Introduction

The porosities and fractures of coal seams influence coalbed methane (CBM) accumulation zones and migration channels, therefore highlighting the importance of understanding these structural features to optimise CBM exploitation (Fan et al. 2010; Gerami et al. 2016; Mostaghimi et al. 2017). Previous studies have shown that the development of coal rock porosities and fractures is controlled by the coalification process and the geological evolution of the tectonic stress field, with the extension direction of the natural fractures primarily influenced by the modern tectonic stress state (Shen et al. 2014; Matsumoto et al. 2015; Guo et al. 2016).

In situ stresses consist of tectonic and gravitational stresses. The tectonic stresses, which extend horizontally, are classified into maximum and minimum horizontal stresses, whereas the gravitational stress extends vertically and originates from the overburden rock. The gravitational stress is therefore calculated as the product of the rock bulk density and depth (Brown and Hoek 1978; Hoek and Brown 1980). However, the tectonic stresses change with geological evolution of the strata and belong to the relatively complex spatial distribution of the unsteady stress field (Kang et al. 2009a, b). Determination of the stress field distribution is therefore important for estimating the geological structures and types of permeable fractures, both of which shape the production potential of CBM reservoirs (Gentzis 2009; Chatterjee and Pal 2010; Liu et al. 2016).

Permeability is the main reservoir parameter that determines CBM production. Numerous studies have observed the negative exponential relationship between the effective stress and coal reservoir permeability (Connell et al. 2010; Yin et al. 2012; Shi et al. 2014a; Zhang et al. 2015; Zhao et al. 2015; Wang et al. 2017). A large number of permeability prediction models based on the effective stress have also been established (Pan and Connell. 2012; Xu et al. 2014; Chen et al. 2014; Shi et al. 2014b; Connell 2016). However, most of these models were developed under a pseudo/true triaxial stress state in laboratory settings. There are some significant differences between experimental and in situ coal seam conditions, such as the size of coal samples, the number and width of fractures and geological structures. Furthermore, the porosity and permeability of coal reservoirs are extremely low in China, which results in the permeability being highly sensitive to stress changes (Palmer and Mansoori 1996; Connell 2009; Lin and Kovscek 2014). This combination of the complicated in situ stress distribution, strong stress sensitivity to stress changes and low permeability complicates the feasibility of estimating CBM development potential. It is therefore necessary to study the spatiotemporal evolution of the in situ stress states throughout the targeted coal seam and its influence on coal reservoir permeability, which will provide a theoretical basis for CBM development in the study area.

In this paper, in situ stress data from 54 CBM wells in the southern Qinshui Basin, China, were obtained by the injection/falloff test method to study the distribution rule of the in situ stress state and its influence on coal reservoir permeability.

Geological setting

The study area is located in the southern Qinshui Basin, Shanxi Province, China. The main tectonic features of the Qinshui Basin consist of a large NNE–SSW-striking complex syncline, some NNE-striking sub-folds and NE-striking sub-faults (Fig. 1). The northern extent of southern Qinshui Basin reaches 36° N, is fold- and fault-bounded around the rest of the basin and covers an area of approximately 1 × 104 km2.

Fig. 1
figure 1

Geological structure map of the Qinshui Basin, China, and the location of the study area

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The main coal seams in the southern Qinshui Basin are the no.3 coal seam in the Permian Shanxi Formation and no.15 coal seam in the Upper Carboniferous Taiyuan Formation. The no.3 coal seam is distributed throughout the entire area, with an average coal seam thickness of 5.93 m that ranges from 2.4 to 8.1 m. It is the target zone of CBM development. The no.3 coal mainly consists of bituminous and anthracite coal with a high rank and Ro,max values in the 1.87–4.26% range.

Methodology

Injection/falloff well tests were used to acquire the coal reservoir parameters, such as the reservoir pressure, permeability and temperature. The injection/falloff well test procedure is as follows. Water is injected into the coal reservoir at a constant rate for 12 h and is then stopped, with the injection shut down for at least 24 h to obtain a complete injection/falloff curve. The bottom-hole pressure was measured using a down-hole pressure gauge during the injection and shut-in periods. The coal reservoir parameters were estimated by processing the injection/falloff curve. The straight-line analysis method and chart-board -matching analysis method were available to process the well test data. The straight-line analysis method was employed here. Pressure history matching curves were used to guarantee the validity of the data and confirm the results. However, the maximum injection pressure must be taken into account to obtain credible test results because of the impact stress has on the coal reservoir permeability. A minifrac test is therefore necessary to determinate the maximum injection pressure.

A multi-cycle hydraulic fracturing test was conducted to accurately calculate the breakdown and shut-in pressures. Two to three curves with better breakdown and shut-in effects were selected from the injection/falloff curves to calculate the parameter values. The pressure injection and pressure falloff curves were used to calculate the breakdown and shut-in pressures, respectively.

