Alicia M. Wilson, Department of Geological Sciences, University of South Carolina, Columbia, SC 29208, USA. Email: email@example.com. Tel. (803) 777 1240. Fax: (803) 777 6610.
Topography-driven flow is normally considered to be the dominant groundwater flow system in uplifted sedimentary basins. In the U.S. midcontinent region east of the Rocky Mountains, the presence of brines derived from dissolution of halite suggests that significant topography-driven flushing has occurred to remove older brines that presumably formed concurrently with Permian evaporites in the basin. However, the presence of evaporites and brines in the modern basin suggests that buoyancy-driven flow could limit topography-driven flushing significantly. Here we used numerical models of variable-density fluid flow, halite dissolution, solute transport, and heat transport to quantify flow patterns and brine migration. Results indicate the coexistence of large-scale topography- and buoyancy-driven flow. Buoyancy-driven flow and low permeability evaporites act to isolate brines, and the residence time of the brines was found to be quite long, at least 50 Myr. The modern distribution of salinity appears to reflect near-steady-state conditions. Results suggest that flushing of original evaporatively-concentrated brines occurred tens of millions of years ago, possibly concurrent with maximum uplift ca. 60 Ma. Simulations also suggest that buoyancy-driven convection could drive chemical exchange with crystalline basement rocks, which could supply significant Ca2+, Sr2+, and metals to brines.
Topography-driven flow is thought to dominate regional-scale groundwater flow in uplifted sedimentary basins (Freeze & Witherspoon 1967). Flow occurs when differences in elevation create differences in potential energy that drive fluid from high elevation to low elevation, developing typical maximum flow rates of 1–10 m year−1 in deep aquifers (Garven & Freeze 1984a,b). Stable isotope analyses of porewaters in many basins have provided evidence for large-scale topography-driven influx of meteoric water in recharge zones and substantial flow of these fluids to depths of kilometers (Hitchon et al. 1971; Connolly et al. 1990a; Stueber & Walter 1991). However, the existence of vigorous topography-driven flushing appears to be at odds with geochemical evidence for the long-term preservation of brines in many sedimentary basins (Connolly et al. 1990b; Deming & Nunn 1991; Ranganathan 1993). The presence of deep brines also indicates substantial fluid density gradients, which can modify topography-driven flow or create distinct buoyancy-driven flow cells. Density gradients can drive free convection at flow rates approaching 1 m year−1 (Evans & Nunn 1989). The interactions between topography- and buoyancy-driven flow remain largely unstudied, however, and topography-driven flow is commonly assumed to overpower buoyancy-driven flow.
Bjørlykke et al. (1988) argued that density gradients are unlikely to drive large-scale buoyancy-driven flow in sedimentary basins for three reasons: (1) salinity increases with depth, which is a stable configuration, (2) although temperature increases with depth, which is an unstable configuration, this effect is overshadowed by the increase in density because of high salinity, and (3) if convection were taking place, large concentration gradients would not be preserved. Previous modeling studies have explored conditions under which topography-driven flow and geothermal convection could coexist (López & Smith 1995; Raffensperger & Garven 1995). In general, these studies showed that geothermal convection can develop in permeable zones if topography-driven flow rates are limited by a low topographic gradient or by low permeabilities in the surrounding basin. These studies did not consider salinity variations, which can cause larger density gradients than thermal variations.
Early hydrogeologic models of topography-driven flow in uplifted basins on the eastern flank of the Rocky Mountains neglected brine migration because of computational limitations (Garven & Freeze 1984a,b; Belitz & Bredehoeft 1988). Other studies have focused on haline convection in the vicinity of salt domes (Ranganathan & Hanor 1988; Evans & Nunn 1989; Evans et al. 1991) and beneath horizontal salt sheets (Sarkar et al. 1995), where unstable density gradients are present. Sarkar et al. (1995) showed that significant haline convection could develop beneath salt sheets in sediments with permeabilities as low as 10−17 m2, but with the exception of Evans et al. (1991), these studies did not consider topography-driven flow. Evans et al. (1991) simulated horizontal flow of fresh groundwater with a velocity of 0.1 m year−1 above a salt dome. They found that salinity gradients on the downstream side of a salt ridge could cause strong downward convection that significantly modified the original horizontal flow field. Paleohydrologic modeling of the Dead Sea Basin has also shown that buoyancy-driven flow may have coexisted with topography-driven flow as evaporated seawater began to sink (Stanislavsky & Gvirtzman 1999).
