BASIN-SCALE GROUNDWATER FLOW AND ADVECTIVE HEAT FLOW: AN EXAMPLE FROM THE NORTHERN GREAT PLAINS

ABSTRACT

William D. Gosnold, Jr.

Department of Geology and Geological Engineering University of North Dakota Grand Forks, ND 58202

Gravity-driven groundwater flow in a confined aquifer system that extends several hundred kilometers eastward from the Black Hills causes anomalous surface heat-flow over an 80,000 km2 area in southern South Dakota and northern Nebraska. Data from 16 new heat­flow holes, existing heat-flow data, and heat-flow values calculated from BHT data show a systematic variation in heat-flow from 20 m W m-2 in the recharge zone to 140 m W m-2 in the discharge zone. Ninety-four conventional heat-flow values and 62 heat-flow values calculated from BHT data yield an average heat-flow of 58 ± 9 mW m-2 for the northern Great Plains exclusive of the anomalous area. The advective heat-flow system is unusual in that temperature gradients in boreholes ranging from 2000 meters deep near the Black Hills to 500 meters deep in central South Dakota show only conductive heat-flow. In effect, the advective system is masked by 500 to 2000 meters oflow permeability marine shales that overlie a 600-meter thick confined aquifer system. Numerical models of coupled groundwater heat-flow in the aquifer system suggest that confined water flow at Darcy velocities of 3.17 x 10-8 m S-I to 6.34 x 1O-8 m S-I (1 to 2 my-I») causes the anomalous heat-flow.

INTRODUCTION

The empirical linear relation between heat flow and heat generation (Birch and others, 1968)

Q=Q*+Ab (1)

provides a basis for delineating heat-flow provinces with characteristic values of reduced heat­flow, Q., and the radiogenic layer parameter, b (Roy and others, 1968; Roy, Blackwell, and Decker, 1972). In this relationship, Q represents surface heat flow determined from borehole

99

A. Förster et al. (eds.), Geothermics in Basin Analysis© Kluwer Academic/Plenum Publishers 1999

100 GOSNOLD

data, Ab is the product of radioactive heat production at the surface and the slope of linear regression, and Q* is heat flow from below the heat producing zone. Equation (1) applies fairly well in the tectonically stable region east of the Rocky Mountains where average surface heat flow, Q is 51 ± 20 m W m-2 (n = 530), reduced heat flow is 31 ± 1 m W m-2 (n = 20), and the radiogenic layer parameter is 8.4 ± 0.4 km (Morgan and Gosnold, 1989). However, the relationship clearly does not apply in the tectonically active Rocky Mountain provinces where average surface heat-flow is 149 ± 181 mW m-2 (n = 110) (Morgan and Gosnold, 1989). Variability in surface heat flow in tectonically stable provinces results from variation in the crustal radiogenic component of heat-flow and may be related either to crustal thickness or to the thickness of the upper crustal radioactive layer (Morgan and Gosnold, 1989). However, some of the heat-flow variability in the Great Plains province, which has the highest average heat flow east of the Rocky Mountains (66 ± 26 mW m-2, n = 87), has been attributed to advective heat transport by groundwater flow (Gosnold, 1985, 1990).

A recent analysis of heat flow in the Great Plains, mainly based on bottom-hole temperature data, suggested that a large region in southern South Dakota and northern Nebraska is characterized by heat flows greater than 100 mW m-2 (Gosnold, 1991). If the anomalously high heat flow is the result of regional groundwater flow, it may be possible to quantify the advective component by making heat-flow measurements at locations that test the advection model. In this paper, I present new heat-flow data from sites located specifically to test the advection hypothesis and use model simulations of the system to quantify the advective and conductive heat-flow components in the Great Plains. First, heat-flow data and geothermal gradients acquired during continental heat flow and geothermal resource investigations are combined to better delineate surface heat flow in the region. Next, the relevant aspects of the regional groundwater systems are described in the context of an advective heat-flow system. Finally, analytical and numerical models coupling heat flow and groundwater flow are tested against both heat flow and hydrogeologic data.

THE HEAT-FLOW ANOMALY

The heat-flow anomaly was recognized first as a "Hot Water Belt" covering an area of about 7,200 km2 in South Dakota (Fig. 1) and initially was delineated by about 200 temperature gradients calculated from temperatures measured in artesian water wells (Adolphson and LeRoux, 1968). Later, Schoon and McGregor (1974) compiled temperature data from more than 1000 wells, including surface temperatures of artesian wells and bottom­hole temperatures obtained in oil exploration wells, and produced a geothermal gradient map of South Dakota that shows higher-than-average geothermal gradients occurring over a large area in South Dakota with apparent extension into north-central Nebraska (Fig. 1). Prior to this study, 19 heat-flow measurements were made in or close to the anomalous region. Eleven measurements within the anomaly, excluding the Black Hills Uplift, average 93.5 ± 15.9 mW m-2, and eight measurements on the margin of the anomaly average 62.8 ± 5.8 mW m-2

(Gosnold, 1990). The general pattern of the heat-flow anomaly delineated by these combined data and published analyses of regional groundwater systems (Downey, 1986) led to earlier interpretations of an advective heat-flow anomaly (Gosnold, 1985, 1990).

BASIN-SCALE GROUNDWATER FLOW AND ADVECTIVE HEAT FLOW 101

km

Figure I. Geothermal gradient map of South Dakota modified from Schoon and McGregor (1974). Area within bold line is the "hot water belt" identified by Adolphson and LeRoux (1968). Temperature gradients are °C lan-I.

