basin-scale hydrogeologic modeling

BASIN-SCALE HYDROGEOLOGIC MODELING

Mark Person"2

Jeff P. Raffensperger 3 Shemin Ge 4 Grant Garven 5

Abstract. Mathematical modeling of coupled groundwater flow, heat transfer, and chemical mass transport at the sedimentary basin scale has been increasingly used by Earth scientists studying a wide range of geologic processes including the formation of excess pore pressures, infiltration-driven metamorphism, heat flow anomalies, nuclear waste isolation, hydrothermal ore genesis, sediment diagenesis, basin tectonics, and petroleum generation and migration. These models have provided important insights into the rates and pathways of groundwater migration through basins, the relative importance of different driving mechanisms for fluid flow, and the nature of coupling between the hydraulic, ther-

mal, chemical, and stress regimes. The mathematical descriptions of basin transport processes, the analytical and numerical solution methods employed, and the application of modeling to sedimentary basins around the world are the subject of this review paper. The special considerations made to represent coupled transport processes at the basin scale are emphasized. Future modeling efforts will probably utilize three-dimensional descriptions of transport processes, incorporate greater information regarding natural geological heterogeneity, further explore coupled processes, and involve greater field applications.

1. INTRODUCTION

Sedimentary basins are complex systems modified by fluid flow, heat transfer, mass transport, and rock-water interactions of many types [Person and Baumgartner, 1995]. Understanding how subsurface flow systems within sedimentary basins operate is of great practical relevance because they contain much of the world's mineral, energy, and water resources. Sedimentary basins develop over long periods of time (10 s to 108 years) as sediments are deposited into broad depressions cre- ated by subsidence of the Earth's crust. Basins can vary in thickness from about 1 to 15 km and extend laterally over distances of up to 1500 km. Temperature and salinity of pore fluids typically increase with depth from about 10 ø to 300øC and 200 to 300,000 mg L -•, respectively [Hanor, 1987]. In many instances, sedimentary basins are subsequently deformed during episodes of mountain building associated with crustal plate move-

1Department of Geology and Geophysics, University of Minnesota, Minneapolis.

2On sabbatical at New Mexico Institute of Mining and Technology, Socorro.

3Department of Environmental Sciences, University of Vir- ginia, Charlottesville.

4Department of Geological Sciences, University of Colo- rado, Boulder.

SDepartment of Earth and Planetary Sciences, Johns Hop- kins University, Baltimore, Maryland.

ment. Uplift of mountains and compressional forces are thought to have driven basinai fluids (petroleum and metal-bearing brines) hundreds of kilometers across the continents, forming some of the world's largest mineral and hydrocarbon deposits [Oliver, 1986; Bethke and Mar- shak, 1990].

Understanding transport processes within sedimentary basins requires an integrated approach involving geological field studies, laboratory investigations, mathematical modeling, and field measurements of pore fluid pressure and brine geochemistry. Measurements of hydraulic parameters in the laboratory or direct field observations of subsurface fluid pressures, temperatures, and pore fluid chemistry [On- and Kreitler, 1985] provide data regarding active transport processes within flow systems and help to constrain rock parameter information. Field studies help to constrain the timing and migration pathways of ancient hydrological systems as they have evolved through time [Shelton et al., 1992; McManus and Hanor, 1993]. However, the study of sedimentary basin evolution in the laboratory and field is hindered, to some extent, by the slow rates and long distances over which transport processes operate in basins. The formation of energy and mineral deposits within the crust, for example, typically occurs over time periods of millions of years and can involve lateral fluid migrations over hundreds of kilometers [Garven, 1995]. The simplifying assumptions required to reproduce these processes in the laboratory or the data limitations associated with making direct observations in the field

Copyright 1996 by the American Geophysical Union.

8755-1209/96/95 RG-03286515.00

e61e

Reviews of Geophysics, 34, 1 / February 1996 pages 61-87

Paper number 95RG03286

62 ß Person et al.' HYDROGEOLOGIC MODELING 34, 1 / REVIEWS OF GEOPHYSICS

have left gaps in our understanding of all aspects of basin fluid interactions [Bethke e! al., 1988].

During the last decade, mathematical modeling of subsurface fluid flow and heat and chemical mass trans-

port have been increasingly called upon to study a wide range of transport-limited geologic processes within sedimentary basins, including. the formation of excess fluid pressures, anomalous heat flow, hydrothermal ore genesis, sediment diagenesis (physical and chemical trans- formation of sediments occurring after deposition), faulting and seismicity, and petroleum generation and migration. While these models have differed greatly in their complexity and the processes represented, they all share a common set of assumptions and basic flow laws. Because mathematical models can represent geologic processes that occur at very slow rates and over continental length scales, they complement field- or laboratory-based investigations. In addition, mathematical modeling represents an important research tool because of the need to consider the behavior of the transport processes occurring in sedimentary basins simultaneously [Tsang, 1987; Bredehoeft and Norton, 1990; Per- son and Gatyen, 1994]. As Chen et al. [1990, p. 104] notes, "Although we tend to think of a single process, it often happens that a variety of processes are coupled so strongly that qualitatively new effects and system behav- iors arise because of this coupling."

This paper provides a review of the recent advances that have been made in the mathematical modeling of groundwater flow, rock mechanics, heat transfer, and reactive chemical mass transport processes within sedimentary basins. This work is intended to complement the reviews that have been published recently on modeling subsurface fluid flow [Konikow and Mercer, 1988; Bethke, 1989; BjOrlykke, 1993], heat transfer [Furlong et al., 1991; Lowell, 1991], and petroleum generation and migration [Ungerer e! al., 1990].

2. DESCRIPTION OF TRANSPORT PROCESSES

IN SEDIMENTARY BASINS

2.1. Fluid Flow

Subsurface fluid flow plays a critical role in a number of geochemical, geothermal, and tectonic processes within sedimentary basins. Groundwater flow is the most important agent in solute mass transport and is a rate- limiting step in hydrothermal ore genesis [Garven, 1985; Raffensperger and Garven, 1995a, b] and in the formation of diagenetic cements and minerals [Wood and Hewett, 1984]. Basin hydrodynamics also has important implications for long-range (10 to 1000 km) secondary petroleum migration within gently dipping carrier beds [Gar- yen, 1989; Bethke et al., 1991; Berg et al., 1994]. While it has been known for some time that groundwater flow also has an important, albeit second-order, effect on subsurface heat transfer within basins [Bredehoeft and Papadopulos, 1965], petroleum researchers have only

recently shown that thermal anomalies induced by vertical groundwater flow rates of a few millimeters per year can shift the depth to petroleum generation by over 1000 rn within actively subsiding basins [Person e! al., 1995]. Finally, excess fluid pressures play a critical role in fault mechanics [Hubbert and Rubey, 1959; Rubey and Hub- bert, 1959] and primary petroleum migration out of low-permeability source rocks [Ungerer et al., 1990].

Subsurface fluid migration within sedimentary basins is driven by a number of mechanisms including sediment and tectonic loading, gradients in (water table) topography, lateral variations in fluid density, seismogenic pumping, and the production of diagenetic fluids. Dif- ferent fluid flow-driving mechanisms interact within various tectonic environments and during different periods of the plate tectonic cycle (Plate 1). The relative importance of these driving forces on fluid flow varies depending on the tectonic and lithologic conditions (e.g., permeability, porosity, and mineralogy). Some studies have examined the role of specific driving mechanisms on fluid flow within different tectonic environments [e.g., Garven and Freeze, 1984a, b; Bethke, 1985; Ge and Gar- yen, 1992]. Other studies have examined how several different driving mechanisms interact with each other through geologic time [Garven et al., 1993; Person and Garven, 1994]. Reviews of these different fluid-flow- driving mechanisms are provided by Bethke [1989] and Garven [1995].

An important feature of deep groundwater flow systems within sedimentary basins is that hydrological, mechanical, thermal, and chemical mass transfer processes are all closely coupled. Increases in subsurface fluid pressures induce rock dilation and porosity increase. Mineral precipitation reduces porosity, decreasing groundwater flow rates. Increases in temperature with depth in permeable sediments and sedimentary rocks create density instabilities that induce free convection. These conditions necessitate greater complexity in basin-scale hydrogeological models than in models required to simulate groundwater flow in shallow aquifers over human timescales. Quantifying the complex feedbacks between fluid flow, rock deformation, heat transfer, and reactive mass transport processes will continue to be an area of active research over the next decade

[National Research Council, 1990; Steefel and Lasaga, 1994].

2.2. Heat Transfer

Thermal processes within basins have important implications for modifying geochemical reaction rates and fluid properties (viscosity and density) and for inducing fluid flow. Temperature increase during burial, for example, is considered by petroleum researchers to be the primary factor controlling petroleum generation within sedimentary basins [Tissot et al., 1987]. This has made the accurate representation of the thermal history of sedimentary rocks a critical component of basin exploration strategies [Doligez et al., 1986]. Geochemical re-

34, 1 / REVIEWS OF GEOPHYSICS Person et al.- HYDROGEOLOGIC MODELING ß 63

64 ß Person et al.- HYDROGEOLOGIC MODELING 34, 1 /REVIEWS OF GEOPHYSICS

A. Reaction Fronts ., [ ß '.:..".•.' I :--"'-.' -. ......... "•'"'•' •' :•' '- '••'! ............... ........... '" '•' ' '"•- ' ' ' ''•' ' ' ' ' '••••:- - - -••••-.'-i'•:!f .................................... "••' • ' ''"•'•••••' ' ' ' • '•••••:

I ! .':'.'.'.' - ..'. :'•'.:. :... ;' -. :. ' ". :' """•"'• '' ' •" ''' •" '• '' • ''"'' '' "••'••••••••.f '""'""'•'•'" "' •:•••- ß '•• ß ,. '•'"•"

ii ii ii ii iii I I

B. Gradient Reactions

Maximum Fluid C_ooling Rate/ Maximum Solid !-'recip•tation Maximum Fluid Heating Rate/ Maximum Solid Dissolution

C. Mixing Zone Reactions

Freshwater

Seawater

I Zone of Fluid Mixing

and Geochemical Reactions

Plate 2. Flow-controlled reactions (defined by Phi/lips [1990]) in a variety of hydrogeological environments. Isothermal reaction fronts (Plate 2a) propagate in the direction of flow from mineralogical boundaries. Gradient reactions (Plate 2b) are more pervasive, driven by fluid flow through temperature or pressure gradients. Mixing zone reactions (Plate 2c) occur when two or more fluids mix, often producing highly localized alteration.

actions can also occur as fluids transport dissolved mass through temperature gradients [Wood and Hewett, 1982].

Subsurface heat transfer can occur as a result of

conduction, advection, exothermic chemical reactions, and radionuclide decay. Conductive heat transfer is gov-

erned by Fourier's law: enthalpy transfer resulting from Brownian motion within the solid and fluid phases. Ad- vective heat transfer results from enthalpy transport associated with fluid motion. Thermal dispersion results from mechanical mixing of thermal energy in the fluid

34, 1 / REVIEWS OF GEOPHYSICS Person et al.: HYDROGEOLOGIC MODELING ß 65

phase due to the tortuous nature of groundwater motion at a variety of scales. Convective heat transfer effects are especially important in recharge and discharge areas where vertical fluid motion is important. However, convective thermal effects are sometimes difficult to distin-

guish from the effects of spatial variations in thermal conductivity with depth or between different lithologic units [Vasseur et al., 1993].

The effects of groundwater flow on the thermal history of sedimentary basins has been of great interest to a variety of Earth science disciplines for a variety of reasons. Geophysicists interested in determining crustal heat flow within different tectonic terrains have had to

differentiate between conductive and convective components of heat flow within basins [Smith and Chapman, 1983]. Hydrogeologists, on the other hand, have used temperature data to infer regional subsurface flow patterns and vertical groundwater flow rates using field data [Deming et al., 1992; Wade and Reiter, 1994] and mathematical modeling [Garven and Freeze, 1984b; Woodbury and Smith, 1985]. In addition, recent hydrogeological inverse modeling techniques have incorporated thermal data as a means of improving estimates of aquifer parameters [Woodbury and Smith, 1988; Wang and Beck, 1989].

2.3. Reactive Mass Transport Geochemical and mass transport processes in sedi-

mentary basins are coupled to groundwater flow patterns and basin thermal structure and ultimately are largely responsible for sediment diagenesis and the formation of economic mineral and petroleum deposits. Aqueous-phase mass transport in sedimentary basins occurs by (1) advection, the physical transport of mass in moving groundwater; (2) hydrodynamic dispersion, a mechanical mixing produced by heterogeneities that occur at a variety of scales; and (3) diffusion, a physical process involving solute mass flux from high to low concentration, which will develop in either static or flowing groundwater. In most geologic environments the transport of aqueous species by moving groundwater is not a conservative process. Rather, chemical species in solution will interact to form complexes, will be ad- sorbed onto clays, oxides, and other materials, and may react with the solid matrix to dissolve minerals and

precipitate new mineral phases. Chemical changes will be a complex function of the flow pattern and velocity, space, time, pressure, and temperature. In general, flow rates will be sufficiently small that the fluid will reach approximate equilibrium with each lithology along the flow path at the ambient temperature and pressure. These successive equilibria produce changes in the chemical composition of the fluid, resulting in reactions with the medium (i.e., precipitation, dissolution), which in turn modify the porosity and permeability. This modification may be insignificant at a human timescale but very significant over geological timescales.

Numerical modeling studies have noted the impor-

tance of hydrodynamic dispersion and its control on the spatial distribution of reaction rates and products [Steefel and Lasaga, 1992]. Recently, numerical models have been developed to couple fluid flow with geochemical reactions. Geologic problems approached using reactive mass transport models include the formation of uranium ores [Raffensperger and Garven, 19958, b], copper [Ague and Brimhall, 1989; Lichtner and Biino, 1992] and lead-zinc deposits [Garven, 1995], carbonate [San- ford and Konikow, 19898, b] and sandstone diagenesis [Hewett, 1986; Lee and Bethke, 1994], and the nature of hydrothermal systems [Steefel and Lasaga, 1994]. These studies note the importance of transport-controlled reaction front propagation, fluid mixing, and gradient reactions [Phillips, 1990, 1991] (Plate 2), all of which occur to varying degrees in heterogeneous basins.

