Multi-Scale Investigationsof Liquid Flow in a FracturedBasaltVadoseZone
Boris Faybishenko,Paul A. Witherspoon,ChristineDoughty,and Jil T. Geller
LawrenceBerkeleyNational Laboratory,Berkeley,CA
ThomasR. Wood and RobertK. Podgomey
ParsonsInJ?astructure
and Technologies,
Inc., Idaho Falls, ID
Currently,with Idaho National Engineeringand EnvironmentalLaboratory,Idaho Falls, ID
This paper introducesan approachto the problem of characterizingflow and
transportin a fracturedbasaltvadosezone.We proposethe developmentof physically basedconceptualmodelson a hierarchyof scales.This approachis derived
from field investigationsthat were conductedin the vadosezone of the Snake
River Plain in southeasternIdaho. Three scalesof pondedinfiltration testswere
carriedout: a Large ScaleInfiltration Test (LSIT) conductedat the IdahoNational
Engineering
andEnvironmental
Laboratory
(INEEL)(pondarea•26,000m2),intermediate-scale
infiltration
tests(pondarea56m2)conducted
attheBoxCanyon
site(nearArco,Idaho),andsmall-scale
infiltration
tests(pondarea0.5m2)conductedat the Hell's Half Acre Lava Flow Site (near Shelly, Idaho). Laboratory
water-drippingexperimentswere also conductedusingfracturemodelswith constantand variable apertures.We find that, at each scaleof investigation,different
modelsfor flow phenomenamustbe usedto explainthe observedbehavior.These
modelscan be usedto describethe flow processes
on differentscales,with no apparentscalingprinciplesevident.To characterize
flow phenomenain fracturedbasalt, we recommendthat investigationsbe carried out at four scales:elemental,
small-scale,intermediate-scale,
and large-scale.An elementalcomponentis a single fractureor a blockof homogeneous
porousmedia.Small-scalecomponents
include one or a few fractures and the surroundingmatrix. Intermediate-scale
(mesoscale)components
includea basaltflow with its fracturenetworkand other
parts(fracturezones,vesicularlenses,soil, massivebasalt,rubblezone)of a single basaltflow. Large-scale(regional)components
includemultiplebasaltflows
andtheir surrounding
networkof rubblezonesandsedimentaryinterbeds.
phenomenain fracturedrocks,primarily under saturatedconditions (National ResearchCouncil, 1996). The modeling
Motivation and Practical Importance.For a number of
methodsinclude continuumapproachesthat perform volume
years, several theoretical,experimental,and modeling ap- averagingusing the effective continuum(Long et al., 1982;
proacheshave been used to investigateflow and transport Petersand Klavetter, 1988; Pruesset al., 1985), doubleporosity (Barenblatt et al., 1960; Warren and Root, 1963), dual
Flow andTransportThroughUnsaturated
Fractured
Rock
permeability, and multiple interactingcontinua(Pruessand
Second Edition
Narasimhan,1985) concepts,as well as fracturenetworkmodGeophysical
Monograph42
els (Bear et al., 1993; Dershowitz et al., 1992; Kwicklis and
Thispaperisnotsubject
to U.S.copyright
Healey, 1993; Rasmussen,1987; Smith and Schwartz,1993).
Published
in 2001by theAmerican
Geophysical
Union
Models developedfor saturatedconditionscannot,however,
1. INTRODUCTION
162 MULTI-SCALE INVESTIGATIONS OF LIQUID FLOW
describethe significantspatialand temporallyvarying nature
of preferentialflow causedby stronglyheterogeneous
unsaturated flow conditions(Wang and Narasimhan,1993). A numerical modelingstudyby Pruess(1998) has shownthat flow
in an unsaturatedfracturewith randomlydistributedhydraulic
parametersdoesnot occur as sheetflow, but rather as a dendritic structurewith zonesof preferentialflow. When Birkholzer and Tsang (1997) simulatedflow and solutetransportin
unsaturatedmedia with randomly distributedhydraulic parameters,they determinedthat solutetransportcan developa
channelingeffect even under conditionsof steady-state
water
flow.
Significantefforts have been devotedto the development
of alternativemodelsfor water flow and chemicaltransportin
heterogeneousmedia using simple approximationslike the
transfer function approach(Chesnut, 1994; Jury and Roth,
1990) and percolationtheory (Sahimi, 1993). Basic laws governing flow and transportin fracturedrock were initially developedfrom theoreticalstudies(Snow, 1964; Witherspoonet
al., 1980). Yet for most fracturedrocks, and particularlythe
complex systemof fracturedbasalt, it is not yet possibleto
develop models directly from first principles;the results of
field and laboratoryinvestigationsare of primaryimportance,
becausethey providethe foundationsfor the basictheoriesand
modelsgoverningflow andtransport.
To developan understandingof the flow processes
in heterogeneousfracturedrocks from experiments,one must recognize the inherentfeaturesand limitationsof the different
typesof measurements
that can be obtainedunderfield conditions. To monitor flow and transportin the vadosezone, we
may use point-typeprobes,suchas tensiometers,thermistors,
and suction lysimeters;and geophysicalimaging methods,
suchas seismicsurveys,groundpenetratingradar (GPR) and
3-D electricalresistivitytomography(ERT) (Hubbard et al.,
1997; Majer et al., 1997; Petersonand Williams, 1997). The
point-type probes may or may not intersectsingle fractures.
Responsesfrom multiple probesmust be combinedusing either deterministicor stochasticmodels to developa macroscaleconceptualmodel of the flow system(Yeh et al., 1985).
The shortcomingof point-typeprobemeasurements
is the difficulty of combining their responsesin a meaningful way,
such as integrating or volume averagingresponsesfrom a
number of point measurements,especiallywhen the practicalitiesof an investigationdo not allow for a sufficientnumber of measurementlocations.Geophysicalimagingmethods
complementpoint-typemeasurements
by providinga spatially
averagedview of subsurfaceconditions.The shortcomingof
geophysicalmethodsis their lack of resolutionand the difficulty of correlatingelectromagneticresponses,seismicvelocities, etc. with the hydrogeologicparametersgovemingfluid
flow. Neither method can be used to observeflow in single
fractures or fluid movement
at the fracture-matrix
interface
in
sufficientdetail to accuratelyrepresenttransport.Field measurementsgenerallyprovide only averagecharacteristics
of the
rock and fracturepropertiesover spaceand time. The actual
resolution
of the measurements
and the volume of rock in-
volved in averagingremain unknown.It is also importantto
keepin mind that, in contrastto porousmedia,differentgeological, mechanical,and geochemicalprocesses
govem the
physicsof flow in fracturedrocks, such as basalt.The wide
variety of processes
controllingflow in fracturedbasaltat different scalesmakesconventionalscalingprocedures
in applicable.
Basaltic rocks are widely distributedin the United States
and throughoutthe world (Korvin, 1992; Long and Wood,
1986; Tomkeieff, 1940). Our investigations
were conductedin
fractured basalt of the Eastern Snake River Plain in southeast-
ern Idaho near the Idaho National Engineeringand Environmental Laboratory.Contaminantsof concern,suchas VOCs
(TCE, carbontetrachloride,etc.) and radionuclides(Cs, Sr, U,
Pu, etc.), were buriedin soilsoverlyingthe basaltvadosezone
or were injecteddirectly into basaltusingwells and pits. The
prevailingthoughtat the time of burial was that contaminants
would not migrate downwardto the underlyingSnakeRiver
Plain aquifer. However, contaminantshave been found in
perchedwater zones,interbedsediments,andthe aquifer.Currently, severalINEEL sitesare being remediatedand instrumentedfor long-termmonitoring.It has becomeapparentthat
monitoring technologies,characterizationmethods,and prediction proceduresdevelopedfor porousmedia are not sufficientwhen investigatingfracturedbasalt.
Objectives.The objectivesof this paperare to introducea
new approachto the multi-scalecharacterizationof flow and
transportin the fracturedbasaltof the vadosezone and to develop physicallybased conceptualmodels on a hierarchyof
scales.We illustratethis new approachusing resultsof field
and laboratoryinvestigations
conductedin the fracturedbasalt
near the INEEL.
The results were obtained from field tests
carried out at three different sites:(1) small-scaleinfiltration
tests(ponded
area0.5 m2) conducted
at theHell'sHalfAcre
site (near Shelly, Idaho), (2) intermediatescale infiltration
tests(ponded
area56 m2) conducted
at theBoxCanyon
site
(near Arco, Idaho), and (3) a Large Scale Infiltration Test
conductednear the INEEL RadioactiveWaste Management
Complex
(ponded
area-26,000
m2).In addition
tothese
field
tests, laboratory investigationsincluded measurementson
fracturedbasaltcoresand small-scaledrippingexperiments
in
fracture models.
The paperbriefly describesthe geologyof the SnakeRiver
Plain basalt flows and the variousprocessesinvolved in flow
and transport in fractured basalts. A hierarchy of hydrogeologicalscalesis describedfor use in constructingmodels
and developingobservationalmethods.A descriptionof the
resultsfrom laboratorywater drippingexperimentson an
FAYBISHENKO
ET At.
163
PRECIPITATION
CONTAMINANT.
SOURCE
...................................................
SOILS
..............
•'i!....?......:•
...........
FLoW
3"
FL
FLOW
2/•--'•'•---•'
•••
':'••'
' '
-:••[; '-'"-'-'"••'•"
PERCHED
WATER
•"'""'•-"
••1................................
•I........................
.i"••
SEDIMENT
INTERBED
.................................
...........
...................
!!............::i,
................
......
Figure 1. Schematic
illustration
of waterflow andcontamJnant
transport
in fractured
b•alL including
flow through
rubblezonesbetweenbasaltflowsandthroughanintra-basalt
flow fracturepattern.Notethatperched
waterzonesare
formedabovethe sedimentarylayer.
mental scale is followed by an interpretationof the results
from
the three field
infiltration
tests. We conclude
with
a
summaryandpresentsomepracticalapplications.