The purpose of this work was to determine the importance of buoyancy-driven flow in an uplifted sedimentary basin in the U.S. midcontinent region, where topography-driven flow has long been thought to dominate. As described in further detail below, the presence of Permian evaporites in this basin strongly suggests that buoyancy-driven flow could be significant, and understanding this flow has important implications for the evolution and residence time of brines. Here we present a new profile of the distribution of salinity in the region and numerical models of basin-scale fluid flow that were used to evaluate driving forces for flow and controls on the distribution of brines in the basin.
Hydrostratigraphy and hydrogeology of the U.S. midcontinent
This study focuses on the U.S. midcontinent region east of the Rocky Mountains and specifically on an 800-km cross section that extends from northeastern Colorado through central Kansas into southwestern Missouri (Fig. 1A). This cross section intersects the Denver Basin, the Hugoton embayment of the Anadarko Basin, and adjacent areas to the east. Along this section the thickness of the basin decreases from west to east from approximately 4 to 0.4 km. Sedimentary rocks in the basin range in age from Cambrian through Quaternary.
This broad and relatively shallow basin contains five major regional hydrogeologic units (Fig. 1B). The Northern Western Interior Plains aquifer system (NWIPA) directly overlies Precambrian crystalline igneous and metamorphic rocks. It is divided into lower and upper aquifer units separated by a confining unit of low permeability shale. The lower aquifer unit is composed of Cambrian through Ordovician dolostone, limestone, and sandstone and the upper unit is composed of permeable upper Devonian and Mississippian limestone. The Northern Western Interior Plains confining system (NWIPC) consists of Late Mississippian through Jurassic shale, redbeds, sandstone, and evaporites. Within the NWIPC, the Permian-age Hutchinson Salt Member of the Wellington Formation system reaches a maximum thickness of 150 m beneath south central Kansas and parts of Oklahoma (Walters 1978). These thick, laterally extensive halite-dominated evaporite deposits may limit downward vertical flow to the NWIPA system. The eastern margin of the Hutchinson Salt has been undergoing dissolution since late Tertiary, as evidenced by land-surface subsidence and sinkhole development (Walters 1978; Gogel 1981; Anderson et al. 1994). The Great Plains aquifer system (GPA) overlies the NWIPC system and is divided into the upper Maha and the lower Apishapa aquifer units and is composed predominately of permeable Lower Cretaceous sandstone. It is overlain by the Great Plains confining system (GPC), dominated by a thick sequence of Cretaceous shales.
Geochemical studies have provided further clues to the hydrogeology of the basin. High salinity water found in the deep NWIPA system is a mixture of water that originated as meteoric precipitation at high altitudes along the Front Range of the Rocky Mountains and brines derived from the subsurface dissolution of halite-dominated evaporite deposits in the overlying confining system (Banner et al. 1989; Musgrove & Banner 1993). These findings support the existence of a regional-scale topography-driven flow system. These results also suggest that buoyancy-driven free convection has occurred in the past, because porefluids of meteoric origin cannot intrude beneath a salt layer without introducing instabilities.
Musgrove & Banner (1993) also found high strontium ratios (87Sr/86Sr) in groundwater in the NWIPA system, and determined that interaction with silicate minerals could account for these ratios. Silicate minerals are present in the overlying confining system and in the underlying crystalline basement rock. There must be vertical flow and solute exchange across the confining system if dissolution of Permian evaporites is the source of the high salinity (Banner et al. 1989), but we suggest here that buoyancy-driven convection could also provide a mechanism for geochemical exchange and transport of solutes from the crystalline basement rock.
The origin of brines in this basin is also significant for understanding regional groundwater flow. Brines in other North American basins appear to have formed long ago by evaporative concentration, implying residence times of hundreds of millions of years (Connolly et al. 1990a,b; Stueber & Walter 1991). Brines that form through dissolution of halite, such as those in the midcontinent region, could have a much shorter residence time if they reflect a balance between active topography-driven flushing and creation of new brines by halite dissolution. Hydrogeologic models of topography-driven flushing of brines from huge sedimentary basins have suggested residence times of <5 Myr (Deming & Nunn 1991; Appold & Garven 1999). If these models are correct, then the distribution of brines in the midcontinent could reflect steady-state conditions determined by the modern configuration of the basin. If the residence time of the brines is long, then the current distribution of brines could instead reflect ancient flow and geochemical processes associated with the long-term evolution of the basin.
