Chen Guo,Yong Qin,Dongmin M,Zhobio Yng,Lingling Lu

a College of Geology and Environment,Xi’an University of Science &Technology,Xi’an 710054,China

b Stations for Post-doctoral Research of Geological Resources and Geological Engineering,Xi’an University of Science and Technology,Xi’an 710054,China

c Key Laboratory of CBM Resources and Reservoir Formation Process,Ministry of Education,China University of Mining &Technology,Xuzhou 221116,China

Keywords:Geotemperature Gray sequence Geothermal gradient Heat damage Coal Coal bed methane

ABSTRACT The geothermal fields of coal-bearing strata have become a key topic in geological research into coal and coal bed methane (CBM).Based on temperature data from 135 boreholes that penetrate the Upper Permian coal-bearing strata in the Bide-Santang basin,western Guizhou,the precisions of geothermal predictions made using a geothermal gradient model and a gray sequence GM(1,1)model are analyzed and compared.The results indicate that the gray sequence GM(1,1)model is more appropriate for the prediction of geothermal fields.The GM(1,1)model is used to predict the geothermal field at three levels with depths of 500,1000,and 1500 m,as well as within the No.6,No.16,and No.27 coal seams.The results indicate that the geotemperatures of the 500 m depth level are between 21.0 and 30.0°C,indicating no heat damage;the geotemperatures of the 1000 m depth level are between 29.4 and 44.7°C,indicating the first level of heat damage;and the geotemperatures of the 1500 m depth level are between 35.6 and 63.4°C,indicating the second level of heat damage.The CBM contents are positively correlated with the geotemperatures of the coal seams.The target area for CBM development is identified.

1.Introduction

Temperature is a key geological parameter in fossil energy exploration and exploitation [1,2].Geothermal research presently focuses on the factors that control the distribution of formation temperatures,geothermal gradients,and terrestrial heat flow and has recently received considerable attention related to the exploration for and exploitation of coal,petroleum,and natural gas[3-13].The present-day geothermal fields of coal-accumulating basins significantly influence the mining of coal resources and the occurrence and migration characteristics of coal bed methane(CBM)[14,15].In particular,the prediction of heat damage is necessary for the mining of coal at depth.Geothermal fields are of great significance for the exploration and development of coal and coalbed methane,the prediction of heat damage and the prevention of geological hazards in coal mines.Guizhou province is very rich in coal resources,and its coal reserves exceed the total reserves of the other provinces in South China.The coal resources in western Guizhou occur mainly in Upper Permian strata.During the preliminary phases of exploration,large amounts of coal field temperature data were accumulated.In recent years,the exploration and development of CBM have been progressively promoted,and a breakthrough in gas production capacity has been achieved[16].With coal mining and gas production continuously expanding to greater depths,research on the prediction of geothermal fields and heat damage in deep coal measures is urgently needed[17].

Therefore,the Bide-Santang Basin in the Zhina coalfield in western Guizhou is selected for investigation as a case study in this paper.Temperature data were obtained from 135 boreholes in 16 exploration areas,and the geotemperature prediction accuracies of the geothermal gradient method and the gray sequence method are compared.On this basis,the distribution of the geothermal field and the potential for heat damage are predicted at different burial depth levels and major coal seams to permit the efficient and safe exploitation of the coal resources of the Upper Permian in Southwest China.

2.Geologic setting

The Zhina Coal Field is one of the most important coal fields in Guizhou province,and it is characterized by an abundance of high-quality anthracite.It is located in a tectonic triangle zone formed by the crossing of four peripheral faults,and its tectonic characteristics are significantly controlled by the faults.The Bide-Santang Basin is located in the southwestern part of the Zhina coalfield and contains the majority of the coalfield.This basin has a total area of 1692 km2and a predicted coal-bearing area of 1000 km2(Fig.1).The Bide-Santang Basin contains the Bide,Shuigonghe,Santang,Agong,and Zhucang coal-bearing synclines and numerous stacked coal seams.The structures in the region are predominantly NW-and NE-trending.The NE-oriented structures (folds and faults)cut the NW-oriented structures,demonstrating that the NW-trending structures formed before the NE-trending structures.The structures in the study area were mainly formed during the Yanshanian orogeny (Fig.1).Under the early Yanshanian E-W maximum principle stress,a series of NW folds and faults were formed at the western border near the fault zone.Subsequently,the principal stress had turned into an SE-NW direction and NE direction folds and faults were formed in the middle and eastern part of the basin;thus,the basic tectonic framework of the Bide-Santang basin settled.During the late Yanshanian deformation,the early stage NE structures were sinistrally sheared into an‘‘S”shape.The late Yanshanian and Himalayan tectonic movements have shown inherited development of the early stage Yanshanian structures [18].The structures in the study area are characterized by open synclines and closed anticlines,and most of the anticlines were destroyed by faulting and seriously eroded.The coal and CBM resources mainly accumulated in the synclines [19].

