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A fully coupled coal deformation and compositional flow model for the control of the pre-mining coal seam gas extraction
International Journal of Rock Mechanics & Mining Sciences 72 (2014) 138–148
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A fully coupled coal deformation and compositional flow model for the control of the pre-mining coal seam gas extraction Tongqiang Xia a,b,d, Fubao Zhou a,c,n, Jishan Liu e, Shengyong Hu a, Yingke Liu a,c a
Key Laboratory of Gas and Fire Control for Coal Mines, China University of Mining and Technology, Xuzhou, China State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China c State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Xuzhou, China d State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou, China e School of Mechanical and Chemical Engineering, University of Western Australia, Crawley, WA, Australia b
art ic l e i nf o
a b s t r a c t
Article history: Received 12 October 2013 Received in revised form 10 January 2014 Accepted 11 August 2014
Fully coupled compositional (coal seam gas and air) model of coal deformation, coal gas flow and transport, and air flow in coal seams is developed to better understand the gas drainage processes and the coal gas–air mixing mechanisms during pre-mining coal seem gas extraction. The model was first verified by showing that the modelled gas concentration profiles match reasonably with the in-situ measured ones. The verified model was then applied to evaluate how the drained gas concentration could be controlled under different conditions of the sealing length, the leakage rate and the leakage fracture width. These modelled results provides the basis of a new in-situ control technology of gas–air mixing, which uses fine expansive particles to seal the leakage fractures around the borehole. This technology has been commercially applied to enhance the concentration of the pre-mining gas drainage. The field test shows that the characteristics of the leakage fractures are greatly changed after the particles are injected into the in-seam drainage borehole when the gas concentration declines. Once the leakage fractures are blocked with the particles, the outside air is prevented from entering the coal seam. Thus, an ideal gas concentration can be maintained, and the duration of higher gas concentration is extended. For boreholes with an originally low gas concentration (0–30%), the new technology can increase the gas concentration by 10–65% and extend the production time by approximately two to three months. The total amount of gas drainage increases to 2000–3000 m3 per borehole. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Coal seam gas drainage Coal–gas interactions Compositional flow Fracture sealing
1. Introduction Gas drainage, which is an interesting topic worldwide, can reduce gas pressure, eliminate the risk induced by coal gas in mines, provide a new resource and protect the environment [1]. However, in China, coal seams are characterised by low permeability, strong adsorption and high gas pressure. The coal seam permeability in most Chinese mines (except the southern Qinshui coalfields) ranges between 10 4 and 10 3 mD, which is four and three orders of magnitude lower than those in the U.S. and Australia, respectively [2,3]. All of these reasons restrict the feasibility of surface drilling drainage in China. Therefore, the widely used method to control coal gas in China is underground drilling drainage [4–7]. Unfortunately, this method has many n Corresponding author at: Key Laboratory of Gas and Fire Control for Coal Mines, China University of Mining and Technology, Xuzhou, China. Tel.: þ 86 516 83899753; fax: þ 86 516 83995053. E-mail address: [email protected] (F. Zhou).
http://dx.doi.org/10.1016/j.ijrmms.2014.08.012 1365-1609/& 2014 Elsevier Ltd. All rights reserved.
problems such as the small flow of single-hole gas drainage, the low concentration and its rapid decrease, particularly in the inseam drilling drainage, which is one of the most important and effective measures to pre-drain the coal seam gas before coal mining to eliminate the risk of outburst [8–11]. According to statistics, the gas drainage concentration of 80% in-seam boreholes varies from 6% to 20% in a short time, and the average pre-drained rate of coal seam gas is less than 23% [12]. Such low concentration may lead to a low utilisation ratio, which will result in more serious environmental pollution if the gas is directly released. Furthermore, the low concentration of gas drainage may lead to many hazards such as spontaneous combustion of coal, gas combustion and gas explosion [13–15]. To enhance the quality of gas drainage in coal seams or to make a large flow and a high methane concentration is a valuable goal for research workers of coal mines. Most scholars and engineers agree that increasing the seam permeability can achieve the high efficiency of gas drainage in coal seams. The seam permeability is closely related with the evolution of coal pores/fractures, which
T. Xia et al. / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 138–148
originates from coal–gas interactions such as the swelling/shrinkage of the coal matrix, which is introduced by adsorption/desorption, and the effective stresses and temperature changes. Based on experimental observations, many models have been formulated to quantify the permeability evolution during coal swelling/ shrinkage. Gray [16] presented a coal permeability model that represents the effects of the matrix shrinkage and the pore pressure changes on the coal permeability. Since then, many theoretical and empirical permeability models have been proposed, including Harpalani and Zhao [17], Sawyer et al. [18], Seidle et al. [19], Seidle and Huitt [20], Palmer and Mansoori [21], Gilman and Beckie [22], Shi and Durucan [23,24], Palmer [25], etc., where both the shrinkage and the pore pressure effects are included. However, most of these studies assumed either a constant overburden load, or they are derived from the compressibility concept of porosity, which may provide incorrect outcomes or overestimates of the permeability change [26,27]. These critical and limiting assumptions have been relaxed in the new models [25,28–32], which rigorously incorporate the in-situ stress conditions. Besides, since the concept of gas sequestration was first proposed by Macdonald of Alberta Energy during discussions with Gunter and co-workers in 1991 [33,34], greenhouse gas sequestration enhanced coal bed methane (ECBM) recovery has recently attracted attention worldwide. A number of field ECBM storage pilot projects [33–38] have been undertaken in North America, Europe, Poland, China, Japan, etc. In addition, a large number of experiments [39–46] associated with the competitive adsorption characteristics of multi-component gas in the coal matrix are discussed, and many theory models of gas adsorption, desorption and percolation have also been developed under the competitive adsorption of multi-component gas. Wei et al. [47,48] presented an alternative model to address the model of multi-component gas diffusion and flow in bulk coals, which focused on the CH4–CO2 counter-diffusion that was associated with the CO2-sequestration enhanced coal bed methane (CO2–ECBM) recovery. Connell and Detournay [49] conducted a coupled numerical model for CO2– ECBM. Similarly, Wang et al. [50] proposed a deformation-flow coupled model to address CO2–ECBM. Chen et al. [51,52] extended the single poroelastic model of Zhang et al. [28] to include the flow and the transport of gas mixtures (binary gasses: CO2 and CH4). More recently, Wu et al. [53] developed a dual poroelastic model (dual solid media-coal matrix and fracture) for CO2–ECBM under variable stress conditions. However, the enhanced recovery of methane using CO2 or flue gas as an injectant may be deemed unattractive in active underground coal mines because of the potential for toxic concentrations of CO2 to arise during mining [54]. Yang et al. [55] proposed a multi-physics coupled model that included seepage, diffusion and competitive adsorption of the multi-component gas, and the methane quantity in releasing holes and degassing holes was simulated under N2 or CO2 injection into the coal bed. Subsequently, a series of underground experiments of N2 injection into the coal bed to accelerate the coal seam gas emission were carried out, whose results indicated that the pure methane drainage flow in these boreholes within 2 m increased more than two times after 16 h of N2 injection [56]. To conclude, although a certain degree of success has been achieved using the above models to explain and match the experimental data, a key point, which is the common phenomenon of low concentration in the gas drainage process, has not been addressed in these models. This will easily result in the overestimation of gas drainage for an unfavourable drilling design, particularly at high gas pressure and outburst coal seam. The lowconcentration phenomenon of gas drainage can be explained as follows: because of the excavation of both roadways and boreholes, many leakage fractures occur around the borehole [57,58], and much roadway air floods into the seam borehole under
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negative-pressure driven, which results in a significant decline in the gas concentration (Figs. 3a and 8a). Based on the dual-porosity medium model, the leakage evaluation model of the in-seam drainage borehole is established in this paper by considering the coal deformation, the gas flow and the gas transport in the matrix/ fracture system and the blocking effect of drilling on the gas drainage quality is also evaluated. Finally, a new borehole sealing technology is proposed to improve the gas drainage quality.
