129 Geologische Rundschau 78/1 I 129-154 I Stuttgart 1989 Modeling subsurface flow in sedimentary basins By CRAIG M. BETHKE, Urbana*) With 16 figures Zusammenfassung raines qui se manifestent dans les bassins sedimentaires, et qui resultent du relief topographique, de la convection, de la Grundwasserbewegungen in sedimentaren Becken, die compaction des sediments, de la decharge due l'erosio? et von dem topographischen Relief, konvektionsbedingtem a de la combinaison de ces divers facteurs. Dans ces modeles, Auftrieb, Sedimentkompaktion, isostatischen Ausgleichsbe­ on peut prendre en con~ideration les effets d~s tr:'nsferts d,e wegungen in Folge von Erosion und v~n ~mbinati~n~n chaleur et de matieres dlssoutes lors de la migration du pe­ dieser Kriifte gesteuert werden, konnen mit Hilfe quanutattv trole et ceux de I'interaction chimique de I'eau avec les modellierender Techniken beschrieben werden. In diesen roches. Toutefois la precision des previsions que I'on peut en Modellen kann man die Auswirkungen des Transports von deduire est limitee par la difficulte d'estimer I'echelle regia­ Warme und gel osten Stoffen, Petroleum-Migration und die a nale les proprietes hydrologiques des sediments, de reconsti­ chemische Interaktion zwischen Wasser und dem grund­ tuer les conditions anciennes, et de connaitre de quelle wasserleitenden Gestein beriicksichtigen. maniere les processus physiques et chimiques interferent Die Genauigkeit der Modell-Voraussagen ist allerdings a I'echelle des temps geologiques. La modelisation des bassins begrenzt wegen der Schwierigkeit, hydrologische Ei­ progressera dans la mesure ou la recherche hydrogeologique genschaften von Sedimenten in einem regionalen Rahmen ser mieux integree acelles d'autres disciplines telles que la se­ vorauszusagen, dem Schatzen vergangener Bedingungen und dimentologie, la mecanique des roches et la geochimie. dem Problem der Abschatzung von Wechselwirkungen physikalischer und chemischer Prozesse in geologischen Zeitriiumen. Fortschritte fUr das Modellieren von Becken KpaTKoe COAeplKaHHe werden mit der Integration hydrologischer Forschungsan­ C nOMO~blO MOAenH peKOHCTpYHpOBanH MHrpa~HIO strengungen in benachbarte Fachebiete wie Sedimentologie, rpYHTOBblX BOA B OCaj\O'lHbIX 6acceHHax, npHHHMaSi BO Gesteinsmechanik und Geochemie zunehmen. BHHMaHHe TonorpacpHIO pen be cpa , B03MOlKHOCTH KOHBeK­ ~HH, nnOTHoCTb ceAHMeHTHblX OTJlO>KeHHH, H30CTaTH'IeC­ Abstract KHe ABHlKeHHSI B pe3ynbTaTe 3P03HH, a TaKlKe KOM6HHa­ ~HIO Bcex 3THX cpaKTopOB. TIPH pa3paGoTKe TaKHX MOAe­ Groundwater flows that arise in sedimentary basins from neH cneAyeT Y'lHTbIBaTb BnHSlHHe BblCOKOH TeMnepayY­ the effects of topographic relief, buoyant convection, sedi­ Pbl, nepeHoca paCTBopeHHblX Be~eCTB, MHrpa~HIO HecpyH ment compaction, erosional unloading, and combinations H XHMH'IeCKOe B3aHMOAeHCTBHe MelKAY rpYHTOBblMH of these driving forces can be described using quantitative BOAaMH H oKpy>KalO~HMH HX nopOAaMH. modeling techniques. Models can be constructed to consider CaMO COGOH pa3YMeeTCSI, TO'lHOCTb nporH030B no the effects of heat and solute transport, petroleum migra­ TaKHM MOAenSiM orpaHH'IeHa H3-3a TPYAHOCTeH npeACKa- tion, and the chemical interaction of water and rocks. The 3aHHSI perHOHanbHbIX rHApOJlOrH'IeCKHX CBOHCTB ceAH­ accuracy of model predictions, however, is limited by the MeHTOB H H3-3a TonbKO npH6nH3HTenbHOH o~eHKH, KaK difficulty of predicting hydrologic properties of sediments npeAweBCTBYIO~HX B3aHMOOTHoweHHH, TaK H B3aHMO­ on regional dimensions, estimating past conditions such as AeHCTBHSI cpH3H'IeCKHX H XHMH'IeCKHX npo~eCCOB B Te'le­ topographic relief, and knowledge of how physical and che­ HHe reonoru'leCKOrO BpeMeHH. MOAenHpOBaHHe 6acceH­ mical processes interact over gelogic time scales. Progress in HOB oGe~aeT 3Ha'lHTenbHblH ycnex TonbKO npH KOM­ basin modeling will accelerate as hydrologic research efforts nneKCHblX HccneAoBaHHSlX no rHAponorHH, ceAHMeHTono­ are better integrated with those of other specialities such as rHH, MexaHHKe nopOA H reOXHMHH. sedimentology, rock mechanics, and geochemistry. Resume 1. Introduction n est possible, par l'utilisation de techniques quantitatives In recent years the interest in describing quantita­ de modelisation, de decrire les mouvements des eaux souter- tively the subsurface movement of fluids in sedime~lt­ *) Author's address: Dr. C. M. BETHKE, Department of ary basins and the effects of such movements has In­ Geology, 1301 West Green Street, University of Illinois, creased rapidly. Fluids in basins, whether groundwa­ Urbana, Illinois 61801, USA. ters, hydrocarbons, or gases, are mobile over geologic no CRAIG M. BETHKE time periods. Moving fluids create and localize econo­ along the water table. Given adequate rainfall, the mic