Environ Earth Sci DOI 10.1007/s12665-015-4280-3

THEMATIC ISSUE

The relationships among stress, effective porosity and permeability of coal considering the distribution of natural fractures: theoretical and experimental analyses Zetian Zhang1,2 • Ru Zhang1,2 • Heping Xie1,2 • Mingzhong Gao1,2

Received: 3 November 2014 / Accepted: 5 March 2015 Ó Springer-Verlag Berlin Heidelberg 2015

Abstract Although the relationships among stress, effective porosity and permeability of coal are a fundamental research topic that has been studied for decades and are widely used in analyzing the mechanical behavior of coal seams and predicting coalbed methane production, most relevant studies are based on idealized models and do not consider the influence of natural fracture distributions. To obtain a comprehensive understanding of the interrelationships among stress, effective porosity and permeability of coal, a series of effective porosity and permeability determinations have been conducted under different overburden stresses using an automated permeameter– porosimeter considering the directional distribution of natural fractures in coal. The experimental results show that the directional distribution of natural fractures provides a substantial contribution to the anisotropy of the effective porosity and absolute permeability of coal, which exponentially decrease with increasing overburden stress. An existing permeability model was modified to reflect the influence of the natural fracture distribution on the power

& Ru Zhang [email protected] Zetian Zhang [email protected] Heping Xie [email protected] Mingzhong Gao [email protected] 1

State Key Laboratory of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, China

2

College of Water Resource and Hydropower, Sichuan University, No. 24 South Section 1, Yihuan Road, Chengdu 610065, China

law relationship between effective porosity and permeability, i.e., the exponent is not constant, but a variable related to the natural fracture distribution. The anisotropic effective porosity sensitivity and stress sensitivity of coal are also discussed, and the coal mass is shown to have the highest effective porosity sensitivity and lowest stress sensitivity in the direction perpendicular to the bedding planes compared to those in other directions. Keywords Coal  Fracture  Stress  Effective porosity  Permeability

Introduction With the reduction in coal resource reserves at shallow depths and increasing demand for energy in developing countries due to economic development, the mining depths and mining intensity for coal resources are continuously increasing and have been accompanied by more disasters. In underground coal mining practices, coalbed methane (CBM) flow has a significant influence on the strength and stability of coal seams. The disaster failure process of coal, including the occurrence of severe accidents and possible fault reactivation induced by deep underground CO2 injection, is a situation induced by CBM flow that the coal mining industry is currently attempting to address (Beamish and Crosdale 1998; Cappa and Rutqvist 2011). The permeability of coal mass is an important parameter that is used to evaluate the flow capacity of coal seams and is an important property for understanding CBM production (Palmer 2009; Flores 1998; Ried et al. 1992; Sparks et al. 1995). Various studies have shown that the permeability of coal is associated with many impact factors, such as effective stresses, porosity characteristics, temperature

