Numerical assessment of CMM drainage in the remote unloaded coal body: Insights of geostress-relief gas migration and coal permeability

Journal of Natural Gas Science and Engineering 45 (2017) 487e501

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Numerical assessment of CMM drainage in the remote unloaded coal body: Insights of geostress-relief gas migration and coal permeability Zhengdong Liu a, b, c, Yuanping Cheng a, b, c, *, Qingquan Liu a, b, c, Jingyu Jiang a, b, c, Wei Li a, b, c, Kaizhong Zhang a, b, c a b c

Key Laboratory of Coal Methane and Fire Control, Ministry of Education, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China National Engineering Research Center for Coal and Gas Control, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China School of Safety Engineering, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 3 February 2017 Received in revised form 22 June 2017 Accepted 23 June 2017 Available online 27 June 2017

Unloading mining can effectively reduce geo-stress around coal seams and increase coal permeability, which results in the improvement of coal mine methane drainage and ensures the coal mining safety. Remote unloading mining is one of the several forms of unloading mining. To study coal mine methane drainage of these remote unloaded coal seams which are under the specific geologic conditions, we analyzed the characteristics of geostress-relief gas migration and the changes in permeability. A suitable mathematical model about coal permeability was established based on some existed theories. Comsol Multiphysics software was adopted to create different numerical simulation models that study coal mine methane drainage processes of original and remote unloaded coal seams. Situations of gas pressure change and daily gas drainage volume reveal that the gas extraction effect of coal seams affected by remote unloading mining is better than that of original coal seams. Besides, coal permeability affected by remote unloading mining and variations in permeability during geostress-relief gas extraction were compared and discussed. The above results indicate that remote unloading mining could effectively change the level of coal permeability and improve gas extraction amount. In addition, data of gas extraction amount obtained from numerical simulation were compared with that of field, and these two kinds of data are relatively consistent, which can demonstrate the effectiveness of the proposed mathematical model. Over the longer term, the mathematical model could be used to predict and evaluate variations in geostress-relief gas extraction levels. © 2017 Elsevier B.V. All rights reserved.

Keywords: Remote unloading mining Numerical modeling Geostress-relief gas extraction Coal permeability

1. Introduction China is rich in coal and coal mine methane (CMM) resources (Feng et al., 2013; Wang et al., 2013b). According to the latest resource survey, approximately 3.68
1013 m3 of CMM is stored at depths of over 2000 m countrywide. CMM is a self-generated and self-reservoir gas generated in the coalification process and accumulated in coal seams (Bao et al., 2016; Jin et al., 2016). In fact, while CMM can provide clean energy, it also can pose major hazards in terms of coal mining safety (Karacan et al., 2011; Kong et al., 2014; Luo and Dai, 2009; Luo et al., 2011; Zhao et al., 2016). Due to the presence of complex coal seam conditions and low levels of

* Corresponding author. National Engineering Research Center for Coal and Gas Control, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China. E-mail address: [email protected] (Y. Cheng). http://dx.doi.org/10.1016/j.jngse.2017.06.017 1875-5100/© 2017 Elsevier B.V. All rights reserved.

coal permeability, underground CMM drainage has become increasingly challenging (Zhou et al., 2015). In that case, there are a large amount of methane was directly discharged into the atmosphere in China, which will cause a serious greenhouse effect (Cheng et al., 2011; Yu et al., 2016). Since the greenhouse effect of methane is 21 times more potent than carbon dioxide (Warmuzinski, 2008). Large-flow and high-concentration CMM drainage methods are essential to the guarantee of safe coal production and efficient gas utilization. And as is well-known, coal permeability is regarded as a key factor influencing the effect of methane drainage. At present, most of these coal permeability models have been established to study the permeability evolution laws during gas extraction of the original coal seam. In general, they were proposed primarily based on principles of poroelasticity and used to predict the production of coalbed methane wells (Chen et al., 2011; Detournay and Cheng, 1993; Liu et al., 2015; Mazumder et al., 2002; Pan et al., 2010;