2. Governing equations The following assumptions are considered in the model: (1) coal is a dual poroelastic continuum, and the strains are infinitesimal; (2) coal is saturated with gas, and the conditions are isothermal; (3) the gas contained in the pores is ideal, and its viscosity is constant under isothermal conditions; (4) the gas flow satisfies Darcy’s law in the coal matrix and the fractures; (5) the outside air pressure is much smaller than the pressure in the pores, so the air adsorption in the coal matrix is not considered here; in other words, the air may only flow in the coal fractures. In the following derivations, the dual-porosity fractured coal is conceptualised as shown in Fig. 1 [53,59], which comprises the coal matrix and the coal fractures. The edge dimension of the matrix blocks and the fracture aperture are represented by a and b, respectively, Kn is the fracture stiffness, and σ e is the effective stress. 2.1. Gas flow and transport The mass balance equation of the gas component κ can be expressed for a static medium, which incorporates these convective and dispersion modes of transport but involves the interchange between free gas and adsorbed gas as ∂mκ þ ∇ u ρgκ þ ∇ Dκ ∇mκ f ¼ Q sκ ð1Þ ∂t where the subscript “κ ” (κ ¼1,2) represents the component of CH4 and air (mainly O2 and N2), respectively, ρg is the gas density, t denotes the time variable, Q s is the gas source or sink, m is the gas content, and mf is the gas content of the free state in the matrix or the fracture. For a binary gas system, the mixture gas pressure p and the gas pressure pm in the matrix and the pressure pf in the fracture can be
Fig. 1. Schematic of a dual-porosity fractured medium.
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expressed as p ¼ ∑pκ ; pm ¼ pm1 ; pf ¼ pf 1 þ pf 2
ð2Þ
The mass of each component in the fracture and in the matrix which are contained in 1 unit volume of coal can be defined as mf κ ¼ ϕf ρf κ ; mm1 ¼ ϕm ρm1 þ ρs ρa
V L pm1 ; and mm2 ¼ 0; P L þ pm1
ð3Þ
respectively, where ρf κ ¼ M κ pf κ =RT and ρmκ ¼ M κ pmκ =RT. The subscripts “m” and “f” represent the matrix and the fracture system, respectively, ρfk is the density of the gas component κ in the fractures, ρa is the CH4 density at standard conditions, ρs is the coal density, VL is the CH4 Langmuir volume constant, M κ is the molar mass of component κ , and ϕ is the porosity. In Eq. (1), the vector of convective velocity u can be expressed as follows (the effect of gravity is neglected) uf ¼
kf
μ
∇pf ; um ¼
km
μ
∇pm
ð4Þ
where k is the permeability, and μ is the average coefficient of dynamic viscosity for the mixed gas. Each component of the hydrodynamic dispersion coefficient Dκ is defined as Df κ ¼ β c uf þ Df κ 0 ; Dmκ ¼ β c um þDmκ 0
ð5Þ
where Dκ 0 is the coefficient of molecular diffusion of component κ , and βc is the dynamic dispersivity. By substituting Eqs. (2)–(5) into Eq. (1), the governing equations for gas flow can be obtained: "
#
ϕm þ
ρs pa V L P L ∂pm1 P L þpm1
2
∂t
þpm1
∂ϕm km þ∇ pm1 ∇pm1 ∂t μ
þ ∇ð ϕm Dm1 ∇pm1 ¼ ωðpm1 pf 1 Þ
where εV ¼ ε11 þ ε22 þ ε33 is the volumetric strain of the coal matrix, Kf ¼aKn is the modified fracture stiffness, and the subscript “0” denotes the initial value of the corresponding variables. By variable separation and integration of Eq. (10), the coal matrix porosity can be obtained as " # 1 1 1 b0 þ ϕm ¼ α þ ϕm0 α exp ðεV εV 0 εs þ εs0 Þ ð11Þ K K a0 K f Previous work [53,59,61,62] suggested that the porosity and permeability model for coal fracture could be defined as
ϕf Δb 3 ¼ 1þ ¼ 1þ ðεV εV 0 þ εs0 εs Þ b0 ϕf 0 ϕf 0 þ 3K f
The partial derivative of ϕm and ϕf with respect to time is respectively expressed as follows: # 1" 1 1 ∂ϕm b0 ∂εV εL P L ∂pm þ ¼ ϕm α ð13Þ K K a0 K f ∂t ∂t RT P L þ p 2 ∂t m
"
# 1 ∂ϕf ϕf 0 1 b0 ∂ εV εL P L ∂pm þ ¼ ∂t K f K a0 K f ∂t RT P L þp 2 ∂t
∂ϕ ∂p k ϕf f 2 þ pf 2 f þ ∇ f pf 2 ∇pf þ ∇ð ϕf Df 2 ∇pf 2 Þ ¼ 0 ð8Þ ∂t ∂t μ where ω ¼ 8 1 þ 2=a2 km =μ is the transfer coefficient between the matrix and the fracture.
ð14Þ
m
The cubic law is chosen to calculate the relation between permeability and porosity; we thereby obtain 8 > km ϕm 3 < α α ¼ ¼ þ 1 > km0 ϕm0 ϕm0 :ϕm0 9 " #>3 1 = 1 1 b0 þ exp ðεV εV 0 þ εs0 εs Þ > K K a0 K f ;
ð6Þ
∂ϕ ∂p k ϕf f 1 þ pf 1 f þ ∇ f pf 1 ∇pf þ ∇ð ϕf Df 1 ∇pf 1 Þ ¼ ωðpm1 pf 1 Þ ∂t ∂t μ ð7Þ
ð12Þ
K
kf ¼ kf 0
ϕf ϕf 0
!3
" ¼ 1þ
#3 1 1 1 b0 þ ðεV εV0 þ εs0 εs Þ K f K a0 K f
ð15Þ
ð16Þ
where the initial permeability kf0 of the coal seam fracture, which depends on the degree of development of the fracture in the coal seam, can be calculated as following [63,64]: ϕf 0 ¼ 3b0 =a0 , and 3 kf 0 ¼ b0 =ð12a0 Þ.