2. GEOLOGY
OF THE
SNAKE
RIVER
BASALT
2.1. GeneralInformation
The SnakeRiver Plain is primarily composedof fractured
Quaternarybasalts,inter-layeredwith sedimentarydeposits
(Knutsonet al., 1993;LindholmandVaccaro,1988).Multiple
basaltflows (Figure 1) within a flow unit were formedby
closelyrelatederuptionevents(LindholmandVaccaro,1988).
Individual basaltflows are typically highly fractured,with a
thicknessthat rangesfrom lessthan 1 m to more than 30 m,
and an areal extent of up to severalthousandsquaremeters.
Fracturing was caused by thermal contractionas the flow
cooledand formedpolygonal,oftenhexagonal,columns(Korvin, 1992). The upperportionof the flow is usuallydensely
fractured,even mbblelized(Grossenbacher
and Faybishenko,
1995; Lore, 1997), as a resultof exposureto the atmosphere,
which producedan increasedcoolingrate. Therefore,fracture
densitydecreasestoward the centerof the flow. The lower half
of the flow contains fewer fractures because of a slower cool-
ing rate. Whenthe basaltcolumnswere exposedto weathering
over geologic time, their surfacesweatheredto breccia and
were often coveredwith sedimentsthat separatedthe flow
units (Welhan and Reed, 1997). Sedimentaryinterbedsmay
have a significantlateral extent(often exceedingthat of the
individualbasaltflows) and their thicknessrangesfrom a few
centimeters
to asmuchas 15 m. Geophysical
loggingsuggests
that the total thickness of the basalt in the Snake River Plain
may exceedthree kilometers.In the region near INEEL, the
depthto the watertableof the regionalaquiferrangesfrom 60
to 200 m.
The unusuallycomplicatedgeometryof basaltflows with
wide contrastsin the permeabilityof densebasaltandhighly
fractured rabble zones has raised concerns over how such
systems should be characterized. For the Columbia basalt
flows in the Stateof Washington,
the Departmentof Energy
(1986) has identifiedfour domainsfor basaltflows: (a) the
domainof a singlefracture;(b) the domainof multiplefractureswithin the entablatureand colonnade;(c) the domainof
entablatures,
colonnades,
andflow tops;and(d) the domainof
multiple basalt flows. Note that Domains a, b, and c are restrictedto a singleflow. We have foundthis classificationuseful for examiningthe basaltsof the EasternSnakeRiver Plain,
andwe haveusedit in developingthe conceptof a hierarchy
of hydrogeologicalscales.
2.2. The Research Sites
Hell's Half Acre Site. The site is locatedwithin the Hell's
Half Acre (HHA) Lava Field in southeastem
Idaho. The site
consistsof an overhangingbasaltblock on the edgeof a collapsedlava tube. The basaltis moderatelyvesicularto dense,
with a singlefractureexposedon the surfaceof the block. The
fracturebifurcatesin the lowerpart of the block,resulting
164 MULTI-SCALE INVESTIGATIONS OF LIQUID FLOW
two fracture traces on the underside. A horizontal fracture,
which intersectsthe verticalfracture,is exposedon the face of
the block, approximately25 cm from the underside.The,
physicallayoutof the site permittedaccessto the top, front,
and undersidefacesof the basaltblock, thus allowingthe implementationof detailedinstrumentation
to collectdata on
both infiltration and outflow rates from the fracture. Access to
the underside also allowed for collection of time intervals
betweendripsfalling from discretelocationsalongthe fracture,whichwerethenusedin an analysisof chaoticbehavior.
Box CanyonSite. The Box Canyonsite is locatedin the
EasternSnakeRiver Plainnearthe INEEL (Long et al., 1995).
Minimal soil cover and a nearbycliff-face exposureprovide
an excellentopportunityto studyrelationships
betweenthe
fracturegeologyandthehydrogeologic
response
to infiltration
tests.The surfaceof the Box Canyonsiteconsists
of exposed
weatheredbasalt and soils (clays and silts), which infill the
near-surfacefractures and basalt column joints (Engelder,
1987).The depthto theregionalaquiferis about200 m at the
BoxCanyonsite,with a perched
waterzonelocatedat a depth
of about20 m. Alongthe cliff face,about30m fromthe infiltrationpond,two distinctbasaltflowswith a rubblezonebetweenthemare exposed.The fracturedbasaltvadosezoneis
comprised
of the followinggeological
components:
a surface
sedimentary
layer includingbasaltrubble,uppervesicular
zones with numerous near-surface soil-infilled fractures, mas-
sive basalt,verticaland sub-verticalcolumn-bounding
joints,
horizontal and subhorizontalfractures, central fracture zone,
lower vesicular zone, and underlying rubble zone [Faybishenkoet al., 1998].
LargeScaleInfiltrationTestSite.TheLSIT siteis located
1.4 km southof the RadioactiveWasteManagementComplex
(RWMC) at theINEEL. TheRWMC includes
oneof thelargest subsurface
wastedisposalfacilitiesin the DOE complex.
Pastdisposal
of low-level,mixed,andtransuranic
radioactive
wastesoccurredby directdischargeor burialin shallow,unlinedpitsandtrenches
withinthesurficialsediments.
Flooding
of the RWMC has occurredthreetimesin the past,potentially
test investigated
the hydrologicpropertiesof a hypothetical
"cylinder"of basaltthatis 55 m thickand183m in diameter.
3. HIERARCHY
OF HYDROGEOLOGICAL
PROCESSES
3.1. Flow Processesand Monitoring Techniques
for Different
Scales
In our investigations,
we havefoundthat differentconditions affect flow processesin fracturedbasalt at different
scales.Regional groundwaterflow throughthe aquifer is
commonlystudiedon a regional scale, where observation
wells are thousandsof meters apart and model domainsencompass
hundredsof squarekilometers.At thisscale,the aquifer is highly transmissive
and verticallyanisotropic,
with
nearlyall the permeabilityarisingfrom the networkof rubble
zonessurrounding
individualbasaltflows.Brunoet al. (1992)
found that fractal models can describethe shapeof basalt
flows.Pumpingtestshaverevealedthat the horizontalpermeability is higherthanthe verticalbecauseof the largeaspect
ratio of individualbasaltflows (Welhan andReed, 1997). Becauseof anisotropy,
large-scale
infiltrationmay leadto lateral
spreading
of infiltratingwater.The sedimentary
interbeds
are
of relativelylow permeabilityand may act as aquitardsfor
perchedwaterzones,in whichcontaminants
canaccumulate.
In contrast,at the intermediatescale,we may be interested
in a site that hasneither a network of rubblezonesto provide
high permeabilityflow pathsnor a sedimentary
interbedto
block flow. At this scale,we investigatethe intra-basaltflow
fracturepattern.Figure2 showsa photograph
of the basalt
outcrop at the Box Canyon site and the corresponding
lithologicalcrossection,
which identifythe main geological
features of the vertical section. These features include a flow-
top breccia,vesicularand massivebasaltlayers,a central
fractured zone, a rubble zone, and vertical and horizontal
fractures(Faybishenkoet al., 1998). During infiltrationfrom
rainfall and snowmelt,sedimentparticleshave migratedinto
the subsurface and accumulated in both vertical and horizontal
fracturesto a depthof at least2-3 m. As watermovesthrough
increasing
the downward
mobilityof the subsurface
contaminants.The time requiredfor contaminant
migrationto reach
the aquiferis fundamentally
significant
to management
decisionsregardingremediationoptions.
In 1994,the INEEL conducted
the LSIT to investigate
hydrologicproperties
of the vadosezonebasalts.The vadose
morerestrictedbecauseof the wide spacingof fracturesin the
consistsof a bermedbasin 183 m in diameter,which contained
dead-end,nonconductivefractures,which are difficult, if not
zone thickness near the RWMC is about 190 m. The LSIT site
32 millionlitersof waterduringthetest.Beneaththebasinis a
thick sequence
of stackedbasalticlava flowswith the first
majorinterbedat a depthof 55 m. A totalof 70 wellswere
drilled in 16 nestedclustersand in concentricrings aboutthe
basin. Four clusterswere situated in the basin, the first con-
thesesoil-filled fractures,it can be imbibed into the adjacent
porous,vesicularand densebasaltmatrix. Watermay also
flow laterallyin the vesicularlayersandthe centralfractured
zone. Below the central fracturedzone, the downwardflow is
lowerpartof the basaltflow. Figure2 showsthe presence
of
impossible,to recognizefrom point-typemeasurements
in
boreholes.Contaminantscan be trapped in these dead-end
fracturesandon top of horizontalfracturesfollowedby diffusion into the basalt matrix.
Becausefracturedbasaltis characterizedby drasticdiffer-
betweenfractures
andmatrix,theresults
centricring wasat 15 fromthe basinperimeter,
the second encesin permeability
ringwasat 91 m andthethirdat 230 m. Mostof thewells of hydraulictestsdependonthescalethatis affectedby these
terminatedin the sedimentaryinterbed.Therefore,the LSIT
field or laboratory
experiments.
For example,if we takea
FAYBISHENKO
ET AL.
..
Flow-top
•::.:
•
:
5if-
•
•:•
Breccia
165
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:•
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ß
........:
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I
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...... :.>:-:.;.:.>:.:
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::::::::::::::::::::::::::::::::::::::::::::::::::::::
================================================
•:•:•:::.: •;.).-'•
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....................................................
