In-situ stress distribution and coalbed methane reservoir permeability in the Linxing area, eastern Ordos Basin, China

Abstract

Understanding the distribution of in-situ stresses is extremely important in a wide range of fields such as oil and gas exploration and development, CO₂ sequestration, borehole stability, and stress-related geohazards assessment. In the present study, the in-situ stress distribution in the Linxing area of eastern Ordos Basin, China, was analyzed based on well tested parameters. The maximum horizontal principal stress (S_Hmax), minimum horizontal principal stress (S_hmin), and vertical stress (S_v) were calculated, and they were linearly correlated with burial depth. In general, two types of in-situ stress fields were determined in the Linxing area: (i) the in-situ stress state followed the relation S_v>S_Hmax>S_hmin in shallow layers with burial depths of less than about 940 m, indicating a normal faulting stress regime; (ii) the S_Hmax magnitude increased conspicuously and was greater than the S_v magnitude in deep layers with depths more than about 940 m, and the in-situ stress state followed the relation S_Hmax>S_v>S_hmin, demonstrating a strike-slip faulting stress regime. The horizontal differential stress (S_Hmax–S_hmin) increased with burial depth, indicating that wellbore instability may be a potentially significant problem when drilling deep vertical wells. The lateral stress coefficient ranged from 0.73 to 1.08 with an average of 0.93 in the Linxing area. The coalbed methane (CBM) reservoir permeability was also analyzed. No obvious exponential relationship was found between coal permeability and effective in-situ stress magnitude. Coal permeability was relatively high under a larger effective in-situ stress magnitude. Multiple factors, including fracture development, contribute to the variation of CBM reservoir permeability in the Linxing area of eastern Ordos Basin.

Keywords

in-situ stress / coalbed methane / permeability / lateral stress coefficient / Linxing area / Ordos Basin

Introduction

In general, the in-situ stress field and permeability are fundamental factors for coalbed methane (CBM) development (^{Zhao et al., 2016}; ^{Sun et al., 2017}). In-situ stress is a type of internal stress in the Earth’s crust, and it is greatly affected by tectonic and gravitational forces (^{Zoback et al., 2003}; ^{Kang et al., 2010}; ^{Zhou and Burbey, 2016}). Knowledge of in-situ stress is significant in the fields of geologic science and engineering because it is essential to achieve a better understanding of phenomena related to oil and gas exploration and development (^{Finkbeiner et al., 2001}; ^{Bell, 2006}; ^{Tingay et al., 2009}, ²⁰¹⁰; ^{Meng et al., 2011}; ^{Li et al., 2014}; ^{Ju and Sun, 2016}; ^{Ju et al., 2017}), borehole stability (^{Zoback et al., 2003}; ^{Tingay et al., 2009}; ^{Nian et al., 2016}; ^{Rajabi et al., 2016}; ^{Ju et al., 2017}), CO₂ sequestration (^{Bustin et al., 2008}; ^{Konstantinovskaya et al., 2012}), reservoir management (^{Sibson, 1994}; ^{Binh et al., 2007}; ^{Nian et al., 2016}), etc.

Coal seams serve as important reservoirs as they contain CBM adsorbed onto the inner surfaces. Estimation of in-situ stress for coal bearing strata has been applied widely in underground coal mines and CBM explorations within many coal basins (^{Bell and Bachu, 2003}; ^{Bell, 2006}; ^{Gentzis, 2009}; ^{Meng et al., 2011}). Coal permeability is the dominant factor in CBM productivity, which is greatly influenced by the in-situ stress magnitude and orientation. Until now, it was generally accepted that, when other factors (e.g., fracture development; ^{McKee et al., 1988}; ^{Ye et al., 1999}) are equal, coal permeability decreases exponentially with increased effective stress magnitude (^{White et al., 2005}; ^{Bustin et al., 2008}; ^{Li et al., 2014}). Information of in-situ stress can facilitate the prediction of permeability and fluid flow in CBM reservoirs (^{Bell and Bachu, 2003}; ^{Bell, 2006}). Therefore, an accurate understanding of the in-situ stress distribution is of immense importance for CBM reservoir permeability evaluation and recoverability assessment during CBM development (^{Meng et al., 2011}; ^{Paul and Chatterjee, 2011}; ^{Li et al., 2014}; ^{Zhao et al., 2016}).