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conditions, fracture geometry, water content, coal types, gas types and coal matrix swelling/shrinkage effects (Somerton et al. 1975; Perera et al. 2011; Lagny 2014; Wang et al. 2011). Many models have been developed to describe the permeability of coal considering the abovementioned impact factors (Connell et al. 2010; Cui and Bustin 2005; Gray 1987; Palmer 2009; Palmer and Mansoori 1998; Liu and Rutqvist 2010; Robertson and Christiansen 2008; Seidle and Huitt 1995; Shi and Durucan 2005; Wang et al. 2012). However, few models have considered the anisotropy of permeability (Gu and Chalaturnyk 2005, 2010; Liu et al. 2010; Pan and Connell 2011; Wang et al. 2009), which plays an important role in determining the optimal arrangement of wells and the CBM production rate (Wold and Jeffrey 1999). Coal seams are well known for their dual porosity characteristic, which greatly influences the feasibility of their use as carbon dioxide storage (Gonzalez-Nicieza et al. 2014; Hou et al. 2012; Perera et al. 2011). Such seams contain micro- and macropores (Davidson et al. 1995). Macropores mainly provide conduits for gas flow and are nearly uniformly spaced natural fractures, which are called cleats; micropores exist in a coal matrix and store most of the methane by adsorption, which is the main component of coalbed gas (Gu and Chalaturnyk 2010). Coal cleats can be classified into two types, face and butt cleats, which are often normal to bedding planes and may be perpendicular to each other (Nelson 2000; Close 1993; Pattison et al. 1996). Coalbed gas permeation is a filling and adsorption process with gas in the pore space of coal, and the permeation capacity of coal is dominated by the distribution of its natural fractures, such as bedding structures, face and butt cleats. The permeability of coal is mainly a function of its cleat system, and the coal fracture geometry and stiffness heavily influence its permeability evolution (Palmer 2009; Wang et al. 2011, 2012). The permeability of the coal matrix blocks divided by the cleat system is related to the micropore characteristics of coal, which may be influenced by its bedding structure distribution. In most modeling work, the vertical permeability is often ignored because the bedding planes are always closed due to the high overburden stress and of little interest in the flow of gas in coal (Harpalani 1999). However, the vertical flow can play an important role for thick coal seams and horizontal well applications, and the vertical permeability is of interest in gas extraction. The distinguishing natural fracture distribution has a predictable influence on the anisotropy of the permeation capacity, the effective porosity of coal and the relationship between them, which is considered in the present study.

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Deep mining practices are always conducted under high and complex in situ stress conditions, and the effective porosity and permeability of coal mass are clearly stress dependent, which is supported by extensive laboratory tests (McKee et al. 1988; Seidle et al. 1992; Somerton et al. 1975) and field studies (Enever and Henning 1997; Sparks et al. 1995). Therefore, it is critical to obtain a better understanding of the coalbed gas flow and to further the study the interrelationships among stress, effective porosity and permeability of coal considering the distribution of natural fractures to optimize mining designs and increase the safety of mining activities (Liu et al. 1999).

Experimental setup and procedure Experimental equipment To determine the effective porosity and permeability of coal under different overburden stresses, an automated permeameter–porosimeter (AP-608, Coretest Systems, INC.) was used to conduct laboratory tests (Fig. 1). The effective porosity and permeability measurements are based on the unsteady pressure drop method and Boyle’s law, respectively (Jones 1972). The equipment uses a modern unsteady-state permeameter and an advanced procedure that allows the pressure decay process to stabilize in the core sample faster than in more common methods. The testing procedure and result output are entirely automated and thus enable accurate and repeatable measurements. A Hassler-type coreholder featuring a quick release end is equipped in the AP-608, and the range of the confining pressure is approximately 3.45–65.50 MPa. The pore pressure used in the tests was automatically controlled. The measurable permeability range of the equipment is from 0.0001 to 10,000 mD, whereas the measurable effective porosity ranges from 0.1 to 40 %. Sample preparation To reduce the discreteness of specimens, lump bituminous coal blocks were taken from a same 500 m depth underground mining face 8202 at the Tashan mine in Datong, Shanxi Province, China. The coal samples were prepared as cylinders with dimensions of U25 mm 9 H40 mm. To investigate the effect of the natural fracture distribution on the permeation property and effective porosity of coal, the axes of the cylindrical samples were drilled parallel to the face (32A) and butt cleat (32B) directions from coal block 32#, which is

Environ Earth Sci Fig. 1 Automated permeameter–porosimeter (AP-608, Coretest Systems, INC.)

