Characteristics of in situ stress and its influence on coal seam permeability in the Liupanshui Coalfield, Western Guizhou

The current in situ stress regime is of great significance to the exploration and development of coalbed methane (CBM). In this study, the vertical stress ( σV ), maximum horizontal principal stress ( σH ), and minimum horizontal principal stress ( σh ) in the Liupanshui Coalfield were studied. Variations of the maximum and minimum envelopes and trend lines of the lateral pressure coefficient ( λ ) with depth were obtained, and the non‐monotonic decrease of permeability with burial depth was determined. On this basis, the effect of in situ stress on the coal reservoir permeability was evaluated. The results show that the average vertical stress gradient of the main coal seam in the Liupanshui Coalfield is 0.024 MPa/m. Generally, there are two stress regimes of σH > σV > σh (44.23%) and σV > σH > σh (46.15%); σH > σh > σV accounts for a smaller proportion (9.62%), and only occurs in relatively shallow coal seams (<622.85 m). In the range of the tested burial depths, for <600 m, σH > σV > σh is dominant; σV > σH > σh is dominant between 600 and 800 m; and between 800 and 980 m, the coal reservoir is affected by both σH > σV > σh and σV > σH > σh , representing a transition zone between the two stress states. With the increase of burial depth, the permeability of the coal reservoir shows a complex non‐monotonic decline, and the variation of the permeability of the coal reservoir differs under the influence of different stress regimes. Further analysis shows that under the background of stress regime transformation, permeability is mainly affected by the stress value, horizontal principal stress difference, stress regime, and coal cleat, indicating that in situ stress is the main controlling factor of coal reservoir permeability in the Liupanshui Coalfield.


| INTRODUCTION
China is rich in coalbed methane (CBM) resources. According to the available statistics, the amount of CBM resources at shallow depths up to 2000 m is 3.681 × 10 4 billion m 3 . 1 However, most coal seams experience multistage superposition and transformation, as well as tectonic stresses of different properties and intensities, and thus show the characteristics of strong heterogeneity and strong stress sensitivity. The exploration and development of CBM is greatly affected by the current in situ stress changes of coal reservoirs. 2,3 Generally, in situ stress refers to the internal stress that exists in the crust, which is mainly formed by the combination of gravity stress, tectonic stress, pore pressure, thermal stress, and residual stress, among which tectonic stress and gravity stress are the main sources of in situ stress. 4 Tectonic stress is mainly controlled by tectonic movement and rock geological structure, with high complexity and uneven spatial distribution, and its planar and vertical distributions are difficult to describe by mathematical functions. 5 According to the relative relationship between vertical stress ( V ) and tectonic stress (including maximum horizontal principal stress ( H ) and minimum horizontal principal stress ( h )), Anderson (1951) divided in situ stress into the normal faulting stress regime ( V > H > h ), strike-slip faulting stress regime ( H > V > h ), and reverse faulting stress regime ( H > h > V ). 6 The current in situ stress regime is not only one of the main parameters affecting the construction effect of hydraulic fracturing, but also an important factor affecting reservoir fluid migration and accumulation. 4,[7][8][9] Therefore, in the initial stage of CBM development in China, 10,11 using various methods to better understand in situ stress is an effective means of CBM exploration and development. 12 At present, the commonly used methods for in situ stress measurement include mechanical methods, geophysical methods, and geological methods. 13,14 For this paper, based on 25 CBM vertical wells in the Liupanshui Coalfield, the average vertical stress gradient of strata at depths <980 m in this area was estimated using density logging data, and the horizontal principal stress components were calculated using injection/fall-off and in situ stress measurement data. The three components of the stress tensor ( V , H , and h ) and the main stress regimes of coalbearing strata were determined. Based on the above research, combined with the variation of coal reservoir permeability with burial depth in this area, the control mechanism of permeability was explored, including different stress values, horizontal principal stress differences, and the stress regime.

