Geotechnical and Geological Engineering 22: 1–17, 2004. # 2004 Kluwer Academic Publishers. Printed in the Netherlands.

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Numerical simulations for coupled rock deformation and gas leak flow in parallel coal seams PEIDE SUN Department of Environmental Engineering, Hangzhou University of Commerce, Hangzhou, 310035, China. Key Laboratory for the Exploitation of Southwestern Resources and Environmental Disaster Control Engineering, Ministry of Education, Chongqing Univ., Chongqing, 400044, China. e-mail: [email protected] or [email protected] (Received 1 February 2001; revised 12 June 2002; accepted 3 February 2003) Abstract. Based on the new viewpoint of interaction mechanics for solid and gas, gas leakage in parallel deformable coal seams can be understood. That is, under the action of varied geophysical fields, the methane gas flow in a double deformable coal seam can be essentially considered to be compressible with time-dependent and mixed permeation and diffusion through a pore-cleat deformable, heterogeneous and anisotropic medium. From this new viewpoint, coupled mathematical models for coal seam deformation and gas leak flow in parallel coal seams were formulated and the numerical simulations for slow gas emission from the parallel coal seams are presented. It is found that coupled models might be close to reality. Meanwhile, a coupled model for solid deformation and gas leak flow can be applied to the problems of gas leak flow including mining engineering, gas drainage engineering and mining safety engineering in particular the prediction of the safe range using protective layer mining where coal and gas outbursts can efficiently be prevented. Key words. coupled models, gas leak flow, numerical simulation, parallel coal seams, solid deformation

Nomenclature Qmd Qms Dm Tm wm Pm
0m amj grad Mmd Mmt Mm0 Mmf am bm R(t) ijm

¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

gas diffusion in coal seam m; gas seepage in coal seam m; gas diffusion coefficient in coal seam m; gas permeability coefficient in coal seam m; desorbable gas content in coal seam m; pore pressure in coal seam m; effective overall stress in coal seam m; fit constant, j ¼ 0; 1; 2; 3; m is coal seam m; gradient; desorbable average gas content in coal seam m; adsorbed gas content in coal seam m; gas content in coal seam m at initial time t0; fee gas content in coal seam m; maximum adsorption gas coefficient in coal seam m; adsorption gas coefficient in coal seam m; gas desorbing rate from adsorption state in coal; stress tensor in coal seam m;

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PEIDE SUN 0

m ij "ijm em m Gm m ij
m bmj mb ms mp nm m Qm T3 bm* t Dn dm Fmi Um Pm0 Pa em0 Umi Qm E  m Mm  q0

¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼ ¼

effective stress tensor in coal seam m; strain tensor in coal seam m; deformation rate in coal seam m; Lame-constant of coal seam m; shear modulus of coal seam m; effective stress coefficient of pore pressure in coal seam m; Kronecker function; overall stress in coal seam m; fit constant, j ¼ 1; 2; 3; 4; bulk strain in coal seam m; solid mass deformation rate in coal seam m; pore deformation rate in coal seam m; porosity in coal seam m; methane gas density in coal seam m; gas flow rate in coal seam m; gas permeability of intercalation; average thickness of coal seam m; b3* for intercalation; time; gas diffusion coefficient at pore pressure equal Pn, Pn ¼ 1 atmospheric; average coal micro-grain size of coal seam m; free term for stress in coal seam m; displacement function in seam m; initial pore pressure in coal seam m; pressure in free space; initial deformation rate in coal seam m; boundary value for displacement in coal seam m; quality vector for gas outflow from boundary surface in coal seam m; modulus of elasticity of coal or rock; Poisson ratio of coal or rock; unit weight of coal in coal seam m; gas content in coal seam m; slope angle of coal seam m; overburden stress.