25mm

(b)

(c)

Bedding plane

Bedding plane

Face Cleat

40mm

(a)

32A

Butt cleat Axis of specimen

32B

33A

Axis of specimen

33B

Fig. 2 Schematic diagram of the coal samples: a sample size, b samples drilled from coal block 32#, c samples drilled from coal block 33#

schematically shown in Fig. 2b. They were also parallel to the bedding planes. The axes of other cylindrical samples, which were drilled from coal block 33# and are shown in Fig. 2c, were set to be parallel (33A) or perpendicular (33B) to the bedding planes to investigate their influence. The axes of the samples of group 33A are also parallel to the butt cleats. The number of samples in groups 32A, 32B, 33A and 33B are 16, 15, 13 and 14, respectively. All 58 samples were tested according to the scheduled experimental procedures. The mineral components of the samples were mainly organic compounds containing carbon (71.44 %), kaolinite (20.13 %) and calcite (6.98 %), measured by an X-ray diffraction meter (DMAX-3C) and X-ray fluorescence spectrometer (XRF1800 CCED). Experimental procedures To obtain a complete understanding of the effect of the overburden stress (depth) on the effective porosity and

permeability of coal, the confining pressures used in the tests were set at an equal interval, i.e., five overburden stresses from 7.5 (at 300 m) to 27.5 MPa (at 1100 m) with an interval of 5 MPa assuming a vertical stress gradient of 25 kPa/m. These pressures covered the stress conditions of the sampling location, which is a 500-m-deep underground mining face. The effective porosity and permeability of each sample were measured under hydrostatic pressure conditions at the five above-mentioned stress levels from the extreme values referred. In the tests, nitrogen (N2) was utilized as the flow gas to minimize the errors because the permeability of the initially intact coal sample was typically below 0.05 mD. Because the testing procedure was automated, the samples were tested under the same condition; therefore, the measurements were not complicated by low-level nitrogen sorption-induced swelling effects and eliminated the influence of Biot’s coefficient. The change in effective stress was only due to the changing confining pressure (overburden stress).

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Results and discussion

ki ¼

Linking stress, effective porosity and permeability of coal The effective porosity / of coal was calculated using the following equation: /¼

Vp ; Vb

ð1Þ

where Vp is the connected pore volume and Vb is the bulk volume. The effective porosity change under loading conditions is defined as:   Vp Vp dVp dVb d/ ¼d ¼  ¼ deb  dep ; ð2Þ / Vb Vb Vp Vb where deb = -dVb/Vb is the bulk coal strain, and dep = -dVp/Vp is the pore strain. Equation (2) can be integrated and yields the following relationship: 0 1   Zeb Zep / B C ln ð3Þ debA; ¼ @ dep  /0 ep0

eb0

where the subscript 0 refers to the reference state. From Zimmerman et al. (1986) and Jaeger et al. (2007), deb ¼ Cbr ðdr  dpÞ þ Cm dp and dep ¼ Cpr ðdr  dpÞ þ Cm dp;

ð4Þ

where Cbr = -(qVb/qr)b/Vb, Cpr = -(qVp/qr)p/Vp, r is the mean stress, p is the flow pressure and Cm is the compressibility of the coal matrix. Substituting Eq. (4) into Eq. (3) yields 

/ ln /0

 ¼

Zr;p

ðCpr  Cbr Þðdr  dpÞ:

b3i ; 12ai

ð7Þ

where i = 1, 2 and 3 represent the x, y and z directions, respectively; k is the permeability of coal; b is the aperture of the cleat and a is the spacing of the idealized parallel cleat system. For the anisotropic case presented in Fig. 3, the corresponding cleat porosity (/*) can be expressed as: X bi bx by bz / ¼ þ þ ¼ : ð8Þ ax ay az i¼x;y;z ai Assuming that the size change in the coal matrix due to swelling/shrinkage and external forces is negligible compared with the change in effective porosity, the fractures or cleats in the coal are isotropic, and the degree of anisotropy in the fracture apertures or permeability is also negligible. The permeability change with respect to a reference state can be obtained as:   3 ki /i ¼ : ð9Þ ki0 /i0 Equation (9) is widely used to describe the permeability changes with respective to porosity changes in the permeability model of coal (e.g., Wang et al. 2014; Shi et al. 2014; Cui and Bustin 2005; Palmer and Mansoori 1998), and this relation is directly supported by the experimental results obtained by Jones (1975). Considering that the macro- and mesopore content of a coal mass is limited, the effective porosity (/) and cleat porosity (/*) of coal can be assumed to be equal to each other. Then, substituting Eq. (6) into Eq. (9) yields