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: •..••
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Figure 2. Schematic
illustrationof geologicalfeaturesandprocesses
of waterflow andchemicaltransportin fractured
basalt(left): 1-flow throughnear-surfacesoil-infilledfractures,2-fracture-to-matrixdiffusion,3-flow in a horizontal
fracture connectingvertical fractures,4-vesicularbasalt-to-massive
basalt diffusion, 5-funneling effect, 6-vesicular
basalt-to-nonconductivefracture diffusion, 7-conductivefracture-to-vesicularbasalt flow and diffusion, 8-lateral flow
and advectivetransportin the centralfracturezone, 9-lateral flow and advectivetransportin the rubble zone, and 10flow in the underlyingbasaltflow, and photoof the Box Canyoncliff fare 30m for the field site (right). The depthto
the rubble zone is 10m.
containinga fracture,the permeabilitymay be very high, but
the permeabilityof this fracturewhen determinedunderfield
conditionsmay appearto be much less,becausethe fracture
may not be connectedto the main water pathway.In addition
to the effects of the flow geometryand lithology, the flow
processes
in the vadosezone are alsocontrolledby variations
in moisturecontentand permeabilityof boththe fracturesand
matrix (Mantoglou and Gelhat, 1987a,b). Becausethe relationshipbetweenmoisturecontentand permeabilityof partially saturatedrocks is nonlinear(Pruessand Tsang, 1990;
Persoft and Pruess, 1995), the flow processesin the vadose
zone are alsononlinear.It is known from the theoryof nonlinear dynamicsthat a combinationof severalnonlinearprocessesmay lead to chaoticvariationsof the systemparameters
(Abarbanel, 1996; Tsonis, 1992). In such systems,small
changesin initial and boundaryconditionsmay createnew
macro-flowstructuresfor differentflow processes
with no ap-
parent scaling principles involved (Gleick, 1987; Haken,
1983).
Becausea variety of flow and transportprocessesoccurin
different pans of the fracturedbasalt and rubble zones,the
overall systemis complex,requiringcomplexmodelsto describeit. In order to obtain realistic data to developand calibrate such models, it is necessaryto use the proper instrumentation consistentwith the nature of the hydrogeological
processes
that controlthe behaviorof the total system.However, we face the problem of an inconsistencybetweenthe
scaleof measurementsandthe scaleof flow and transportprocessesin fracturedbasalt.For example,the radiusof influence
for singleprobes(e.g., tensiometers,
suctionlysimeters)used
to monitor flow and contarninanttransportin the vadosezone
is aboutto 30-40 cm. Obviously,this is much smallerthan the
rock volume being characterized.Thus, singleprobesusedto
investigatestronglyheterogeneous
and fracturedrocks
166 MULTI-SCALE INVESTIGATIONS OF LIQUID FLOW
reveal a limited volume, and the collecteddata may not be
representativeof the total system.
As the investigatedrock volumeincreases,additionalpoint
measurements
over largervolumesmay not improvethe characterization of the medium. This is because the number of
monitoring points is limited in a practical sense,and these
pointsmay be locatedin differentpartsof the system,which
are not hydraulically connected.To determinehow well the
point measurementsrepresentthe system,we need additional
independentinformation.A promisingmethodfor obtaining
this informationis to combinepoint-typemeasurements
with
geophysicalmethods, such as GPR and ERT. GPR can be
used to determinethe spatial distributionof wetted zonesin
basaltbetweenboreholesthat are separatedfrom 2 to 4 m, but
cannotbe used in monitoringthe dynamicsof fast fluid flow
in individualfractures(as will be shownbelow in Section7).
The hydraulic propertiesof saturatedgeologicmedia are
known
to correlate
with the scale of observations
from the
undergroundopenings;(2) film flow (Tokunagaand Wan,
1996) and water meanderingalong a fracturesurfacein laboratory experiments(Suet al., 1998); and (3) water dripping
within flow channels,or flow intermittencealong a fracture
surfacein laboratoryexperiments.The size of the elemental
componentis from a few centimeters
to 10-20 cm.
Small-scalecomponentsincludea volumeof rock within a
singlebasaltflow with one or a few fractures.Resultsof field
local experimentson this scalecan be usedto describein detail someof the flow and transportprocessesin one or a few
intersectingfractures.Small-scaleinfiltrationexperiments
are
conductedto investigate fracture-matrix interaction,water
drippingphenomena,and small-scaleaveragingof flow rates
and water pressuresmeasuredin fracturesand matrix. The
areal extent of small-scalecomponentsis approximately0.5-1
m2'
Intermediate-scale (mesoscale)componentsinclude the
volume of rock within a basalt flow involving all types of
laboratoryscaleto thousandsof meters(Dagan, 1989; Gelhar, fractures,includingthe fracturedflow top, denseflow interior,
the less fracturedflow bottom and fracturesintersectingthe
1993; Neuman, 1990; 1994; Molz and Boman, 1995). However, the approachusedfor scalingof saturatedhydraulicpa- basaltflow and rubble zone. The resultsof field experiments
rametersmay not be applicablefor the unsaturatedfractured at this scalecan be usedto describevolumeaveragedflow and
basalt,because:(1) differenthydraulicprocesses
governflow transportprocesseswithin a single basalt flow. The essential
on different scales,and (2) the scaleof measurements
in the issueis the studyof movementin the fracture-networkwithin
vadose zone (using point-type, near-borehole,and cross- a singlebasaltflow. We also studyother basalt-flowfeatures
boreholemeasurements)is inconsistentwith the scaleof flow
suchas vesicularor massivebasalt,fracturezonesin the upper
processesin the field. Heffer and Koutsabeloulis(1993) de- and lower fractured colonnade,and the central fracturedzone
terminedthat despitethe presenceof a scalingrelationshipfor or entablature.The areal extent of intermediate-scale
compothe fracturefrequencyand the fracturetracelengthsfrom sin- nents
isapproximately
10-100m2.
Large-scale (regional) componentsinvolve the volume of
gle cores to thousandsof meters, the scaling of hydraulic
propertiesdeterminedfor smalldimensionscannotbe applied rock containingseveralbasaltflows and the rubblezonesbeto the larger dimensions.Thus, in order to provide a proper tween them. At this scale,we can study flow in the fracture
which are
descriptionof the processesgoverningflow and transportin networksand regional hydrogeologicalprocesses,
basalt, we use a hierarchy of scaleswith appropriatemodels affected by the network of vertical and horizontal rubble
zones,as well as sedimentaryinterbeds.The areal extentof a
and methodsof investigation
3.2. The Conceptof a Hierarchy of HydrogeologicalScales
The conceptof a hierarchyof scalesfor investigationof
fracturedrocks is basedon the assumptionthat the whole system is composedof a numberof components
that behavedifferentlyon differentscales.In describingflow problemsin basalt, we proposea four-level hierarchyof hydrogeological
components,
which includeselemental,small-scale,intermediate-scale,and large-scalecomponents.
The relationshipbetweenthesecomponents
is illustratedin Figure3.
Elementalcomponents
of the flow systemincludea single
fractureor a block of porousmedia (matrix). Elementalcomponentscan be studiedusingsmall laboratorycores,fracture
replicas,or point-sizeprobesunderfield conditions.
Resultsof
experiments
on this scalecanbe usedto describethe detailsof
specificflow and transportprocessesin fractures,matrix, or
fracture-matrix interactions(Ho, 1997). Some examples of
these flow processesare: (1) water drippingfrom a fracture
under field conditions in boreholes,tunnels, caves, and other
large-scale
component
usually
exceeds
1,000m2.
To analyzethe time-seriesdata setsobtainedfrom monitoring water-dripping phenomenain laboratory and smallscale field infiltration tests, we use the methodsof nonlinear
dynamics,describedbelow.
4. USING
NONLINEAR
ANALYZE
DYNAMICS
TIME-SERIES
METHODS
DATA
TO
SETS
A conventionalmethodfor analyzingtime-seriesdatais to
conduct a Fourier type analysis,which decomposesa signal
into different frequencycomponents.This methodis effective
for linear systems,but the resulting frequencycomponents
may appear as noise for deterministic-chaoticfunctions
(Abarbanel, 1996), becausethere are an infinite number of
frequenciescomprisingchaoticmotion. The Fourier transfor-
mationis usedto analyzetime-varyingscalarsignalswith no
assumptionaboutthe underlyingphysicsof the processes.
In
contrast,the methodsof nonlinearanalysisassumethat (1)
FAYBISHENKO
ET AL.
167
Coring
Sample
Small
Scale
0.5-1 sq.m
.
Intermediate
Scale
.
."....- -10-100
.....
sq. rn
?:•:"
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•:""
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>
Large
1000
Scale
sq.
m
......
;-, ...:-;•..
--:.:.. ;........
. ..:.:
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..-..:-*;:•
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.:.-',•;-. :,::•11;•:•:.•1Ji•..•.•½S:..-:'
:,:•!r•.,-•;•:•::s'•
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.............
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:..•:•
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......•':•'":'%½E'/:2.•;?;•!!-,,::?.iE•?x?:•;;.???•.•:';¾??:"
:"•'•/•;;•:?:;;*'"•'
":'::
.................
'"'":
..................
'..............................
Sediment
"'::':'"'"
.:
.":"ß '
Interbed
Figure 3. A four-levelhierarchyof scalesof hydrogeological
components
in fracturedbasalt.
time-varying function containsinformation about the processesaffecting this function, and (2) multi-dimensionalvectors describethe time evolutionof the function.The spacein
which these vectors evolve is called a state space or phase
space, for which the dimension is an integer (Abarbanel,
1996).
In unsaturatedrocks, useful phase-spacevariables are
moisturecontent,water pressure,and flow velocity,which depend on each other in a nonlinearfashion.Another variable,
that one can measuredirectly in laboratoryand small-scale
field experiments,is a water drippingfrequency.The nonlinear flow processesin the fracturedrock vadosezone are subject to chaoticfluctuations,implying that trajectoriesthrough
phasespacemay not be steadyor periodic.Furthermore,becausethe vadosezoneprocesses
are dissipative,the volumeof
a phasespaceoccupiedby the trajectoriesdecreases
with time.
For such a system,the basic idea behindthe nonlineartimeseriesanalysisis to reconstructthe phase-space
and then plot
an attractorin the phasespace.The attractoris a set of points
in phase-spacetoward which nearly all trajectoriesconverge
(Grassbergerand Procaccia,1983). In other words, the attractor describesthe typical systembehavior. An attractorfor a
chaoticsystemoften has a fractal structure,and it is called a
strange,or chaotic,attractor(Moon, 1987).
