GRC Transactions, Vol. 36, 2012

663

KeywordsHeat flow, thermal conductivity, thermal gradient, borehole-temperatures, co-produced fluids, sedimentary basins

ABSTRACT

We present a scheme for determining temperatures of strata in a sedimentary basin using heat flow, formation lithology, thickness and thermal conductivity. We calibrated the scheme on five sites in the Williston Basin where temperature vs. depth profiles enabled an iterative analysis of temperature gradient, thermal conductivity and heat flow. Comparison of the temperature projections to bot-tom hole temperatures provides insight on determining a reliable correction for BHT data. Large scale application of the scheme using stacked structure contours can provide a complete and ac-curate assessment of geothermal resources in a basin.

The Geothermal Resource in Sedimentary Basins

Large-scale adoption of alternatives to fossil fuels has long been delayed for a number of reasons such as non-competitive economics, marginal technology, and the apparent abundance of conventional resources. At present, the economic disincentive and its attendant effects are declining due to record-high crude oil prices. Consequently, opportunities for shifting to alternative energies such as geothermal, nuclear, solar, wind, unconventional gas, hydrogen, and ethanol are growing. A potentially significant, accessible, sustainable and environmentally benign domestic energy resource is geothermal energy in sedimentary basins.

The geothermal resource in sedimentary basins includes hot waters that are coproduced with oil and gas, hot waters from permeable formations and the heat energy stored in impermeable formations. The thermal energy in coproduced fluids is estimated to be between 9.44 x 1016 J and 4.51 x 1017 J (McKenna et al, 2005) and the total thermal energy in permeable sedimentary formations is estimated to be approximately 1 x 1023 J (Tester et al., 2006). However, the estimate by Tester et al. (2006) was based on a prior USGS report (Sorey et al., 1983) that considered only

one or two aquifers in each basin. The estimate by Sorey et al., (1983) was based on only the principal water-producing forma-tions and generally excluded petroleum-bearing formations. A later analysis (Gosnold, 1999a) indicated that if all formations that have capacity for hot water production are considered, the resource would be significantly greater. Specifically, the USGS estimate of the resource for North Dakota and South Dakota (Sorey et al., 1983) included only the Dakota Group and the Madison aquifer in the Williston and Kennedy basins and totaled approximately 8.2 x 1021 J. Analysis of all formations with capacity for fluid production in those basins indicates that the accessible resource base is approximately 6.6 x 1022 J (Gosnold, 1999a). If this analy-sis applies to all basins, the total resource might be eight times larger than the estimate reported by Tester et al. (2006). Perhaps more significant is that the resource base would be yet an order of magnitude larger if the heat contained in impermeable forma-tions could be extracted with EGS technology or down-hole heat exchanger systems (Gosnold et al., 2010).

The essential data for assessing the feasibility of producing geothermal power are temperature and depth of the resource and availability of fluid to transport the energy to the surface. Additional considerations include detailed stratigraphy, fluid composition, surface climate, geographic location, and acces-sibility of the power grid, as well as hydrologic, mechanical, geochemical, and thermal properties of the basin. We present five calibration tests of thermostratigraphy to estimate subsurface temperatures and to iteratively determine heat flow and thermal conductivity.

MethodologyThermostratigraphy has been applied in regional and detailed

assessments of geothermal resources in sedimentary basins (Gosnold, 1984, 1991, 1999b; Gosnold et al., 2010; Crowell and Gosnold, 2011; Crowell et al., 2011) and in the Geothermal Map of North America (Blackwell and Richards, 2004). Assuming

heat flow, q, is conductive and constant, the temperature gradient, dTdz, varies inversely with thermal conductivity (λ) according to

Thermostratigraphy of the Williston Basin

William D. Gosnold1, Mark R. McDonald1, Robert Klenner1, and Daniel Merriam2

1Department of Geology and Geological Engineering,University of North Dakota, Grand Forks ND

2 Kansas Geological Survey, Lawrence KS

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Fourier’s law,

q = dTdz

λ (1)

and the temperature at depth can be calculated from,

T z( ) = T0+ qziλii=1

n∑ (2)

where: T (z) is temperature at depth z, T0 is surface temperature, q is heat flow (mW m-2), zi is formation thickness (m), λi is the formation thermal conductivity (W m-1 K-1) and dT

dz (K km-1) is

the temperature gradient. Hereafter we refer to Eq. 2 as TSTRAT.