ð5Þ

r0 ;p0

Because Cbr  Cpr and supposing the compressibility and flow pressure are constant, we obtain / ¼ /0 eCpr ðrr0 Þ :

ð6Þ

The bundled matchstick conceptual model has been widely used as a basis to describe the cleat system of coal, and many permeability models have been derived based on this model (Seidle et al. 1992; Gilman and Beckie 2000; Liu and Rutqvist 2010; Gu and Chalaturnyk 2010; Ma et al. 2011). Figure 2 presents a generalized form of this conceptual model. The cubic law for fracture flow can describe gas flow through the cleat systems, and the permeability of fractured coal mass with anisotropic cleats can be expressed as (Van Golf-Racht 1982):

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Fig. 3 Idealized anisotropic geometry of the coal cleat system (after Van Golf-Racht 1982)

Environ Earth Sci

ki ¼ ki0 e3Cpr ðri ri0 Þ :

ð10Þ

Equation (10) is similar to the cleat permeability given by Seidle et al. (1992) assuming an idealized coal cleat system. Nevertheless, the natural fractures in the coal mass are not ideal; their distribution can significantly influence the relationship between the effective porosity and permeability. The experimental results of Somerton et al. (1975), who studied the relationship between the effective porosity and permeability of coalbeds, indicate that Eq. (9) is not applicable to coal seams. They found that the curves of (k/k0)1/3 and ///0 against the log of the mean stress did not overlap and their results indicated a substantial divergence. Assuming that the cleats are homogenous and isotropic before and after cleat deformation, from the empirical model presented by Barton et al. (1985), 8 < ð bm Þ 2 when bm  bh and JRC [ 0 ; 2:5 bh ¼ ð11Þ : JRC bm otherwise which describes the relationship between the hydraulic apertures and mechanical apertures. The relationship between the change ratio of permeability with effective porosity can be obtained as   6 ki /i ¼ : ð12Þ ki0 /i0 Based on permeability data and initial porosity data, porosities at different confining pressures were estimated and compared to the measured porosity results by Wang et al. (2013) using Eqs. (9) and (12). The results show that the curves of (k/k0)1/6 and ///0 against the log of stress are closer than the curves of (k/k0)1/3 and ///0. One can draw the same conclusion using data in Somerton et al. (1975). This implies that the power to 1/6 is more applicable than the power to 1/3 for coal seams. Gu and Chalaturnyk (2010) noted that k/k0 to which power (i.e., 1/6, 1/3 or other values) yields a straight line with ///0 (based on mechanical apertures) has not been determined for coal seams, and that this is most likely caused by anisotropies of cleats and the lack of accurate experimental data. Therefore, based on the directional fracture distribution in coal, an anisotropic relationship between effective porosity and permeability can be defined as:   ai ki /i ¼ ; ð13Þ ki0 /i0 where ai is the power ratio determined by the fracture distribution along the x, y or z directions, which can be measured by corresponding experiments and used to describe the permeability changes with respective to porosity changes in the anisotropic permeability model of coal. This

can be regarded as the effective porosity sensitivity of coal permeability. Substituting Eq. (6) into Eq. (13), the corresponding stress–permeability relationship can be given as: ki ¼ ki0 eai Cpr ðri ri0 Þ :