Becausethe phase-spacevariablesdependon each other,
the time-seriesanalysisof any one of thosevariablesmay give
us an understandingabout the physicsof the whole system.
Therefore, we choosea single scalar variable P (e.g., water
pressure,drippingfrequency)and plot its trajectorythrougha
pseudo phase space whose dimensions are P(t), P(t+x),
P(t+2x), ...P(t+(n-1)x). In orderto plot the attractor,we need
to determine the correlation time, x, which is the time interval
betweendata pointswhen the relationshipbetweenthe points
almost vanishes,and the embeddingdimension,n, of the attractor. The embeddingdimension is the dimensionof the
pseudophasespaceneededto unfoldthe attractorof a nonlinear systemfrom the observationof a scalarsignal.That is, it is
the number of coordinatesrequired in order that the
168 MULTI-SCALE INVESTIGATIONS OF LIQUID FLOW
containsa deterministic-chaotic
componentin otherwiserandom-lookingtime-seriesdata(Moon, 1987).
Chaotic phenomenaare commonin the fields of physics,
ecology, biology, economics,geology, etc. (Tsonis, 1992).
However, the claims for chaosin hydrologicsystemshave to
be carefully assessed,
becausethe numberof observationsare
often limited and not sufficient to calculatediagnosticparametersof chaos(Pasternak,1996). Despitethe fact that we
cannotpreciselyidentifyall factorsandprocesses
affectingthe
system,we can determinethe systemboundswithin which the
system is supposed to behave over long periods of
time.Identifying the chaotic nature of a systemenablesthe
determination
of the number of variables that must be meas-
ured to define behavior. It also indicatesthat for chaoticsystems, which are sensitiveto initial conditions,only short-term
predictionsof the time-trendof the datafunctionsare possible.
Long-termpredictionsof the time-seriesof the data functions
are not possible,but the attractorscanbe usedto determinethe
boundsof the parameterscharacterizingthe long-termbehavior of the system.
5. LABORATORY
INVESTIGATIONS
FRACTURE
OF FLOW
IN
MODELS
5.1. TestDesign
Figure 4. Video imagesof a cycleof water drippingwithin a flow
channel along a dense basalt fracture surface mated to a
transparentreplica of the secondhalf of the fracture. Time is
given in the left-bottomcomer of eachimage.Water was applied
at 0.33 mL/hr to the top of the fracture.Fluoresceinwas addedto
the water to promotevisualizationby near-UV light. The fracture
was inclined at 20 ø from the horizontal.
composingthe attractorno longer crossone anotherin the
pseudophasespace.The methodof false nearestneighbors
(Kennel et al., 1992) is usedto determinethe embeddingdimensionof the attractor.Some diagnosticparameters(capacity dimension,correlationdimension,Hurstexponent,andLyapunovexponent)are usedto recognizewhetherthe system
Water seepagewithin a fracturecanproceedthroughchannels that undergocyclesof snapping(dripping)and reformation under low-flow conditionseven in the presenceof constantboundaryconditions(Suet al., 1998). Figure 4 showsa
cycle of water drippingwithin a flow channelalong a dense
basalt fracture surface mated to a transparentreplica of the
otherfracturehalf (Geller et al., 1996). In orderto investigate
the physicsof this time-varyingintermittentflow underlaboratoryconditions,we designeda seriesof water drippingtests
within smooth-walledand rough-walledtransparentfracture
modelshavingsub-millimeterapertures(Figure5). Water was
suppliedat constantrate througha capillarytube insertedinto
the fracturemodels.The time variationof the waterpressureat
the tube entrancewas measuredover a range of flow rates.
Video imagesof flow confirmedthatthe pressurefluctuations
occurredin responseto flow behavior,as dropsformed and
detachedwithin the flow channel (Figure 6). Pressuredata
were also acquiredfor drippingfrom the tube opento atmosphere.
5.2. TestResultsand ConceptualModel of Flow in Fracture
Models
Figure6 comparesthe time variationof pressureandcorrespondingattractorsfor the flow rate of 0.25 ml/hr for three
differentcasesof water flow througha 0.18 mm ID capillary
tube:(1) openair, (2) a constantaperturefracturemodel(0.35
mm separationbetweensmoothglassplates),and (3) a
FAYBISHENKO
ET AL.
169
2 mL/hr, smooth glass plates
PC
data
10
acquisition
•
,
,
,
,
0
:t:
9
E
[.•: ,•rsm•--•.•...•.
..•L..•.-•:,.-'.
•:•
"
943
pump
temperature
•
insulation
fracture model
939.10
939.20
939.73
939.90
939.87
939.95
939.97
drip J
.....
• drip
snaps dripformsat end snaps
of capillary tube
(a)
(b)
Figure 5. Experimentalsetupfor monitoringwater-drippingin fracturemodels:(a) The fracturemodel is 20 cm x 30
cmglassplatepairs,smoothor textured,separated
by 0.35 mm shims;themodelis inclined60øfromthehorizontal;(b)
Time-seriesof water pressuremeasuredat the entranceto the capillarytube and corresponding
video imagesof drip
formation.Note that the water threadsnapswhenthe pressureis minimal. We assumethat the weight of the water drop
overcomescapillaryforcesarisingfrom the presenceof the smallfracturemodelaperture.
002onl
O02snw2
3.
12
ß
O02mwl
2
0.$
%
200
400time
(s)600 800 1000
(a)Open
Air
200 400time
(s)600
800
(b)Constant
Aperture
(0.36
mm)
i0 200
400
600
800
1000
time(s)
(c)Variable
Aperture
(0-1mm)
Figure 6. Time-seriesdata(above)andattractors
(below)for 0.25 mL/hrflow ratethrough0.18 mm ID capillarytube:
(a) Open-airdrips,(b) Constantaperture,0.35 mm, glassplatepair,and(c) Variableaperture,0-1 mm, fracturemodel.
As the geometrysurrounding
thetubebecomesmorecomplex,themagnitudeof pressure
fluctuations
increases
andthe
attractorschangefrom noisyto moredeterministic
170 MULTI-SCALE INVESTIGATIONS OF LIQUID FLOW
Figure 7. Design of a small-scaleinfiltration test at the Hell's
Acre site in Idaho and the types of measurements
conducted:1Water level and infiltration rate in the water gallery, 2-Basaltmatrix water pressureusingtensiometers,3-Fracture-matrixwater
pressureusing tensiometers,4-Temperatureof rocks, 5-Ambient
air and water temperature,6-Barometricpressure,7-Precipitation,
8-Outflow drip intervals,and 9-Outflow volumetricflow rate in
20x30 cm pans.
able aperturefracturemodel (textured-glassplates).Comparison of the attractors-inFigure 6 showsa progressionof the
systemsfrom noisy to more deterministic-chaotic,
as the geometry surroundingthe dripping water becomesmore complex. Calculation of the diagnosticparametersof chaosconfirms that the magnitudeof the randomcomponentdecreases
and the contributionof the deterministiccomponentincreases
from the open air, to constantaperture,to variable aperture
system.Pressuredata at higher flow rates(up to 10 ml/hr) and
for larger diametertubes (0.8 mm ID) had an increasedrandom component.
These experimentsshow that under certain conditions,
flow behavioralong water channelsin a fracturemodel has a
significantchaotic component.For such systems,a deterministic-chaoticmodelwith a randomcomponentshouldbe used
to describe flow behavior.
6. SMALL-SCALE
INFILTRATION
TEST
6.1. TestDesign
The objectiveof the field investigationconductedat the
Hell's Half Acre site was to evaluateflow processeson the
meter scale(Podgorneyet al., 1997; 1999). The researchsite
consistsof an overhangingbasalt block (approximately1 m
thick and an areal extent of 2 by 3 m) on the edge of a collapsedlava tube. A singlevertical fractureis exposedat the
surface of the basalt block.
This fracture bifurcates
in the
lower part of the block, resultingin two fracturetraceson the
underside. A horizontal fracture, which intersectsthe vertical
fracture,is exposedon the face of the block, approximately25
cm from the underside.
A 40 x 80 cm infiltrationpond was built on the uppersurface of the basaltblock, surroundingthe surfaceexpressionof
the fracture (Figure 7). The site was instrumentedto collect
extensivedata setsto describeboth the temporaland spatial
variationsof the following parameters:water headin the infiltration pond, water and rock temperature,tensiometricpressuresat 14 locations,barometricpressures,infiltrationrates,
and outflow rates as water drip intervals from 20 dripping
points and as volume from 12 pans on the undersideof the
outcrop.The designof this test allowed us to investigatethe
flow processes
for elemental(e.g., water drippingat individual
drip points) and small-scale(e.g., flow rates at individual
pans)components.The water drippingrates,or time intervals
betweendrip events,canbe usedto characterizethe elemental
components.The area below the fractureis coveredwith a
grid of 20 x 30 cm pans,which are usedto collectthe water
dripping from the fracture.Each pan collectedone or more
drips,combiningseveralelementalcomponents,
averagingthe
outflow rate from the area above it. The water is routed from
the pans to bottles attachedto load cells to measurethe outflow. The outflow ratesdeterminedfrom the panscanbe used
to characterizethe small-scalecomponents.
During infiltrationexperiments,the upperboundarycondition was a constantwater level in the surfacepond.The infil-
trationtestswere run for 1 to 18 days.The drainageperiods
betweeninfiltrationtestslastedup to severalweeksto allow
for sufficient drying of the fracture space.Successivetests
startedwhenthe waterpressurein the rockwas approximately
-100 mbars.We can assumethat underthis pressurethe fractureswere dry, andthe matrix was partially desaturated.
6.2. TestResultsand ConceptualModel of Flow on a Small
Scale
We assumethat the drip ratescollectedduringthesetests
can be usedto characterize
the elementalcomponents,
while
the infiltration and volumetric outflow rates combined with
the tensiometricpressurescan be usedto characterizesmall-
scalecomponents.
In orderto providea generalunderstanding
of the flow processes,
we beginwith the analysisof dataobtained using the infiltration and volumetric outflow rates.