NEW HEAT-FLOW DATA

Heat-Flow Sites

In this study, thirteen specially completed heat-flow holes and three holes of opportunity were occupied to test the advective heat-flow model (Filg. 2). The advective system is a group of four confined aquifers that recharge on the eastern side of the Black Hills and discharge over a broad zone some 200-400 km to the east in south-central South Dakota (Fig. 3). Consequently, most of the new heat-flow locations were selected to provide a profile from the recharge to the discharge zone. Also of interest was the possibility of heat advection by localized vertical discharge from the uppermost aquifer to the surface through fractures in the Pierre Shale (Bredehoeft, Neuzil, and Milley, 1983; Neuzil, Bredehoeft, and Wolff, 1984). To investigate this question, three of the new heat-flow holes were drilled in an area west of

the confluence ofthe White and Missouri rivers in south-central South Dakota (Fig. 2) where high geothermal gradients coincide with a region that Neuzil, Bredehoeft, and Wolff (1984) show as having vertical fracture-leakage velocities of the order of approximately 10 -10 m S-I.

Resolution of Temperature Gradients and Thermal Conductivitif~s

Heat flow is the product of temperature gradient and thermal conductivity, that is

Q=dT/dz)"

and the errors associated with temperature measurements, temperature gradient calculations, and measurement ofthermal conductivity determine the error of a heat-flow measurement.

102

NORTH DAKOTA

104 103 102 101 100 ---I -

99 98 ~-

97

GOSNOLD

N

1

Figure 2. Locations of heat-flow sites. Sites previously published are shown by dots (Sass and others, 1971; Sass and Galanis, 1983; Gosnold,1990) and new sites are shown by triangles. TIrree heat-flow holes at White River site lie within ellipse. Line A - A' locates cross section for Figures 3, 8, and 9.

2.0

km

1.0

o o 100 200 300

km

Figure 3. Four regional aquifers, Al - A4, and three confming units, QI - Q3 are shown in schematic cross section along line A - A' in Figure 2. Al - Fall River, Lakota and Dakota Sandstones (Cretaceous); A2 -Pahasapa (Madison) Limestone (Mississippian); A3 - Minnelusa Formation (Pennsylvanian); A4 - Deadwood Sandstone and Red River Formation (Cambrian - Ordovician). QI - Cretaceous shales; Q2 - shales of Permian to Jurassic age; Q3 - crystalline basement.

Temperatures were measured with a thermistor probe having a precision of ±O.OOl cC and an absolute accuracy of ±O.02 cC. Depths were determined with a precision of ±O.OOl m and temperature gradients were calculated as least-squares fits to the selected depth interval for each borehole. The temperature measurements were made several years after drilling so that the borehole temperatures were at equilibrium conditions.

BASIN-SCALE GROUNDWATER FLOW AND ADVECTIVE HEAT FLOW 103

Thermal Conductivity

Thermal conductivity determinations for the Pierre Shale were problematic and a reliable technique for measuring thermal conductivity on shales was not available until the final borehole in this study was drilled at Wall, South Dakota in 1995. Consequently, thermal conductivities were estimated based on published values for nearby sites and published descriptions of the lithology of the Pierre Shale. The thermal conductivity of shale is one of the lowest values for any rock type, for example, granite typically has a conductivity of 2.5 to 3.5 W mol °C-l whereas the most recently published values for the conductivity the Pierre Shale range from 1.0 - 1.2 W mol °C-l (Blackwell and Steele, 1989; Sass and Galanis, 1983; Gosnold and Todhunter, 1994). Using a half-space needle-probe technique, we measured a thermal conductivity of 1.2 ± 0.2 W mol °C-l (n = 60) on Pierre Shale cores from a heat-flow site in southwestern Manitoba and a thermal conductivity of2.0 ± 0.25 W mol °C-l (n = 60) at a site in western South Dakota. Clay fraction analysis of the Pierre Shale samples showed that the difference is the result of a higher quartz content in the samples from the Wall, South Dakota site. The Pierre Shale is divided into eastern, median, and western facies on the basis oflithology (Tourtelot, 1962; Gill and Cobban, 1965). All heat-flow sites in this study except the Wall site lie within the clay-rich eastern facies that is characterized by low-thermal conductivity. Therefore, the thermal conductivity of the Pierre Shale was assumed to be 1.2 W mol °C-I±0.2 for all localities but the Wall heat-flow site in South Dakota.

T -z Profiles

Climatic warming since the end of the Little Ice Age, c.a. 1850, has influenced temperatures in the upper 80 meters of all of the boreholes (Gosnold, Todhunter, and Schmidt, 1997). However, the temperature gradients below 80 meters are remarkably linear in all but three boreholes (Fig. 4) and the standard error for least-square gradient calculations averages only 0.9% (Table 1). This observation is significant because linear temperature gradients below the climatic disturbance in the Pierre Shale suggest that only conductive heat flow occurs within the formation. The Pierre Shale has a low fluid permeability (Bredehoeft Neuzil, and Milley, 1983), thus it could mask the thermal signals from any advective system beneath it. The thickness of the Pierre Shale plus the underlying Niobrara Formation, Carlile

60 30 150·c/km

50 I:- lOO·C/km 25

40 ~ 50·c/km

u 20 U

~ g'30 Ol

CD 015 0

20

10 10

0 5 0 200 400 600 800 0 50 100 150 200 250

Depth (m) Depth (m)

Figure 4. Temperature-depth profiles for new heat-flow holes in South Dakota. A, shows T-z profiles for specially completed heat-flow holes; and B, shows T-z profiles from 5 holes of opportunity. Profiles are spaced on temperature scale for better visibility_Profiles with lower temperature gradients are from sites in west of study area and those with higher temperature gradients are from sites in east of study area.