3. TRANSPORT THEORY

Fluid, solute, and energy conservation expressions within compacting sedimentary basins can be derived assuming either a Eulerian or a Lagrangian coordinate framework [Bethke, 1985]. Eulerian-based transport equations have been used in studies where sediment deformation is not explicitly addressed [e.g., Garven and Freeze, 19848, b; Senger and Fogg, 1987; Belitz and Bre- dehoeft, 1988]. Lagrangian-based transport equations are applied when basin subsidence must be represented continuously through time, as in the case of compaction- driven groundwater flow [e.g., Bethke, 1985; Harrison and Summa, 1991; Deming et al., 1990; Person and Gar- yen, 1994] or petroleum generation and migration [Un- gerer et al., 1990; Person and Garven, 1992]. In the La- grangian approach, the advective terms for the porous media are absent because the equations are derived with respect to a control volume that moves through space and helps to minimize the amount of bookkeeping [Be- thke, 1985].

3.1. Fluid Flow

Governing, Lagrangian-based expressions for groundwater flow in a compacting system can be developed using conservation of mass expressions relating the net mass flux across the surfaces of a control volume to

changes in mass storage within the volume [Domenico and Palciauskas, 1979]:

c•o' T

--[- Olp --•- --

-- V' (pfq) (1)

The variables listed in equation (1) are defined in the notation section. Domenico and Palciauskas [1979] used scaling arguments to show that the material derivative D( )/Dt, which is traditionally used in Lagrangian- based transport equations, can be replaced by the local partial derivative a( )/at, provided that the basin is

66 ß Person et al.: HYDROGEOLOGIC MODELING 34, 1 / REVIEWS OF GEOPHYSICS

much thicker than the amount of consolidation. This

simplification also assumes that the fluid flow rate is much larger than the velocity of the solids. The terms on the left side of (1) represent the time rate of change of fluid mass stored within a deforming control volume due to changes in hydraulic head, mechanical loading, thermal expansion, and salinity effects on fluid density, respectively. Given the range of conditions within basins, the mechanical loading term is most important in controlling excess heads [Shi and Wang, 1986; Luo and Vasseur, 1992], and the temporal derivatives involving solute concentration and temperature are usually not represented in most basin models. The right side of (1) is the net fluid mass flux across a control volume. The

fluid flow equation represented by (1) can account for compaction-, density-, and topography-driven fluid flow- inducing mechanisms as well as seismogenic pumping. Darcy's law for a variable-density fluid may be written as

q - -k p0g (Vh + Pf-- P•0 •7Z) (2) }xf P0

Equations (1) and (2) account for single-phase, variable- density groundwater flow in heterogeneous and anisotropic porous media.

If separate-phase oil migration is considered, then additional transport equations analogous to (1) must be developed for each fluid phase (oil, gas, water), and modified to account for the effects of capillary pressures, relative saturation, and effective permeability. Numeri- cal approaches include traditional multiphase flow [Ros- tron and T6th, 1989; Ungerer et al., 1990], sharp-interface theory [Lehner et al., 1987; Rhea et al., 1994], particle tracking [Gatyen, 1989; Person et al., 1993], and oil potential maps [Hubbert, 1953; Bethke et al., 1991]. One underlying assumption in the latter two approaches is that secondary petroleum migration directions through a coarse-grained aquifer can be approximated using oil heads or potentials [Gatyen, 1989]:

Pf h + ( pail- pf) - -- z (3) hail Pail Pail If petroleum migration is assumed to occur near the top of a aquifer under (oil-) saturated conditions, then Dar- cy's law can be used to approximate oil migration rates and directions:

•f Pfg (Pai• -- Pf) q o.- tXoi• q + k Vz (4) [Jk'f Pail

Petroleum researchers have frequently adopted this linearized approach for representing long-range oil migration because of the inherent difficulties involved in solv-

ing a system of nonlinear, multiphase transport equations at the basin scale on a relatively coarse grid. However, while equations (3) and (4) provide quantitative estimates of oil migration directions and rates due to the effects of buoyancy and hydrodynamics impelling forces, they do not account for capillary forces, a fluid-

impelling mechanism for oil migration which is important in fine-grained sedimentary layers where oil is generated.

3.2. Porous Medium Deformation

While the fluid mass conservation principle governs fluid motion, the mechanical state of the solid phase must be derived using a force equilibrium expression [Ge and Gatyen, 1992, 1994]. For an infinitesimal volume of a porous medium, the external forces applied must be balanced by the internal stress and inertial forces. For sedimentary basins, inertial forces may be safely neglected on account of the slow rates of deformation and therefore the following force balance expression may be used:

-F (s)

It is typically assumed that F represents the imposed tectonic stresses from the emplacement of thrust sheets or the vertical loading due to sedimentation. A consti- tutive relation is needed to relate stress tensor ({r) in (5) to strain that includes the effects of pore pressure [Biot, 1941]:

1 P

•; = • [[1 + v]o' - vTr({r)ai;] + • (6)

The strain-displacement relationship for the porous medium under the small displacement assumption is given by

Vu (7)

The development of equations (5)-(7) is based on the assumption of small elastic strain that is applicable to macroscopically continuous porous media. When large displacements occur, such as along faults in basins, special treatment of deformation is required. Ge and Gar- yen [1994] used a slip element technique to deal with large displacements along a fault zone. Alternatively, some researchers have utilized kinematic models of fault

block displacements that conserve rock volume but do not account for stress and strain rigorously [Wang et al., 1990; Wieck et al., 1995].

Equations (5)-(7) and associated boundary conditions fully define the mechanical state of the saturated porous media. Many studies have bypassed a rigorous, multidimensional representation of porous media deformation and have assumed that sediment consolidation

occurs only in the vertical direction. This is typically the case for studies of actively forming basins where mechanical loading takes place as a result of sedimentation (OL/Ot). Assuming that sediment compaction only takes place in the vertical (œ • Az/z), and defining bulk compressibility a v as Oœ/O(rv, a term using the specific storage coefficient and the sedimentation rate can re- place the temporal derivative of total stress in equation

34, 1 / REVIEWS OF GEOPHYSICS Person et al.' HYDROGEOLOGIC MODELING ß 67

00' T [3 's -- Pf OL

Otp W • Ss pf Ot

3.3. Heat Transfer

Time-dependent conductive-convective heat transfer through sedimentary basins is represented by an energy conservation equation [Sharp and Domenico, 1976]'

OT pfhf (p0c + psCs( - 0)) + _ 0) at

: V. [XVT] - qpfcfVT (8)

In this treatment of heat transport it is implicitly assumed that the solid phase is in thermal equilibrium with the fluid phase. The first and second terms on the left side of (8) account for changes in enthalpy with temperature and sediment compaction, respectively. Heat transfer by conduction and advection is represented by the first and second terms on the right side of (8). Enthalpy changes due to effects of anisotropy and heterogeneity in thermal properties of the porous medium are accounted for in (8) through the tensor properties:

)•- kfk, + pfcfD (9)

Values of thermal conductivity, heat capacity (cf), and thermal dispersivity (embedded in the thermal dispersion tensor) are compiled by Garven and Freeze [1984a] and de Marsily [1986]. The second term on the right side of (9) represents thermal energy dispersion due to the mechanical mixing of groundwater at the pore scale along a tortuous flow path, while the first term accounts for conductive energy dissipation for the solid and fluid phases. Because the thermal conductivity of the solid phase (hf) is several times larger than that of the fluid phase (hf), the thermal conduction-dispersion tensor will increase with decreasing porosity.

3.4. Reactive Mass Transport A solute mass conservation statement for reactive

transport in nondeforming media is [Garven and Freeze, 1984a, b]

V' ((bDVci) - OVVCi- Od)c •

Ot dr- ogi (10)

i- 1,2,...,I

where the terms on the left side account for dispersion and advection, and R i is the net rate of addition of species i to the fluid by all reactions. R i is negative if the ith species is removed from the fluid by adsorption or precipitation of solids. Equation (10) is often written in terms of the global or total concentration of a chemical component in order to reduce the number of dependent variables. Chemical components in this sense are defined as linearly independent chemical entities, such that every species can be uniquely represented as a combination of these components, yet no one component is a

combination of other components. In addition, these components are sometimes defined to correspond to species in the aqueous phase, referred to as "component species" [Reed, 1982]. The use of these components, rather than neutral species, elements, or oxides, reduces the computer storage requirements significantly [Helge- son et al., 1970]. The total or global mass of a component defined in this manner will be reaction-invariant [Rubin, 1983], and a mass balance expression may be written for each component as

Mc T -Mc + Z l•csMs + Z l•cmMm (1•) s=l m=l

where M is the molar concentration, c refers to a component species (• total), s refers to a secondary species (e.g., a complex, i total), m refers to a mineral (th total), v cs and V cm are stoichiometric coefficients indicating the number of moles of component species c per mole of secondary species s or mineral m, and the superscript T refers to the total concentration. Using this definition, the advection-dispersion-reaction equation (11) may be rewritten as

V' ((bD T __ , : Vmc•,aq) OVVmcTaq OOM• T

ot (12)

where the subscript c,aq refers to the total aqueous concentration of component c. The result is a set of nonlinear partial differential equations, one for each chemical component. The governing equations in this form require knowledge of how mass is partitioned between the different phases. Alternatively, reaction rates may be incorporated directly into the general expression

0 T rh O/cl'aq ør- Z l•cmrm V ' (O/V/cT, aq) -- OVV/cT'aq = Ot

m=l

(13)

where rm is the rate of precipitation or dissolution of mineral m.

3.5. Geochemical Reactions

In order to solve equations of the form (10), (12), or (13), additional expressions for the rate of mass transfer between solution and solid phases are required. Descrip- tions of the geochemical reactions are generally based on two different descriptions, either kinetic or local equilibrium. A kinetic description is the most general, and some modeling efforts include theoretical rate laws of the form [Steefel and Lasaga, 1994]

rate = rm = Skmf(ai)f(AG) (14)

where rm is the rate of mineral precipitation or dissolution per unit rock volume, S is the mineral specific reactive surface area, k m is a rate constant, f(ai) is some function of the activities of the individual ions in solu-

68 ß Person et al.' HYDROGEOLOGIC MODELING 34, 1 /REVIEWS OF GEOPHYSICS

tion, and f(AG) is some function of the free energy of the solution.

Chemical equilibrium is described by the law of mass action. Incorporating the notation for aqueous component species, complexes, and precipitated species, we may write mass action expressions for each dissociation and dissolution reaction as follows [Reed, 1982]:

• •/•csm•cs c=l

K: (15a) %ms

-I l•cm l•cm % mc c=l

g sp = (15b) am

where K is the dissociation constant for an aqueous complex, r sp is the solubility product for a mineral, m is the molality of the subscripted species, and •/ is the activity coefficient of the subscripted species. Reactions are assumed to be written for 1 mol of the species under consideration (complex or solid). Thus at each point in the system, under the local equilibrium assumption, we may write • mass balance equations, one for each component; • mass action expressions for the complexes (15a), and rh mass action expressions for mineral phases (15b). The result is • + • + rh equations t-hat must be solved simultaneously for the • + • + rh (concentrations of all species) unknowns.

3.6. Equations of State In order to fully couple groundwater flow, heat trans-

fer, and solute transport, equations of state relating fluid density and viscosity to temperature and salinity variations must be introduced. Fitted polynomial expressions (linear, quadratic, or higher order) are commonly used [Garven and Freeze, 1984a]:

pf- pf(P, T, C) !xf- !xf(P, T, C) (16)

In general, fluid density variations are not as sensitive to changes in fluid pressure as to temperature and salinity increases over the range of environments encountered in sedimentary basins. In almost all cases the behavior of groundwater near the critical point and phase separation due to boiling are neglected, although these effects have been incorporated into some hydrothermal models (see, for example, Hayba and Ingebritsen [1994]).

conditions in the absence of better information. There is

a clearly need for more interdisciplinary work here, especially in site specific modeling studies, between geologists, geophysicists, and hydrogeologists to construct more realistic, quantitative representation of past boundary conditions.

For groundwater flow the water table boundary is generally assumed to be a subdued replica of the pa- leotopography, and no-flow conditions are assumed along the base and lateral sides of the sedimentary pile. Paleo-water table configurations have typically been estimated on the basis of ancient mountain building events, erosional data, and geophysical logs indicating "overcompacted" sediments. Few studies have considered the role of changing climatic conditions on paleo- water table configurations [England and Freeze, 1988]. In addition, most modeling studies have neglected fluid flow between the sedimentary pile and underlying crys- talline rocks. This assumption has been called into question in some settings. For example, mineralogical and isotopic evidence suggests that basinal fluids have moved vertically through fractured igneous and metamorphic basement below sediment-hosted lead-zinc deposits of southeastern Missouri [Burnstein et al., 1992] and Ire- land [Dixon et al., 1990]. In addition, Nut and Walder [1990] cite evidence of meteoric fluids at depths of up to 20 km.

For heat transfer, a specified temperature boundary is typically assigned to the upper boundary, and a specified heat flux boundary is applied along the base of the sedimentary pile [Garven and Freeze, 1984a, b]. The sidewalls of the basin are usually assumed to coincide with hydrologic divides and to be insulated. In order to represent elevated temperatures at thermal springs, For- ster and Smith [1988a, b] applied a specified (convective) heat flux boundary condition along fault zones in regional discharge areas. In order to specify temporal changes in basement heat flux (and tectonic subsidence) through time, some recent studies have incorporated geomechanical models of the thermomechanical evolution of the underlying lithosphere [Burrus and Audebert, 1990; Person and Garven, 1994].