Typical plots of the time variationsin the volumetricinfiltration rate and outflowratesat five locationsalongthe fracture
on the undersideof the outcropare shownin Figures8a and
8b.We subdivided
thetimeof theexperiment
intotwoperiods
(indicatedthesefigures).
Period 1. Immediatelyfollowing the beginningof flooding, the infiltrationrate increases
dueto the quicksaturation
of
fracturesandinitiallyhighwaterimbibitionintothedrybasalt.
As water imbibesinto the porousmatrix, air is presumably
pushedout into the surroundingfractures.In fractures,air becomesentrappedin the low aperturezones,thus blocking
some flow pathways. This blockage leads to an overall decrease in the hydraulic conductivity of rocks and, consequently, to a decreasein both infiltration and outflow rates
FAYBISHENKO
ET AL.
171
tions. The trend of the outflow rates for Locations 8 and 12 is
"E• ....
•
• •'eriod
1
........
Period
!
.................
Elasped Time (hours)
Figure 8. Resultsof a small-scaleinfiltrationtest:(a) Infiltration
rate, (b) Outflow ratesin five pans,and (c) Tensiometerfracture
and matrix pressures.
minimum values at times between50 and 100 hours (Figures
8a and 8b). Other factorsthat couldaffectthe dynamicflow
behavior are dissolution,colloid and particle translocation,
sealing of fractures and matrix by biofilms, air pressure,
barometricpressure,swellingclays,andearthtides.Figure8b
showsthat the outflow ratesbecomenearlythe sameat all ob-
servationlocations.At this time, the water pressuremeasured
in the fractureand matrix is practicallythe same(Figure 8c,
tensiometers
2,4, and 5), which indicatesno flow betweenthe
fracture and matrix. Note that tensiometer9, which is located
differentbecausethey are situatedoutsideof the footprintof
the pond.The magnitudeof the flow rate increaseat different
locationsalongthe fractureis quitevariedandis accompanied
by significanthigh frequencyflow-ratefluctuations.
In general,it can be seenthat smallvariationsin the minimum valuesof the flow rate (between50 and 100 hoursduring
Period 1) may lead to a wide range of flow ratesthereafter.
This showsthat flow is quite unstablein time and space.The
cumulativeoutflow throughfractureswas about 60% of the
cumulative inflow, indicating that the remainder was presumablyimbibed into the matrix, trappedin dead-endfractures,or lostto evaporation.
Figure 8c showsthat despitean initial rapid increasein
flow duringPeriod2, the trendof the increasein tensiometric
pressure
remainedessentially
the sameasthatduringPeriod1.
This indicates that the saturation of the matrix continued with
time, but the rock was not fully saturated.It is importantto
note that tensiometersare not able to reflect rapid, highfrequencyfluctuations,
whichwereobservedfor thisflow rate.
Furthermore,under field conditionstensiometersmay not detect a positivewater pressure,which is likely to developin
fracturesunder pondedconditions.This occursbecausethe
poroustip of the tensiometeraveragesthe pressureover the
volume of the tensiometer(Finsterleand Faybishenko,1998),
which is connectedto both fractureand the adjacentunsaturated rock matrix, resultingin a negativecapillary pressure.
Despitethese limitations,the water pressuretrends(Figure
8c), combinedwith the flow rate data(Figures8a and 8b), indicate:(1) a rapid fracturesaturation
just after the beginning
of flooding,(2) waterimbibitionintothematrix,and(3) water
flow throughfractures.
An analysisof theresultsof waterdrippingobserved
at one
of the drip points,Drip Point 6, is shownin Figure9. A random-lookingtime variationof water-dripintervalsis shownin
outsidethe footprintof the infiltrationgallery,alsoshoweda Figure9a. The analysisof thesedatashowedthatthe optimum
decreasein water pressure.
time delayx = 3, andthe dimensionneededto unfoldthe atSubsequently,
the flow rate increases,presumablyas en- tractoris n- 5. Figure9b showsa three-dimensional
attractor
trappedair dissolvesinto moving water and is removedin with a definitestructure.The spreadof pointson the attractor
both free and dissolvedphases.An identical flow behavior revealsthepresence
of a combination
of bothchaoticandranwas observedin soils in the presenceof entrappedair (Fay- domcomponents
for thefrequency
of waterdrippingfromthe
bishenko,1995). Comparisonof Figures8a and 8b showsthat fracture.
duringPeriod 1, the trend and magnitudeof the volumetric
outflow rates are different from those of the infiltration rate.
The simultaneous increase in the flow rates and tensiometric
pressure
(Figure8c) supports
thehypothesis
of increasing
rock
saturation.
The
flow
rates
increased
until
the
saturation
reacheda critical value, andmostlikely someflow pathswere
opened,at whichtimethe flow rateincreased
drastically.
This
changeis shownin Figure8a asa boundarybetweenPeriods1
and 2.
Period 2. During Period2, the patternof the infiltration
rate is identical to that of the volumetric outflow rates for Lo-
cations2, 3, and 8. This correspondence
indicatesa directhydraulic connectionbetweenthe surfacepond and theseloca-
7. INTERMEDIATE-SCALE
THE
BOX
INFILTRATION
CANYON
TEST AT
SITE
7.1. TestDesign
The field investigationat the Box Canyonsite was conductedin orderto developa conceptualmodelof the geometry
andphysicsof flow andtransportat the intermediate
scale.We
investigated
a fracturepatternat the Box Canyonoutcropand
conducteda seriesof pondedinfiltrationtestsat the centerof
the basaltflow about30 m away from the outcropexposure
(Faybishenkoet al., 1998b; 1999). Becausethe spacingbetween the largestbasaltcolumnboundingfractures
172 MULTI-SCALE
INVESTIGATIONS
OF LIQUID FLO-
terminedusingneutronlogging,groundpenetratingradar,and
ER tomography.
(a)
i
;•
40
7.2. ConceptualModel of the Geometryof theFracture
Pattern
35
•
30
ßm
2õ
.i,
0
I
I
I
50
100
150
200
Time (min)
(b)
..
.. 'i
ß
Figure 10 showsa map of the Box Canyonoutcrop.In the
upper-2/3 of the flow thickness,the joint spacingincreases
with depth. The base of the basalt flow showsan inverted
fracturepattern,in which the lower basaltcontactcontainsa
smallerfracturespacingthan in the centerof the flow. At the
exposedupper surface,the spacingis as small as 0.3 - 0.5
meters. The upper 2/3 of the basalt flow has more fractures
than the lower 1/3. In some basalt flows, a region near the
centerof the flow containshighly fracturedrock that doesnot
displaythe typical columnarstructure(Long andWood, 1986;
Tomkeieff, 1940). The fracturemap in Figure 10 showsthat
the central fracture zone can be seen below the infiltration
•+ 35, . ..:....:,•57;•-•.•
i'"..::':i, i ..:""
*-'30t' : '"•"
:'".',•.
,:.;':?•?,':
: ß
25• ';':"'"'
"'•••k;;.:...>'..
40"--,....'"""
35-""• ' '"•½.
½";.•,"35
t+2 30 "'---•30 t
25 25
Figure 9. Variationsof time-intervalsof water dripping:(a) timeseriesdata (only first 200 points are shown), (b) a 2D attractor
usingx = 2, which was plottedusing2,000 points.
corresponds
to the diameterof largestbasaltcolumns)is as
large as 4 - 4.5 m, we constructeda 7 x 8 m pond. We assumedthat all types of fracturesexist beneaththe pond, including at least a few fracturestransectingthe entire basalt
flow. Monitoring of water flow and tracertransportwas conducted in 38 vertical and slant boreholes,which were instru-
mented using tensiometers,suctionlysimeters,electricalresistivity (ER) probes, time domain reflectometry (TDR)
probes, and thermistors.Water-contentdistributionwas de-
site.
The map shownon Figure 10 was usedto constructa 2D
conceptualmodel of the geometryof the fracturepattem(Figure 11). This model is basedon the assumptionthat there are
four generationsof vertical column-boundingfractures.Starting from the surface,the two smallestbasaltcolumnsof sizen
(lst generation)merge into a columnof size 2n (2nd generation). Below this, two columnsof size 2 n merge into a column of size 4n (3rd generation),andthen two columnsof size
4n mergeinto a columnof the size 8n (4th generation).Visual
inspectionof severalbasaltoutcropsin the field showedthat
every set of vertical fracturesis connectedthroughhorizontal
vesicularlayersand fractures,which are includedin the model
as well. In addition,Figure 11 showsthe presenceof some
dead-end,or nonconductive,fractures.However, at this time
we do not have a quantitativeevaluationof dead-endfracture
spatialdistribution.
7.3. ConceptualModel of Flow
FieM Observations.
During floodingat the surface,the upper 30-60 cm of vesicular,highly weatheredbasaltbehaves
INFILTRATION
POND
5m
Figure 10. Fracturemap of the basaltflow outcropat the Box Canyonsite locatedabout30 m from the researchsite.
Figure showsthat the width of the infiltrationpondwas abouttwice as much as the width of the largestbasaltcolumns
(Faybishenkoet al.,
FAYBISHENKO
Horizontal Distance (m)
-1
I
3
5
7
9
2
ET AL.
173
identify a priori which fractureswill transmitwater and contaminantsduring an infiltrationtest.
A complex flow geometrywas observedusing the GPR
survey. Plate 1 showsan example of the radar velocitiesbetweentwo boreholeslocatedfour metersapartjust outsidethe
pond. This figure also shows generalizedlithological and
fracturelogs for thesewells. The red color indicatesa low radar velocity associatedwith higher moisturecontent,and the
blue color indicatesa higher velocity as affected by lower
moisture content. This could indicate either drier conditions or
4
v
E
6
8
10
12
Figure 11. A conceptualmodelof the fracturepatternshowing
the vertical(VF) and horizontalfractures(HF), centralfracture
zones(CFZ) , rubblezone (RZ) and dead-endfractures(DEF).