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Robertson, 2005). Among of these models, some models were developed by using the relationship between fracture width and permeability. For example, assuming that coal was under isotropic conditions, Reiss and Louis (1980) proposed a permeability model with the function of fracture porosity and fracture width. Gu et al. (2005) raised a mathematical model through treating fractured coal as an equivalent elastic continuum. Liu and Rutqvist (2009) developed a new permeability model which pointed out the interaction between fracture and matrix during coal deformation. Moreover, a broad variety of models were established based on the relationship between stress and permeability. For instance, Gray (1987) proposed a new permeability model through assuming that the changes in fracture permeability were controlled by prevailing effective horizontal stress. Palmer and Mansoori (1998) developed a mathematical model by assuming that coal was in a state of uniaxial strain and constant vertical stress. Shi and Durucan (2004) developed another permeability model driven by stress whose principle was the same as that of PM model. Cui and Bustin (2005) handled the relationship between the mechanical response of coal and the volume response in accordance with elasticity theory. Robertson and Christiansen (2007) developed a new model under the assumption of a cubic geometry and variable stress. Similarly, Connell (2009) also provided a mathematical model considering that coal was under variable stress. From the above-mentioned permeability models, they just only can be used to study the change of coal permeability affected by gas extraction. In fact, the theoretical and field studies have proven that reducing geo-stress is the most basic and effective method for changing coal permeability, especially for engineering practice in field (Durucan and Edwards, 1986; Konecny and Kozusnikova, 2011). According to the existing theoretical and experimental results, unloading mining is the main technique used to reduce geostress and increase coal permeability. To obtain some nature of the effects of unloading mining on permeability and stress change around coal seam, a large of work have been conducted. Yang et al. (2011) investigated the stress distribution, strata deformation and permeability evolution during unloading mining. Zhang et al. (2015a) raised a new method for evaluating the geostress-relief effects based on the extraction data of surface gas vent hole after unloading mining. Liu et al. (2014a) studied the pressure relief and deformation effects when an extra-thin coal seam as the mined coal seam during unloading mining. Studies on the application of unloading mining in field reveal the effect on stress and permeability change are considerable. However, among of these unloading mining methods, the method of remote unloading mining is more and more adopted by mining corporation in China. Because coal permeability decreases rapidly with increase of mining depth, and it becomes a necessary measure under certain geological conditions (Jianpo et al., 2016; Wang et al., 2013c). Remote unloading mining belongs to a type of unloading mining, and there are two other types: close-distance unloading mining, mid-distance unloading mining. The ratio of thickness of the mined coal seam and the vertical distance between the mined and unloaded coal seam can be regarded as a parameter (R) to judge the unloading mining type (Cheng, 2010; SCIAC, 1993; Wang et al., 2013a). When the mined coal seam is above the unloaded coal seam and the value of R is between 20 and 50, or the mined coal seam is below the unloaded coal seam and the value of R is more than 40, the unloading mining can be defined as remote unloading mining (Cheng, 2010). In general, the geostress-relief gas will be extracted after remote unloading mining. Under this condition, coal permeability is not only affected by execution of remote mining but also affected by gas extraction. However, these existing models cannot describe the whole process of permeability change

and predict the production of geostress-relief gas. In this study, a suitable mathematical model (RUMD model) was established which can effectively explain some evolution laws and gas extraction production of the unloaded coal seam after remote unloading mining. And the rock in the roof and floor of unloaded coal seam has specific lithology such as excellent hardness, and no fractures will be produced after remote unloading mining. The RUMD model was applied to a numerical model of remote unloaded coal seams to simulate geostress-relief gas drainage, and meanwhile some of their features were compared with those of original coal seams. The results illustrate that remote unloading mining can improve the efficiency of CMM drainage. To verify the validity of the mathematical model, the numerical simulation data were fitted with field drainage data. 2. Description of the theoretical foundation 2.1. Coal seams characteristics during unloading 2.1.1. Characteristics changes in relative permeability of original and unloaded coal seams For coal seams of low permeability and high gas content, gas extraction engineering should be implemented first to reduce gas content before mining. However, even if this measure is implemented, only a minuscule amount of adsorption gas can be transformed into free gas during gas extraction. Thus, coal matrix deformation is also insignificant. Moreover, the effective stress remains almost the same, because of small change in gas pressure and constant geo-stress during gas extraction. Geo-stress condition and changes in effective stress levels are shown in Fig. 1. As is wellknown, coal permeability is mainly controlled by effective stress changes and coal matrix deformation (Jasinge et al., 2012; Zhang et al., 2008), so the relative permeability K/K0 is slightly affected by gas extraction. On the contrary, unloading mining can cause changes in geostress effectively, which leads to coal seam and rock deformation, destruction, movement and internal fractures expansion and connection. The effects of unloading mining technologies which are widely used in engineering have been verified through field application and numerical simulation. The value of relative expansion deformation in Chinese coal mines is shown in Fig. 2 (Cheng, 2010). The magnitude of coal permeability is essentially dependent on the quantity and width of fractures. Moreover, coal permeability is sensitive to stress, as the change in stress causes changes in fracturing. Chen et al. (2013) performed numerical simulations to study whether unloading mining affected stress condition around a coal seam. It can be seen from Fig. 3 that unloading mining has a significant influence on the vertical stress level. Similarly, it can be inferred according to the above analysis that the relative permeability K/K0 is largely affected by unloading mining. 2.1.2. Macroscopic and microscopic changes after unloading mining Here, Fig. 4 shows a typical multiple-coalbed condition based on which the changes in coal seams and rocks during unloading mining are explained. According to geostress-relief theory, upper rocks and coal seams can be divided into continuous deformation zone, fractured zone and caving zone in the vertical direction after mining coal seam #1 (Jin et al., 2016; Wei et al., 2011; Xu et al., 2014). Coal seam #2 can be divided into the fractured zone and coal seam #3 belongs to a continuous deformation zone based on the vertical distance. The condition of different zones is shown in Fig. 4. When the rock in the roof and floor of unloaded coal seams has specific lithology that disallows fracturing, all of the gas will be

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Fig. 1. Geo-stress conditions and changes in the effective stress of the original coal seam before and after gas extraction.

Fig. 2. The relative expansion deformation of coal mines in China.

stored in coal seams. If a coal seam has this geological characteristic and is affected by remote unloading mining like coal seam #3, it could be our research object. Fig. 5 illustrates local coal conditions in the unloaded coal seam #3 before and after unloading mining. Remote unloading mining changes stress conditions of the coal seam, causing the deformation, fracturing and even rupturing of coal in turn. Deformation and new fractures result in gas pressure imbalance in the fracture, i.e., the equilibrium of gas adsorption and desorption is disturbed, and a fraction of the adsorbed gas is converted into free gas. The change in gas pressure affects the effective stress of the unloaded coal seam, #3. Gas in the coal fracture and matrix is in a state of dynamic balance before unloading mining:pm0 ¼ pf 0 ¼ p0 . The coal volume can be defined as the sum of matrix and fracture volume:V0 ¼ Vm0 þ Vf 0 . Fracture porosity and permeability can be

expressed as f0 and k0 respectively. The unloaded coal recovers to a stable condition over time. Meanwhile, gas in the coal fracture and matrix is in a new state of dynamic balance:pm1 ¼ pf 1 ¼ p1 and p1 < p0 . The coal volume can be defined as the sum of the matrix volume and fracture volume:V1 ¼ Vm1 þ Vf 1 and V1 > V0 . Fracture porosity and permeability can be expressed as f1 and k1 respectively. 2.2. Mathematical model The permeability evolution of remote unloaded coal seams can be divided into two stages controlled by different factors respectively. Stage one involves the execution of remote mining which causes changes in stress, while stage two involves gas-coupling effects of gas and coal during geostress-relief gas extraction. Most researchers have made assumptions to simplify physical processes

