signals during the fall and winter months andby lower-frequency, small-amplitude synoptic-pressuresignals during the spring and summer months. The largeamplitude can be up to five times larger than the daily(diurnal) signal. Mean atmospheric pressure valuesare also higher during the fall and winter months thanduring the spring and summer months. Note that withthe construction of an underground tunnel, the Explor-atory Studies Facility (ESF) of Yucca Mountain, theunderground barometric records were disturbed to acertain extent by additional barometric signal sources.Comparison of the barometric signals in the tunnel andat the land surface shows that they are nearly identical.As construction of the tunnels brought signal sourcesclose to the pneumatic monitoring boreholes, the down-hole pressure in nearby borehole signals changed. Thesechanges will be enhanced at the locations near faults orfractures that intersect the tunnels (Ahlers et al., 1999).Such interference effects from multiple sources at the sur-face and in the tunnels were observed in nearby boreholes.In this study, to reduce the uncertainties associated

with the impact of ESF tunnel construction on pneu-matic responses within the UZ, only the in situ pressuredata from four boreholes (NRG-7a, UZ-7a, SD-7, andSD-12) are used for estimating fracture permeabilityin model calibration. In particular, all calibrations andanalyses are made for the periods before data at any ofthe boreholes are affected by penetration of the tunnel.Table 2 shows sensor locations (elevations and depths)and observation periods used in this study. Each bore-

hole has four or five observation points. At least onesensor in each borehole is located in each of the TCw,PTn, and TSw units.

Conceptual Model and Physical ProcessesVariations in subsurface gas pressures are caused

by bulk gas flow, mainly through relatively dry andwell-connected fractures within the UZ. The gas flow isdriven primarily by atmospheric barometric-pressurefluctuations on the land surface and geothermal-gradient-induced density differences, in addition tosome minor effects (e.g., wind speeds over the mountainand atmospheric tide responses). As shown in Fig. 1,a barometric pressure cycle signal on the land surfaceis rapidly transmitted down into the mountain throughthe highly permeable and well-connected fractures ofthe TCw unit, with little flow resistance (see Fig. 3). Thelow-permeability matrix may have negligible impacton rapid gas transmission through this top unit. How-ever, moving down into the nonwelded PTn, the largematrix porosity, higher matrix permeability and fewfractures of this unit provide significant storage volumeas well as resistance to downward gas flow, leading tolarge attenuation and phase lag in response to surfacechanges. Further down into the densely fractured TSwunit, similar patterns in gas-pressure changes to thoseon the land surface may be found. The significant at-tenuation or lag, seen in the TSw unit, results mainlyfrom effects or energy loss while traveling through thePTn unit.

In general, the daily or seasonal gas-pressure fluctu-ation at the land surface causes corresponding changes

84

85

86

87

88

89

90

30 40 50 60 70 80 90Time (days from 02/24/95)

Gas

pre

ssu

re (K

pa)

Surface

TCw

PTn

TSw

TSw

Fig. 3. Pneumatic pressure data from Borehole NRG-7a for typical pneumatic pressure responses at the site. Data from sensors located in themiddle TSw, upper TSw, PTn, and TCw geological layers, and land surface are shown.

Table 2. Sensor locations and observation periods for pneumatic pressure measurements at the four boreholes used in this study.

Borehole Sensor elevations Sensor depth Observation periods

mNRG-7a 1276.8, 1235.7, 1164.0, 1087.7 0.2, 41.3, 113.0, 189.3 27 Mar. 1995–26 May 1995UZ-7a 1243.0, 1232.3, 1221.6, 1213.4, 1177.8 47.5, 58.2, 68.9, 77.1, 112.7 1 Dec. 1995–29 Jan. 1996SD-7 1271.6, 1256.4, 1241.4, 1119.2 76.1, 91.3, 106.3, 228.5 5 Apr. 1996–4 June 1996SD-12 1258.5, 1232.0, 1217.1, 1001.3 63.6, 90.1, 105.0, 320.8 1 Dec. 1995–29 Jan. 1996