| GEOLOGICAL SETTING
Located in the passive margin fold belt of the upper Yangtze Block of the southern Yangtze Plate, the western Guizhou area is an important part of the upper Yangtze coal-accumulating sedimentary basin in the Upper Permian of western Guizhou, eastern Yunnan, and southern Sichuan. 15 Tectonic activities during the Yanshanian and Himalayan led to the disintegration of the prototype basin, and formed a large number of synclines and synclinoria, which became important coalcontrolling structures in this area ( Figure 1). 16,17 These coalbearing synclines are ideal for the commercial development of CBM in southwestern China.
The Liupanshui Coalfield is located along the middlenorth segment of the Liupanshui fault in southern Guizhou, Yangtze Block. The coalfield is bounded and controlled by the Yadu-Ziyun fault, NW-trending folds and faults are formed in the northeast, the syncline is open, and the anticline is closed. The south of the coalfield is bounded by the Huangnihe-Panjiazhuang fault and is affected by it, characterized by a NE-trending fold and fault structure. The central part of the coalfield is compressed from the north and blocked to the south, forming a mountain-shaped structure, which is dominated by NW-trending ejective folds. 18,19 The main strata exposed in the study area cover a large time span, including Carboniferous, Permian, Triassic, Jurassic, Paleogene, and Quaternary deposits, among which the Permian and Triassic are the most widely distributed. In the Late Permian, the area was characterized by continental, continental-marine transitional, and shallow marine sedimentary environments. 20 During this interval, because of frequent transgression and regression, multiple coal-bearing strata were formed, represented by the Longtan and Changxing formations ( Figure 1).

| Data
In most CBM wells in the study area, density logging, injection/fall-off tests, and in situ stress measurement were used to test reservoir physical properties after completion and before production. For this paper, the data of 54 levels of coal seams in 25 CBM wells were collected and collated; of these wells, density logging data were available for 11 wells, and the density logging sections covered 32 layers. Prior to the calculation phase, the quality of the collected data was checked and corrected. Figure 2 shows the workflow of calculating stress parameters using density logging data, injection/fall-off tests, and in situ stress measurements in this work. The vertical stress of the tested coal seam in each well was calculated using the density logging data, the vertical stress gradient of the shallow layers up to 980 m depth in the study area was then estimated, and the horizontal principal stress of the main coal seams was calculated using the well test and in situ stress measurement data.

F I G U R E 1
Tectonic framework and distribution of coal-bearing synclines in western Guizhou Province, China F I G U R E 2 Workflow for calculating stress parameters using injection/fall-off tests, in situ stress measurements, and density logging data

| Density logging
Density logging data are typically used to estimate overburden pressure or V . 21,22 The calculation equation is as follows: where V is the vertical stress (MPa), (H) is the density of the formation at the depth H (g/cm 3 ), and g is the gravitational acceleration (m/s 2 ).
The necessary curve depth correction and environmental impact correction for density logging were carried out. Some vertical well density logging data in the study area were not recorded from the surface (eg, Well 4 had a depth of 887 m and the starting point of density logging was 250 m), resulting in a lack of shallow density logging data. Thus, an exponential equation was used to fit the formation density of the missing sections of shallow logging data to fill the data gaps between the surface and the starting points of logging. 23,24 The equation is as follows: where (H) syn is the fitting density for the shallow section, R S is the surface sediment density (with a default value of 1.90 g/ cm 3 , based on the Gulf of Mexico), TVD is the true vertical depth, AG is air gas, is the exponent coefficient (default value: 0.6, for Gulf of Mexico), and all depths in the equation are in feet. 25