104 GOSNOLD

Table I. New heat-flow data. Temperature gradients are linear least-squares fits to indicated depth intervals. Thennal conductivities for all sites but Wall-I and Wall-2 are estimates based on measured thennal conductivites of Pierre Shale from drill cores taken at Hayes, S. D. (Sass and Galanis, 1983) and at Wawanesa, Manitoba (Gosnold and Todhunter, 1994). Conductivities at Wall site were measured using half-space needle probe technique (Gosnold and Todhunter, 1994, Gosnold, Todhunter, and Schmidt, 1997).

LOCATION LAT. LONG GRADIENT DEPTH THERMAL HEAT ELEV MkM" INTERVAL CONDo FLOW m

m Wm"K' mWm·2

WhiteR. 1 43.83 99.57 54.2±0.2 99-181 1.2±O.2 65.0±O.4 545 WhiteR. 2 43.82 99.72 90.9±O.2 91-179 1.2±0.2 109.1±0.4 540 White R. 3 43.79 99.74 95.1±0.1 95-175 1.2±0.2 114.1±0.3 545 WhiteR. 4 43.74 100.04 108.6±0.1 107-179 1.2+0.2 130.3±0.3 570 WhiteR. 5 43.70 100.04 85.6±0.5 95-175 1.2±O.2 102.7±0.3 480 WhiteR. 6 43.68 100.04 91.1±0.1 95-175 1.2±0.2 109.3±0.3 540 Goodman 43.45 99.18 50.7±0.2 115-260 1.2±0.2 60.8±0.4 547 Dixon 44.90 101.80 76.6±0.3 145-315 1.2±0.2 91.9±0.5 590 Belvidere 43.85 101.26 65.7±0.1 81-181 1.2±0.2 78.7±0.3 707 Kadoka 43.81 101.50 50.1±0.2 81-181 1.2±0.2 60.1±0.2 747 Wall-I 43.74 102.22 32.1±0.01 100-181 2.0±0.3 63.8±0.3 848 Wall-2 43.74 102.23 33.7±0.01 150-202 2.0±0.3 67.4±0.3 840 Koch 34-17 45.84 102.93 48.1±O.1 300-470 1.2±0.2 57.7±0.3 935 Koch 14-15 45.87 102.96 54.0±0.1 300-470 1.2±0.2 64.9±0.3 929 Sheep Draw 43.19 103.90 53.6±0.1 300-470 1.2±0.2 64.3±0.3 421 Sisseton 45.71 96.92 42.9±0.2 200-275 1.2±O.2 51.5±0.4 387

Shale, and Belle Fourche Shale ranges from 400 m to 750 m across the study area and only one heat-flow hole has been logged below these Cretaceous age shales. That site, near Burton, Nebraska (Gosnold, 1990), shows a 20% decrease in heat flow below the Pierre Shale which suggests a possible advective heat-flow component resulting from fluid flow in the underlying formations.

A Special Case

Three of the T-z profiles in the high heat-flow region along the White River in central South Dakota show a concave upward curvature from the ground surface to the top of the Niobrara and a convex curvature within and below the Niobrara formation (Fig. 5). Part of the concave curvature is the result of climatic warming, but the curvature increases rather than decreases with depth which suggests a thermal effect in addition to the climate signal. Assuming a homogeneous thermal conductivity for the overlying Pierre Shale and the underlying Carlile Shale, these T -z profiles suggest that heat flow systematically increases toward the Niobrara from above and from below. Neuzil (1993, 1995) demonstrated the existence of abnormal fluid pressures in the Cretaceous shales in South Dakota and has suggested (C.E. Neuzil, pers. comm., 1997) that groundwater should be flowing by fracture leakage into the Niobrara from the Pierre Shale and Carlile Shale. Advective heat flow calculations using the one-dimensional relationship of Stallman (1963), that is

Qe VDaCp In - = --.!... Qe A

where QI is heat flow at the base of the water-flow zone, ~ is heat flow at the top of the zone, V is Darcy velocity in m S-I, D is the length of the zone in meters, a is density of the fluid in kg m-3, Cp is heat capacity of the fluid in W s, and kgl °CI,.A. is thennal conductivity in W m 1

BASIN-SCALE GROUNDWATER FLOW AND ADVECTIVE HEAT FLOW 105

26

24

22

() 20

!6'18 0 16

14

12

10 0 50 100 150 200

Depth (m)

140

120

100

-l:1 ~ 80 "0

60

40 20 L-____________________ __

110 120 130 140 150 160 170 180 190 Depth (m)

Figure 5. T-z and dT/dz profiles White River heat-flow sites 4, 5, and 6. dT/dz plots were made with Niobrara Formation as datum. Increase in temperature gradient above the Niobrara is interpreted to be result of combination of ground-surface warming and heat advection by fracture leakage from surface into Niobrara. Decrease in temperature gradient below Niobrara is interpreted to be result of heat advection by upward fracture leakage.

zone in meters, 0 is density of the fluid in kg m-3, Cp is heat capacity of the fluid in W s, and Kg-I °el , A is thermal conductivity in W m-I °el , suggest that downward groundwater flow in the lower 30 meters of Pierre Shale at 5 X 10-9 m S-I and upward groundwater flow in the upper 30 meters of Carlile Shale at 5.410-9 m 8"1 could cause the inferred increase in heat flow toward the Niobrara formation.