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in the unsaturated subsurface. The typical behavior ofsubsurface pneumatics consists of three different char-acteristic periods (Ahlers et al., 1999), as shown in Fig. 3by measured borehole data. Short periodic cycles cor-respond to daily (every half day) heating and coolingevents in the atmosphere, as well as tidal effects. Inter-mediate period variations, on the order of days to weeks,result from weather frontal systems as they move acrossthe mountain. The longest period occurs yearly, causedby seasonal temperature variations in the local atmo-sphere. Note that pneumatically static pressure decreaseswith increasing elevation and that the surface baromet-ric pressures have the lowest mean value. As the surfacepressure signal propagates into the subsurface, the am-plitude of the signal gradually decreases, and the phaseof the signal will be delayed. Furthermore, faults andmore permeable fractured zones, where they exist, willprovide a shortcut for transmitting rapid gas flow deeperinto the UZ.In addition to pneumatic processes, the ambient UZ

system is also subject to other hydrologic, geochemical,and geothermal processes. Because gas flow caused bybarometric pressure variations is a short-time phenom-enon relative to other processes, only moisture and heatflow are included as relevant in our modeling study. Thebarometrically induced transient gas flow is analyzedunder steady-state water and heat-flow conditions underthe present-day infiltration and ambient geothermal con-ditions. In particular, the following two conceptualiza-tions and assumptions are made in this study. First,ambient water and heat flow in the UZ system is at aquasi-steady-state condition, subject to spatially varyingsteady-state infiltration on the ground surface. Second,hydrogeological units and layers, as defined by the geo-logical model, are internally homogeneous, unless inter-rupted by faults or alterations.

MODELING APPROACH ANDNUMERICAL MODEL

The three-dimensional nature and complexity of theUZ geological system, as well as the coupling of liquidand heat flow, make it necessary to use a numericalmodeling approach for conducting gas flow analyses. Inthis section, we describe the modeling approach used forsimulating transient gas flow and for handling fracture–matrix interaction, the numerical scheme and codes,numerical model grids, and input parameters. We alsodiscuss treatment of initial and boundary conditionsused in the modeling study.

Modeling Approach and Numerical CodeThe dual-permeability concept, as built into the UZ

flow and transport model (Wu et al., 2003), is used in thisstudy to simulate transient gas flow as well as matrix–fracture interaction in the unsaturated fractured rock.In this approach, global fluid flow is considered to occurnot only between fractures but also between matrixblocks. In addition, the fluid and heat flow between frac-tures and the matrix is evaluated using a quasi-steady-

state approximation (Warren and Root, 1963; Pruessand Narasimhan, 1985).

Model calibration and simulation of gas flow in thisstudy were performed using the EOS3 module of theTOUGH2 code (Pruess et al., 1999; Wu et al., 1996). Inthe TOUGH2 code, gas and liquid two-phase fluid flowand heat transfer are described using the general multi-phase Darcy’s Law associated with energy andmass trans-fer through porous media. An integral finite-differencescheme is used for spatial discretization, and time dis-cretization is performed with a backward first-order,finite-difference scheme. The resulting discrete nonlin-ear algebraic equations are written in a residual formand solved using Newton–Raphson iterations.

Numerical Model GridThe three-dimensional numerical model grid used

in this study is shown in plan view in Fig. 2. The three-dimensional model grid was generated from an integralfinite-difference scheme (Pan et al., 2000) using an ir-regular, unstructured, three-dimensional control-volumespatial discretization. As shown in Fig. 2, the three-dimensional model grid covers a model domain approxi-mately 20 km2 in area. The model grid consists of 980mesh columns of fracture and matrix continua per gridlayer, for a total of 86 440 gridblocks and 350 000 con-nections in a dual-permeability mesh. Vertically, themodelgridhasanaverageof45computational grid layers.This model grid was designed initially for modelingambient heat flow within the UZ (Wu et al., 2003). Notethat in the three-dimensional model, faults are explicitlyrepresented by vertical 30-m-wide zones.

Model Input ParametersMost rock and fluid-flow parameters, except fracture

permeability, are taken from several related researchreports of UZ flow investigations (Wu et al., 2003;Ghezzehei and Liu, 2004; Pan and Liu, 2004). These pa-rameters include matrix and fracture porosities, matrixpermeability, and matrix and fracture van Genuchten pa-rameters. Table 3 lists fracture permeability and porosityfor all the model layers. Fracture permeability data ofTable 3 consists of (i) uncalibrated or initially estimatedvalues of Column2 (Pan andLiu, 2004), (ii) results of one-dimensional model inversions of Column 3 (Ghezzeheiand Liu, 2004), and (iii) the three-dimensional calibratedresults ofColumn4 from this study.Among the three typesof fracture permeability data, the permeability values inColumn 2 are estimated using air-injection tests andused as initial conditions for one-dimensional model in-versions, while one-dimensional model results of Col-umn3 are used for initial conditions for three-dimensionalmodel calibration. Note that ranges of air injectiontesting–derived fracture permeability values of Column 2of Table 3 for geological units of Yucca Mountain UZ aresimilar to those obtained from cross-hole injection tests(Table 2; Illman and Neuman, 2001) at a different site.