The Carboniferous and Permian sedimentary rocks in the Linxing area of eastern Ordos Basin host a significant volume of CBM resources in China (^{Guo et al., 2012}). Insights into the in-situ stress state can effectively guide CBM exploration and development. Therefore, in this study, based on the well test parameters in the Linxing area, the in-situ stress distribution and types were first studied. Subsequently, the variation of coal permeability and the influencing factors were analyzed. The results can provide a reference for CBM accumulation and production in the Linxing area of eastern Ordos Basin.

Geological setting

The Ordos Basin is a typical intra-continental basin situated in central China. It extends over 2.5×10⁵ km² (^{Ritts et al., 2004}; ^{Ju et al., 2015}; Fig. 1). The Linxing area is economically significant and is located in the eastern Ordos Basin (Fig. 1), which is famous for widely distributed CBM resources (^{Guo et al., 2012}). The tectonic structure is relatively stable and the stratigraphic strike is approximately NE-SW-trending with a westward dip of approximately 5°–10° (^{Yang, 2002}; ^{Ju et al., 2015}).

In the Linxing area, the Carboniferous and Permian (mainly the Shanxi, Taiyuan, and Benxi Formations) sedimentary rocks contain a significant volume of CBM resources (^{Yang, 2002}; ^{Guo et al., 2012}). The Benxi Formation (e.g., Well L-8, –1922.50 m to –1853.10 m), containing 1–4 coal seams, developed in a tidal flat-lagoon depositional system with a thickness of 51–70 m. The Taiyuan Formation (e.g., Well L-8, –1853.10 m to –1783.20 m) was predominantly deposited in a tidal flat and delta system, and its thickness ranges from 33 m to 76 m. The Shanxi Formation (e.g., Well L-8, –1783.20 m to –1678.00 m), containing 2–5 coal seams, was essentially deposited in a shallow water delta, lagoon-gulf sedimentary environment with a thickness of approximately 87–130 m (^{Gu et al., 2016}; ^{Zhao et al., 2016}). These three large and well preserved coal-bearing formations in the Linxing area provide a good basis for CBM generation and accumulation (^{Guo et al., 2012}; ^{Zhao et al., 2016}).

The commercial coal seams in the Linxing area are No. 4+5 coal seam of Shanxi Formation and No. 8+9 coal seam of Benxi Formation. The No. 4+5 coal seam is 0–8.8 m thick with an average thickness of 4.8 m. The No. 8+9 coal seam is 2.7–11.8 m thick with an average thickness of 7.1 m. The average vitrinite reflectance of the No. 4+5 and No. 8+9 coal seam varies primarily in the intervals of 0.75%–1.46% and 0.73%–1.50%, respectively, indicating that they are in the middle to late maturation stage, and can generate large amounts of hydrocarbons.

In-situ stress distribution

Methodology

The S_v, that is the lithostatic or overburden stress, is induced by the weight of overlying formations. The magnitude of S_v is usually assumed to be the most easily obtained component of the in-situ stress tensor because it can be calculated by integrating density logs (Eq. (1); ^{Bell and Bachu, 2003}; ^{Meng et al., 2011}; ^{Rajabi et al., 2016}).

(1){{\displaystyle S}}_v={\displaystyle {\int }_{\mathrm{0}}^z\rho (z)}g\mathrm{dz,}

where r(z) is the density, z is depth and g is the acceleration due to gravity.