The breakdown and shut-in pressures of the coal reservoir were used to calculate the in situ stress parameters (Bredehoeft et al. 1976; Haimson and Cornet 2003). The horizontal principal stresses can be obtained from Eqs. (1) and (2):

$$ {p}_{\mathrm{c}}={\sigma}_{\mathrm{h}} $$
(1)
$$ {\sigma}_{\mathrm{H}}=3{p}_{\mathrm{c}}-{p}_{\mathrm{f}}-{p}_0+T $$
(2)

where σh and σH represent the minimum and maximum horizontal principal stresses (MPa), respectively; pc is the fracture shut-in pressure (MPa); pf is the breakdown pressure of the coal seam (MPa); p0 is the reservoir pressure (MPa); and T is the tensile strength of the coal seam (MPa).

The fracture was fractured repeatedly to obtain the reopened fracture pressure from the multi-cycle hydraulic fracturing process. The tensile strength of the coal seam approached zero after the coal seam fractured, and the reopened pressure of fracture could be expressed as:

$$ {p}_{\mathrm{r}}=3{p}_{\mathrm{c}}-{\sigma}_{\mathrm{H}}-{p}_0 $$
(3)

where pr is the reopened fracture pressure (MPa).

The computational formula for the tensile strength was obtained by substituting Eqs. (1) and (3) into Eq. (2) as follows:

$$ T={p}_{\mathrm{f}}-{p}_{\mathrm{r}} $$
(4)

The vertical principal stress is mainly due to the weight of the overlying rock strata. The vertical principal stress can be calculated from Eq. (5) (Brown and Hoek 1978; Hoek and Brown 1980):

$$ {\sigma}_{\mathrm{v}}=\gamma H=0.027H $$
(5)

where σv is the vertical principal stress (MPa); γ is the rock bulk density (kN/m3); and H is coal seam depth (m).

Results

Test parameters

The relevant parameters for the test data from the 54 CBM wells that sampled the no.3 coal seam in the southern Qinshui Basin are listed in Table 1.

Table 1 Injection/falloff and in situ stress test parameters in the study area (the range and mean of each parameter value are provided)
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The test results (Table 1) indicate that the initial reservoir pressure gradient (δ0) is 0.07–1.08 MPa/100 m, with a mean value of 0.70 MPa/100 m, and 96% of the test wells possessing a pressure gradient that is lower than the hydrostatic gradient (0.98 MPa/100 m). The coal reservoir permeability is 0.01–1.02 mD, with a mean value of 0.14 mD, and 98% of the test wells yielding values lower than 1 mD. The coal reservoir in the study area should therefore be classified as an underpressured, low-permeability reservoir according to Pashin (2007) and Mazumder et al. (2012).

The positive linear relationships between the coal seam depth and the reservoir, breakdown and the shut-in pressures are shown in Fig. 2. The fitting formulas are as follows:

$$ {p}_0=0.01H-2.2726 $$
(6)
$$ {p}_{\mathrm{f}}=0.0182H+3.2136 $$
(7)
$$ {p}_{\mathrm{c}}=0.0178H+2.6093 $$
(8)
Fig. 2
figure 2

Relationship between the injection/falloff test parameters and coal seam depth. a Relationship between the reservoir pressure and coal seam depth. b Relationship between the breakdown pressure and coal seam depth. c Relationship between the shut-in pressure and coal seam depth

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The distribution rule of the in situ stress state

Positive linear relationships exist between the coal seam depth and the maximum and minimum horizontal principal stresses, as shown in Fig. 3. The relevant relationships are as follows:

$$ {\sigma}_{\mathrm{H}}=19.303H+281.71 $$
(9)
$$ {\sigma}_{\mathrm{h}}=35.348H+211.17 $$
(10)
Fig. 3
figure 3

Relationships between the principal stresses and coal seam depth

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Three different in situ stress states are observed in the study area, as shown in Fig. 4. For σH > σh > σv, the coal seam depth ranges from 518 to 846 m, with a mean depth of 626 m. For σH > σv > σh, the coal seam depth ranges from 461 to 1272 m, with a mean depth of 828 m. For σv > σH > σh, the coal seam depth ranges from 641 to 1423 m, with a mean value of 905 m. The in situ stress states of the coal seam from its shallow to deep extent are therefore σH > σh > σv, σH > σv > σh and σv > σH > σh, respectively.

Fig. 4
figure 4

The coal seam depth under the different in situ stress states

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The quantity and percentage of the different in situ states in the study area are shown in Fig. 5. There are five CBM wells where σH > σh > σv, which accounts for 9% of the test wells. There are 41 CBM wells where σH > σv > σh, which accounts for 76% of the test wells. There are eight CBM wells where σv > σH > σh, which accounts for 15% of the test wells. The in situ stress state of the coal seam is therefore dominated by σH > σv > σh in the study area.