resources in sedimentary basins, including petro­ water table forms a subdued replica of the land sur­ leum and gas reservoirs and metallic ores. The increas­ face so that to a first approximation topography de­ ing interest in quantifying subsurface flow stems scribes the drive for flow. DARTON (1909), in his stu­ from escalating costs of locating new resources as well dy of the Dakota aquifer system in North America, as the need to isolate radioactive and chemical wastes was among the first to recognize the role of topogra­ from the biosphere for long periods of time. phy in causing groundwater flow on regional scales. There is a strong need in petroleum geology to pre­ The isotopic compositions of sedimentary brines dict the effects of hydrocarbon migration. Oil reser­ (e. g., CLAYTON et al. 1966) provide chemical eviden­ voirs sometimes are found more than 150 kilometres ce that meteoric water circulates deeply in many from source rocks; others are separated vertically basins. from their sources by kilometers of overpressured shale. The distribution of mature source beds is rou­ 2.1 Mathematical model tinely determined during basin exploration, but the The subsurface flow field can be predicted accord­ distance and even direction that oil migrates after be­ ing to a continuum model for any subsurface perme­ ing released from source rocks are commonly un­ ability distribution and water table configuration. known. Efficient mineral exploration also requires Ignoring the effects of varying fluid density, ground­ knowledge of present and past hydrologic conditions. water flows according to Darcy's law Sedimentary brines migrate for hundreds of kilo-' metres from deep strata onto basin margins where Ie, a~ they precipitate the metallic ores of Mississippi Val­ q, :;;: --;;:81 (1) ley-type deposits. Oxidizing surface waters infiltrate where q{ is specific discharge (the volumetric flow basins and leach uranium and other elements, and rate per unit area) in an arbitrary direction I, p, is fluid then precipitate ores in roll-front deposits as they viscosity, and k{ is directional permeability. Herein encounter reducing conditions at depth. Promising the directions of the coordinate axes are assumed to exploration targets could be identified more accurate­ corespond to the principal permeability values; in ly in each of these cases with knowledge of the pre­ this case permeability is described as a' vector (or, sent or past groundwater hydrology of the basin be­ more accurately, a diagonal tensor) rather than a full ing explored. tensor quantity. 4> is hydraulic potential Understanding present-day hydrologic conditions is also of economic and societal concern. Predicting ~ :;;: P - pgz (2) subsurface fluid pressures can be critically important when oil wells are drilled, especially in provinces the mechanical energy per unit volume of ground­ where overpressures can blowout wells. Safely dispos­ water (HUBBERT 1940). P and p are fluid pressure and ing of persistent toxins and radioactive elements with density, g is the acceleration of gravity, and z is depth half-lives of geologic duration requires knowledge of relative to a fixed datum. Hydraulic potential ac­ the rates and directions of transport by subsurface counts for the work of compression and elevation fluids. performed in moving a groundwater of constant den­ Quantitative modeling techniques combined with sity along a flow path; the vector - \7~ is the driving the results of observational and experimental studies force per volume of groundwater. have proved successful in analyzing flow and trans­ Given sufficient time, flow will adjust to a steady port in sedimentary basins on natural time and dist­ state for a given water table configuration. Combin­ ing Darcy's law with conservation of mass gives the ance scales (BETHKE et al. 1988). The purpose of this paper is to examine the variety of models that have equation for steady groundwater flow been applied to analyze basin processes and consider some of the principal uncertainties in applying these models to study groundwater hydrology in the pre­ sent and geologic past. in three dimensions, where x and yare horizontal di­ rections. If the medium can be assumed to be homo­ 2. Flow driven by topographic relief genous and viscosity constant, this equation can be simplified to give Topographic relief along basin surfaces can drive groundwater through deep strata. The flow is driven 2 2 Ie a2~ + Ie a c1> + Ie a c1> c: 0 (3 b) by variation in the potential energy of groundwater s az2 u ay2 • az2 Modeling subsurface flow in sedimentary basins 131 and to V2c1> =0 (3c) r~ if permeability everywhere is isotropic. Equation (3c) is Laplace's equation which has many known solu­ z tions from the theories of electrostatics,