The Kandian Upland was the dominant sediment-source region for the late Permian coal-bearing strata,and the accumulation of organic matter was accompanied by frequent active volcanism and related hydrothermal processes [20].The depositional environment of the coal-bearing strata was in a typical sea-land transition in the Late Permian.The Changxing and Longtan Formations in the Upper Permian contain 35 coal seams,of which 3-17 are minable.The composite thickness of all the coal seams is 24-41 m,with an average thickness of 33 m,and the total thickness of the minable seams is 9-23 m [21].Four sets of third-order sequences(SQ)were identified in the coal-bearing strata (Fig.2)[22].The gas contents of the coal seams range from 3.88 to 28.12 cm3/g with an average of 13.81 cm3/g [23].The coal rank is dominated by anthracite with Ro,maxbetween 1.92% and 3.14%,and meagre coal occurs along the western edge of the Bide-Santang basin [24,25].

Fig.1.Structural outline map of the Bide-Santang basin.

Fig.2.Stratigraphic column showing the lithology,depositional facies,and sequence stratigraphy of the Upper Permian coal series within the study area(modified from [28]).

The permeability of coal seams ranges from 0.0002 to 1.5621 mD,averages in 0.2775 mD.And the porosity of coal seams ranges from 1.3% to 14.7%,averages in 5.18% [26,27].The permeability presents an increased tendency from the western margin to the interior of the basin.For example,the permeability obtained by well test of borehole ZK1602 in Huale exploration area is 0.4 mD,and the permeability of borehole ZK1101 in Nayong exploration area is 1.4 mD.Both of Huale and Nayong exploration areas are located in the margin of the Bide-Santang Bain.Conversely,in the interior of the basin,the permeability of borehole 503 in Zhongzhai exploration area is 0.03 mD,and the permeability of borehole Z-2 in Feiyi exploration area is 0.0002 mD.It can be reasonably concluded that the marginal faults (F1 and F2)of the Bide-Santang Basin increase the permeability of coal seams(Fig.1).

3.Methods for geotemperature prediction

3.1.Geothermal gradient method

The geothermal gradient method is based on the principle of heat conduction.In this method,information on the geothermal gradient in the shallow part of the borehole is used to calculate the temperatures of the strata at depth.The relevant equation is:

where T is the temperature of the predicted point,°C;Z the depth of the predicted point,hm;H0the depth of the constant temperature surface,hm;G the average geothermal gradient below the constant temperature surface in the borehole,°C/hm;and T0the temperature of the constant temperature surface,°C.

Taking the approximate steady-state temperature measurements in borehole 02-4 in the Feiyi exploration area as an example,it is determinedthat the depthof the constant temperature surfaceis 20 m,the average temperature of the constant temperature surface is 14°C,and the average geothermal gradient is 2.4°C/hm.Therefore,the prediction model of the deep geothermal temperature is:

Table 1 Comparison between the measured values and the values predicted using the geothermal gradient model.

The geotemperatures of the borehole are predicted according to Eq.(2).The results show that the predicted values are generally less than the measured values,and the error increases with increasing depth (Table 1,Fig.3).Thus,the geothermal gradient method is not suitable for the prediction of geotemperatures at depth.This lack of suitability may stem from the gradual increase in the geothermal gradient with depth;thus,the average geothermal gradient obtained from the shallow temperature data cannot reflect geological conditions at depth and leads to the increasing prediction error with depth [21].

3.2.Gray sequence method

3.2.1.Principle of gray sequence prediction

The gray sequence prediction model of gray system theory is based on the exponential variation law of a new sequence generated by the accumulation of an irregular original sequence.Previous studies have shown that the geotemperatures in a borehole increase with nonlinearly increasing depth and fall close to a curve described by an exponential function.Additionally,the geothermal system is also a gray system,so it is feasible to use the gray sequence method to predict the geotemperatures of deep coalbearing strata [29].