Large databases of chemical analysis records were obtained from the United States Geological Survey and the Kansas Geological Survey to construct a salinity profile for the basin. Nearly 9500 records were examined for this study. Data were rejected based on several criteria, which were applied to the data set in successive order of importance (Table 1).
Table 1. Rejection criteria used to create a geochemical database for use in this study, ranked in order of application.
TDS, total dissolved solid.
Record outside the box of 37° to 40°N and −94° to −104°W
No rock formation identified
Missing Ca, Mg, Na, K, Cl, HCO3, or SO4
Some analyses did not contain information on well depth or land surface elevation, but instead recorded the deepest rock formation encountered. A Matlab computer program was written that used analyses containing well depth, land surface elevation, and rock formation information to interpolate the depth for nearby analyses (<10 km radially) that contained only information on rock formation. This interpolation can be considered accurate as most of the strata in the midcontinent are relatively undeformed, flat-lying, and continuous. The sample depth for all of the analyses was assumed to be equal to the well depth as sample depth intervals were not reported for any of the records. Note that secondary recovery procedures associated with petroleum production can cause dilution, so reported salinities should be viewed as lower bound estimates. Data were clustered in localities of oil and gas production and therefore were not available from the deep western part of the basin. The final database consists of approximately 950 records, and clear trends are evident.
The final database was used to plot the modern distribution of salinity with depth along the cross section (Fig. 2). The concentration of total dissolved solids (TDS) ranges from 1000 to >300 000 mg l−1. The profile shows high salinity in close proximity to halite-dominated evaporite deposits. This distribution is consistent with previous geochemical findings of Musgrove & Banner (1993) that suggest salinity was derived from the subsurface dissolution of halite. Fresh water is found further to the east approaching the transition zone between the NWIPA system and the Ozark Plateau aquifer (OPA) system. Salinity >35 000 mg l−1 is found in the overlying GPA system in close proximity to the evaporites.
Numerical models of topography-driven flow and brine migration were generated using the code RST2D (Raffensperger 1996). RST2D uses a 2-D triangular finite element method to solve the coupled partial differential equations that govern transient variable-density fluid flow, heat transport, solute transport, and geochemical reactions. Fluid density was calculated using the equation of state presented by Batzle & Wang (1992), which is applicable for salinities ranging from 0 to 330 000 p.p.m. TDS and temperatures from 20 to 350°C. The cross section of the basin was divided into 121 columns and 30 rows, and the resulting finite element mesh consisted of 3630 nodes and 6960 elements (Fig. 3A). Elements were approximately 7300 m wide. The cross section is parallel to the west–east topographic gradients in the region, which allows 2-D approximation of a 3-D flow system.
Boundary conditions for fluid flow, solute concentration, and temperature were required for all simulations (Fig. 3A). Along the upper boundary, hydraulic head was set equal to the land surface elevation. At large scales the difference between the elevation of the land surface and the elevation of the water table is negligible. Water entering along the upper boundary was specified as freshwater. The lower boundary between the Paleozoic sedimentary rocks and the Precambrian crystalline rocks was assumed to be impermeable to fluid flow and solute transport. A uniform basal heat flux of 60 mW m−2 was imposed along the lower boundary, and the specified temperature for the upper boundary was 20°C. The ends of the cross section were chosen to correspond to topographic highs, which create hydrologic divides. Accordingly, no fluid, heat or solute flux was allowed across these boundaries.
For modeling purposes, rocks on a detailed geologic cross section were divided into five generalized types: shale, sandstone, limestone, evaporite, and a sedimentary mixture (Fig. 3B) and assigned material properties shown in Table 2. The sedimentary mixture contains beds of limestone, shale, and sandstone at a scale finer than can be resolved in these regional-scale simulations.
Table 2. Rock properties assigned to each generalized rock type. Unless indicated, property refers to sediment grains rather than the bulk porous medium.