The fracture porosity is estimated from gas tracer testsconducted in the unsaturated zone of Yucca Mountain(Ghezzehei and Liu, 2004), and its average value is at

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1% (Column 4 of Table 3) for most of the upper geo-logical units above the CHn. Note that the fracture po-rosity values, as used in the current study in Table 3, areon the same order of magnitude as estimated air-filledporosity in the studies by Illman and Neuman (2001)for a different site and by Vesselinov et al. (2001b) foranother site. Except in the lower CHn units, Table 3shows that the Yucca Mountain tuff has relatively lowerfracture porosity values. Temperature- and pressure-dependent fluid properties, such as density, viscosity,and specific enthalpy, are calculated internally using theformulation embedded in the TOUGH2 code.

Boundary and Initial ConditionsIn this study, UZ liquid and heat flow are assumed to be

at a steady state under ambient conditions. This assump-tion establishes boundary and initial conditions for the gasflow analysis by running the three-dimensional model tosteady state under the present-day infiltration rate. Themodeluses thegroundsurfaceof themountain(or thetuff–alluvium contact in areas of significant alluvial cover) asthe topmodel boundary and thewater table as the bottommodel boundary. Both the top and bottom boundaries ofthe model are treated as Dirichlet-type conditions withspatially varying temperatures and pressures that remainunchanged through time. In addition, surface water re-charge, as described by the net infiltration map, is appliedusing a source term in the fracture gridblocks.All lateral side boundaries, as shown in Fig. 2, are

treated as no-flow (closed) boundaries, which allow

flow only along the vertical plane. The water table, thebottom boundary of the three-dimensional model, isshown to be a relatively flat surface, and for most modelareas, the flat portion of the water table is about 730 mabove sea level. The gas pressures are specified at 92 kPaat an elevation of 730 m, while surface gas pressuresare determined by running the TOUGH2 code to steadystate under given temperature, bottom pressure, andsurface-infiltration conditions. This is necessary to gen-erate a steady-state, equilibrated pneumatic-pressureboundary condition to avoid artificial airflow or circula-tion, which may occur if nonequilibrated pressures areimposed on both the top and bottom boundaries.

The top boundary temperature condition is determinedbycorrelatingaverageatmospheric temperaturewith sur-face elevations. Measured mean surface temperaturesare used with a linear equation that correlates surfacetemperature with elevation. The surface temperaturesTs

(8C) at any elevation Z (m) are then computed as con-stants according to the following equation (Wu et al., 1999):

Ts 5 18:23 2 0:01(Z 2 1231) [1]

The initial estimates of the temperature distribution at thewater table were made by contouring the temperaturedata, measured from 25 boreholes, at an elevation of 730m(Sass et al., 1988; Rousseau et al., 1999). Because the watertable is not perfectly flat over the model main, the actualwater table temperatures are determined by linearly inter-polating the values at 730 m and the model surface bound-ary elevation.

Water recharge imposed on the UZ model surfaceboundary is described by the steady-state net infiltrationmap. The mean infiltration map, estimated by studies ofsite climate and infiltration (BSC, 2004a, 2004b), is used.A plan view of the spatial distribution for the infiltra-tion, as interpolated onto the three-dimensional modelgrid of Fig. 2, is shown in Fig. 4. The figure shows a fluxdistribution for the present infiltration, with higher infil-tration rates in the northern part of the model domainand along the mountain ridge east of the SolitarioCanyon fault. The average annual net infiltration rateis 3.6 mm yr21 over the model domain.

With the surface recharge, surface and bottom tem-perature, and bottom gas pressure conditions specifiedas described, the three-dimensional model is run tosteady state. The steady-state simulation results give es-timates of the initial condition and gas pressures at eachsurface gridblock, which corresponds to a pneumaticstatic condition. The surface, time-dependent, baromet-ric gas pressure condition is then imposed by adding atime-varying pressure change to the steady-state gas pres-sure at each surface block. The time-varying pressurechange is defined by taking the actual barometric pres-sures, measured at one surface location, and subtractingthe time-average gas pressure value over the entire mea-surement period. This approach for specifying rapidlyvarying gas pressures at the surface is equivalent toassuming the same pressure time-varying patterns or cy-cles for all the surface nodes or assuming static pneu-matic conditions in the atmosphere. Nevertheless, theactual gas pressure values imposed are still correlated to

Table 3. Fracture permeability and porosity data.