Heat Flow

The most critical element in thermostratigraphy is reliability of the heat flow data. Adequate sampling of continental heat flow would require boreholes spaced on a 10 km X 10 km grid and thermal conductivity measurements on cores extracted from multiple levels in the boreholes. The 10 km X 10 km grid spacing, 1 site per 100 km2, would allow discrimination of variations in heat flow due to variability of radiogenic sources in the crust and due to different heat flow provinces (Roy et al., 1968). Unfortunately, the actual density of conventional heat flow sites in the Williston Basin is closer to 1 site per 11,000 km2. Also of concern is that few published heat flow data include evaluations of quality that can guide the user. We address these matters for the Williston Basin by examination of prior heat flow research in the basin and by calibrating projections of TSTRAT with equilibrium temperature vs. depth logs from five boreholes ranging in depth from 940 m to 2,845 m. We then use TSTRAT to calculate temperatures on formation tops to the Precambrian surface at each of the five sites

and compare the results with BHT data.The first heat flow reported for the Williston Basin was 58.6

mW m-2 in the Lone Tree oil field (Fig. 1) based on a measured temperature gradient of 39.9 K km-1 and an estimated thermal conductivity of 1.5 W m-1 K-1 (Blackwell, 1969). Combs and Simmons (1973) reported heat flow of 92 mW m-2 at two sites, NDGS 3342 and NDGS 3479, (Fig. 1) near the Lone Tree site based on measured temperature gradients of 55 K km-1 and 56 K km-1 and estimated thermal conductivity of 1.7 W m-1 K-1. Scat-tolini (1978) reported heat flow for 31 sites in North Dakota, but rated only seven of the sites as high quality. These seven sites average 55.3 ± 15.7 mW m-2 based on measured temperature gradients and thermal conductivities measured on chips and fragments as described by Sass et al., (1971). Majorowicz et al., (1986) reported heat flows of 70 to 100 mW m-2 for portions of the Williston Basin in northwestern North Dakota, southwestern Manitoba and southeastern Saskatchewan based temperature gradients calculated from bottom hole temperatures (BHT) and estimated thermal conductivities. Gosnold (1990) reexamined these previous heat flow determinations and found the reported high heat flow was due to thermal conductivity estimates that were too high by as much as 40 percent.

All temperature gradients used in heat flow determinations in the Williston Basin were measured in shales, mudstones and clay-stones that are the dominant lithology in the upper 1 km to 2 km. In the subsurface these rock types are solid heat conductors, but when extracted by coring they quickly undergo decompaction and dehydration. Consequently measurement of thermal conductivity must occur within hours of core extraction and the samples must be sealed to prevent dehydration and compressed to prevent decompac-tion. Unfortunately none of the measurements by Scattolini (1978) met the necessary requirements for handling and all other thermal conductivities used in the heat flow determinations were estimated. The heat flow estimates by Combs and Simmons (1973); Scattolini (1978); Majorowicz et al., (1986) and Blackwell (1969) referenced thermal conductivities of 1.7 W m-1 K-1 reported by Benfield (1947) and Garland and Lenox (1962), and we infer that those values in-fluenced estimates for the shales in the Williston Basin.

The question of thermal conductivity of shales and similar rocks was best answered by Blackwell and Steele (1989) who used temperature gradients in a “shale sandwich” between Paleozoic limestones in boreholes in Kansas. Thermal conductivities of the limestones were measured and heat flow in the limestones was used with the temperature gradients to determine that the thermal conductivity of the shales is of the order of 1.1 W m-1 K-1. Gosnold et al., (1997) used a half-space needle probe technique to measure thermal conductivities of 1.1 W m-1 K-1 and 1.2 W m-1 K-1 on fresh cores from the Pierre shale in southern Manitoba and South Dakota and the Eagleford shale in Texas. Recently, we were fortunate to obtain 23 fresh cores from a 1-km deep scientific borehole drilled for methane tests in the Pierre shale in southern Manitoba. Thermal conductivity measurements made with a portable electronic divided bar (Antriasian, 2010) average 0.9 W m-1 K-± 0.26 W m-1 K-1 and show an exponential decrease with depth described by

λ = 1.2396e-6E-°4z (3)

which we infer is due to increasing methane content.