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Fig. 3. Vertical stress distribution in an unloaded coal seam with the workface of the mining coal seam located at 80 m, 140 m and 200 m. Chen et al., 2013

when establishing the permeability evolution model (Liu et al., 2015; Wu et al., 2010; Zhang et al., 2008). Considering the characteristics of remote unloading mining and previous research results, the following assumptions were made to simplify the mathematical model: [A1] The effect of gas-solid coupling on coal permeability during remote unloading mining can be disregarded. [A2] The increase in the macroscopic volume of coal body is caused by the appearance of new fractures and the expansion of old fractures completely at stage one. [A3] The rock in the roof and floor of unloaded coal seams has specific lithology such as excellent hardness, and meanwhile no fractures are produced under the influence of remote unloading mining. [A4] The effect of water on gas-solid coupling and coal permeability can be ignored.

2.2.1. Gas occurrence characteristics of coal seams under remote unloading mining As the coal seam permeability is affected by execution of remote unloading mining and geostress-relief gas extraction respectively,

the initial gas pressure of unloaded coal seam can be regarded as an intermediate variable to connect them. And in order to get the value, the condition of the assumption [A3] was utilized, which ensures that the geostress-relief gas cannot flow to adjacent coal seams or rock strata. Under this condition, the total gas content of coal seam and some other parameters of coal keep unchanged after being affected by remote unloading mining, whereas only the volume of the unloaded coal seam will change. For a porous medium, the volume V includes fracture volume Vf and matrix volume Vm (Cui and Bustin, 2005). The porosities of original and unloaded coal seams are respectively, defined as:

f0 ¼

Vf 0 V0  Vm0 ¼ V0 V0

(1)

f1 ¼

Vf 1 V1  Vm1 ¼ V1 V1

(2)

where f0 is the fracture porosity of original coal seams, %; f1 is the fracture porosity of unloaded coal seams, %. According to the assumptions [A1] and [A2], the matrix volume Vm is constant before and after unloading mining: Vm0 ¼ Vm1 . From a combination of Eq. (1) and Eq. (2), the following equation was obtained:

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Fig. 4. Stress condition and physical configuration of coal seams and rocks after unloading mining.

Fig. 5. Local conditions of unloaded coal seams before and after unloading mining. Liu et al., 2011

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f1 ¼ 1 

V0 ð1  f0 Þ V1

(3)

Gas content of original coal seams is equal to that of unloaded coal seams, and the general relationship between gas content and gas pressure was defined as (SAC/TC288/SC1, 2008; Wang et al., 2014):

8 abp0 f p > >
Sþ 0 0 X0 ¼ > > > 1 þ bp0 10r > < abp1 f1 p1 >
Sþ X1 ¼ > > 1 þ bp1 10r > > > : X0 ¼ X1

(4)

1 ad Mad where S ¼ 100A
1þ0:31M ; X0 is gas content of original coal 100 ad seams, m3/t; X1 is gas content of unloaded coal seams, m3/t; a is the volume constant, m3/t; b is the pressure constant, MPa1; p0 is the initial gas pressure of original coal seams, MPa;p1 is the initial gas pressure of unloaded coal seams, MPa; r is the apparent relative density of coal, t/m3; Aad is the ash of coal, %; and Mad is the coal moisture, %. By solving Eq. (4), the initial gas pressure of unloaded coal seams can be described by fracture porosity and gas content of original coal seams:

p1 ¼

V1 B±

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V 21 B2 þ V 21 40brX0  40brX0 V0 V1 ð1  f0 Þ 2bðV1  V0 þ V0 f0 Þ

(5)

0Þ where B ¼ 10brX0  10Srab  1 þ V0 ð1f ; V0 is the initial volume V1 of original coal seams; and V1 is the initial volume of unloaded coal seams. Two values from Eq. (5) are obtained, but default conditions must be considered. According to p1 < p0 and p1 > 0, Eq. (5) can be simplified as:

p1 ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi V1 B þ V 21 B2 þ V 21 40brX0  40brX0 V0 V1 ð1  f0 Þ 2bðV1  V0 þ V0 f0 Þ

(6)

2.2.2. Dynamic permeability model Coal has the typical structure of a natural porous medium. It is widely accepted by researchers that coal consists of matrixes and fractures (Gray, 1987), as shown in Fig. 6.