The locationsof dead-endfracturesarearbitrary.
more or lesslike a uniformly saturated,porousmedium.A series of infiltrationtests(Faybishenkoet al., 2000) showedthat
theinfiltrationrateintothe subsurface
decreased
exponentially
with time accordingto Horton'smodel (Horton, 1940). The
near-surface
basaltis supposed
to be subjectto sealingby biofilms, soil particles,and entrappedair that can reduce the
fractureand matrix permeability.As the infiltrationflux decreases,the fracturesbelow 30-60 cm, which were saturatedat
the beginningof flooding,may laterbecomedesaturated.
Becauseof the complexityof the fracturenetwork, it is
possibleto have the effectsof both divergenceand convergenceof flow pathsin differentpartsof the basaltflow. An
importantfactoraffectingwaterflow in basaltis the funneling
that developsas a result of the convergence
of flow paths
causedby the decreasein the numberof conductingfractures
with depth.At the sametime, drasticvariationsin permeability of fracturesandmatrixmay createa significantdivergence
of flow pathsand a significantdispersivityeffectfor chemical
transport.This processdecreasesthe tracer concentrationin
the rubblezone,whichwas investigated
duringthe infiltration
testsat Box Canyon (Faybishenkoet al., 1999). We assume
that dead-endfracturesmay accumulatecontaminants
thatwill
diffuseovertime intothe matrix.However,it is impossible
to
lower porosityin the rocks.This figure showsthree horizontal
low-velocity zones,presumablywetted zones, locatedin vesicularbasalt and the central fracturezone. We hypothesize
that subvertical column-bounding fractures connect these
horizontal zones and extend below them to the underlying
rubble zone. Unfortunately,individualfracturescannotbe resolvedby the GPR tomogramsbecauseof the small volumeof
the fractures.Assuming an apertureof 1 mm and a fracture
spacingof 2 m, the effective fractureporosityis 1 mm/2 m =
0.0005, which is quite small comparedto the matrix porosity
(-5%). Therefore, we cannotexpect such small fracturesto
show up on the tomogram, even though they are the main
conduits for water flow under both saturated and unsaturated
conditions.
Field investigationsshowed that becausethe number of
probesis limited, the resultsof measurements
are usually incomplete and are significantlydependenton the type of instrumentation.
For example,tensiometers,
ER and TDR provide "point"-type,passivemeasurements
overthe lengthof the
sensors,
whichis usually5-20 cm, andtheydetectwateronly
if watercontacts
theprobe(Figure12).Neutronloggingof the
moisturecontentand water samplingwith suctionlysimeters
provide small-scale,near-boreholemeasurementswithin dis-
tances of 30-40 cm from the borehole. The cross-borehole ra-
dar tomographyand electricalresistivitytomographymeas-
urements,which are effective over a distanceof 2-4 m, can
provideimportantinformationon the relativemoisturecontent
within fracturedzones,but the resolutioncannotprovideinformation about flow in individual fractures. Because infor-
mation abouttheseflow processes
providedby field meas-
urements is limited, we supplementedthe field data with
mathematicalmodeling to investigateflow and chemical
transport.
Modelingof WaterFlow and TracerBreakthrough
Curves.
We generateda relativelysimple2D numericalmodelusing
the numericalsimulatorTOUGH2 (Pruess,1987; 1991) to
simulatewater flow and conservative
tracermigrationunderneaththe Box Canyonpond (Doughty, 1998). We createda
verticalcross-section
modelof 20 x 20 m in extent,usinga
regularrectangulargrid with a 0.5-m grid spacing(as shown
in Plate2a). The flow properties
of themodelwereassigned
usinga deterministic
approachdesignedto approximately
duplicatethe fracturepatternandtypesof rocksobservedat the
Box Canyoncliff face (Figure 10). Gridblocks
174 MULTI-SCALE INVESTIGATIONS OF LIQUID FLOW
(a)
I
2
3
Pond
0
distance(m)
•.
4•
Typesof Rocks
.....
and Fractures
. ;...:..-•
-
' Maasive Basalt
.
Soil
.
,• - %
Vesicular Zone
Other Fractures
Horizontal Fracture
SecondaryVerticalFracture
fracture
Central Veaicular Zone
MajorVedicalFracture
•,•;•,."••-• 0 ......
4
zone
Rubble Zone
vesicular layer
lB :•;.,-_.•:.:.
•
vesicular layer •.......:*
vesicular layer
7
fracture
Central Fracture Zone
single fractures
3
,.
Dis•nce along•nd Diagonal(m)
(b)
zone
----1
.8
-
--4 ..........
4..........
• ..........
•----
lO
rubble
zone
.4
.2
85
9O
95
lOO
Velocity (m/ns)
Plate 1. An example of the radar velocities between two
boreholeslocatedfour metersapartjust outsidethe pond.The red
color indicateslow radarvelocityzonesassociated
with a higher
moisturecontent,and the blue color indicateshigher velocity
zones with a lower moisture content.-The field data were taken in
October 1998 by K.H. Williams, and the data inversionwas
conductedby J. Petersonof LBNL.
.o!•
0
..x,r,.... ;: ....
5
10
'! ,,
15
20
Time (Days)
Plate 2. The geometryand typesof rocks(a) usedfor the 2-D
modelingof Box Canyon infiltrationtest, and breakthrough
curves(b) obtainedfor different locations.Location numberson
plate(a) correspond
to numbersof breakthrough
curveson plate
FAYBISHENKO
ET AL.
175
of the fracturepattern,includingthe fracturesaboveand below the monitoringlocation.
Summaryof theconceptual
modelofflow. Thetree-typeof
the intra-basaltflow fracturepattern,which can createflow
funneling,andthe chaoticnatureof flow processes
discovered
on the elementaland small scalessupportthe hypothesisthat
flow andtransportin basaltat the intermediate-scale
canalso
be chaotic. At the same time, the limited number of singlepoint probesusuallyavailableto monitorintermediate
scale
field experiments
cannotbe expectedto explicitlyrevealspatially chaoticflow characteristics,
whichmay occurasa result
of a fractalflow-pathstructure(BartonandLarsen,1985;Cox
andWang,1993;FedderandJossang,
1995;HardyandBeier,
1994). Furthermore,for the observations
at the intermediate
scale,processes
all alongthe flow pathfrom the pondto the
monitoringpoint affect behavior,leadingto higherattractor
Figure 12. Schematicpresentationof types of measurements
in
andprecludingunequivocal
identification
of chaos
fractured rocks using: 1- Point-type, passive, probes dimensions
(tensiometers,
ER andTDR) of a 5-20'cmsize,whichdetectwater in time-seriesdata.Therefore,we believethat the optimalway
only if water contactsthe probe; 2-Near-boreholemoisture to analyzethe field monitoringdatais to simulatethe geomecontentmeasurements
usingneutronlogging,and water sampling try of the fracturepatternwith deterministic
models(suchas
usingsuctionlysimeterswithin the distanceof 30-40 cm from the those shown in Figures 11 and 14a), along with stochastic
borehole;and 3-Cross-boreholeradar and 3D ER tomographyon
models of hydraulic parameters(Mantoglou and Gelhat,
the distanceup to 10-12 m.
1987a,b;Yeh et al., 1985) for the differenttypesof fractures
vertical fracturesare assignedhigh vertical permeabilityto
allow preferentialflow throughthe fractures,low horizontal
permeabilityto limit fracture-matrixflow, and small porosity
to accountfor the small apertureof the fractures.For gridblocks representinghorizontal fractures,the assignmentof
horizontalandverticalpermeabilityis reversed.
The processesthat were modeledincludedwater and air
flow, as well as transportof a conservativeliquid tracer.The
pond was treatedas a constantheadand concentration
boundary. Plate 2a showsthe locationsof the monitoringpointsfor
tracer breakthroughcurves (BTCs). Plate 2b shows a wide
rangein the behaviorof the BTCs. For example,Curves1 and
4 showsharppeaks,suggesting
stronglypreferentialflow with
a small fracture-matrix interaction.Curves 2, 3, 5, and 7 show
longtails, suggestingsignificantmatrix diffusion.Curves4, 5,
6, and 7 show double humps, suggestinga convergenceof
multiple flow paths. This modeling of breakthroughcurves
thusconfirmsthe notionthat fracturenetworkgeometry,along
with the type of rocks in which the fracturesare imbedded,
determinesthe overall patternof flow and transport.Results
from the modelingof moisturechanges(Doughty, 1998) are
consistentwith field observationsand showthat verticalpreferential flows occur primarily along the column-bounding
fractures. A slower imbibition occurs into the surrounding
rock matrix. Layers and lensesof vesicularbasalt,the central
fracturezone, and the rubblezone provideconduitsfor lateral
flow of both water and air, resulting in the wide variety of
BTCs
seen in Plate 2b. The character of the BTCs does not
show a correlationwith depth or lithology of the monitoring
point.Rather,the BTCs are dependenton the overallgeometry
and rocks.
8. LARGE-SCALE
INFILTRATION
TEST AT THE
RADIOACTIVE
WASTE MANAGEMENT
COMPLEX
8.1. TestDesign
The LSIT, which was conductedsouthof the RWMC at
the 1NEEL,wasprobablythe largestinfiltrationtesteverconductedin the United States.It was designedto assessflow and
transportphenomena
at the scaleof severalbasaltflows,separatedby rubblezones,betweenthe surfaceanda sedimentary
interbedat a depthof 55 m. An areaof approximately
26,000
m2wasfloodedfora monthusingwaterthatwaspumped
from
the underlyingEasternSnake River Plain aquifer and then
piped into the 183 m diameterinfiltrationbasin(Wood and
Norrell, 1996). After 6 days of flooding, severalshort-lived
radioactivetracers,as well as a NaBr tracer,were addedto the
infiltration basin. The total volume of water suppliedto into
the pond was 134 million liters. After mixing was accomplished,no waterwas addedto the basinfor 11 dayswhile the
tracerpulse infiltrated.The total durationof the infiltration
test was 7 months.Subsurfacemigrationof infiltratingwater
andtracerswas monitoredby severaltechniques(as described
below).