2.2. Coal seam deformation 2.4. Cross coupling The Navier-type equation for the dual-porosity model can be expressed as Gui;kk þ
G u αpm;i βpf ;i K εs;i þ f i ¼ 0 1 2υ k;ki
ð9Þ
where G ¼ D=2ð1 þ υÞ, D ¼ ½ð1=EÞ þ ð1=aK n Þ 1 , K ¼ D=3ð1 2υÞ, α ¼ 1 ðK=K s Þ, β ¼ 1 ðK=aK n Þ, and εs ¼ εL pm1 =ðP L þ pm1 Þ, E is the elastic modulus, G is the shear stiffness, σkk denotes the components of the mean stress, α and β are Biot coefficients [60], K is the bulk modulus, Ks is the grain elastic modulus, Kn is the normal stiffness of the individual fractures, fi is the component of the body force, εs is the strain induced by gas sorption, and εL and PL are the CH4 Langmuir matrix swelling and pressure constants, respectively.
Substituting Eq. (2) into Eq. (9), we rewrite the governing equation for coal seam deformation as " # G K εL P L u αþ Gui;kk þ pm1;i βðpf 1 þ pf 2 Þ;i þ f i ¼ 0 1 2υ k;ki ðP L þ pm1 Þ2 ð17Þ After the substitution of Eqs. (13)–(16) into the gas flow Eqs. (6)–(8), the final gas flow equations yield 1 ∂pm1 km ϕm þ ρs pa V L PL 2 ðϕmK αÞ εL PL pm1 2 K1 þ a0bK0 f ∂t þ∇ μ pm1 ∇pm1 ðPL þ pm1 Þ ðP L þ pm1 Þ 2 km þ ∇ ϕm Dm1 ∇pm1 ¼ 8 1 þ 2 ðp p Þ μ m1 f 1 a 1 ϕ α pm1 1 b0 ∂ εV þ m K a0 K f K ∂t
2.3. Dynamic permeability models Following our previous work [61], the porosity model of the matrix is defined as follows (the effect of temperature is neglected): ϕ α 1 b0 1 dϕm ¼ m þ ðdεs dεV Þ ð10Þ K a0 K f K
ϕf
∂pf 1 kf þ ∇ pf 1 ∇pf þ ∇ð ϕf Df 1 ∇pf 1 Þ ∂t μ 2 km ¼ 8 1þ 2 ðp p Þ μ m1 f 1 a
ð18Þ
T. Xia et al. / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 138–148
141
Fig. 2. The cross coupling of the field equations.
# 1" pf 1 ϕf 0 1 b0 ∂ εV εL P L ∂pm1 þ 2 K a0 K f Kf ∂t ∂t PL þ p
ð19Þ
m1
ϕf
∂pf 2 kf þ ∇ pf 2 ∇pf þ ∇ð ϕf Df 1 ∇pf 2 Þ ∂t μ # 1" pf 2 ϕf 0 1 b0 ∂ εV εL P L ∂pm1 þ ¼ 2 K a0 K f Kf ∂t ∂t PL þ p
ð20Þ
m1
Eqs. (17)–(20) define the coupled model including coal deformation and multi-component gas flow in a dual-porosity medium. Cross coupling between the field equations for coal deformation and multi-component gas flow are illustrated in Fig. 2. The above governing equations, particularly the multi-component gas flow equation, are nonlinear second-order partial differential equations (PDEs) in space and first-order PDEs in time. These equations cannot be theoretically solved because of the nonlinearity in both the space and time domains. Therefore, they are implemented into COMSOL Multiphysics and solved using the finite-element method.
3. Model validation 3.1. Model case Huachu coal mine of Liuzhi Coal Mining Group, located in Guizhou province of southern west China, is under the threat of coal and gas outburst. There are 80 times of outburst occurred since the first production year of 1974. Currently, ♯7 seam is mineable seam and the original gas content within the seam varies from 12.97 m3/t to 19.35 m3/t, and the average value is 16.16 m3/t. In-seam gas pressure is from 1.09 MPa to 1.75 MPa with the average of 1.42 MPa. The in-seam borehole’s diameter is about 94 mm and its negative drainage pressure is about 12 kPa to 20 kPa. The monitor date shows that it only took 10 to 30 days for the concentration dropped to 30% or even smaller. The average pure CH4 flow rate of a single hole was between 0.0015 m3/min and 0.0125 m3/min and the flow decay factor was 0.0562– 0.8167 d 1. In the following work, the correctness of our model will be first verified against actual gas drainage data in coal seam ♯7 of the Huachu coal mine. 3.2. Physical model and boundary conditions The schematic of the seam drainage zone in coal seam ♯7 with half of the vertical borehole section is shown in Fig. 3a, where the
physical model for calculation is divided into two regions: the mining influence area (ABCHIFGA) and the no-mining influence area (CDEFIHC). The radius of the broken area around the drilling hole is five times the borehole radius, and the influence area distance GF induced by roadway excavation is expressed as [65] hΘ λ γ H tan φ þ C GF ¼ ð21Þ ln C 2tg φ where h is the mining height of the coal seam, H is the buried depth of the mining roadway, C is the cohesion of coal, φ is the internal friction angel of coal, γ is the bulk density of overburden strata, λ is the stress concentration factor of the vertical direction in front of the coal wall,and Θ is the coefficient of side pressure coal wall defined as Θ ¼ 1 sin φ = 1 þ sin φ . In the test place h¼3.8 m, H¼ 320 m, γ ¼ 25 kN/m3, C ¼98 kPa, ϕ ¼151 and λ ¼ 2.2, the affected zone’s distance of excavation GF¼ 16 m can be calculated. The initial pressure in the coal is p0 ¼1.42 MPa, the borehole sealing length is AB ¼8 m, and the effective drainage length is BC¼ 72 m. The model boundary conditions are implemented in the modelling as follows: (a) For solid deformation: the model top border has the stress boundary q ¼ γ H and free boundary condition, the left border has free boundary condition and no stress, and the other borders have the normal displacement constraint and no stress; (b) for the CH4 flow in the coal matrix and the fracture: all borders have no flow boundary condition in the matrix; however, the pressure boundary condition p0CH4 ¼ 9350 Pa is imposed on BC, and the remaining borders have no flow boundary conditions in the fracture; (c) for the air flow in the fracture: AG has the pressure boundary condition p0Air ¼ 101,350 Pa, BC is regarded as the export flow boundary N0, which is estimated according to the measured leakage amount, and the remaining borders have no flow boundary condition. 3.3. Validation Grid generation of the model, including 3000 elements and 85,827 degrees of freedom, is through mapped mesh method as shown in Fig. 3b. Most parameters of the model (as listed in Table 1) are chosen from the experimental results, whereas the unreported parameters are substituted from the contemporary literature [28,53,59]. The parameters of different boreholes are shown in Table 2, in which the fracture aperture b2 of the affected zone is obtained from the history matching of gas drainage and the numerical parameter inversion. In order to better understand the gas drainage processes and the coal gas–air mixing mechanisms, the contours of gas
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Fig. 3. Model boundary conditions and mesh generation. Table 1 Modelling parameters for the numerical simulation. Parameter