Fig. 6. Illustration of coal, which is typically a dual-fracture porosity system. Liu et al., 2017

Chilingar (1964) defined the functional relationship among permeability, fracture porosity and grain-size in porous media. The following cubic relationship between coal permeability and fracture porosity was obtained:

k ¼ k1



f f1

3 (7)

where k is permeability of unloaded coal seams, m2; k1 is the initial permeability of unloaded coal seams, m2; f is fracture porosity of unloaded coal seams, %; and f1 is the initial fracture porosity of unloaded coal seams, %. When coal is considered under uniaxial strain, strain changes have a small impact on coal sample. Therefore, the relationship among coal volume strain, grain volume strain, pore volume strain and fracture porosity can be expressed as (Palmer and Mansoori, 1998):

dεm ¼

  dεn 1f dεk  f f

(8)

where εm is pore volume strain; εn is coal volume strain; andεk is grain volume strain. A change in pore volume strain εm leads to a change in fracture porosity, and fracture porosity is controlled by effective stress and sorption-included volume changes. The effective stress changes were defined as (Nur and Byerlee, 1971):

seij ¼ sij  apdij

(9)

where dij is the Kronecker delta tensor which equals 1 when i ¼ j and equals 0 in other cases. a, the effective stress coefficient, can be expressed as (Wang et al., 2012):

a¼1

K Ks

(10)

where K is the bulk modulus of the porous skeleton, MPa, and Ks is the bulk modulus of individual coal matrix or grain, MPa. Sorption-induced volume strain can be expressed by the following Langmuir equation (Harpalani and Schraufnagel, 1990):

εT ¼

εL p p þ pL

(11)

where εT is sorption-induced volume strain. pL is Langmuir

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pressure constant at which the measured volumetric strain equals 0:5εL , Pa; εL is Langmuir volumetric strain. Combining the influence of effective stress changes and sorption-induced volume changes, a change in fracture porosity can be expressed as follows:

df ¼

1 ðds  adpÞ M |fflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflffl} Effect of effective stress

   K εL p 1 d M p þ pL |fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl ffl} 



(12)

Effect of sorption induced deformation

where M is the constrained axial modulus, MPa, M ¼ Eð1  vÞ=½ð1 þ vÞð1  2vÞ; and v is the Poisson's ration of coal. Based on the theory of multivariable differential calculus, the resulting constitutive Eq. (13) was obtained (Details of derivation procedure are discussed in “Appendix A”):

   f 1 ε K P P1 1 ¼1þ ½aðp  p1 Þ þ L  f1 Mf1 P þ PL P1 þ PL f1 M (13) For remote unloaded coal seams, the above parts have illustrated that the evolution process of coal permeability can be divided into two continuous stages. However, Eq. (13) only can describe the process of stage two. To establish a new mathematical model which can describe the whole process, the intermediate variable (gas pressure) was utilized. It is common knowledge that the traditional coal permeability models are based on the initial parameters; the new model in this paper is no exception. However, the initial parameters of unloaded coal seams are difficult to obtain, while those of original coal seams are relatively easy. Moreover, the intermediate variable (gas pressure) can be a bridge to connect the initial parameters of unloaded coal seams with those of original coal seams, as described in Eq. (6). Coal is also can be considered a kind of material, which meets a special failure criterion. And the coal mass of unloaded coal seam will yield and fail when the stress state around it changes due to remote unloading mining. Meanwhile, the development of fractures leads to a rapid increase in coal permeability, so the initial value of coal permeability in unloaded coal seams is far greater than that of original coal seams. The jump coefficient of coal permeability was raised to describe the phenomenon (Wang et al., 2013c; Zhang et al., 2007). After the unloaded mining of coal seam, the geologic stress of adjacent coal seam will be unloaded, and coal mass of unloaded coal seam will expand, which introduces cracks or bed-parallel fractures into the unloaded coal seam. Thus, the permeability of unloaded coal seam will be significantly improved (Liu et al., 2009; Zhang et al., 2015b). In the whole process of coal permeability change, the value of coal permeability increases gradually in the initial stage, and then the coal mass failure occurs rapidly after the stress around the coal mass reaches a critical value, which induces the coal permeability to increase sharply. The increasing ratio of coal permeability is defined as the jump coefficient. The resulting constitutive equation for remote unloaded coal permeability derived from Eqs. (6), (7) and (13) takes the form:

493

where z is the jump coefficient of coal permeability. 2.3. Governing equations 2.3.1. Coal deformation The control equation of the deformation field of coal containing methane is mainly composed of the stress equilibrium equation, the geometric equation and the constitutive equation and can be expressed as (Liu et al., 2015) (Derivation procedure are discussed in “Appendix B”):

Gui;jj þ

G u  ap;i þ Fi ¼ 0 1  2y j;ji

(15)

2.3.2. Gas flow In the unloaded coal seam, free gas and adsorbed gas are controlled by a mass conservation equation:

vðcð1  fÞÞ vðrfÞ þ ¼ Vm  VðrVÞ vt vt

(16)

where c is the quantity of adsorbed gas per volume of coal matrix, kg/m3; r is the gas density, kg/m3; f is the fracture porosity, %; m is the mass diffusion flux of the adsorbed gas, kg/(m3$s); and V is the gas velocity of the free gas, m/s. For the coal matrix system, diffusion from it is assumed to be driven by the concentration gradient, and the value of c can be calculated by using the Langmuir equation:

c¼

pVL Mc r p þ pL Vm c

(17)

where VL denotes the maximum adsorption capacity of coal, m3/kg; PL denotes the Langmuir pressure constant, pa; P is the gas pressure of coal, pa; Vm is the molar volume of methane under standard conditions, m3/mol; rc is the coal density, kg/m3; and Mc is the molar mass of methane, kg/mol. m is the mass diffusion flux of adsorbed gas, and the gas diffusion in the coal matrix can be calculated using Fick's law:

m ¼ DVC

(18)

where D is the gas diffusion coefficient, m2/s. For the coal fracture system, the relationship between gas density and pressure agrees with to the ideal gas law so that the gas densityr can be expressed by:

r¼

Mc p RT

(19)

where Mc is the molar mass of methane, kg/mol; R is the universal gas constant, J/(mol$k); and T is the thermodynamic temperature of coal, K. Gas flow in coal fractures according to Darcy's law can be calculated as:

8 qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi > > V B þ V 21 B2 þ V 21 40brX0  40brX0 V0 V1 ð1  f0 Þ > 1 > > < p1 ¼ 2bðV1  V0 þ V0 f0 Þ >   3  3   3 > > f f 1 ε K P P1 > > 1 ¼ zk0 ¼ zk0 1 þ ½aðp  p1 Þ þ L  : k ¼ k1 f1 f1 Mf1 P þ PL P1 þ PL f1 M

(14)

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k V ¼  Vp

(20)

m

where V is the gas velocity in the fracture, m/s; k is the fracture permeability, m2; and m is the methane viscosity, pa$s. Combining Eqs. (16)e(20), the control equation of the geostressrelief gas flow field was formed:

rc VL Mc pL ð1  fÞ vp

þ

rc pVL Mc vð1  fÞ

vt Vm ðp þ pL Þ Vm ðp þ pL Þ2   rk  V DVc þ Vp

vt

þ

(22) (23)

3.2. Results and analyses

m

¼0 (21) 2.3.3. Boundary and initial conditions Standard initial and boundary conditions for the coal seam deformation field of Eq. (15) were defined according to the actual stress state of coal seams and rocks (Liu et al., 2015). Displacement and stress conditions at the boundaries were as follows:

sij ! n ¼ fi ðtÞ

on

vU

3.1. Simulation example It is an appropriate decision to take Panyi coal mine as the case of this study. This mine, which is one of the first coal mines to apply remote unloading mining techniques, has received widespread attention and plays a central role in the gas control and mining safety. However, most importantly, the coal mine matches the assumption [A3]. The state-owned Panyi coal mine is located in the northeastern part of the Huainan coalfield, a major production mine. The sequence of the coal-beds is illustrated in Fig. 7. The mine's primary mineable coal-beds are coal seams #11 and #13. These seams are spaced at an average vertical distance of 65 m. With an average thickness of 6 m, coal seam #13 is identified as a coal and gas outburst coal seam due to its specific characteristics (i.e., soft coal, low permeability and high gas content). Its coal permeability reaches 2.80039
1019 m2, and gas content is measured at approximately 12e22 m3/t. To ensure the safety of production and the efficiency methane energy use, remote unloading mining and gas extraction technology were applied to reduce geo-stress and promote gas flow.

  Mc vp vf f þP vt vt RT

ui ¼ ui ðtÞ on vU

strain of coal were calculated with the “Solid Mechanics module” and the “PDE module” was used to control the gas diffusion and seepage.

where ui ðtÞ and fi ðtÞ are components of known displacement ! and stress at the boundary, respectively; and n is the vector of direction at the boundary. Initial displacement and stress conditions in the solved region were as follows:

ui ð0Þ ¼ u0 in U

(24)

sij ð0Þ ¼ s0 in U

(25)

A numerical simulation model was created to study gas extraction evolution of the original and unloaded coal seam. The

where u0 and s0 are initial values of displacement and stress in the domain respectively. Generally speaking, for gas flow field, the boundary conditions can be defined as gas boundary and flux boundary, they were also called the Dirichlet and Neumann boundary in some papers and defined as:

p ¼ pðtÞ on vU

(26)

k ! Vp$ n ¼ Q ðtÞ on vU u

(27)

where pðtÞ and Q ðtÞ are the known constant gas pressure and gas flux on the boundaries. Initial conditions for gas flow in the domain can be expressed as:

p ¼ p01 in U

(28)

where p01 is the initial value of gas pressure. 3. Numerical simulation and model analysis In this paper, numerical simulation software was used to study the evolution rules of original and unloaded coal seams. All of the governing equations used were controlled and expressed by the COMSOL Multiphysics finite element software. Two modules were adopted to solve the mathematic model, of which the stress and

Fig. 7. Generalized stratigraphy of Panyi Coal Mine.

Z. Liu et al. / Journal of Natural Gas Science and Engineering 45 (2017) 487e501

simplified geometric model and its boundary conditions are shown in Fig. 8. The 2D geometric model is a simplification of the 3D real coal seam, which was set to a rectangle of 100 m in length and 50 m in width. The unloaded coal seam deformation is mainly axial, with a measured value of 2.633%. Reasonable boundary conditions for stress and flow field are described in detail in Section 2.3.3. Actually, all the boundaries of the coal mass should be set to stress boundary, which is best consistent with the field condition. However, it is found that the model cannot be calculated if all the boundaries of the model are set to stress boundary. In order to ensure that the numerical simulation can be calculated, some researchers simplified the boundary conditions reasonably. In our paper, we chosen the more simplified boundary condition, and the left and right sides and the base are rollered and the top is exposed to constant stress. In addition, the boundaries of the drainage borehole were set as constant pressure boundary which belongs to the Dirichlet boundary. Moreover, no flow conditions were applied to the other boundaries which belong to the Neumann boundary. The input parameters used in the original and unloaded coal seam model are listed in Table 1. However, as partial input parameters were not measured in the field or laboratory, they were drawn from recently published papers (An et al., 2013; Liu et al., 2014b). As can be seen from Table 1, only the molar mass of methane and the in-situ stress were referenced from other literature. Among of them, the molar mass represents the mass of per

Fig. 8. Geometry and boundary conditions of the original and unloaded coal seams.