For solute transport, a specified concentration for each solute species is typically assumed at the land surface and no-flux boundary conditions along the other edges of the sedimentary pile. Internal specified concentration conditions are sometimes assumed for sedimen-

tary layers that contain soluble evaporite minerals [Bethke et al., 1993]. For reactive multicomponent solute transport, boundary values need to be specified for each

3.7. Boundary Conditions An additional step in constructing numerical models

involves selection of geologically relevant hydraulic, thermal, geochemical, and mechanical boundary conditions. Much uncertainty exists in estimating boundary conditions through geologic time. This information must be inferred from the rock record, which has led most hydrogeologists to imposed simple, idealized boundary

chemical component. For porous media deformation there are two basic

types of mechanical boundary conditions: a specified stress and specified strain-displacement. The choice of which boundary condition should be used may well depend on which is better constrained by geologic data. In some cases the amount of displacement that has oc- curred along a given boundary (e.g., a thrust sheet) is

34, 1 /REVIEWS OF GEOPHYSICS Person et al.' HYDROGEOLOGIC MODELING ß 69

'1:3

o

10-2 -

10--4

10-6

10.-8 10-1

• k = 1 darcy

Laboratory _

Basin

100 101 102 103 104

Scale of Measurement (m)

Effect of Karst

and Regional Fracture Networks

Effect of Macroscale Fra•iure

Effect of

Primary Porosity and Microfractures

Figure 1. Effect of scale of measurement on the hydraulic conductivity of carbonate rocks in central

Kiraly [1975]). The open circles denote average permeability data as determined from core plugs, borehole tests, and calibration of a regional flow model. Bulk permeability appears to grow with the scale of measurement because carbonate aquifers are perva- sively fractured and karstic in nature.

known. In other situations one might be more confident about the stress state along a boundary. To represent compressional forces and thrust sheet loading (equations (5)-(7)), horizontal and vertical stress or displacement is applied to the side and top (proximal) boundaries of the sedimentary basin. Over the remaining (distal) portion of the top boundary, a no-stress condition is imposed [Ge and Garven, 1992, 1994]. For the distal side boundary, a no-horizontal-displacement condition is often applied. For basin models that consider only one-dimensional sediment compaction, specified sedimentation and subsidence rates are assigned for the nodes at the base of the sedimentary pile [Bethke, 1985]. Typically, the land surface is pinned so that sedimentation keeps pace with subsidence.

3.8. Basin-Scale Rock Properties Specification of material properties in basin models

requires special considerations. These include issues of permeability heterogeneity and scale effects associated with the use of permeability data obtained from drill cores or packer tests in basin-scale models, and the effect of mechanical compaction and diagenesis on spatial and temporal changes in permeability, porosity, and thermal conductivity during basin evolution.

Laboratory and field-scale studies conducted during the last few decades have documented that important variations in permeability in sedimentary deposits exist in both vertical and lateral directions and at many different spatial scales [Dreyer et al., 1990; Davis et al., 1993]. It is now widely regarded that these heterogeneities are the rule rather than the exception in natural sedimentary deposits. Recent investigations by petroleum researchers have emphasized the importance of characterizing permeability heterogeneities using geostatistical or fractal methods [HaMorsen and Dams- leth, 1990; Rhea et al., 1994]. Yet continuum assumptions require volume averaging of borehole- or outcrop-scale heterogeneities in basin-scale transport models. These scale effects have important consequences for the selection of representative rock properties in the basin model. Garven [1986] argues that permeability data used

in basin-scale models may be up to 3 orders of magnitude larger than permeability measurements of drill core samples in the laboratory or from packer tests in the field due to scale effects (Figure 1). Bethke [1989] dis- cusses how shale lenses within sandstone aquifers can increase the "basin-scale" anisotropy by several orders of magnitude relative to anisotropies measured in the laboratory. These findings are supported, in part, by scaling arguments based on fractal theory [Neuman, 1990]. However, such findings have not gone unchal- lenged. For example, Neuzil [1994] found that the permeability of shales, in some instances, is not scale-dependent. These scaling issues may be resolved over the next decade by detailed field studies that measure hydraulic parameters at many different scales.

The effect of the scale of measurement on dispersivity, like hydraulic conductivity, is well known [Schwartz, 1977; Pickens and Grisak, 1981]. In general, measurements at the laboratory scale are much smaller than those at the field scale [Neuman, 1990; Gelhar et al., 1992]. The cause of this scale effect has received considerable attention in recent years. Transverse dispersivities are generally smaller than longitudinal dispersivities, typically by an order of magnitude or more. In addition, Gelhat et al. [1992] summarize data that indicate that transverse dispersivities measured in the vertical direction are typically an order of magnitude smaller than those measured in the horizontal direction.

Temporal variations in porosity, permeability, specific storage, and thermal conductivity also represent important issues in basin-scale modeling. Because porosity is relatively easy to measure and can be empirically related to other rock parameters, it is routinely measured during basin studies. Porosity is typically observed to decrease in sedimentary basins with depth owing to the effects of mechanical loading during burial and diagenesis. One practical relation used to describe mechanical porosity reduction with depth is given by Hubbert and Rubey [1959]:

q)- q)0e -b•e (17)

The effective stress (O'e) is sometimes approximated by depth (L - z) in (17) in some studies of compaction-

70 ß Person et al.: HYDROGEOLOGIC MODELING 34, 1 /REVIEWS OF GEOPHYSICS

driven groundwater flow [e.g., Bethke, 1985; Deming et al., 1990; Person and Garven, 1992, 1994] by introducing the concept of compaction disequilibrium [Magara, 1975]. A major shortcoming of (17) is that it does not account for potentially significant porosity reduction due to diagenetic reactions. In addition, Luo and Vasseur [1992] point out that when the effective stress acting on a sediment column is decreased below the maximum

value imposed on the sediments, porosity does not increase back to its earlier value. Some researchers have

compensated for this deviation from elasticity theory by utilizing different consolidation coefficients (b) depending on whether sediment loading or unloading is occurring [e.g., Corbet and Bethke, 1992].

Because of the large contrast in thermal conductivity between the fluid and solid phases, decreases in porosity with depth lead to increases in thermal conductivity in deeper portions of the basin. This is accounted for by the first term in (9). In a similar manner, a number of studies have tried to relate permeability to changes in porosity. Analysis of many basin drill core data from well-sorted clastic deposits suggests that porosity is sometimes linearly related to the log of permeability [Bethke, 1985; Nelson, 1994]:

log (kx) = CO) + D (18)

The coefficients C and D in (18) are estimated from regression fitting of laboratory measurements of core porosity and permeability. Bethke [1985], Neuzil [1994], and Sanford and Konikow [1989b] present values of C and D for sand, shales, and carbonate rocks. Lucia and Fogg [1990] developed separate permeability-porosity relations using (18) for different pore systems (intergranular, intercrystalline, and mixed) within a carbonate reservoir. It should be pointed out, however, that equation (18) is empirical; theoretical arguments indicate that permeability cannot be predicted from porosity alone except in some highly idealized cases such as bundles of capillary tubes or parallel fracture sets [Neu- man, 1977]. Less easily addressed are the effects of mineral precipitation and dissolution on temporal variations in permeability. Studies of relating porosity-permeability changes during fluid flow in a reactive porous media are rare and scattered throughout various disciplines [Lund and Fogler, 1976]. Some of the most sophis- ticated analyses to date have been related to the problem of porosity reduction during the acidification of sandstone reservoirs. Some early theoretical work indicates that rapid (minutes) permeability reduction of up to 3 orders of magnitude can occur as a result of mineral precipitation reactions [Schecter and Gidley, 1969]. With a few exceptions [Sanford and Konikow, 1989a, b; Steefel and Lasaga, 1994], modeling studies have not attempted to address reactive chemical transport and associated changes in porosity and permeability at the basin scale. Finally, the specific storage coefficient is another hydraulic parameter that can be related to porosity using the following relation given by Bethke and Corbet [1988]:

pf bq>

Ss(q>) p's- pf 1 - q> (19) Equation (19) indicates that the compressibility of the porous medium is significantly reduced as the sediments become highly compacted. Bethke and Corbet [1988] argue that failure to incorporate this nonlinear relationship (as well as the permeability-porosity relation in (18)) can result in significant overestimation of excess hydraulic heads due to sediment loading.

Faults represent an important complicating factor in representing basin hydrodynamics because of their effects on subsurface permeability [Forster and Smith, 1988a, b; Garven and Freeze, 1984b; Roberts and Nunn, 1995]. Fault block motion over long time periods can significantly modify the subsurface plumbing of basins due to aquifer-aquitard juxtaposition [Wieck et al., 1995]. The hydrological response to earthquake strain is another important issue in basin modeling. Earthquake strain occurs in the vicinity of moving fault blocks [Muir- Wood, 1994]. The strains caused by earthquakes can accumulate and release in a short period of time, inducing episodic fluid flow [Sibson, 1994]. While it is reason- ably clear that the fluxes involved in reequilibrating fluid pressure changes due to seismic strain are small and involve short transport distances, this phenomenon may be an important mechanism for solute mass transfer on geologic timescales. This mechanism has been proposed to explain elevated surface and groundwater discharges following an earthquake, although Rojstaczer and Wolf [1992] argue that this is due to permeability increases induced by seismic activity. On the other hand, fault zones can act as low-permeability barriers due to processes such as pressure solution, deformation of adjacent strata, clay smearing, and hydrothermal mineralization [Yaxley, 1987; Berg and Avery, 1995].

4. SOLUTION METHODS AND APPLICATIONS

Quantitative analysis of transport processes in sedimentary basins can be obtained at many different levels of complexity using either numerical or analytical methods. At one extreme, models can be constructed that incorporate complex, spatially varying material properties and time-dependent boundary conditions. Because such variability is the rule rather than the exception in nature, a systematic study of these conditions is of great value and typically utilizes numerical methods. A shortcoming of this approach, however, is that the numerical model results generally are nonunique and sometimes difficult to interpret. An alternative approach is to construct more simplified analytical models of sedimentary basins. In this approach, homogeneous material properties and simple hydrological and thermal boundary conditions are used. While these models are lacking in geologic complexity, they can provide important insights and order of magnitude estimates of various transport

34, 1 /REVIEWS OF GEOPHYSICS Person et al.' HYDROGEOLOGIC MODELING ß 71

TABLE 1. Analytical Solutions of Coupled Transport Processes in Basins

Authors Solution Type Processes Represented

Biot [1940], Bredehoeft and Hanshaw [1968a], Rice transient, 1-D and Cleary [1976], Gibson [1958]

T6th [1963] Bredehoeft and Papadopulos [1965] Bredehoeft and Hanshaw [1968b] Domenico and Palcjauskas [ 1973] Combarnous and Bories [1975]* Straus and Schubert [1977]

flow, sediment consolidation

McKibbin and O'Sullivan [1980, 1981]

Palciauskas and Domenico [1982] Wood and Hewett [1982] Cathles [1987] McTigue [1986] Vasseur et al. [1993] Rubin [ 1981 ], Braester and Vadasz [ 1993]

Lowell et aL [1993]

steady-state, 2-D fluid flow steady-state, 1-D flow, heat transfer transient, 1-D flow, fluid producing diagenetic reaction steady-state, 2-D fluid flow, convective heat transfer (forced) steady-state, 2-D fluid flow, heat transfer, Boussinesq assumption steady-state, 2-D fluid flow, heat transfer, temperatures dependent

viscosity and thermal expansivity steady-state, 2-D fluid flow, heat transfer in a layered porous

medium

transient, 1-D flow, sediment consolidation, heat transfer steady-state, 2-D fluid flow, heat transfer steady-state, quasi 2-D fluid flow, heat transfer transient, 1-D flow, heat transfer, sediment deformation transient, quasi 2-D fluid flow, heat transfer steady-state, 2-D fluid flow, heat transfer in a heterogenous

porous medium transient, 1-D fluid flow, heat transfer, silica precipitation

Abbreviations are l-D, one dimensional; 2-D, two dimensional. *Analytical solutions of natural convection in porous media are too numerous to list. Some representative references are included, however.

processes. Analytical methods should always be considered as a first (and perhaps most informative and useful) step in any quantitative study [Phillips, 1990]. In addition, despite the approximations and simplifications inherent in these studies, analytical solutions provide a benchmark for verifying numerical models and for ana- lyzing some of the important effects of coupled flow and chemical reactions.

4.1. Analytical Models Numerous one-dimensional, analytical solutions are

available that quantify different basin-scale transport processes (Table 1). However, the equations governing

coupled flow, heat, and mechanical deformation are generally difficult to solve analytically. These analytical solutions commonly invoke fully linearized theory and therefore should be interpreted with caution. This is because the assumptions made to simplify the coupled equations, such as constant material properties and feedbacks between transport processes, may be unreal- istic. For example, the analytical solution of Gibson [1958] for sediment compaction shown in Figure 2b (dashed lines) consistently overpredicts excess heads compared with the numerical solutions (solid lines in Figure 2b) of Bethke and Corbet [1988], which accounts for changes in specific storage Ss and permeability k

?•,lmpermeable ,• .;,;.Basement;,;,;,

Excess Head (m)

0 4000 8000 12000

01• ' ' ' , , , B Numerical

/ [•,• --- Analytical

4[ •i k x[ x

il

Porosity

0.1 0.3 I I i I

c

?

Figure 2. (a) Schematic diagram depicting mechanical loading of sedimentary column due to subsidence and sedimentation. (b) Comparison of analytical (dashed lines) and numerical (solid lines) solutions for excess head generation due to sediment compaction. The numbers on the lines indicate (he

sedimentation rate in centimeters per year. The analytical solution was computed using a porosity of 0.3, a specific storage of 10 -4 m-•, and a hydraulic conductivity of 2.7 x l0 -•2 m s -•. (c) Computed changes in porosity with depth due to changes in effective stress predicted by the coupled, one-dimensional numerical solution of sediment com-

paction described by Bethke and Corbet [1988]. The specific storage and permeability were allowed to vary with porosity using equations (18)-(19) in their finite difference solution.


resulting from changes in porosity (Figure 2c) associated with effective stress variations represented by equations (17)-(19).

Two-dimensional analytical solutions have been developed also to investigate the effects of the water table configuration on regional groundwater flow patterns in sedimentary basins [T6th, 1962, 1963]. These pioneering studies helped define local-, intermediate-, and regional- scale flow systems within watersheds. Because of important control of subsurface permeability variations and variable density on regional flow patterns [Freeze and Witherspoon, 1967; Garven and Freeze, 1984b], however, these analytical methods are now seen as representing special cases.

