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. 2021 Jul 14;6(29):18914–18927. doi: 10.1021/acsomega.1c02147

Geothermal Distribution Characteristics in the Qinshui Basin and Its Significance to the Production of Coalbed Methane

Yina Yu †,*, Zhaoping Meng †,‡
PMCID: PMC8320166  PMID: 34337231

Abstract

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Temperature significantly affects the storage and transport of coalbed methane (CBM). Studies of geothermal distribution characteristics are important for the exploration and exploitation of CBM. In this study, more than 150 heat flow temperature data from coalbed methane wells in the Qinshui Basin were analyzed to investigate the geothermal distribution and its controlling factors. The results show that the geothermal gradient of the no. 3 coal seam ranges from 0 to 3.7 °C/hm with an average of 1.6 °C/hm, and the terrestrial heat flow of the no. 3 coal reservoir ranges from 0.9 to 94.6 mW/m2 with an average of 41.5 mW/m2. The reservoir temperature shows high values in the central and northwest parts of the basin, while the east and west edges of the basin show negative geothermal anomalies. It is found that groundwater has significant effects on the geothermal distribution in the Qinshui Basin, and with the increase of the groundwater level, the geothermal gradient decreases linearly. In addition, the geothermal gradient and terrestrial heat flow first increase and then tend to be stable with the increase in value of the total dissolved substances. Besides, with an increase in floor elevation, the geothermal gradient first increases linearly and then decreases linearly, obtaining a maximum value at about 450 m (transition floor elevation). This phenomenon is the result of the balance between heat supplying and heat losing. The geothermal distribution characteristics in the Qinshui Basin determine the reservoir temperature of the coalbed methane, and in turn, the reservoir temperature affects the adsorption, desorption, and diffusion behaviors of coalbed methane in situ.

1. Introduction

The commercial extraction of coalbed methane (CBM) is now well established in many countries such as the United States, Australia, China, India, and Canada.1 Previous studies have shown that temperature has a great effect on the storage and migration of CBM, which has become a key studying area in CBM exploitation.2 Many scholars found that with an increase in the coal reservoir temperature, the methane adsorption capacity gradually decreased due to the high desorption rate caused by the increased average kinetic energy of gas molecular in the relatively high-temperature environment of coal formation.3,4 Furthermore, the adsorption capacity determines the maximum diffusion volume of gas; thus, the gas diffusion property is affected by temperature.5 The methane diffusion coefficient showed an upward trend with the temperature increased, and this can be described by the revised Arrhenius-style equation.6,7 Meanwhile, temperature also has important effects on the thermal swell, adsorption deformation, and coal damages, which are highly related to the seepage characteristics of gases in coal formations.8,9 Therefore, the study on the temperature condition of the coal seam is of great significance for CBM exploitation.

The distribution of geothermal fields in coal reservoirs is important for the development of CBM. Since the end of the 19th century, there have been numerous achievements in the study of geothermal fields of coal basins (Table 1). The terrestrial heat flow, geothermal gradient, and rock thermal conductivity are often considered the basic parameters to determine the characteristics of geothermal fields.10,11 The controlling factors of geothermal fields, including tectonic setting, basement structure, cap rock thickness, groundwater, magmatic activity, and other geological factors, have been explored. Jiang et al. found that the heat flow in continental China shows a good correlation with crustal thickness, elevation, and the tectonic background.12 Freymark et al. considered that the thick Cenozoic sediments and the high radioactive heat of the lower crust were the regional controlling factors of the geothermal field, but groundwater caused geothermal field changes logically.13 Reiter and Mansure14 suggested that shallower heat flow data might be influenced by local hydrologic movement, weathered conductivity samples, topographic variations, and paleoclimate effects, while the deeper heat flow data had a lower influencing potential. The simulation results of dyke intrusion showed that intrusion with an average area of 16 km2 and a thickness of about 10 km has a disturbance time of about 1 Ma with an influence range of about 3 km on the surrounding rock geothermal field.15

Table 1. Statistics of Present-Day Geothermal Parameters of CBM Basins.

sedimentary basin geothermal gradient (°C/hm) heat flow (mW/m2) source
United States SAN Juan Basin   65 (14)
  Powder river basin 2.9 40–60 (15)
  Black warrior basin 1.09–3.62   (16, 17)
Canada Alberta Basin 2.48–3.79 40–80 (18)
Australia Southeast   42–90 (19)
South China Jianghan Basin 3.359 52.3 (20)
  Sichuan Basin 2.28 53.2 (21)
  Lower Yangtze area 3 60 (22)
North China Ordos Basin 2.9 62 (23)
  Bohai Bay Basin 3.08 60.8 ± 8.7 (24)
  Qinshui Basin 2.82 ± 1.03 62.7 ± 15.2 (25)
Northwest Qaidam Basin 3.2 57.4 (26)
  Jungar Basin 2.13 ± 0.37 42.5 ± 7.4 (27)
  Tarim Basin 2.26 ± 0.3 43.0 ± 8.5 (28)
Northeast Songliao Basin 3.8 70 (29)
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This study aims to investigate the variations of the geothermal field in the Qinshui Basin, which is the largest CBM production base in China. In this paper, we supplemented and improved precise geothermal data of the study area by collecting the temperature data from the published references and measured CBM exploration wells. Then, the spatial distribution of the geothermal field in the whole Qinshui Basin was characterized, and the potential controlling factors of the geothermal field were analyzed. This research is of significance for estimating the gas reserves in coal reservoirs and providing a theoretical basis for CBM exploitation in the Qinshui Basin.