Figure 1. Locations of Williston Basin heat flow sites (black triangles and solid red star), deep wells with equilibrium temperatures (open red stars) and cored well sites with thermal conductivity measurements (open diamonds). Numbers identify wells in Figures 3-7 and Tables 2-6. Solid red star designated “Lone Tree” is an oil field site where the first heat flow measurement in the basin was made (Blackwell, 1969).

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TSTRAT Tests

The Williston Basin has a bimodal composition with a 1 to 2 km thick layer of Cenozoic and Mesozoic strata consisting principally of shales overlying 2 to 3 km of Paleozoic lime-stones and dolomites. There are 54 distinct formations within the Williston Basin and thermal conductivity values have been measured on only fourteen of the Paleozoic formations and one of the Mesozoic formations (Gosnold et al., 2010). Interest-ingly, thermal conductivity was found to vary significantly

within formations (Figure 2), thus selecting a single value for a specific formation is questionable. However the range of thermal conductivity variation is useful in fitting calculated temperatures to observed equilibrium profiles.

In this analysis we use five temperature vs. depth profiles that were measured in boreholes at thermal equilibrium. Four of the profiles are entirely in the shale section, but one profile, NDGS 6840, reached a depth of 2845 m and extends through the Madison Group carbonates. The temperature gradient in the Madison be-tween 2640 and 2845 m averages 16.9 ± 2.4 K km-1 but we do not have thermal conductivity measurements on Madison cores from those depths at nearby wells. However, the average temperature gradient in the shale section of NDGS 6840 is 46.9 ± 11.6 K km-1

Figure 2. Thermal conductivities vs. depth measured with a divided bar on 15 formations in the Williston Basin. Forma-tion lithologies are given in Tables 1-5.

Figure 3. Temperature vs. depth (smooth blue line) and gra-dient vs. depth (jagged multi-colored line) in NDGS 6840, a 2,850 m deep well on the North Dakota – Montana border. The temperature gradient in the shale units (green section) is 46.9 ± 11.6 K km-1 and the gradient in the carbonates (purple section) averages 21.4 ±9.2 K km-1.

Table 1. TSTRAT calculations for NDGS 6840. Heat flow used for calculations is 51 mW m-2 except in upper 1 km where post-glacial warming (Gosnold et al., 2011; Majorowicz et al., 2012) has reduced the temperature gradient by about 10 percent.

NDGS 6840Formation

Depthmeters

Temp. °C

Therm Cond.W m-1

K-1

LithologyMurphy et al., 2009

Tertiary Cannonball . 190 14.14 1.10 sandstone, siltstone, claystoneLudlow 263 17.44 1.10 sandstone, siltstone, claystone

Cretaceous Hell Creek 350 21.28 1.10 sandstone, siltstone, claystoneFox hills 492 27.61 1.20 mudstone, siltsone, sandstonePierre 606 32.26 1.10 shaleNiobrara 1269 61.81 1.10 shaleCarlille 1302 63.28 1.20 shaleGreenhorn 1421 68.14 1.10 shaleBelle fourche 1484 70.94 1.20 shaleMowry 1552 73.72 1.20 shaleNewcastle 1596 75.52 1.50 sandstoneSkull Creek 1630 76.63 1.20 shaleInyan Kara 1857 85.90 1.60 sandstone, shale

Jurassic Swift 1961 89.08 1.20 shaleRierdon 2015 91.29 1.60 shale, limestonePiper 2033 91.83 1.60 shale, gypsum, limestone