Permeability

Modellayer Uncalibrated

One-dimensionalcalibrated

Three-dimensionalcalibrated

Fractureporosity

m2

tcw11 3.0E-11 4.24E-11 4.24E-11 2.4E-2tcw12 5.3E-12 9.53E-11 9.53E-11 1.7E-2tcw13 4.5E-12 1.32E-11 1.32E-11 1.3E-2ptn21 3.2E-12 2.11E-11 1.86E-12 9.2E-3ptn22 3.0E-13 9.41E-12 2.00E-11 1.0E-2ptn23 3.0E-13 5.35E-13 2.60E-13 2.1E-3ptn24 3.0E-12 1.00E-11 4.67E-13 1.0E-2ptn25 1.7E-13 1.24E-12 7.03E-13 5.5E-3ptn26 2.2E-13 3.17E-13 4.44E-13 3.1E-3tsw31 8.10E-13 8.13E-11 5.42E-12 5.0E-3tsw32 7.10E-13 7.08E-11 4.72E-12 8.3E-3tsw33 7.80E-13 7.76E-11 5.18E-12 5.8E-3tsw34 3.30E-13 3.31E-11 2.21E-12 8.5E-3tsw35 1.50E-13 9.12E-11 6.08E-12 5.0E-3tsw36 9.10E-13 1.35E-10 8.99E-12 8.3E-3tsw37 1.30E-12 1.35E-10 8.99E-12 8.3E-3tsw38 8.10E-13 8.10E-13 8.10E-13 5.8E-3tsw39 8.10E-13 8.10E-13 8.10E-13 8.5E-3ch1z 2.50E-14 2.50E-14 2.50E-14 1.6E-4ch2z 2.50E-14 2.50E-14 2.50E-14 3.7E-4ch3z 2.50E-14 2.50E-14 2.50E-14 3.7E-4ch4z 2.50E-14 2.50E-14 2.50E-14 3.7E-4ch5z 2.50E-14 2.50E-14 2.50E-14 3.7E-4ch6z 2.50E-14 2.50E-14 2.50E-14 1.6E-4pp4 2.50E-14 2.50E-14 2.50E-14 3.7E-4pp3 2.20E-13 2.20E-13 2.20E-13 9.7E-4pp2 2.20E-13 2.20E-13 2.20E-13 9.7E-4pp1 2.50E-14 2.50E-14 2.50E-14 3.7E-4bf3 2.20E-13 2.20E-13 2.20E-13 9.7E-4bf2 2.50E-14 2.50E-14 2.50E-14 3.7E-4tr3 2.20E-13 2.20E-13 2.20E-13 9.7E-4tr2 2.50E-14 2.50E-14 2.50E-14 3.7E-4

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elevations of the location through superposing onto thesteady-state gas pressure, estimated by the steady-stateflow simulation.

MODEL RESULTS AND ANALYSESAs discussed above, the main objective of the three-

dimensional model calibration to pneumatic data is toaid in estimating large-scale fracture permeability forthe three-dimensional UZ system. Past investigations(e.g., Ghezzehei and Liu, 2004; Wu et al., 2003; Ahlerset al., 1999) have found that transient time-dependentpneumatic data are among the most important datasources for estimating large-scale fracture permeability.By contrast, many other types of data, such as liquidsaturation, water potential, temperature, or chloridedata, are found to be relatively insensitive to constrain-ing fracture properties. This study uses matrix and otherrock properties (except fracture permeability), as deter-mined from core samples, field observations, and steady-state moisture data (Ghezzehei and Liu, 2004; Pan andLiu, 2004; Wu et al., 2003). In addition, this study sepa-rates fracture permeability from fracture porosity inpneumatic diffusivities in different layers, using reliablefracture porosity data determined from different studiesusing gas tracers and other methods (Ghezzehei and Liu,2004). In general, fracture permeability and porositycannot easily be estimated separately using pneumaticdata alone under nearly single-phase gas flow condition(Ahlers et al., 1999).