The porosity and permeability of the sandstone and limestone in the models decreased with depth based on empirical equations fit to values presented by Jorgensen et al. (1996). The resulting equations for the porosity and hydraulic conductivity of the sandstone were:
where Φ is porosity, z is depth in m, and Kmax is hydraulic conductivity parallel to bedding in m year−1. The anisotropy ratio (Kmax/Kmin) was 100 for all rock types. The porosity and hydraulic conductivity of the limestone were calculated according to:
The sedimentary mixture is limited in extent, so for simplicity a constant porosity (0.30) and hydraulic conductivity (10 m year−1) were assigned to this rock type. Permeability data were not available for the shale, so again for simplicity the porosity and hydraulic conductivity of the shale were set to be constant with depth. The hydraulic conductivity of the shale was then varied in sensitivity studies, described below. For the baseline simulation, the porosity of the shale was assumed to be 0.25 and Kmax was 10−3 m year−1. This hydraulic conductivity falls toward the high end of the range for shale compiled by Neuzil (1994).
The hydraulic properties of evaporites and other very low-permeability rocks are poorly known (Neuzil 1986). Halite-dominated evaporite deposits have persisted in the basin for hundreds of millions of years even though subsurface dissolution of these highly soluble deposits is the likely source of salinity in the groundwater. An extremely low permeability is one way to account for the fact that relatively little of the Permian-age evaporite deposits have apparently been dissolved (Walters 1978; Anderson et al. 1994). For the baseline simulation, hydraulic conductivities of Kmax = 10−6 m year−1 and Kmin = 10−8 m year−1 were assigned to the evaporite section. Sensitivity studies were used to determine the effect of increasing and decreasing the hydraulic conductivity of the evaporite as well as the effect of assuming that the evaporites were impermeable. The evaporite section was specified to be impermeable by setting the corresponding nodes to be no flow nodes. Dissolution of evaporites was not coupled to porosity, permeability, or deformation of the numerical mesh, because little dissolution occurs in the simulations.
Transient simulations were set to run until an approximate steady-state was reached. The simulations were initially run for 80 Myr, and results stopped changing by 60 Myr, indicating near-steady-state conditions. The initial conditions do not affect the final simulation results, although they could affect the amount of time it takes to reach the approximate steady-state solution.
Initial conditions for hydraulic head and temperature were generated from a steady-state simulation of constant-salinity fluid flow and heat transport. Under these conditions, topography-driven flow dominated throughout the basin, with flow rates of <1 cm year−1 beneath the evaporite layer (Fig. 4A,B). In transient simulations, the flow system responded rapidly to the addition of solute transport, so the initial conditions for fluid flow did not affect the time it took for the transient simulations to reach an approximate steady-state. The initial thermal profile was very similar to a conductive profile except in the very shallowest parts of the basin, where flow rates of tens of cm per year or greater caused advective cooling (Fig. 4C).
Dissolution of halite was the only geochemical reaction simulated, and results are presented in terms of chloride (Cl−) concentration. The ratio of Cl− to TDS ranges from 0.55 for seawater to roughly 0.62 or higher for concentrated brines in the midcontinent because of changes in cation ratios during brine evolution. Initial conditions for solute transport were generated by specifying the Cl− concentration to be equal to freshwater in the top half of the basin and equal to seawater in the bottom half of the basin, below the evaporites. The initial Cl− concentration in the area of the evaporite layers was specified to be in equilibrium with halite.
Large-scale topography-driven and buoyancy-driven flow systems developed in all simulations. In the baseline simulation, a large topography-driven flow cell developed in the upper western half of the basin, concentrating flow into the GPA system and discharging approximately 500 km along the cross section (Fig. 5A,B). The maximum flow rate in the GPA system was nearly 5 m year−1. A small volume of flow from the large topography-driven flow cell reached the deep part of the basin before flowing eastward and upward to rejoin the GPA system, but flow rates in this area were as low as 10−8 m year−1. Two intermediate-scale topography-driven flow cells developed further east along the cross section. A large-scale counter-clockwise convection cell associated with buoyancy-driven flow is present near the eastern extent of the evaporite layers (Fig. 5B) with flow rates of 0.001–0.01 m year−1. The thermal structure (not shown) differs negligibly from the initial conditions shown in Fig. 4C.