ð14Þ

According to Eqs. (6) and (14), both the effective porosity and permeability of coal are stress-dependent parameters, which was proven experimentally. Effective porosity and permeability of coal under different overburden stresses The effective porosity and permeability of coal were measured at five different pressures from 7.5 to 27.5 MPa with an interval of 5 MPa representing five equivalent depths from 300 to 1100 m with an interval of 200 m. The experimental results with average amounts are listed in Table 1 and plotted in Figs. 4 and 5. The test results show that the effective porosity and permeability of the samples decreased nearly exponentially with increasing overburden stress. Due to the high compressibility of the pores and fractures of coal under lowpressure conditions, there is a significant reduction in the effective permeation paths of coal mass, which results in a clear decrease in the permeability of coal. With increasing overburden stress, the compressibility of the pores and fractures of coal samples take on extremely low values, and the permeability and effective porosity of coal samples exhibit small variations. The cylindrical samples of group 32A were drilled parallel to the face cleat direction from coal block 32#, whereas the samples of group 32B were drilled parallel to the butt cleat direction (see Fig. 2). The axes of all samples were also parallel to the bedding planes. Although the samples of the two groups were drilled from the same coal block, there are substantial variations in the effective porosity and permeability under the same overburden stress conditions. The results in Figs. 4a and 5a clearly show that the average effective porosity and permeability of the samples in group 32B were substantially smaller than the corresponding average values of the samples in group 32A under the same overburden stress. The average effective porosity and permeability of the samples in group 32A under a hydrostatic pressure of approximately 12.5 MPa, corresponding to a coal mine depth of approximately 500 m, were approximately 4.84 9 10-3 mD and 2.27 %, respectively; moreover, these values were 7.45 times and 5 times as high, respectively, as the corresponding values of the samples in group 32B. According to Figs. 4a and 5a, the change in average effective porosity and permeability of the samples in group 32A with a unit change in overburden stress is considerably larger than that of samples in

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Environ Earth Sci Table 1 Average effective porosity and average permeability of coal samples under different overburden stresses Overburden stress r (MPa)

32A (16 samples)

32B (15 samples)

33A (13 samples)

33B (14 samples)

Average effective porosity / (%)

Average permeability k (mD)

Average effective porosity / (%)

Average permeability k (mD)

Average effective porosity / (%)

Average permeability k (mD)

Average effective porosity / (%)

Average permeability k (mD)

7.5 12.5

2.704 2.268

0.0093 0.0048

0.562 0.457

0.0018 0.0007

0.706 0.556

0.0187 0.0064

0.527 0.432

0.0043 0.0011

17.5

1.602

0.0029

0.403

0.0004

0.494

0.0035

0.397

0.0002

22.5

1.541

0.0025

0.377

0.0003

0.453

0.0018

0.379

0.0002

27.5

1.334

0.0016

0.373

0.0002

0.35

0.0012

0.345

0.0001

(a) 0.01

3

300m 2.5

32A

32B

500m y = 3.4245e-0.036x R² = 0.937

2 1.5

700m

900m 1100m

1

y = 0.6116e-0.02x R² = 0.8751

0.5

Average Permeability/mD

Average Effective Porosity/%

(a)

300m

0.009

32A

32B

0.008 0.007

y = 0.0152e-0.084x R² = 0.9626

0.006 0.005

500m

0.004

700m 900m

0.003

0.003e-0.103x

y= R² = 0.9326

0.002

1100m

0.001 0

0

7.5

7.5

12.5

17.5

22.5

12.5

27.5

17.5

22.5

27.5

Overburden Stress/MPa

Overburden Stress/MPa

(b) 0.02

Average Effective Porosity/%

0.8

33A

Average Permeability/mD

(b) 33B

300m 0.7

y = 0.875e-0.032x R² = 0.9674

0.6

500m

700m

0.5

900m

0.4

1100m

0.5797e-0.02x

y= R² = 0.9318 12.5

22.5

27.5

Overburden Stress/MPa Fig. 4 The relationship between average effective porosity and overburden stress of coal: a samples of groups 32A and 32B, b samples of groups 33A and 33B

group 32B. The coal mass has a higher stress sensitivity in the direction parallel to the face cleats compared to parallel to the butt cleats. The face cleats of coal have a higher compressibility than the butt cleats (Szwilski 1984), and the cleats constitute the