Initial EstimatesThe first step is to estimate fracture permeabilities

using inverse modeling to match the observed pressuresignals. Since an automatic inversion involves a greatnumber of forward runs anddemands intensive computa-tional effort, one-dimensional models (corresponding toselected boreholes where the pressure signal data areavailable, including NRG#5, NRG-7a, SD-7, and SD-12)are employed for the automatic inversion, using theiTOUGH2 code (Finsterle, 1999). Note that becauseairflow in the unsaturated fractured rock is a three-dimensional diffusive process, the one-dimensional modelscannot in general capture the process accurately. Here,one-dimensional models are used for providing initialestimates only; that is, fracture permeability valuesobtained from the one-dimensional models will be ad-justed in the following three-dimensional modeling studyconsidering multidimensional flow effects.

Grids for the one-dimensional models are directly ex-tracted from the three-dimensional model grid, and con-sequently the one-dimensional models in the verticaldirection have the same spatial scale as that in the three-dimensional model. For a given one-dimensional modelrepresenting a borehole, the top boundary condition forthe airflow is described using observed time-varyingpneumatic pressure over a time period of 240 d. Beforeinversion, the combination of a steady-state liquid waterflow field and pneumatically static conditions are deter-mined and used as initial conditions for the inversion,

1514131211109876543210

Infiltration Rate(mm/year)

Nevada Coordinate E-W (m)

Nev

ada

Coo

rdin

ate

N-S

(m

)

170000 172000 174000230000

231000

232000

233000

234000

235000

236000

237000

NRG-7A UZ#4

NRG-6

SD-7

SD-12

UZ-7

Soli

tari

oC

any o

nF

ault

Gh o

stD

anc e

Fau

lt

Imb r

icat

eF

ault

Drillhole

Wash

FaultPagany

Wash

Fault

SeverWash

Fault

Infiltration at Land Surface

Fig. 4. Plan view of net infiltration distributed over the three-dimensional model domain of the present-day mean infiltration, used for gasflow analysis.

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similar to the approach used in specifying boundary andinitial conditions for the three-dimensional model. Aprevious study by Ahlers et al. (1999) indicated that af-ter 30 d, the initial conditions for the pneumatic pres-sures have an insignificant effect on simulation results.To exclude possible initial-condition effects, we matchedthe data observed after 30 d from simulation start forboth one-dimensional and three-dimensional model-ing studies.Automatic inversion is applied to determine fracture

permeabilities for the top two hydrologic units of TCwand PTn only (i.e., fracture permeabilities were esti-mated directly by the ITOUGH2 code) using simulta-neous inversion of the pneumatic data measured fromseveral boreholes in these two units. Fracture perme-ability values were estimated for each model layer inthese units (Table 1). The objective function used in theinversion is defined as a summation of the square of thedifference between simulated and measure air pressurevalues. A different analysis approach, as discussed below,was developed and employed to estimate permeabilityvalues for the lower TSw unit (below the PTn). This isbecause pneumatic data not only are limited, but alsoshow little attenuation in gas-pressure signals across theTSw unit, which are difficult to match by simultaneousand automatic inversion using gas-pressure data in asso-ciation with TCw and PTn units. However, the lack ofsignificant attenuation in the TSw unit is considered animportant feature because it implies that the TSw frac-tures are highly permeable and well connected. The cal-ibrated fracture permeabilities for the model layers inthe TSw unit must be consistent with the observation.Therefore, fracture permeabilities in the TSw aredetermined by forcing the simulated and observed gaspressure signals at the upper and lower sensor locationsin the TSw to have similar degrees of attenuation forBorehole SD-12. Borehole SD-12 was chosen becausethe distance between the two TSw sensors within thisborehole is the largest among all the relevant boreholes.The degree of attenuation in the barometric signalthrough the TSw in SD-12, or the relative differencebetween the signals at the two sensor locations, is de-termined quantitatively by evaluating

F 51NONi51

{[Pu(ti) 2 Pu(t1)] 2 [Pb(ti) 2 Pb(t1)]}2

!1/2

[2]

whereN is the total number of calibration time points, Pis the gas pressure, and subscripts u and b refer to thesensors in the upper and lower (bottom) portions of theTSwwithin Borehole SD-12. Obviously, if the gas signalsfrom the two sensors are identical, F should be equal tozero. For the SD-12 gas-signal data, the F value is 2.0131023 kPa. In this study, fracture permeabilities to be de-termined should give F values similar to the value calcu-lated from the data, such that the simulated and observedgas-pressure signals have similar degrees of attenuation.Since the gas-pressure data from the TSw unit are rela-