| Injection/fall-off tests and in situ stress measurement
Injection/fall-off is a single transient test of well pressure, which is suitable for high-and low-pressure reservoirs, and is the most commonly used well testing method in CBM wells ( Figure 3). In this test, water is injected into the well for a period of time with a relatively stable displacement and an injection pressure lower than the fracture pressure of the coal seam, and is then the well is closed, such that the pressure and the original reservoir pressure tend to gradually become balanced. 26 Pressure gauges are used to record the variation of bottom hole pressure with time in the injection and shutin stages. The semilogarithmic curve and double logarithmic curve fitting methods are used to analyze the data, and falloff curve fitting is used to test the analysis results. The parameters of the target coal seam permeability, investigation radius, skin factor, formation coefficient, and reservoir pressure of each CBM well are thus obtained. In addition, combined with the burial depth of the coal seams, the reservoir pressure gradient can be calculated.
After the end of the fall-off test, in situ stress measurement is carried out. During this measurement, fluid is injected into the wellbore at a high injection rate over a very short time. When the bottom hole pressure is higher than the coal seam fracture pressure (P f ), the target layer is opened under the action of the minimum horizontal principal stress. At the moment of the rupture of the coal seam, the pressure is greatly reduced because the liquid cannot be replenished in time; thus, the critical pressure recorded by the digital pressure gauge represents the P f of the coal seam. Then, the well is shut and the pressure fall-off data are obtained through the digital pressure gauge. According to the hydraulic fracturing method of onshore vertical wells, when the fracture is closed, the fracture closure pressure (P C ) is considered equal to h . 27 Therefore, the P f of the coal seam can be obtained from the water injection curve, and the P C can be determined according to the pressure falloff curve. To ensure the accuracy of the measured data, four periods of in situ stress measurements are carried out, and the periods with good fracture and closure effects are selected and analyzed by the time square root method. Then, parameters such as the fracture pressure, and closure pressure of the target coal seam of each CBM well are obtained. Combined with the burial depth of coal seams, the fracture pressure gradient, and closure pressure gradient can be calculated.

| In situ stress magnitude calculation
There are three main methods to determine the current in situ stress 5,10,28-30 : (1) actual stress measurement, (2) calculation based on the logging curve and an empirical model, and (3) numerical simulation. In this study, H and h were calculated using the actual stress measurement data, and the V values of some wells were calculated using density logging data. Based on the vertical stress gradient ( ) of the optimized synthetic density logging, the V values of the target coal seams of the CBM wells with non-density logging data were calculated.
Generally, in case of no fluid flow in vertical wells, h is considered to be equal to P C , and its equation is as follows: According to the theory of elasticity, H can be expressed as: where P f is the fracture pressure of the target layer (MPa), P 0 is the reservoir pressure (MPa), and T is the tensile strength of the coal and rock.
The in situ stress measurement goes through four cycles. For the second to fourth cycles, the fracture is reopened after the water is injected into the wellbore from the wellhead, and the repeated fracture pressure is determined. Because the crack has been produced in the first injection/fall-off cycle, the T of the rock is 0. Therefore, the above equation can be rewritten as follows: For CBM wells without density logging data, V can be estimated from the stress gradient of the overlying strata and the depth of the target layer 31,32 : where is the stress gradient (MP/m), and H is the burial depth (m).

| In situ stress anisotropy
The lateral pressure coefficient ( ) refers to the ratio of the average horizontal principal stress to V , which is an effective parameter to characterize the in situ stress distribution. Its calculation equation is shown in Equation 7. 32 In addition, is generally considered to be proportional to the reciprocal of burial depth, as indicated in Equation 8 10,33 : In this equation, both a and b are coefficients.
In order to quantitatively evaluate the difference of stress in different directions of coal reservoir, the concept of in situ stress anisotropy is introduced, 34,35 and the formula is as follows: where AI is the anisotropy parameter of in situ stress, is the average value of H , h , and V . The increase in AI means that the anisotropy increases, and the decrease of AI means that H , h , and V tend to be the same.

| Magnitude of vertical stress ( V )
As a key step in the workflow, the lack of shallow density logging data is considered to be a challenge for this study. Therefore, in the absence of shallow logging data, synthetic density logging data were used for five CBM wells (Wells 4, 7, 9, 10, and 11). The vertical stress profiles of the above wells were generated by combining the shallow exponential equation fitting density and logging measured density for the whole formation. The calculation equation for shallow synthetic density is shown in Equation 2. Because the density calculated based on the default fitting parameters is not consistent with the actual density, R S and are modified, and the fitting effect of the modified curve is better. Taking Well 4 as an example, two density profiles were simulated. The values of were 0.6 and 0.1, and values of R S were 1.9 g/cm 3 and 1.72 g/cm 3 , respectively. As shown in Figure 4, when the vertical depth was 886 m, V was 21.95 MPa, and the stress gradient was 0.025 MPa/m.
The density logging data of 11 wells in the study area were collected. Among them, six wells were in the Panguan syncline, which had an average stress gradient of ~0.024 MPa/m; two wells were in the Faer syncline, which had an average stress gradient of ~0.023 MPa/m; two wells were in the Tucheng syncline, which had an average stress gradient of ~0.025 MPa/m; and one well was in the Dahebian syncline, which had an average stress gradient is ~0.025 MPa/m. It was determined that the average stress gradient of the 11 wells was ~0.024 MPa/m, and that the stress gradient of different coal-bearing synclines in the study area was stable (0.024 ± 0.001 MPa/m). The density logging section covered 30 well testing levels, accounting for 57.69% of the total well testing levels. This value is considered to be relatively representative ( Table 1).
The above average stress gradient (0.024 MPa/m) was taken as the average value of the drilled strata in the study area, and the vertical stress of the main coal seams in other wells was then calculated ( Table 2).