Triassic Spearfish 2146 95.30 1.60 siltstone, sandstone, mudstoneMinnekahta 2283 99.49 2.50 limestoneOpeche 2294 99.71 1.20 shale to mudstoneBroom Creek 2344 101.77 2.20 sandstone, dolomite, anhydrite

Permian Amsden 2386 102.70 4.00 dolostoneTyler 2443 103.39 1.20 shale to mudstone

Pennnsylvanian Otter 2484 105.07 1.20 shale to mudstoneKibbey 2545 107.56 2.70 sandstone

Mississippian Charles 2636 109.21 3.05 limestoneMission Canyon 2823 112.22 3.05 limestoneLodgepole 3004 115.11 3.05 limestone

Ordovician Bakken 3029 115.52 1.10 shaleThree Forks 3083 117.93 3.10 dolostone and limestoneBird Bear 3112 118.39 3.13 limestoneDuperow 3213 119.97 3.19 limestoneSouris R. 3289 121.14 2.92 limestoneDawson Bay 3328 121.80 2.75 limestone and dolostonePrairie 3473 124.38 4.00 evaporitesWinnepegosis 3552 125.35 2.99 limestone and dolostone

Silurian Interlake 3794 129.31 3.77 dolostone and limestoneStonewall 3819 129.64 3.89 dolostone and limestoneStony Mountain 3863 130.19 3.79 dolostone and limestoneRed River 4018 132.19 3.28 limestoneWinnipeg 4108 133.54 4.07 carbonaceous sandstone

Cambrian Deadwood 4325 136.15 3.46 limestone, sandstone, shale

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Table 2. TSTRAT calculations for NDGS 5086. Heat flow used for calcu-lations is 51 mW m-2 except in upper 1 km where post-glacial warming (Gosnold et al., 2011; Majorowicz et al., 2012) has reduced the tempera-ture gradient by about 10 percent.

NDGS 5086Formation

Depthmeters

Temp. °C

Therm Cond.W m-1

K-1

LithologyMurphy et al.,

2009

Tertiary Golden Valley 0 7.00 1.20 claystone, sand-stone, siltstone

Sentinal Butte 144 13.11 1.30 sandstone, siltstone, claystone

Slope 455 25.30 1.30 sandstone, siltstone, claystone

Cannonball 610 31.40 1.10 sandstone, siltstone, claystone

Ludlow 610 31.40 1.10 sandstone, siltstone, claystone

Cretaceous Hell Creek 610 31.40 1.10 sandstone, siltstone, claystone

Fox hills 726 36.80 1.20 mudstone, siltsone, sandstone

Pierre 820 40.76 1.10 shaleNiobrara 1364 65.98 1.10 shaleCarlille 1422 68.68 1.20 shaleGreenhorn 1515 72.64 1.10 shaleBelle Fourche 1599 76.54 1.20 shaleMowry 1658 79.04 1.20 shaleNewcastle 1689 80.35 1.50 sandstoneSkull Creek 1714 81.52 1.20 shaleInyan Kara 1764 83.63 1.60 sandstone, shale

Jurassic Swift 1931 88.96 1.20 shaleRierdon 2117 96.86 1.60 shale, limestonePiper 2154 98.05 1.60 shale, gypsum,

limestoneTriassic Spearfish 2252 101.17 1.60 siltstone, sandstone,

mudstoneMinnekahta 2398 105.82 2.50 limestoneOpeche 2408 106.03 1.20 shale to mudstoneBroom Creek 2485 109.30 2.20 sandstone, dolomite,

anhydritePermian Amsden 2529 110.37 4.00 dolostone

Tyler 2588 111.12 1.20 shale to mudstonePennnsylvanian Otter 2626 111.84 1.20 shale to mudstone

Kibbey 2698 113.20 2.70 sandstoneMississippian Charles 2792 116.29 3.05 limestone

