Disequilibrium Fluid Pressures and Groundwater Flow in the Western

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 97, NO. B5, PAGES 7203-7217, MAY 10, 1992

DisequilibriumFluid Pressuresand GroundwaterFlow in the Western Canada SedimentaryBasin

THOMAS F. CORBET• AND CRAIG M. BETHKE

Departmentof Geology,University of Illinois, Urbana

Fluid pressurestoo low to be in equilibriumwith the topographyof the land surfaceoccur in Cretaceous sedimentsover muchof the westernCanada sedimentary basin. We useda numericalmodel to studythe origin of low pressurein southernAlberta and its effectson patternsof regional groundwaterflow over the past 5 million years.The model accountsfor changesin basintopography, conduction and advection of heat,cooling of pore fluid, and reboundof pore volumeduring erosion. Results show that the -3 MPa of underpressuringobserved in this region could have formed becausethe pore volume of sediments expandedslightly as Pliocene-Pleistoceneerosion removed some of the confiningload. Our calculations provide an estimatefor the upper limit for the permeabilityof Cretaceousshales on a regional scale becauseresults match observed pressures only if we assignvertical permeabilities less than 3 x 10-20 m 2 to thesesediments. Pore fluid cooledand contractedas erosionreduced the burial depth of the sediments, but this effectcould not haveplayed a significantrole in generatinglow pressureunless Cretaceous shales in southernAlberta are extremelystiff (pore compressibilitiesof the order of 6x10 -•ø Pa-•) and have regionalpermeabilities of about10 -22 m 2. In our simulations,erosion generates potential gradients that drive groundwateralong deep aquifers toward regions of lowest pressure in adjacent aquitards. Groundwater,however, moves too slowlyto transporta significantamount of heat.The observedwest-to- east increasein the geothermalgradient across the studyarea most likely occursbecause sediments that were deeplybuffed in the westare more compactedand hencemore thermallyconductive than thosein the east.

INTRODUCTION minimahave dissipated. Once the systemequilibrates, hydraulic potential reachesits minimum value at the point of lowest Givensufficient time, the distributionof fluid pressureand the elevationof the water table, not at depthin the basin. In this associatedpattern of groundwaterflow in a sedimentarybasin paperwe usea hydraulicpotential equal to the potentialdefined adjust to an equilibrium with the land surface. Equilibrium by Hubbert[1940] multipliedby fluid density;it hasthe unitsof pressurepersists if the position of the water table and the pressure. distributionof permeability,porosity, and temperaturein basin The presenceof minimain hydraulicpotential at depthin the sedimentsdo not change. Erosion can disrupt equilibrium westernCanada basin suggests to usthat fluid movementhas not pressureand the flow patternbecause it modifiesthe shapeof the yet adjustedto the surfacetopography. In contrastto this water table, the stress distribution in the basin, and the interpretation,some models of regionalgroundwater flow in this temperatureof the sediments.In this paper we considerhow basin[Hitchon, 1969a,b, 1984;Majorowicz and Jessop,1981; disequilibriumpressure (the amount by which fluid pressure Schwartzet al., 1981;Garven, 1989] assume that the present-day differs from the pressurethat would exist if the flow system patternof groundwaterflow is in equilibriumwith the surface equilibratedwith the land surface)and the correspondingpattern topography. of groundwater flow developed in the western Canada A numberof physicaland chemicalprocesses might produce sedimentarybasin. disequilibriumunderpressure. When surficial erosion or glacial Expressingthe pressuredistribution in Lower Cretaceous retreat removespart of the confiningload from sedimentsat sedimentsof the western Canadabasin in terms of hydraulic depth,the pore spacein the sedimentsexpands. Pore pressure headreveals minima (Figure 1) that appearto be closedin three decreasesas pore fluidsexpand to fill the increasedpore space dimensions[Berry and Hanshaw, 1960; Hitchon, 1969b]. Such [Russell, 1972; Neuzil and Pollock, 1983; Koppula and a potentialdistribution contrasts with thoseof groundwaterflow Morgenstern,1984]. Erosionalso decreases fluid pressureby a systemsthat haveequilibrated with th•• surface (Figure 2). (We thermaleffect [Barker, 1972; Russell,1972; Bradley, 1975]. avoid describingequilibrium flow systemsas being in steady Sedimentscool as erosion reduces their burial depth. Pressure on statebecause even a flow regimethat remainsequilibrated with the pore fluid decreaseswith coolingbecause water contracts the changingtopography of a basinvaries with time.) Minima in more than the sediment framework that contains it. Dis- hydraulic potential at depth cannot exist indefinitely. equilibriumpressure can form, even in the absenceof unloading Groundwater,which flows from high to low potential, migrates or coolingeffects, because pressure at depthadjusts slowly to radially inward toward the minima. Groundwateraccumulates, changesof surfacetopography [T6th, 1978; T6th and Millar, increasingpore pressure,and hencehydraulic potential, until the 1983].We call thistendency for changesin porepressure to lag behindchanges in equilibriumpressure the "memoryeffect." •Nowat FluidFlow and Transport Division, Sandia National Osmosiscan cause a pressuregradient across a semipermeable Laboratories,Albuquerque, New Mexico. membrane,such as a shale layer, that separatestwo ground- waters of different salinity. The process might generate Copyright1992 by theAmerican Geophysical Union. underpressurein aquifersenclosed in shalemembranes [Berry, 1960; Berry and Hanshaw, 1960]. Finally, Bradley [1975] Paper number 91JB02993. suggestedthat underpressurecould form if a stiff aquifer 0148-0227/92/91J B-02993 $05.00 enclosed in impermeable sedimentswere buried in a basin.

7203 7204 CORBET AND BETHKE: GROUNDWATER FLOW IN WESTERN CANADA

pressurethere has not yet adjustedto topographicchanges caused by Pliocene-Pleistoceneerosion (the memoryeffect). However, Neuzil [1985] questionedwhether sediments in the Red Earth regionare stiff enoughfor erosionto generateoverpressure. Magara [1976] recognizedthat unloadingduring erosion works to decreasepressure but consideredfluid coolingto be a more significantcause of underpressure.T6th and Corbet [1986] linked the origin of underpressurein southernAlberta to erosionalunloading. No completequantitative analysis of how thesemechanisms affectpressure distributions and regional patterns of groundwater flow in sedimentarybasins has been published.Senger and Fogg's[1984, 1987] simulationsof Cenozoicflow in the Palo Duro basin, Texas, are the only calculationsof which we are aware that considerthe effects of erosionon lateral flow. They ,700 foundthat unloadingduring the erosionalretreat of the Eastern , CaprockEscarpment caused underpressuring in a limitedregion 15•0krn •,• of the aquitardnear the escarpment,but the overallpattern of flow remainedin approximateequilibrium with the changing A- StudyArea topography. B.C. •" We used a numerical model to simulate in two dimensions the MONTANA effectsof erosionon porepressure and groundwater flow in the Fig. 1. Distributionof hydraulic potential in the Lower regionof southernAlberta studied by TSthand Corbet[1986]. CretaceousViking Formation [Hitchon, 1969b, Figure 4]. Cretaceousstrata in this region contain extensiveareas of Potential decreasesfrom all directionstoward the region of disequilibriumunderpressure that composea southeastward potential less than 400 m. Line A-A' is the trace of extensionof the area of low hydraulicpotential mapped by hydrogeologiccross sections in Figures4 and 5. Hitchon [1969b]. The model accountsfor modificationsof basin topography,conduction and advectionof heat, coolingof pore

Pressurein such an aquifer would remain constant,so that it DISEQUILIBRIUM would fall below the hydrostaticgradient projectedfrom the increasinglydistant land surface. Initial Surface Calculationsthat describevertical groundwaterflow have given considerableinsight into the effectsof erosionon pore pressure. Neuzil and Pollock [1983] analyzed the effects of erosional unloading on pore pressure in sedimentsof small hydraulic ii!iiiiiii!3.0 iiiiiil 2.7 i!! 2.4 iii!2.1 i::::iii 1.8iiiii::i 1.5::ii::::il 1.2iiii::i 0.9 ::iii0.6 •::•i0.3 diffusivity. Their calculationsshow that erosion at rates of severaltenths of a millimeter per year (hundredsof metersper 1 million years) can decreasevertical stressquickly enoughto reducepressure in thesesediments to severalmegapascals below hydrostatic.The magnitudeof the underpressuredepends on the rate of erosionas well as the permeability,compressibility, and thickness of the sediments. Disequilibriumpressure starts to form instantaneouslywhen its generating process begins, is reinforced for as long as the EQUILIBRIUM 500m, processcontinues, and persistsfor some time at•er the process stops. Bredehoefi and Hanshaw [1968] calculated the time required for disequilibriumpressure to decay through a thick aquitard of known hydraulic conductivityand specific storage. Tdth and Millar [1983] calculatedadjustment times for systems iiiiii'"-'•3.0•iiii::!2.7 i::!2.4 iiii 2.1 iilii! 1.8iliiil 1.5::iii::ii •1.2 !i!!!0.9 ii::i0.6 iiii'O.3 with multiplelayers. Thesecalculations show that disequilibrium pressurecan persistfor geologicallysignificant periods of time at•er generatingprocesses stop. Hence underpressure may reflect i...-...... ,...... processesacting in the presentor in the past, or both. In any case, the pressurechanges resulting from all current and past processesare superimposed[Neuzil, 1986]. Fig. 2. Calculation showing how erosion generates According to previous studies,four of the above mechanisms disequilibriumflow as it dissectsa landsurface (dashed line) that might explainthe origin of disequilibriumpressure in the western was initially flat [Bethke,1989]. Minimum potentialoccurs at Canadabasin. Berry [1960], Berry and Hanshaw [1960], van depthin the aquitard(open unit). Oncethe systemequilibrates, Everdingen[1968], andHitchon [1969b] attributedunderpressure minimum potential occurs at the lowest elevationof the water in deep strata to osmosis. T6th [1978] suggestedthat over- table. Equipotentials(in megapascals)arecontoured relative to pressureoccurs in the Red Earth region of Alberta because the surfacepotential at the right sideof the figure. CORBETAND BETHKE:GROUNDWATER FLOW IN WESTERNCANADA 7205