tively limited compared with the two upper units, TCw

and PTn, the insignificant attenuation and time lag be-tween the upper-most and lower-most sensors are usedfor calibration.Otherwise, fracture permeabilities for dif-ferent model layers in the TSw unit could not be inde-pendently estimated reliably or uniquely. Note that theattenuation and time lag are determined by the overallhydraulic properties between the two sensors, ratherthan by properties in a single model layer (or subunit).Permeability values derived from small-scale air-k testdata for each model layer are multiplied by a commonfactor, d. To calculate an F value for the d factor, we runforward simulations, generating gas pressures for Eq. [2].The best estimate of the d factor is obtained by match-ing the calculated F value with that derived from the ob-servations through changing fracture permeabilities forthe TSw unit only. Figure 5 shows calculated F values asa function of factor d. The F value is quite sensitive to d.

Figure 6 shows a comparison between simulated andobserved pneumatic pressures at Borehole SD-12, ob-tained through one-dimensional model inversion. Simi-larly excellent matches were also obtained for otherboreholes. Fracture permeability values (as listed in thethird column of Table 3) obtained from one-dimensionalmodels are on average about one to two orders of mag-nitude higher than those inferred from single-hole air-injection tests performed in the TSWor upper geologicalunits (e.g., Pan and Liu, 2004). The difference betweenpermeability estimates from in situ pneumatic pressuredata and the air-injection test results is caused mainly byscale effects. The test condition for the air-injection testsimplies that permeability estimates are representative ofvalues on the order of meters (corresponding to the in-jection interval). On the other hand, pneumatic signalsobserved in the depth of the Yucca Mountain unsatu-rated zone are likely representative of large-scale flowprocesses on the order of 10 to 100 m (corresponding tothe vertical distance from the ground surface and sensor

d

F r

atio

1 1.25 1.5 1.75 20

1

2

3

4

5

6

Fig. 5. Estimated F ratio as a function of factor d. The F ratio is de-termined as the ratio of the calculated F value to the F value for thegas pressure signal.

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locations where pneumatic signals are observed). It hasbeen noted that large-scale effective permeabilities aregenerally larger than smaller-scale ones (e.g., Neuman,1994). An intuitive explanation for such scale-dependentbehavior is that a large observation scale, in an averagesense, corresponds to a larger opportunity to encountermore permeable zones or paths where observations aremade, which considerably increases the value of theobserved effective permeability.

Three-Dimensional Model CalibrationThe second step is to calibrate, by a trial-and-error ap-

proach, fracture permeability using three-dimensionalpneumatic simulation results against measured subsur-face pneumatic data. A forward, rather than inverse,modeling approach was chosen primarily because of thecomputational intensity required by automatic inversionof the large-scale three-dimensional gas flow model.To capture the details of periodic gas-pressure variationsfor peak and valley values, the maximum time step is setto be 13000 s. The results of these gas flow simulationsare then compared with field-measured pneumatic datafrom several boreholes simultaneously to examine theresults of the above one-dimensional models and to re-estimate fracture permeability in several TSw layers.This section focuses on the model calibration and anal-ysis using these three-dimensional pneumatic simula-tion results.Note that the above one-dimensional calibration was

performed for fracture networks located in nonfaultzones.A two-dimensionalmodel is used for the fault frac-ture permeability calibration using iTOUGH2 (Ghezzeheiand Liu, 2004). Because faults are relatively planar ingeometry, flow in and around a fault zone can be ap-proximately captured by the two-dimensional modelthat is aligned approximately parallel to the dip of the

beds and parallel to the dip of the fault. The data fromBorehole UZ-7a represent the most complete data setwithin a fault zone and were used for calibrating thefault properties. The methodology and the data set usedhere are identical to those of Ahlers et al. (1999). Theestimated fault fracture permeability values are slightlyhigher than nonfault ones (Ghezzehei and Liu, 2004),and they are used here directly (without further adjust-ment) in the three-dimensional simulations.