1. Introduction In China, underground coal seams are mostly distributed in multi-layers near to coal seams. Problems in mining engineering such as prediction and control of methane gas emission from the coal face during mining, safe mining area prevention issues related to coal and gas outbursts in protective layer mining, prediction of firedamp drainage rate for gas drainage near to the seam and from virgin coal seams, as well as prediction of gas flow rate in multi-coal-seam etc., remain to be solved. The above problems can be studied as a gas leakage flow problem. (Sun 1998; 2000, 2002a,b; Sun and Xian 1998, 1999) Due to gas flows from coal mining and gas drainage, the effective stress of the solid skeleton of coal or rock changes, so that the pore pressure around a coal face or gas drainage bore also changes. This causes a gas flow through a network made of micro-pores and micro-cracks. Moreover, the gas flowing through coal or rock cracks also changes because the gas permeability changes. (Sun 2001; Sun et al 1999; Jaeger and Cooke 1979; Sommerton et al 1975). Therefore, the interaction

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between the solid and gas must take account of the action of methane gas. Under the action of a pore pressure gradient in the multi-coal-seam system, slow gas emission occurs near to the seam, and this can leak through the lower permeability layer of intercalation, and flow into mining coal faces or drain it. This is referred to as methane gas leak flow (Sun, 1998). In this study, the gas leak flow systems for coupled rock deformation and gas seepage in double coal seams are studied. It is a well-established fact that although the study of the interaction between coal or rock and gas in the gas leak flow system is difficult, the problem of gas leak flow has to be studied for the safety of coal mining in multi-coal-seams. Therefore, it is necessary that the stress-leaky flow through multi-coal-seams should be considered by accounting for the interaction between the coal or rock and methane gas using the theory of solid deformation and the fundamentals of coal gas seepage.

2. Assumptions The theory of coupled solid deformation and gas leak flow involves seepage mechanics, rock mechanics and mining science, etc. The interaction mechanism between the coal or rock deformation and gas leak flow through multi-coal-seams (as shown in Figure 1) is considered as follow. The gas leak flow through multi-coal-seams is assumed to be a compressible, mixed, time-dependent flow with permeability and diffusion through anisotropy and heterogeneous deformable media containing pores and crevices, subject to varying mechanical fields. The following assumptions can be applied in establishing the coupled mathematical model. (1) The gas flow process can be divided into two stages. First, gas flows from micro-pores into crevices, which can be formulated by Fick’s law of diffusion (Equation (1)). Second, gas flows from crevices into the free space of underground mining, which can be formulated by Darcy’s law of nonlinear seepage (Equation (2)). So we have (Sun 1991; Sun et al 1996; Zhao 1994a,b) Qdm ¼ Dm grad wm

ð1Þ

Qsm ¼ Tm grad Pm

ð2Þ

Tm ¼ am0 expðam1 Y0m þ am2 P2m þ am3 Pm Y0m Þ;

ðm ¼ 1; 2; 3Þ

ð3Þ

where, Qdm ¼ gas diffusion in coal seam m; Qsm ¼ gas seepage in coal seam m; Dm ¼ gas diffusion coefficient in coal seam m; Tm ¼ gas permeability in coal seam m (m ¼ 1, 2); T3 ¼ gas permeability of intercalation; wm ¼ desorbable gas content in coal seam m; Pm ¼ pore pressure in coal seam m; Y0m ¼ overall effective stress in coal seam m; amj ¼ fit constant, j ¼ 0,1,2,3; m is coal seam m; grad ¼ gradient. (2) The gas in the coal seam is composed of both free and adsorbed gas, and the adsorption gas content can be formulated by Langmuir’s isothermal law. For the adsorption gas content in coal, we have (Sun 1998; 2002a)