Previous studies (e.g., ^{Brown and Hoek, 1978}; ^{Hoek and Brown, 1980}; ^{Meng et al., 2011}) suggested that the magnitude of S_v can be accurately estimated by using Eq. (2):

(2){{\displaystyle S}}_v=\mathrm{0.027}z.

The S_hmin is a key parameter in the designs of well drilling and reservoir stimulation. Several methods are available to determine the magnitude of S_hmin, and among them, the leak-off test (LOT) is an effective approach (^{Enever et al., 1996}; ^{White et al., 2002}; ^{Bell and Bachu, 2003}; ^{Zoback, 2007}). In LOTs, the mud pressure in an open and isolated section of wellbore is increased to create a small tensile fracture (^{Zoback et al., 2003}). In this study, extended leak-off tests (XLOTs), which can provide reliable information for calculating the magnitude of S_hmin, were conducted. XLOTs are longer and more comprehensive LOTs, wherein pumping is not stopped immediately after the leak-off pressure is observed. In addition, the fracture closure pressures (P_c) can be obtained through XLOTs (^{Enever et al., 1996}; ^{White et al., 2002}; ^{Brooke-Barnett et al., 2015}; ^{Rajabi et al., 2016}).

Depending on the parameters obtained from the XLOTs, the magnitude of S_hmin, which is the magnitude of P_c at the test depth, can be determined (Eq. (3); ^{White et al., 2002}; ^{Zoback et al., 2003}).

(3){{\displaystyle S}}_{h\min }={{\displaystyle P}}_c,

where P_c is the fracture closure pressure.

The S_Hmax magnitude is estimated based on additional information or assumptions (^{Zoback, 2007}). For a vertical borehole and no fluid penetration in the formation, the magnitude of S_Hmax can be estimated based on Eq.4 (^{Hubbert and Willis, 1957}).

(4){{\displaystyle S}}_{H\max }=\mathrm{3}{{\displaystyle S}}_{H\min }-{{\displaystyle P}}_f-{{\displaystyle P}}_o+T,

where P_f is the recorded formation break-down pressure, P_o is the pore pressure, and T is the tensile strength of the rock.

All the parameters except for T can be obtained from the XLOT pressure records in Eq. (4). As the existing fractures retain no tensile strength during the second pressurizations, ^{Bredehoeft et al. (1976)} suggested that Eq. (4) can be simplified and rewritten as Eq. (5).

(5){{\displaystyle S}}_{H\max }=\mathrm{3}{{\displaystyle S}}_{H\min }-{{\displaystyle P}}_r-{{\displaystyle P}}_o

where P_r is the reopening pressure at which closed fractures begin to reopen during repeated pressurizations.

In general, three types of in-situ stress regimes can be determined based on the relative magnitudes of S_Hmax, S_hmin, and S_v (^{Anderson, 1951}; Fig. 2):

(i) normal faulting stress regime: S_v>S_Hmax>S_hmin;

(ii) strike-slip faulting stress regime: S_Hmax>S_v>S_hmin;

(iii) reverse faulting stress regime: S_Hmax>S_hmin>S_v.

Variation in the in-situ stress magnitudes with depth

The parameters of P_o, P_f, P_r, and P_c are important for calculating in-situ stress magnitudes. In the Linxing area, all these parameters increase linearly with burial depth (Fig. 3).

(i) pore pressure, (R= 0.91);

(ii) formation break-down pressure, (R= 0.80);

(iii) reopening pressure, (R= 0.73);

(iv) fracture closure pressure, (R= 0.81).

In the present study, based on 11 sets of parameters in the Linxing area, the magnitudes of S_v, S_Hmax, and S_hmin were calculated using Eqs. (2), (3), and (5) (Table 1), and further, they were both linearly correlated with burial depth (Fig. 4).

(i) S_Hmax: (R= 0.60);

(ii) S_hmin: (R= 0.81).