fluids, and changesin the pore volumeof sediments.We did not basin in southernAlberta (crosssection A-A', Figure 1). We include osmosis in our calculations because we do not know the chose this line of section for the simulations because distributiono f groundwatersalinity in the basin'sshales, nor can underpressureoccurs here and hasbeen mappedin somedetail, we adequatelyestimate the osmoticproperties of the shalesat a the present-dayflow pattern is known, and some information field scale. about recent rates and patterns of erosion is available. We Our calculationsshow that erosionover the past 5 Ma could presenthere a brief descriptionof the area'shydrostratigraphy, have significantlyaltered the pressuredistribution and flow erosionhistory, and present-daypattern of groundwaterflow; patternsin Cretaceousstrata in southernAlberta. The calcu- Tdth and Corbet[1986] give more details. lations suggestthat underpressuresformed as pore space expandedwhen erosionunloaded sediments with smallpermea- Hydrostratigraphy bilities. Groundwatercooling probably played a small role in Sedimentfill in this portionof the basinconsists of 1800 to decreasingfluid pressure.Model resultscan predict disequi- 2600 m of carbonates,evaporites, and elastics. Following T6th librium underpressuresof the magnitudeobserved in the basinif and Corbet [1986], we divide the shales, siltstones, and the vertical permeabilityused for shale aquitardsis less than sandstonesthat make up the upperhalf of the sequenceinto four about3x10 -2øm 2. If our conceptualmodel is correct,the hydrostratigraphicunits which consistof one or more rock mathematicalmodel provides an independentestimate of the stratigraphicunits (Figures 3 and 4). We assumethat each upperlimit of shalepermeability on a regionalscale. hydrostratigraphicunit behaves as a singleaquitard or aquiferat In our simulations,fluid migratesalong Cretaceousaquifers the scale of the simulation. toward the areas of most rapid erosion, where the greatest The Lower Cretaceousaquifer overlies dense Mississippian underpressurein the aquifer's confining layers occurs. Some limestonesof the RundleGroup thatwe useas the basal no-flow flow is oppositeto the regional slope of the land surface,in boundaryfor the simulations.This aquiferconsists of bioelastic contrastto what would be predictedby an equilibriummodel of limestone,calcareous shale, and fine- to coarse-grainedsand- groundwaterflow. Flow velocitiesare just a couple of milli- stone.The overlyingColorado aquitard is about500 m thick. metersper year or less, suggestingthat the fluid in these strata Like its stratigraphicequivalents over muchof the westernGreat traversedless than perhaps10 km in responseto unloading Plains,this aquitardstrongly influences the regionalpattern of during the interval of erosion. This flux was too small to groundwaterflow. It consistsmainly of Upper Cretaceous transporta significantamount of solutes,to affecthydrocarbon marine (Colorado Group) and Lower Cretaceousnonmarine migration, or to disturb conductiveheat flow from the lower (UpperMannville) shales but containsthin sandyintervals. One crust. The west-to-eastincrease in the geothermalgradient of these sandy intervals, the Bow Island Formation, has observedin the studyarea probablyoccurs because the thermal sufficientlateral continuityto be treatedas separateaquifer in conductivityof sedimentsvaries with their degree of compaction. the simulations.The Milk River aquiferconsists of a nonmarine sequenceof about 120 m of Upper Cretaceoussandstone, HYDROGEOLOGIC SETrING siltstone,and sandyshale. Over most of the crosssection the Upper Cretaceousaquitard consists of the Pakowkimarine shale, We simulatedgroundwater flow in a shale, siltstone, and overlain by argillaeeoussandstones, siltstones, and shalesof the sandstonesequence on the easternflank of the western Canada Foremost and Oldman formations. The Oldman Formation is a minor aquifer. The Bearpaw marine shale is presentunder ,, topographicallyhigh areasalong the eastend o f the crosssection •..._Bearpaw Fm. but has been eroded elsewhere. ::?•i'8'"•"•'•"'le'r•-'-:ii!ii Upper ::'':::::::::::::::::::::::::::::::::::::::::::::::::::'::::::' CretaceousPattern of Erosion

PakowkiForemost Fm.Fm. Aquitard Cenozoic erosion has stripped as muchas 800 m of Cretaceous and Tertiary sedimentsfrom the plains of southernAlberta [Magara, 1976; Hacquebard, 1977; Hitchon, 1984]. Much of ':•:•:•:•M•lkR•verFm.::•:•:•:•:•: •:•:•:•:;...... A_uifer..:.::;•;;;½;:;:•: thismaterial was removed during short intervals o f rapiderosion in Plioeene-Pleistoeenetime. Tertiary and Pleistoceneerosion ...... :.::::i::::i. formed a vertical sequenceof gravel-cappedbenches and

Colorado "• Hat::'.:'!!i CYPRESS PLAIN

Group Colorado Aquitard -- .._..... NO2BENE•..•'"' 7_• - Lower ½i!i!iiiiBow.>;.:.:.:.:.:.:.:.:.:._.._..•.•.-.-...... ;.;.;.;.:.:.'.:.:.:.:.:.;.;;;;;;;:.:Island ...... •'-'---J .. '"...... • -• NO.3BENCH Cretaceous Upper Mannville i::i::iLower Man nville :::::::::::::: 'ii•;"'""...... :':':':':':':':':•i':':[•:;:'•':';'•:'•:;':;':'•'l•':':'•': .....•'•'1";';•';';" AQ''"'•

Jurassic : :!:!:i:i:i:i:i::.:.:.:.:?....::::::::::::::::::?:::Ellis"Gi;•ij'15':;::iii::!ii::iiiii::i...... ::::::::::::::::::::::::::::::::::::::::::::::,• u re,accoo.wer u s :i:i:i:i:!. I:':"'":': ...... '/ ...... • ...... '•-'•.:"'""""•"...... ' '"'":.:'"::::::: ...... /::2:::': / \ :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::!:i:i:i:i:i:,•q Ulfe r :i:i:::::i:!:::::i!i AQUIFER AQUIFER MILKRIVER LOWER CRETACEOUS 500m[ i Mississippian'iii!i!i!: RundleGroup 20 km Fig. 3. Definitionof hydrostratigraphicunits, showing aquifers Fig. 4. Hydrostratigraphyand inferredpattern of erosionalong (stippled)and aquitards(open) [TCth and Corbet, 1986]. cross section A-A' [Tdth and Corbet, 1986]. 7206 CORBETAND BETHICE:GROUNDWATER FLOW IN WESTERNCANADA

plateausin the studyarea which Alden [1924, 1932] and obtainedfrom a potentiometricsurface map from a reportof Westgate[1968] correlatedwith similarfeatures along the hydrogeologicinvestigation [Meyboom, 1960] and from MissouriRiver drainage in Montana.Alden [1932] suggested that unpublishedrecords of water levelsthat were measuredin wells the gravel-cappeduplands are erosionalremnants of extensive as part of that investigation. land surfacesthat covered much of the northernGreat Plains. He The lowest observedpotentials occur in the Bow Island namedthe past land surfaces,from oldestto youngest,the Formation(stratigraphically equivalent to theViking Formation, CypressPlain and the No. 1, No. 2, and No. 3 Benches.The Figure 1). We assumethat pressuresin the Bow Island typelocality of the CypressPlain, the CypressHills, is located Formationrepresent pressure conditions in thecentral portion of at the east end of the cross section. It is not known when erosion theColorado aquitard and that groundwater in thisaquitard flows startedto dissectthe CypressPlain, but AMen [1932] believed vertically toward the Bow Island Formation(Figure 5). thatthe No. 1 Benchformed by the endof Mioceneor early However,the minimumpotential might actually occur above the Pliocenetime and was not greatly eroded until Pleistocene time. Bow Island Formation in the thickest shale of the Colorado Aldendated the No. 2 Benchas earlyPleistocene and the No. 3 aquitard. The potentiometric surface of the Bow Island Bench as middle Pleistocene. The No. 3 Bench correlates with Formationin southernAlberta containsonly local minima; thepreglacial land surface in southernAlberta [Westgate, 1968]. potentialdecreases toward the northand west edges of the map T6thand Corbet [1986] inferred a post-Eoceneerosion pattern (Figure6). Potentialdecreases gradually to the northbut drops alongthe crosssection (Figure 4) from erosionalremnants that sharplyto the westwhere the potentiometricsurface is as much correlatewith Alden's [1932] past land surfaces.Following as 800 m below the land surface.Figure 6 showsthat the band Westgate[1968, Figure 8], theyprojected remnants of pastland of potentialless than 400 m actuallyextends farther south than surfaceswestward. The oldestof theprojected surfaces forms a Figure 1 indicates.Presumably, the maps differ becausea topographichigh over the axisof a northeasttrending structural greater densityof pressuremeasurements in southernAlberta arch. was usedto constructFigure 6. Groundwaterabove the Coloradoaquitard flows throughthe GroundwaterFlow in the PresentDay Milk Riveraquifer and its confining layer, the Upper Cretaceous The present-daydistribution of fluid potentialreflects two aquitard.The Milk Riveris a classicexample of an outcropping importantfeatures of the groundwaterflow patternin southern confinedaquifer; it outcrops50 km southof the crosssection Alberta. First, fluid potentialwithin the Coloradois less than and plungesnorthward for about80 km, whereit pinchesout thatin theoverlying and underlying aquifers, suggesting that the [Meyboom,1960]. Groundwatergenerally flows northward from Colorado aquitard acts as a fluid sink. Second,the Milk River the aquifer'soutcrop. Water dischargesfrom the aquiferby aquiferand the overlyingUpper Cretaceousaquitard form a leakingupward across the Upper Cretaceous aquitard [Meyboom, confinedsystem which appears to haveadjusted to thepreglacial 1960] and downwardinto the Coloradoaquitard [Schwartz et al., land surface. 1981]. Closecorrespondence of the potentiometricsurface of the The potentialdistributions shown in Figure 5 for unitsdeeper Milk River aquifer with the bedrocktopography [T6th and than the Milk River aquiferand in Figure 6 for the Bow Island Corbet,1986, Figure23] suggeststhat additional recharge to the Formation are based on pressuresmeasured during drill stem Milk River aquifer occurs at topographichighs and that tests [T6th and Corbet, 1986; T6th and Rakhit, 1988]. Pressures, dischargeis focusedalong buried valleys. Flow directionsin the selectedto representvirgin conditions,were extrapolatedto UpperCretaceous aquitard shown in Figure5 wereinferred from stabilizedvalues using Horner's [1951] method.About 150 and this relationship. 725 pressurevalues were used to constructFigures 5 and 6, MATHEMATICAL MODEL respectively.Pressures in the Coloradoaquitard were measured in thin sandstonesinterbedded with the shale; we assume that The rate at whichpore pressure varies in responseto changes these measurementsalso representconditions in the adjacent in totalvertical stress and temperature in thesubsurface is given shales.The potentialdistribution for the Milk River aquiferwas by