Value
Parameter
Value
Young’s modulus of coal, E (MPa) Young’s modulus of coal grains, Es (MPa) Fracture stiffness, Kn (MPa) Poisson’s ratio of coal (υ) Density of coal, ρs (kg/m3) Initial porosity of matrix (ϕm) Initial permeability of matrix, km0 (m2) Fracture width of original coal b1, (m) Fracture spacing of coal, a (m) Gas dynamic viscosity μ, (N s/m2)
2823 8469 4800 0.339 1250 0.05 2.8 10 16 5 10 6 0.005 1.84 10 5
Bulk density of coal and rock, μ (kN/m3) Vertical depth of the roadway mining, H (m) Standard atmospheric pressure, pa (MPa) CH4 Langmuir pressure constant, PL (MPa) CH4 Langmuir volume constant, VL (m3/kg) CH4 Langmuir volumetric strain constant (εL) Molar gas constant, R (J/(mol K) Coal temperature, T (K) CH4 diffusion coefficient, D1 (m2 s) Air diffusion coefficient, D2 (m2 s)
2.5 320 0.101325 2.45 0.016 0.0128 8.3143 300 3.6 10 12 5.8 10 12
Table 2 Simulation parameters for the different boreholes. Borehole Fracture spacing of coal, a (m)
Fracture width Initial fracture of original width of coal, b1 (m) disturbed coal, b2 (m)
Leakage rates of BC segment, N0, (mol/(m2 s))
No. 1 No. 2 No. 3
5 10 6 5 10 6 5 10 6
8 10 5 2 10 4 5 10 5
0.001 0.005 0.005
6 10 5 8 10 4 6 10 5
concentration in coal fractures during the gas drainage processes of the borehole No. 1 are shown in Fig. 4a, and the dynamic evolutions of matrix/fracture permeability and gas pressure in the matrix at point I (90, 1) are shown in Fig. 4b. It observed from Fig. 4 that the excavation-induced fractures around drainage boreholes accelerate the release of gas in the vicinity of a drainage borehole. As the gas in this region is released, these fractures widen further due to coal matrix shrinkage, which responds to the increase of fracture permeability and the decrease of matrix permeability. Through these widened fractures, a large amount
T. Xia et al. / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 138–148
143
Fig. 4. Dynamic evolution of gas concentration, gas pressure and dual-permeability. (a) The contours of gas concentration in the coal fracture with time, (b) the dynamic evolutions of matrix/fracture permeability and gas pressure in the matrix.
of air flows into the coal seam and mixes with the desorbed gas, resulting in the low gas drained concentration. Furthermore, the theoretical model is verified against the actual gas drainage data as shown in Fig. 5.
4. The simulation of leakage sealing effect
Fig. 5. The comparison between the simulation results and the field data of gas drainage.
The effect of gas drainage is closely related to the basic properties of coal such as the porosity, the permeability and the adsorption characteristics. In this paper, we mainly focus on the gas drainage quality under different sealing effects, and the coal properties that affect the gas drainage quality will be discussed in another paper. Practice has proved that increasing the length of the sealing segment AB can improve the gas drainage concentration. The numerical simulation of the gas drainage quality is shown in Fig. 6 for different sealing lengths AB and leakage rates N0. It is observed from Fig. 6 that the smaller leakage rate corresponds to the higher gas concentration for the same sealing borehole length AB, whereas the effect of the leakage rate on the
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Fig. 6. Gas drainage quality for different sealing lengths and leakage rates.
pure CH4 flow is sufficiently weak to be negligible. For example, when AB ¼ 20 m, the trends of the CH4 flow with time are basically corresponding under the leakage rates N0 ¼ 2 10 5 mol/(m2 s) and N0 ¼ 1 10 6 mol/(m2 s) in the gas drainage. However, the concentrations of gas drainage are significantly different: the average gas concentration is 30%, and the lowest gas concentration is 7% for 115.7 d when N0 ¼ 2 10 5 mol/(m2 s), whereas the average gas concentration is 82.2%, and the lowest gas concentration is 59.3% when N0 ¼ 1 10 6 mol/(m2 s). When N0 changes from 2 10 5 mol/(m2 s) to 1 10 6 mol/(m2 s), the average gas concentration increases by 174%. For the same leakage rate, the longer sealing length of the borehole corresponds to the higher concentration of gas drainage. For example, for the borehole sealing length AB ¼8 m, the average concentration of gas drainage is 24.2% for 115.7 d under N0 ¼ 2 10 5 mol/(m2 s), whereas the concentration is 27.3% and 30% for AB ¼16 m and AB ¼20 m, respectively. Thus, when AB ¼16 m and 20 m, the concentration increases by only 12.8% and 24%, respectively, comparing with that for AB ¼8 m. However, it is also observed from Fig. 6a that there is no linear relationship between the sealing length and the pure CH4 flow. In addition, increasing the sealing length can enhance the gas concentration at the expense of less pure CH4 flow because the increase in sealing length reduces the effective drainage length, which may reduce the total amount of pure CH4 flow. For example, for the sealing lengths AB ¼ 8 m, AB ¼16 m and AB ¼20 m, the pure CH4 flow are 0.0032 m3/s, 0.0045 m3/s and 0.0043 m3/s, respectively, at the
Fig. 7. The influence of changing the leakage fracture characteristics on the gas drainage concentration (in the figures, I and II are the drainage stage before and after the change of leakage permeability, respectively).
beginning of the gas drainage. Thus, the low gas concentration essentially results from the leakage fractures around the drilling borehole. If the characteristics of the leakage fractures can be improved, the gas effect will increase. To better illustrate this problem, the simulation with reference to the gas drainage quality is performed for different leakage characteristics as shown in Fig. 7. It is observed from Fig. 7(a) and (b) that both the gas concentration and the pure CH4 flow are closely related to the leakage fracture width b2. When the permeability of the mining
T. Xia et al. / International Journal of Rock Mechanics & Mining Sciences 72 (2014) 138–148
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Fig. 8. The process of sealing the air-leakage fractures around the borehole using particles. (a) Schematic diagram of the borehole plugging-up stage, (b) schematic diagram of fracture sealing using particles.