The three-dimensional pneumatic model was calibratedagainst the field-measured pneumatic data from fourboreholes, SD-7, SD-12, NRG-7a and UZ-7a, observedbetween December 1995 and June 1996 (Wu et al., 2003).The model calibration results indicated that modifica-tion of fractured rock properties, as estimated by one-dimensional inversion in the TSw layers, is necessary formatching field-observed gas pressures. In particular, itwas found necessary to reduce the fracture permeabilityof the subunits within the TSw by a factor of 15, as wellas for the PTn units by a factor from 1.8 to 21. The finalcalibration results are provided in Table 3 (Column 4).In the top unit of the TCw, however, no adjustments infracturepermeability fromone-dimensionalmodel inver-sions were made. This is because one-dimensional flowappears to provide a good approximation for gas flowthrough the top, shallowTCwunit. Figure 7 shows a com-parison between the observed gas-pressure and simula-tion results, in which the curve labeled “noncalibrated”is plotted using the simulations with the one-dimensionalmodel estimated fracture properties and “calibrated”using the three-dimensional model results, with TSwsubunit fracture permeability reduced by a factor of 15.As shown in Fig. 7, three-dimensional model calibratedresults significantly improved the model match of theobserved gas-pressure data, whereas the simulations withnoncalibrated or one-dimensional model fracture per-meability overestimated gas pressure responses at thecorresponding elevation.

The comparison in Fig. 7 indicates that the fracturepermeability of three-dimensional gas flow through theUZ should be lower than the one-dimensional model es-timates. As discussed above, the lower fracture perme-ability for the three-dimensional model is attributed tothe one-dimensional model fracture permeability beingestimated by considering one-dimensional vertical flowpaths only. In a three-dimensional model, where thereexist some high-permeability channels, such as faults, orzones with high fracture density, or varying thicknessesof different permeable layers, three-dimensional gas flowis able to find those high-permeability pathways with theleast resistance. As a result, the fracture permeability ofa three-dimensional model will in general be lower thanthat estimated from one-dimensional models.

Comparisons of the model simulation results with thefield-measurement data for boreholes SD-7, SD-12, andUZ-7a are shown in Fig. 8, 9, and 10, respectively. Thesimulation results demonstrate a good match with mea-surement data in general. Except in the TSw unit ofBorehole SD-7, the three-dimensional simulation pre-dicts a slightly smaller or delayed amplitude signal thanthe observation data. Many comparisons between simu-

0 10 20 30

Time (days after 12/1/95)

87

87.5

88

88.5

89

89.5

90

90.5

Pre

ssu

re (

kPa)

Tptpll

Tptrn

Tpbt2

Tpcp

Fig.6. Comparisonbetweensimulated(brokenline)andobservedpneu-matic gas-pressure data at Borehole SD-12, obtained though one-dimensional model inversion (subunits of the Tpcp and Tpbt2 arelocated within the TCw and PTn, respectively, while Tptrn and Tptpllcorrespond to upper and lower portions of the TSw, respectively).

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lated gas pressures, with andwithout fracture-permeabilitymodifications, and field measurements show that thecalibrated three-dimensional model has improved con-sistently in matching observation data. Note that forBorehole SD-7, the calibrated fracture-permeabilityvalues of the TSw unit may be even lower for a bettermatch. This difference between simulations and datain this borehole might be caused by how the nearbyfault affects pneumatic signal propagation. In addition,slightly greater differences between simulated and ob-served gas pressures in the lower TSw unit may becaused by coarse spatial discreteization or the effect ofheterogeneity encountered over larger travel distance orthrough longer flow paths with depth.Note that when comparing simulated and observed gas

pressures at different locations of the three boreholes(Fig. 8, 9, and 10),we find that simulated gaspressures and

their patterns of variation are in general consistent withobserved values. In particular, the simulations consis-tently reproduce increases and decreases of pressure re-sulting fromchanges inbarometric pressure at thegroundsurface. Overall, a reduction by a factor of 15 for the TSwfracture permeability and reduction by a factor of 1.8 toPTn layers 21 provide a better fit to observed pneumaticdata for all locations and time periods and providesfurther confidence in the model’s capability to simulatethree-dimensional gas flow behavior within the UZ.

CONCLUSIONSWe presented a three-dimensional modeling study of

gas flow to estimate the large-scale fracture permeabilityof the Yucca Mountain unsaturated zone. Our modelingapproach incorporates changes in subsurface pneumatic

SD-7

85.6

86.1

86.6

87.1

87.6

88.1

88.6

89.1

89.6

0 10 20 30 40 50 60

Time (days from 04/05/96)

Pre

ssu

re (

KP

a)

Observation Model prediction

TCw

PTn

TSw

TSw

Fig. 8. Comparison of simulated and observed gas pressures at Borehole SD-7 over a 60-d period, with three-dimensional calibration.