495

unit material, and it is immutable for a particular compound. The in-situ stress value was referenced from Liu et al. (2014b), which has been measured in field at Panyi coal mine. 3.2.1. Gas pressure distribution of the original and unloaded coal seam Suitable permeability evolution models were chosen to study gas extraction processes under different conditions. Gas pressures levels in the original and unloaded coal seam at different times (1 d, 10 d, 50 d, 100 d, 200 d and 365 d) are illustrated in Fig. 9 and Fig. 10. Fig. 9 shows that the extraction effect of the original coal seam is limited. The gas pressure level of 4.4 MPa did not change in almost all areas except in a small area around the borehole after extraction 1 d. Although drilling extraction effects increase gradually with an increase in extraction time, the extraction effect of the borehole was limited, as gas pressure in the coal seam did not decline significantly even after 365 days. The extraction effect of the unloaded coal seam shown in Fig. 10 is better compared with that shown in Fig. 9 when the gas extraction time is the same. The gas pressure level in the whole coal seam decreased significantly over a gas extraction period of only 50 d. To quantify the extraction effect on the original and unloaded coal seams, detection lines A1B1 and A2B2 were set to monitor gas pressure (Figs. 11 and 12). The coordinates of the endpoints are as follows: A1 (50 m, 25 m), B1 (100 m, 25 m), A2 (50 m, 25.65 m) and B2 (100 m, 25.65 m). With the increase of gas extraction time, the affected area increased gradually in the original coal seam. The affected radii were approximately 1.9 m, 6.3 m, 11.2 m, 16.8 m, 20.5 m and 24 m at 1 d, 10 d, 50 d, 100 d, 200 d and 365 d, respectively (Fig. 11). Meanwhile, maximum gas pressures levels in the unloaded coal seam were 3.63 MPa, 3.15 MPa, 2.25 MPa, 1.8 MPa, 1.48 MPa and 1.2 MPa, respectively, as shown in Fig. 12. It is noteworthy that most regions in the original coal seam were not influenced by gas extraction, even when the gas extraction time was set to 365 d. In contrast, gas pressure in the unloaded coal seam decreased to 1.2 MPa after extraction 365 d. As can be found via the comparison of results, gas extraction effects in the unloaded coal seam were greater than those in the original coal seam. 3.2.2. Daily gas drainage volume of the original and unloaded coal seam Daily gas drainage volumes in the original and unloaded coal seam are shown in Fig. 13. Daily maximum gas drainage volume in the unloaded coal seam reached 337.2 m3/d which eventually

Table 1 Property parameters used in the numerical simulation model. Parameter

Value

Reference

Young's modulus of coal, E Thermodynamic temperature, T Density of coal, rc Langmuir volume constant, VL Langmuir pressure constant, PL Langmuir volumetric strain constant, εL Initial pressure of original coal seam, p0 Passion's ratio of coal, n Initial fracture porosity of fractures, F Initial gas permeability, k0 Diffusion coefficient, D Molar mass of methane, Mc Increment coefficient of coal permeability, x Value of axial deformation, b Moisture content of coal, Mad Ash content of coal, Aad Volatile content of coal, Vdaf In situ stress, F

2713 MPa 293 K 1250 kg/m3 0.0228 m3/kg 1.41 MPa 0.012 4.4 MPa 0.339 0.012 0.000268 md 3.3*1012 m2/s 0.016 kg/mol 3280 2.633% 1.69 31.62 27.01 12.18 MPa

Laboratory test Field test Laboratory test Laboratory test Laboratory test Laboratory test Field test Laboratory test Laboratory test Field test Laboratory test An et al. (2013) Field test Field test Laboratory test Laboratory test Laboratory test Liu et al. (2014b)

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Fig. 9. Gas pressure distribution in the original coal seam over different extraction times.

Fig. 10. Gas pressure distribution in the unloaded coal seam over different extraction times.

Fig. 11. Gas pressure distribution in the original coal seam along the detection line.

stabilized to approximately 24 m3/d. However, the daily maximum gas drainage volume in the original coal seam only reached 0.82 m3/d which eventually stabilized to approximately 0.48 m3/d. The daily gas drainage volume declined rapidly with extraction time. According to the change rate of gas drainage amount per day, the high-efficiency extraction stage of the extraction curve was obtained. As can be seen from Fig. 13, the change rate is relatively steep in the high-efficiency extraction stage, while it is relatively smooth outside the high-efficiency extraction stage. Highefficiency extraction stages of the original and unloaded coal

Fig. 12. Gas pressure distribution in the unloaded coal seam along the detection line.

seam were approximately 75e80 d and 120e125 d respectively. Because it is difficult to define a specific value as the critical value to divide the high-efficiency extraction stage, so the vague scopes of division were given respectively. The unloaded coal seam was more conducive to gas extraction, independent of maximum gas drainage volume per day and the high-efficiency extraction time. 3.3. Model verification As is well known, these existing classic permeability models

Z. Liu et al. / Journal of Natural Gas Science and Engineering 45 (2017) 487e501

497

Fig. 13. Gas drainage amount per day in the original and unloaded coal seam.