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0.016 0.014

y = 0.042e-0.136x R² = 0.9752

0.012 0.01 0.008 0.006

500m

700m

0.004

y = 0.0106e-0.18x R² = 0.8878 900m

0.002 7.5

17.5

33B

1100m

0

0.3 7.5

33A

300m

0.018

12.5

17.5

22.5

27.5

Overburden Stress/MPa Fig. 5 The relationship between average permeability and overburden stress of coal: a samples of groups 32A and 32B, b samples of groups 33A and 33B

main component of effective porosity. The samples in group 32A have higher face cleat contents and initial effective porosities compared to the samples in group 32B; therefore, there is a higher change in effective porosity and permeability for the samples in group 32A with unit increase in overburden stress; specifically, there is a higher stress

Environ Earth Sci

sensitivity in the direction parallel to the face cleats compared to parallel to the butt cleats in the coal mass. The other two groups of samples were drilled parallel (33A) and perpendicular (33B) to the bedding planes from the same coal block 33#, respectively (see Fig. 2). The average effective porosities of samples in group 33A were slightly larger than the values of the corresponding perpendicular samples (see Fig. 4b); therefore, the bedding structures have a smaller effect on the effective porosity than the cleats of coal as a result of fewer opening fractures distributing along bedding planes. Nevertheless, the average permeability of the samples in group 33A at a hydrostatic pressure of approximately 12.5 MPa corresponding to approximately 500 m depth at the sampling location was about 6.42 9 10-3 mD. This value was six times as high as the average permeability of the corresponding samples in group 33B (see Fig. 5b). According to Figs. 4b and 5b, the change in the average effective porosity and permeability of the samples in group 33A with a unit change in overburden stress is substantially larger than that of samples in group 33B. The coal mass has a higher stress sensitivity in the direction parallel to bedding planes compared to perpendicular to bedding planes as a result of the higher compressibility in the direction parallel to the bedding planes. The testing results (see Figs. 4b, 5b; Table 1) show that the bedding structures contribute to the anisotropy of the effective porosity, permeability and stress sensitivity of coal, and the maximum permeating direction of gas in coal seams is parallel to the bedding planes. Considering the above-mentioned test results, the maximum permeating direction is determined by the cleat system in coal seams, and the maximum permeability of coal seams tends to be in the direction parallel to the face cleats and bedding planes. The bedding planes of coal are natural fractures mainly filled with sand and mud. Compared with cleats, bedding planes have a lower permeation capacity and compressibility; however, these values remain higher than those of the coal matrix. There is no clear cleat distribution in coal samples of group 33#; therefore, bedding planes constitute the main component of the effective porosity and permeation paths of the samples. The samples in group 33A have higher bedding plane contents and initial effective porosities compared to the samples of group 33B; therefore, there is a higher change in effective porosity and permeability for the samples of group 33A with a unit overburden stress change, especially when the overburden stress is lower than 17.5 MPa. Specifically, there is a higher stress sensitivity in the direction parallel to the bedding planes compared to perpendicular to the bedding planes in coal mass. The test results showed that the distribution of natural fractures in coal seams contributes to the anisotropy of the effective porosity, absolute permeability and stress sensitivity of coal (see Figs. 4, 5; Table 1), which may further influence