In gray system theory,the gray model used for prediction is generally a GM(n,1)model.Previous researchers have always used GM(1,1)models in the prediction of geotemperatures;such models have several advantages,including simple calculation,wide applicability and high precision.Therefore,we also use the GM(1,1)model to predict the geotemperatures in the Feiyi exploration area.The principles used in the model are as follows [30]:

The original sequence of the variable x is listed as:

The original sequence is treated with a first-order accumulated generating operation (1-AGO)and transformed to:

The new sequence can be approximated by the following exponential differential equation:

Therefore,the identification parameters a and b in the above equation can be obtained by means of (a,b)′=(BB)-1BY,where

Fig.3.Plots of the predicted value and measured value of temperatures and their relative errors.

The coefficients a and b can be calculated by the least-squares method,and the solution of the differential equation is substituted.An equation that is a function of time is then obtained.

The sequence predicted by the above model can be processed by a first-order inverse accumulated generating operation(1-IAGO),and the gray prediction value of the model based on the original sequence can be obtained using the following equation:

3.2.2.Mathematical modeling of gray sequence prediction

The original sequence used in the prediction model represents temperature data collected from borehole 02-4 in the Feiyi exploration area.The borehole extends to a depth of 640 m,and temperature measurements were collected every 20 m.The selected data(the measured temperatures and the corresponding depths)were all obtained below the depth of the neutral point.

According to the gray sequence prediction method,the parameters a and b are obtained by applying the gray prediction model to the original sequence in Table 2.

Thus,we obtain the following differential equation:

For which the discrete solution is

Eq.(12)is the gray sequence prediction model.

3.2.3.Evaluation of the prediction accuracy of the gray model

Based on gray system theory,a gray sequence prediction program is written using Matlab 7.0.According to the prediction model,we can determine the fitted values of the sequentially accumulated sequence,including the fitted values of the original sequence,and the residual errors between the fitted values and the measured values (Table 3).

By comparing the temperature data obtained from the borehole and the data predicted by the geothermal gradient method and the gray sequence method (Tables 1 and 3),it shows that the prediction error of the linear geothermal gradient method is larger.These larger errors occur because,in this prediction method,the variations in the thermal conductivity of the formations and the geothermal gradient in the vertical direction are not fully taken into account.The gray sequence prediction method is more accurate in predicting the geotemperatures at depth.

The accuracy of the gray prediction model is verified using an a posteriori test.According to Table 3,the average value of the residual error is

Therefore,the deviation of the average value of the residual error and the average value of the original sequence is

The ratio of the posterior variance can be obtained as follows:

The small error probability is:

The variance ratio C ＜0.35,and p ＞0.95.Thus,according to the posterior error detection and accuracy assessment of the gray prediction model,the accuracy of the above gray sequence prediction model appears to be satisfactory.

Therefore,in the prediction of geotemperatures at depth,the gray sequence prediction model GM(1,1)results in high prediction accuracy,and the fitting degree for the temperature measuring curve is also very good.The principle of the gray prediction model is based on the actual borehole temperature data used to construct the model and fully accounts for the variations in lithology and burial depth where the predictions are made.Thus,the prediction results are relatively close to the actual values (Fig.3).

4.Results

4.1.Prediction of geothermal temperatures at different burial depths

Based on the gray sequence method,the geothermal temperatures at three levels with depths of 500,1000,and 1500 m are predicted.The temperatures of the 500 m depth level range from 21.0 to 30.0°C,with average 25.6°C,the geotemperatures within the Shuigonghe syncline and the Zhucang syncline are higher,and the Santang syncline displays lower geotemperatures (Fig.4a).According to the criterion of the heat damage assessment(the first level of heat damage:31～37°C,and the second level of heat damage:≥37°C),no heat damage is present at a burial depth of 500 m within the study area [31].The geotemperatures of the 1000 m burial depth level range from 29.4 to 44.7°C,with an average of36.5°C,and most of the study area displays the first level of heat damage (Fig.4b).The geotemperatures in the Bide syncline and the Santang syncline are lower,whereas those in the Shuigonghe syncline and the Zhucang syncline are higher,reaching the second level of heat damage.The geotemperatures within the 1500 m depth level range from 36.6 to 63.4°C with an average value of 48.0°C,and the geotemperatures generally reach the second level of heat damage (Fig.4c).

Table 2 Original sequence used in gray sequence prediction.

Table 3 Comparison between the value predicted by the gray sequence model and the measured data.