Studies of forced convection within sedimentary basins have also employed analytical methods (Table 1). These have been developed to interpret thermal anomalies observed in basins with very simple aquifer geom- etry. Calculations provided by Vasseur et al. [1993] indicate that large lateral flow rates are necessary (1.5 m yr -• through a 100-m-thick aquifer) in order to produce noticeable convective heat transfer effects within gently dipping aquifers (6 degrees). However, analytical solutions developed by Bredehoeft and Papadopulos [1965] indicate that only modest vertical groundwater flow rates (about 1 mm yr -•) are needed to disturb conductive conditions within thick (about 6 km) sedimentary basins.

Analytical models of free convection in porous media are too numerous to discuss in this review [e.g., Com- barnous and Bories, 1975]. Many of these analyses invoke simplifying (Boussinesq) assumptions regarding fluid and porous media properties, although recent analytical work has relaxed these constraints [Braester and Vadasz, 1993]. Many analytical models of natural convection have been applied to the study of hydrothermal circulation near mid-ocean ridge systems [Lowell, 1991]. Wood and Hewett [1982] and Phillips [1990] applied analytical models of free convection to analyze the effects of fluid flow on sandstone and limestone diagenesis.

Analytical solutions have been developed for problems involving reactive mass transport [Lund and Foglet, 1976; Baumgartner and Ferry, 1991] but are restricted by the physical processes represented and the complexity of the chemical system. For instance, one-dimensional flow is commonly assumed, and solute dispersion or diffusion processes are ignored. Typically, these solutions have been 'applied to simple binary ion exchange, although Palciauskas and Domenico [1976] derive analytical expressions that incorporate dissolution of calcium carbonate. Knapp [1989] and Lichtner [1993] provide solutions to a one-dimensional, single-component (SiO2) advection-dispersion (diffusion) reaction (14), including kinetic dissolution of quartz. Phillips [1990] also derives similar relations, based on dimensional analysis, which are useful in describing the general nature of different types of flow-controlled reactions.

4.2. Numerical Models

Numerical models have been used extensively in recent years to quantify basin transport processes within a number of tectonic settings including foreland basins, intracratonic sags, continental rifts, and accretionary prisms. The fluid flow mechanisms represented have varied depending on the perceptions of the dominant processes in various geologic environments. Numerical methods have been employed because of their distinct advantages over analytical techniques in representing heterogeneous and anisotropic porous media properties and complex basin geometries. With the advent of fast computer workstations, numerical models have been more frequently employed in case studies of basins. In addition, the coupled and nonlinear nature of variable- density groundwater flow, heat transfer, and multicomponent reactive mass transport within porous media is most tractable with numerical approaches. Both finite difference and finite element techniques have been extensively utilized in studies of basin transport processes (Tables 2 and 3). Finite difference methods, while having some restrictions in representing complex basin geometries, have been used with success by a number of authors including Bethke [1985, 1986a, b], Deming et al. [1990], and Deming and Nunn [1991]. Studies utilizing finite element models, which have more flexibility in representing complex basin geometries and mechanical deformation along faults, include those of Smith and Chapman [1983], Garven and Freeze [1984a, b], Garven [1985, 1986, 1989], Ravenhurst and Zentilli [1987], Ge and Garven [1992, 1994], Person and Garven [1992, 1994], Raffensperger and Garven [1995a, b], and Wieck et al. [1995]. Other numerical methods, such as integrated finite difference or boundary integral methods, have not seen wide application in sedimentary basin research.

Both finite difference and finite element numerical

solution procedures require that the flow domain be discretized by a numerical mesh. The numerical mesh is typically composed of a regular grid of rows and columns of nodes to help minimize the amount of bookkeeping required. Some authors have represented basin paleohydrology with nondeforming meshes to study topography-driven flow [Garven and Freeze, 1984a, b; Garven, 1986] (Figure 3), while others have utilized an evolving (accreting; Figure 4) grid of nodal columns using either the finite difference [Bethke, 1985; Deming et al., 1990] or the finite element [Ravenhurst and Zentilli, 1987; Person and Garven, 1994] method. Only three studies have represented large-scale displacements along faults; these have focused on hydromechanica! processes within foreland basins [Ge and Garven, 1994] (Figure 5), accretionary prisms [Borja and Dreiss, 1989], and continental rifts [Wieck et al., 1995]. However, much work still needs to be done to incorporate more tectonic complexity into basin-scale models.

Numerical models of fluid flow in foreland basins

have been most frequently applied in the study of fluid migration and associated ore genesis [Garven, 1985;


TABLE 2. Numerical Solutions of Coupled Transport Processes in Basins

Authors Study Area Processes Represented

Gatyen and Freeze [1984a, b]

Gatyen [1985, 1989]

Bethke [1986a], Bethke et al. [1988], Harrison and Summa [1991]

Bethke [1986b], Garven et al. [1993]

Bredehoefi et al. [1988] Burrus and Audebert [1990]

Evans and Nunn [1989], Evans et al. [1991] Clauser [1989], Person and Gatyen [1992]

Bethke et al. [1991 ] Deming and Nunn [1991 ] Ge and Gatyen [1992] Raffensperger and Gatyen [ 1995 a, b]

Ungerer et al. [1990]

Doligez et al. [1986], Burrus et al. [1991]

generic

Western Canada Basin

U.S. Gulf Coast

U.S. midcontinent

south Caspian Basin Gulf of Lions

Generic salt domes Rhine Graben

Illinois Basin

generic Arkoma Basin

McArthur Basin, Australia Athabasca Basin, Canada Mahakam Delta,

Indonesia North Sea Rift

steady state groundwater flow, heat transfer, solute transport in ore formation

fluid flow, heat transfer, solute transport, oil migration

transient groundwater flow, heat transfer, solute transport in compacting basins

flow, heat transfer, sediment deformation in MVT ore genesis

flow, sediment consolidation, heat transfer compaction driven flow and heat transfer oil

generation and migration fluid flow, heat, and solute transport transient groundwater flow, heat transfer,

petroleum generation transient groundwater flow and oil migration fluid flow, heat transfer, brine migration tectonically induced fluid flow groundwater flow, heat transport, solute transport,

rock-water chemical interactions

compaction driven flow and heat transfer oil generation and migration

compaction driven flow and heat transfer oil generation and migration

Bethke, 1986b] during uplift of foreland basins. Numer- ical calculations of the magnitude of groundwater flow rates due to sediment compaction associated with over- thrusting [Deming et al., 1990] and tectonic shortening [Ge and Garven, 1989, 1992] cannot account for the large quantities of metals transported to the site of ore deposition and would produce only modest temperature anomalies [Deming et al., 1990; Garven et al., 1993]. In contrast, finite element and finite difference model results of Garven [1985], Bethke [1986b], Bethke et al. [1991], and Garven et al., [1993] indicate that during orogenic events, uplift of the land surface and water table can induce regional topography-driven flow systems that can generate thermal and salinity anomalies

that are consistent with those observed in fluid inclusion

studies of stratabound ore deposits. These studies have revolutionized ore deposit studies by providing geologists with physically based generic and site specific models of the subsurface flow patterns and mechanisms associated with the ore genesis.

Results from numerical modeling studies of compaction-driven flow within accretionary wedge environments suggest that this is the most viable fluid-flow- inducing mechanism for explaining excess pressures, low-salinity fluid vents, and anomalous methane fluxes at the base of the sediment prisms [Screaton et al., 1990; Wang et al., 1990]. Platt [1990] studied thrust mechanics in the Makran accretionary wedge and suggested that

TABLE 3. Summary of Selected Reactive Flow Models

Solution Methods* Dimensions Application

Rubin and James [1973] Schwartz and Domenico [1973] Miller and Benson [1983] Walsh et al. [1984] Lichtner [1985, 1988, 1992] Hewett [1986] Ortoleva et al. [1987] Sanford and Konikow [1989a, b] Liu and Narasimhan [1989a, b] Phillips [1990, 19911 Steefel and Lasaga [1992, 1994] Yeh and Tripathi [1991] Engesgaard and Kipp [1992] Raffensperger [1993]

FD/dir/(C-T) 1 ion exchange FD/dir/(C-T) 2 watershed hydrochemistry FD/dir/(C-T) 1 contaminant transport FD/seq/(C-T) 1 uranium roll front ores FD/dir/(C-T) 1 weathering, supergene Cu ores ANL/dir/(C-T) 2 diagenesis FD/dir/(C-F) 1 various applications FD/MOC/seq/(C-F) 2 carbonate dissolution IFD/seq/(C-F) 2-3 supergene Cu enrichment ANL/dir/(C-T) 1 flow-controlled reactions FD/dir/(C-F-H) 1-2 hydrothermal systems FE/dir or seq/(C-T) 2 various applications FD/seq/(C-T) 1 pyrite oxidation FE/seq/C-F-H 2 sedimentary ore formation

*Abbreviations are FD, finite difference; FE, finite element; ANL, analytical; MOC, method of characteristics; dir, direct; seq, sequential; C-T, chemistry-solute transport; C-F, chemistry-fluid flow; C-F-H, chemistry-fluid flow-heat transport.


I !

120 ø 110 ø

Great Slave ......

-62 ø Lake

I [ 0 100 200km

B.C. I Alberta '

HYDROSTRATIGRAPHIC UNITS

Unit F. L K x (]) •'s Number (m) (m/yr) (W/m_oC)

4 10 25 0.15 2.0

3 10 50 0.1 2.5

2 10 20 0.1 1.9

I 50 500 0.25 3.0

4 B

2

1

o

STREAM FUNCTIONS

(A• = 50 m2/yr)

4

TEMPERATURES (øC)

0 1 O0 200 300 400 500

Distance (km)

Figure 3. Steady state finite element simulation of late Tertiary topography-driven flow and conductive- convective heat transfer within the Western Canadian Basin [from Garven, 1985, 1986]. Model calculations indicate that regional groundwater flow induced positive thermal anomalies within the discharge area in the basal dolomite aquifer and near the Pine Point ore body. Rock properties and the location of the section line are shown.

rapid tectonic loading may have caused sudden pressure increases within saturated sediments that subsequently caused hydraulic fracturing. Wang et al. [1990] modeled the thrust-fluid flow problem in the Oregon accretionary prism considering the gravitational loading of imbricated and thickened sediments. They found that high pore pressures can be generated beneath active thrust faults. A hydrogeologic study of the Barbados ridge complex by Screaton et al. [1990] applied a steady state flow model to estimate permeabilities from pore pressure and flow rate data. They proposed that the dficollement (detachment structure associated with folding and thrust faulting) may be a high-permeability zone.

Recent numerical modeling studies within rifts and intracratonic sag basins have helped to establish which fluid flow mechanisms (compaction-, density-, or topog-

raphy-driven flow) interact during basin evolution. Un- der marine incursion or low topographic relief, free convection can occur within thick (>1 km), permeable (>10 -]3 m 2) basal aquifers [Raffensperger and Garven, 1995a, b]. For rapidly subsiding continental rifts, such as the U.S. Gulf Coast, Bethke [1985, 1986a] and Harrison and Summa [1991] have present two-dimensional finite difference models that demonstrate that excess pressures can approach lithostatic levels owing to the effects of sediment compaction. Roberts and Nunn [1995] present numerical calculations that indicate that the buildup of high pore pressures in rift basins probably occurs on timescales of 10 4 to 10 5 years and can episodically release large volumes of heat and fluids over short (> 100 years) time periods along faults. Salinity effects can be especially important within continental rifts that are

34 1 / REVIEWS OF GEOPHYSICS Person et al.: HYDROGEOLOGIC MODELING ß 75

A PRESSURE (MPa) A'

2 km •16 14 0 100 km

I^, [•.Gr -31 o \ \

FI

Tx

-26 ø

I

PRESSURE (MPa) HYDROSTRATIGRAPHY

> 60

Figure 4. Calculated basin evolution Oligocene to present and excess fluid pressures contour lines along a cross section through the U.S. Gulf Coast. Excess pressures, which were computed using the finite difference model of Bethke [1985], are highest in the deepest portion of the basin in the center of low-permeability layers that are being loaded by sedimentation [after Harrison and Summa, 1991]. Depth of seawater (stippled pattern), location of section line A-A', and the percentage of sand used to adjust sediment permeability are also shown. Reprinted by permission of American Journal of Science.

hydrologically closed [Duffy and A1-Hassan, 1988] or contain salt domes [Evans et al., 1991]. However, it is unclear from recent field observations whether salinity plumes above Gulf Coast salt domes are due to convection or upward flow of compaction driven fluids episodically released along fault zones. Hydrodynamic models of rifts and intermontane basins have been used to help understand the effects of convective heat transfer on oil

generation [Willet and Chapman, 1989; Person and Gar- yen, 1992; Person et al., 1993] (Figure 6) and hydrothermal ore genesis [Person and Garven, 1994]. These studies have shown that only modest groundwater flow rates (--•1 mm yr -•) are required to shift the depth of oil generation by hundreds of meters and have promoted the concept of hydrodynamically generated petroleum [Kvenvolden and Simoneit, 1992].

A number of numerical modeling studies have addressed the issue of petroleum migration through basins of various tectonic origins in an attempt to understand the hydrologic controls on the formation of giant oil reservoirs. For example, Garven [1989] and Bethke et al. [1991] studied long-range oil migration in western Can- ada and Illinois, respectively, using two-dimensional cross-sectional models that incorporated oil head and velocity relations (equations (3) and (4)). These studies

found that lateral hydraulic gradients established during regional, topography-driven paleofiow systems were suf- ficient to drive separate-phase hydrocarbons towards the edge of these basins forming world class energy deposits. Oil migration times required to form these petroleum reservoirs were geologically instantaneous (105 years). However, more recent geostatistical, quasi-three-dimensional models of long-range oil migration through basins by Rhea et al. [1994] indicates that oil transport directions are very sensitivity to lateral permeability variations (Plate 3) and calls into question the use of cross- sectional models in representing long-range oil migration. These findings combined with recent im- provements in process sedimentation modeling [Kolter- mann and Gorelick, 1992] suggest that during the next 10 years the development of fully integrated, three-dimensional basin models will be a fruitful area of study by petroleum researchers.