Mission Canyon 2943 3.09 3.05 limestoneLodgepole 151 3.09 3.05 limestone

Ordovician Bakken 151 3.09 1.10 shaleThree Forks 151 3.09 3.10 dolostone and

limestoneBird Bear 151 3.09 3.13 limestoneDuperow 151 3.09 3.19 limestoneSouris R. 151 3.09 2.92 limestoneDawson Bay 151 3.09 2.75 limestone and

dolostonePrairie 151 3.09 4.00 evaporitesWinnepegosis 151 3.09 2.99 limestone and

dolostoneSilurian Interlake 151 3.09 3.77 dolostone and

limestoneStonewall 151 3.09 3.89 dolostone and

limestoneStony Mountain 151 3.09 3.79 dolostone and

limestoneRed River 151 3.09 3.28 limestoneWinnipeg 151 3.09 4.07 carbonaceous

sandstoneCambrian Deadwood 151 3.09 3.46 limestone, sand-

stone, shale

Table 3. TSTRAT calculations for NDGS 2894. Heat flow used for calcu-lations is 51 mW m-2 except in upper 1 km where post-glacial warming (Gosnold et al., 2011; Majorowicz et al., 2012) has reduced the tempera-ture gradient by about 10 percent.

NDGS 2894Formation

Depthmeters

Temp. °C

Therm Cond.W m-1

K-1

LithologyMurphy et al., 2009

Tertiary Golden Valley 0 7.00 1.40 claystone, sandstone, siltstone

Sentinal Butte 97 10.25 1.30 sandstone, siltstone, claystone

Slope 306 17.82 1.30 sandstone, siltstone, claystone

Cretaceous Hell Creek 411 21.60 1.30 sandstone, siltstone, claystone

Fox hills 489 24.44 1.20 mudstone, siltsone, sandstone

Pierre 552 26.90 1.20 shaleNiobrara 1242 55.65 1.10 shaleCarlille 1308 58.71 1.20 shaleGreenhorn 1414 63.21 1.10 shaleBelle Fourche 1500 67.22 1.10 shaleMowry 1561 70.03 1.10 shaleNewcastle 1601 71.88 1.50 sandstoneSkull Creek 1827 79.57 1.30 shaleInyan Kara 2028 87.45 1.60 sandstone, shale

Jurassic Swift 2051 88.19 1.20 shaleRierdon 2077 89.29 1.60 shale, limestonePiper 2082 89.46 1.60 shale, gypsum, lime-

stoneTriassic Spearfish 2115 90.50 1.60 siltstone, sandstone,

mudstoneMinnekahta 2254 94.93 2.50 limestoneOpeche 2266 95.17 1.20 shale to mudstoneBroom Creek 2352 98.83 2.20 sandstone, dolomite,

anhydritePermian Amsden 2406 100.09 4.00 dolostone

Tyler 2480 101.03 1.20 shale to mudstonePennnsylvanian Otter 2521 102.77 1.20 shale to mudstone

Kibbey 2613 106.68 2.70 sandstoneMississippian Charles 2657 107.51 3.05 limestone

Mission Canyon 2808 110.04 3.05 limestoneLodgepole 3270 117.76 3.05 limestone

Ordovician Bakken 3458 120.91 1.10 shaleThree Forks 3469 121.42 3.10 dolostone and lime-

stoneBird Bear 3532 122.45 3.13 limestoneDuperow 3559 122.89 3.19 limestoneSouris R. 3679 124.81 2.92 limestoneDawson Bay 3730 125.70 2.75 limestone and dolos-

tonePrairie 3749 126.05 4.00 evaporitesWinnepegosis 3816 126.91 2.99 limestone and dolos-

toneSilurian Interlake 3853 127.54 3.77 dolostone and lime-

stoneStonewall 4112 131.04 3.89 dolostone and lime-

stoneStony Mountain 4139 131.40 3.79 dolostone and lime-

stoneRed River 4160 131.68 3.28 limestoneWinnipeg 4185 132.07 4.07 carbonaceous sand-

stoneCambrian Deadwood 4245 132.82 3.46 limestone, sandstone,

shale

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Figure 5. Plot of equilibrium temperatures vs. depth (solid line), computed temperatures (triangles) and bottom-hole temperatures (solid red circles) near NDGS 5086. Temperature vs. depth data are from Scattolini (1978). Bottom-hole temperatures are from oil exploration wells that lie within 10 km of NDGS 5086. Computed temperatures are from Eq. 2 and are shown with thermal conductivities and depths to formation tops in Table 2.