Estimated Heat-Flow Values

With the determination of several key parameters for both the heat flow and the ground-water flow systems, quantitative modeling of the coupled systems should reveal the degree to which the systems interact. Ideally, the models should include both lateral transport, represented by two-dimensional cross sections, and areal heat flux models. The data acquired for the east-west heat-flow profile provide a reasonable basis for two-dimensional modeling of a cross section of the coupled systems. However, these data do not cover a sufficient surface area to provide an estimate of the areal heat flux.

The lack of areal coverage by the conventional heat-flow data was overcome by including heat-flow values estimated from Schoon and McGregor's (1974) temperature gradient data. Many of the temperature gradient data were determined from the differences between the surface and bottom-hole or inferred bottom-hole temperatures of wells that penetrate the top of the Dakota Sandstone. Normally two-point gradients do not adequately sample subsurface temperatures and are not useful for calculating heat-flow. In this situation, however, the temperature gradient between the ground surface and the top of the Dakota Sandstone is the actual temperature gradient in the thick section of Cretaceous shales that blanket the region. The predominant lithologies between the two points are marine shales, mostly the Pierre Shale (Table 2). Temperature gradients measured in heat-flow holes in the Pierre Shale and the underlying shales are typically linear, which suggests that these shales have a relatively uniform thermal conductivity. Geologically, this is a reasonable inference because the members of the Pierre Shale tend to be laterally continuous and lithologically uniform (Tourtelot, 1962; Schultz, 1964, 1965). Therefore, assuming that the effective thermal

106 GOSNOLD

Table 2. Generalized stratigraphy of southern South Dakota. Units included in major regional aquifers are designated AI, A2, A3, and A4.

SYSTEM FORMATION LITHOLOGY MAX. THICKNESS (meters)

PIERRE SHALE SHALE 610 NIOBRARA FORMATION CHALK 70

LOWER CARLILE FORMATION SHALE 220 CRETACEOUS GREENHORN FORMATION IMPURE LIMESTONE 110

BELLE FOURCHE SHALE SHALE 170 MOWRY SHALE SHALE 77 NEWCASTLE SANDSTONE SANDSTONE 20 SKULL CREEK SHALE SHALE 83

Ai INYAN KARA GROUP SANDSTONE 280

JURASSIC MORRISON FORMATION SHALE 67 UNKPAPA SANDSTONE SANDSTONE 69 SUNDANCE FORMATION SHALEISANDSTONE 138

TRIASSIC SPEARFISH FORMATION SANDY SHALE 210

MINNEKAHTA LIMESTONE LIMESTONE 16 PERMIAN OPECHE FORMATION SHALE/SANDSTONE 41

PENNSYLVANIAN A2 MINNELUSA FORMATION SANDSTONEILIMESTON 270

MISSISSIPPIAN A3 PASAHAPA LIMESTONE LIMESTONE 192

A4 ENGLEWOOD LIMESTONE LIMESTONE 20 DEVONIAN A4 RED RIVER FORMATION DOLOMITEILIMESTONE 20

ORDOVICIAN WINNIPEG FORMATION SHALE 30

CAMBRIAN A4 DEADWOOD FORMATION SANDSTONE 122

PRE-CAMBRIAN METAMORPHIC and IGNEOUS ROCKS

conductivity of the Pierre Shale is approximately 1.2 W m· l °e-l heat-flow values were estimated for 62 sites (Table 3) selected from Schoon and McGregor's (1974) compilation.

It is important to distinguish between these heat-flow estimates and conventional heat­flow values. A conventional heat-flow value requires temperature gradients measured in a borehole and mUltiple thermal conductivity values measured on samples from the measured gradient interval or from a nearby site having equivalent lithology. Statistical analysis ofthese values provides a measure of the accuracy and quality of the heat-flow determination. However, no statistical measure of accuracy is possible for the estimated heat-flow values.

The accuracy of these estimated heat-flow values was tested by comparing the temperature gradients measured at 12 conventional heat-flow holes in the thermal anomaly to the nearest two-point gradient contours in Figure 1. The results (Table 4) show that four of the measured temperature gradients lie within the contour values, one is 6% low, two are approximately 10% high, and the remainder are high by 14, 20, 29, 59, and 101 percent compared to the nearest gradient contour line. Ifthis comparison is representative of the total popUlation of estimated heat-flow values, it indicates that approximately 2/3 of the estimated heat-flow values are accurate within ± 10% and 113 underestimate heat flow by at least 20%.

BASIN-SCALE GROUNDWATER FLOW AND ADVECTIVE HEAT FLOW 107

Table 3. Estimated heat-flow values. Type designations are WW (water well) and BHT (bottom-hole temperature in oil well).