the mechanical properties of coal and gas migration in coal seams. In the direction parallel to the face cleat and bedding plane, coal mass has the highest effective porosity, absolute permeability and stress sensitivity and the lowest such values in the direction perpendicular to the bedding planes as a result of the natural fracture directional distribution and compressibility anisotropy in different directions. Anisotropic relationship between effective porosity and permeability of coal Equation (13) shows that there is a directional power law relationship between the effective porosity and permeability of coal, which can also be regarded as an anisotropic relationship between the effective porosity and permeability of coal. The test results used to determine the relationship between the average effective porosity and average permeability of each coal sample group are shown in Fig. 6, and the power ratios determined by the average test results, which show the characteristics of the testing results of all 58 tested samples, are listed in Table 2. According to Fig. 6, the test results of the average permeability and average effective porosity of the sample groups closely follow a power law relationship, which is also described by Eq. (13). Many researchers have proved or assumed that the exponent a is a constant and equals to 3 or 6 (Jones 1975; Somerton et al. 1975; Palmer and Mansoori 1998; Cui and Bustin 2005; Wang et al. 2013). However, the test results listed in Table 2 show that the exponents a of samples with different drilling directions are different, which shows that the effective porosity is influenced by the distribution of natural fractures in coal. Therefore, the effective porosity can be regarded as a directional property. The permeability is strongly related to the effective porosity along the flow direction. The relationship between the effective porosity and permeability of coal is also directional due to directional distribution of natural fractures. Considering that the test results of samples drilled from the same coal block are more comparable (see Tables 1, 2), the average effective porosity, average permeability and exponent a in the direction parallel to the face cleats and butt cleats and perpendicular to the bedding planes have the following general relationships, respectively: /kface cleats [ /kbutt cleats [ /?bedding planes ;

ð15Þ

kkface cleats [ kkbutt cleats [ k?bedding planes ;

ð16Þ

akface cleats \akbutt cleats \a?bedding planes :

ð17Þ

The results in Table 2 show that the exponent of sample group 32B is 4.85, which is approximately twice the value of group 32A. There is a greater effective porosity sensitivity exhibited by the coal permeability along the direction

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(a)

(b) 1.4

1.8

32A

32B

1.6

1.2

Present model fit(Eq.13)

Present model fit(Eq.13) 1.4

Testing results (Average amount of 16 samples)

1.2

Bedding plane

0.8

α=2.42

Face cleat

0.6

500m 0.4

Bedding plane

1

300m

0.8

0.4

Butt cleat 32A Axis of specimen

Butt cleat Axis of specimen

0.2

1100m 0

32B

0 0

0.3

0.6

0.9

1.2

0

0.3

700m 900m 1100m

500m

0.6

0.9

1.2

(d)

(c)

2

1.6

33B

33A 1.8

1.4

Present model fit(Eq.13) Testing results (Average amount of 13 samples)

1

Testing results (Average amount of 14 samples)

1.4

300m

Bedding plane

1.2

α=4.38

0.8

Present model fit(Eq.13)

1.6

k/k0

1.2

k/k0

α=4.85

Face cleat

0.6

700m 900m

0.2

Testing results (Average amount of 15 samples)

300m

k/k0

k/k0

1

Bedding plane

α=9.10

1

300m

0.8

0.6

0.6 0.4

33A

500m

0.4

500m 0.2 Axis of specimen

700m 900m

1100m

0.2 0

0 0

0.3

0.6

33B Axis of specimen

0.9

0

1.2

0.3

900m 1100m 700m 0.6

0.9

1.2

Fig. 6 Relationship between k/k0 and ///0 based on average testing results: a samples of group 32A, b samples of group 32B, c samples of group 33A, d samples of group 33B

Table 2 Testing results of power ratio in anisotropic relationship between effective porosity and permeability Sample group no.

32A (16 samples)

32B (15 samples)

33A (13 samples)

33B (14 samples)

Drilling direction

Parallel to face cleats and bedding planes

Parallel to butt cleats and bedding planes

Parallel to bedding planes

Perpendicular to bedding planes

aa

2.42

4.85

4.38

9.10

a

The power ratio a is calculated based on the average testing results in Table 1, and totally 58 samples were tested to get the above-mentioned relationships

parallel to butt cleats compared to the direction parallel to face cleats. The test results for sample groups 33A and 33B show a relationship that is similar to that of the former

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groups. The exponent of sample group 33B is 9.10, which is also approximately twice that of 33A. The exponent in Eq. (13) represents the effective porosity sensitivity to coal