WEST BOUNDARY i• •'OF SIMULATIONS

'--8

500rn[ 20km

Fig. 5. Observeddistribution of hydraulicpotential and flow directions[T6th and Corbet,1986]. Flow in the Coloradoaquitard converges into the regionof lessthan 8 MPa of potential. CORBET AND BETHKE: GROUNDWATER FLOW IN WESTERN CANADA ?20?

-50 ø

49 ø

I i 112 ø 111ø 30 krn Fig. 6. Distributionof hydraulicpotential of the Bow IslandFormation [Tdth and Corbet, 1986; TSthand Rakhit, 1988] in the studyarea. Contourinterval is 50 m. The potentialdistribution differs from the distributionshown in Figure 2 becausea greaterdensity of pressuremeasurements was usedto constructFigure 6.

DP (first term on the right) and the rates at which unloadingand cooling of pore fluids generatepressure. Dt We solvedequations describing fluid flow, heat transportby conductionand advection,and continuityof the rock grains for otv DO'v •Pott DT the distributionof pressure,temperature, and porosity across the • + (1) domain.The flow equationis a nonlinearform of (1) in which the coefficients4•, k, /3, /•, p, •, and at vary in magnitude. The compressibilitya• relateschanges in porosityto variation in effective stress. If the rock grains are taken to be [Domenico and Palciauskas, 1979]. Here, D/Dt is the material derivative taken in a reference frame that moves with the rock incompressible,vertical compressibilitycan be expressedas framework;P is pressure;otv is verticalrock compressibility;qb is porosity;/3is fluid compressibility;/•is fluid viscosity;k x and k• are permeabilityin the horizontaland vertical directions, O•v-- --(1--1p'•• do'e (2) respectively;p is fluid density;g is gravitationalacceleration; av whereeffective stress a. is thedifference av - P. Substitutinginto is totalvertical stress; at is the thermalexpansivity of the fluid; (1) and rearrangingyield and T is temperature. Implicit in this equation are the assumptionsthat only changesin vertical stressaffect porosity and that lateral strainis negligible. Equation(1) is the transientequation of flow commonlyused Dt = •xx • + o•z[,• k.c•z Pg by hydrogeologistsbut is castin termsof pressureand with two additional terms. The first additional term accounts for the DT 1 3•p D•re change in pressure with total vertical stress. It shows that + •Pott (3) unloadingdoes not causepressure to changeif the matrix is (1-,) at perfectlystiff (c•v=0). At the otherextreme a changeof pore pressurenearly equal to the changein total vertical stresswould In solvingthis equation,we assumethat permeabilityand occur if the matrix compressibilityis much larger than the thermalconductivity vary with rock type and porosity (Table 1); product of porosity and fluid compressibility.The second we treated densityand viscosityof the fluid as functionsof additionalterm accountsfor the change in pressurewith temperatureand pressure. temperature.It showsthat the effecton pressureis proportional During compaction,sediments at different elevationssubside to the thermal expansivityof the fluid but decreasesas the at differentvelocities. The relationshipof subsidencevelocity compressibilityof the sedimentmatrix increases. A largematrix v•,,,to changein porosityis givenby compressibilitydampens the responseto temperaturechange becausethe pore space deforms to accommodatethe fluid's 3 1 thermalexpansion. Because the thermalexpansivity o f the pore -- = (4) volume is probably much smaller than that of the fluid 03•Vzm (l--(p) at [Palciauskas and Domenico, 1982], we assume that thermal deformationof the rock frameworkcan be ignored.Equation (1) [Bethke, 1985]. If porosity is calculatedfrom a constitutive showsthat the changeof pressureequals the imbalancebetween relationship (below), (4) can be used to calculate the the rate at whichDarcy flow dissipatesdisequilibrium pressure displacementrate v•,, of nodalblocks over a time step. 7208 CORBET AND BETHKE: GROUNDWATER FLOW IN WESTERN CANADA

TABLE 1. Rock PropertiesUsed in the Simulations .6-

Value

Porosity'for shale ½o 0.55 ½• 0.05 b 6.5 x 10 4 Pa -• b.t 1.3 x 104 Pa-• sandstone Porosity'for sandstone ½0 0.40 shale ½• 0.05 b 3.9 x 10 4 Pa -• b ul 7.8 x 10-9 Pa-•

Permeability"for shale 0 I I I A 8 0 10 20 3•0 40 5•0 perm EFFECTIVE STRESS (MPa) B -21 perm kx/k• 10 0 1 2 3 4 Permeability"for sandstone DEPTH (km) A 15 perm Fig. 7. Assumedfunctions of porosityversus effective stress for Bperm -- 15 shaleand sandstone.Rocks, as theyare unloaded,do not fully k ,/ k • 2.5 recover the porositylost during compaction,so the curve is flatter (b coefficient less) if effective stress is less than the Thermal conductivityfor shale maximumthat the rock hasexperienced. Arrows show the path -1.84 ½+ 2.24 W m -• øC-• and sandstone,K, of porosity changeas the effective stresson a shale first increasesto 25 MPa, is then reducedto 5 MPa, and finally Shale fraction increases to 50 MPa. Lower Cretaceousaquifer 0.2 Colorado aquitard (exceptBow Island) 1.0 compaction.The coefficients used to calculateporosity are given Bow Island 0.5 in Table 1. Milk River aquifer 0.4 Bethke [1985] gives an equationdescribing heat transferby Upper Cretaceousaquitard 0.8 conductionand advectionby movinggroundwater. We evaluate the effect of thermalcontraction of pore fluidsby couplingthat * Coefficients are for (5) and (7). equationto (3) throughthe temperatureand flux terms. We use ** Unitof measure:square meter; log k• = Aperm½ •' Bperm.an implicit finite-difference model to iteratively couple and solve (3), (4), and the heattransfer equation. Be&ke [1985] andBelhke and Corbet [1988] providedetails of the numericalprocedure, as We used an exponentialfunction similar to Athy's [1930] applied to basins receiving sediments. We modified that equation procedureto simulateerosion and to calculatethe recoverable • = •oe-ha, + • (5) portionof porositylost duringcompaction. Each hydrostratigraphicunit in our calculationsis a mixtureof to describethe loss of porosity as effective stressincreases shaleand sandstone.We calculatethe hydraulicand mechanical duringburial. Here ½0 is reducibleporosity at smallstress, ½• is properties of the hydrostratigraphicunits by averaging the irreducibleporosity, and b is a porecompressibility defined as estimatedproperties of two such lithologies(Table 1). We use harmonicand geometricaverages for vertical and horizontal permeability,respectively. Bulk permeabilitiesobtained using b = - • (6) this averaging techniquerepresent lenticular environmentsin which the lensesare randomly distributedand not necessarily Porositylost during burial is onlypartly recovered as erosion connected. reduceseffective stress (Figure 7). Wheneffective stress is less RESULTS than the maximumexperienced by the sediment,we calculate porosity as Oursimulations start 5 millionyears ago and run to thepresent q = (•min- 0'1)e-ba/(o'e-o'max) + •1 (7) day(Figure 8). We usethe erosion pattern inferred by T6thand Corbet[1986] and assume that the CypressPlain was stable and not erodeduntil approximatelythe end of the Miocene, 5 Ma whereo m,xis the maximumtotal vertical stress the sedimenthas ago.The initial conditions for thesimulations are the steady state experienced,½ mi, is the correspondingporosity, and b,t is the flow patterndriven by the inferredtopographic relief of the pore compressibilityduring unloading. The valuesof b•t are CypressPlain and the associateddistributions of porosityand qmaller than b to reflect the hystereticnature of sediment permeability.Erosion occurs during 1- and 1.6-Ma intervals CORBET AND BETHKE: GROUNDWATERFLOW IN WESTERN CANADA 7209