Fig. 9. 2372 Roadway field test photos.
influence area is small, which corresponds to a low leakage rate, the flow and the concentration of pure CH4 drainage are high. For example, for b2 ¼8 10 6 m and N0 ¼ 8 10 7 mol/(m2 s), the amount of gas drainage is 36.5 m3, and the average concentration of gas drainage is 83.48% for 115.7 d. However, when b2 ¼ 8 10 4 m and N0 ¼ 2 10 4 mol/(m2 s), the amount of gas drainage is 34.5 m3, and the average concentration of gas drainage is 6.34% for 115.7 d. Thus, the change in leakage characteristics has little effect on the total amount of gas drainage, but it can significantly improve the gas drainage concentration. To clearly describe the relationship between the leakage fracture characteristics and the gas drainage concentration, we take the history data of the borehole No. 1 before and after the change of leakage permeability as an example, in which the borehole No. 1 is the same as 1♯ gas drainage drilling in Fig. 10. The simulation shows the effect of changing the leakage fracture characteristics on the gas drainage concentration when the gas concentration declines. It is observed from Fig. 7(c) that the gas drainage concentration is
significantly enhanced by changing the leakage characteristics. For example, when b2 ¼6 10 5 m and N0 ¼ 8 10 6 mol/(m2 s), the gas drainage concentration decreases from 100% (t¼ 0 d) to 20.8% after 12 d. If the leakage fracture width is changed, the gas drainage concentration will significantly increase, and the duration of gas production is also extended. For example, for b2 ¼ 2 10 6 m and N0 ¼ 5 10 7 mol/(m2 s), the highest gas concentration increases to 91.9%, and the average gas drainage concentration is 48.9% during 12–90 d, which increases by 15.1 times compared to the original natural drainage for b2 ¼ 6 10 5 m and N0 ¼ 8 10 5 mol/(m2 s).
5. A technology to control the gas quality When performing gas drainage, effectively sealing the leakage passages of roadway air into the borehole is the key to solve the engineering problems of low concentration and small flow. However, overall, the existing borehole sealing methods [66–71] are
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Fig. 10. Concentration variation curves before and after fracture sealing (in the figures, a and b are the drainage duration before and after fracture sealing, respectively).
only performed at the sealing stage inside the borehole, which does not address the problem of decreasing gas drainage concentration because of the evolution and development of the leakage fractures that are caused by the mining activities and the gas drainage. Therefore, a new approach of using particles to seal the leakage fractures around the boreholes is proposed in this paper. In this method, when the gas drainage concentration rapidly decreases, the fine expansive particles are injected into the borehole sealing section using high-pressure air, and the particles penetrate the leakage fractures in the coal seam. After a period of time, the particles will deposit/coagulate to block up the fracture channels. Hence, the size and the number of fractures will decrease, which increases the leakage resistance to resist the outside air that enters. Thus, the gas concentration substantially increases, and the duration of gas production is also extended. The process can be divided into two different stages: the borehole plugging-up stage and the fracture sealing stage. During the first stage (Fig. 8a), once the borehole is drilled to the expected length, the drainage pipe, which is twined with foam polymeric materials, is delivered into the borehole to plug up the outside air. The length of the plugging segment with foam polymeric materials is L1 (73 m), whereas the distance to the borehole outlet, which is filled with expansive cement, is L2 (77 m). Then, the drainage pipe is connected for gas drainage. As the drainage continues, the methane pressure in the coal will decrease, which causes the CH4 flow to slowly decrease.
Simultaneously, the outside air under the driven pressure is sucked into the drainage system and causes the concentration to decrease. When the concentration decreases to less than 30%, the fracture sealing stage is started as shown in Fig. 8b. To prevent the roadway air from infiltrating the borehole, the fine expansive particles seep into the air leakage fractures of the sealing segment (L1 þ L2) in the coal seam under the common effect of highpressure gas and negative drainage pressure. Then, the gas drainage concentration is increased, and the gas drainage period with a higher concentration (4 30%) is extended. It should be noted that the fine expansive particles to seal fractures [72] in the coal seam, which consist of bentonite, magnesium oxide, talc, polyacrylamide, super absorbent resin and additives, are specifically compounded for this technology. The particles are characterised by their easy conveyability, high volume expansibility and strong cohesive in moist atmosphere. The fine expansive particles, which transport in the fractures, can roll up more solid particles to improve the sealing effect and are not easily inhaled into the gas drainage system by the negative drainage pressure.
6. Field application This technology has been commercially applied to enhance the concentration of pre-mining gas drainage in the Huachu coal mine in China. The process is illustrated in Fig. 8. The MK-II particle
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conveyor [73] was used to transport the particles. The transport power is an underground high-pressure gas source. The particle transport pressure is controlled between 0.2 and 0.3 MPa. When the borehole is fully filled with fine expansive particles, the air source of the particle transport is cut off to use the quick-setting cement sealing borehole orifice. Then, the sealing stage of leakage fractures using solid particles is completed. The field test and the gas drainage results are shown in Figs. 9 and 10, respectively. Fig. 10 shows that the stage “a” represents the state of gas concentration decay, and when the gas concentration declines, the gas drainage concentration is significantly improved in the gas drainage stage “b” after the particles seal the drainage borehole. In addition, a gas drainage period of 2–3 months at a higher concentration is maintained. After solid particle sealing is performed in boreholes 1♯–6♯, the gas drainage concentrations quickly increase, whereas the concentrations in boreholes 7♯and 8♯ have a small delay effect. This result shows that fine expansive particle sealing for the leakage fractures is a complex dynamic process. It includes not only the deposition and agglomeration of particles under the negative drainage pressure, but also the water absorption-induced particle expansion. That may be the reason why the simulation result deviates from the field borehole data after particle injection as shown in Fig. 7c. However, the same conclusion can be easily found from the theoretical simulations and field experiments that reducing the width and the number of leakage fractures can significantly enhance the gas drainage concentration. The test shows that the gas drainage concentration can be improved by 10%–65% after the solid particles seal the leakage fractures in the coal seam. The higher-concentration gas production is also extended by 2–3 months. Thus, this method can greatly improve the amount of gas drainage for a single borehole by 2000 m3–3000 m3, where the average is 2500 m3.