Gas pressure at SD12 at elevation 1001.3m

89.4

89.6

89.8

90

90.2

90.4

90.6

90.8

91

91.2

91.4

0 10 20 30 40 50 60

Time (days 12/01/95)

Gas

pre

ssu

re (

Kp

a)

Measured

Calibrated

Non-Calibrated

Fig. 7. Comparison of simulated and observed gas pressures at Borehole SD-12 during a 60-d period, using simulation results with and withoutthree-dimensional calibration.

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pressure (in response to barometric pressure changes onthe land surface) into the UZ flow model developed forthe site. Results from gas flow simulations are comparedwith the measured pneumatic data from undergroundboreholes for the purposes of estimating fracture prop-erties. As a result of calibration, fracture permeabilities,initially estimated by small-scale air-injection testing andone-dimensional model inversion, are found to need ad-justment. In particular, a reduction factor of 15 is neededfor the TSw layer fracture permeability (relative to theone-dimensional inversion results) to obtain an overallgood match between the three-dimensional model pre-dictions and pneumatic data. The ability to match fieldpneumatic data observed from multiple sources, includ-ing pneumatic data for a long time period, indicates thereliability of the numerical model to describe air andwater flow processes within the YuccaMountain UZ sys-tem through better estimates of fracture flow properties.

The results of this study indicate that using field-measured pneumatic data in combination with numer-ical modeling analyses provides a practical and powerfultechnique for estimating flow properties of vadose zoneformations. As shown in this work, periodic responses ofsubsurface gas-pressure signals to surface barometric-pressure changes, which are easy to measure, revealinvaluable information on gas mobility in unsaturatedporous media. Many other data sources, such as moistureand heat flow data, prove to be insensitive to the fracturepermeability of the unsaturated fractured-porous mediaunder ambient, low-infiltration conditions at YuccaMountain. In addition, this work demonstrates thatmultidimensional effects on model-estimated perme-ability are significant when determining fracture perme-ability in heterogeneous fractured media. These effectscan be captured only by three-dimensional modelinganalyses on relevant model scales.

UZ-7a

85

86

87

88

89

90

91

92

0 10 20 30 40 50 60


Pre

ssu

re (

KP

a)


TCw

PTn

TSw

TSw

TCw

Fig. 10. Comparison of simulated and observed gas pressures at Borehole UZ-7a over a 60-d period, with three-dimensional calibration.


SD-12

86

86.5

87

87.5

88

88.5

89

89.5

90

90.5

91

0 10 20 30 40 50 60


Gas

Pre

ssu

re (

Kp

a)PTn

TSw

TSw

TCw

Fig. 9. Comparison of simulated and observed gas pressures at Borehole SD-12 over a 60-d period, with three-dimensional calibration.

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This study presents one example of our current re-search efforts in characterizing flow and transport pro-cesses of the UZ system at Yucca Mountain. It isimportant to mention that certain limitations and uncer-tainties exist for the mountain-scale gas flow model. Onesignificant limitation presented in this paper is that itdoes not incorporate small-scale heterogeneities withineach stratigraphic units, other than layer-wise conceptu-alization. The model grid used is relatively coarse forinvestigating details of gas flow in different units. In ad-dition, the effects of seasonal changes in surface tem-peratures on gas flow are not included in the analysis.Future modeling efforts may be needed if these issuesare considered to be important. Nevertheless, note thatpneumatic data are generally easy to measure and ef-fective to use for estimating permeabilities within thevadose zone. Pneumatic data analysis using a numericalmodeling approach will likely find wider application infuture characterization of the vadose zone.

ACKNOWLEDGMENTS

Theauthors thankStefanFinsterle andDanHawkes for theirreview of this paper, and thank the USGS scientists for provid-ing pneumatic data and thank our colleagues, Lehua Pan andDiana Swantek, for their help in preparing the manuscript. Wealso thank the VZJ reviewers for their insightful, critical, andconstructive reviews and suggestions for improving this manu-script. This work was supported by the Director, Office of Ci-vilian Radioactive Waste Management, U.S. Department ofEnergy, throughMemorandumPurchaseOrderEA9013MC5XbetweenBechtel SAICCompany,LLC,and theErnestOrlandoLawrence Berkeley National Laboratory (Berkeley Lab). Thesupport is provided to Berkeley Lab through the U.S. Depart-ment of Energy Contract no. DE-AC03-76SF00098.

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Estimating Large-Scale Fracture Permeability of ... Wu et al. Vodose Zone... · lic conductivity many orders of magnitude higher than infiltration rates. Under such conditions, slight