INFERRED LAND SURFACE ratesare not symmetricalabout that boundary.It is locatednear 5 Ma B.P. the west edge of a high plateau (Cypress Hills) which experiencedlittle erosionduring the simulatedperiod of time. ....,,- ,--'"''"''"'"" '"' '"' '"' "' "''"' - - - -- '"•'• •' "" •'"" •• • • • • • _ However,the effecton calculationresults is negligibleabove the Colorado aquitard where topographicrelief drives flow and is small in the Coloradoaquitard where lateral flow is very slow...... '""'"""'"•'••'""•""•!:i!i:!i:::::::::::-:-:.:.:.:.:,:-:.:.:.:,:.:-:.: ' ....'.'.'.:.:.:.:.:, In order for the simulationsto reproducethe observedpressure distribution,boundary conditions below the Colorado aquitard must provide a sourcefor the water that seepsupward into the ::::i:i:i:i:::::::?:•i::•i•i•i•i•i•!•i•i•!iiiiii!i!!!i!i!!iiii!•i•i•i•i•i::iii•iii:.i::!•!•iiiiiii{!•...... ::::::::::::::::::::::•:underpressured portions of the aquitard. The potentiometric I surfaceof the Lower Cretaceousaquifer [Tdth and Corbet, 1986, ERODEDBETWEEN 5AND 4MaB.P. Figure 26] suggeststhat in the real system,this sourceis lateral flow out of the planeof the modeledsection. We accountfor the fluid that enters laterally by keeping fluid potentialsalong the • .d•..ERODEDBETWEEN1.6AND0Ma B.P. portion of eachside boundary below the Coloradoaquitard equal to the potential at the top of that side. Lateral flow acrossthe BOUNDARY•...•. lower portion of the sideboundaries also carriesheat. Using the fluid potential that occurs at the basin surface for the lower NO-FLOW:::: :::::::: ::::::::; :::::::::::""'" ::: :::::::::5:::::::: ::::::.:.:.:.. y.....,...... :..... :.:...... '/•'...... "ß':'ß':'".':":- :":::i::.:i::•i!:•:!:i:!:i:i:•:•:!:•:•:½ii:!:i:!:!:i:i:i:i:!:!:•:i:i•: portions of the side boundariesis an arbitraryway to provide a source of water and, at the same time, maintain reasonable BOUND A R Y • • ...... ::::::...... potentials in the Lower Cretaceousaquifer. Thereforethe entire I ...... '"'"'"":':':'•':':':::•:•:•:•:::':':':':':':'?F':':':':'r"'"'"'"v I Lower Cretaceousaquifer shouldbe consideredas part of the boundary condition for the simulations. These boundary Fig. 8. Mappingof the hydrostratigraphiccross section (top) conditionsallow flow processesand patternsabove the Lower onto the simulation cross section (bottom) and the assumed Cretaceousaquifer to be examinedbut provide no information patternof erosion.Vertical boundariesoccur at topographic about conditionsin the Lower Cretaceousaquifer itself. The divideson the CypressPlain. A and B are pointsat which lateralno-flow boundariesalong the Coloradoaquitard (including simulationvariables are trackedwith time in Figures 11 and 12. the Bow Island Formation) also require some comment. This boundarycondition does not accountfor lateralflow in the Bow Island Formation that either crosses the side boundaries or flows separatedby a 2.4-Ma hiatusin erosion.The first period of from out of the plane of the simulation. Therefore the only erosionremoves the upperblock of sediments,which represents driving forces for simulatedflow in the Bow Island Formation material betweenthe CypressPlain and the No. 1 Bench, in 1 are the topographicrelief of the modeled cross section and Ma. The 2.4-million-year hiatusin erosionrepresents the time erosion. The calculations do not account for lateral flow due to duringwhich the No. 1 Benchwas not greatly eroded[AMen, regional gradients in potential. We placed a basal no-flow 1932]. We simulatedPleistocene erosion (1.6 to 0 Ma before boundaryat the top of a denselimestone aquitard in the Rundle present)by continuouslyremoving the sedimentbetween the No. Group.Because the Lower Cretaceousaquifer acts as a boundary 1 Bench and the preglacialland surface.Maximum apparent conditionfor fluid flow, the most importantfunction of the basal erosion rates are 0.77 and 0.42 mm/yr during the first and boundaryis to provide heat to the basin. The conductiveheat secondperiods of erosion.Actual erosion rates in the simulations flux acrossthe basalboundary is 48 mW/m2. are slightlygreater because the sedimentsexpand somewhat as Over the course of the simulations, flow above the Colorado theyare unloaded.The patternof erosionduring the firstperiod aquitard remains in approximateequilibrium with the changing of erosion, and consequentlyerosion rates, are largely topography. Flow deeper in the basin, on the other hand, hypotheticalbecause the actualshape of the CypressPlain and deviatessignificantly from equilibriumwith the topographyfor the time that erosionstarted to removeit are poorly constrained. about 80% of the time period of the simulation.During periods We includedthis part of the simulationto examinehow flow of erosion, groundwaterin the shale layers of the Colorado driven by topographicrelief interactswith flow generatedby aquitard flows vertically toward underpressured areas. erosion and to considerwhether this past interval of erosion Groundwater in the Bow Island Formation flows horizontally might affect pressurein the presentday. toward the west side of the basin where the greatesterosion The upperboundary of the simulationsis a watertable that is rates, and consequentlythe greatestunderpressures, occur. assumedto coincidewith the land surface.Fluid potentialsalong Flow Pattern Evolution the watertable are fixedat everytime stepbut changewith time as erosion modifies the topographyof the land surface. We assumethat the flow patternis in equilibriumwith the land Temperaturealong the watertable remains fixed at 5øC for the surface at the start of the simulation. More than 500 m of relief duration of the simulations. We located the east and west drives groundwaterfrom areas of high topographyto areas of boundariesof the simulatedregion at topographicdivides on the low topography(Figure 9, 5 Ma before present). Most of the inferredCypress Plain (Figure 8). We assumedthat abovethe total flow occurs in the shallow part of the basin, above the Lower Cretaceousaquifer, verticalboundaries are parallel to Coloradoaquitard. A smallamount of groundwaterflows across flow lines and therefore treated them as no-flow boundaries for the shalesin the Colorado aquitard and then flows laterally in fluid and heat. This assumptionis valid along the west side deepaquifers before crossing the shalesagain and dischargingat because the simulated topographyand erosion pattern are the surface. symmetricalabout that boundary. Using a no-flowboundary for One million years of erosion changes the flow pattern the east side, however, introducessome error becauseerosion considerably(Figure 9, 4 Ma before present). Flow above the 7210 CORBET AND BETHKE: GROUNDWATER FLOW IN WESTERN CANADA

.P.

4 Ma B.P.

200mI I0 km

Present Day

Fig. 9. Simulatedevolution of groundwaterflow duringerosion of the westernCanada basin over the past5 Ma. Heavy linesare equipotentials.Contour intervals are 0.5 MPa at 5 and 1.6 Ma and 1 MPa at 4 and 0 Ma. Arrows show flow directions,but arrow lengthsdo not reflect flow rates, which vary over severalorders of magnitude from aquitardsto aquifers. aquitardremains in equilibriumwith the surface topography, but flow patterns,the 9-MPa contoursrun alongthe baseof the flow rates are much smaller becausethe surface is now flatter. Coloradoaquitard and alongthe easternhalf of its top. The 8- The Coloradoaquitard acts as a fluid sink. Groundwaterflows MPa contour forms a closed loop in each figure, but the into the aquitardfrom overlyingand underlyingaquifers to observedregion of potentialless than 8 MPa extendsfarther dissipatedisequilibrium pressure in the aquitard.The steepest toward the east. Given the uncertaintiesin estimatingerosion gradientsof fluidpotential occur in the Coloradoaquitard along ratesand material properties, we havenot tried to furtherrefine the westside of the crosssection where the greatest thickness of our calculation. sedimentshas been eroded. Fluid potentialin thispart of the aquitardfalls short of equilibriumpotential by about5 MPa. Figure9 (1.6 Ma beforepresent) shows the flowpattern aRer a 2.4-Ma hiatusin erosion.Flow abovethe aquitardhas not changedsignificantly, but underpressurein the aquitardhas dissipated.Flow throughoutthe basinhas equilibrated with the surfacetopography. The flow patterncalculated for the presentday (Figure9) is much like the patternfor 4 Ma beforepresent, except that steeperpresent-day topography causes more vigorous flow above the Coloradoaquitard. The distributionof fluidpotential above the aquitardis essentiallythe sameas the potentialdistribution calculatedassuming equilibrium with the landsurface (Figure 10). Disequilibriumpotential in the westernportion of the 200mF Coloradoaquitard is 2.5 to 3 MPa less than equilibrium IO km potential. The simulatedflow pattern for the disequilibriumcase is Fig. 10. Simulateddistribution of hydraulicpotential for a flow similarto the observedpattern (Figure 5). (Whencomparing systemin equilibriumwith the present-daytopography. Contour Figures5 and 9, notethe positionof westernboundary of the interval is 1 MPa. Potential in the western portion of the simulatedsection in Figure 5.) In the calculatedand observed Coloradoaquitard is about 9.25 MPa. CORBET AND BETHKE: GROUNDWATER FLOW IN WESTERN CANADA 7211