Figure 6. Plot of equilibrium temperatures vs. depth (solid line), computed temperatures (trian-gles) and bottom-hole temperatures near NDGS 2894. Temperature vs. depth data are from Scattolini (1978). Bottom-hole temperatures are from oil exploration wells that lie within 10 km of NDGS 2894. Computed temperatures are from Eq. 1 and are shown with thermal conduc-tivities and depths to formation tops in Table 3.

Figure 7. Plot of equilibrium temperatures vs. depth (solid line), computed temperatures (triangles) and bottom-hole temperatures (solid red circles) near NDGS 3479. Tem-perature vs. depth data are from Combs (1970). Bottom-hole temperatures are from oil exploration wells that lie within 10 km of NDGS 3479. Computed temperatures are from Eq. 2 and are shown with thermal conductivities and depths to formation tops in Table 4.

Figure 4. Plot of equilibrium temperatures vs. depth (solid line), computed temperatures (triangles) and bottom-hole temperatures (solid red circles) near NDGS 6840. Temperature vs. depth data are from Blackwell, pers. comm., 1995. Bottom-hole temperatures are from oil exploration wells that lie within 10 km of NDGS 6840. Computed temperatures are from Eq. 2 and are shown with thermal conductivi-ties and depths to formation tops in Table 1.

Figure 8. Plot of equilibrium temperatures vs. depth (solid line), computed temperatures (triangles) and bottom-hole temperatures near

NDGS 3342. Temperature vs. depth data are from Combs (1970). Bottom-hole tem-

peratures are from oil exploration wells that lie within 10 km of NDGS 3342. Computed

temperatures are from Eq. 1 and are shown with thermal conductivities and depths to

formation tops in Table 6.

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Table 4. TSTRAT calculations for NDGS 3479. Heat flow used for calcu-lations is 51 mW m-2 except in upper 1 km where post-glacial warming (Gosnold et al., 2011; Majorowicz et al., 2012) has reduced the tempera-ture gradient by about 10 percent.