4.3. Reactive Mass Transport Numerical models of reactive multicomponent chem-

ical transport have been developed by researchers in a variety of fields, such as chemical engineering, petroleum engineering, soil science, geochemistry, and hydrogeology. Because of the nonlinearity'of the problem,


90 '•' "• .... • ;"'•"' • • ..z-•

' '-"•",•,•:•.',.•__F 35ø

HYDROSTRATIGRAPHIC UNITS

Unit

Number Kx (m/yr) • E(Pa) ps(kg/m3) 9 0.10 0.25 2.0x10 lo 2400 8 1.00 0.20 4.0x10 lo 2400 7 0.01 0.10 4.0x10 TM 2400 6 2.00 0.10 4.0x101ø 2400 5 5.00 0.10 4.0x10 TM 2400 4 50.0 0.20 4.0x101ø 2400 3 1.00 0.10 2.0x101ø 2400 2 100. 0.30 6.0x101ø 2400 I 0.01 0.02 7.0x101ø 2400

Tectonic

A' A Loading

6

4

HYDR G, RAPHY, ' , , --, , ,"•.• •.•.• o O, STRTI õ 160 years

• •-• • •..=.••_•_.•.•_.-._:__-. :•_;---_------= =•: ;.:......-.:....,•,..:.:,::..• ,•, 6 t • --- 000 `---...•.•i-•.-•.•.•:..•i•..•;....•.•.•..•..•.•;•;..•.•.•.:`•.....•:•;;.•`:• ';...:......':•'¾?.:....:•;•%:.,.• _•. . ........... ' '"'•"• ........ '•_' ............ ..:•...•.• ....... .•,.,-,-':•:.,•i•g• •'.--.'•!• _ • • • • • • • ..... •• • ••=• . ..._:...ii!•;:.•........•::.:• ..i-r-:::.'..'.i•i.•

2 HYDRAULIC HEADS .(m) VELOCITY VECTORS q = ;•.•) m/yr

o

o ,• 1•) 1'5 2• 2'5 E•o 3•5 4•) 4,•

Distance (km)

Figure 5. Hydromechanical flow model for the Pine Mountain thrust system in eastern Tennessee [from Garven et al., 1993], 160 years after a tectonic force of 800 MPa was applied to the right margin to initiate deformation along a thrust plane (unit 7). Flow is from southeast to northwest (right to left in the figure), with focusing in aquifers of Cambrian sandstone (unit 1) and Ordovician carbonates (unit 4). The simulation is intended to assess the role of Appalachian and Ouachita orogens in driving pore fluids hundreds of kilometers acrosss the continents. Reprinted by permission of American Journal of Science.

mathematical models are generally solved numerically. Although models of flow and reaction in porous media have existed for at least 20 years, their application to geologic settings is a relatively recent advance and has not received recent review. Therefore these advances in

coupled modeling'of large-scale flow and reactive mass transport will be discussed here in some detail.

Several approaches to numerically solving the reactive mass transport equations have been taken (Table 3), which fall into two main categories: direct substitution and sequential iteration. Direct methods incorporate chemical equilibrium expressions or rate expressions directly in the transport equations, thereby solving both sets of equations simultaneously. The earliest modeling efforts generally used direct coupling methods, but with limitations imposed by simple chemistry or flow systems. Many of these studies examined ion exchange, following pioneering work by Rubin and James [1973]. The CHEMTRN code [Miller and Benson, 1983] solves both sets of equations simultaneously and has undergone several revisions [Carnahan, 1987]. Lichtner [1985, 1988,

1992] developed a one-dimensional finite difference model of multicomponent reactive solute transport, using a kinetic description of mass transfer. This code, which uses a quasi-stationary state approximation, is particularly well suited to performing calculations over long timescales such as occur with weathering and redox front propagation [Lichtner and Waber, 1992] and supergene copper enrichment [Lichtner and Biino, 1992].

Ortoleva et al. [1987] describe a two-dimensional model that is fully coupled; they have used their model to examine a variety of geochemically self-organizing phenomena [Chen et al., 1990; Dewers and Ortoleva, 1988; Wei and Ortoleva, 1990]. In addition, Dewers and Ortoleva [1990, 1994] have combined a reactive solute transport model with a description of mechanical deformation in sediments and sedimentary basins in order to attempt to understand the role of pressure solution on diagenesis and the compartmentalization of sedimentary basins.

Steefel and Lasaga [1994] use a global implicit (one step) technique to couple kinetically described mass

34, 1 / REVIEWS OF GEOPHYSICS Person et al.' HYDROGEOLOGIC MODELING ß 77

Pechelbronn .•,. •q'•"/[ _. ?½ /"-'1

A Strasb(•urg = / 20•_•__•km I Northwest Location map

6

i

Southeast

:.t•;. .-..• . . . .•

o

o 5 1 o 15 2o 25 3o 35 4o

Kilometers

> "• ..... • - 10 Vma x = O. 13 m/yr Oil generation Deviations from

conductive thermal regime

Figure 6. Computed present-day groundwater flow directions (arrows), convective thermal anomalies (solid lines, in degrees Celsius), and zone of oil generation (stippled pattern) across the Rhine Graben along transect A-A'. The magnitude of the log of the Darcy velocity is proportional to the length of the vector shaft. The location of the section line A-A' is depicted in the inset. The zone of oil generation was computed by calculating the time-temperature history of the sediments using an evolving finite element grid over a 40-million-year period. The establishment of convective heat transfer has caused cooler than conductive conditions within groundwater recharge areas and positive thermal anomalies within discharge areas during the past 15 M yr. The simulation illustrates the important control of groundwater flow on the depth to the onset of oil generation within basins [after Person and Garven, 1992] (reprinted by permission).

transfer with mass transport in two spatial dimensions. Their model includes heat transport and was used to assess the validity of the local equilibrium assumption in single phase hydrothermal systems. Because the model is fully coupled, their results indicate that reaction-induced permeability change is likely to have a significant impact on the character and dynamic evolution of hydrothermal systems.

In general, sequential solution methods have been more common, owing to their ease of programming. The mass transport and chemical reaction equations are solved separately and sequentially; iteration may be required to treat the nonlinearities. One example of a code that makes use of the sequential method is provided by Walsh et al. [1984]. Often these transport codes will incorporate external chemical speciation codes [Kirkner et al., 1985; Lee and Bethke, 1994], or reaction path codes [Ague and Brimhall, 1989]. Sanford and Konikow [1989a, b] describe a unique sequential solution approach, which couples the results from a reaction path model (determined before coupled simulations and provided in a tabular form) with a variable-density flow and transport model. The limitation of this approach is that only relatively simple geochemical systems may be studied. They applied this model to calcite dissolution in a coastal mixing zone (Figure 7). Their results indicate that calcite dissolution rates are nearly independent of the kinetics of calcite dissolution and that porosity and permeability modification can dramatically alter the flow system over time spans of the order of tens of thousands of years.

Raffensperger [1993] describes a two-dimensional model that uses a predictor-corrector time-stepping scheme to sequentially solve the transport and chemical equations and assumes local chemical equilibrium. Raffensperger and Garven [1995a, b] use this model to examine the formation of Middle Proterozoic unconfor-

mity-type uranium deposits in Proterozoic basins (Plate 4). An important result of this work is that geochemical patterns of alteration can provide a constraint on the nature (i.e., flow mechanisms and patterns) of basin- scale hydrogeologic systems. Garven and Raffensperger (in press) calculated patterns of mineralization in a topography-driven flow system in order to test geochemical hypotheses of Mississippi Valley type (MVT) ore formation.

Many flow models of reactive mass transport assume local chemical equilibrium, that is, at any point in the system, no mutually incompatible phases are in contact, even though the system as a whole may not be in equilibrium. Knapp [1989] concluded that local chemical equilibrium would be a valid assumption as long as the problem time and length scales are much greater than the scales required for equilibration, a situation that would likely occur in large sedimentary basins. Difficul- ties will clearly arise in attempts to use the local equilibrium assumption for problems involving smaller time and space and scales [Lichtner, 1993]. In addition, the actual length scale of interest for geologic problems is subject to debate, especially when thermal boundary

78 ß Person et al.- HYDROGEOLOGIC MODELING 34, 1 / REVIEWS OF GEOPHYSICS

/

m !//'

34, 1 /REVIEWS OF GEOPHYSICS Person et al.: HYDROGEOLOGIC MODELING ß 79

• 20 250 m/yr • q -•o • 40 Pco2 10

• 80 ''•-" •1 • Porosity (%) • A •A//.-' .... ,A• 0.5p_ Fraction Seawateq • , , •f..',• , _,'•; • - _; .... 100 500 1000 1500

0 .... • .... i2• , ,.p , • Time = 10,000 years •.,•' ,' • 20 q = 250 m/yr = 4o cos= • • • 5 Additional porosity (%) • 60 •.•O- Fraction Seawater ,•••t

a • , , , ,•'";'', , 4 .... 1 O0 500 1000 1500

0

• Time = 10,000 years m 20 • q = 25 m/yr

m - 10 -• o • 40 Pco•

• 60

• 80 C • •1 • Porosity (%) • , , , I ....

100 ß ' 500 1000 1500 01 .... • ' ' . .... •' • '/' /' ' I

• / q = 25 m/yr ........ /• • • / 20 • p 10 -• o ........ • / co• = . ........ ,' / ..•*•/ /

- . .... / ,,,,;';• z 6oF .... / • • "'" / ......... '• n ,. .......

/. ,. ..... , Z/. . , .... / ooo

1000's of

years

1% seawater 50% seawater

0

50

100 ........................................

• Direction of mixing zone migration

Figure 7. Numerical simulations of variable-density groundwater flow and reactive mass transport, showing porosity evolution within the seawater mixing zone of a homogeneous (Fig- ure 7a) and heterogeneous (Figure 7b) coastal carbonate aquifer. The freshwater inflow rate q is 250 m yr -• in both simulations. In the homogeneous case (Figure 7a), dissolution is most pronounced at the base and top of the mixing zone. This pattern, however, is strongly modified when heterogeneity is considered (Figure 7b). Fully coupled simulations, allowing feedback between the flow system and evolving porosity-permeability structure, demonstrate the dynamic nature of the flow pattern (Figure 7d) resulting from porosity modification (Figure 7c). After Sanford and Konikow [1989b].

layers and other local phenomena are present [Steefel and Lasaga, 1994].

5. DISCUSSION

The last 10 years have seen a prolific growth in the development and application of basin-scale hydrological models in the study of transport-limited geologic processes. While the analytical and numerical models described above vary considerably in their complexity and

the number of coupled transport processes represented, both approaches are widely used. Analytical (and scaling) methods have probably seen most use in calculating "order of magnitude" estimates of various transport processes. Numerical model development and application has focused on coupled studies of nonlinear hydrologic, thermal, chemical, and mechanical transport processes at specific field sites. While the development of "fully coupled" basin-scale models is still a long way off, the next 10 years should see considerable progress in accounting for the complex feedbacks between porosity- permeability changes associated with geochemical, thermal, and mechanical processes. Issues of scale with respect to estimation of rock parameters and the incorporation of aquifer-aquitard heterogeneities in basin-scale hydrological models will also receive increasing attention as well in the next decade [e.g., Gerdes et al., 1995]. Finally, much of the work done to date has utilized cross-sectional representations of basin transport processes, which at best crudely approximate the three-dimensional nature of regional or local fluid flow. The next generation of basin models will need to be three-dimensional and account for subbasin-scale heter-

ogeneities. The development of fully three-dimensional models of sedimentary basin evolution has only recently been initiated [Garven, 1994].

Probably the most significant contribution that basin hydrogeologic modeling studies have made to the Earth science community is testing of hypotheses and estimate large-scale flow patterns associated with different transport processes operating within sedimentary basins. For example, sediment compaction associated with over- thrusting [Deming et al., 1990], accretionary prisms [Wang et al., 1993], and tectonic shortening during continental compression [Ge and Garven, 1989] would only produce maximum flow velocities of 1 cm yr -1 and temperature anomalies of about 5øC. However, if pressure dissipation of overpressures is accommodated along fault zones and released episodically, then much higher flow rates and some thermal perturbations may occur [Sharp, 1978; Roberts and Nunn, 1995]. Topography- driven groundwater flow, on the other hand, can produce groundwater flow rates of up to 10 m yr -1 over long periods of time and generate large temperature, salinity, and mineralization anomalies at the margins of basins [Garven and Freeze, 1984b; Person and Garven, 1994]. Density-driven flow within sedimentary basins can pro-

-1 duce subsurface flow rates as high as 0.1 to 1.0 m yr [Garven, 1989; Evans et al., 1991; Person and Garven, 1994; Raffensperger and Garven, 1995a, b] in thick aquifer units. This information is of paramount importance for geologists interested in determining the timing of energy and mineral deposit formation. However, these results must be viewed with some caution because of issues

associated with sparse data and long timescales. Increasingly, quantitative studies of sedimentary ba-

sin transport processes are being compared with field- based data as a means of providing "ground truth" in the

80 ß Person et al.- HYDROGEOLOGIC MODELING 34, 1 /REVIEWS OF GEOPHYSICS

(ur'4) z (u.4) z (m•) z

o

(ma) z


study of geologic processes. For example, studies that utilize mathematical modeling [Garven and Freeze, 1984b], remagnetization of sediments [McCabe and El- more, 1989], analysis of elemental and stable isotope patterns in diagenetic cements [Hay et al., 1988; Gregg et al., 1993], radioisotope dating of ore minerals [Brannon et al., 1991] and authigenic clays [Elliott and Aronson, 1993], and apatite fission track analysis lame et al., 1990] have helped to establish that the MVT Pb-Zn deposits within the midcontinent basins of North America were

formed by great fluid migrations associated with Appa- lachian and Ouachita mountain-building events hundreds of kilometers away [Garven et al., 1993]. While some controversy still exists regarding the fluid-flow- driving mechanism [e.g., Oliver, 1992; Deming and Nunn, 1991] and the timing of migration [Sverjensky and Gar- yen, 1992], seemingly little doubt now remains regarding the existence of these ancient regional flow systems or of the important role these flow systems have had in the genesis of ore deposits and oil accumulations.