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PEIDE SUN

Mmt ¼

am bm pm 1 þ bm pm

ðm ¼ 1; 2Þ

ð4Þ

where, Mmt ¼ adsorbed gas content in coal seam m; am ¼ maximum adsorption gas coefficient in coal seam m; bm ¼ adsorption gas coefficient in coal seam m. Based on Equation (4), the average desorbable gas content in the coal seam m is that of the between the initial gas content and adsorbed gas, that is (Sun 1998; Sun 2000, 2002a,b; Sun and Xian 1998, 1999; Saghafi et al 1987) Z

t

Mmd ¼ Mm0  t0

dðMm0  Mmt Þ  RðtÞ dt dt

ð5Þ

where, Mmd ¼ desorbable average gas content in coal seam m; Mm0 ¼ gas content in coal seam m at initial time t0; R(t) ¼ gas desorbing rate from adsorption state in coal. (3) The coal gas can be treated as ideal and its flow can be considered as an isothermal process. (4) The coal seam is saturated with a single phase of methane gas. (5) The coal or rock is linearly elastic so that the deformation can be formulated by Hooke’s generalized law: (Terzaghi 1943; Biot 1941) 0

m sm ij ¼ lm dij em þ 2Gm eij

ðm ¼ 1; 2Þ

ð6Þ

0

m where, sm ij ¼ effective stress tensor in coal seam m; eij ¼ strain tensor in coal seam m; em ¼ deformation rate in coal seam m; lm ¼ Lame-constant of coal seam m; Gm ¼ shear modulus of coal seam m; dij ¼ Kronecker function. Moreover, Terzaghi’s law gives the effective stress of the solid skeleton. For the effective stress of a coal seam (Zhao et al 1994; Zhao 1994b; Terzaghi 1943), we have: 0

m sm ij ¼ sij þ am Pm dij

ði; j ¼ 1; 2; 3Þ

ð7Þ

sijm ¼ stress

where, tensor in coal seam m; am is called as effective stress coefficient, given by the experimental data (Sun 1998, 2002a). Formula (8) is a fit to experimental data: (Zhao 1994a,b; Zhao et al 1994) am ¼ bm1  bm2 Ym þ bm3 Pm  bm4 Ym Pm ¼

bm1  bm2 Y0m þ bm3 Pm  bm4 Y0m Pm 1 þ 3bm2 þ 3bm4 P2m

ð8Þ

where, Ym ¼ overall stress in coal seam m; Y0m ¼ effective overall stress in coal seam m; bmj ¼ fit constant, j ¼ 1,2,3,4. The second equation of Equation (8) is derived by substituting the equation Ym ¼ Y0m þ 3am Pm into the first part of Equation (8). (6) The deformation of the coal or rock is due to pores and a crevice saturated by gas is equal to the deformation of the solid skeleton plus the deformation of pores and crevices, (Bear 1972; Bear and Bachmat 1991) i.e. amb ¼ ð1  nm Þams þ nm amp

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Figure 1. Scheme for gas leakage field in parallel coal seams

where, amb ¼ bulk strain in coal seam m; ams ¼ solid mass deformation rate in coal seam m; amp ¼ pore deformation rate in coal seam m; nm ¼ porosity in coal seam m. If ð1  nm Þams 4 nm amp , then the pore deformation is equal to the deformation of coal or rock. (7) Gas leak flow through coal seam m is as shown in Figure 1. The continuity equations for gas leak flow can be formulated as: (Sun 1998; 2002a) divðrm Qm Þ 

T3 @Mmf @Mmd þ ; ðP21  P22 Þ ¼ 2bm b3 @t @t

ðm ¼ 1; 2Þ

ð9Þ

where, Mmf ¼ free gas content in coal seam m; rm ¼ methane gas density in coal seam m; Qm ¼ gas flow rate in coal seam m; T3 ¼ gas permeability of intercalation; b*m ¼ average thickness of coal seam m; b*3 for intercalation; t ¼ gas flow time. (8) The direction of gas leak flow through a low permeability intercalation is vertical and the direction of gas flow in coal seam is horizontal, as shown in Figure 1.