2. Geological Settings

The Qinshui Basin is situated in the southeast of Shanxi Province, China, and is well known for its abundant CBM resources.30 It is located in the Moho depression zone of the North China plate, with a smooth and continuous Moho surface, and its crust thickness is large, about 38–41 km (Figure 1a).31−33 The Qinshui Basin is a large synclinorium (bilateral symmetry) with the axial striking NNE–SSW (Figure 1b). It is surrounded by the Taihang mountains, Huo mountains, Wutai mountains, and Zhongtiao mountains. The faults in the basin are mainly distributed in the northwest, southwest, and southeast margins and the shallow part of the east–west edge. The strata from the bottom to top in the basin comprise the Paleozoic Ordovician Fengfeng Formation (O2f), Benxi Formation (C2b), Carboniferous Taiyuan Formation (C3t), Shanxi Formation (P1s), Lower Shihezi Formation (P1x), Upper Shihezi Formation (P2s), Upper Paleozoic Permian Shiqianfeng Formation (P2sh), Mesozoic Triassic System (T), Neogene (N), and Quaternary (Q) in the study area. The main minable coal reservoirs are the no. 3 coal reservoir in the Permian Shanxi Formation and the no. 15 coal reservoir in the Carboniferous Taiyuan Formation (Figure 1c). The no. 3 coal reservoir is our research object, with its net thickness being ∼5.0–6.5 m.

Figure 1.

Figure 1

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(a) Location of the Qinshui Basin in China and crustal thickness of the North China plate. (b) Floor elevation of the no. 3 coal reservoir and the distribution of temperature logging wells. (c) Stratigraphic column of the Permo-Carboniferous coal-bearing strata (reprinted with permission from ref (35); copyright (2017) American Chemical Society).

Four episodes of tectonic thermal evolution in the Qinshui Basin are distinguished (Figure 2). The first episode corresponds to before J3 (150 Ma), and during this stage, the paleo-geothermal gradient fluctuated slightly between 2.5 and 4 °C/hm. The second episode was from the Late Jurassic to early Cretaceous (150–100 Ma). In this stage, a tectonic thermal event happened under the influence of the Yanshan movement. This tectonic thermal event caused a significant increase in the paleo-geothermal gradient in the range of 4.7–6.1 °C/hm, and the high-temperature field lasted until the Cenozoic Eocene (24 Ma). The third episode corresponds to Oligocene to Miocene (24–5.33 Ma). In this stage, the crust rapidly uplifted and suffered from erosion, the overburden sedimentary strata became thinner, and the heat flow was seriously lost, resulting in the geothermal gradient dropping to 4.2 °C/hm. Since Miocene (5.33 Ma), the geothermal field gradually became stable and kept at a low geothermal state.34,35

Figure 2.

Figure 2

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Burial depth and thermal history of Carboniferous-Permian coal-bearing strata (reprinted (adapted) with permission from ref (35); copyright (2017) American Chemical Society).

3. Methods and Theories

The accuracy of geothermal field distribution depends on the temperature measurement method, drilling depth, and the time after drilling circulation stopped. Temperature data of 138 steady-state temperature boreholes and 363 approximate steady-state temperature boreholes were obtained, and several published temperature data were gathered. The steady-state well temperature was determined by KR-SB-01 CBM downhole pressure and a temperature-sensing system. Its sensitivity and limiting accuracy are 0.1 °C and 0.5%, respectively. The approximate steady-state well temperature was determined by the PSWL-1 well temperature fluid resistivity probing tube; the measurement error of the instrument is less than 0.5 °C. Additionally, it was measured during the short drilling stop interval of about 10–24 h, when the CBM well was drilled into the coal reservoir. Those temperature data were fast-measured at the bottom of testing wells one or two times without long-term monitoring. The temperature of the bottom of drilling wells experiencing a 72 h equilibrium with a depth less than 1 km can be regarded as the temperature of the original rock.36 There is a certain deviation between the hole temperature and the authentic temperature, which needs to be corrected before it can be used.

It is assumed that all approximately steady-state wells are measured with the same drilling stop interval. When the burial depths of temperature measuring points are similar, the time for the well temperature to recover to the original rock temperature is the same. The temperature measuring wells with both approximate steady-state and steady-state temperature measurements are selected. The correction increment between the approximate steady-state temperature and the steady-state temperature of different burial depths is calculated using eq 1.37Table 2 lists the results of the horizontal correction coefficients of −250, −300, −350, −400, −450, −500, −600, and −850 m calculated by eq 1. Then, the corrected coal reservoir temperature can be obtained by taking the measured approximate steady-state well temperature in eq 2.37

3. 1
3. 2

where n is the horizontal correction coefficient; Ts is the steady-state temperature value of the coal reservoir, °C; Ta is the approximate steady-state temperature value of the coal reservoir, °C; and Tc is the calibrated temperature of approximate steady-state wells, °C.