Fig.4.Isoline maps of formation temperatures at different burial depths within the Bide-Santang basin.

On the whole,the distribution of geotemperatures coincides with the tectonic pattern of the basin,indicating that the geothermal field is macroscopically controlled by the tectonic framework[32-34].The Liupanshui-Ziyun fault along the western margin of the basin leads to the relatively active groundwater in the Bide syncline;as a result,the geotemperatures are relatively low [35].The Santang syncline is the most open syncline in the study area,and its lower geotemperature is consistent with the basic law that states that‘‘anticlines favor heat accumulation and synclines favor heat dissipation”[36,37].Heat flow is generally low in the Bide-Santang Basin,which may be ascribed to its tectonic characteristics of open synclines and closed anticlines since the coal-bearing strata occur mainly in the synclines[21].Faulting provides a channel for the conduction of heat flow and allows deep geothermal water to transfer heat to the upper crust,increasing the geotemperature and geothermal gradient in the shallow crust[38].There are more than 71 hot springs in Guizhou province,which reflects the thermal conduction that results from modern active faults[39].High angle normal faults are well developed in Paleogene and older strata in the Shuigonghe syncline,and deep geothermal water is transmitted to the upper crust along these faults.Heat is concentrated in upper Paleogene strata due to its unconsolidated overburden,and the heat is transmitted laterally to the surrounding strata,leading to the high geotemperature in the Shuigonghe syncline.

4.2.Prediction of geothermal temperatures of the major coal seams

Based on the coal seam burial depth data,the geotemperatures of the No.6,No.16 and No.27 coal seams are predicted using the gray sequence method.The burial depth of the No.6 coal seam ranges from 120 to 450 m,and its temperatures range from 16.3 to 28.5°C with an average value of 20.1°C.These values reflect no heat damage(Fig.5a).The burial depth of the No.16 coal seam ranges from 161 to 536 m;the coalbed temperatures range from 16.5 to 29.7°C,and the corresponding average is 22.3°C,indicating no heat damage(Fig.5b).The burial depth of the No.27 coal seam is 223-582 m;the temperature of the No.27 coal seam ranges from 17.2 to 31.4°C,with an average of 23.8°C.The geotemperatures of the Wulunshan exploration area in the Shuigonghe syncline exceed 31°C,reflecting the first level of heat damage(Fig.5c).Generally,the distribution of geotemperatures in the major coal seams is basically consistent,and it is consistent with the trend of the contour lines of the floors of the coal seams.The coal seam temperatures favor underground operations.

4.3.Prediction of the depth of heat damage for coal mining

Based on the calculated average geothermal gradients of typical boreholes in the study area,Eq.(17)is used to calculate the critical depth of heat damage:

where G is the average geothermal gradient below the constant temperature surface,°C/hm;T0the temperature of the constant temperature surface,°C;Z0the depth of the constant temperature surface,m;and 31 (37)the critical value of the temperature of the first level (second level)of heat damage.

The results show that the depth of the first level of heat damage in the study area ranges from 564 to 923 m with average 740 m,whereas the depth of the second level of heat damage ranges from 784 to 1228 m with average 1001 m (Table 4).The current coal mining in the Bide-Santang Basin has reached the depth level of the first level of heat damage in a few areas;no seam has reached the depth of the second level of heat damage.

Fig.5.Isoline maps of the temperatures of the major coal seams in the Bide-Santang Basin.

Table 4 Prediction of the depth of thermal damage based on borehole temperature measurements in the Bide-Santang Basin.

The Wulunshan exploration area displays the highest geotemperatures within the study area;the geothermal gradients within this area range from 1.52 to 4.31°C/hm with average 3.34°C/hm.The coal-bearing strata in this area display both the first and second levels of heat damage.The first level of heat damage occurs locally in the southeastern part in the No.3 and No.8 coal seams.As the burial depths of the coal seams increase,the geotemperatures also gradually increase,and the area covered by the first level of heat damage area also gradually expands.The first and second levels of heat damage are widely distributed in the No.33 coal seam (Fig.6).The high geotemperature will increase the risk of hyperthermia of workers operating in the underground mines.