| Test parameters of injection/fall-off tests and in situ stress measurements
In this study, the injection/fall-off and in situ stress measurement data of 52 well test levels in the study area were collected, and the burial depth of coal seams was between 236.295 and 978.66 m. the coal seam P f , P C , and P 0 all increased linearly with increasing depth, and the correlations are as follows ( Figure 5). This law of change is consistent with the southern Qinshui Basin, the southeastern margin of the Ordos Basin, the southern margin of the Junggar Basin, and eastern Yunnan.
(1) Fracture pressure ( Figure 5A): (2) Shut-in pressure ( Figure 5B): (3) Reservoir pressure ( Figure 5C): In addition, there is an obvious positive correlation between P f and P C (Figure 5D), and the fitting equation is as follows: The injection/fall-off test results show that the permeability was between 0.0018 and 1.46 mD, with an average value of 0.26 mD, which is consistent with a typical low permeability reservoir ( Figure 6).
(10) P f = 0.0694h + 2.6378 (11) P C = 0.0157h + 1.6978 the United States ( h , 1-6 MPa) and the Sydney and Bowen basins in Australia ( h , 1-10 MPa). 36 Within the total dataset, 23 sets of data belong to a strikeslip faulting stress regime ( H > V > h ), accounting for 44.23%; 24 sets of data belong to a normal faulting stress regime ( V > H > h ), accounting for 46.15%; and five sets of data belong to a reverse faulting stress regime ( V > H > h ), accounting for 9.62% (Figure 8). These results are consistent with the understanding obtained from the statistics of several major CBM fields in China by Chen et al. 37 Liupanshui Coalfield has experienced multiperiod tectonic stresses, thus leading to a complex stress regime. As shown in Figures 8 and 9, there are three types of stress fields in the study area, which may be caused by complex local structures. With an increase in depth, the probability of the occurrence of a reverse faulting stress regime decreases to 0, indicating that the growth rate of h is less than those of H and V .
When the burial depth is <600 m, the strike-slip faulting stress regime is dominant, and the normal faulting and F I G U R E 6 Stock chart of in situ stress parameters and permeability in the Liupanshui Coalfield (P coe represents the pressure coefficient, 0 represents the initial reservoir pressure gradient, C represents the shut-in pressure gradient, f represents the fracturing pressure gradient, and k represents the permeability) reverse faulting stress regimes each account for certain proportions, which indicates that there are differences in the stress states of shallow coal seams in different parts of the study area. Shallow coal seams are greatly affected by the structure. When the burial depth is between 600 and 800 m, the proportion of the normal faulting stress regime increases greatly. In this depth range, V increases linearly with increasing burial depth, and the growth rate of H is less than that of V and tends to first decrease and then increase. The growth rate of h is the smallest. When the burial depth is between 800 and 980 m, the normal faulting and strike-slip faulting stress regimes each account for 50%. In addition, V increases linearly with increasing burial depth, and the growth rate of H tends to increase, showing an overall stress state of V ≈ H > h . This can be considered to represent the transition zone between the strike-slip faulting stress regime and the normal faulting stress regime, and the reverse faulting stress regime no longer exists at this depth. The in situ stress regime is not simply transformed from the shallow strike-slip faulting stress regime to the deep normal faulting stress regime. Actually, there is a reversal phenomenon in the vertical.
Generally, when the burial depth is <600 m, the coal seams are dominated by the strike-slip faulting stress regime; when the burial depth is more than 600 m, V of the coal seams increases steadily, the increasing rate of H first decreases and then increases, and the proportion of the normal faulting stress regime increases. In the depth range of 600-980 m, the main coal-bearing strata are affected by both the normal faulting and strike-slip faulting stress regimes. The deep (>1,000 m) well data collected by Kang, et al 38 in the Bide-Santang Basin in an adjacent area show that the stress regime was of the normal fault type. Based on this, it is inferred that with the further increase in drilling depth in the future, the deep coal seams in the study area will mainly be controlled by the stress regime of the normal fault type.