3. Solid-gas coupled mathematical models 3.1.

EQUATIONS SET FOR GAS LEAK FLOW

Based on the above assumptions, the following equations for gas leak flow can be obtained by substituting Equations (2) and (5) into Equation (9), as well as by substituting Mmf ¼ nmPm into Equation (9). Using tensor notation in Cartesian coordinates, we have (Sun 1998; 2002a) ðTmi P2m;i Þ;i 

T3 @P2m @em 2 2  2Pm ðm ¼ 1; 2; i ¼ 1; 2; 3Þ ðP  P Þ ¼ SunðP ; tÞ m 1 2 b m b 3 @t @t pffi l m t

SunðPm ; tÞ ¼

l m

12 ¼ dm

nm am bm ð1  e Þ þ 2 Pm Pm ð1 þ bm Pm Þ

rffiffiffiffiffiffiffiffiffiffiffiffiffiffi Dn P n pbm Pm

ð10Þ ð11Þ

ð12Þ

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PEIDE SUN

where, Sun( p, t) is called Sun function which is a state to describe the methane gas flow; In used general, the gas flow is growing fast as the function value of Sun( p, t) increase and the converses is true; the deduction details of Sun function formula (11) are given by Sun (1998; 2002a). Dn ¼ gas diffusion coefficient at pore pressure equal to Pn, Pn ¼ 1 atmospher; dm ¼ average coal micro-grain size of coal seam m. 3.2.

EQUATIONS FOR COAL OR ROCK DEFORMATION

The equations for the coal or rock deformation can be obtained by substituting Equation (6) into Equation (7) and using the equilibrium Equation (13) for overall stress. sm ij; j þ Fmi ¼ 0

ðm ¼ 1; 2Þ

ð13Þ

Taking into account the action of the pore pressure, we have (Sun 1998; 2002a) Umj; ji ðlm þ Gm Þ þ Umi; jj Gm þ Fmi þ ðam Pm Þ;i ¼ 0

ðm ¼ 1; 2; i; j ¼ 1; 2; 3Þ ð14Þ

where, Fmi ¼ free term for stress in coal seam m; Um ¼ displacement function in seam m. 3.3.

SOLID-GAS COUPLED MODELS FOR GAS LEAK FLOW

The equation set (15) gives the boundary and initial conditions and the mathematical model for coupled for solid elastic-deformation and gas leak flow. 9 P21  P22 @P21 @e1 > >  2P1 þT3 ¼ SunðP1 ; tÞ > b1 b3 @t @t > > > > > > 2 2 2 P  P @P @e > 2> 2 1 2 2 >  2P2 ðT2i P2;i Þ;i T3 ¼ SunðP2 ; tÞ > > b2 b3 @t @t > > > > > > Umj; ji ðlm þ Gm Þ þ Umi; jj Gm þ Fmi þ ðam Pm Þ;i ¼ 0 > > > > > > em ¼ Umi;i ; ðm ¼ 1; 2; i; j ¼ 1; 2; 3Þ > = Pm ðx; y; z; 0Þ ¼ Pm0 ðx; y; zÞ; >  > > > Pm ðx0 ; y0 ; z0 ; tÞt2ð0;þ1Þ ¼ Pa ; > > > >  > > ~m ðx; y; z; tÞ; > nt2ð0;þ1Þ ¼ Q Tmi @Pm =@~ > > > >  > >  em ðx; y; z; tÞ t¼0 ¼ em0 ; > > > >  > > Umi ðx; y; z; tÞt¼0 ¼ 0; > > > >  ;  ¼ Umi : Umi ðx; y; z; tÞ

ðT1i P21;i Þ;i

ð15Þ

t2ð0;þ1Þ

where, Pm0 ¼ initial pore pressure in coal seam m; Pa ¼ pressure in free space; em0 ¼ initial deformation rate in coal seam m; Umi ¼ boundary value for displacement in coal seam m; Qm ¼ quality vector for gas outflow from boundary surface in coal seam m. Equation (15) is characterized by: (1) The main consolidation of

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NUMERICAL SIMULATIONS FOR COUPLED ROCK DEFORMATION

gas leak flow through coal or rock due to gas drainage or coal mining can be described by the linear-elastic deformation in the coal or rock; (2) The mechanism for gas leak flow (both seepage and diffusion) is given by the equations of gas leak flow; (3) The gas desorption due to pore pressure is also given by the equation of gas leak flow; (4) The interaction between the gas leak flow and coal or rock elastic deformation is given by the coupled mathematical model.