Generally, in sedimentary basins, the magnitude of S_hmin is usually around 70% of the S_v magnitude (^{Meng et al., 2011}). However, based on the calculation results (Fig. 4(a)), the calculated S_hmin may not accurately describe the actual S_hmin magnitude and its variation in the Linxing area of eastern Ordos Basin.

In the Linxing area, the stress regime in the main coal-bearing strata was a strike-slip faulting regime (S_Hmax>S_v>S_hmin; Fig. 4). Furthermore, the in-situ magnitude variation suggested that the stress regime followed the relation S_v>S_Hmax>S_hmin at depths less than approximately 940 m, indicating a normal faulting stress regime. In deep layers, the S_Hmax magnitude increased conspicuously and was greater than the S_v magnitude at depths more than approximately 940 m. The in-situ stress regime changed to S_Hmax>S_v>S_hmin in the deep layers, indicating a strike-slip faulting stress regime (Fig. 4(b)). The vertical transformation depth of the in-situ stress regime in the Linxing area was approximately 940 m (Fig. 4(b)).

The Zijinshan intrusive complex, situated at the east of Linxing area, formed mainly in 136.7–130.4 Ma of the Early Cretaceous (^{Chen et al., 2012}). The rapid uplift-cooling process that occurred since 10 Ma at an average rate of 7°C/Ma caused changes in the subsurface structures. This resulted in the formation of many radial faults and variations in the burial depth of the overlying strata. As the S_v, S_Hmax, and S_hmin magnitude all increased linearly with burial depth, the in-situ stress distribution in regions near the Zijinshan intrusive complex also changed.

In addition, the relationship between the in-situ stress magnitudes and burial depth also indicated that the horizontal differential stress (S_Hmax–S_hmin) increased with burial depth (Fig. 4(b)). Therefore, for a vertical well, wellbore instability may be a potentially significant problem when drilling deep wells in the Linxing area because of the increasing (S_Hmax–S_hmin) magnitude.

Stress ratio variation with burial depth

Generally, the lateral stress coefficient (\lambda) is defined and used to express the in-situ stress state at some point underground (Fig. 5; Brown and Hoek, 1978; Hoek and Brown, 1980; Meng et al., 2011; Yang et al., 2012). The coefficient is the ratio of the average horizontal stress magnitude (namely S_Hmax/2+S_Hmix/2) to vertical stress magnitude (Eq. (6)):

(6)\lambda ={\displaystyle \frac{{{\displaystyle S}}_{H\max }+{{\displaystyle S}}_{H\min }}{{{\displaystyle \mathrm{2}S}}_v}},

where l is the lateral stress coefficient.

^{Brown and Hoek (1978)} summarized the in-situ stresses worldwide (Fig. 5(a)) and found that the l generally varied within limits defined by Eq. (7):

(7){\displaystyle \frac{\mathrm{100}}{h}}+\mathrm{0.30}\le \lambda \le {\displaystyle \frac{\mathrm{1500}}{h}}+\mathrm{0.50.}

Based on the expression of the inner and outer Hoek-Brown envelopes, l can be rewritten in a general form (Eq. (8)) to reveal the linear relationship between l and the reciprocal of burial depth.

(8)\lambda ={\displaystyle \frac{a}{h}}+b,

where h is the burial depth, and a and b are coefficients.

Following Brown and Hoek’s method, ^{Yang et al. (2012)} analyzed the in-situ distribution pattern in China (Fig. 5(b)) based on 3586 data values. The results indicated that l in China generally varied within the limits defined by Eq. (9):

{\displaystyle \frac{\mathrm{8.57}}{h}}+\mathrm{0.322}\le \lambda \le {\displaystyle \frac{\mathrm{350.16}}{h}}+\mathrm{1.003.}

In the Linxing area, l ranged from 0.73 to 1.08 with an average of 0.93 (Fig. 6). Obviously, all the values lie between the inner and outer Hoek-Brown in-situ stress envelopes representing the relationship between lateral stress coefficient and burial depth worldwide as well as in China (Fig. 6). The l value also indicated that the in-situ stresses determined from the XLOTs were credible.