| Principal stress ratio variation with depth
For the Liupanshui Coalfield, is between 0.49 and 1.57, with an average of 0.91. In the Panguan syncline, this value ranges from 0.49 to 1.34, with an average of 0.91; in the Tucheng syncline, it ranges from 0.70 to 1.57, with an average of 0.95; and in the Faer syncline, it ranges from 0.63 to 0.99, with an average of 0.87 ( Figure 10A).
According to an analysis of 3,586 data points collected by Yang et al, 39  In-situ stress magnitude(MPa)  The value of can characterize the relative magnitude between the horizontal principal stress and V . With the increase in burial depth, decreases slowly, indicating that gravity stress has progressively more influence on in situ stress. Meanwhile, AI and H − h show similar characteristics of change. Both of them take 700 m as the limit, and gradually increase when the burial depth is <700 m and decrease when the burial depth is more than 700 m. It shows that under the background that V increases steadily with the burial depth, AI is mainly controlled by H − h (Figure 10B,C).
When the burial depth is more than 800 m, AI and H − h are significantly reduced. Most values of are <1, indicating that at 800 m, gravity stress begins to become dominant in the overlying strata of the deep coal seams ( Figure 10A). This finding is consistent with the analysis results in Section 4.3.
also shows a small increase in the depth, which is consistent with the reversal of the stress regime.