Responseof Aquitardsand Aquifers to Erosion Figure 11 showshow total stress,effective stress, pressure, .003 andporosity in the shaleaquitard at pointA (Figure8) change with time. The total stresssupported by the saturatedsediments decreasesas erosion removes overburden, and remains constant -'"; OA duringthe periodof no erosion.Pressure begins to decreaseas soonas erosionstarts and starts to recovertoward its equilibrium value as soonas erosionstops. Influx of water into the shale continuesat•er the end of the first period of erosionuntil .001 pressureapproaches equilibrium about 1 Ma later. Effective stress (total stress minus pressure) continuesto decrease ai•er total stress becomes constant because fluid flow 0

intothe aquitardincreases fluid pressure and thereby decreases I I the portionof the total load supportedby rock framework. 5 4 3 2 1 Effectivestress increases slightly at thebeginning of the second MILLION YEARS AGO periodof erosionbecause the pressure at pointA respondsto the relativelyrapid erosion that occurs in the centralpart of the Fig. 12. Lateralflow ratesin theBow Island Formation at point modeledsection. Drawdown on the pressureat point A caused B (Figure 8). Velocity is positiveto the west. The dashedline by the distanterosion supplements the amountby whichlocal showsthe velocity that would occur if pressureremained in erosiondecreases pressure, allowing pressure to decreasefaster equilibriumwith the changingtopography. Flow is mostrapid thantotal stress at pointA for 250,000years. This increasein during erosionalevents but doesnot exceedseveral millimeters effective stressdid not occur in a similar calculation in which we per year. removedthe valley from the final land surfaceto reducethe erosionrate in the centralpart of the section. During unloading,porosity is approximatelyinversely used. Porosityincreases only a small amount(from about 16.5 proportionalto effectivestress, for the poreeompressibilities to 19%) duringthe simulation,and effectivestress decreases by about 14 MPa. Differencesin erosionrates along the cross section cause fluids to migrate slowly along aquifers toward areas of greatest underpressure,i.e., toward regionsof relatively rapid erosion. Figure 12 shows how lr,teral flow rates in the Bow Island 30 Formation at point B (Figure 8) changeduring the simulation. The dashedline indicatesthe very slow rate of lateral flow that would occur in the aquifer if the flow pattern remainedin total stress equilibriumwith the land surface.Flow ratesincrease by nearly n- 2o an orderof magnitudeduring erosion, and depending on position in the basin, they change direction. However, even during

o erosion, flow rates and distancesin the Bow Island Formation •,,..•effective__ are extremelysmall; groundwater travels less than 2.4 km during eachof the erosionperiods. •) lO pressure Componentsof Present-DayUnderpressure The effectsof unloading,cooling, and the memoryeffect on pressureare additive. Figure 13 shows how each of them I I I I I contributedto present-dayunderpressure. The profile in this figure is locatednear the westboundary of the simulationwhere .19 erosionhas been mostrapid, but the relativemagnitudes of the three componentsof disequilibriumpressure are representative of the rest of the crosssection. The memoryeffect generateda • .18 0 maximumoverpressure of 1.7 MPa. This overpressureis offset by the effectsof unloadingand coolingof pore fluids, which 0 a_ .17 decrease pressure by 4.4 and 0.1 MPa, respectively. The

I I I maximumnet underpressureis about2.7 MPa. 5 4 3 2 1 0 Heat Flow MILLION YEARS AGO There has been some discussion in the literature about whether Fig. 11. Responseof the Coloradoaquitard at point A (Figure or not groundwaterin the westernCanada basin movesrapidly 8) to erosion, showing how total stress, effective stress, enoughto disturbconductive heat flow (seeBachu [1988] for a pressure,and porositytrack with time. Pressureapproaches the review). Heat transportin our simulationsis almostentirely by equilibriumvalue (dashedline) about 1 Ma after the first period conduction. We know this because results of calculations that of erosionends. Porositymirrors effective stressbecause the account only for conductionare nearly the same as results assumedporosity function (equation (7)) is nearly linear during (presentedhere) of calculationsthat consider advection and unloading. conductiono f heat. Althoughthe vertical flux of heat is uniform 7212 CORBET AND BETHKE: GROUNDWATER FLOW IN WESTERN CANADA

4[ .2 MEMORY

E COOLING

NET -4 i

UNLOADING 1.2

I I I I I I -4 -3 -2 -1 0 1 2 -8 i i 0 1 2 3 DISEQUILIBRIUM PRESSURE ('MPa) PORE COMPRESSIBILITY(10 -8 pa-1) Fig. 13. Calculatedcomponents of disequilibriumpressure for Fig. 14. Disequilibriumpressure in the Coloradoaquitard at the presentday along a vertical profile locatednear the west point A (Figure8) versuspore compressibilityb,l. The heavy boundary of the simulation (Figure 9). A maximum net solid line is the sum of three componentsof disequilibrium underpressureof 2.7 MPa occursin the Coloradoaquitard. pressure.Short dashesindicate the compressibilityused in the Hydrostratigraphicunits are abbreviated:Milk River aquifer simulationand the correspondingdisequilibrium pressure. Long (M.R.), Coloradoaquitard (C), Bow Island Formation(B.I.), dashesshow the line of zero disequilibriumpressure. and Lower Cretaceousaquifer (L.C.). distribution is similar to the observed distribution if the underpressureat point A is between2 and4 MPa. In Figures14, acrossthe simulation,geothermal gradients vary with the thermal 15, and 16, all calculationparameters except for the aquitard conductivityof the sediments.Thermal conductivity, in turn, propertyor propertiesplotted are the sameas thoseused in the dependson the stateof compactionof the sediments:compaction simulationpresented above. increasesthermal conductivitybecause rock grainstransmit heat Figure14 showshow the calculateddisequilibrium pressure more effectively than water. Gradientsare less steep in the western portion of the simulation where sedimentshave experienced greater burial depths and therefore are more MEMORY compactedand conductive. a_ 4 We used a uniform basal heat flux of 48 mW/m2, a relationshipfor thermal conductivity(Table 1) basedon data COOLING \ compiledby Sclater and Christie [1980, Figure B1] for North \ Sea shales,and a constantsurface temperature of 5øC to match • -4 \ NET observed geothermal gradients [Hitchon, 1984, Figure 8]. \\ 1.6Ma B.P. Calculated geothermalgradients from the Lower Cretaceous aquifer to the land surface in the present day range from • -12 26.7øC/km along the west side of the simulationto 29.2øC/km alongthe eastside. The regionaltrend in thermalconductivity of Cretaceousshales exerts the main influenceon thesegradients. Thermal conductivityof the shaleincreases with depth in our - -20 calculations'the averageconductivities of shalesin the Colorado o UNLOADING aquitardalong vertical profiles locatednear the west and east boundaries are 1.89 and 1.81 W m -• øC -•. Measurements of • -28 i I I I the thermal conductivityof these shalesare not available for - 19 - 20 - 21 - 22 - 23 comparison,but our values fall within the range (1.5 to 1.9 Bperm

W m-• *C -1) that Majorowiczand Jessop[1981] usedfor i i i i i Cretaceous shales to calculate heat flow in the western Canada - 18 - 19 - 20 - 21 - 22 basin. VERTICAL PERMEABILITY (log m2) Sensitivityof Resultsto AquitardProperties Fig. 15. Disequilibriumpressure in the Coloradoaquitard at We performeda seriesof calculationsto see how sensitivethe pointA (Figure8) versusbp,r,,. Vertical permeability shown on simulationresults are to valuesassumed for thepermeability and the secondaxis is for shale with a porosity of 25%. (The pore compressibilityof the aquitard. The metric for the calculatedporosities of shalesin the Coloradoaquitard, for the sensitivitystudy is the amountof disequilibriumunderpressure presentday, range from 16 to 36%).For bp,,, lessthan -21 (kv calculated for the present day at the site of greatest lessthan 10 -20 m2), underpressure remains from the first period underpressure(point A, Figure 8). The calculatedpotential of erosion. CORBET AND BETHKE: GROUNDWATER FLOW IN WESTERN CANADA 7213

2.5- underpressurefrom the first periodof erosionthat has yet to dissipate. Figure 16 shows how net disequilibriumpressure for the presentday at pointA (Figure8) varieswith the compressibility and permeability of the aquitard. The calculationspredict a pressuredistribution similar to the observeddistribution if the -• 1.5- net disequilibriumpressure at this point is about3 MPa. We can obtain an acceptablematch with observedconditions using any value for pore compressibilityover the range considered.The "' 1.0 vertical permeabilityof the aquitardin successfulruns is about 10-2ø m2 when relativelylarge valuesof compressibilityare o assumedand is up to 2 orders of magnitude less at small o 0.5 compressibility.As discussedbelow, these results provide an upper limit on the permeabilityof shaleon the regional scalein o the study area. i - 19 -20 - 21 - 22 - 23 - 24 DISCUSSION Bperm