Latitude Longitude Gradient Type Heat flow Latitude Longitude Gradient Type Heat Flow 43.00 98.60 89.2 VWI/ 107 43.72 99.50 93.3 VWI/ 112 43.02 98.48 69.2 VWI/ 83 43.73 99.69 93.3 VWI/ 112 43.04 98.61 110.8 VWI/ 133 43.79 99.70 93.3 VWI/ 112 43.05 98.25 105.0 VWI/ 126 43.80 99.51 93.3 VWI/ 112

43.10 98.67 67.5 VWI/ 81 43.84 100.28 70.0 VWI/ 84

43.11 98.61 70.8 VWI/ 85 43.86 100.10 83.3 VWI/ 100 43.16 98.38 42.5 VWI/ 51 43.93 102.69 29.9 BHT 36

43.16 98.87 89.2 VWI/ 107 43.98 99.13 41.7 VWI/ 50

43.17 98.82 74.2 VWI/ 89 44.06 99.48 50.8 VWI/ 61

43.17 99.07 107.5 VWI/ 129 44.08 99.53 49.2 VWI/ 59

43.18 98.96 82.5 VWI/ 99 44.11 99.66 42.5 VWI/ 51

43.22 98.95 100.8 VWI/ 121 44.14 101.79 16.4 BHT 20

43.31 99.08 97.5 VWI/ 117 44.17 99.46 47.5 VWI/ 57

43.31 99.13 99.2 VWI/ 119 44.25 100.62 75.8 VWI/ 91

43.38 99.37 116.7 VWI/ 140 44.31 101.52 26.1 BHT 31

43.39 99.15 79.2 VWI/ 95 44.32 102.77 22.4 BHT 27

43.41 99.13 92.5 VWI/ 111 44.34 102.02 18.2 VWI/ 22

43.44 99.25 115.8 VWI/ 139 44.35 100.39 68.3 VWI/ 82

43.44 99.30 115.8 VWI/ 139 44.38 101.58 27.6 VWI/ 33

43.45 99.11 95.8 VWI/ 115 44.46 101.76 21.6 BHT 26

43.46 99.28 102.5 VWI/ 123 44.49 101.59 13.8 BHT 17

43.52 98.97 69.2 VWI/ 83 44.49 102.04 22.3 VWI/ 27

43.54 99.57 97.5 VWI/ 117 44.51 102.01 25.1 VWI/ 30

43.55 99.84 104.2 VWI/ 125 44.52 102.54 18.4 BHT 22

43.58 99.85 100.8 VWI/ 121 44.54 101.59 19.5 BHT 23

43.59 99.39 82.5 VWI/ 99 44.63 102.56 22.2 BHT 27

43.62 99.72 104.2 VWI/ 125 44.75 102.53 32.5 BHT 39

43.67 99.40 70.8 VWI/ 85 44.75 103.16 21.9 BHT 26

43.67 99.44 70.8 VWI/ 85 44.77 102.96 21.8 BHT 26

43.67 99.75 92.5 VWI/ 111 44.80 102.88 14.0 BHT 17

43.71 102.88 29.8 BHT 36 44.82 102.01 15.9 BHT 19

Table 4. Temperature gradients (mK m· l ) measured in heat-flow holes (rows 2-5) compared to nearest temperature gradient contour lines in Figure 1 (row 1).

Contour range Contour range Contour range Contour range 36 - 54 54 -72 72 - 90 90 -108

44 82 68 90

59 93 90 96

60 108

86

109

The low estimates are not surprising considering that many of Schoon and McGregor's (1974) geothermal gradients were determined using the discharge temperature from a flowing well as the bottom-hole temperature. Although several factors may be involved, such as, well

108 GOSNOLD

depth, well age, type of casing, hole diameter, and discharge rate, heat loss as the water flows up the well results in a low estimate of the bottom-hole temperature. However, the important point is that none of the estimated heat flows seem to overestimate heat-flow and incorrectly extend the high heat flow region.

HEAT-FLOW RESULTS AND A HEAT-FLOW CONTOUR MAP OF THE NORTHERN PLAINS

Eight of the new heat-flow data lie within the anomalous heat-flow region and average 102 ± 20.2 m W m·2• The eight new data outside the anomalous region average 62.0 ± 4.8 m W m·2• Heat flow at 94 sites in the northern Great Plains, including the 16 new sites reported here, and the 62 estimated heat-flow values were combined to produce a contour heat-flow map (Fig. 6). If only heat-flow points lying between the 30 mWm·2 and 70 mW m·2 contours are included, the average of the conventional heat-flow values is 58 ± 9 mW m·2• The heat­flow pattern that appears east of the Black Hills shows the expected variation for advective heat transport across a tilted basin. Heat flow is low in the recharge area, systematically

o

Figure 6. Heat-flow contour map of northern Great Plains region. Heat-flow values are in mW m·2•

Conventional heat-flow sites are shown as filled squares and asterisks for previously published data and as filled circles for data reported in this study. Estimated heat-flow sites are shown as open triangles. Region between bold lines in central South Dakota is general area where Paleozoic aquifers discharge into Dakota Sandstone (Cretaceous) through subcrop contacts.

BASIN-SCALE GROUNDWATER FLOW AND ADVECTIVE HEAT FLOW 109

increases to high values in the discharge area and falls to the regional value beyond the discharge area.