were used to study the variation laws of original coal seams during gas extraction. Unlike them, the studied object in our paper is the unloaded coal seam after remote unloading mining. More importantly, the rock in the roof and floor of unloaded coal seam has specific lithology such as excellent hardness, and no fractures will be produced after remote unloading mining. This geological condition ensures that the gas occurrence state is different from the general condition. So the numerical simulation results of these classic models are not suitable for comparison with that of our model. In order to illustrate the reliability of the above obtained laws, the accuracy of our model must be verified. Here, the simulated gas extraction data were compared with field data in Panyi coal mine to illustrate the validity of the proposed model. Field data variations are shown in Fig. 14. The changing curve can be divided into three stages, namely, growth stage, active stage and attenuation stage. The drilling yard includes four boreholes that are evenly distributed. The thickness of the original and unloaded coal seam is 6 m and 6.16 m. However, the simulated gas extraction data are based on a 1 m thick coal seam and one extraction borehole. The basic units of simulated and field data are different. Drawing comparisons between them requires determining the field gas extraction value of one borehole and converting the m3/min unit into a m3/d unit. The interaction between drainage boreholes should be disregarded during transformation, and the gas extraction amount should be evenly distributed between boreholes. The final results are shown in Fig. 15. In contrast to simulation data, there is a growth stage in the gas extraction changing curve of field (Fig. 15). Since most of the gas around the borehole is lost because the original equilibrium state of the coal seam around the borehole is disturbed in process of drilling borehole. After drilling the borehole, the front end of the borehole must be sealed, and then the suction negative pressure is applied to the borehole. In the beginning phase of extraction, the gas extraction amount is very small as the most gas around the borehole has

Fig. 14. Variations in gas extraction quality levels in one drilling yard overtime. Cheng et al., 2004

been lost during drilling, yet the extraction amount will increase as the gas of distal coal mass gradually flows into the coal mass around the borehole. When the extraction amount reached the maximum value, a new equilibrium state of the coal seam around the borehole was formed. Under these conditions, a growth stage of gas extraction was formed. Actually, not only the above factor affects the formation of growth stage but also other factors may influence it. For example, the effect of water may inhibit the gas extraction amount, but the effect is very small in our studied coal seam due to no free water exists in the coal seam and the moisture content of coal is small. Combining the effect of water is small, the factor of water was ignored when we established the mathematic model. So

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4. Discussion

Fig. 15. Variations in gas extraction quality levels in one drilling borehole based on field and simulated data.

all the results of numerical simulation were obtained under an ideal state. Hence, the early growth stage of the extraction curve in numerical simulation is default compared to field data. In field data, the time of the new equilibrium state should be regarded as the initial extraction time. Fig. 15 shows that the field extraction data are fluctuant due to relatively complex geological conditions and other factors such as changes in extraction pressure, interaction between boreholes and artificial statistical errors. However, the curve of the simulated data is smooth, due to the numerical modeling of an ideal state. Although some differences were found between the data, the overall change trend is consistent. The comparative analysis shows that the RUMD model is scientific and effective to some extent. Over the longer term, it can also be used to predict and evaluate variations in geostress-relief gas extraction levels.

Different monitoring points (A3 (60 m, 25 m) and B3 (80 m, 25 m)) were set as shown in Fig. 16 which illustrates the permeability of the original and unloaded coal seam at different monitoring points and over different gas extraction periods. The permeability of the original coal seam remains almost unchanged at monitoring point B3, even when the extraction time reaches 365 d. This phenomenon shows that the effects of gas extraction on permeability are quite limited. On the contrary, the changes in permeability are identical for the unloaded coal seam at monitoring points A3 and B3, and the changes are obvious. Over the same gas extraction time, the affected area of the unloaded coal seam is significantly larger than that of the original coal seam indicating that change in the permeability of the unloaded coal seam is more notable than that of the original coal seam during gas-solid coupling. Because the change in coal permeability indirectly reflects the geostress-relief gas extraction efficiency level, the above phenomenon illustrates that the gas extraction efficiency of the unloaded coal seam is much higher than that of the original coal seam. The evolution of coal permeability is controlled by the effective stress and sorption-induced volume changes during gas extraction, where the relationship between them is competitive (Lu et al., 2016; Pan et al., 2010). Fig. 16 shows that for the original and unloaded coal seams, coal permeability is continuously decreasing due to the presence of dominant effective stress during this stage. However, this trend gradually declines with extraction time. The effects of sorption-induced volume change gradually grow more pronounced. When the gas extraction time reaches a certain value, the variation trend of coal permeability will show a rebound phenomenon. According to variation trends (Fig. 16), this rebound phenomenon should occur earlier in the unloaded coal seam than in the original coal seam. With the advent of rebound time, coal permeability slowly increases. This phenomenon also implies that gas extraction from the unloaded coal seam is better than that achieved from the original coal seam later on. Permeability of the unloaded coal seam is influenced by

Fig. 16. Permeability of two detection points within the original and unloaded coal seam.

Z. Liu et al. / Journal of Natural Gas Science and Engineering 45 (2017) 487e501

unloading mining and gas extraction, which are independent and based on different principles. Unloading mining affects the geostress conditions around coal seam, and gas extraction influences the gas pressure levels. Point A3 (60 m, 25 m) was selected as a detection point to monitor the value of permeability during remote unloading mining and gas extraction. Moreover, ka reflects the original coal permeability, while kb is the value of coal permeability after unloading mining. Values of coal permeability are kc, ke, kf, kg, kh and ki for extraction period of 1 d, 10 d, 50 d, 100 d, 200 d and 365 d respectively, as shown in Fig. 17. The kb/ka ratio represents the degree of coal permeability change, which is influenced by remote unloading mining. Meanwhile, kb/kc, kb/ke, kb/kf, kb/kg, kb/kh and kb/ki denote degrees of coal permeability change, which are influenced by gas extraction at different periods. The value of kb/ka is higher than that of the others, as shown in Fig. 17. This indicates that the degree of coal permeability change, which is influenced by remote unloading mining, is greater than that affected by gas extraction. Therefore, the primary way to affect coal permeability involves changing geo-stress levels around coal seams, i.e., unloading mining.