NDGS 3479Formation

Depthmeters

Temp. °C

Therm Cond.W m-1

K-1

LithologyMurphy et al., 2009

Tertiary Cannonball 0 7.00 1.20 sandstone, siltstone, claystone

Ludlow 23 8.01 1.25 sandstone, siltstone, claystone

Cretaceous Hell Creek 25 8.11 1.30 sandstone, siltstone, claystone

Fox hills 29 8.29 1.20 mudstone, siltsone, sandstone

Pierre 32 8.41 1.10 shale

Niobrara 786 42.00 1.10 shale

Carlille 867 45.60 1.20 shale

Greenhorn 996 50.88 1.10 shale

Belle fourche 1046 53.19 1.20 shale

Mowry 1081 54.68 1.20 shale

Newcastle 1112 56.00 1.50 sandstone

Skull Creek 1144 57.10 1.20 shale

Inyan Kara 1173 58.32 1.60 sandstone, shale

Jurassic Swift 1282 61.79 1.20 shale

Rierdon 1383 66.08 1.60 shale, limestone

Piper 1383 66.08 1.60 shale, gypsum, limestone

Triassic Spearfish 1565 71.89 1.60 siltstone, sandstone, mudstone

Minnekahta 1591 72.71 2.50 limestone

Opeche 1592 72.74 1.20 shale to mudstone

Broom Creek 1606 73.33 2.20 sandstone, dolomite, anhydrite

Permian Amsden 1618 73.59 4.00 dolostone

Tyler 1633 73.79 1.20 shale to mudstone

Pennnsylvanian Otter 1642 74.18 1.20 shale to mudstone

Kibbey 1649 74.48 2.70 sandstone

Mississippian Charles 1658 74.64 3.05 limestone

Mission Canyon 1839 77.66 3.05 limestone

Lodgepole 2019 80.68 3.05 limestone

Ordovician Bakken 2044 81.10 1.10 shale

Three Forks 2098 83.61 3.10 dolostone and limestone

Bird Bear 2127 84.09 3.13 limestone

Duperow 2228 85.73 3.19 limestone

Souris R. 2304 86.95 2.92 limestone

Dawson Bay 2344 87.64 2.75 limestone and dolostone

Prairie 2488 90.32 4.00 evaporites

Winnepegosis 2568 91.33 2.99 limestone and dolostone

Silurian Interlake 2810 95.46 3.77 dolostone and limestone

Stonewall 2835 95.80 3.89 dolostone and limestone

Stony Mountain 2878 96.37 3.79 dolostone and limestone

Red River 3033 98.45 3.28 limestone

Winnipeg 3124 99.86 4.07 carbonaceous sandstone

Cambrian Deadwood 3340 102.57 3.46 limestone, sandstone, shale

Gosnold, et al.

Table 5. TSTRAT calculations for NDGS 3342. Heat flow used for calcu-lations is 49 mW m-2 except in upper 1 km where post-glacial warming (Gosnold et al., 2011; Majorowicz et al., 2012) has reduced the tempera-ture gradient by about 10 percent.

NDGS 3342Formation

Depthmeters

Temp. °C

Therm Cond.W m-1

K-1

LithologyMurphy et al., 2009

Cretaceous Pierre 10 7.43 1.10 shale

Niobrara 381 17.19 1.10 shale

Carlille 420 26.45 1.20 shale

Greenhorn 484 29.16 1.10 shale

Belle Fourche 530 31.28 1.20 shale

Mowry 562 32.65 1.20 shale

Newcastle 586 33.65 1.10 sandstone

Skull Creek 605 34.54 1.20 shale

Inyan Kara 622 35.27 1.60 sandstone, shale

Jurassic Swift 714 38.21 1.20 shale

Rierdon 793 41.58 1.60 shale, limestone

Piper 809 42.09 1.60 shale, gypsum, limestone

Triassic Spearfish 910 45.30 1.60 siltstone, sandstone, mudstone

Minnekahta 919 45.60 2.50 limestone

Opeche 920 45.61 1.20 shale to mudstone

Broom Creek 925 45.82 2.20 sandstone, dolomite, anhydrite

Permian Amsden 929 45.92 4.00 dolostone

Tyler 935 45.99 1.20 shale to mudstone

Pennnsylvanian Otter 938 46.14 1.20 shale to mudstone

Kibbey 941 46.25 2.70 sandstone

Mississippian Charles 944 46.30 3.05 limestone

Mission Canyon 1125 50.00 3.05 limestone

Lodgepole 1305 53.70 3.05 limestone

Ordovician Bakken 1330 54.22 1.10 shale

Three Forks 1384 56.73 3.10 dolostone and limestone

Bird Bear 1413 57.20 3.13 limestone

Duperow 1514 58.85 3.19 limestone

Souris R. 1590 60.06 2.92 limestone

Dawson Bay 1630 60.75 2.75 limestone and dolostone

Prairie 1774 63.43 4.00 evaporites

Winnepegosis 1854 64.45 2.99 limestone and dolostone

Silurian Interlake 2096 68.57 3.77 dolostone and limestone

Stonewall 2121 68.91 3.89 dolostone and limestone

Stony Mountain 2164 69.48 3.79 dolostone and limestone

Red River 2319 71.57 3.28 limestone

Winnipeg 2410 72.97 4.07 carbonaceous sand-stone

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and it is reasonable to accept a thermal conductivity of 1.1 W m-1 K-1 for the shales. This yields a heat flow of 51.6 mW m-2 for that site. Assuming constant heat flow in the borehole, we calculated thermal conductivity of the Madison as 3.05 W m-1 K-1. Using heat flow of 51 mW m-2 and adjusting thermal conductivities of each formation penetrated by the borehole, we used TSTRAT to fit a calculated temperature profile to the observed profile. We then calculated temperatures on all formation tops from the bottom of the observed temperature data to the Precambrian basement. (Figure 4, Table 1). Formation thicknesses were taken from NDGS 6840 well log that was downloaded from the North Dakota Industrial Commission (NDIC) website https://www.dmr.nd.gov/oilgas/. The borehole did not reach basement but we were able to estimate formation thickness from other wells and from the North Dakota Stratigraphic Column (Murphy et al., 2009).

