Three-dimensional flow in the Florida platform: Theoretical analysis of Kohout convection at its type locality
Keywords: Kohout convection, Floridan aquifer system, Boulder Zone, geothermal, heat flow, dolomitization, groundwater. INTRODUCTION Francis A. Kohout (1965) proposed that the deep saline groundwater beneath Florida is not static; rather, geothermal heat flow causes a regional circulation in which cold seawater enters the lower Floridan aquifer system (FAS) from the Straits of Florida, then rises because of thermally induced buoyancy and mixes with seaward-flowing meteoric groundwater from the upper FAS (Fig. 1). The evidence was temperature anomalies (inverse geothermal gradients) in oil exploration wells at the south end of the Florida peninsula (Fig. 2). After Kohout proposed and promoted the concept of regional cyclic flow of saltwater within the Florida platform (e.g., Kohout et al., 1977), Simms (1984) labeled the phenomenon Kohout convection, and proffered it as an Mg pump to explain large-scale dolomitization. This type of convection has been invoked as a conceptual model for dolomitization in numerous modern carbonate platforms, including the Bahamas (Whitaker et al., 1994; Caspard et al., 2004), Enewetak Atoll (Saller, 1984), Mururoa (Buigues, 1997), French Polynesia (Rougerie et al., 1997), and other atolls (Leclerc et al., 1999). Numerical simulation of two-dimensional (2-D) flow in generalized carbonate platforms has suggested that geothermal heat flow can cause convective circulation to depths of several kilometers (e.g., Kohout et al., 1977; Sanford et al., 1998; Wilson et al., 2001). *E-mail:
[email protected]. Current address: DHI Water and Environment, 2909 W. Bay to Bay Boulevard, Suite 206, Tampa, Florida 33629, USA.
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ABSTRACT Kohout convection is the name given to the circulation of saline groundwater deep within carbonate platforms, first proposed by F.A. Kohout in the 1960s for south Florida. It is now seen as an Mg pump for dolomitization by seawater. As proposed by Kohout, cold seawater is drawn into the Florida platform from the deep Straits of Florida as part of a geothermally driven circulation in which the seawater then rises in the interior of the platform to mix and exit with the discharging meteoric water of the Floridan aquifer system. Simulation of the asymmetrically emergent Florida platform with the new three-dimensional (3-D), finite-element groundwater flow and transport model SUTRA-MS, which couples salinity- and temperaturedependent density variations, allows analysis of how much of the cyclic flow is due to geothermal heating (free convection) as opposed to mixing with meteoric water discharging to the shoreline (forced convection). Simulation of the system with and without geothermal heating reveals that the inflow of seawater from the Straits of Florida would be similar without the heat flow, but the distribution would differ significantly. The addition of heat flow reduces the asymmetry of the circulation: it decreases seawater inflows on the Atlantic side by 8% and on the Gulf of Mexico side by half. The study illustrates the complex interplay of freshwater-saltwater mixing, geothermal heat flow, and projected dolomitization in complicated 3-D settings with asymmetric boundary conditions and realistic horizontal and vertical variations in hydraulic properties.
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Joseph D. Hughes* Department of Geology, University of South Florida, Tampa, Florida 33620, USA H.L. Vacher Ward E. Sanford U.S. Geological Survey, MS 431, 12202 Sunrise Valley Drive, Reston, Virginia 20192, USA
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Figure 1. Conceptual cross section of cyclic flow of saltwater induced by geothermal heating (Kohout convection) in Florida (adapted from Kohout et al., 1977). Vertical exaggeration is 300.