7. Conclusions A fully coupled compositional (coal seam gas and air) model of coal deformation, coal gas flow and transport, and air flow in coal seams is developed to better understand the gas drainage processes, the coal gas–air mixing mechanisms, and their implications on the in-situ control of the pre-mining drained gas concentration. Based on the results of this study, the following conclusions can be drawn: (1) The excavation-induced fractures around drainage boreholes accelerate the release of gas in the vicinity of a drainage borehole. This is why the initial drained gas concentration is high. As the gas in this region is released, these fractures widen further due to coal matrix shrinkage. Through these widened fractures, air flows into the coal seam and mixes with the desorbed gas. This air–gas mixing decreases the drained gas concentration rapidly if the air flow channels were not sealed. (2) The quantification of complex interactions between binary gas mixtures (CH4 and air) and dual solid media (coal matrix and fracture), such as matrix shrinkage induced by gas desorption within the coal matrix, fracture dilation or compaction caused by the flow of free gas and air in the fracture, and coal effective stress alteration which results in the dynamic evolution of dual-porosity and dual-permeability, provides a practical tool to effectively control the air–gas mixing processes. (3) The successful application of the quantification tool to evaluate the effectiveness of a new in-situ control technology by injecting fine expansive particles into the leakage fractures around the borehole proves its feasibility. The field test shows that the characteristics of the leakage fractures are
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significantly changed after the technology was applied. For boreholes with an originally low gas concentration (0–30%), the new technology can increase the gas concentration by 10– 65% and extend the production time by approximately 2–3 months. The total amount of gas drainage increases to 2000– 3000 m³ per borehole.
Acknowledgements This work was supported by the National Natural Science Foundation of China (51174199). Jiangsu Province Outstanding Youth Scientific Fund (BK2012003), Jiangsu Natural Science Funds (SBK201021648), Fok Ying Tung Education Foundation, Center of Cooperative Innovation of CUMT (2014XT02), Colleges and Universities Young Teacher Fund for Basic Research Subject (131049) and the College Graduate Research and Innovation Program of Jiangsu (CXZZ130925) are gratefully acknowledged. This work was also a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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International Journal of Rock Mechanics & Mining Sciences journal homepage: www.elsevier.com/locate/ijrmms
A fully coupled coal deformation and compositional flow model for the control of the pre-mining coal seam gas extraction Tongqiang Xia a,b,d, Fubao Zhou a,c,n, Jishan Liu e, Shengyong Hu a, Yingke Liu a,c a
Key Laboratory of Gas and Fire Control for Coal Mines, China University of Mining and Technology, Xuzhou, China State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences, Wuhan, China c State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Xuzhou, China d State Key Laboratory for Geomechanics & Deep Underground Engineering, China University of Mining and Technology, Xuzhou, China e School of Mechanical and Chemical Engineering, University of Western Australia, Crawley, WA, Australia b
art ic l e i nf o
a b s t r a c t
Article history: Received 12 October 2013 Received in revised form 10 January 2014 Accepted 11 August 2014
Fully coupled compositional (coal seam gas and air) model of coal deformation, coal gas flow and transport, and air flow in coal seams is developed to better understand the gas drainage processes and the coal gas–air mixing mechanisms during pre-mining coal seem gas extraction. The model was first verified by showing that the modelled gas concentration profiles match reasonably with the in-situ measured ones. The verified model was then applied to evaluate how the drained gas concentration could be controlled under different conditions of the sealing length, the leakage rate and the leakage fracture width. These modelled results provides the basis of a new in-situ control technology of gas–air mixing, which uses fine expansive particles to seal the leakage fractures around the borehole. This technology has been commercially applied to enhance the concentration of the pre-mining gas drainage. The field test shows that the characteristics of the leakage fractures are greatly changed after the particles are injected into the in-seam drainage borehole when the gas concentration declines. Once the leakage fractures are blocked with the particles, the outside air is prevented from entering the coal seam. Thus, an ideal gas concentration can be maintained, and the duration of higher gas concentration is extended. For boreholes with an originally low gas concentration (0–30%), the new technology can increase the gas concentration by 10–65% and extend the production time by approximately two to three months. The total amount of gas drainage increases to 2000–3000 m3 per borehole. & 2014 Elsevier Ltd. All rights reserved.
Keywords: Coal seam gas drainage Coal–gas interactions Compositional flow Fracture sealing
1. Introduction Gas drainage, which is an interesting topic worldwide, can reduce gas pressure, eliminate the risk induced by coal gas in mines, provide a new resource and protect the environment [1]. However, in China, coal seams are characterised by low permeability, strong adsorption and high gas pressure. The coal seam permeability in most Chinese mines (except the southern Qinshui coalfields) ranges between 10 4 and 10 3 mD, which is four and three orders of magnitude lower than those in the U.S. and Australia, respectively [2,3]. All of these reasons restrict the feasibility of surface drilling drainage in China. Therefore, the widely used method to control coal gas in China is underground drilling drainage [4–7]. Unfortunately, this method has many n Corresponding author at: Key Laboratory of Gas and Fire Control for Coal Mines, China University of Mining and Technology, Xuzhou, China. Tel.: þ 86 516 83899753; fax: þ 86 516 83995053. E-mail address: [email protected] (F. Zhou).
http://dx.doi.org/10.1016/j.ijrmms.2014.08.012 1365-1609/& 2014 Elsevier Ltd. All rights reserved.