I i i i i I The originof underpressurein the westernCanada sedimentary - 18 - 19 - 20 - 21 - 22 - 23 basin is a long-standingproblem. Erosion is one possible VERTICAL PERMEABILITY(log m 2) mechanism for generating underpressure in this basin. Uncertaintyin estimatingerosion rates and regional values of Fig. 16. Disequilibriumpressure in the Coloradoaquitard at permeability and poor understanding of how sediments pointA (Figure8) versusbp,r, , andb,t. The averagevertical decompactas they are unloadedover geologic time [Neuzil, permeabilityis for shalewith a porosityof 25%. Calculated 1986] make it difficult to validate calculationsof pressuresin pressuredistributions are similarto observeddistributions if the basins undergoing erosion. Nonetheless, the simulations disequilibriumunderpressure at point A is between2 and4 MPa presentedhere show that a mathematicalmodel incorporating (hatchedarea). Coolingaccounts for more than half of the reasonableassumptions about erosion rates and rock properties underpressurein successful simulations for combinations of b p,r,, can reproducethe regional featuresof the pressuredistribution and b ul in the solid area. observedin our study area. We believe that these simulations composea conceptualtool that offers a better understandingof how the pressure distribution and flow pattern in southern Alberta evolved. varieswith thepore compressibility bul of the aquitardat point The simulationssuggest that underpressurein southernAlberta A. Memoryand unloadingeffects increase significantly as b formedas pore spaceexpanded during erosion. Cooling of pore getslarger, but the effect of coolingdecreases slightly. Equation fluids during erosion probably did not generate significant (1) showswhy these scaling relations occur. First, b •t affectsthe underpressure.By choosingvalues less than 6 x 10-•ø Pa-• for unloadingand cooling terms. The parameterb •t doesnot appear the pore compressibilityb •t of shales(Figure 16), we were able directlyin (1), but b • is directlyproportional to o•vfor a given to reproducethe underpressuringin the basin suchthat cooling porosity.The effect of coolingdecreases asb •t increasesbecause accountedfor more than half of the observedunderpressure. The otv appearsin the denominatorof the term for thermaleffects. permeabilitiesrequired in these calculations,however, seem In contrast,the unloadingterm increaseswith b ,t becauseit is unreasonablysmall. The averagevertical permeability calculated proportionalto a term,o•/( o• + •b/•), whichincreases with for shalesin theColorado aquitard was about 10 -22 m 2, or about unlessot• is muchgreater than the product an order of magnitudesmaller than the lowest values measured Second,the rate at which disequilibriumpressure dissipates for coresfrom a stratigraphicallyequivalent Cretaceous shale in dependspartially on b •t. The dissipationrate decreasesas b ul SouthDakota [Bredehoefiet al., 1983; Neuzil, 1986]. Calculated increasesbecause otv is in the denominatorof the diffusion term permeabilitiesfor more compactedshales near the baseoff the of (1). The memory curve in Figure 14 illustrates this aquitard are even smaller. For example, the vertical shale relationshipbecause we calculatedit by solving (1) with the permeabilitycorresponding to B•,,,, = -23 andporosity=0.16 unloadingand coolingterms set equalto zero. is 2x10 -23 m2. Further,the compressibilityassumed in this Permeabilityaffects the rate at which disequilibriumpressure simulationseems prohibitively small. If the pore compressibility diffuses,but not the rate at which it is generated.Figure 15 is 6x10 -•ø Pa-•, the verticalcompressibility (equations (2) and showsthat the magnitudeof each of the three componentsof (6)) of the sameshale is 8 x 10-•z Pa-•, i.e., of the sameorder disequilibriumpressure at point A increasesas the permeability as the compressibilityof mineral grains. of the aquitarddecreases. In this figurewe plotteddisequilibrium pressureagainst the interceptb•,,r,• in the equationfor shale Other Causesof Underpressure permeability (Table 1). This figure also shows the net Underpressureoccursnot only underdisequilibrium conditions, underpressure,at 1.6 Ma before present,that persistsfrom the but also in equilibriumflow patterns,for example, in recharge first interval of erosion. Significant disequilibriumpressure areas. The presenceof extensivestrata with low permeabilityin persistsif b•,,r,• is less than about -21.5. Below this rechargeareas accentuates this effect [T6th, 1978]. For example, permeabilitythe net disequilibriumpressure shown for the subhydrostaticpressure occurs in deep aquifersof the Denver presentday is the sum of disequilibriumpressure generated basin [Belitz and Bredehoefi, 1983, 1988] and '.he Palo Duro during the second period of erosion and the portion of basin [Sengerand Fogg, 1984, 1987; Sengeret al., 1987a,b] 7214 CORBET AND BETHKE: GROUNDWATER FLOW IN WESTERN CANADA