THE AQUIFER SYSTEM

Investigation of the relationship between the heat-flow anomaly and groundwater flow requires understanding the system of confined aquifers underlying the area. Groundwater flow in the aquifer system is gravity driven from the recharge area at 1200 m elevation to the discharge area at about 400 m elevation (Fig. 7 A-7E). Downey (1986) divided the system into four major confined aquifers that are recharged where eastward-flowing streams cross their outcrops along the eastern margin of the Black Hills (Swenson, 1968). The three lower

Cambrian..Qrdovician Aquifer Pennsylvanian Aquifer

104 103 102 101 100 99 98 97 104 103 102 101 100 99 98 97

LongHude Longitude

Mississippian Aquifer Cretaceous Aquifer

104 103 102 101 100 99 98 97 104 103 102 101 100 99 98 97 LongHude LongHude

Figure 7. Potentiometric surface contours on tops of four major aquifer systems showing west to east flow pattern modified from Downey (1986). Contours are in meters and datum is sea level. East-west dashed line designates heat-flow profile shown in Figure 8.

aquifers discharge at subcrop contacts with the uppermost aquifer beginning about 200 km east of the Black Hills and extending eastward for another 100 km (Swenson, 1968; Downey, 1986). Waters from the uppermost aquifer discharge primarily at outcrops to the east

110 GOSNOLD

(Downey, 1986) and secondarily through vertical fracture leakage (Neuzil, Bredehoeft, and Wolff, 1984; Downey, 1986). A detailed description ofthe aquifers is beyond the scope of this study, but the following general description of the system provides information necessary to construct analytical and numerical models of the thermal effects of water flow in the system.

The lowermost aquifer is composed of limestones and dolomites of the Red River Formation (Ordovician) and includes sandstones of the Deadwood and Winnipeg Formations (Cambrian - Ordovician). Calculated Darcy velocities (Darcy velocity) in this aquifer range from 0.6 m y.1 to 22.8 m y.1 (Downey, 1986). In the area of the heat-flow anomaly, the Cambrian-Ordovician aquifer is confined below by the crystalline basement. The Mississippian aquifer, the Pahasapa Limestone, directly overlies the Cambrian-Ordovician aquifer in the Black Hills and in southern South Dakota. Computed Darcy velocities for the Mississippian aquifer range from 0.6 my-I to 6 m yl (Downey, 1986). The third major aquifer, the Pennsylvanian aquifer, overlies the Pahasapa Limestone and consists of sandstones and limestones of the Minnelusa Formation. The Minnelusa, with an average thickness of about 300 meters, is the thickest single aquifer in the area. It is confined above by shales and siltstones of Permian, Triassic, and Jurassic age. Groundwater flow velocities for the Minnelusa were not determined in any prior studies, but Downey (1986) determined that the transmissivity of the Minnelusa Formation is similar to that of the Pahasapa Limestone, that is 2.7 - 8.1 x 10-4 m2 S-I. Therefore, this aquifer is assumed to permit water flow at velocities equal to those of the Pahasapa. The Lower Cretaceous aquifer consists of the Fall River, Lakota, and Dakota Sandstones which have a total porosity of 26% (Rahn, 1985). Transmissivities range from 2.2 x 10-3 to 1.6 x 10-2 m2 8"1 which are 1 to 2 orders of magnitude greater than those in the Paleozoic units. The hydraulic gradient of the Lower Cretaceous aquifer essentially equals that of the Paleozoic rocks, thus, for a first approximation, Darcy velocities in the Lower Cretaceous aquifer are assumed to be at least an order of magnitude greater than the Darcy velocities in the Pahasapa Limestone. The Lower Cretaceous aquifer is confined above by 400 - 750 meters of shale and minor amounts oflimestone.

The three lower aquifers, the Cambrian-Ordovician aquifer, the Mississippian aquifer, and the Pennsylvanian aquifer are essentially a single system not separated by confining layers in the area of anomalous heat flow. This lower system has a maximum combined thickness of about 650 meters in the recharge area and thins to the east where it is truncated and forms an angular unconformity with the overlying Lower Cretaceous aquifer.

The subcrop contact between the lower aquifer system and the Lower Cretaceous aquifer is a zone of vertical leakage where waters are discharged into the Dakota Sandstone (Swenson, 1968; Downey, 1986). Evidence of this vertical leakage is contained in chemical analyses of waters in the Dakota which indicate that the aquifer is extensively flushed with meteoric water in the recharge area but contains calcium-sulfate waters derived from the Paleozoic formations in the discharge area (Swenson, 1968; Schoon, 1971). The region where the subcrops of the three lower aquifers contact the Dakota lies between the bold lines in Figure 6. Thus, the area of highest heat flow generally coincides with the zone where waters from the lower aquifers discharge into the Dakota.

TEST OF THE HYPOTHESIS BY MODELING

For a first approximation, the relation between the heat-flow anomaly and the ground­water-flow system can be tested with simple analytical models such as the basin model of Domenico and Palciauskus (1973) and the wedge model of Jessop (1991). The average heat-

BASIN-SCALE GROUNDWATER FLOW AND ADVECTIVE HEAT FLOW III

flow value for the thermal anomaly is about twice the background heat flow, 120 m W m,2 vs. 58 m W m,2, and both analytical models indicate that fluid flow across the basin structure at a Darcy velocity of I m y'l would cause a doubling of surface heat flow in the discharge area. However, these simple analytical models do not address the dynamics of the groundwater

system in South Dakota. The system of four aquifers is asymmetrical, in thickness, computed Darcy velocities differ between aquifers and within the aquifers (Downey, 1986).