problems such as the small flow of single-hole gas drainage, the low concentration and its rapid decrease, particularly in the inseam drilling drainage, which is one of the most important and effective measures to pre-drain the coal seam gas before coal mining to eliminate the risk of outburst [8–11]. According to statistics, the gas drainage concentration of 80% in-seam boreholes varies from 6% to 20% in a short time, and the average pre-drained rate of coal seam gas is less than 23% [12]. Such low concentration may lead to a low utilisation ratio, which will result in more serious environmental pollution if the gas is directly released. Furthermore, the low concentration of gas drainage may lead to many hazards such as spontaneous combustion of coal, gas combustion and gas explosion [13–15]. To enhance the quality of gas drainage in coal seams or to make a large flow and a high methane concentration is a valuable goal for research workers of coal mines. Most scholars and engineers agree that increasing the seam permeability can achieve the high efficiency of gas drainage in coal seams. The seam permeability is closely related with the evolution of coal pores/fractures, which
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originates from coal–gas interactions such as the swelling/shrinkage of the coal matrix, which is introduced by adsorption/desorption, and the effective stresses and temperature changes. Based on experimental observations, many models have been formulated to quantify the permeability evolution during coal swelling/ shrinkage. Gray [16] presented a coal permeability model that represents the effects of the matrix shrinkage and the pore pressure changes on the coal permeability. Since then, many theoretical and empirical permeability models have been proposed, including Harpalani and Zhao [17], Sawyer et al. [18], Seidle et al. [19], Seidle and Huitt [20], Palmer and Mansoori [21], Gilman and Beckie [22], Shi and Durucan [23,24], Palmer [25], etc., where both the shrinkage and the pore pressure effects are included. However, most of these studies assumed either a constant overburden load, or they are derived from the compressibility concept of porosity, which may provide incorrect outcomes or overestimates of the permeability change [26,27]. These critical and limiting assumptions have been relaxed in the new models [25,28–32], which rigorously incorporate the in-situ stress conditions. Besides, since the concept of gas sequestration was first proposed by Macdonald of Alberta Energy during discussions with Gunter and co-workers in 1991 [33,34], greenhouse gas sequestration enhanced coal bed methane (ECBM) recovery has recently attracted attention worldwide. A number of field ECBM storage pilot projects [33–38] have been undertaken in North America, Europe, Poland, China, Japan, etc. In addition, a large number of experiments [39–46] associated with the competitive adsorption characteristics of multi-component gas in the coal matrix are discussed, and many theory models of gas adsorption, desorption and percolation have also been developed under the competitive adsorption of multi-component gas. Wei et al. [47,48] presented an alternative model to address the model of multi-component gas diffusion and flow in bulk coals, which focused on the CH4–CO2 counter-diffusion that was associated with the CO2-sequestration enhanced coal bed methane (CO2–ECBM) recovery. Connell and Detournay [49] conducted a coupled numerical model for CO2– ECBM. Similarly, Wang et al. [50] proposed a deformation-flow coupled model to address CO2–ECBM. Chen et al. [51,52] extended the single poroelastic model of Zhang et al. [28] to include the flow and the transport of gas mixtures (binary gasses: CO2 and CH4). More recently, Wu et al. [53] developed a dual poroelastic model (dual solid media-coal matrix and fracture) for CO2–ECBM under variable stress conditions. However, the enhanced recovery of methane using CO2 or flue gas as an injectant may be deemed unattractive in active underground coal mines because of the potential for toxic concentrations of CO2 to arise during mining [54]. Yang et al. [55] proposed a multi-physics coupled model that included seepage, diffusion and competitive adsorption of the multi-component gas, and the methane quantity in releasing holes and degassing holes was simulated under N2 or CO2 injection into the coal bed. Subsequently, a series of underground experiments of N2 injection into the coal bed to accelerate the coal seam gas emission were carried out, whose results indicated that the pure methane drainage flow in these boreholes within 2 m increased more than two times after 16 h of N2 injection [56]. To conclude, although a certain degree of success has been achieved using the above models to explain and match the experimental data, a key point, which is the common phenomenon of low concentration in the gas drainage process, has not been addressed in these models. This will easily result in the overestimation of gas drainage for an unfavourable drilling design, particularly at high gas pressure and outburst coal seam. The lowconcentration phenomenon of gas drainage can be explained as follows: because of the excavation of both roadways and boreholes, many leakage fractures occur around the borehole [57,58], and much roadway air floods into the seam borehole under
139
negative-pressure driven, which results in a significant decline in the gas concentration (Figs. 3a and 8a). Based on the dual-porosity medium model, the leakage evaluation model of the in-seam drainage borehole is established in this paper by considering the coal deformation, the gas flow and the gas transport in the matrix/ fracture system and the blocking effect of drilling on the gas drainage quality is also evaluated. Finally, a new borehole sealing technology is proposed to improve the gas drainage quality.
2. Governing equations The following assumptions are considered in the model: (1) coal is a dual poroelastic continuum, and the strains are infinitesimal; (2) coal is saturated with gas, and the conditions are isothermal; (3) the gas contained in the pores is ideal, and its viscosity is constant under isothermal conditions; (4) the gas flow satisfies Darcy’s law in the coal matrix and the fractures; (5) the outside air pressure is much smaller than the pressure in the pores, so the air adsorption in the coal matrix is not considered here; in other words, the air may only flow in the coal fractures. In the following derivations, the dual-porosity fractured coal is conceptualised as shown in Fig. 1 [53,59], which comprises the coal matrix and the coal fractures. The edge dimension of the matrix blocks and the fracture aperture are represented by a and b, respectively, Kn is the fracture stiffness, and σ e is the effective stress. 2.1. Gas flow and transport The mass balance equation of the gas component κ can be expressed for a static medium, which incorporates these convective and dispersion modes of transport but involves the interchange between free gas and adsorbed gas as ∂mκ þ ∇ u ρgκ þ ∇ Dκ ∇mκ f ¼ Q sκ ð1Þ ∂t where the subscript “κ ” (κ ¼1,2) represents the component of CH4 and air (mainly O2 and N2), respectively, ρg is the gas density, t denotes the time variable, Q s is the gas source or sink, m is the gas content, and mf is the gas content of the free state in the matrix or the fracture. For a binary gas system, the mixture gas pressure p and the gas pressure pm in the matrix and the pressure pf in the fracture can be
Fig. 1. Schematic of a dual-porosity fractured medium.
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expressed as p ¼ ∑pκ ; pm ¼ pm1 ; pf ¼ pf 1 þ pf 2
ð2Þ
The mass of each component in the fracture and in the matrix which are contained in 1 unit volume of coal can be defined as mf κ ¼ ϕf ρf κ ; mm1 ¼ ϕm ρm1 þ ρs ρa
V L pm1 ; and mm2 ¼ 0; P L þ pm1
ð3Þ
respectively, where ρf κ ¼ M κ pf κ =RT and ρmκ ¼ M κ pmκ =RT. The subscripts “m” and “f” represent the matrix and the fracture system, respectively, ρfk is the density of the gas component κ in the fractures, ρa is the CH4 density at standard conditions, ρs is the coal density, VL is the CH4 Langmuir volume constant, M κ is the molar mass of component κ , and ϕ is the porosity. In Eq. (1), the vector of convective velocity u can be expressed as follows (the effect of gravity is neglected) uf ¼
kf
μ
∇pf ; um ¼
km
μ
∇pm
ð4Þ
where k is the permeability, and μ is the average coefficient of dynamic viscosity for the mixed gas. Each component of the hydrodynamic dispersion coefficient Dκ is defined as Df κ ¼ β c uf þ Df κ 0 ; Dmκ ¼ β c um þDmκ 0
ð5Þ
where Dκ 0 is the coefficient of molecular diffusion of component κ , and βc is the dynamic dispersivity. By substituting Eqs. (2)–(5) into Eq. (1), the governing equations for gas flow can be obtained: "
#
ϕm þ
ρs pa V L P L ∂pm1 P L þpm1
2
∂t
þpm1
∂ϕm km þ∇ pm1 ∇pm1 ∂t μ
þ ∇ð ϕm Dm1 ∇pm1 ¼ ωðpm1 pf 1 Þ
where εV ¼ ε11 þ ε22 þ ε33 is the volumetric strain of the coal matrix, Kf ¼aKn is the modified fracture stiffness, and the subscript “0” denotes the initial value of the corresponding variables. By variable separation and integration of Eq. (10), the coal matrix porosity can be obtained as " # 1 1 1 b0 þ ϕm ¼ α þ ϕm0 α exp ðεV εV 0 εs þ εs0 Þ ð11Þ K K a0 K f Previous work [53,59,61,62] suggested that the porosity and permeability model for coal fracture could be defined as
ϕf Δb 3 ¼ 1þ ¼ 1þ ðεV εV 0 þ εs0 εs Þ b0 ϕf 0 ϕf 0 þ 3K f
The partial derivative of ϕm and ϕf with respect to time is respectively expressed as follows: # 1" 1 1 ∂ϕm b0 ∂εV εL P L ∂pm þ ¼ ϕm α ð13Þ K K a0 K f ∂t ∂t RT P L þ p 2 ∂t m
"
# 1 ∂ϕf ϕf 0 1 b0 ∂ εV εL P L ∂pm þ ¼ ∂t K f K a0 K f ∂t RT P L þp 2 ∂t
∂ϕ ∂p k ϕf f 2 þ pf 2 f þ ∇ f pf 2 ∇pf þ ∇ð ϕf Df 2 ∇pf 2 Þ ¼ 0 ð8Þ ∂t ∂t μ where ω ¼ 8 1 þ 2=a2 km =μ is the transfer coefficient between the matrix and the fracture.