Fig. 5
figure 5

The quantity and percentage of the different in situ stress states

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The influence of the in situ stress state on permeability

Coal reservoir permeability directly influences the productivity of a CBM well. Field and laboratory tests both show that there is a negative exponential relationship between the coal reservoir permeability and effective stress as follows (Connell et al. 2010; Yin et al. 2012; Shi et al. 2014a; Zhang et al. 2015; Zhao et al. 2015; Wang et al. 2017):

$$ k={k}_0{e}^{-a{\sigma}_e} $$
(11)

where k represents the permeability (mD); k0 is the initial permeability (mD); σe represents the effective stress (MPa); and α is the fitting coefficient.

The variations in permeability with the principal stresses are analysed in Fig. 6. There is a rapid decrease in permeability with increasing σH when σH is less than 22 MPa, as shown in Fig.6a. The decrease in permeability slows down when σH is greater than 22 MPa. The permeability rapidly decreases with increasing σh when σh is less than 15 MPa, as shown in Fig. 6b. The decrease in permeability slows down when σh is greater than 15 MPa. The permeability first decreases with increasing σv, then increases and finally decreases, as shown in Fig. 6c. This indicates that the coal reservoir permeability variations due to σv are relatively complex. The observed variation in permeability with σv is consistent with that of Zhao et al. (2016).

Fig. 6
figure 6

The variations in permeability with the principal stresses. a The variation in permeability with the maximum horizontal principal stress. b The variation in permeability with the minimum horizontal principal stress. c The variation in permeability with the vertical principal stress

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The mean permeability exhibits a decrease-increase variation with the in situ stress states from the shallow to deep extent of the coal seam, as shown in Fig. 7. The mean permeability is lowest when σH > σv > σh, and the mean permeability is largest when σv > σH > σh. The mean permeability is intermediate when σH > σh > σv.

Fig. 7
figure 7

The variations in mean permeability under the different in situ stress states

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A comparison of Fig. 6c with Fig. 7 illustrates how the variation in permeability with σv (< 24 MPa) has the same variation trend as the variation in mean permeability with the shallow to deep in situ stress states. The principal stresses continue to increase after σv > σH > σh, and the in situ stress state eventually reaches a hydrostatic stress state, where σv = σH = σh (Hoek and Brown 1980). This results in the coal reservoir being under compression, which promotes fracture closure (Meng et al. 2010). This indicates that the coal reservoir permeability is extremely low when σv = σH = σh and rapidly decreases after σv > σH > σh. The variation in permeability with the in situ stress states from the shallow to deep extent of the coal seam therefore follows a decrease-increase-decrease trend that is consistent with the variation in permeability with σv. The variation in permeability with σv is due to the conversion of the in situ stress states.

Discussion

Anderson’s three stress regimes classified the in situ stress states into normal stress, strike-slip and thrust regimes (Anderson 1951). σv is the largest principal stress in the normal stress regime, where σv > σH > σh. σv is the intermediate principal stress in the strike-slip regime, where σH > σv > σh. σv is the least principal stress in the thrust regime, where σH > σh > σv.

The strike-slip regime (σH > σv > σh) is conducive to forming a strike-slip fault, where the fracture propagation shape of the rock strata is shear fracture with horizontal movement, as shown in Fig. 8a. The normal stress regime (σv > σH > σh) is conducive to forming a normal fault, where the fracture propagation shape of the rock strata is tensile fracture with vertical movement, as shown in Fig. 8b. The thrust regime (σH > σh > σv) is conducive to forming a reverse fault, where the fracture propagation shape of the rock strata is shear fracture with vertical movement, as shown in Fig. 8c.

Fig. 8
figure 8

Tectonic settings under the different in situ stresses. a The strike-slip regime. b The normal stress regime. c The thrust regime

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The mean permeability has obvious differences under the different in situ stress states, as shown in Fig. 7. The mean permeability decreases from σH > σh > σv to σH > σv > σh, and the fracture propagation shape changes from shear fracture with vertical movement to shear fracture with horizontal movement. This demonstrates that the horizontal movement of the coal seam decreases the coal reservoir permeability, whereas the vertical movement of the coal seam is conducive to enhancing the coal reservoir permeability. The mean permeability increases from σH > σv > σh to σv > σH > σh, and the fracture propagation shape changes from shear fracture with horizontal movement to tensile fracture with vertical movement. This indicates that tensile fracture is conducive to enhancing the coal reservoir permeability. The permeability differences are therefore caused by the fracture propagation shape of rock strata.

Conclusions

  1. 1.

    The maximum and minimum horizontal principal stresses have positive linear relationships with coal seam depth in the southern Qinshui Basin. The three in situ stress states are σH > σh > σv, σH > σv > σh and σv > σH > σh from the shallow to deep extent of the coal seam, respectively. The in situ stress state of the coal seam is dominated by σH > σv > σh in the study area.

  2. 2.

    Coal reservoir permeability decreases with increasing horizontal principal stresses, whereas it first decreases with increasing σv, then increases and finally decreases. This variation in permeability with σv is due to the conversion of the in situ stress states.

  3. 3.

    The permeability is the largest when σv > σH > σh, followed by σH > σh > σv and smallest when σH > σv > σh for the three different in situ stress states. The permeability differences are caused by the fracture propagation shape of the rock strata under different in situ stress states.