6. CONCLUSIONS

Quantitative models of groundwater flow are being applied today in virtually every tectonic environment as Earth scientists seek to understand a wide variety of geologic processes. While these hydrogeologic basin models vary considerably in their complexity and the processes represented, they have already provided important insights into the rates and migration patterns of fluids on geologic time scales. Hydrogeologic modeling should help lead the way in providing important new insights into the dynamic nature of coupling between hydrologic, thermal, mechanical, and chemical processes in the decades to come as well as in better constraining transport-limited geologic processes. However, despite the recent advances made in numerical methods and the

wider availability of very fast computer workstations, basin-scale hydrogeologic modeling is still in its infancy. Much work remains to be done toward the development of "fully coupled" models of hydrologic, thermal, mechanical and geochemical processes in three spatial dimensions within sedimentary basins.

In concluding, it is important to emphasize that while mathematical modeling represents a powerful tool for basin studies, it is not a panacea [Furlong et al., 1991]. This is due to the dearth of accurate rock property and boundary condition information that must be provided to mathematical models for the quantitative results to be meaningful. Quantitative results from basin-scale hydrological models must be carefully compared with "paleo- flow meters" in the rock record. Thus mathematical

modeling may help provide the impetus for multidisci- plinary basin studies between hydrologists and geologists.

NOTATION

a i

aq b

cf, c s

C

C,D

D

F

# h

h oil hf H

km

Kx

k

K

L

m

M

M x

q

qoil

R i

Ss

sol

t

T

u

V, Vx, V z

equilibrium activity of the ith species. subscript referring to the aqueous phase. porosity consolidation coefficient due to changes in effective stress (m 2 N-•). a component or aqueous component species. number of chemical components. specific heat capacities of the fluid and solid phases (J øC- 1 kg-1). total dissolved solids concentration (mg

empirical porosity•permeability fit coefficients.

hydrodynamic dispersion tensor (m 2 s-•). applied tectonic stress vector (N m-2). acceleration due to gravity (m s-2). equivalent freshwater hydraulic head (m). oil head (m). specific enthalpy of the fluid (J kg-•). bulk modulus of porous medium. rate constant (tool m -2 s). intrinsic permeability in x direction (m2). hydraulic connectivity in x direction (m yr-•). intrinsic permeability tensor (m2). equilibrium constant or solubility product. sediment elevation (m) a solid mineral species. number of precipitated or solid mineral species. concentration (molarity). total concentration (molarity). horizontal and vertical Darcy velocity vector (ms -•) with respect to a moving coordinate framework (m s-•). horizontal and vertical oil velocity vector (m s -•) with respect to a moving coordinate framework (m s-•). mineral precipitation or dissolution rate per unit rock volume (mol m -3 yr). net rate of addition of chemical species i to the fluid by all reactions. an aqueous complex or secondary aqueous species. number of secondary aqueous species. mineral specific reactive surface area (m specific storage coefficient of porous medium (m- •). subscript referring to the solid phase. time (s). temperature (øC). displacement vector (m). specific discharge, equal to q/O) (m s-•). average linear velocity vector and components (m s- •).


z elevation above datum (m). V gradient operator.

I7. divergence operator. O•p compressibility of the porous media due

to changes in total stress (ms 2 kg-•). o• r thermal expansivity of the porous media

(oc-'). (x c density coefficient due to salinity changes

(L mg- •). o•v vertical compressibility of porous medium

due to changes in vertical compressive stress (m 2 N-•).

•/c activity coefficient. œ• longitudinal thermal dispersivity

coefficient (m). œt transverse thermal dispersivity coefficient

(m). • porous media strain tensor

(dimensionless). thermal conductivity of the fluid and solid phases (W øC- • m- •).

• thermal conductivity tensor (W øC-• m-l). dynamic viscosity of the water and oil phases, respectively (kg m- • s- •). Poisson's ratio.

composition coefficient (moles of c per formula weight m).

Vcs composition coefficient (moles of c per formula weight s).

vi stoichiometric reaction coefficient for the ith species. density of the fluid, solid, and oil phases (kg m-3).

p• submerged sediment-density (kg m-3). P0 reference density of the fluid phase (10øC,

0 mg L -•, atmospheric pressure; kg m-3). O' T total stress on porous medium (N m-2). cr½ effective stress on porous medium (N

m-2). cr• vertical compressive stress on porous

medium (N m-3). {r porous media stress tensor (N m-2). cb porosity (dimensionless).

cb0 porosity at the land surface (dimensionless).

)kf, )k s

[&f, •oil

Pf, Ps, Poil

SI (International System of Units) derived units used in the definitions are newtons (force; 1 N = 1 kg m s-2), joules (energy; 1 J - 1 N m = 1 kg m 2 s-2), and watts (heat fl .... • xx7 - I J s -• - 1 kg m 2 s-3).

GLOSSARY

Compaction-driven flow: Flow within young sedimentary basins and accretionary prisms during subsidence and sedimentation and/or emplacement of thrust

sheets, induced by mechanical loading of the sedimentary pile. The combination of low-permeability sedimentary fill and pore space collapse causes groundwater to become anomalously pressured. Fluid pressures can approach lithostatic levels if sediment permeability is sufficiently low and sedimentation or thrust sheet loading rates are high.

Density-driven flow: Flow arising from fluid-density gradients. The density gradients can be produced by temperature or compositional variations in the fluids or by phase changes. Temperature perturbations within the basins are caused by radiogenic decay, magmatic intru- sions, crustal thinning, and thermal conductivity con- trasts. Fluid compositional gradients arise as a result of a number of physical and chemical processes including evaporative concentration in hydrologically closed basins, saltwater intrusion due to sea level variations, and rock-water geochemical reactions such as evaporite dissolution.

1opography-driven flow: Groundwater flow induced by elevation changes along the water table across a basin. Flow is from areas of higher to lower elevation, assuming the water table configuration is a subdued replica of the land surface. Depending on the water table configuration and subsurface permeability conditions, topography-driven flow systems can be continental in scale. On geologic timescales, topography-driven flow persists as long as uplift or erosion maintains elevation differences.

$eismogenic pumping: Here, groundwater flow induced by pore dilation/reduction and permeability changes along fault zones leading up to and following seismic events. This mechanism has been called upon to explain geochemical and mineralogical evidence of episodic fluid flow along faults.

ACKNOWLEDGMENTS. The authors wish to thank

Chris Neuzil for his helpful comments and suggestions in revising this manuscript.

James Smith was the editor responsible for this paper. He wishes to thank Chris Neuzil and one anonymous reviewer for their technical reviews and one anonymous cross disciplinary reviewer.

REFERENCES

Ague, J. J., and G. H. Brimhall, Geochemical modeling of steady state fluid flow and chemical reaction during super-

•,•,.,,,,•,L of copper Econ. Geol., pu pny• y ueposns,

84, 506-528, 1989. Arne, D., P. F. Green, and I. R. Duddy, Thermochronologic

constraints on the timing of Mississippi Valley-type ore formation from apatite fission track analysis, Nucl Tracks Radiat. Meas., 17, 319-323, 1990.

Baumgartner, L. P., and J. M. Ferry, A model for coupled fluid-flow and mixed-volatile mineral reactions with applications to regional metamorphism, Contrib. Mineral Petrol., 106, 273-285, 1991.


Belitz, K., and J. Bredehoeft, Hydrodynamics of Denver Basin: Explanation of subnormal fluid pressures, AAPG Bull., 72, 1334-1359, 1988.

Berg, R. R., and A. H. Avery, Sealing properties of tertiary growth faults, Texas Gulf Coast, A,4PG Bull., 79, 375-393, 1995.

Berg, R. R., W. D. DeMis, and A. R. Mitsdarffer, Hydrody- namic effects on Mission Canyon (Mississippian) oil accumulations, Bilings Nose area, North Dakota, A,4PG Bull., 78, 508-518, 1994.

Bethke, C. M., A numerical model of compaction-driven groundwater flow and heat transfer and its application to the paleohydrology of intracratonic sedimentary basins, J. Geophys. Res., 90, 6817-6828, 1985.

Bethke, C. M., Inverse hydrologic analysis of the distribution and origin of Gulf Coast-type geopressured zones, J. Geo- phys. Res., 91, 6535-6545, 1986a.

Bethke, C. M., Hydrologic constraints on the genesis of the upper Mississippi valley mineral district from Illinois Basin brines, Econ. Geol., 81,233-249, 1986b.

Bethke, C. M., Modeling subsurface flow in sedimentary basins, Geol. Rundsch., 78(1), 129-154, 1989.

Bethke, C. M., and T. F. Corbet, Linear and nonlinear solutions for one-dimensional compaction flow in sedimentary basins, Water Resour. Res., 24, 461-467, 1988.

Bethke, C. M., and S. Marshak, Brine migrations across North America--The plate tectonics of groundwater, Annu. Rev. Earth Planet. Sci., 18, 287-315, 1990.

Bethke, C. M., W. J. Harrison, C. Upson, and S. P. Altaner, Supercomputer analysis of sedimentary basins, Science, 239, 261-267, 1988.

Bethke, C. M., J. D. Reed, and D. F. Oltz, Long-range petroleum migration in the Illinois Basin, AAPG Bull., 75, 925- 945, 1991.

Bethke, C. M., M.-K. Lee, H. A.M. Quinodoz, and W. N. Kreling, Basin Modeling with Basin2, A Guide to Using Basin2, B2plot, B2video, and B2view, 225 pp., Univ. of Ill., Urbana, 1993.

Biot, M. A., General theory of three-dimensional consolidation, J. Appl. Phys., 26, 155-164, 1941.

Bjorlykke, K., Fluid flow in sedimentary basins, Sediment. Geol., 116, 137-158, 1993.

Borja, R. I., and S. J. Dreiss, Numerical modeling of accretionary wedge mechanics: Application to the Barbados Sub- duction Zone, J. Geophys. Res., 94, 9323-9339, 1989.

Braester, C., and P. Vadasz, The effect of a weak heterogeneity of a porous medium on natural convection, J. Fluid Mech., 254, 345-362, 1993.

Brannon, J. C., F. A. Podoser, J. G. Viets, D. L. Leach, M. Goldhaber, and E. L. Rowan, Strontium isotopic constraints on the origin of ore-forming fluids of the Viburnum Trend, southeast Missouri, Geochim. Cosmochim. Acta, 55, 1407-1419, 1991.

Bredehoeft, J. D., and B. Hanshaw, On the maintenance of anomalous fluid pressures, I, Thick sedimentary sequences, Geol. Soc. Am. Bull., 79, 1097-1106, 1968a.

Bredehoeft, J. D., and B. Hanshaw, On the maintenance of anomalous fluid pressures, II, Source layer at depth, Geol. Soc. Am. Bull., 79, 1107-1122, 1968b.

Bredehoeft, J. D., and D. L. Norton, Mass and energy transport in a deforming Earth's crust, in The Role of Fluids in Crustal Processes, Studies in Geophysics., pp. 27-41, Natl. Acad. Press, Washington, D.C., 1990.

Bredehoeft, J. D., and I. S. Papadopulos, Rates of vertical groundwater movement estimated from the Earth's thermal profile, Water Resour. Res., 1,325-328, 1965.

Bredehoeft, J. D., R. D. Djevanshir, and K. R. Belitz, Lateral fluid flow in a compacting sand-shale sequence: South Cas- pian Basin, A,4PG Bull., 72, 416-424, 1988.

Burnstein, I. B., K. L. Shelton, R. D. Hagni, and R. T. Bran- dom, Mobilization of copper by MVT fluids penetrating igneous basement rocks: Sulfur isotope studies of the Pre- cambrian Boss-Bixby Fe-Cu deposits, southeastern Mis- souri (abstract), Geol. Soc. Am. Abstr. Programs, 24, A234, 1992.

Burrus, J., and F. Audebert, Thermal and compaction processes in young rifted basins in the presence of evaporites; Consequences for petroleum potential; The Gulf of Lions case study, A,4PG Bull., 74, 1420-1440, 1990.

Burrus, J., A. Kuhfuss, B. Doligez, and P. Ungerer, Are numerical models useful in reconstructing the migration of hydrocarbons?, A discussion based on the northern Viking Graben, in Petroleum Migration, edited by W. A. England and A. J. Fleet, Geol. Soc. Spec. Publ. London, 59, 89-109, 1991.

Carnahan, C. L., Simulation of chemically reactive solute transport under conditions of changing temperature, in Coupled Processes Associated With Nuclear Waste Reposito- ries, edited by C.-F. Tsang, pp. 249-257, Academic, San Diego, Calif., 1987.

Cathles, L. M., A simple analytical method for calculating temperature perturbations in a basin caused by the flow of water through thin, shallow dipping aquifers, Appl. Geo- chem., 2, 649-655, 1987.

Chen, W., A. Ghaith, A. Park, and P. Ortoleva, Diagenesis through coupled processes: Modeling approach, selfrorga- nization, and implications for exploration, in Prediction of Reservoir Quality Through Chemical Modeling, edited by I.D. Meshri and P. J. Ortoleva, A,4PG Mem. 49, 103-130, 1990.

Clauser, C., Conductive and convective heat flow components in the Rhinegraben and implications for the deep permeability distribution, in Hydrogeological Regimes and Their Subsurface Thermal Effects, Geophys. Monogr. Ser., vol. 47, edited by A. E. Beck, G. Garven, and L. Stegena, pp. 56-64, AGU, Washington, D.C., 1989.

Combarnous, M. A., and S. A. Bories, Hydrothermal convection in saturated porous media, Adv. Hydrosci., 10, 231-307, 1975.

Corbet, T., and C. M. Bethke, Disequilibrium fluid pressures and groundwater flow in the western Canada sedimenary basins, J. Geophys. Res., 97, 7203-7217, 1992.

Davis, M. J., R. Lohmann, F. M. Phillips, J. L, Wilson, and D. Love, Architecture of the Sierra Ladrones Formation, central New Mexico: Depositional controls on the permeability correlation structure, Geol. Soc. Am. Bull., 105, 998- 1007, 1993.

de Marsily, G., Quantitative Hydrogeology, translated from French by G. de Marsily, 440 pp., Academic, San Diego, Calif., 1986.

Deming, D., and J. A. Nunn, Numerical simulations of brine migration by topographically driven recharge, J. Geophys. Res., 96, 2485-2499, 1991.

Deming, D., J. A. Nunn, and D. G. Evans, Thermal effects of compaction-driven groundwater flow from overthrust belts, J. Geophys. Res., 95, 6669-6683, 1990.