Table 2. Horizontal Correction Coefficients of the Qinshui Basin.

burial depth (m) Ta (°C) Ts (°C) correction factor burial depth (m) Ta (°C) Ts (°C) correction factor
–250 13.20 13.50 2.22 –500 17.706 17.5 –1.18
–300 12.75 13.65 6.59 –550 14.56 14.90 2.28
–350 14.97 14.1 –6.17 –600 16.35 17.28 5.38
–400 15.66 13.6 –15.15 –650 15.80 16.2 2.47
–450 15.9 15 –6 –850 20.24 19.2 –5.42
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Rock thermal conductivity (k) is one of the key parameters affecting the distribution of the geothermal field, which can be calculated using the weighted average method24

3. 3

where i is the sample number; n is the number of lithologic column segments; δi is the thickness of the strata represented by sample i; ki is the thermal conductivity of sample i, W/m·°C; and δ is the total thickness of the calculated sediments, m.

Geothermal gradient refers to the change ratios of temperature when the burial depth increases per 100 m below the constant-temperature zone. In this paper, the least-square method is used to calculate the geothermal gradient, and the linear regression equation is shown as follows

3. 4

where G is the geothermal gradient, °C/hm; T is the temperature of the well bottom, °C; T0 is the temperature of the constant-temperature zone, °C; D is the depth of the well bottom, m; and D0 is the burial depth of the constant-temperature zone, m. When the geothermal gradient is used to characterize the distribution of the basin geothermal field, comparison of geothermal gradients of different burial depths should be avoided. In this paper, the geothermal gradient is “normalized” to the depth of 1000 m through the following equation38

3. 5

where Gg is the normalized geothermal gradient, °C/km; Tz is the temperature at the depth of normalization, °C; T0 is the temperature of the constant-temperature zone, °C; Z is the depth of normalization, km; D0 is the burial depth of the constant-temperature zone, km; Q is the surface heat flow, mW/m2; k is the thermal conductivity of the rock in the calculation section, W/m·°C; and A is the heat generation rate, μW/m3.

Terrestrial heat flow is a physical quantity that can characterize the thermal state of the Earth’s interior and the regional shallow stratum. It combines the thermal conductivity of rocks with the spatially variable temperature, which can more accurately reflect the characteristics of the regional geothermal field than the ground temperature, geothermal gradient, and other geothermal parameters. The following mathematical expression was used to calculate the terrestrial heat flow

3. 6

where Q is the terrestrial heat flow, mW/m2; k is the thermal conductivity of the rock in the calculation section, W/m·°C; G is the geothermal gradient value in the calculation section, °C·km–1; and the negative sign indicates that the direction of the terrestrial heat flow is opposite to the geothermal gradient.

4. Results

4.1. Distribution of Coal Reservoir Temperature

The distribution map of the ground temperature for the no. 3 coal seam in the Qinshui Basin (Figure 3) has been plotted using the Kriging interpolation method based on the steady-state data and corrected approximate steady-state data. The result shows that the temperature of the no. 3 coal reservoir ranges from 14.6 to 100.9 °C with an average of 30.6 °C and gradually increases from the basin margin to the basin hinterland. The temperature in the margin is usually less than 30 °C, but in the central basin, the temperature can be greater than 50 °C. It was found that there is a good positive correlation between the temperature and the burial depth of the targeted coal reservoir. Specifically, the ground temperature of the Jinzhong Fault depression with the greatest burial depth corresponds to the highest temperature, which can even reach up to 100 °C.

Figure 3.

Figure 3

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Ground-temperature distribution of the no. 3 coal reservoir in the Qinshui Basin.

4.2. Distribution of Geothermal Gradient

According to the national-scale constant-temperature zone depth and temperature distribution map,39 the burial depth and temperature values of the constant-temperature zone in the Qinshui Basin were extracted by GIS refutations. The results show that the temperature values in the constant-temperature zone range from 13.2 to 15.2 °C with an average of 14.2 °C, and the burial depth in the constant-temperature zone varies from 27.4 to 33.1 m with an average of 31.1 m. The constant-temperature value gradually increases from the northwest to southeast, and the burial depth gradually becomes shallower from the north to south.

Geothermal gradient values of 155 temperature wells were calculated by eq 4, which can basically represent the spatial distribution of the geothermal gradient of the no. 3 coal reservoir. The results show that the geothermal gradient of the no. 3 coal reservoir ranges from 0 to 3.7 °C/hm with an average of 1.6 °C/hm (Figure 4). Within the Qinshui Basin, the geothermal gradient of the coal reservoir gradually increases from the east, southeast, and west to the central, northwest, and southwest regions. Specifically, the geothermal gradient in the east is lower than 1.6 °C/hm and that in the central part of the basin is between 1.6 and 2 °C/hm. The higher geothermal gradient is concentrated in the northwest area with a value higher than 2 °C/hm.

Figure 4.

Figure 4

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Geothermal gradient distribution of the no. 3 coal reservoir in the Qinshui Basin.

At present, the recommended geothermal gradient threshold values are used to divide the geothermal field grades in China, such as the negative geothermal anomaly (<1.6 °C/hm), geothermal normal (1.6–3 °C/hm), and positive geothermal anomaly (>3 °C/hm). Sometimes, 3.5 °C/hm is also used as the critical value to classify positive geothermal anomaly.40 Actually, there is no additional heat source in the hinterland of the Qinshui Basin, and it belongs to a stable structural area, so its geothermal field should be in the geothermal normal range. Combined with the characteristics of geothermal gradient distribution in the basin, a classification scheme of the geothermal field (Table 3) has been proposed in this paper.