To address the complexities of the system, I applied a two-dimensional finite­difference model which couples heat flow and groundwater flow using the method of Brott, Blackwell, and Mitchell (1978) and Brott, Blackwell, and Ziagos (1981). That is, groundwater velocity is a parameter of the model rather than a quantity calculated from the hydrologic and thermal properties of the aquifers. This method applies appropriately in this situation because gravity rather than heat is the driving force in the aquifer and velocities have been calculated independently (Downey, 1986).

The cross section used for the simulation lies along the east-west dashed lines in Figure 7. The finite-difference grid contains 53 vertical and 103 horizontal nodes with 50-m vertical and 3000-m horizontal spacings. The parameters specified for each node are: thermal conductivity, radioactive heat production (basement rocks only), fluid heat capacity, rock heat capacity, Darcy velocity, and flow direction. Thermal conductivities of the distinctive lithologic units were taken from Gosnold (1991) and were assigned in the model as follows: The two shale units, QI & Q2 were assigned a thermal conductivity of 1.2 W m'l °C'l. The crystalline basement was assigned a thermal conductivity of 3,0 W m'l °C'l. The Lower Cretaceous aquifer, AI, was assigned a conductivity of2.7 W m'l °C I , and the three carbonate aquifers, A2, A3, A4, were assigned a thermal conductivity of 2.5 W m'l °C,l.

The initial thermal structure of the model was a purely conductive thermal regime with heat flow in the Black Hills at 90 mW m,2 and heat flow elsewhere at 58 mW m'2. The ground­surface temperature was fixed at 10°C, and prior to running the advection models, the conductive model was run for a sufficient time, 300,000 years to achieve equilibrium allowing for refraction along the margin of the Black Hills Uplift.

The modeling process involved testing different combinations of groundwater velocities to obtain the best agreement between the modeled and observed heat-flow profiles. The wedge model predicts that a constant updip velocity of 6.34 x 10,8 m S'l in a single aquifer 400 m thick would generate a heat flow of about 140 m W m,2 at the discharge end of the basin. Thus, to compare the wedge model to the numerical model, one model run was made using a constant velocity of 6.34 x 10,8 m S'l in AI, A2, A3, and A4. The resultant heat-flow maximum for the numerical model was 168 mW m'2. Running the model with no water flow in Al produced a maximum of 140 mW m,2 which agrees with the wedge model. This exercise demonstrates agreement between the wedge and numerical models for similar geometries, but, significantly, it shows the importance of inclusion of the Dakota Sandstone in the model. Subsequent models were based on the variable flow velocities given by Downey (1986), that is velocities decreased from the recharge side to the discharge side of the models. Excellent agreement between observed heat-flow values and the model (Fig. 8) was obtained with a recharge velocity of6.34 x lO'8 m S'l for A2, A3, and A4 with a decrease to 4.76 x 10,8 m S'l toward the discharge side of the model. The velocity of Al used in the best-fitting model was 1.902 x 10'7 m S'l although the contribution from Al is relatively small.

Isotherms along the model cross section for the best-fitting model and the initial (conductive) model are shown in Figure 9. Variation in the geothermal gradient along the section is shown in Figure 10 which includes two model profiles along the cross section and two observed temperature-depth profiles. The T-z profile at Wall, South Dakota is

112 GOSNOLD

140 West East

120 N E 100 3: .s 80 ... :;: 60 0

0;;:: ... ... iii 40 OJ J:

20

0 0 100 200 300 400 500 600

Distance (km)

Figure 8. Model heat-flow profile (solid line) superimposed on observed heat flow and estimated heat-flow values (triangles).

superimposed on the model curve; both have the lowest temperature gradients. The model profile in the high heat-flow zone (thin line with dark square symbols) closely matches the observed T -z profile from Burton, Nebraska (thick line without symbols). The T -z profile at the Burton site exhibits a drop in heat flow from 106 m W mo2 to 80 m W mo2 at the contact between the shale and the Dakota. The high heat flow, 80 mW mo2, in the lower section of the Burton hole is assumed to be the result of water flow in A3 and A4, both of which underlie the area.

Initial conditions.

Figure 9. Isotherms (deg C) for initial and advective conditions for model scheme shown in Figure 6. Aquifers A2-A4 are shown as single unit in this figure for better visibility of isotherms.

BASIN-SCALE GROUNDWATER FLOW AND ADVECTIVE HEAT FLOW 113

80 )!I4-i../U

70

60 . . . () 50

g>40 0 30

20

10

0 0 200 400 600 800 1000

Depth (m)

Figure 10. Observed T-z profiles agree with T-z profiles generated by numerical model of advective heat transport in recharge and discharge sections of aquifer system. Thick lines with closed circles and no symbols are observed T-z profIles at Wall, SD and Burton, NE respectively. Thin lines with triangles and closed squares are model profiles for those sites.