Brines formed adjacent to the evaporite layers (Fig. 5C). The simulated distribution is consistent with the mapped distribution of salinity in the basin shown in Fig. 2. The Cl− concentrations were highest directly below the halite layers and decreased to freshwater concentrations to the east and west. The halite layers were well preserved after 60 Ma in the baseline simulation. The only dissolution of any significance occurred on the far eastern end of the evaporite layers, consistent with observed dissolution patterns (Walters 1978; Anderson et al. 1994). The maximum simulated Cl− concentrations correspond to a salinity of approximately 280 p.p.m., roughly 10% higher than the maximum salinities observed in this area. As previously indicated, observed salinities may reflect dilution during petroleum production. Below we present sensitivity studies designed to examine factors that could affect freshwater flushing. Additional factors that could affect salinity in the basin are considered in the Discussion.
Sensitivity studies were used to explore the effects of varying the hydraulic conductivity of the shale and evaporite. Increasing the hydraulic conductivity of the shale by an order of magnitude from Kmax = 10−3 and Kmin = 10−5 m year−1 to Kmax = 10−2 and Kmin = 10−4 m year−1 did little to change the overall flow patterns of the baseline simulation, but dissolved Cl− was not present above the evaporite layer after 60 Ma. This is the result of higher velocities in the overlying shale and is contrary to the field observations of high Cl− concentrations in the GP aquifer system. Decreasing the hydraulic conductivity of the shale by an order of magnitude caused numerical errors related to the 5-orders-of-magnitude contrast between the conductivities of the shale and the overlying aquifer. Once the contrast between units exceeds 3–4 orders of magnitude, little additional change in overall flow patterns can be expected in any case.
Increasing the hydraulic conductivity of the evaporite layers to Kmax = 10−5 m year−1 and Kmin = 10−7 m year−1 allowed extensive dissolution of the halite evaporite layers by 60 Ma, and the amount of halite remaining was not representative of the extent to which it is preserved in the basin today. The hydraulic conductivity of the evaporite layers used in the baseline simulation may therefore represent an upper-bound estimate. We note that increasing the conductivity of the evaporite layers also resulted in increased flow rates in the large-scale topography-driven flow system (Fig. 6A), but did not significantly affect the distribution of salinity. Similar to the baseline simulation, a convection cell formed at the eastern end of the evaporate section that was not present in the initial conditions (Fig. 6B).
In simulations where halite evaporite layers were specified to be impermeable, the westernmost topography-driven flow cell was entirely restricted to the top half of the basin (Fig. 6C), which allowed additional free convection cells to develop beneath the halite evaporite layers (Fig. 6D). Flow rates in the convection cells were between 10−5 and 10−4 m year−1. The evaporites thus appear to play a dual role in the development of buoyancy-driven flow by supplying dissolved solutes and by limiting the depth of topography-driven flow.
The distribution of salinity was relatively insensitive to the hydraulic conductivity of the evaporite layers and was consistent with field data in all three simulations. The hydraulic conductivity of the evaporite did not affect flow rates above the evaporite layer, and in all three simulations the flow rates beneath the evaporites were so low that mass transport was dominated by diffusion. Therefore these simulations were also relatively insensitive to transport parameters like dispersivity.
Vigorous topography-driven flow in sedimentary basins poses problems not only for preserving evaporite deposits, but also for retaining ancient brines. This problem is particularly well documented in the Western Canada sedimentary basin, where geochemical studies suggest that brines formed by evaporation of seawater must have been preserved for hundreds of millions of years (Spencer 1987; Connolly et al. 1990a; Wilson et al. 2003; Adams et al. 2004). Here we hypothesized that brines derived from the dissolution of evaporites could have a relatively short (approximately 5 Ma) residence time, consistent with previous hydrogeologic models, because brines could be replenished by dissolving evaporites. Simulation results suggest that the distribution of brines is consistent with steady-state conditions in the basin, but brines beneath the evaporites were isolated from topography-driven flushing and migrated very slowly (<1 cm year−1) due to buoyancy-driven flow. Thus these brines likely have a very long residence time, on the order of 50 Myr.