Table 3. Geothermal Zoning of the No. 3 Coal Reservoir Based on the Geothermal Gradient.

    normal geothermal range
  
standards negative geothermal anomaly below normal middle normal high normal positive geothermal anomaly
geothermal gradient (°C/hm) <1. 6 1.6–2.0 2.0–3.0 3.0–3.5 >3.5
area (km2) 8985.42 16 724.57 6082.81 356.21 56.24
proportion (%) 27.9 51.93 18.89 1.11 0.17
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The distribution of the geothermal gradient reveals that the values of the geothermal gradient in the Qinshui Basin differ greatly (Table 3). The areas of the negative geothermal anomaly of the no. 3 coal reservoir constituted 27.9%, which are mainly distributed in the western and eastern basins. The normal geothermal zone comprised about 72%, distributed in the central, southwest, and northwest parts of the basin. Moreover, the positive anomaly area of the no. 3 coal reservoir accounts for about 0.17% of the total basin area, mainly concentrated in the northwest of the basin (Figure 4).

Figure 5 shows the geothermal gradient distribution map at a burial depth of 1000 m in the Qinshui Basin. It is based on the normalized geothermal gradient values of 100 temperature wells calculated by eq 5, and the heat generation rate is obtained by the weighted calculation from radioactive test results of rocks in the North China platform.41 The results show that the geothermal gradient value at 1000 m burial depth ranges from 0 to 4.0 °C/hm with an average of 1.9 °C/hm. The geothermal gradient at the depth of 1000 m is generally consistent with that of the no. 3 coal reservoir. Some local difference is caused by the undulation changes with the terrain of the no. 3 coal reservoir. The burial depth of the no. 3 coal reservoir in the southern basin and the margin of the basin is less than 1000 m, which results in the geothermal gradient of the no. 3 coal reservoir being greater than 1000 m. While the burial depth of the no. 3 coal reservoir in the hinterland of the basin and the Jinzhong Fault depression zone is more than 1000 m, the geothermal gradient value of the no. 3 coal reservoir is less than the geothermal gradient of 1000 m.

Figure 5.

Figure 5

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Geothermal gradient distribution at the depth of 1000 m in the Qinshui Basin.

4.3. Distribution of Terrestrial Heat Flow

Based on some published thermal conductivity values with reference to the Qinshui Basin and the empirical values of Chinese continental heat flow data compilation, the rock thermal conductivity column (Table 4) was obtained. Then, the harmonic means of the thermal conductivity of each well were calculated by the weighted average method of eq 3.

Table 4. Thermal Conductivity of the Sedimentary Strata in the Qinshui Basin.

stratum lithology number of samples thermal conductivity (W/(m·K) stratum lithology number of samples thermal conductivity (W/(m·K)
Liujiagou Formation (T1l) siltstone 4 1.6942 Shanxi Formation (P1s) mudstone 2 2.21
mudstone 3 1.38 sandy mudstoneb 1 2.635
sandy mudstone 2 1.7234 carbon mudstoneb 1 0.782
fine-grained sandstone 2 1.59 fine-grained sandstonea 1 2.51
medium-grained sandstonea 1 2.14 medium-grained sandstonea 2 2.445
Shiqianfeng Formation (P2sh) siltstone 3 3.0654 Taiyuan Formation (C3t) coala 2 0.481
mudstone 1 1.384 argillaceous limestone 1 2.809
sandy mudstoneb 1 1.784 siltstoneb 3 2.667
fine-grained sandstonea 1 2.2 mudstone 2 2.642
medium-grained sandstonea 2 2.13 sandy mudstone 3 2.785
Upper Shihezi Formation (P2s) siltstone 3 3.9345 carbon mudstoneb 1 1.25
mudstone 2 1.497 fine-grained sandstonea 1 2.65
sandy mudstone 2 2.2195 medium-grained sandstonea 2 2.35
fine-grained sandstonea 2 2.581 limestonea 1 2.96
Lower Shihezi Formation (P1x) siltstone 2 3.729 mudstone 1 2.728
mudstone 2 1.81 sandy mudstone 2 2.845
sandy mudstoneb 1 2.635 fine-grained sandstoneb 4 2.883
fine-grained sandstonea 2 2.735 limestoneb 1 2.517
medium-grained sandstonea 2 2.56 Fengfeng Formation (O) limestoneb 1 3.337
Shanxi Formation (P1s) coalb 1 0.402   sandy mudstoneb 1 3.312
siltstoneb 1 2.296        
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a

Data from Sun et al.25

b

Data from Yang et al.42

As shown in Table 5, the thermal conductivity harmonic means of 44 wells of the no. 3 coal reservoir were calculated using eq 3. Based on the thermal conductivity value and their geothermal gradient, the distribution of terrestrial heat flow in the Qinshui Basin (Figure 6) was plotted. The results show that the terrestrial heat flow ranges from 0.93 to 94.6 mW/m2 with an average of 41.5 mW/m2. It can be seen that the terrestrial heat flow in the Qinshui Basin is lower than the average Chinese continental heat flow (63 mW/m2). The terrestrial heat flow of the northwest basin is the highest, reaching from 56 to 94.6 mW/m2, followed by the middle, southwest, and south sections of the basin, which ranges from 50 to 56 mW/m2. The lowest heat flow is in the northeast, east, and west sections of the basin, which is lower than 50 mW/m2, and the minimum terrestrial heat flow value can be as low as 0.9 mW/m2 in the northwest.