Furthermore, in the Linxing area, the ratio of S_Hmax/S_hmin ranged from 1.08 to 1.51 with an average of 1.38, the S_v/S_Hmax ratio varied between 0.78 and 1.26 with an average of 0.97, and the S_v/S_hmin ratio changed in the interval of 1.14 and 1.52 with an average of 1.29 (Fig. 7). All the three stress ratios slowly decreased with burial depth (Fig. 7), suggesting that the horizontal stresses became dominant in deeper layers.

^{Sun et al. (2017)} indicated that the tectonic stress intensity controlled the vertical transformation of in-situ stress types. The CBM basins in China experienced strong tectonic stress because of the effects of plate tectonics. However, owing to the differences in the tectonic stress intensity in different basins or in different parts of the same basin, various in-situ stress types were induced for different burial depths and different in-situ stress vertical transformation depths. For example, the vertical transformation depth is approximately 600–700 m in the southern Qinshui Basin (^{Meng et al., 2011}) and approximately 700–1000 m in the eastern margin of Ordos Basin (^{Zhao et al., 2016}).

Pore pressure/stress coupling

Pore pressure is an important component of the stress tensor, which is necessary for calculating stress magnitudes and effective stresses. Generally, the spatial-temporal changes in the components of the stress tensor (DS) are a function of changes in pore pressure (DP₀), and this behavior is termed “pore pressure/stress coupling (DS/DP₀)” (^{Hillis, 2001}; ^{Tingay et al., 2009}).

The S_hmin is a primary controlling factor for the fracture gradient and a major constant on the propagation of hydraulic fractures (^{Meng et al., 2011}), which is dependent upon pore pressure. For example, ^{Altmann et al. (2010)} reported that change in S_hmin magnitude was on average approximately 64% of the change in pore pressure according to worldwide measurement data.

Based on the theory of ^{Matthews and Kelly (1967)}, the relationship between effective S_hmin and effective S_v follows Eq. (10):

{{\displaystyle S}}_{h\min }={{\displaystyle K}}_{\mathrm{0}}({{\displaystyle S}}_v-{{\displaystyle P}}_{\mathrm{0}})+{{\displaystyle P}}_{\mathrm{0}},

where K₀ is the effective stress ratio.

In the Linxing area, this relationship (Fig. (8)) is expressed as shown in Eq. (11). This equation indicates a relationship between the effective stresses similar to that in other sedimentary basins or areas (e.g., the southern Qinshui Basin; ^{Meng et al., 2011}).

{{\displaystyle S}}_{h\min }=\mathrm{0.7708}({{\displaystyle S}}_v-{{\displaystyle P}}_{\mathrm{0}})+{{\displaystyle P}}_{\mathrm{0}}.

In the Linxing area, the effective stress ratio is 0.7708, which is lower than the commonly used value (K₀=0.80) in shales in deep petroleum basins (^{Zhang et al., 2008}), and larger than the values (K₀=0.505–0.540) in coal seams of southern Qinshui Basin (^{Meng et al., 2011}).

In addition, ^{Zoback et al. (2003)} stated that as the Earth’s crust contains widely distributed faults, fractures, and planar discontinuities at different scales and with different orientations, the ratio of effective S_Hmax (s₁, s₁≡S_Hmax–P₀) and effective S_hmin (s₃, s₃≡S_hmin–P₀) cannot exceed the frictional strength of planar discontinuities.

CBM reservoir permeability

Variation in coal permeability

In the present study, 14 coal pillars (length approximately 5.00 cm, diameter approximately 2.45 cm) obtained from No. 4+5 and No. 8+9 coal seams in the Linxing area were prepared for permeability tests. The permeability was measured based on the unsteady pressure drop method (^{Jones, 1972}). The experimental results indicated that, in the Linxing area, the permeability in No. 4+5 coal seam varied between 0.036 mD and 9.620 mD with an average of 1.999 Md, and that in No. 8+9 coal seam ranged between 0.080 mD and 9.860 mD with an average of 2.310 mD (Table 2).