because groundwater recharging these aquifers must flow ShalePermeability downwardacross thick aquitards.Underpressure in the aquifers hasequilibrated with the landelevation along the easternmargins Our calculations suggestthat if erosion caused observed of the basins.This explanation,however, doesnot hold for the underpressurein southernAlberta, the regionalpermeability of western Canada basin becausefluid potentialsat the lowest Cretaceousshales in the Colorado Group there is less than elevationsof the basin'sland surfaceare greaterthan the lowest 3x10 -2ø m2. In our simulation(Figure 9) the vertical potentialsat depth[Berry and Hanshaw,1960]. permeabilityof theseshales ranges from 2 x 10-21 to 6 x 10-20 m 2 Petroleumproduction from sandy intervals of the Colorado dependingon burialdepth. These values fall withinthe rangeof aquitardmight be responsiblefor part or all of the observed permeabilitymeasured for core samplestaken from Cretaceous underpressuring.The Medicine Hat and Bow Island sands,for shaleat similarburial depths in SouthDakota [Bredehoefi et al., example, contain major gas fields. However, T6th and Corbet 1983; Neuzil, 1986]. The averagevertical permeability that can [1986] used productionrecords to identify the pressuresthat be usedto calculatea satisfactorymatch of observedpressures mightreflect production from nearbywells. The potentiometric is withinhalf an orderof magnitudeof 10-20 m 2 for mostof the surfaceof the Bow Island Formationis, in places,locally porecompressibilities considered (Figure 16). Extremelysmall depressedin the vicinityof thesepressures, but productiondoes pore compressibilitiesrequire permeabilities about 2 ordersof not seemto have alteredthe larger-scalefeatures of the surface. magnitudesmaller to match observedconditions. Thereforewe believethat the potentiometricsurface represents Bredehoefiet al. [1983] notedthat the permeabilitiesmeasured approximatenatural conditions. for coresare 1 to 2 ordersof magnitudeless than the regional Previousdiscussions of the role of osmosisin forming values that they inferred from numerical simulations.They underpressurein the westernCanada basin [e.g., Berry and hypothesizedthat the regional value of shale permeability is Hanshaw, 1960; Hitchon, 1969b] consider the difference greater becausewater flows through fracturesthat are unlikely betweensalinities of fluidsin aquifersseparated by shales.In our to be sampledin cores. Neuzil et al. [1984] estimatedthat the studyarea, water in the aquiferoverlying the Coloradoshales averagespacing between the fracturesis of the order of 100 or (Milk River) is fresh,and salinitiesin the underlyingaquifer 1000 m. (Lower Cretaceous)do not differ significantlyfrom thosein the Our resultssuggest that fracturesdo not increasethe regional Bow Island Formation.Although comparing salinities in the permeability of Cretaceousshales in southernAlberta; instead, overlyingand underlyingaquifers ignores the osmoticpressure our inferredregional permeabilities are in the rangeexpected for betweenthe fluidsin theaquifers and the shales [Phillips, 1983], core values. Belitz and Bredehoefi [1988] obtained a similar it showsthat underpressuresin the Bow IslandFormation cannot result from their simulationsof groundwaterflow in the Denver be dueto chemicalosmosis acting across the Coloradoaquitard. basin. They obtainedgood agreementbetween calculatedand We cannotfully evaluatethe possibilitythat observedunder observedhydraulic heads in the Dakotaaquifer only with model pressuresare due to an osmoticpressure between fluids in the permeabilitiesless than 3 x 10-20 m 2 for the Cretaceousshales in Bow Island Formation and fluids in the shales of the Colorado that basin. Similarly, we were unable to simulate observed aquitardbecause we donot know the salinity of porewaters in underpressuresin southernAlberta using average permeabilities theshales. If salinitiesin the Coloradoshales are muchhigher greaterthan the samevalue (Figure 16). thanthe 10,000- to 15,000-mg/Lsalinity observed in the Bow IslandFormation, an osmotic flux of waterfrom the sandy layers Shale Compressibility into the shale could account for the underpressures. Thecompressibility of sedimentary rocks as they are loaded by Disequilibriumunderpressure in the Bow Island Formation sedimentation,or unloadedby erosion,cannot be determined averagesabout 2 MPa in the vicinity of our simulations. directlyfor severalreasons. First, it dependson the time scale Assuminga NaC1 solution,calculations using the classical considered.The compressibilityof a rock over geologictime osmoticequation (as cited by Hanshaw [1972]) show that may be 1 to 3 orders of magnitudegreater than the salinitiesin the shaleswould have to be about30,000 to 35,000 compressibilityof that rock measuredin laboratorytests. The mg/L to accountfor the underpressure.This, however,is a timedependence may indicate that rocks deform viscoelastically conservativeestimate of the salinityrequired in the shales over geologictime [Neuzil, 1986]. Second,compressibility is because the calculation assumes that the shale acts as a hysteretic:rocks do not fully recoverthe porositylost during membranewith 100%efficiency. In nature,geologic materials compaction.Finally, it probably dependson temperature are likelyto be muchless efficient [Phillips, 1983]. [Palciauskasand Domenico, 1989]. Thenet effect of glaciationon present-day pressure in southern Reasonableestimates of compressibilityduring loading can be Albertawas probablysmall because ice coveredthe area for a calculatedfrom porosityversus effective stress relationships relativelyshort time. Pore pressure likely rose rapidly as the ice observedin sedimentarybasins. We usedthis approach to obtain firstcovered the area,decreased slowly as the loadsqueezed a pore compressibilityof 6.5x10 -8 Pa-l for shales.Vertical water out of the aquitard,and droppedrapidly when the ice compressibilitiesfor Colorado shales calculated using this pore retreated.The rapid increaseand decreaseof pressurehad compressibilityrange from 8.5x10 -9 to 3.1x10 -8 Pa-l. approximatelythe samemagnitude; a net decreasein pressure Estimatesof compressibilityduring unloading are moredifficult couldhave occurred only if enoughwater was squeezed out of to obtain. Compressibilityhas been estimatedto be aboutan theshales to dissipatea significant amount of theoverpressure. order of magnitudeless during unloading than during loading Thepressure line in Figure11 (4 to 3 Ma beforepresent) shows [Jumikis,1965; Domenicoand Palciauskas,1979]. that hundredsof thousandsof yearsare requiredfor flow to Althoughour calculationsare not sensitiveenough to pore dissipatea few megapascalsof disequilibriumpressure. In compressibility(Figure 16) to tightlyconstrain this parameter, contrast,the ice was present only for tens of thousandsof years. theydo showthat a goodmatch with observed pressures can be The mostrecent ice sheetscovered the study area for lessthan obtainedusing compressibilities about an order o f magnitudeless 50,000years and retreated about 20,000 years ago [Westgate, thanthe valuewe estimatefor compressibilityduring loading. 19681. We assumeda ratio o f loadingto unloadingcompressibility equal CORBET AND BETHI{E: GROUNDWATERFLOW IN WESTERN CANADA 7215 to 5 in the calculationspresented here (Figure 9). Calculatedthis GroundwaterFlow Arising From Erosion way, unloadingcompressibilities of shalesfall along the upper The potentiometricsurfaces of Lower Cretaceousaquifers in limitof experimentallydetermined values [Neuzil, 1986, Figure southern Alberta have distinct features that are not related to 4]. Decreasingthe unloadingcompressibility to a full order of eitherlocal topography or the regionalwest-to-east slope of the magnitudeless than the loading compressibility (bul '-' 6.5 )<10 -9 land surface. The potentiometricsurface of the Bow Island Pa'l) requiressomewhat lower, but still reasonable,shale Formation(Figure 6) is a goodexample. The highesthydraulic permeabilitiesto simulateobserved underpressures. The smallest headson this map (greaterthan 850 m) occur in a region permeabilities(9.6x 10-22 m2), in thisease, are half the smallest extending from the Alberta-Montanaborder that does not valuesmeasured for core samplesby Bredehoefiet al. [1983]. correspondto an area of high elevationon the currentland Calculationsperformed by Palciauskasand Domenico[1989] surface. Heads decrease toward the northwest, north, and suggestthat the ratio of inelasticto elasticcompressibility of northeast.In the northwestportion of Figure6, hydraulichead sandstoneis about 50. The magnitudeof elastic deformation decreasesrapidly toward the west,i.e., oppositeto the regional mightrepresent a conceptuallower limit to but. This concept slopeof the land surface.The potentiometricsurface of the leads to the questionof how resultsof our calculationsare Lower Cretaceousaquifer (not shown)has similar features affected if we assume a ratio of loading to unloading [Schwartzet al., 1981, Figure4; T6thand Corbet,1986, Figures compressibilityof 50, therebyreducing b•t to 0.78x10-9 and 25 and 26]. 0.13x10-8 Pa-• for sandstoneand shale, respectively. Our results At leasttwo explanationsfor thedistribution of hydraulichead are not sensitiveto the value of but for sandstonebecause the in the deep Cretaceousaquifers in southernAlberta have been aquifers(i.e., the hydrostratigraphicunits assigneda high advanced.Schwartz et al. [1981] suggestedthat deepflow in the percentageof sandstone)serve mainly as conduitsfor lateral regionis partof anextremely long flow system that recharges in flow. The resultsare, however,sensitive to a decreasein but for Montana, where stratigraphicequivalents of the aquifersare the unitscomposed mainly of shale.Figure 16 showsthat if closeto the land surface,and dischargesin northeasternAlberta. b•t=0.13x10-8 Pa-•, we must reducethe averagevertical They felt that southto north,rather than west to east,regional permeabilityof shale to about 2x10 -22 m 2 in orderto calculatea flow occurs becausethrust faulting has disrupted east-west pressuredistribution that is similarto theobserved distribution. hydrauliccommunication with a possiblerecharge area in the foothillsof the RockyMountains to the west.This modelcould explain why hydraulichead increasestoward the Montana RegionalTrends of the GeothermalGradient border, but it doesnot explaineither the rapid drop of head Geothermalgradients in Alberta generallyincrease with towardthe west or the presenceof underpressurein the Bow Island Formation. distancefrom the Rocky Mountains;gradients are less than 30ø.C/kmin the foothillsregion and are greaterthan 40øC/km Tdthand Corbet[1986] suggestedthat directions of lateralflow over much of the north and northeastparts of the province in thedeep aquifers reflect a pastlocal topography that has since [Hitchon,1984]. Majorowiczand Jessop[1981] and Hitchon beenmodified by Pliocene-Pleistoceneerosion. In effect,they [1984]attributed this regional trend of thegeothermal gradient suggestedthe lateralflow hadsufficient momentum to retainits flow direction for some time after erosion removed the to advectionof heatby groundwaterflowing across the basin. Accordingtothis model, low geothermal gradients occur beneath topographicrelief that drove the flow. Our simulationsshow that flow directionsin deep aquiferscannot reflect topographic topographicallyhigh areaswhere cool meteoricwater moves features that have been eroded. Instead, potential gradients downward.Intermediate gradients are foundin regionsof lateral flow,and high gradients occur where warm water flows upward generatedby topographicrelief are interruptedwhen erosion to dischargeat the surface.Hitchon [1984] also examined the beginsand flow directions deflect rapidly toward underpressured patternof thegeothermal gradient in southernAlberta in detail areas. and concludedthat groundwaterflow generatedby local Our calculationsshow that erosioncould have generatedat topographyalso affects l'.eat flow in thisportion of the basin. least some of the featuresof the Bow Island potentiometric Bachu[1988], however, used dimensional analysis to showthat surface.In particular,the increasein erosionrate towardthe groundwaterprobably moves too slowly in thewestern Canada west best explainsthe rapid drop of hydraulichead in that basinto carrya significantamount of heat.He suggeststhat direction. However, in the calculations,only erosionand the differencesin heat flux from the basementcause the regional local relief of the water table drive flow in the Bow Island scaletrends in the geothermalgradient in the basin. Formation.In naturea flowsystem that extehds beyond the Our conceptualizationof heat transfer in southernAlberta boundariesof the simulatedregion might modify or overwhelm differs from theseanalyses in that we assumethat thermal flowdriven by erosionor thelocal relief of thewater table. The conductivityvaries with degree of compaction.Our simulations extent to which basin-wide flow [Schwartz et al., 1981] also supportBachu's [1988] conclusion that groundwater in the basin affectspotential distributions in Lower Cretaceous aquifers is not movestoo slowlyto transportmuch heat. In addition,our known. simulationsshow that neither advectivetransport of heat nor Erosionprobably affects potential patterns at thebasin scale as well. The thickness of sediments eroded from the western spatialvariations in heatflux from the basement are required to accountfor regionaltrends in the geothermalgradient in Canadasedimentary basin since the Eocenegenerally increases southernAlberta. Calculationsthat assumeheat transportby toward the Rocky Mountains[Hacquebard, 1977; Hitchon, conductiononly, a uniformheat flow fromthe basement, and 1984]. The largeregion of closedpotential in lowerCretaceous thermalconductivities that vary with degreeof compaction aquifers(Figure 1) mightbe due to rapid erosionthat has accuratelyreproduce the observed west-to-east increase of the occurred basinward from the fold-and-thrust belt. geothermalgradient. The regional trend in geothermalgradient over the restof the westernCanada sedimentary basin might be Acknowledgments.We thankDan Hayba, Rob Lander, Kurt explainedin the sameway. Larson,Ming-Kuo Lee, ChuckNorris, and J6zsefT6th for many 7216 CORBET AND BETHKE: GROUNDWATER FLOW IN WESTERN CANADA