Table 5. Harmonic Mean of the Thermal Conductivity of Temperature Wells from the Surface to the No. 3 Coal Reservoir in the Qinshui Basin.

number sign burial depth (m) k (W/m·°C) number sign burial depth (m) k (W/m·°C)
CP-004 468.53 2.01 YL10-5 707.16 2.32
CP-023 568.43 2.08 ZH-124 754.34 2.46
CP-091 672.33 2.22 ZH-183 789.7 2.22
CP-095 777.65 2.36 ZH-311 910.87 2.31
CP-098 813.7 2.07 ZH-342 683.21 2.42
CP-129 758.1 2.5 ZH-396 685.16 2.37
CZ-155 263.28 2.48 ZH-421 1051.2 2.1
CZ-160 328.46 2.36 ZQZM-005 476 2.4
CZ-219 429 2.36 ZQZM-027 683.62 2.85
CZ-224 414.03 2.34 ZQZT-068 467.53 2.79
CZ-300 414 2.33 ZQZT-153 486.89 2.5
XSD-091 361.56 2.56 ZZ-045 616.46 2.08
XSD-093 371.8 2.42 ZZ-052 601.09 2.32
XSD-130 469.5 2.37 ZZ-111 790.85 2.07
XSDU-012 664.72 2.28 ZZ-144 782.99 2.29
XSM-049 639.2 2.28 ZZ-158 728.7 2.01
XSM-053 797.3 2.32 ZZ-233 875 2.23
XSM-079 546.87 2.41 ZZCD-02 643.9 2.42
XST-048 575.5 2.2 ZK0102 1327 1.84
XST-064 546.79 2.46 ZK0402 1134.9 1.95
YL7-3 478.1 2.73 ZK0403 502.11 2.29
YL9-2 1025.1 2.39 ZK0101 1377.2 1.93
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Figure 6.

Figure 6

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Terrestrial heat flow distribution of the Qinshui Basin.

5. Discussion

5.1. Control Factors on the Geothermal Field of the Region

5.1.1. Crustal Uplift and Denudation

Due to the different structural forms of uplift and depression, the thermal conductivity of rocks changes in the vertical and horizontal directions, resulting in the redistribution of heat flow.43 To reveal the relationship between syncline structure and geothermal field, we selected the profile A–A′ to analyze the heat flow state of the coal reservoir (Figure 7). In section “b” of profile A–A′, the variation trend of heat flow is consistent with the undulation of the basement, which is in accordance with the “thermal reflection” law. Section “c” is the transition region with constant heat flow. In section “d” of profile A–A′, the heat flow decreases greatly with the rise of the coal reservoir due to crust denudation. In contrast, the terrestrial heat flow in section “a” maintains an upward trend, which may be related to the concealed magmatic bodies.

Figure 7.

Figure 7

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Geological structure and terrestrial heat flow profile of the profile A–A′. (Qs is the deep supplementary terrestrial heat flow, Qm is the terrestrial heat flow from magma, and Ql is the lost terrestrial heat flow.)

Floor elevation is a numerical expression of coal reservoir uplift. The effective burial depth can reflect the strength of coal reservoir denudation. The effective burial depth decreases with the increase of floor elevation under the premise that the unconformity surface is almost close to the level. The no. 3 coal reservoir temperature decreases with the rise of floor elevation and increases with the increase of effective burial depth by a linear function (Figure 8a,b). The geothermal gradient and terrestrial heat flow first increase linearly and then decrease linearly with the uplift of the coal reservoir (Figure 8c,d). Moreover, the geothermal gradient and terrestrial heat flow also first increase linearly and then decrease linearly with the increase of the effective burial depth (Figure 8e,f). There are transition regions for the heat flow of the no. 3 coal reservoir in both the terrestrial heat flow profile and the numerical relationship. For the floor elevation, the transition region on the profile ranges from 410 to 495 m, and in the numerical relationship, it ranges from 459 to 463.6 m. For the effective burial depth, the transition region on the profile ranges from 731 to 806 m (Figure 7), and in the numerical relationship, it ranges from 708.7 to 805.6 m (Figure 8e,f). When the floor elevation of the no. 3 coal reservoir is lower than transition regions, the sedimentary cover of the coal reservoir is thick enough to prevent heat loss and maintain the normal geothermal field. The geothermal field is mainly controlled by the basement characters. When the floor elevation is greater than the transition region, or the effective burial depth is less than the transition region, the sedimentary cover is severely eroded, and the rate of coal reservoir heat loss is greater than that of the heat supply rate from deep strata. Thus, the geothermal field is highly related to the role of strata denudation in the shallow area. The geothermal gradient and terrestrial heat flow decrease at the rates of 0.1–0.2 °C/hm and 4–7 mW/m2 per 100 m, respectively.

Figure 8.