| Implication for coal permeability
Coal reservoir permeability is one of the key factors determining CBM productivity, 40,41 which is mainly affected by effective stress, matrix shrinkage, and gas slippage in the process of CBM development. [42][43][44] Previous studies generally suggested that the permeability of a coal reservoir decreases exponentially with the increase of effective stress. In the initial stage of CBM development or in an undeveloped coal reservoir, the coal reservoir is in a state of stress equilibrium, and the permeability is mainly affected by in situ stress and the coal cleat system. The increase of burial depth and stress concentration caused by local structure will lead to the exponential decrease of permeability. [45][46][47][48] Under the background of a high-pressure compression structure, the permeability of a coal reservoir changes regularly with burial depth, but its trend is not monotonous. 49 Li, Tang, Xu, and Yu 40 revealed that the permeability of coal decreased to a depth of about 700 m and then increased from a depth of 700 m to about 1050 m in the Liulin area, eastern Ordos Basin. Sun et al 50 found that the coal seam permeability of the Shizhuang CBM block decreased to a depth of (14) 8.57∕h + 0.32 ≤ ≤ 350.16∕h + 1.00 (15) = 135.00∕h + 0.68 (16) 100.26∕h + 0.31 ≤ ≤ 220.96∕h + 1.03 F I G U R E 1 0 Lateral pressure coefficient distribution, anisotropy, and the difference between the maximum and minimum horizontal principal stress. Scatter diagram and fitting results of the parameter λ and burial depth (A), anisotropy as a function of burial depth (B), the difference between the maximum and minimum horizontal principal stress varies with burial depth (C)  about 950 m, increased at depths of 950 and 1100 m, and then decreased at depths of more than 1100 m. Chen, Tang, Tao, Xu, Li, Zhao, Ren, and Fu also found a similar nonmonotonic change in permeability in the south of the Qinshui Basin and at the eastern margin of the Ordos Basin. 37 It was also noted that in the vertical direction, the permeability-depth profile in the study area had the characteristics of high permeability (<400 m)-low permeability (400-600 m)-high permeability (600-800 m)-low permeability (800-980 m) ( Figure 11).
Further analysis shows that the variation of coal reservoir permeability with burial depth differs under different stress regimes. A relative high permeability zone under the control of a normal faulting stress regime mainly appears in the burial depth interval of 600-800 m ( Figure 11A), a relatively high permeability area under the control of a strike-slip faulting stress regime mainly appears in the burial depth ranges of <400 m and 600-800 m ( Figure 11B), and the reverse faulting stress regime mainly appears at depths shallower than 650 m; in addition, the permeability decreases with the increase of burial depth ( Figure 11C). The results of the comparison show that when the burial depth of the coal seam is more than 600m, the coal permeability in a normal faulting stress regime is higher than that in a strike-slip faulting stress regime, which is due to the low compressive stress under normal faulting stress regime. 51,52 With the increase in burial depth, the principal stress increases linearly (Figure 7), but the permeability does not simply decrease exponentially with the increase of principal stress, which is worthy of further exploration. The appearance of the shallow hyperpermeability zone (0-400 m) is essentially attributed to the opening of cracks caused by stress relaxation under near-surface conditions ( Figures 10C, 11B, and 12). The smaller H − h shown in Figure 10C provides evidence for horizontal stress relaxation. The decrease of permeability in the range of 400 to 600 m reflects that the permeability is very sensitive to stress, which is affected by strong structural compression; the horizontal principal stress increases, and the stress regime is mainly of the strike-slip faulting type, which is affected by horizontal compressive stress. The vertical fractures are closed, and the permeability decreases greatly. In the range of 600 to 800 m, H − h and AI reach their peak and then begin to decrease. Between this zone, H − h and AI reach their highest. The high H − h and AI may enhance the initial friction failure state of coal, 38 and its positive effect on permeability is greater than the negative effect of stress increase, which leads to the increase of permeability in this zone. For the points under the control of the normal faulting and strike-slip faulting stress regimes ( Figure 11A and 11B), the permeability of coal increases with the increase of the principal stress difference. In the range of 800 to 980 m, the principal stress values reach 14.50 MPa, 18.45 MPa, and 22.75 MPa, respectively ( Figure 7). Coupled with the decrease of H − h , the coal reservoir is strongly squeezed by three-dimensional stress, and the coal permeability decreases with the increase of stress. The permeability of coal is also controlled by the natural fracture structure and its degree of opening. The structure of the study area is complex, and there are two structural types of coal 53 : the fold genetic type and fault genetic type. The complexity of the coal reservoir cleat system and strong stress sensitivity may be the main reasons for the discrepancy between the permeability variation in the study area and the conventional understanding that permeability decreases exponentially with the increase in burial depth/stress. Generally, the vertical change of permeability is affected by vertical stress, local tectonic stress, and the coal cleat F I G U R E 1 1 Permeability varies with burial depth under different stress regimes. Coal reservoir permeability variation with burial depth under a normal faulting stress regime (A), coal reservoir permeability variation with burial depth under a strike-slip faulting stress regime (B), and coal reservoir permeability variation with burial depth under a reverse faulting stress regime (C) system. The data collected in this study are relatively few, and the above judgment is preliminarily. It needs to be verified and improved after more data are obtained, and the nonmonotonic decline characteristics of increasing permeability with burial depth need to be studied further.

| CONCLUSIONS
In this paper, the in situ stress characteristics of coal seams in Liupanshui Coalfield were studied, the non-monotonic decrease of permeability with burial depth was revealed, and the effect of in situ stress on the coal reservoir permeability was evaluated. The main conclusions are as follows:

The average stress gradient of different coal seams in
Liupanshui Coalfield is about 0.024 MPa/m. There are mainly two stress regimes: normal faulting type (46.15%) and strike-slip faulting type (44.23%). The proportion of reverse faulting type is only 9.62%. 2. In the ranges of different depths, there is a phenomenon of mutual transformation of the stress regime. The stress regime of the shallower than 600 m is mainly of the strikeslip type, the stress regime of 600-800 m is dominated by the normal faulting type, and the 800-980 m interval is influenced roughly equally by both the normal faulting type and strike-slip faulting type. With the increase of burial depth, gradually decreases to a fixed value, and that value is generally <1, indicating that the vertical stress of the deep formation becomes the principal stress. 3. The variation of coal reservoir permeability with burial depth is different under different stress regimes. With the increase in burial depth, the permeability decreases nonmonotonously, and its value is controlled by the relative magnitude of in situ stress.

F I G U R E 1 2
The permeabilities of different depths vary with burial depth, (Note: the blue and green regular triangle with low permeability in the extreme left in Figure 12 is excluded from correlation analysis, these two data points are considered as outlier data points)