Deming, D., J. H. Sass, A. H. Lachenbruch, and R. F. De Rito, Heat flow and subsurface temperature as evidence for basin-scale ground-water flow, North Slope of Alaska, Geol. Soc. Am. Bull., 104, 528-542, 1992.

Dewers, T., and P. Ortoleva, The role of geochemical self- organization in the migration and trapping of hydrocarbons, Appl. Geochem., 3, 287-316, 1988.

Dewers, T., and P. Ortoleva, A coupled reaction/transport/ mechanical model for intergranular pressure solution, stylo- lites, and differential compaction and cementation in clean sandstones, Geochim. Cosmochim. Acta, 54, 1609-1625, 1990.

84 ß Person et al.- HYDROGEOLOGIC MODELING

Dewers, T., and P. Ortoleva, Nonlinear dynamical aspects of deep basin hydrology: Fluid compartment formation and episodic fluid release, Am. J. Sci., 294, 713-755, 1994.

Dixon, P. R., A. P. LeHuray, and D. M. Rye, Basement geology and tectonic evolution of Ireland as deduced from Pb iso- topes, J. Geol. Soc. London, 147, 121-132, 1990.

Doligez, B., F. Bessis, J. Burrus, P. Ungerer, and P. Y. Chenet, Integrated numerical simulation of the sedimentary, heat transfer, hydrocarbon formation, and fluid migration in sedimentary basins: The Themis model, in Thermal Model- ing in Sedimentary Basins, edited by J. Burrus, pp. 173-195, Technip, Paris, 1986.

Domenico, P. A., and V. V. Palciauskas, Theoretical analysis of forced convective heat transfer in regional ground-water flow, Geol. Soc. Am. Bull., 84, 3803-3814, 1973.

Domenico, P. A., and V. V. Palciauskas, Thermal expansion of fluids and fracture initiation in compacting sediments, Geol. Soc. Am. Bull., •)0, 953-979, 1979.

Dreyer, T., A. Scheie, and O. Walderhaug, Minipermeameter- based study of permeability trends in channel sand bodies, AAPG Bull., 74, 359-374, 1990.

Duffy, C. J., and S. A1-Hassan, Groundwater circulation in a closed desert basin: Topographic scaling and climatic forc- ing, Water Resøur. Res., 24, 1675-1688, 1988.

Elliott, W. C., and J. L. Aronson, The timing and extent of illite formation in Ordovician K-bentonites at the Cincinnati

Arch, the Nashville Dome and north-eastern Illinois Basin, Basin Res., 5, 125-135, 1993.

Engesgaard, P., and K. L. Kipp, A geochemical transport model for redox-controlled movement of mineral fronts in

groundwater flow systems: A case of nitrate removal by oxidation of pyrite, Water Resour. Res., 28, 2829-2843, 1992.

England, L. A., and R. A. Freeze, Finite-element simulation of long-term transient regional ground-water flow, Ground Water, 26, 298-308, 1988.

Evans, D. G., and J. A. Nunn, Free thermohaline convection in sediments surrounding a salt column, J. Geophys. Res., 94, 413-422, 1989.

Evans, D. G., J. A. Nunn, and J. S. Hanor, Mechanisms driving groundwater flow near salt domes, Geophys. Res. Lett., •8(5), 927-930, 1991.

Forster, C., and L. Smith, Groundwater flow systems in moun- tainous terrain, 1, Numerical modeling technique, Water Resour. Res., 24, 999-1010, 1988a.

Forster, C., and L. Smith, Groundwater flow systems in moun- tainous terrain, 2, Controlling factors, Water Resour. Res., 24, 1011-1023, 1988b.

Freeze, R. A., and 'P. A. Witherspoon, Theoretical analysis of regional groundwater flow, 2, Effect of water-table configuration and subsurface permeability variation, Water Re- sour. Res., 3, 623-634, 1967.

Furlong, K. P., R. B. Hanson, and J. R. Bowers, Modeling thermal regimes, in Contact Metamo•hism, Rev. Mineral., vol. 26, pp. 437-505, Mineral. Soc.of Am., Washington, D.C., 1991.

Garven, G., The role of regional fluid flow in the genesis of the Pine Point deposit, western Canada sedimentary basin, Econ. Geol., 80, 307-324, 1985.

Garven, G., The role of regional fluid flow in the genesis of the Pine Point deposit, western Canada SedimentaD' basin A reply, Econ. Geol., 81, 10t5-1020, 1986.

Garven, G., A hydrogeologic model for the formation of the giant oil sands deposits of the western Canada Sedimentary Basin, Am. J. Sci., 289, 105-166, 1989.

Garven, G., Coupled hydrogeologic models for MVT ore genesis (abstract), Geol. Soc. Am. Ab str' Programs, 26, A107, 1994.

Garven, G., Continental-scale groundwater flow and geologic processes, Annu. Rev. Earth Planet. Sci., 24, 89-117, 1995.

34, 1 /REVIEWS OF GEOPHYSICS

Garven, G., and R. A. Freeze, Theoretical analysis of the role of groundwater flow in the genesis of stratabound ore deposits, 1, Mathematical and numerical model, Am. J. Sci., 284, 1085-1124, 1984a.

Garven, G., and R. A. Freeze, Theoretical analysis of the role of groundwater flow in the genesis of stratabound ore deposits, 2, Quantitative results, Am. J. Sci., 284, 1125-1174, 1984b.

Garven, G., and J.P. Raffensperger, Hydrogeology and geochemistry of ore genesis in sedimentary basins, in Geochem- istry of Hydrothermal Ore Deposits, 3rd ed., edited by H. L. Barnes, John •Wiley, New York, in press, 1996.

Garven, G., S. Ge, M. A. Person, and D. A. Sverjensky, Genesis of stratabound ore deposits in the midcontinent basins of North America, 1, The role of regional groundwater flow, Am. J. Sci., 293, 497-568, 1993.

Ge, S., and G. Garven, Tectonically induced transient groundwater flow in foreland basin, in Origin and Evolution of Sedimentary Basins and Their Energy and Mineral Resources, Geophys. Monogr. Ser., vol. 48, edited by R. A. Price, pp. 145-157, AGU, Washington, D.C., 1989.

Ge, S., and G. Garven, Hydromechanical modeling of tectonically driven groundwater flow with application to the Arkoma foreland basin, J. Geophys. Res., 97, 9119-9144, 1992.

Ge, S., and G. Garven, A theoretical model for thrust-induced deep groundwater expulsion with application to the Cana- dian Rocky Mountains, J. Geophys. Res., 99, 13,851-13,868, 1994.

Gelhar, L. W., C. Welty, and K. R. Rehfeldt, A critical review of data on field-scale dispersion in aquifers, Water Resour. Res., 28, 1955-1974, 1992.

Gerdes, M., L. Baumgartner, and M. Person, Stochastic permeability model of fluid flow during contact metamorphism, Geology, 23, 945-948, 1995.

Gibson, R. E., The progress of consolidation in a clay layer increasing in thickness with time, Geotechnique, 8, 171-182, 1958.

Gregg, J. M., P. R. Laudon, R. E. Woody, and K. L. Shelton, Porosity evolution of the Cambrian Bonneterre Dolomite, south-eastern Missouri, USA, Sedimentology, 40, 1153- 1169, 1993.

Haldor•sen, H. H., and E. Damsleth, Stochastic modeling, J. Pet. Technol., 42, 404-412, 1990.

Hanor, J. S., Origin and Migration of Subsurface Sedimentary Brines, SEPM Short Course, 21,247 pp., 1987.

Harrison, W. J., and L. L. Summa, Paleohydrology of the Gulf of Mexico Basin, Am. J. Sci., 291, 109-176, 1991.

Hay, R. L., M. Lee, D. R. Kolata, J. C. Mathews, and J.P. Morton, Episodic potassic diagenesis of Ordovician tuffs in the Mississippi Valley area, Geology, 16, 743-747, 1988.

Hayba, D., and S. E. Ingebritsen, The computer model HYDROTHERM, A three-dimensional finite-difference model to simulate ground-water flow and heat transport in the temperature range of 0 to 1,200øC, U.S. Geol. Surv. Water Resour. Invest. Rep.; 94-4045, 85 pp., 1994.

Helgeson, H. C., T. H. Brown, A. Nigrini, and T. A. Jones, Calculation of mass transfer in geochemical processes in- vo!ving aqueous ...... •,.•, •Jcc, ct•ttr•. •c•arrtocrttrrt. •,•cttt, o•, 569-592, 1970.

Hewett, T. A., Porosity and mineral alteration by fluid flow through a temperature field, in Reservoir Characterization, edited by Lake, L. W., and H. B. Carroll, pp. 83-140, Academic, San Diego, Calif., 1986.

Hubbert, M. K., Entrapment of petroleum under hydrodynamic conditions, AAPG Bull., 37, 1954-2026, 1953.

Hubbert, M. K., and W. W. Rubey, Role of fluid pressure in mechanics of overthrust faulting, I, Mechanics of fluid-filled


porous solids and its application to overthrust faulting, Geol. Soc. Am. Bull., 70, 115-166, 1959.

Kiraly, L., Rapport sur l'6tat actuel des connaissances dans le domaine des caract•,res physiques des roches kartiques, Int. Union Geol. Sci., Ser. B, no. 3, 53-67, 1975.

Kirkner, D. J., A. A. Jennings, and T. L. Theis, Multisolute mass transport with chemical interaction kinetics, J. Hydrol., 76, 107-117, 1985.

Knapp, R. B., Spatial and temporal scales of local equilibrium in dynamic fluid-rock systems, Geochim. Cosmochim. Acta, 53, 1955-1964, 1989.

Koltermann, C. E., and S. M. Gorelick, Paleoclimatic signature in terrestrial flood deposits, Science, 256, 1775-1782, 1992.

Konikow, L. F., and J. W. Mercer, Groundwater flow and transport modeling, J. Hydrol., 100, 379-409, 1988.

Kvenvolden, K. A. and B. R. T. Simoneit, Hydrothermally derived petroleum: Examples from Guaymas Basin, Gulf of California, and Escanaba Trough, northeast Pacific Ocean, AAPG Bull., 74, 223-237, 1990.

Lee, M.-K., and C. M. Bethke, Groundwater flow, late cementation, and petroleum accumulation in the Permian Lyons Sandstone, Denver Basin, AAPG Bull., 78, 217-237, 1994.

Lehner, F. K., D. Marsal, L. Hermans, and A. Van Kuyk, A model of secondary hydrocarbon migration as a buoyancy- driven separate phase flow, in Migration of Hydrocarbons in Sedimentary Basins, edited by B. Doligez, pp. 457-471, Technip, Paris, 1987.

Lichtner, P. C., Continuum model for simultaneous chemical reactions and mass transport in hydrothermal systems, Geochim. Cosmochim. Acta, 49, 779-800, 1985.

Lichtner, P. C., The quasi-stationary state approximation to coupled mass transport and fluid-rock interaction in a porous medium, Geochim. Cosmochim. Acta, 52, 143-165, 1988.

Lichtner, P. C., Time-space continuum description of fluid/ rock interaction in permeable media, Water Resour. Res., 28, 3135-3155, 1992.

Lichtner, P. C., Scaling properties of time-space kinetic mass transport equations and the local equilibrium limit, Am. J. Sci., 293, 257-296, 1993.

Lichtner, P. C., and G. G. Biino, A first principles approach to supergene enrichment of a porphyry copper protore, I, Cu-Fe-S subsystem, Geochim. Cosmochim. Acta, 56, 3987- 4013, 1992.

Lichtner, P. C., and N. Waber, Redox front geochemistry and weathering: Theory with application to the Osamu Utsumi uranium mine, Poqos de Caldas, Brazil, J. Geochem. Explor., 45, 521-564, 1992.

Liu, C. W., and T. N. Narasimhan, Redox-controlled multiple- species reactive chemical transport, 1, Model development, Water Resour. Res., 25, 869-882, 1989a.

Liu, C. W., and T. N. Narasimhan, Redox-controlled multiple- species reactive chemical transport, 2, Verification and application, Water Resour. Res., 25, 883-910, 1989b.

Lowell, R. P., Modeling continental and submarine hydrothermal systems, Rev. Geophys., 29, 457-476, 1991.

Lowell, R. P., P. V. Cappellen, and L. N. Germanovich, Silica precipitation in fractures and the evolution of permeability in hydrothermal upflow zones, Science, 260, 192-194, 1993.

Lucia, F. J., and G. E. Fogg, Geologic/stochastic mapping of heterogeneity in a carbonate reservoir, J. Petr. Technol., 42, 1298-1303, 1990.

Lund, K., and H. S. Fogler, Acidization, V, The prediction of the movement of acid and permeability fronts in sandstone, Chem. Eng. Sci., 31,381-392, 1976.

Luo, X., and G. Vasseur, Contributions of compaction and aquathermal pressuring to geopressure and the influence of environmental conditions, AAPG Bull., 76, 1550-1559, 1992.

Magara, K., Reevaluation of montmorillonite dehydration as a cause of abnormal pressure and hydrocarbon migration, AAPG Bull., 59, 292-302, 1975.

McCabe, C., and R. D. Elmore, The occurrence and origin of late paleozoic remagnetization in the sedimentary rocks of North America, Rev. Geophys., 27, 471-494, 1989.

McKibbin, R., and M. J. O'Sullivan, Onset of convection in a layered porous medium heated from below, J. Fluid Mech., 96, 375-393, 1980.

McManus, K. M., and J. S. Hanor, Diagenetic evidence for massive evaporite dissolution, fluid flow, and mass transfer in the Louisiana Gulf Coast, Geology, 21,727-730, 1993.

McTigue, D. F., Thermoelastic response of fluid-saturated porous rock, J. Geophys. Res., 91, 9533-9543, 1986.

Miller, C. W., and L. V. Benson, Simulation of solute transport in a chemically reactive heterogeneous system: Model development and application, Water Resour. Res., 19, 381-391, 1983.

Muir-Wood, R., Earthquakes, strain-cycling, and the mobilization of fluids, in Geofiuids: Origin, Migration and Evolu- tion of Fluids in Sedimentary Basins, edited by J. Parnell, Geol. Soc. Spec. Publ. London, 78, 85-98, 1994.

National Research Council, The Role of Fluids in Crustal Pro- cesses, Stud. Geophys., 170 pp., Natl. Acad. Press, Washing- ton, D.C., 1990.