HEAT-FLUX ESTIMATES

Agreement between modeled and observed heat-flow profiles suggests that groundwater flow at velocities of6.34 x 1O.sm S·l in the recharge area and 4.76 x 1O.sm S·l in the discharge area for A2, A3, and A4 can account for both the low and high heat-flow anomalies east of the Black Hills. In this situation, the positive heat flux in the discharge area should equal the negative heat flux resulting from downward water movement in the recharge area. One way of testing this is to compare positive and negative heat fluxes determined using the heat-flow contours in Figure 6. The heat-source region is defined as the area having heat­flow values above 58 mW m·2• The heat sink region includes the Black Hills Uplift where two heat-flow values of 82 m W m-2 have been recorded (Sass and others, 1971). The high heat flow in the Black Hills region is partly a residual effect from the uplift of the Black Hills in the Laramide Orogeny and partly from the thermal effects of mid-to-late Tertiary magmatism. The background heat-flow value for the area near the Black Hills that provides a balanced heat flux for the heat source and heat sink is 91 m W m-2• The heat flux estimates for 10 m W m-2

intervals in the source and sink areas are given in Table 5.

CONCLUSIONS

Conventional and estimated heat-flow data delineate adjacent regions of anomalously high and anomalously low heat flow between the Black Hills and eastern South Dakota (Fig. 5). A gravity-driven regional groundwater flow system in confined aquifers that underlie the region is characterized by downward groundwater flow in the region of low heat flow and by upward groundwater flow in the region of high heat flow (Fig. 2). Analysis of the overall hydrothermal regime by simple analytical models and a more complex numerical model suggests that the groundwater flow system causes the areas of anomalous heat flow. Groundwater flow velocities sufficient to generate the anomalous heat flow are 3.17 x 1 O-s m sol for the analytical models and 6.34 x 10-8 m Sol in the recharge area and 4.76 x 1 O-s m sol in

114 GOSNOLD

Table 5. Heat-flux calculations for discharge and recharge areas. Heat flow anomaly (HFA) used to calculate heat flux is difference between background heat flow, 58 m W m·2 and mean value of heat flow in each area for discharge area. HF A in recharge area was based on background heat flow of 58 m W m·2 in plains region having contoured heat-flow value of 43 mW m-2 and background of91 mW m-2 in Black Hills region.

Discharge Area Recharge Area

Heat Flow Area (km2) HFA x area Heat Flow Area (km2) HFAx area mWm-2 (gigawatts) (mWm-2) (gigawatts)

73 24674 0_37 43 22309 -0.45

83 13684 0_34 33 20785 -1.14

93 12932 0.45 23 15492 -1.01

103 10104 0.45

113 8590 0.97

123 4678 0_30

133 3154 0_24

TOTAL 2_63 -2.64 FLUX

the discharge area for the numerical model. These flow velocities lie with the range of velocities calculated from hydrologic parameters by Downey (1986), but the heat-flow results suggest that the lower end of the Downey's velocity values yield better agreement. Heat-flux calculations based on the areas defined as high and low heat-flow balance at 2.63 GW for the discharge area and -2.64 GW for the recharge area. The background surface heat flow of 58 m W m-2 used in the analytical and numerical models was based on the average of all heat flow data outside the anomalous region. Because this background heat-flow value yielded model heat-flow results consistent with observations, it is assumed to characterize surface heat-flow in the region should the groundwater flow system not exist. The heat-flow value of 66 m W m-2 for the Great Plains given by Morgan and Gosnold (1989) included some of the anomalously high heat-flow values from South Dakota and Nebraska. Important remaining questions concern the length of time that this hydrothermal regime has existed and the implications for temperatures in the lower crust.

ACKNOWLEDGMENTS

The author gratefully acknowledges reviews by two anonymous reviewers and constructive comments on an earlier version of this paper by Jeffery Nunn and John Sass. The heat-flow data used in this research was acquired with support by Department of Energy contracts DE FG07-85IDI2606, DE FG07-88ID12736, C85-11768, and DE FC03-90ER61010. Financial support does not constitute an endorsement by DOE of the views expressed in this article.

BASIN-SCALE GROUNDWATER FLOW AND ADVECTIVE HEAT FLOW 115

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Blackwell, D. D., 1971, The thermal structure of the continental crust, in Heacock, J. G., ed., The Structure and Physical Properties of the Earth's Crust: Am. Geophys. Union, Geophys. Mon. Ser., v. 14, p. 169-184.

Combs, J., and Simmons, G., 1973, Terrestrial heat flow determinations in the north central united States: Jour. Geophys. Res., v. 78, no. 2, p. 441-461.

Deming, D., Sass, J. H., Lachenbruch, A. H., and DeRito, R. F., 1992, Heat flow and subsurface temperature as evidence for basin-scale ground-water flow, North Slope of Alaska: Geol. Soc. America Bull., v. 104, no. 5, p. 528-542.

Donaldson, I. G., 1962, Temperature gradients in the upper layers of the earth's crust due to convective water flows: Jour. Geophys. Res., v. 67, no. 9, p. 3449-3459.

Head, W. J., Kilty, K. T., and Knottek, R. K., 1978, Maps showing temperatures and configurations of the tops of the Minnelusa Formation and the Madison Limestone, Powder River Basin, Wyoming, Montana, and adjacent areas: U. S. Geol. Survey Open-File Rept. 78-905, 2 sheets.

Hildenbrand, T. G., and Kucks, R. P., 1985, Model of the geothermal system in southwestern South Dakota from gravity and aeromagnetic studies, in Hinze, W. J., ed., The Utility of Regional Gravity and Magnetic Anomaly Maps: Soc. Expl. Geophys., p. 258-266.

Lachenbruch, A. H., and Sass, J. H., 1977, Heat flow in the United States and the thermal regime of the crust, in Heacock, J. G., ed., The Earth's Crust: Am. Geophys. Union Mon. Ser. 20, p. 626-675.

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