Environ Earth Sci

permeability. A higher effective porosity sensitivity means that if there is a small change in the effective porosity of coal, there will be a large change in permeability. There is a higher effective porosity sensitivity to coal permeability along the direction perpendicular to bedding planes compared to along the direction parallel to butt cleats and bedding planes. In the direction perpendicular to bedding planes, coal samples have the lowest effective porosity and permeability, and the highest effective porosity sensitivity. However, in the direction parallel to face cleats, coal samples have the highest effective porosity and permeability, but the lowest effective porosity sensitivity. The above-mentioned relationship (Eqs. 15–17) can be briefly explained as a result of the unique distribution of natural fractures in coal. The face cleats are always connected and open fractures, whereas the butt cleats are always unconnected and open fractures, and the bedding planes are filled and closed fractures. In the direction perpendicular to the bedding planes, when the size of the pores decreases and the connectivity of the pores is poor, the permeability and porosity are minimized. In the direction parallel to the face cleat, the density of the butt cleat is considerably greater than that of the face cleat; therefore, the porosity is larger. However, because the connectivity of the butt cleat is not as noteworthy as that of the face cleat, the permeability is smaller in the direction parallel to the butt cleat. Combining with previous analyses on the permeability–stress relationship and effective porosity–stress relationship, the distribution of natural fractures in coal can have notable influences on the general relationships of the effective porosity and permeability of coal given by Eqs. (15) and (16). According to the test results shown in Table 2, the effective porosity sensitivity a follows the general relationship shown in Eq. (17). A unit change in the effective porosity will produce the largest percent change in the effective porosity in the direction perpendicular to the bedding planes relative to its small initial value, whereas the smallest percent change will be in the direction parallel to the face cleat relative to its large initial value due to the differences in the initial fracture filling condition and compressibility. Correspondingly, the permeability of coal in the direction perpendicular to the bedding planes and in the direction parallel to the face cleats will exhibit the largest and smallest variations, respectively, relative to their initial value; therefore, the effective porosity sensitivity follows the general relationship shown in Eq. (17). The test results show the clear anisotropy of coal in orthogonal directions and that the distribution of natural fractures in coal contribute to the anisotropy of the effective porosity and absolute permeability of coal.

Conclusions To obtain a comprehensive understanding of the interrelationships among stress, effective porosity and permeability of coal, effective porosity and permeability measurements under different overburden stresses were obtained using an automated permeameter–porosimeter for 58 intact coal samples, which were prepared considering the directional natural fracture distribution. The existing permeability model was modified to reflect the influence of the natural fracture distribution on the relationship between the effective porosity and permeability. Theoretical analyses demonstrate that the effective porosity and permeability of coal are both stress dependent. The permeability of coal follows a power law as a function of the effective porosity, but the exponent a is not a constant (i.e., 3, 6 or other values). The exponent a can be defined as a variable related to the directional distribution of natural fractures in coal, which can also reflect the effective porosity sensitivity to coal permeability. The exponent of the power law implied by the experiments ranged from 2 to 10 for the Tashan coal samples. The experimental results showed that the distribution of natural fractures in coal clearly contributed to the anisotropy of the effective porosity, absolute permeability, stress sensitivity and effective porosity sensitivity of coal. The effective porosity and absolute permeability of coal samples decreased exponentially with increasing overburden stress. Due to natural fractures’ directional distribution and property difference, the coal samples have the lowest effective porosity, absolute permeability and stress sensitivity, but the highest effective porosity sensitivity in the direction perpendicular to bedding planes. However, in the direction parallel to face cleats, the coal samples have the highest effective porosity, absolute permeability and stress sensitivity, but the lowest effective porosity sensitivity. The experiments were conducted under hydrostatic pressure conditions to simulate the overburden stress of the coal samples, but the experiments did not simulate the initial crustal stress conditions of the sampling spots, which shall be considered in future studies. Acknowledgments This research was funded by the State Key Basic Research Program of China (No. 2011CB201201) and the National Natural Science Foundation of China (No. 51204113, 51134018).

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