We applied the same analysis to each of the other four wells and added the bottom hole temperature data from all boreholes within a 10 km of the well (Figures 5-8, Tables 1-6). A small but persistent misfit between the calculated temperature vs. depth profile and the observed profiles occurs in the upper km of each of the five boreholes. We attribute this misfit to a transient dis-turbance of the temperature gradient in the upper 1 km from the effects of post-glacial warming (Gosnold et al., 2011; Majorowicz et al., 2012). We adjusted the calculations by using a lower heat flow in the upper sections of the profiles.

Discussion

The critical elements necessary to apply TSTRAT in sedi-mentary basin are a reliable estimate of heat flow and accurate thermal conductivity data. Stratigraphic data are essential, but heat flow and thermal conductivity control the geothermal gradi-ent. To emphasize how critical accurate heat flow data are, we compare the heat flow determinations we made in this analysis for six wells in the Williston Basin with previously published heat flow data (Table 6).

The differences between our heat flow calculations and the previously published heat flow values range from 31 percent to 91 percent and are entirely due to lack of accurate thermal conductivi-ties on shales. That is no fault of the earlier researchers who made

the best possible estimates for shale conductivities. However, such data exist in the literature and on databases and can lead to serious missteps in esti-mating subsurface temperatures. For example, the Geothermal Map of North America (Blackwell and Richards, 2004) shows heat flow of 60 mW m-1 to 75 mW m-2 in the regions in the Williston Basin that include the wells in Table 6.

The comparison of calculated temperatures with bottom hole temperatures gives an expected result, i.e., BHTs underestimate subsurface temperatures. The comparison also leads us to suggest that an improved correction scheme for BHTs can be de-veloped by this analysis. Calculation of a general temperature vs. depth profile for a basin based on heat flow, lithostratigraphy and thermal conductivity can be compared to a temperature vs. depth plot of BHTs. Fitting reasonable curves, i.e., linear or 2nd

order polynomials, to each data set and determining the differ-ence between them yields a curve that could be used to correct the average value of a group of BHTs.

The principal application of TSTRAT in assessing geothermal resources would be to generate temperature contour maps for aquifers in a basin. We are beginning to apply this concept to a number of basins in the mid-continent region and anticipate an improved assessment of geothermal resources will result.

ReferencesAntriasian, A. M., 2010, The portable Electronic Divided Bar (PEDB): A

tool for measuring thermal conductivity of rock samples, Proc. World Geothermal Congress 2010, 6 pp.

Benfield, A. E., (1947), A heat flow value for a well in California, Am. J. Sci. 245, 1-18.

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Well Name NDGS No.

Gradient°C km-1

Intervalm

Cond.W m-1

K-1

Heat Flow

mW m-2

Gradient°C km-1

Cond.W m-1

K-1

Heat Flow

mW m-2Ref.

Carrie Hovland 1 3479 42.9 786-112 1.12 48.0 56.0 1.7 92.0 a

E.L. K. 1 Nelson 3342 44.0 420-586 1.12 49.3 55.0 1.7 92.0 a

Shell USA 6840 43.8 606-1596 1.17 51.3 * * *

5086 5086 45.6 820-1689 1.12 51.1 45.6 1.5 69.6 b

2984 2984 42.7 552-1601 1.13 48.3 44.5 1.8 81.2 b

Lone Tree ? 39.8 0-1143 1.12 44.6 39.8 1.4 58.6 c

Table 6. Heat flow determined is this analysis in shown in on the left in black text and previ-ously published heat flow determinations for the same sites is shown on the right in red text. References: a = Combs and Simmons, 1973; b = Scattolini, 1978; c = Blackwell, 1969.

670

Gosnold, et al.

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