As Kohout knew, however, geothermal heating is not a necessary condition for cyclic flow of saltwater at a coastline. Cooper (1959) proposed that mixing in the freshwater-saltwater transition zone induces a cyclic flow of saltwater beneath the freshwater discharge, a phenomenon that Bear (1960) attributed to conservation of salt. Cooper’s work was coupled to Kohout’s study of the Biscayne aquifer (Kohout, 1960). How much of Kohout’s cyclic flow of saltwater deep within the Florida platform is due to geothermal heating (free convection) and how much is due simply to mixing caused by discharge of meteoric water to the shoreline (forced convection)? Flow systems of carbonate platforms can be expected to be more complicated than shown in generalized cross sections such as Figure 1. In particular, the 3-D nature of the Florida platform is evident because the Gulf of Mexico overlies the western half, and the classic Kohout cross section is located across the southern tip of the peninsula, where flow paths diverge radially away from a potentiometric high in the center of the emergent platform (Fig. 2). In this paper we use SUTRA-MS (Hughes and Sanford, 2004) to simulate and compare the 3-D flow in the FAS with (geothermal) and without (isothermal) heat flow across the Cedar Keys Formation “hotplate” (Kohout et al., 1977). The difference isolates the effect of geothermal heat flow on Kohout convection at its type locality. NUMERICAL MODEL We model the central and southern portion of the entire Florida platform (Fig. 2) in order to avoid uncertainties associated with specifying arbitrary boundaries at the shoreline. The model includes the surficial aquifer system to allow for realistic simulation of groundwater recharge, and the upper portion of the Cedar Keys Formation to represent the geothermal flux at the base of the FAS. The top of the model is the estimated water-table elevation in the emergent part of the platform and the seafloor in the Atlantic Ocean and the Gulf of Mexico. The 3-D hydrostratigraphic model was derived from data sets of Miller (1986), Mullins et al. (1988), and Jee (1993). Horizontal node spac-
© 2007 The Geological Society of America. For permission to copy, contact Copyright Permissions, GSA, or
[email protected]. GEOLOGY, 2007 Geology, JulyJuly 2007; v. 35; no. 7; p. 663–666; doi: 10.1130/G23374A.1; 4 figures; Data Repository item 2007163.
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ing between 1 km (onshore) and 5 km (offshore) was used, and each hydrostratigraphic unit was vertically discretized into five elements. Initial aquifer parameters for the units were developed from data sets of Meyer (1989), Hutchinson (1992), Sepulveda (2002), the United States Environmental Protection Agency (2003), and Budd and Vacher (2004), and calibrated using 85 head, 251 salinity, and 133 temperature observations from 315 wells. Calibrated FAS horizontal permeabilities and horizontal to vertical permeability ratios ranged from 3.6 × 10−14 to 2.3 × 10−9 m2, and 1 to 1000, respectively (see the GSA Data Repository1 for a summary of their spatial distribution). Effective porosity was assumed to be 70% of total porosity, and effective porosities of 21% and 35% were specified for the FAS and the Boulder Zone of the FAS, respectively. Horizontal and vertical dispersivities that satisfy mesh Peclet number numerical stability criteria were specified as 500 and 50 m in onshore areas to 1250 and 125 m in offshore areas, respectively, and are consistent with scale-dependent dispersivity values (Gelhar, 1986). Time-step lengths were determined to restrict transport of simulated fronts to a small fraction of an element per time step (Voss and Provost, 2002). No-flow side and bottom boundaries were specified, and a heat flux of 60 mW/m2 (Smith and Lord, 1997) was assigned to the basal boundary. Ocean-boundary temperatures were specified using a temperature-depth relation (25e–0.0015z) developed from data available in the U.S. Navy Generalized Digital Environmental Model (Teague et al., 1990). Ocean boundary salinities were set at 36‰ (unmodified seawater) and fluid pressures were assumed to be hydrostatic. For the emergent part of the platform, net groundwater recharge was applied to the uppermost nodes to represent recharge and discharge in appropriate areas. Estimates of net recharge with freshwater concentrations (0‰) and a mean annual air temperature of 23.5 °C (Florida Department of Natural Resources, 1974) were developed from spatially distributed data (Aucott, 1988; Langevin, 2001). 1 GSA Data Repository item 2007163, hydraulic properties used in the model for the defined hydrostratigraphic units, is available online at www. geosociety.org/pubs/ft2007.htm, or on request from
[email protected] or Documents Secretary, GSA, P.O. Box 9140, Boulder, CO 80301, USA.