Nelson, P. H., Permeability-porosity relationships in sedimentary rocks, Log Analyst, 35, 38-62, 1994.

Neuman, S. P., Theoretical derivation of Darcy's law, Acta Mechanica, 25, 153-170, 1977.

Neuman, S. P., Universal scaling of hydraulic conductivities and dispersivities in geologic media, Water Resour. Res., 26, 1749-1758, 1990.

Neuzil, C. E., How permeable are clays and shales?, Water Resour. Res., 30, 145-150, 1994.

Nur, A. N., and J. Walder, Time-dependent hydraulics in the Earth's crust, in The Role of Fluids in Crustal Processes, pp. 113-127, Comm. on Geosci. Environ., and Resour., Natl. Sci. Found., Washington, D.C., 1990.

Oliver, J., Fluids expelled tectonically from orogenic belts: Their role in hydrocarbon migration and other geologic phenomena, Geology, 14, 99-102, 1986.

Oliver, J., The spots and stains of plate tectonics, Earth Sci. Rev., 32, 77-106, 1992.

Orr, E. D., and C. W. Kreitler, Interpretation of pressure- depth from confined underpressured aquifers examplified by the deep-basin brine aquifer, Palo Duro Basin, Texas, Water Resour. Res., 21, 533-544, 1985.

Ortoleva, P., E. Merino, C. Moore, and J. Chadam, Geochemi- cal self-organization, I, Reaction-transport feedbacks and modeling approach, Am. J. Sci., 287, 979-1007, 1987.

Palciauskas, V. V., and P. A. Domenico, Solution chemistry, mass transfer, the approach to chemical equilibrium in porous carbonate rocks and sediments, Geol. Soc. Am. Bull., 87, 207-214, 1976.

Palciauskas, V. V., and P. A. Domenico, Characterization of drained and undrained response of thermally loaded repos- itory rocks, Water Resour. Res., 18, 281-290, 1982.

Person, M., and L. Baumgartner, New evidence for long- distance fluid migration within the Earth's crust, U.S. Natl. Rep. Int. Union Geod. Geophys., 1991-1994, Rev. Geophys., 33, 1083-1091, 1995.

Person, M., and G. Garven, Hydrologic constraints on petroleum generation within continental rift basins: Theory and application to the Rhine graben, AAPG Bull., 76, 468-488, 1992.

Person, M., and G. Garven, A sensitivity study of the driving forces on fluid flow during continental-rift basin evolution, Geol. Soc. Am. Bull., 106, 461-475, 1994.


Person, M., E. Bekele, and G. de Marsily, Is secondary oil migration inherently three-dimensional? An example from the Paris Basin, France, in Geofiuids 93' Extended Abstracts, pp. 251-254, British Gas, London, 1993.

Person, M., D. Toupin, and P. Eadington, Effects of convective heat transfer on the thermal history of sediments and petroleum generation within continental rift basins, Basin Res., 7, 81-96, 1995.

Phillips, O. M., Flow-controlled reactions in rock fabrics, J. Fluid Mech., 212, 263-278, 1990.

Phillips, O. M., Flow and Reactions in Permeable Rocks, 285 pp., Cambridge Univ. Press, New York, 1991.

Pickens, J. F., and G. E. Grisak, Scale-dependent dispersion in a stratified granular aquifer, Water Resour. Res., 17, 1191- 1211, 1981.

Platt, J.P., Thrust mechanics in highly overpressured acrre- tionary wedges, J. Geophys. Res., 89, 9025-9034, 1990.

Raffensperger, J.P., Quantitative evaluation of the hydrologic and geochemical processes involved in the formation of unconformity-type uranium deposits, Ph.D. thesis, 679 pp., Johns Hopkins Univ., Baltimore, Md., 1993.

Raffensperger, J.P., and G. Garven, The formation of unconformity-type uranium ore deposits, 1, Coupled groundwater flow and heat transport modeling, Am. J. Sci., 295, 581-636, 1995a.

Raffensperger, J.P., and G. Garven, The formation of unconformity-type uranium ore deposits, 2, Coupled hydrochemi- cal modeling, Amer. J. Sci., 295, 639-696, 1995b.

Ravenhurst, C., and M. Zentilli, A model for the evolution of hot (>200øC) overpressured brines under an evaporite seal: The Fundy/Magdalen Carboniferous Basin of Atlantic Can- ada and its associated Pb-Zn-Ba Deposits, Mere. Can. Soc. Petr. Geol., 12, 335-349, 1987.

Reed, M. H., Calculation of multicomponent chemical equilibria and reaction processes in systems involving minerals, gases and an aqueous phase, Geochim. Cosmochim. Acta, 46, 513-528, 1982.

Rhea, L., M. Person, G. de Marsily, E. Ledoux, and A. Galli, Geostatistical models of secondary petroleum within heterogeneous carrier beds: A theoretical example, AAPG Bull., 78, 1679-1691, 1994.

Rice, J. R., and M.P. Cleary, Some basic stress diffusion solutions for fluid-saturated elastic porous media with compressibility constituents, Rev. Geophys., 14, 227-241, 1976.

Roberts, S. J., and J. A. Nunn, Episodic fluid flow from geopressured sediments, Mar. Pet. Geol., 12, 195-204, 1995.

Rojstaczer, S., and S. Wolf, Permeability changes associated with large earthquakes: An example from Loma Prieta, California, Geology, 20, 211-214, 1992.

Rostron, B. J., and J. T6th, Computer simulation of potentio- metric anomalies as an aid to exploration for lenticular reservoirs in developed basins, Geobyte, 4(4), 39-45, 1989.

Rubey, W. W., and M. K. Hubbert, Role of fluid pressure in mechanics of overthrust faulting, II, Overthrust belt in geo- synclinal area of western Wyoming in light of fluid-pressure hypothesis, Geol. Soc. Am. Bull., 70, 167-206, 1959.

Rubin, H., Thermal convection in a nonhomogenous aquifer, J. Hydrol., 50, 317-331, 1981.

Rubin, J., Transport of reacting solutes in porous media: Relation between mathematical nature of problem formu- lation and chemical nature of reactions, Water Resour. Res., 19, 1231-1252, 1983.

Rubin, J., and R. V. James, Dispersion-affected transport of reacting solutes in saturated porous media: Galerkin method applied to equilibrium-controlled exchange in uni- directional steady water flow, Water Resour. Res., 9, 1332- 1356, 1973.

Sanford, W. E., and L. F. Konikow, Porosity development in coastal carbonate aquifers, Geology, 17, 249-252, 1989a.

Sanford, W. E., and L. F. Konikow, Simulation of calcite dissolution and porosity changes in saltwater mixing zones in coastal aquifers, Water Resour. Res., 25, 655-667, 1989b.

Schecter, R. S., and J. L. Gidley, The change in pore size distribution from surface reactions in porous media, AIChE J., 15(3), 339-350, 1969.

Schwartz, F. W., Macroscopic dispersion in porous media: The controlling factors, Water Resour. Res., 13, 743-752, 1977.

Schwartz, F. W., and P. A. Domenico, Simulation of hydro- chemical patterns in regional groundwater flow, Water Re- sour. Res., 9, 707-720, 1973.

Screaton, E. J., D. R. Wuthrich, and S. Dreiss, Permeability, fluid pressures, and flow rates in the Barbados ridge complex, J. Geophys. Res., 95, 8997-9007, 1990.

Senger, R. K., and G. E. Fogg, Regional underpressuring in deep brine aquifers, Palo Duro Basin, Texas, 1, Effects of hydrostratigraphy and topography, Water Resour. Res., 23, 1481-1493, 1987.

Sharp, J. M., Jr., Energy and momentum transport model of the Ouachita basin and its possible impact on formation of economic mineral deposits, Econ. Geol., 73, 1057-1068, 1978.

Sharp, J. M., Jr., and P. A. Domenico, Energy transport in thick sequences of compacting sediment, Geol. Soc. Am. Bull., 87, 390-400, 1976.

Shelton, K. L., R. M. Bauer, and J. M. Gregg, Fluid-inclusion studies of regionally extensive epigenetic dolomites, Bonneterre Dolomite (Cambrian), southeast Missouri: Evi- dence of multiple fluids during dolomitization and lead-zinc mineralization, Geol. Soc. Am. Bull., 104, 675-683, 1992.

Shi, Y., and C.-Y. Wang, Pore pressure generation in sedimentary basins: Overloading versus aquathermal, J. Geophys. Res., 91, 2153-2162, 1986.

Sibson, R. H., Crustal stress, faulting, and fluid flow, in Geofluids: Origin, Migration and Evolution of Fluids in Sed- imentary Basins, edited by J. Parnell, Geol. Soc. Spec. Pub. London, 78, 69-84, 1994.

Smith, L., and D. S. Chapman, On the thermal effects of groundwater flow, 1, Regional scale systems, J. Geophys. Res., 88, 593-608, 1983.

Steefel, C. I., and A. C. Lasaga, Evolution of dissolution patterns: Permeability change due to coupled flow and reaction, in Chemical Modeling in Aqueous Systems II, edited by D.C. Melchior, and R. L. Bassett, ACS Syrup. Ser., 416, 212-225, 1990.

Steefel, C. I., and A. C. Lasaga, Putting transport into water- rock interaction models, Geology, 20, 680-684, 1992.

Steefel, C. I., and A. C. Lasaga, A coupled model for transport of multiple chemical species and kinetic precipitation/dissolution reactions with application to reactive flow in single phase hydrothermal systems, Am. J. Sci., 294, 529-592, 1994.

Straus, J. M., and G. Schubert, Thermal convection of water in a porous medium: Effects of temperature- and pressure- dependent thermodynamic and transport properties, J. Geophys. Res., 82, 325-333, 1977.

Sverjensky, D., and G. Garven, Tracing great fluid migrations, Nature, 356, 481-482, 1992.

Tissot, B. P., R. Pelet, and P. H. Ungerer, Thermal history of sedimentary basins, maturation indices, and kinetics of oil and gas generation, AAPG Bull., 71, 1445-1466, 1987.

T6th, J., A theory of groundwater motion in small drainage basins in central Alberta, Canada, J. Geophys. Res., 67, 4375-4387, 1962.

T6th, J., A theoretical analysis of groundwater flow in small drainage basins, J. Geophys. Res., 68, 4795-4812, 1963.

Tsang, C.-F., Introduction to coupled processes, in Coupled Processes Associated with Nuclear Waste Repositories, edited by C.-F. Tsang, pp. 1-6, Academic, San Diego, Calif., 1987.


Ungerer, P., J. Burrus, B. Doligez, P. Y. Chenet, and F. Bessis, Basin evaluation by integrated two-dimensional modeling of heat transfer, fluid flow, hydrocarbon generation, and migration, AAPG Bull., 74, 309-335, 1990.

Vasseur, G., L. Demongodin, and A. Bonneville, Thermal modeling of fluid flow effects in thin dipping aquifers, Geophys. J. Int., 112, 276-289, 1993.

Wade, S.C., and M. Reiter, Hydrothermal estimation of vertical ground-water flow, Canutillo, Texas, Ground Water, 32, 735-742, 1994.

Walsh, M.P., S. L. Bryant, R. S. Schechter, and L. W. Lake, Precipitation and dissolution of solids attending flow through porous media, AICEJ, 30(2), 317-328, 1984.

Wang, C. Y., G. Liang, and Y. Shi, Hydrologic processes in the Oregon-Washington accretionary complex, J. Geophys. Res., 95, 9009-9023, 1990.

Wang, C. Y., G. Liang, and Y. Shi, Heat flow across the toe of accretionary prisms--The role of fluid flux, Geophys. Res. Lett., 20, 659-662, 1993.

Wang, K., and A. E. Beck, An inverse approach to heat flow study in hydrogeologically active areas, Geophys. J. Int., 98, 69-84, 1989.

Wei, C., and P. Ortoleva, Reaction front fingering in carbonate-cemented sandstones, Earth Sci. Rev., 29, 183-198, 1990.

Wieck, J., M. Person, and L. Strayer, A finite element method for simulating fault block motion and hydrothermal fluid flow within rifting basins, Water Resour. Res., 31, 3241-3258, 1995.

Willet, S. D., and D. S. Chapman, Temperatures, fluid flow and heat transfer mechanisms in the Uinta Basin, in Hydrogeo- logical Regimes and Their Subsurface Thermal Effects, Geo- phys. Monogr. Set., vol. 47, edited by A. E. Beck, G. Garven, and L. Stegena, pp. 29-33, AGU, Washington, D.C., 1989.

Wood, J. R., and T. A. Hewett, Fluid convection and mass transfer in porous sandstones--A theoretical model, Geochim. Cosmochim. Acta, 46, 1707-1713, 1982.

Wood, J. R., and T. A. Hewett, Reservoir diagenesis and convective fluid flow, in Clastic Diagenesis, edited by D. A. McDonald and W. C. Surdam, A_APG Mem. 27, 99-111, 1984.

Woodbury, A.D., and L. Smith, On the thermal effects of three-dimensional groundwater flow, J. Geophys. Res., 90, 759-767, 1985.

Woodbury, A.D., and L. Smith, Simultaneous inversion of hydrogeologic and thermal data, 2, Incorporation of thermal data, Water Resour. Res., 24, 356-372, 1988.

Yaxley, L. M., Effect of a partially communicating fault on transient pressure behavior, SPE Form. Eval., 2, 590-598, 1987.

Yeh, G. T., and V. S. Tripathi, A model for simulating transport of reactive multispecies components: Model development and demonstration, Water Resour. Res., 27, 3075-3094, 1991.

G. Garven, Morton K. Blaustein Department of Earth and Planetary Sciences, Johns Hopkins University, Baltimore, MD 21218.

S. Ge, Department of Geological Sciences, University of Colorado, Campus Box 250, Boulder, CO 80309-0250.

M. Person (corresponding author), Department of Geology and Geophysics, University of Minnesota, 310 Pillsbury Drive SE, Minneapolis, MN 55455. (e-mail: [email protected]. umn.edu)

J.P. Raffensperger, Department of Environmental Sciences, University of Virginia, Charlottesville, VA 22903.

basin-scale hydrogeologic modeling

Documents