4. The numerical simulation for methane gas leak flow 4.1.

MODEL SIMPLIFICATIONS

The numerical simulations for gas leak flow have been carried out using the data measured from coal face N1709 in the Datong mine 2, China, to test these models. At coal face N1709, coal seams 7 and 8 are mostly horizontal and the average distance between the two seams is 7.20 m. The coal face N1709 in coal seam 7 has a length of 120 m. The coal face advance is at a speed of 1.6 m per day in the direction of the run of the coal seam. The average deposit depth of the coal seam is 330 m, so the overloaded stress q0 is 8.25 MPa. Mechanical and physical properties for coal seams 7 and 8 of the Datong mine 2 are given in Tables 1 and 2. In this study, the numerical simulations for distributions of pore pressure in the coal seam 8 and distributions of gas leak flow in the coal seam 7 from the coal seam 8 have been carried until the coal face N1709 advance at 310 m in 194 day. Table 1. Mechanical properties for coal seams 7 and 8 of Datong mine 2 Coal seam

E (GPa)*

u*

Coal seam 7 Coal seam 8

0.65 0.41

0.294 0.292

*E ¼ modulus of elasticity of coal or rock; u ¼ Poisson ratio of coal or rock.

Table 2. Physical properties for coal seams 7 and 8 of Datong mine 2 Parameters*

Coal seam 7

Coal seam 8

Pm0, MPa bm , m gm, g/cm3 nm, % am, cm3/g bm, (kg/cm2)1 Mm, cm3/g a( ) Dm, cm2/s

0.80 0.90 1.45 1.58 34.48 0.12 18.20 3–5 5.59108

1.20 2.60 1.45 1.56 34.83 0.13 21.19 3–5 5.59108



*Pm0 ¼ initial pore pressure in coal seam m; bm ¼ average thickness of coal seam m; b3* for intercalation; gm ¼ unit weight of coal in coal seam m; nm ¼ porosity in coal seam m; am ¼ maximum gas adsorption coefficient in coal seam m; bm ¼ gas adsorption coefficient in coal seam m; Mm ¼ gas content in coal seam m; a ¼ slope angle of coal seam m; Dm ¼ gas diffusion coefficient in coal seam m.

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PEIDE SUN

Figure 2. A model for gas leakage

The problem for gas leak flow, strictly speaking, is a 3-D problem. It is not difficult to solve but requires a great deal of calculation. Based on in-situ data, models for plane strain can be treated to simplify a cross section in the coal face. Therefore, it is possible to use the equation for coal or rock deformation to yield plane strain model for the solid plane strain and the equation for gas leak flow can be a simplified model for one-dimensional flow of gas concurrent with leakage flow. The following gas permeability and the effective stress coefficient of pore pressure are based on experimental data (Sun, 1998; 2002a) T1 ¼ 2:044  104 expð0:050286Y01 þ 0:22911P21  0:005669Y01 P1 Þ ðcoal seam 8Þ T2 ¼ 1:038  104 expð0:049739Y02 þ 0:28838P22  0:006494Y02 P2 Þ; ðcoal seam 7Þ

Figure 3. A model for coal and rock deformation

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T3 ¼ 2:044  106 expð0:050286Y01 þ 0:22911P21  0:005669Y01 P1 Þ ðintercalationÞ a1 ¼

0:0543  0:00032Y01 þ 0:09748P1  0:00058Y01 P1 1 þ 0:00096P1 þ 0:001734P21 ðcoal seam 8Þ

a2 ¼

0:0233  0:00011Y02 þ 0:06686P2  0:00032Y02 P2 1 þ 0:00033P2 þ 0:000969P22 ðcoal seam 7Þ

4.2.

NUMERICAL SIMULATIONS AND PROGRAM DESIGN

The discrelization of the coupled models for solid deformation equations and gas leak flow equations has been expressed as Strong Implicit Approximation (SIP) finite differences (Xue and Xie 1980; Stone, 1986). A flow chart for the main program is shown in Figure 4. 4.3.