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PATTERN OF THE GEOTHERMAL CIRCULATION We simulated coupled temperature- and salinity-dependent groundwater flow and transport in transient mode for 100 k.y., starting from initial conditions based on simulated near present-day conditions. Results are shown in Figure 3, at the cross section evaluated by Kohout et al. (1977). Note that the 50% seawater isochlor is located within the middle confining unit and Lower Floridan aquifer on the eastern side and within the Upper Floridan aquifer on the western side. Temperatures increase westward toward the axis of the platform, consistent with Kohout’s observations; horizontal flow dominates in the highly permeable Boulder Zone; and vertical flow dominates above the Boulder Zone except in the Upper Floridan aquifer and Intermediate aquifer system. Flow in the FAS is highest where the Intermediate aquifer system is present and generally lower where the intermediate confining unit is thick. Vertical flow and recharge to the Boulder Zone are highest adjacent to the Straits of Florida, where there is a general inflow area (Fig. 4A). The pattern of ocean-aquifer exchange is complicated. PATTERN OF THE ISOTHERMAL CIRCULATION To eliminate temperature effects, we removed the dependence of fluid properties on temperature by using a viscosity at 20 °C (0.001 kg/m·s), a zero temperature-density coefficient, and we assumed isothermal, hydrostatic seawater boundary conditions with a zero pressure-temperature coefficient. Otherwise, the isothermal case was identical to the geothermal case and produced the spatial distribution of ocean-aquifer exchanges shown in Figure 4B. A comparison of the two cases (Fig. 4) reveals significant differences in the distribution of ocean-aquifer exchange, e.g., the area of coastal outflow is greater in the geothermal case, localized areas of inflow and outflow develop in the geothermal case, inflow dominates in the Straits of Florida in the geothermal case, and the isothermal case is dominated by inflow. In the geothermal case, effects related to the ocean temperature-depth relation and geothermal heat flux cause localized areas of inflow and outflow to develop as a result of sloping density surfaces and associated convection (Wilson, 2005). Substantial inflow occurs in the geothermal case in the deep portions of the Straits of Florida as a result of the proximity to the Boulder Zone and the higher relative pressures. QUANTIFYING THE EFFECT OF HEAT FLOW ON THE SALTWATER CIRCULATION To further evaluate Kohout’s hypothesis, we examine total simulated ocean-aquifer exchange rates for the Atlantic Ocean and Gulf of Mexico. There are striking differences. Taking the geothermal case as the more realistic baseline condition, seawater inflow exceeds submarine discharge for both the Atlantic Ocean (1.4 versus 0.53 kg/s·km2) and Gulf of Mexico (1.5 versus 0.70 kg/s·km2). The net magnitudes of the ocean-aquifer exchanges (inflows-outflows) are approximately equal on the two sides (0.90 kg/s·km2 for the Atlantic and 0.77 kg/s·km2 for the Gulf of Mexico). Removal of the heat flow effectively increases the seawater inflow from the Atlantic Ocean by ~10% (+0.11 kg/s·km2), and doubles the seawater inflow from the Gulf of Mexico (+1.7 kg/s·km2). Removal of the heat flow increases the submarine discharge into the Atlantic by ~15% (+0.09 kg/s·km2), decreases the submarine discharge into the Gulf of Mexico by ~85% (−0.63 kg/s·km2), and leads to a change in onshore and offshore discharge areas. Net ocean-aquifer exchange in the Atlantic Ocean is nearly equal in the geothermal case (0.90 kg/s·km2) and the isothermal case (0.93 kg/s·km2), but net ocean-aquifer exchange in the Gulf of Mexico in the geothermal case (0.77 kg/s·km2) is 25% of that in the isothermal case (3.1 kg/s·km2). The asymmetry in the ocean-aquifer exchange rates in the
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geothermal case reflects the disparate seawater boundary pressures and temperatures resulting from differences in seafloor bathymetry bounding the platform. Furthermore, the addition of heat decreases seawater inflows because it contributes to fluid buoyancy and counteracts the effect of solute concentrations on fluid density. Increased pressures and lower temperatures in the deep Straits of Florida and the proximity to the Boulder Zone allow for increased seawater inflows in this area (+0.46 kg/s·km2), as pointed out by Kohout (1965).