The monitoringwell networkconsistedof 70 wells combined in 16 clusters,as shownin Figure 13. Given the hetero-
geneous
natureof the fracturedvadosezone,it wasanticipated
that we would be able to detectpreferentialflow and lateral
spreadingof water alongrubblezones,as well as the formation of perchedwaterbodiesabovethe sedimentary
interbeds.
The arrangement
of wells within 100 m of the infiltration
176 MULTI-SCALE INVESTIGATIONS OF LIQUID FLOW
I
i,•o
•
i• •
n91.5m
.
.300
ft)
.X
II o.*
.........................
........
/ _•l____.
I '" ........
,,..................
.
"6o
C-Ring
• • • •02C11
••
B-Ring
•
• C04C11
•
•0
_BlOGll •-••••
•
7•
3OOO
2OOO
0
i.o;....
10
20
30
40
60
30
40
60
46OO
40O0
4000
-
3000
-
2000
-
3600
2600
3000
.
2000:
1600:
600'
::;;::;;;,:;;;;l• •:::
-600!
-
10
20
30
40
60
1ooo
!
o
6
1000
- , .............
•
::::::::::::::::::::::::::::::::::
0
10
20
0
30
40
60
GO
....
.............................
0
10
20
GC
Figure 13. General layout of the infiltration pond and the boreholemonitoringsystemduring the LSIT, and
breakthrough
curvesof Se-75(horizontalaxisis time in dayssincethe tracerwasintroducedin the basin,andvertical
axisis activityof Se-75in pCi/L) determinedin boreholesscreened
in a perchedwaterzone.
sin (in and aroundthe infiltrationbasin)provideda meansof
monitoringwater and tracersflowing verticallybeneathand
laterally away from the infiltration basin.Monitoring the subsurfacewater movementbegan immediatelyafter of flooding
started using multiple monitoring systems.The following
typesof data were collected:(a) neutronloggingto determine
changesin the moisturecontentof rocksin the near vicinity of
the monitoring wells, (b) gamma spectroscopyto track the
movementof the gamma-emittingradioactivetracers,(c) water sampling to determine water and tracer breakthrough
curves,and (d) perchedwater level measurements.
sin suggestshigh permeabilityof intra-basaltverticalfractures
and rubble
Another
zones sufficient
to transmit
all water downward.
reason for unsaturated flow below the infiltration
ba-
sin is that a near-surface, low permeable layer (crust) restricted flow into the vadose zone from the surface.Thus, the
LSIT
showed that in addition
to the effect of an intra-basalt
fracturepattern(studiedat the intermediate-scale),
we haveto
take into accountthe geometryandpermeabilityof inter-basalt
rubble zones.Furthermore,low-permeabilitysedimentarylayers can createperchedwater zonesthat inducea lateralspread
of water and contaminants.
Figure 14 showsthe arrival times forwater at different
depthsof the vadosezone, which was determinedusingneuDespitethe expectationof somelateral flow, no water or tron logging. This figure also includesthe arrival times into
tracer was observedin boreholesbeyondthe footprint of the openboreholesscreenedat the depthof 55 m, indicatingthe
infiltration pond exceptfor perchedwater that formed on top incipientformationof perchedwaters.The left dashedline in
of the sedimentaryinterbedat a depth of 70 m. The perched Figure 14 showsthe first arrival time for water at different
water moved down the slopeof the interbedthrougha wide- depths.From this figure, the velocityof the downwarddistrispread rubble zone immediately above the low permeable butionof the wetting zone is from 10m/day(at a depthof 6m)
sedimentaryinterbed.The fact that infiltratingwater was not to 2 m/day (at a depthof 50m). Smallerscalesof observation
observedin partially saturatedfracturedbasaltoutsidethe ba- would have to considerlocal hydrogeologicfeaturesthat
8.2. TestResultsand ConceptualMode/of Flow
FAYBISHENKO
ET AL.
177
trix. Small laboratory cores, fracture replicas, or point-size
measurements collected under field conditions must be used in
• 08
o oßßß
10
OBo 6> ß
o-o
\7o
20
•30
•o
4O
•ø o
oo o
50
o Water
arrival
ß Tracer
arrival
__
o
Depth= 15.654Time
ø58
0
10
20
30
40
Water and tracer arrival time (Days)
Figure 14. The relationshipbetween the time of water arrival
(determinedfrom neutron logging) and the Se-75 tracer arrival
and depth during the LSIT. Note that the tracer arrival is
theseinvestigations.The size of measurements
is from a few
centimetersto 10-20 cm. Laboratoryinvestigationsof flow in
a single fracture in basalt have revealedthe phenomenonof
film flow (Tokunagaand Wan, 1996) as well as water channeling and meanderingalongnarrowpathwayson the fracture
surface(Suet al., 1998). Laboratoryexperimentsusingcapillary tubesinsertedinto fracturereplicashave shownthat water
does not flow uniformly along a fracture surface,but flows
intermittently with dripping occuring along flow channels.
The drippingand meanderingwithin the fracturesgenerates
nonperiodicfluctuationsin water pressure,which are not stochasticin nature. The pressurefluctuationscan be described
using deterministic-chaotic
models with a certain stochastic
componentthat is not a dominantfactorcontrollingthe system
behavior.
The results of studies on the elemental
level can be
used to develop a better understandingof dripping from a
calculated from the time the tracer was introduced into the basin.
accountfor wide departuresfrom the averagewetting zone
travel time of 5 m/day determined by Bishop and Porro
(1995).
Figure 15 showsa variety of tracer breakthroughcurves
observedat different locationsin the vadosezone during the
LSIT. One can see a conventional BTC near the surface,
multi-modal curves as affected by migration from different
fractures,and no tracer detectedat somepoints.Note that althoughsomelocationsbecamesaturatedquickly after the beginningof flooding,the tracerhad not arrivedafter a month.
This non-appearance
can be attributedto changesof waterflow pathwaysover time. Watermay flow into dead-end,nonconductive fractures easily, but becauseit cannot continue
flowing out of the fractures,no subsequent
tracercan flow into
thesefracturesby advection.Tracer can enterthesefractures
only by diffusionor flow throughthe surroundingbasalt,both
of which arerelatively slowprocesses.
Thus,a combinationof
the water andtracerexperimentscan be usedto identify zones
of preferentialflow and locationsof dead-end,nonconductive
• •Basin••
2. Peakat 21.4 days
1. Peakat 14.5 days
.62 rn depth
4 6 de
":tl'i !
,
10
, "",'
30
40,
20
3. No tracer observed
19.5mdepth
1000
i
50
TIME (days)
TIME (days)
fractures.
TIME (days)
9. DISCUSSION
The complex geometry of basalt flows with their intrabasaltfracturenetworksand wide variationsin the permeability of the densebasaltand highly fracturedrubble zoneshave
raisedconcernsover how flow and contaminanttransportin
such systemsshouldbe characterized.The of geologicaland
hydrogeologicalcomplexity of such systems,as well as the
uncertaintyof measurements,a hierarchyof scales,methods,
and modelsshouldbe usedto characterizeflow and transport
phenomenain fracturedbasalt.
Elementalscale investigationsare neededto studyin detail
the physicalnature of spatialand temporalcharacteristics
of
flow processes
in a singlefractureor a block of the basaltma-
5. No tracer?
4. No tracer observed
6. Peakat 25.1 days
•o
,--,
1800•
'
pt
42.? m depth
•i 37.8
rn
deplh
0
TIME (days)
•0
20
30
40
TIME (days)
50
0
10
2o
TIME
30
40
50
60
(days)
Figure 15. Types of breakthroughcurves for Se-75 activity
(pCi/L) for several locations in vadose zone below the LSIT
basin. Horizontal axis is time in days since the trace was
introducedin the basin(from Wood andNorrell,
178 MULTI-SCALE INVESTIGATIONS OF LIQUID FLOW
Infiltration
Rate
Used
as
Small-Scale
Component
DripIntervals
Usedas /
ß I
Elemental
Components
.•.•,•
..... v,:,.,••
.•.......
•-...;
.....
tors of such high dimensionthat the overall behavior of the
systemdoes in fact look stochastic(despitethe deterministic
chaoticnature exhibited on the elementalscale). Contraryto
laboratoryconditions,water pressurescannotbe measuredso
accuratelyunder field conditionsbecausesingletensiometers,
as used conventionally,provide volume-averagedpressure
measurements
for the liquidswithin porouscup (Finsterleand
Faybishenko, 1997). Thus, the averagedpressuremeasurementsdo not exhibitthe high-frequencyfluctuationsthat actually take place becauseof dripping,as is observedin boththe
field and laboratory.However, a comparisonof water pressuresmeasuredusing tensiometersinstalledin both the fracture and matrix can be used to determinethe generaltrend of
the rock saturations.The most importantpracticalapplication
of thesesmall-scaleinvestigationsis to studythe physicsand
modelsof flow taking into accountthe fracture-matrixinteraction.
Intermediate-scaleinvestigationsare conductedwithin the
volume of rock involving the intra-basalt flow fracture-
network
overanarealextentof approximately
10-100m2.A
To •ter M•
M•sum•nt
•em
Figure 16. A conceptual
modelof a field infiltrationtestshowing
water dripping, which can be considered as an elemental
component,and a collection of water into pans that can be
consideredas a small-scalecomponent.
fracture under field conditions in boreholes, tunnels, caves,
and otherundergroundopenings.However, laboratorystudies
of fractured rocks have certain limitations, becausewe cannot
determinehow to combinethe individualprocesses
in characterizingthe total system.
Small-scaleinvestigations
involvea volumeof rock within
a singlebasaltflow with one or a few fracturesover an areal
extentof approximately
0.5-1m2. Fieldexperiments
onthis
scaleconductedby Nativ et al. (1995) and at the Helrs Half
Acre site (Podgorneyet al., 1997; 1999) confirmedthat the
fracture flow includesdripping. Figure 16 illustratesa conceptual model of flow through a block of fracturedbasalt
dripping phenomenaat many locationsalong the fracture.