Figure 8

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(a) Relationship between the coal reservoir temperature and elevation. (b) Relationship between the coal reservoir temperature and effective burial depth. (c) Relationship between the coal reservoir geothermal gradient and elevation. (d) Relationship between the coal reservoir terrestrial heat flow and elevation. (e) Relationship between the coal reservoir geothermal gradient and effective burial depth. (f) Relationship between the coal reservoir terrestrial heat flow and effective burial depth.

5.1.2. Groundwater Activity

The distribution of the geothermal field can be expressed by eq 7, whose curve is the quadratic polynomial fitting curve of the formation temperature changes with burial depth. The calculation formula of the groundwater flow rate (V) can be deduced as follows44

5.1.2. 7
5.1.2. 8

where T is the formation temperature, °C; c and ρ are the specific heat capacity (kg·°C) and the density of the fluid (kg·°C kg/m3), respectively; λ is the thermal conductivity of rocks, W/m·°C; V is the volume velocity of the fluid in the vertical direction, m3/h; dT/dZ is the geothermal gradient, °C/m; and d2T/dZ2 the change rate of the geothermal gradient in the vertical direction.

As shown in Figure 9, when V is zero, the geothermal gradient keeps invariant with the change of burial depth. It indicates that the surrounding rock temperature is only controlled by conduction without groundwater activity influences, and the quadratic curve tends to be a straight line (line b). When V is negative, the groundwater flows upward, and the surrounding rock geothermal values become higher because of the recharge of deep hot water, and the temperature curve is a convex curve as in line a. When V is positive, the groundwater flows downward to the crust, indicating that the surrounding rock geothermal values become lower under the influence of cold-water flows, and the curve of the temperature is a concave shape (line c).45,46 In this paper, the relationship between temperature and burial depth of a testing temperature well PD-099 was analyzed, and the results are consistent with the characteristic curve of c. The relationship shows that the geothermal field is mainly controlled by low-temperature groundwater movements. The curvature of curve c is the greatest at burial depths from 1050 to 1100 m, indicating that the velocity of groundwater flow at this depth is relatively large.

Figure 9.

Figure 9

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Generalized model of groundwater effects on the geothermal field and the temperature curves of well no. PD-099.

To illustrate the effects of groundwater seepage on the geothermal field, this paper selected two profiles to analyze the heat flow state of the no. 3 coal reservoir (Figure 10). The terrestrial heat flow rises in the west part of section B–B′, which may be associated with the hot-water migration from the lower aquifer by the effects of deep faults, and this situation meets the model curve a in Figure 9. The terrestrial heat flow greatly drops in the east of profile B–B′, while the dynamic characters of groundwater change from weak runoff to strong runoff, which can be explained by the model curve c. In addition, the profile C–C′ confirms that the terrestrial heat flow decreases with the increase in intensity of the groundwater flow. The heat flow in the strong runoff zone is smaller than that in the weak runoff zone and the stagnant zone.

Figure 10.

Figure 10

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Hydrogeology and terrestrial heat flow section of profile B–B′ (a) and profile C–C′ (b).

The height of the groundwater level and the concentration of total dissolved substances (TDSs) are indicators that determine the dynamic strength of the groundwater.47 In this paper, four independent groundwater systems are taken as the objects to analyze the relationships between the groundwater level of the Shanxi Formation and the geothermal field of the no. 3 coal reservoir. Simultaneously, the relationships between the TDS value of the Shanxi Formation aquifer and the geothermal field of the no. 3 coal reservoir are analyzed. Figure 11a,b shows that the geothermal gradient and the terrestrial heat flow of the no. 3 coal reservoir have a good linearly negative correlation with the groundwater level. The reason is that the low-temperature water flows from a high water level to a low water level when the coal seam receives cold-water recharge, and the heat of the surrounding rock is taken away continuously during the flow process. With the decrease in the water level, the water temperature rises gradually and the heat loss of the coal reservoir decreases, thus increasing the geothermal gradient and terrestrial heat flow. As can be seen in Figure 11c,d, with the increase of the TDS value, the geothermal gradient and the terrestrial heat flow first increase and then tend to be stable. This might be because with the increase of the TDS value, the runoff intensity of the groundwater decreases, and the disturbance of the groundwater to the coal reservoir decreases.48,49 When the TDS increases to a certain value, the groundwater is stagnant, and the temperature of the coal reservoir is not disturbed by the groundwater and remains stable.

Figure 11.

Figure 11

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(a) Relationship between the coal reservoir geothermal gradient and the groundwater level. (b) Relationship between the coal reservoir terrestrial heat flow and the groundwater level. (c) Relationship between the coal reservoir geothermal gradient and TDS. (d) Relationship between the coal reservoir terrestrial heat flow and TDS.

5.2. Influence of Geothermal Field on the Production of CBM

CBM production is a continuous process of desorption, diffusion, and migration of gas and water multiphase fluids in the pore-fracture system of a coal reservoir.50 These processes are in the changing environment of stress field, geothermal field, and chemical field.51 Temperature can affect the physical properties of gas and the pore-fracture structure of a coal reservoir, which has an important effect on the production of CBM. Considering the development of CBM, with the increase in temperature, the molecular kinetic energy increases. In addition, with the enhancement of desorption capacity, the diffusion volume of a gas increases, and a larger diffusion volume and higher molecular kinetic energy will increase the gas diffusion capacity in coal reservoirs. In addition, coal has a strong thermoplastic property, and the temperature rise produces thermal stress, which results in the coal matrix thermal expansion deformation. The permeability of coal is affected as a result.