Factors affecting coal permeability

Permeability is an important parameter for CBM reservoirs. The in-situ stresses control the variation in permeability by causing changes in pore structures, variations in the fracture density, and orientation of coal seams (Zhao, 1997). Under identical conditions, ^{Somerton et al. (1975)} and ^{Seidle et al. (1992)} revealed an exponential relationship between coal permeability and the magnitude of in-situ stress by performing regression analysis. It was found that, generally, coal permeability declines exponentially with an increase in the effective stress magnitude (^{White et al., 2005}; ^{Bustin et al., 2008}; ^{Li et al., 2014}).

However, in the Linxing area, the results as presented in Table 2 indicate that coal permeability does not decline exponentially with increased effective in-situ stress magnitude. On the contrary, the permeability is relatively higher for larger stress magnitudes (Table 2). Therefore, the results indicate that coal permeability in the Linxing area is affected by many factors, such as the fracture development and orientation, petrographic constituents, pore structures, and engineering operations (^{Ye et al., 1999}; ^{Zhang et al., 2007}; ^{Li et al., 2014}).

In the present study, the fractures in coal seams were considered to understand the variation in coal permeability. Sample A (depth: –1823.00 m) and sample B (–1827.10 m) were both obtained from the No. 8+9 coal seam in Well L-4 in the Linxing area. These two samples have mostly similar parameters, such as burial depth and the in-situ stress magnitude. However, sample B developed more fractures (fracture density: 6.0/cm) than sample A (fracture density: 1.2/cm), and the majority of these fractures were not filled with materials (Fig. 9). Correspondingly, sample B had a relatively larger coal permeability of 9.860 mD, compared with 0.080 mD for sample A. The results indicated that the development of fractures combined with the degree of filling for fractures in coal seams may have an important or even a dominant controlling effect on the permeability in the Linxing area.

In addition, in this study, coal permeability was measured in the laboratory instead of in-situ, which may also be the reason for the current non-stress-dependent permeability distribution pattern obtained in the Linxing area.

Conclusions

Knowledge of in-situ stresses is useful in a varity of fields, such as hydrocarbon exploration and development, and for the purposes such as examination of borehole stability and stress-related geohazards assessment. In the present study, the in-situ stress distribution and CBM reservoir permeability in the Linxing area, eastern Ordos Basin, China, were studied and analyzed.

1) The distribution patterns of the S_Hmax, S_hmin and S_v magnitude with burial depth were obtained. The results indicated that all three parameters were linearly correlated with burial depth. The linear correlations can be expressed as follows: S_Hmax=0.0325z–5.1692, S_hmin=0.0249z–5.8404, and S_v=0.027z. In addition, the horizontal differential stress (S_Hmax–S_hmin) magnitude increased with burial depth, suggesting that wellbore instability may be a potentially significant problem when drilling deep vertical wells in the Linxing area.

2) In the Linxing area, the presence of two types of in-situ stress fields was determined: (i) in shallow layers with depths less than approximately 940 m, and the in-situ stress state followed the relation S_v>S_Hmax>S_hmin, indicating a normal faulting stress regime; (ii) in deep layers with depths more than approximately 940 m, and the in-situ stress state followed the relation S_Hmax>S_v>S_hmin, indicating a strike-slip faulting stress regime. The vertical transformation depth of the in-situ stress regime in the Linxing area was approximately 940 m.

3) The lateral stress coefficient in the Linxing area ranged from 0.73 to 1.08 with an average of 0.93.

4) No obvious exponential relationships were found between coal permeability and in-situ stress magnitude. Fractures in coal seams may have an important or even a dominant effect on the permeability in the Linxing area.

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