This result suggests the following series of events in this midcontinent basin. Evaporatively-concentrated brines must have formed concurrently with the Permian evaporite beds, but at some point these brines were flushed from the basin and replaced by new brines that formed by dissolution of evaporites. According to our simulations, the later-formed brines could be preserved beneath the evaporites for long periods, at least 50 Myr. If so, a likely scenario is that the original brines were flushed at the time of maximum uplift ca. 60 Ma, which presumably coincided with maximum topography-driven flow. Recalling that our initial conditions specified seawater salinity throughout the lower portion of the basin, the rapid formation of new brines and subsequent preservation of these brines beneath the evaporite layer appears quite feasible. This scenario is consistent with previous modeling studies of carbonate-hosted lead-zinc ore formation, which require a brief (approximately 1 Myr) period of rapid brine migration (Garven et al. 1993; Appold & Garven 1999) even though the modern configurations of the basins in question do not support such rapid flow today (e.g. Adams et al. 2004).
Although it is likely that reported salinities in the basin have been altered to some extent by petroleum production activities, it is worth examining the possibility that salinities in the basin are actually less than those calculated in the near-steady-state simulation results. Our simulation results and sensitivity studies suggest that it is unlikely that modern topography-driven flow could cause significant freshening below the evaporites. Increasing this flow would require raising the permeability of the shale and, likely, raising the permeability of the carbonate bed beyond the field-based values used in our simulations. Instead, observed salinities in the basin could reflect incomplete progress toward a steady-state distribution. The simulations took 60 Myr to reach a near-steady-state configuration. Salinities in the basin might not have yet reached a steady-state (1) if significant freshwater flushing in the midcontinent continued for some time after maximum uplift at 60 Ma or (2) if flow velocities beneath the evaporites are even lower than those calculated here. In the latter case, solute transport beneath the evaporites would be controlled entirely by diffusion.
These simulations also demonstrate the hydrogeologic feasibility of acquiring the observed high values of 87Sr/86Sr (Musgrove & Banner 1993) through interaction with silicate minerals within the confining system and additionally through reaction with crystalline basement rocks. Vertical flow developed across the low-permeability halite evaporite and shale layers in the NWIPC system. The large convection cells that developed at the margins of the evaporites and intermediate-scale convection cells that developed beneath the evaporites in our simulations provide a possible mechanism for geochemical exchange and transport of solutes from the crystalline basement rock.
The high concentration of calcium in brines relative to seawater has also been a persistent geochemical problem (Hardie 1991). Our results suggest that the crystalline basement could be a source of calcium (Spencer 1987) as well as strontium. In the simulations presented here the boundary between the lower Paleozoic sedimentary rocks and the basement was assigned to be no flow, but the fractured bedrock is likely permeable enough to allow fluid exchange. Fractured bedrock can also be an important source of metals that are concentrated in many brines (Doe & Delevaux 1972; LeHuray et al. 1987).
Whereas topography-driven flow is thought to dominate large-scale flow systems in uplifted sedimentary basins, results presented here suggest the coexistence of large-scale topography- and buoyancy-driven flow in the U.S. midcontinent region. Low-permeability evaporite layers limit the depth of topography-driven flow and supply solutes that drive haline convection at either end of the evaporite beds. Results suggest that the maximum vertical hydraulic conductivity of the evaporite beds is on the order of 10−8 m year−1. Larger hydraulic conductivities allowed greater dissolution of evaporite beds than is observed.
Brines derived from halite dissolution do not necessarily indicate a short fluid residence time. The approximate steady-state distribution of brines obtained in simulations was consistent with the observed distribution of salinity in the basin, but the brines were nearly stationary beneath the evaporite layer. Our results also strongly suggest that topography-driven flow was much more vigorous at some point in the geologic history of the basin. If this did not occur, it is unclear how the original evaporatively-concentrated brines could have been replaced by the current dissolution-related brines.
The presence of large haline convection cells at the margins of the evaporite layer and smaller convection cells beneath the evaporite layer provides a mechanism for extensive solute exchange between basin fluids and the crystalline basement. This type of flow could develop in any basin that contained evaporite beds either during evaporite formation or during later flushing with fresh fluids. This type of bedrock exchange could supply calcium, strontium, and metals that characterize brines in sedimentary basins.
We thank R.V. Scheerhorn, J.L. Banner, C.V. Hansen and M. Musgrove for discussions that benefited this work and for their help in acquiring data. Thoughtful reviews by Chris Neuzil and Jeff Nunn resulted in significant improvements in this manuscript. Acknowledgement is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work.