5.2.1. Influence of Geothermal Field on the Adsorption/Desorption Capacity of CBM

Coalbed methane is stored in coal reservoirs in the free, adsorbed, and dissolved states, and the adsorbed phase usually accounts for more than 80% of the total gas. The adsorption capacity of CBM is affected by temperature and pressure and conforms to the Langmuir model, which can be expressed as

5.2.1. 9

where V is the adsorption volume, cm3/g; VL is the Langmuir volume, cm3/g; PL is the Langmuir pressure, MPa; and P is the gas pressure, MPa. The Langmuir volume VL represents the maximum adsorption capacity of the adsorbate, and the Langmuir pressure PL is the pressure corresponding to 50% of the maximum adsorption capacity, which can characterize the difficulty and rate of desorption. PL is dependent on temperature (as shown in Figure 12a), and it can be represented as follows52

5.2.1. 10

where A0 is the pre-exponential coefficient, cm3/g; Ea is the adsorption energy, kJ/mol; R is the universal gas constant, R = 8.314 J/(mol·K); and T is the temperature, K; according to eq 4, the calculation formula of the coal reservoir temperature can be deduced as

5.2.1. 11

where G is the geothermal gradient, °C/hm; T0 is the temperature of the constant-temperature zone, °C; D is the depth of the coal reservoir, m; and D0 is the burial depth of the constant-temperature zone, m.

Figure 12.

Figure 12

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(a) Relationship between PL and temperature. (b) Relationship between the adsorption content and depth at different geothermal gradients.

To study the relationship between the adsorption capacity of CBM and temperature, some isothermal adsorption experiments of CH4 at different temperatures were carried out.5 In this paper, the test temperatures were converted into geothermal gradients according to eq 11. The test pore pressures were converted into coal seam depth according to the empirical formula of the reservoir pressure (eq 12).53 Thus, the relationships between CBM adsorption capacity and burial depth under different geothermal environments are obtained (as shown in Figure 12b).

5.2.1. 12

where D is the depth of the coal reservoir, m; and P is the pore pressure, MPa.

Figure 12b shows that with the increase of depth, the adsorption capacity of the coal reservoir increases first and then decreases, obtaining a maximum value at about 1 km (critical depth). The reason may be that with the increase of burial depth, the gas pressure and the adsorption capacity of the coal reservoir increase as well.54 As the pore pressure increases, the coal gradually reaches adsorption saturation, and the influence of pore pressure gradually decreases,8 but as shown in Figure 13, the coal reservoir temperature increases with the increase of burial depth, which enhances the activity of methane molecules. The van der Waals force between coal surface molecules and methane molecules makes it difficult to capture methane molecules moving at high speed, resulting in the adsorption capacity of coalbed methane beginning to decline.55,56 It indicates that the adsorption capacity is mainly controlled by reservoir pressure when the burial depth is less than the critical depth. As the burial depth further increases, the effect of temperature is far greater than that of pressure, resulting in a significant reduction of the gas content in deep coal reservoirs. Therefore, the negative geothermal anomaly area buried at critical depth often has a high gas content, but the desorption of coalbed methane at this area is difficult.

Figure 13.

Figure 13

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Schematic diagram of the influence of temperature on methane adsorption/desorption capacity.

5.2.2. Influence of Geothermal Field on the Diffusion Capacity of CBM

Gas diffusion is essentially a process of random thermal motion of molecules, which accords with the basic law of a general chemical reaction.57 The Arrhenius equation is generally used to obtain the relationship between temperature and the reaction rate in chemical reactions. Based on the Arrhenius equation, the effective diffusion coefficient (De) was introduced correlating to temperature changes, which can be expressed as58

5.2.2. 13

where De is the effective diffusion coefficient, m2/s; D0 is the experimental constant; and E0 is the minimum energy barrier for gas molecules to exceed during the diffusion process, which is temperature-independent, kJ/mol. In addition, the study retrieves the published data of the diffusion experiment under different temperatures.5 Combined with the relationship between pore pressure and burial depth, the variation of the diffusion coefficient with burial depth under different geothermal gradient conditions can be obtained (Figure 14).

Figure 14.

Figure 14

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Relationship between the diffusion coefficient and depth at different geothermal gradients.

From Figure 14, we found that the diffusion coefficient increases linearly with burial depth under different geothermal gradients, which conforms to the Arrhenius equation model (eq 13). When the burial depth of the coal reservoir is constant, the diffusion capacity of CH4 increases with the increase of the geothermal gradient. This may be because with the increase of burial depth, the coal reservoir temperature increases. However, when the burial depth is constant, the temperature would increase with the increase of the geothermal gradient. As the temperature increases, methane molecules with a lower adsorption potential would escape from the coal surface to be free,59 which provides a sufficient gas source for methane diffusion. Then, the diffusion process of the methane molecule will be accelerated with the increase in the concentration gradient of the coal pore surface.60 However, the spatial difference of the concentration gradient gradually decreases with time and tends to approach a uniform equilibrium (Figure 15). Furthermore, the kinetic activity of methane molecules can be increased with the increase in temperature, thus enhancing their fluidity.5 Therefore, the diffusion capacity is independent of pore pressure, and the positive geothermal anomaly area is more conducive to the diffusion of coalbed methane than the negative geothermal anomaly area.