These locations are not stable and meander with time. The in-
tervals of water dripping from a single locationcan be describedusing a chaoticmodel with somerandomcomponent.
At the sametime, the volumetric outflow ratescombinedfrom
severaldrippinglocationsexhibit spatialand temporalinstability, with primary low frequencyfluctuationsand secondary
high-frequencyfluctuations.The fracture-matrixwater interaction and entrappedair data (Persoft and Pruess, 1995),
which are presumablythe main factorsaffectingthe spatial
and temporalflow instability,were also identifiedin several
studies(Glass et al., 1991; Lenormand and Zarcone, 1989;
Nicholl et al., 1993).
With the increasingscale of the field investigations,the
combinationof many degreesof freedommay lead to attrac-
series of ponded infiltration tests at the Box Canyon site
showedthat during flooding of the surface,the upper 30-60
cm of vesicular,highly weatheredbasaltactsmore or lesslike
a uniformly saturatedporousmedium.The infiltrationrate decreaseswith time exponentially.The fracturesthat were saturated at the beginning of flooding may become desaturated
thereafter.Importantfactorsaffectingthe decreasein the infiltrationrate into fracturedbasaltare pluggingof the fractures
by soil particles,biofilms,and entrappedair, as well as a funnelingeffectresultingfrom a convergence
of flow pathsasthe
numberof conductingfracturesdecreases
with depth.Vertical
flow occursthrough subvertical,colunto-bounding
fractures,
which interconnectthe horizontal layers of vesicularbasalt,
the central fracture zone, and the rubble zone. These highly
permeablezonesprovideconduitsfor lateralflow of bothwater and air and createa divergenceof flow pathsleadingto a
significantdispersivityfor contaminanttransport.
We assumethat the presenceof dead-endfractures,which
may trap andretaincontaminants,
will promotelong-termdiffusion of thesematerialsinto the matrix. Unfortunately,individual fracturescannot be resolvedby existing field hydrogeologicaland geophysical
methods,becauseof the smallvolume in the pore spaceof the fractures.Becausesingleprobes
can easily miss a zone of preferentialflow, field measurementsprovidelimitedinformationaboutthe flow processes.
In
this case,modelingis neededto investigateflow andchemical
transport.
Modeling showedthe importanceof taking into account
coupled processesof two-phase (water and air) flow
(Doughty,1998).Modelingalsorevealedthata differentBTC
behavior exists that reflects strongly preferentialflow with
fracture-matrixinteractionand suggeststhe convergenceof
multiple flow paths.The BTC at a given locationdependson
the entire flow path from the pond to that location and
FAYBISHENKO
ET AL.
179
stronglyaffected by the overall geometryof the path and
lithologyalongthe fracturepattern.
The practicalapplicationof the intermediate-scale
investigationis to understandthe flow processes
underneathsingle
ture, concentrations)
or determinethe rangesof theseparame-
Large-scale investigationsinvolve a volume of rock containing several basalt flows and the rubble zones between
different scales: elemental, small-scale, intermediate-scale,
tanks such as those at the RWMC
in Idaho and at Hanford.
ters.
Becausea variety of naturalconditionsaffect the hydraulic
processesin unsaturatedfracturedbasalt,field and laboratory
investigations
in the vadosezone shouldbe conductedon four
and large-scale.We find that, at each scale of investigation,
themoveranareathatusually
exceeds
1,000m2.At thisscale, differentconceptualmodelsfor flow andtransportphenomena
we can studyflow in the fracturenetworksand regionalhydrogeological
processes,
whichare affectedby the verticaland
horizontalrubblezones,aswell as sedimentaryinterbeds.The
limitednumberof singleprobesthatwere availableto monitor
the LSIT cannotexplicitlyrevealall the spatialand temporal
flow characteristicsof the vadosezone. However, the creation
of the perchedwater zoneabovethe sedimentary
interbedat a
depthof about55 m is a clear indicationof flow throughthe
vadosezone. The wide range of the times (from 10 to more
than30 days)for the waterappearances
at a depthof 55 m indicatestherewas a nonuniformflow of waterthroughthe va-
mustbe usedto explainthe observedbehavior.Becausedif-
ferent methods of measurementare needed, one can obtain
datato use in creatingmodelsdescribingdifferentflow processeswith no apparentscalingprinciplesevident. Instead,a
hierarchyof modelsis neededto discriminatebetweenthe observedflow phenomenaat eachof the differentscales.
Fluid
flow
in fractured
basalt of the vadose zone can be
considereda nonlinear dynamic process,in which the behavior, bothtemporallyandspatially,may be chaotic(Spositoand
Weeks, 1997; Weeks and Sposito,1997). The chaoticnature
of flow resultsfrom nonlinearprocesses
andthe strongspatial
dose zone. The difference in the water and tracer arrival times
and temporal variationsin moisturecontent,hydraulic concanbe attributedto changesin the flow pathwayswith time.
ductivity, and fractureconnectedness.
As a result,a nonlinear
The practicalapplicationof the large-scaleinvestigationis systemin fractured basalt can have small variationsin flow
to understand
the flow processes
and developmodelsin order parametersthat may lead to significantvariationsin the preto studythe distributedflow and contaminant
transportprob- dictedresults.The dissipativenatureof the systemimpliesthat
lems that exist under the RWMC and elsewhere at 1NEEL or
its phase-spacevolume decreaseswith time, leading to the
in the tank farms at Hanford.
formation of strangeattractorsthat characterizethe range in
which the flow parametersare expectedto change.The dy10. CONCLUSIONS
namicsof suchsystemsare sensitiveto the initial conditions.
The laboratoryand field infiltration testshave all shown The responseof suchsystemsmay includea stochasticcomthat a typical featureof flow in fracturedrocksis channeling ponentthat it is not necessarilya dominantfactorin the overthat occursat all scalesof investigation,includingindividual all systembehavior.If the stochasticcomponentis not domifractures,the intra-basaltfracturenetwork, and the inter-basalt nant, then a stochasticanalysiswill not provide useful information.
rubble-zone network. However, the instrumentationused in
We also f'md that under field conditions with a limited
laboratoryand small-scalefield conditions(in particular,to
we can detectneither
record dripping phenomena)is not practicalfor use at the numberof single-probemeasurements,
larger field scales.Field measurements
of flow characteristics the spatial nor temporal chaoticvariationsof the flow pain fracturedrocksusing singleprobes(suchas tensiometers) rmeters, and therefore, one must use conventional(i.e., nonchaotic) stochasticor deterministicmethodsto describeflow
areuncertain,becausethe locationsof the probesin relationto
the flow pathsare not preciselyknown, andtheseprobescan and transportprocesses.If the stochasticcomponentis not a
only providean averagevalue for the fractureand matrix hydominantfactor,then a stochasticanalysiswill provideincordraulic characteristics.
rect answersand shouldbe replacedby a chaoticanalysis.If
An importantfeatureof flow in the basaltvadosezone is the stochasticcomponentis significant(or if the phase-space
that the hydraulicsystemincludesboth unsaturatedand sam- dimensionis so large that the dynamicslook stochastic),then
ratedrocks.During floodingat the surface,the saturatedzones a stochasticanalysisis the most appropriatetool to use. Behave a limited and local extent within flow channels in the
causethe systemexhibitssensitivityto initial conditions,we
fracturesand vesicularzones. Single probes,which crossthe
canpredictonly the rangein whichthe flow rate is expectedto
saturatedfractures, also intersectthe matrix, and hence, these change,but not the exact flow rates. Where elementaland
probesmeasurean averagedwater pressurein the fracture- small-scalecomponentsare involved, the flow data can be
matrix system.However, it is difficult to separatethe contri- analyzedusingmethodsof nonlineardynamics.Where interbution of the fracture from that of the matrix (Finsterle and mediateand large-scalecomponentsare involved,a combinaFaybishenko,1997). Using availablemonitoringtechniques tion of deterministicand stochasticmethodsof flow analysis
underfield conditions,
we cannotperfectour knowledgeof can be used.
initialconditions;
we canonlymeasure
approximate
valuesfor
Acknowledgments.
The authorswould like to thank Michael Steithedifferentparameters
(pressure,
moisturecontent,tempera- ger for participationin the Box Canyoninfiltrationtest, Sharon
180 MULTI-SCALE INVESTIGATIONS OF LIQUID FLOW
glin for conductinglaboratoryexperiments,JanetJacobsenand Lea
dynamical conceptual model to describe fluid flow and
Cox for their help in interpretationof the LSIT data, and Karsten
contaminanttransport in a fractured vadose zone, Lawrence
Pruessand StefanFinsterleof LBNL and Tom Stoopsof INEEL for
BerkeleyNational Laboratory Report LBNL-41223, 1998.
many usefuldiscussions.
Reviewsand suggestions
for improvement Faybishenko,B., Hydraulic behaviorof quasi-saturated
soilsin the
by KarstenPruessand Curt Oldenburgare very much appreciated.
presenceof entrappedair: laboratoryexperiments,WaterResour.
This work was fundedby the Office of EnvironmentalManagement,
Res., 31(10), 2421-2435, 1995.
Office of Scienceand Technology,Characterization,Monitoring,and Faybishenko,B., Evidence of chaotic behavior in flow through
SensorTechnology CrosscuttingProgram, and the Environmental
fracturedrocks, and how we might use chaostheory in fractured
ManagementScienceProgramof the U.S Departmentof Energyunrock hydrogeology,Proceedingsof the InternationalSymposium
der Contract No. DE-AC03-76SF00098.
"Dynamicsof Fluids in Fractured Rocks: Conceptsand Recent
Advances,"
LawrenceBerkeleyNationalLaboratory,Berkeley,
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Christine
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JilT. Geller,andPaul
A. Witherspoon,
University
of California,
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Berkeley
NationalLaboratory,
EarthSciences
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Berkeley,CA 94720.
RobertK. PodgorneyandThomasR. Wood,now locatedat
IdahoNational
Engineering
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Falls,