5.Relationship between the geotemperatures and gas contents of coal seams

The No.16 coal seam is used as a case study of the relationship between the geotemperatures and gas contents in the study area.Figs.7 and 5b indicate that the area with high temperatures coincides with the area of high gas contents in the Wulunshan exploration area,which is located within the western limb of the Shuigonghe syncline.The geotemperatures and gas contents at the western margin of the Bide-Santang Basin are relatively low,which may be due to the marginal Liupanshui-Ziyun fault (F1)and the induced active groundwater [41].As a syndepositional fault,the Liupanshui-Ziyun fault at the western margin of the Bide-Santang Basin serves as a conduit for groundwater recharge from precipitation,reducing the geotemperature and gas content along the fault [21].Additionally,the gas contents in the Zhucang syncline,the Agong syncline,and the Santang syncline,which display low geotemperatures,are also relatively low.Another issue of concern is that the CH4concentrations of the CBM in areas with high geotemperatures are relatively high,represented by Shuigonghe syncline,and these concentrations are relatively low in areas of low geotemperatures,represented by Bide syncline and Zhucang syncline;in these areas,the CH4has been replaced by N2and CO2,and the CH4in the Agong syncline has even been replaced by C2H6(Fig.7).

Potential reasons for the positive relationship between the geotemperatures and gas contents (and CH4concentrations)are as follows:

(1)The present-day geotemperature is inherited from the paleogeothermal background during the period when CBM was generated in large quantities due to intense magmatic activity[42].The Yanshanian produced the most magmatic activity in Guizhou province,and resulted in the widespread high-grade metamorphic anthracite and high CBM content in the study area [39,43].Present-day geotemperature has inherited the abnormally high paleogeothermal background of the Yanshanian period.

(2)High geotemperatures always occur in stagnant groundwater environments,which benefit CBM accumulation and avoid gas weathering [44,45].

(3)As the coal seam temperatures and the corresponding maturity increase,the quantity of alkane molecules with high carbon numbers in natural gas decreases,and such molecules may even disappear altogether;thus,gas wetness(C2-5/C1-5)is negatively correlated with the thermal maturity and geotemperatures of coal seams [46].

The areas with high gas contents and high geotemperatures should be prioritized in CBM development.High geotemperatures will promote the gas desorption form the inner surface of the coal matrix and hence enhance the gas productivity[47-50].Moreover,due to increasing concerns about safety of coal mining,the CBM development will significantly decrease the risk of gas outburst during coal mining.The most favorable area for CBM development in the Bide-Santang basin is identified,centering on the Shuigonghe syncline,with CH4contents more than 13 m3/t and geotemperatures more than 25°C (Fig.8).The target area lacks permeability data,however,the data of boreholes from the adjacent areas,Huale ZK1602 and Nayong ZK1101,indicate the permeability of the coal reservoir in the target area should be favorable to CBM production,to some degree.

Fig.6.Temperature of coal seams Nos.3,8,and 33 in the Wulunshan exploration area.

Fig.7.Gas content distribution and the concentrations of the associated components in the Bide-Santang Basin [40].

Fig.8.Prediction of the target area for CBM development in consideration of geotemperature,gas content,and permeability.

6.Conclusions

(1)The geothermal gradient method is not appropriate for the prediction of geotemperatures.The errors associated with the use of this method increase with the depth due to depth-related changes in the thermal conductivity and the geothermal gradient.The gray sequence prediction model GM(1,1)is more effective in predicting geotemperatures at depth.The principle of the gray prediction model is based on the actual borehole temperature data and fully accounts for the variations in lithology and burial depth where the predictions are made.Thus,the prediction results are relatively close to the actual values.

(2)In general,the temperatures of the coal seams in the study area favor underground operations.The average depths of the first and second levels of heat damage in the study area are 740 m and 1001 m,respectively.The Wulunshan exploration area in the Shuigonghe syncline shows relatively high geotemperatures.Deep coal mining operations should devote additional attention to the risks of heat damage and gas outburst events.

(3)The gas contents of the coal seams are positively correlated with the geotemperatures,indicating that the present-day geotemperatures are inherited from the abnormally high paleogeothermal background during the Yanshanian deformation,when CBM was generated in large quantities due to intense magmatic activity.The areas with high gas contents and high geotemperatures should be prioritized in CBM development.The target area for CBM exploration and development in the Bide-Santang basin is identified,with CH4content more than 13 m3/t and geotemperatures more than 25°C.

Acknowledgements

This paper was jointly sponsored by a National Science and Technology Major Special Project of China (No.2016ZX05044),a Postdoctoral Science Foundation of China (No.2018M631181),and a Key Project of the Natural Science Foundation of China (No.40730422).We thank all of the parties that contributed to this publication.