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daily gas extraction volume and coal permeability show that remote unloading mining technology can greatly increase gas volume and improve extraction efficiency levels. (3) Effects on coal permeability of remote unloading mining and geostress-relief gas extraction were compared. The comparative data show that remote unloading mining has a greater influence on the curve amplitude of coal permeability than gas extraction does. (4) Field data of gas extraction were compared with simulated data. The two sets of data are inconsistent, whereas the overall changes are consistent, thus demonstrating that the RUMD model is scientific and effective to some extent. Over the longer term, the model also can be used to predict and evaluate relief-pressure gas extraction variations and levels. Acknowledgements The authors are grateful to the financial support from the Fundamental Research Funds for the Central Universities (No. 2017BSCXB04) and the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

5. Conclusions In this study, a new mathematical model that considers the effects of effective stress and adsorption deformation was developed to study the evolution laws of unloaded coal body under remote mining. The new model was applied to a finite element model to quantify the multiphysics of coal-gas interactions. Effects of remote unloading mining on coal permeability and characteristics of geostress-relief gas extraction were investigated. Major consequences are summarized as follows: (1) The rock in the roof and floor of the unloaded coal seam is quite hard, and no fractures will be produced under the influence of remote unloading mining. However, the permeability of coal seams significantly changes under this condition. A new mathematical model was established which could describe the permeability evolution process, including the implementation process of remote unloading mining and geostress-relief gas extraction. (2) Numerical simulation models were established to study gas extraction characteristics of both the original and unloaded coal seam. The comparisons and analyses of gas pressure,

Appendix A Palmer and Mansoori (1998) proposed the flowing equation (A1) which reflects strain changes in porous rock, and Eq. (A1) is the same as Eq. (8).

dεm ¼

  dεn 1f dεk  f f

(A1)

where εm is the pore volume strain; εn is the coal volume strain; εk is the grain volume strain; f is the natural fracture porosity %.The above nomenclatures can be seen in (Palmer and Mansoori, 1998). For the single-fracture porosity media, the relationship between effective change and fracture porosity change was obtained by (Palmer and Mansoori, 1998):

    1 K K  ð1  fÞf g ðds  dpÞ þ  ð1  fÞ gdp  M M M   ð1  fÞ tdT

 df ¼

(A2) where g is the grain compressibility, pa1; f is a fraction ranging from 0 to 1; t is the grain thermal expansively,  F1; K is the bulk modulus of the porous skeleton, MPa; M is the constrained axial modulus, MPa,M ¼ Eð1  vÞ=½ð1 þ vÞð1  2vÞ; v is the Poisson's ration of the coal. ðds  dpÞ represents the change of the effective stress (seij ¼ sij  apdij ), the relationship between effective change and fracture porosity change can be rewritten as:

    1 K K  ð1  fÞf g ðds  adpÞ þ  ð1  fÞ gadp  M M M   ð1  fÞ tdT

 df ¼

(A3)

Fig. 17. Permeability of the detection point within the unloaded coal seam at different stages and the degree of permeability change.

Because the coal is under the condition of uniaxial strain, constant vertical stress, there is no change in overburden stress, ds ¼ 0. At the same time, it is known that the fracture porosity f < < 1, and grain compressibility is set to zero, g ¼ 0 [see Table 1 of (Palmer and Mansoori, 1998)]. On the basis of these conditions, Eq. (A3) can be easily converted to the following Eq. (A4):

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  1 K  1 tdT df ¼  ðadpÞ  M M

(A4)

Using the principle of thermal expansion, a change in sorptionincluded volume can be replaced by Eq. (A5):

tdT ¼

  d εL p dp dp p þ pL

(A5)

Combining Eq. (A4) and Eq. (A5), the following equation can be obtained:

df ¼ 

    1 K εL p ðadpÞ  1 d M M p þ pL

(A6)

Solving Eq. (A6), Eq. (A7) can be obtained:

f  f1 ¼

a M

 ðp  p1 Þ 

K 1 M



εL p ε p  L 1 p þ pL p1 þ pL

 (A7)

Diving by f1 leads to:

    f a K ε p p1 ðp  p1 Þ  1 L ¼1þ  f1 M Mf1 f1 p þ pL p1 þ pL

(A8)

Eq. (A8) is the same as Eq. (13) Appendix B The control equation of the deformation field of coal containing methane is mainly composed of the stress equilibrium equation, the geometric equation and the constitutive equation. The stress equilibrium equation is given as follows (Chen and Chen, 1999; Haifei et al., 2016):

sij;j þ Fi ¼ 0

(B1)

where Fi denotes the body force component in the i-direction. The constitutive relation for the coal seam can be expressed as (Wang et al., 2012):

sij ¼ 2Gεij þ

2Gy εy d  api dij 1  2y ij

(B2)

where G ¼ E=2ð1 þ yÞ is the shear modulus of coal, MPa; and εy is the volumetric strain of coal: εy ¼ ε11 þ ε22 þ ε33 . The geometric equation for coal can be given as follows (Liu et al., 2010):

εij ¼

1 uij þ uji 2

(B3)

where εij denotes the component of the total strain tensor (i; j ¼ 1; 2; 3) and uj denotes the displacement component inj direction. A combination of Eqs. (B1)-(B3) for deducing the control equation of the deformation field gives:

Gui;jj þ

G u  ap;i þ Fi ¼ 0 1  2y j;ji

(B4)

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