RESULTS

(1) As the long wall coal face N1709 in the coal seam 7 advances by 310 m, the pore pressure of methane gas in the coal seam 8 changes and is shown in Figure 5. The numerical simulation results reveal that the simulated value of pore pressure in the coal seam is close to the measured one. (2) It can be seen from Figure 5 that the pore pressure of methane gas drops fast in the direction of gob within 50 m from the coal face in coal seam 8. The pore pressures in coal seam 8 drop to 0.4 MPa in the direction of gob within 100 m away from the coal face.

Figure 4. Flow chart for main program

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PEIDE SUN

Figure 5. Distribution of pore pressure in the coal seam 8

(3) The distribution curves for gas content in the coal seam 8 can accurately be predicted according to Figure 5. Moreover the flow rate for gas leak flow from the coal face and gob in coal seam 7 can also be predicted as a function of time. In this case, if the initial pore pressure of gas in coal seam 8 drops to 0.4 MPa, it is predicted that the flow rate for gas leak flow from the coal seam 8 is 2/3 great of the total gas flow rate from both coal seams 7 and 8, and this result is close to experimental measurements (Sun, 1998).

5. The numerical simulation for effective protection range 5.1.

INTRODUCTION OF THE PROJECT

Sonzao mining bureau’s second mine of Datong is a mine with many coal outburst dangers. The protective layer mining technique has been used for many years in this mine. On the basis of local survey parameters and study, this study analyses the effective protection range of the down-proximate layer (the coal seam 8) after exploiting the coal seam 7 as the up-protective layer. Taking the N1709 coal face of the 7th coal seam as the first-exploited up-protective layer and accounting for the exploitation speed of 1.6 meter per day, the analysis shows that when the coal-face reaches 310 m(corresponding to 914 days) the down-proximate layer

Figure 6. A plane model for gas leakage flow

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Figure 7. A plane strain model for coal deformation

(8th coal seam)’s leakage gas gushes up, which leads to redistribution and change of pore pressure in the 8th coal seam. In practice, choosing the average burial depth of the coupled coal seam as 330 m, then the overloaded stress q0 ¼ 8.25 MPa. Mechanical and physical properties for the coal seams 7,8 are listed in Tables 1 and 2. Equation (15) can reflect the interaction process of coal or rock elastic deformation and gas leakage flow by the action of mining. Here we make a little simplification appropriate to practical problem. So under mining conditions, we mainly study the distributing law of pore pressure in the down-proximity layer (the 8th coal seam)’s plane, then solid deformation modelling can choose approximately unit depth in the 8th coal seam for horizontal calculation modeling. Doing this, the solid-gas interaction problem in a couple of coal seam can be changed to the interaction between the leakage’s horizontal flow and coal or rock plane strain, which avoids solving the problem of three-dimensions. The result of numerical simulations can still meet the needs of a practical project. Figure 6 is the plane model for gas leakage flow and Figure 7 is the plane strain mechanical model for coal or rock deformation. Interaction modeling is discrete using SIP in this study, as it fits well with the numerical solution of non-linear mathematical modeling. Using Fortran or

Figure 8. The curve for pressure down angle along the run of coal seam 8

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C languages, program Gas-Leakage 02 can successfully run on a PC. A flow chart for the main program is shown in Figure 4.

5.2.

RESULTS

According to the numerical analysis result of Sun (1998) and this study, Figures 8 and 9 can be produced; from the two charts we can get three results as below.