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IMPLICATIONS OF THE EFFECT OF HEAT FLOW ON DOLOMITIZATION TIME The disparate ocean-aquifer exchange rates imply an asymmetry in dolomitization times for the FAS. Following Caspard et al. (2004), we calculate the time for complete dolomitization by assuming that (1) dolomitization occurs as a replacement process, and (2) dolomitization is limited by seawater inflow rates and seawater Mg molarity (0.045 mol/L). For the geometry of our case, we further assume that (3) the axis of the predevelop-
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ment Upper Floridan aquifer potentiometric surface (Fig. 2) represents the flow divide for the entire FAS, and (4) inflowing seawater from the Atlantic Ocean and Gulf of Mexico is distributed equally to each portion. With these assumptions, a thickness-weighted total porosity of 30%, a molar volume of 6.434 × 10−5 m3/mol, and total volumes of 4.5 × 1013 and 1.6 × 1014 m3 for the Atlantic Ocean and Gulf of Mexico portions of the platform, we find that the slight decrease in seawater inflow rate due to the geothermal heat flow would increase the time for complete dolomitization of the Atlantic Ocean side by ~10% (from 41 to 45 m.y.). Furthermore, the decrease in seawater inflow rate due to the geothermal heat flow would more than double the time for complete dolomitization of the Gulf of Mexico portion of the FAS (from 33 to 70 m.y.). These rates are similar to maximum dolomitization rates calculated by Wilson et al. (2001) for a generic platform. We note that the massively bedded dolomite Boulder Zone as defined by Miller (1986) is qualitatively more extensive along the Atlantic Ocean side of the platform. Because availability of Mg is not the only factor that affects dolomitization and seawater inflows are not equally distributed at the ocean-aquifer boundaries (Fig. 4A), the calculated dolomitization times probably represent minimum times for complete dolomitization of the FAS. CONCLUSION Although Kohout convection is often synonymous with geothermally driven convection in carbonate platforms, a geothermal heat flux is not a necessary condition for the cyclic flow of seawater in an environment like south Florida, where meteoric water flushes through the emergent portion of the platform. In the case of the type locality of Kohout convection, our simulations show that the inflow of seawater from the Atlantic would increase by ~10% if there were no heat flow, and, even more striking, inflow of seawater from the Gulf of Mexico would double without the heat flow as a result of asymmetric platform geometry. Furthermore, the distributions of inflow and outflow are significantly different without the heat flow. The study illustrates that geologically complicated carbonate platforms with asymmetric boundary conditions and variable hydraulic properties do not lend themselves to simple 2-D generalizations: in other words, geometry matters. ACKNOWLEDGMENTS This study was partially funded by the U.S. Geological Survey Office of Groundwater. We thank David Budd and Alden Provost for reviewing an earlier version of the manuscript. REFERENCES CITED Aucott, W.R., 1988, Areal variation in recharge to and discharge from the Floridan aquifer system in Florida: U.S. Geological Survey Water-Resources Investigations Report 88–4057, 1 sheet. Bear, J., 1960, The transition zone between fresh and salt waters in coastal aquifers [Ph.D. thesis]: Berkeley, University of California, 139 p. Budd, D.A., and Vacher, H.L., 2004, Matrix permeability of the confined Floridan Aquifer, Florida, USA: Hydrogeology Journal, v. 12, p. 531–549, doi: 10.1007/s10040–004–0341–5. Buigues, D.C., 1997, Geology and hydrogeology of Mururoa and Fangataufa, in Vacher, H.L., and Quinn, T., eds., Geology and hydrogeology of carbonate islands: Amsterdam, Elsevier, p. 433–451. Caspard, E., Rudkiewicz, J.-L., Eberli, G.P., Brosse, E., and M. Renard, M., 2004, Massive dolomitization of a Messinian reef in the Great Bahama Bank: A numerical modelling evaluation of Kohout geothermal convection: Geofluids, v. 4, p. 40–60, doi: 10.1111/j.1468–8123.2004.00071.x. Cooper, H.H., Jr., 1959, A hypothesis concerning the dynamic balance of fresh water and salt water in a coastal aquifer: Journal of Geophysical Research, v. 64, p. 461–467. Florida Department of Natural Resources, 1974, Kissimmee-Everglades area: Tallahassee, Florida Department of Natural Resources, 180 p. Gelhar, L.W., 1986, Stochastic subsurface hydrology from theory to applications: Water Resources Research, v. 22, p. 135S–145S. Hughes, J.D., and Sanford, W.E., 2004, SUTRA-MS—A version of SUTRA modified to simulate heat and multiple-solute transport: U.S. Geological Survey Open-File Report 2004–1207, 141 p. Hutchinson, C.D., 1992, Assessment of hydrogeologic conditions with emphasis on water quality and wastewater injection, Southwest Sarasota and