Figure 15.

Figure 15

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Schematic diagram of the influence of temperature on the methane diffusion process and diffusion capacity.

5.2.3. Influence of Geothermal Field on the Permeability of CBM

Coal permeability is an important factor affecting CBM production and reservoir exploitation value. Shi and Durucan proposed that the horizontal effective stress is the major factor that affects the permeability of coal, and the relationship between permeability and horizontal effective stress is expressed as follows61

5.2.3. 14

where k is the permeability of coal, 10–3 μm; k0 is the initial permeability of coal, 10–3 μm; Cf is the volume compression coefficient of coal cleat, MPa–1; P is the gas pressure, MPa; P0 is the initial gas pressure, MPa; σh is the horizontal effective stress, MPa; and σh0 is the initial horizontal effective stress, MPa. With the increase of burial depth, the temperature of the coal reservoir increases, and the effect of temperature on permeability should not be ignored. Thus, an improved permeability model that considers the influence of temperature and effective stress has been proposed.62

5.2.3. 15

where v is Poisson’s ratio; E is Young’s modulus; ρ is the density of coal, g/cm3; EA is the expansion modulus caused by coal adsorption, MPa; and V0 is the standard molar volume, L/mol. According to the temperature distribution characters of the Qinshui Basin, this study carried out some experiments to investigate the permeability of coal reservoirs from 25 to 65 °C. By combining formulae (11) and (15), the permeability change regularities of the coal reservoir with burial depth under different temperature field conditions are shown in Figure 16.

Figure 16.

Figure 16

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Relationship between permeability and coal reservoir depth under different geothermal gradients.

It can be seen from Figure 16 that at any geothermal gradient condition, permeability basically demonstrates a logarithmical decrease with an increase in burial depth. The change in coal reservoir permeability is the result of effective stress and temperature. On the one hand, with the increase of burial depth, the external stress increases continuously, the pore and fracture space in the media will be compressed, and the methane seepage channel becomes narrow, showing a sharp decline in permeability.63 On the other hand, coal is a porous medium that is sensitive to temperature, and the thermal stress caused by the increased temperature would make the coal matrix swell. The effective stress produced by surrounding stresses is extremely high compared to thermal stress, which limits the outward swelling. Thus, the swollen coal matrix closes the original fracture space, resulting in the decreased permeable capacity.64 As effective stress and temperature further increased, the rough fracture surface contacted each other, forming new “coal bridges”, thereby increasing the compression resistance and slowing down the reduction rate of fracture and pore volume, resulting in the changing trend of permeability slowing down.65 When the burial depth of the coal reservoir is constant, the change in coal permeability is affected by a single factor of temperature. The permeability of the coal reservoir decreases with the increase of the geothermal gradient, and the interval of the seepage curve decreases with the increase of the geothermal gradient. Therefore, there is generally a higher permeable capacity in the negative geothermal anomaly region; however, the area with a positive geothermal anomaly is not conducive to the seepage of coalbed methane.

6. Conclusions

In this paper, the distributions of ground temperature, geothermal gradient, and terrestrial heat flow of the Qinshui Basin were investigated, and the mechanism of controlling factors was revealed. Meanwhile, the relationships between geothermal field variations and CBM migration characteristics were studied, and the variation model of CBM production was summarized. The main results are as follows.

  • (1)

    The geothermal gradient of the no. 3 coal reservoir ranges from 0 to 3.7 °C/hm with an average of 1.6 °C/hm, and the geothermal gradient at the depth of 1000 m ranges from 0.2 to 4.0 °C/hm with an average of 1.9 °C/hm. The terrestrial heat flow of the Qinshui Basin ranges from 0.9 to 94.6 mW/m2 with an average of 41.5 mW/m2, which is lower than the mean heat flow level of mainland China (63 mW/m2).

  • (2)

    The geothermal gradient and terrestrial heat flow of the no. 3 coal reservoir first increases and then decreases with floor elevation and effective burial depth, and the transition region is about 450 m for the floor elevation and ranges from 700 to 800 m for the effective burial depth. The geothermal field of the coal reservoir is coupling-controlled by crustal uplift, denudation, and groundwater dynamic conditions. The negative geothermal anomaly areas on the edge of the basin are caused by severe uplift and erosion as well as the strong runoff of low-temperature water.

  • (3)

    In the negative geothermal anomaly region, the adsorption capacity and permeability of methane in coals are relatively high, but the diffusion capacity is relatively small, indicating that a higher gas content and permeable ability developed in the negative geothermal anomaly region; however, the area with positive geothermal anomaly is favorable for the desorption and diffusion of coalbed methane.

Acknowledgments

This work was financially supported by the Shanxi Province Science and Technology Major Project (Grant Nos. 20201102001, 20191102001, and 20181101013) and the National Science and Technology Major Project of the Ministry of Science and Technology of China during the “13th Five-Year Plan” (Grant 2016ZX05067001-006). The authors thank the reviewers and the editor for their constructive comments.

The authors declare no competing financial interest.

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