Figure 9a. 2-D isograms showing distribution of pore pressure in coal seam 8 when 100 days of the upprotect seam (coal seam 7) has been exploited in the direction of the run of the coal seam. The unit of the pore pressure isograms is MPa

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Figure 9b. 2-D isograms showing distribution of pore pressure in coal seam 8 when 140 days of the up-protect seam (the coal seam 7) has been exploited in the direction of the run of the coal seam. The unit of the pore pressure isograms is MPa

(1) If we choose the minimum value of safety pore pressure at the 8th layer as Pmin ¼ 0.5 MPa, then we can get the curve for pressure down angle along the run of the coal seam 8 (Figure 8). Of course, the minimum value of safe pore pressure can be decided by observation and study on the spot. From Figure 8 we know that simulation values of pore pressure are consistent with the distribution observed in practice. In addition, a (pressure down angle in numerical simulation) < b (pressure down angle in practice), that is a ¼ 46 , b ¼ 54 , which means that the pore pressure distribution using numerical analysis err on the side of safety.

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PEIDE SUN

Figure 9c. 2-D isograms showing distribution of pore pressure in coal seam 8 when 160 days of the up-protect seam (the coal seam 7) has been exploited in the direction of the run of the coal seam. The unit of the pore pressure isograms is MPa

(2) Figure 9(a) to Figure 9(d) are 2-dimensional isograms for the time-dependent pore pressure distribution in coal seam 8 if coal seam 7 is chosen as the protectiveseam to be exploited first and when it reach 310 m. If the minimum value of safety pore pressure is choses as 0.5 MPa, the region of the pore pressure less than 0.5 MPa in the seam in Figure 9(d) safe protective zone; namely work in the region of

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Figure 9d. 2-D isograms showing distribution of pore pressure in coal seam 8 when 194 days of the upprotect seam (the coal seam 7) has been exploited in the direction of the run of the coal seam. The unit of the pore pressure isograms is MPa

the pore pressure less than 0.5 MPa in coal seam 8 is safe; coal and gas outburst would not appear. The above conclusion has been proved to be right by practice on site. (3) According to Figures 8 and 9, the effective protective-range at coal seam 8 can be done along quantitative space division and the above computer simulation results are all time-dependent. We can know the change of pore pressure along the run of coal seam and the trend distribution in the down-proximate seam (the 8th) any time

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PEIDE SUN

when the up-protective layer is being exploited. The above conclusions can guide safe exploitation for miners and protective measures for outbursts, etc.

6. Conclusions The following conclusions can be drawn. (1) Mathematical models for coupled solid deformation and gas leak flow in parallel coal seams are given according to the new viewpoint of solid-gas interaction, and the interaction between the elastic deformation of coal or rock and gas leak flow has been studied with this coupled model. Numerical simulations have been performed with Strong Implicit Approximation finite difference. It is found that the coupled model for solid deformation and gas leak flow gives results that are close to reality. (2) The solid-gas coupled models can be applied to problems of gas leak flow including mining engineering, gas drainage engineering and mining safety engineering, the prediction of the safe range using protection layer mining where coal and gas outbursts can efficiently be prevented. (3) The interaction theory is used in numerical simulations for the effective protection range during the protective-layer’s exploitation. The interaction models put forward in this study can reflect the practice well and have better application in the future. (4) The exploitation technique in protective-layer mining is an effective way of preventing regions of coal and gas outburst. Quantitative of determination effective protection range is also an engineering question of gas leakage flow. This study has put forward a new, quantitative time-dependent method for solving such problems.

Acknowledgements This study was supported by the Visiting Scholar Foundation of Key Laboratory in University of P. R. China. The author would like to thank to professor Xuefu Xian, Daijun Zhang and Ph. D. Longjun Xu of Chongqing University for their helpful comments. The author would like to thank to professor M. Cross of Center for Numerical Modelling and Process Analysis, University of Greenwich for his great help. Finally, the author would give his grateful to Ph.D. Huagen Wan with Zhejiang University for his help with simulations.

References Bear, J. (1972) Dynamics of Fluids in Porous Media, American Elsevier Publishing Co. Inc. New York. Bear, J. and Bachmat, Y. (1991) Introduction to Modeling of Transport Phenomena in Porous Media, Kluwer Academic Publisher, Netherlands. Biot, M. A. (1941) General theory of three-dimensional consolidations, J. Appl. Phys., 12, 155–164.

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