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West Charlotte Counties, Florida: U.S. Geological Survey Water-Supply Paper 2371, 74 p. Jee, J.L., 1993, Seismic stratigraphy of the Western Florida carbonate platform and history of Eocene strata [Ph.D. thesis]: Gainesville, University of Florida, 215 p. Kohout, F.A., 1960, Cyclic flow of salt water in the Biscayne aquifer of southeastern Florida: Journal of Geophysical Research, v. 65, p. 2133–2141. Kohout, F.A., 1965, A hypothesis concerning cyclic flow of salt water related to geothermal heating in the Floridan aquifer: New York Academy of Sciences Transactions, v. 28, p. 249–271. Kohout, F.A., Henry, H.R., and Banks, J.E., 1977, Hydrogeology related to geothermal conditions of the Floridan Plateau, in Smith, K.L., and Griffin, G.M., eds., The geothermal nature of the Floridan Plateau: Florida Department of Natural Resources Bureau of Geology Special Publication 21, p. 1–41. Langevin, C.D., 2001, Simulation of ground-water discharge to Biscayne Bay, southeastern Florida: U.S. Geological Survey Water-Resources Investigations Report 00–4251, 127 p. Leclerc, A.M., Jean-Baptise, P., and Texier, D., 1999, Density-induced water circulations in atoll coral reefs: A numerical study: Limnology and Oceanography, v. 44, p. 1268–1281. Meyer, F.W., 1989, Hydrogeology, ground-water movement, and subsurface storage in the Floridan aquifer system in Southern Florida: U.S. Geological Survey Professional Paper 1403-G, 59 p. Miller, J.A., 1986, Hydrogeologic framework of the Floridan aquifer system in Florida and in parts of Georgia, Alabama, and South Carolina: U.S. Geological Survey Professional Paper 1403-B, 91 p. Mullins, H.T., Gardulski, A.F., Hine, A.C., Melilli, A.J., Wise, S.W., Jr., and Applegate, J., 1988, 3-D sedimentary framework of the carbonate ramp slope of central west Florida: A sequential seismic stratigraphic perspective: Geological Society of America Bulletin, v. 100, p. 514–533, doi: 10.1130/0016–7606(1988)1002.3.CO;2. Rougerie, F., Fichez, R., and Déjardin, P., 1997, Geomorphology and hydrogeology of selected islands of French Polynesia: Tikehau (Atoll) and Tahiti (Barrier Reef), in Vacher, H.L., and Quinn, T., eds., Geology and hydrogeology of carbonate islands: Amsterdam, Elsevier, p. 475–502. Saller, A.H., 1984, Petrologic and geochemical constraints on the origin of subsurface dolomite, Enewetak Atoll: An example of dolomitization by normal seawater: Geology, v. 12, p. 217–220, doi: 10.1130/0091–7613 (1984)122.0.CO;2. Sanford, W.E., Whitaker, F.F., Smart, P.L., and Jones, G.D., 1998, Numerical analysis of seawater circulation in carbonate platforms: I. Geothermal convection: American Journal of Science, v. 298, p. 801–828. Sepulveda, N., 2002, Simulation of ground-water flow in the Intermediate and Floridan aquifer systems in peninsular Florida: U.S. Geological Survey Water-Resources Investigations Report 02–4009, 130 p. Simms, M., 1984, Dolomitization by groundwater-flow systems in carbonate platforms: Gulf Coast Association of Geological Societies Transactions, v. 34, p. 411–420. Smith, D.L., and Lord, K.M., 1997, Tectonic evolution and geophysics of the Florida basement, in Randazzo, A.F., and Jones, D.S., eds., The geology of Florida: Gainesville, University Press of Florida, p. 13–26. Teague, W.J., Carron, M.J., and Hogan, P.J., 1990, A comparison between the Generalized Digital Environmental Model and Levitus climatologies: Journal of Geophysical Research, v. 95, p. 7167–7183. United States Environmental Protection Agency, 2003, Relative risk assessment of management options for treated wastewater in South Florida: U.S. Environmental Protection Agency Report EPA 816-R-03–010, 390 p. Voss, C.I., and Provost, A.M., 2002, SUTRA—A model for saturated-unsaturated variable-density ground-water flow with solute or energy transport: U.S. Geological Survey Water-Resources Investigations Report 02–4231, 260 p. Whitaker, F.F., Smart, P.L., Vahrenkamp, V.C., Nicholson, H., and Wogelius, R.A., 1994, Dolomitisation by near-normal seawater? Evidence from the Bahamas, in Purser, B., et al., eds., Dolomites, a volume in honor of Dolomieu: International Association of Sedimentologists Special Publication 21, p. 111–132. Wilson, A.M., 2005, Fresh and saline groundwater discharge to the ocean: A regional perspective: Water Resources Research, v. 41, doi: 10.1029/ 2004WR003399. Wilson, A.M., Sanford, W., Whitaker, F., and Smart, P., 2001, Spatial patterns of diagenesis during geothermal circulation in carbonate platforms: American Journal of Science, v. 301, p. 727–752, doi: 10.2475/ajs.301.8.727. Manuscript received 18 October 2006 Revised manuscript received 1 March 2007 Manuscript accepted 11 March 2007 Printed in USA
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