usefuldiscussions over the courseof this project.In particular, fluids and fractureinitiation in tompattingsediments, Geol. discussionswith ChrisNeuzil provided important insight into the Soc. Am. Bull., Part II, 90, 953-979, 1979. mechanicalbehavior of sedimentsduring unloadingand the Garven, G., A hydrogeologicmodel for the formation of the possible effects of chemical osmosis acting within shale giant oil sandsdeposits of the westernCanada sedimentary aquitards.The manuscriptbenefited from thoughtful reviews by basin, Am. J. Sci., 289, 105-166, 1989. Rob Lander, Kurt Larson, Chris Neuzil, V. Palciauskas,Joan Hacquebard, P. A., Rank of coal as an index of organic $toltz, and J6zsefT6th.Jessie Knox andJoan Apperson drafted metamorphismof oil and gas in Alberta, in The Origin and the figures. This work was supportedby National Science Migrationof Petroleumin the WesternCanadian Sedimentary Foundationgrants EAR 85-52649and EAR 86-01178and by a Basin, Alberta, by G. Deroo et al., Geol. Surv. Can. Bull., consortiumof industrialsponsors of the hydrogeologyprogram: 262, 11-22, 1977. Amoco ProductionCompany, ARCO Oil and Gas Company, Hanshaw,B. B., Natural-membranephenomena and subsurface British Petroleum Research, Conoco, Exxon Production wasteemplacement, in UndergroundWaste Management and Research,Japan National Oil Corporation,Lawrence Livermore EnvironmentalImplications, edited by T.D. Cook, Mem. Am. National Laboratory, Mobil Research and Development Assoc. Pet. Geol., 18, 308-317, 1972. Corporation, Marathon Oil Company, Texaco USA, and Hitchon, B., Fluid flow in the Western Canadasedimentary UNOCAL. basin, 1, Effect of topography, Water Resour. Res., 5, 186-195, 1969a. REFERENCES Hitchon, B., Fluid flow in the western Canada sedimentary basin, 2, Effect of geology, Water Resour.Res., 5, 460-469, Alden, W. C., Physiographicdevelopment of the NorthernGreat 1969b. Plains, Geol. Soc. Am. Bull., 35, 385-424, 1924. Hitchon, B., Geothermal gradients, hydrodynamics, and Alden, W. C., Physiographyand glacial geologyof eastern hydrocarbonoccurrences, Alberta, Canada,Am. Assoc. Pet. Montanaand adjacent areas, U.S. Geol. Surv. Prof. Pap., 174, Geol. Bull., 68, 713-743, 1984. 133 pp., 1932. Horner, D. R., Pressurebuild-up in wells, in Proceedingsofthe Athy, L. F., Compactionand oil migration,Am. Assoc. Pet. Third Worm Petroleu•nCongress: Section 11, 503-523, E.J. Geol. Bull., 14, 25-35, 1930. Brill, Leiden, Netherlands, 1951. (reprinted in Pressure Bachu, S., Analysisof heat transferprocesses and geothermal AnalysisMethods, SPE Reprint Series, 9, 25-43, Societyof pattern in the Alberta basin, Canada,J. Geophys.Res., 93, PetroleumEngineers, Dallas, 1967). 7767-7781, 1988. Hubbert, M. K., The theoryof ground-watermotion, J. Geol., Barker, C., Aquithermal pressuring-roleof temperature in 48, 785-944, 1940. developmentof abnormalpressure zones, Am. Assoc. Pet. Jumikis, A. R., Soil Mechanics, 791 pp., D. Van Nostrand, Geol. Bull., 56, 2068-2071, 1972. Princeton, N. J., 1965. Belitz, K., and J. D. Bredehoeft,Hydrodynamics of the Denver Koppula, S. D., and N. R. Morgenstern, Deficient pore basin:An explanationof subnormalfluid pressures(abstract), pressuresin erodingsoil mass,Can. Geotech.J., 21,277-288, Am. Assoc. Pet. Geol. Bull., 67, 422, 1983. 1984. Belitz, K., and J. D. Bredehoeft,Hydrodynamics of the Denver Magara, K., Thicknessof removedsedimentary rocks, paleopore basin: An explanation of subnormal fluid pressures,A•n. pressure,and paleotemperature,southwestern part of western Assoc. Pet. Geol. Bull., 72, 1334-1359, 1988. Canadabasin, Am. Assoc. Pet. Geol. Bull., 60, 554-565, 1976. Berry, F. A. F., Geologicfield evidencesuggesting membrane Majorowicz, J. A., and A.M. Jessop, Regional heat flow propertiesof shales(abstract), Int. Geol. Congr. Rep. Sess. patterns in the western Canadian sedimentary basin, Norden, 21,209, 1960. Tectonophysics,74, 209-238, 1981. Berry, F. A. F., and B. B. Hanshaw,Geologic field evidence Meyboom,P., Geologyand groundwaterresources of the Milk suggestingmembrane properties of shales (abstract), A•n. River sandstonein southernAlberta, Mem. 2, 89 pp., Res. Assoc. Pet. Geol. Bull., 44, 953-954, 1960. Count. of Alberta, Edmonton, Alberta, Can., 1960. Bethke, C. M., A numerical model of compaction-driven Neuzil, C. E., Comment on "Possible effects of erosional groundwaterflow and heat transferand its applicationto the changesof the topographicrelief on pore pressuresat depth" paleohydrologyof intracratonic sedimentarybasins, J. by J. T6th andR. F. Millar, WaterResour. Res., 21,895-898, Geophys.Res., 90, 6817-6828, 1985. 1985. Bethke,C. M., Modelingsubsurface flow in sedimentarybasins, Neuzil, C. E., Groundwater flow in low-permeability Geol. Runtisch., 78, 129-154, 1989. environments,Water Resour. Res., 22, 1163-1195, 1986. Bethke, C. M., and T. F. Corbet, Linear and nonlinearsolutions Neuzil, C. E., and D. W. Pollock,Erosional unloading and fluid for one-dimensionalcompaction-How in sedimentarybasins, pressuresin hydraulically"tight" rocks, J. Geol., 91,179-193, Water Resour. Res., 24, 461-467, 1988. 1983. Bradley, J. S., Abnormal formationpressure, Am. Assoc.Pet. Neuzil, C. E., J. D. Bredehoeft,and R. G. Wolf, Leakageand Geol. Bull., 59, 957-973, 1975. fracture permeabilityin the Cretaceousshales confining the Bredehoeft,J. D., and B. B. Hanshaw,On the maintenaceof Dakota aquifer in South Dakota, in Geohydrologyof the anomalousfluid pressures,I, Thick sedimentarysequences, Dakota Aquifer: Proceedings of the First C. V. Theis Geol. Soc. Am. Bull., 79, 1097-1106, 1968. Conferenceson Geohydrology,edited by D. G. Jorgensenand Bredehoeft,J. D., C. E. Neuzil, and P. C. D. Milly, Regional D.C. Signor, pp. 113-119, NationalWater Well Association, flow in the Dakotaaquifer: A studyof the role of confining Worthington,Ohio, 1984. layers, U.S. Geol. Surv. Water SupplyPap., 2237, 45 pp., Palciauskas, V. V., and P. A. Domenico, Characterization of 1983. drainedand undrainedresponse of thermallyloaded repository Domenico,P. A., andV. V. Palciauskas,Thermal expansion of rocks, Water Resour. Res., 18, 281-290, 1982. CORBET AND BETHKE: GROUNDWATERFLOW IN WESTERN CANADA 7217

Palciauskas,V. V., and P. A. Domenico,Fluid pressuresin T6th, J., Gravity-inducedcross-formational flow of formation deformingporous rocks, Water Resour. Res., 25, 203-213, fluids, Red Earth region,Alberta, Canada:Analysis, patterns, 1989. and evolution, Water Resour. Res., 14, 805-843, 1978. Phillips,F. M., Commenton "Chemicalosmosis, reverse T6th, J., and T. Corbet, Post-Paleoceneevolution of regional chemicalosmosis, and the energyof subsurfacebrines" by D. groundwater flow-systemsand their relation to petroleum L. Graf, Geochim.Cosmochi•n. Acta, 47, 1331, 1983. accumulations, Taber area, southern Alberta, Canada, Bull. Russell,W. L., Pressure-depthrelations in Appalachianregion, Can. Pet. Geol., 34, 339-363, 1986. Am. Assoc. Pet. Geol. Bull., 56, 528-536, 1972. T6th, J., and R. F. Millar, Possibleeffects of erosionalchanges Schwartz, F. W., K. Muelenbachs,and D. W. Chorley, of topographicrelief on pore pressuresat depth, Water. Flow-systemcontrols of the chemical evolution of Resour. Res., 19, 1585-1597, 1983. groundwater,J. Hydrol.,54, 225-243,1981. T6th, J., and K. Rakhit, Explorationfor reservoir quality rock Selater,J. G., andP. A. F. Christie,Continental stretching: An bodies by mappingand simulationof potentiometricsurface explanationfor the post-mid-Cretaceoussubsidence of the anomalies, Bull. Can. Pet. Geol., 36, 362-378, 1988. centralNorth Sea basin,J. Geophys.Res., 85, 3711-3739, van Everdingen, R. O., Studiesof formationwaters in western 1980. Canada:Geochemistry and hydrodynamics, Can. J. Earth $ci., Senger,R. K., andG. E. Fogg,Subnormal fluid pressures in the 5, 523-543, 1968. PaloDuro basin caused by regionalhydrodynamic conditions, Westgate,J. A., Surficialgeology of the Foremost-CypressHills Geol. $oc. Am. Abstr. Programs,16, 650, 1984. region, Alberta, Bull. 22, 122 pp., Res. Counc. of Alberta, Senger,R. K., andG. E. Fogg,Regional underpressuring in Edmonton, Alberta, Can., 1968. deepbrine aquifers, Palo Duro basin,Texas, 1, Effectsof hydrostratigraphyand topography,Water Resour. Res., 23, 1481-1493, 1987. C. M. Bethke,Department of Geology,University of Illinois, Senger,R. K., G. E. Fogg,and C. W. Kreitler,Effects of 1301 W. Green St., Urbana, IL 61801. hydrostratigraphyandbasin development onhydrodynamics of T. F. Corbet, Fluid Flow and TransportDivision 6344, Sandia thePalo Duro basin,Texas, Rep. Invest. 165, 48 pp., Bur. of National Laboratories,Albuquerque, NM 87185. Econ. Geol., Univ. of Tex., Austin, 1987a. Senger,R. K., C. W. Kreitler,and G. E. Fogg, Regional underpressuringin deep brine aquifers,Palo Duro basin, (Received October 29, 1990; Texas, 2, The effect of Cenozoicbasin development, Water revised November 24, 1991; Resour.Res., 23, 1494-1504, 1987b. acceptedDecember 4, 1991.)