ð14Þ
m
The cubic law is chosen to calculate the relation between permeability and porosity; we thereby obtain 8 > km ϕm 3 < α α ¼ ¼ þ 1 > km0 ϕm0 ϕm0 :ϕm0 9 " #>3 1 = 1 1 b0 þ exp ðεV εV 0 þ εs0 εs Þ > K K a0 K f ;
ð6Þ
∂ϕ ∂p k ϕf f 1 þ pf 1 f þ ∇ f pf 1 ∇pf þ ∇ð ϕf Df 1 ∇pf 1 Þ ¼ ωðpm1 pf 1 Þ ∂t ∂t μ ð7Þ
ð12Þ
K
kf ¼ kf 0
ϕf ϕf 0
!3
" ¼ 1þ
#3 1 1 1 b0 þ ðεV εV0 þ εs0 εs Þ K f K a0 K f
ð15Þ
ð16Þ
where the initial permeability kf0 of the coal seam fracture, which depends on the degree of development of the fracture in the coal seam, can be calculated as following [63,64]: ϕf 0 ¼ 3b0 =a0 , and 3 kf 0 ¼ b0 =ð12a0 Þ.
2.2. Coal seam deformation 2.4. Cross coupling The Navier-type equation for the dual-porosity model can be expressed as Gui;kk þ
G u αpm;i βpf ;i K εs;i þ f i ¼ 0 1 2υ k;ki
ð9Þ
where G ¼ D=2ð1 þ υÞ, D ¼ ½ð1=EÞ þ ð1=aK n Þ 1 , K ¼ D=3ð1 2υÞ, α ¼ 1 ðK=K s Þ, β ¼ 1 ðK=aK n Þ, and εs ¼ εL pm1 =ðP L þ pm1 Þ, E is the elastic modulus, G is the shear stiffness, σkk denotes the components of the mean stress, α and β are Biot coefficients [60], K is the bulk modulus, Ks is the grain elastic modulus, Kn is the normal stiffness of the individual fractures, fi is the component of the body force, εs is the strain induced by gas sorption, and εL and PL are the CH4 Langmuir matrix swelling and pressure constants, respectively.
Substituting Eq. (2) into Eq. (9), we rewrite the governing equation for coal seam deformation as " # G K εL P L u αþ Gui;kk þ pm1;i βðpf 1 þ pf 2 Þ;i þ f i ¼ 0 1 2υ k;ki ðP L þ pm1 Þ2 ð17Þ After the substitution of Eqs. (13)–(16) into the gas flow Eqs. (6)–(8), the final gas flow equations yield 1 ∂pm1 km ϕm þ ρs pa V L PL 2 ðϕmK αÞ εL PL pm1 2 K1 þ a0bK0 f ∂t þ∇ μ pm1 ∇pm1 ðPL þ pm1 Þ ðP L þ pm1 Þ 2 km þ ∇ ϕm Dm1 ∇pm1 ¼ 8 1 þ 2 ðp p Þ μ m1 f 1 a 1 ϕ α pm1 1 b0 ∂ εV þ m K a0 K f K ∂t
2.3. Dynamic permeability models Following our previous work [61], the porosity model of the matrix is defined as follows (the effect of temperature is neglected): ϕ α 1 b0 1 dϕm ¼ m þ ðdεs dεV Þ ð10Þ K a0 K f K
ϕf
∂pf 1 kf þ ∇ pf 1 ∇pf þ ∇ð ϕf Df 1 ∇pf 1 Þ ∂t μ 2 km ¼ 8 1þ 2 ðp p Þ μ m1 f 1 a
ð18Þ
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141
Fig. 2. The cross coupling of the field equations.
# 1" pf 1 ϕf 0 1 b0 ∂ εV εL P L ∂pm1 þ 2 K a0 K f Kf ∂t ∂t PL þ p
ð19Þ
m1
ϕf
∂pf 2 kf þ ∇ pf 2 ∇pf þ ∇ð ϕf Df 1 ∇pf 2 Þ ∂t μ # 1" pf 2 ϕf 0 1 b0 ∂ εV εL P L ∂pm1 þ ¼ 2 K a0 K f Kf ∂t ∂t PL þ p
ð20Þ
m1
Eqs. (17)–(20) define the coupled model including coal deformation and multi-component gas flow in a dual-porosity medium. Cross coupling between the field equations for coal deformation and multi-component gas flow are illustrated in Fig. 2. The above governing equations, particularly the multi-component gas flow equation, are nonlinear second-order partial differential equations (PDEs) in space and first-order PDEs in time. These equations cannot be theoretically solved because of the nonlinearity in both the space and time domains. Therefore, they are implemented into COMSOL Multiphysics and solved using the finite-element method.
3. Model validation 3.1. Model case Huachu coal mine of Liuzhi Coal Mining Group, located in Guizhou province of southern west China, is under the threat of coal and gas outburst. There are 80 times of outburst occurred since the first production year of 1974. Currently, ♯7 seam is mineable seam and the original gas content within the seam varies from 12.97 m3/t to 19.35 m3/t, and the average value is 16.16 m3/t. In-seam gas pressure is from 1.09 MPa to 1.75 MPa with the average of 1.42 MPa. The in-seam borehole’s diameter is about 94 mm and its negative drainage pressure is about 12 kPa to 20 kPa. The monitor date shows that it only took 10 to 30 days for the concentration dropped to 30% or even smaller. The average pure CH4 flow rate of a single hole was between 0.0015 m3/min and 0.0125 m3/min and the flow decay factor was 0.0562– 0.8167 d 1. In the following work, the correctness of our model will be first verified against actual gas drainage data in coal seam ♯7 of the Huachu coal mine. 3.2. Physical model and boundary conditions The schematic of the seam drainage zone in coal seam ♯7 with half of the vertical borehole section is shown in Fig. 3a, where the
physical model for calculation is divided into two regions: the mining influence area (ABCHIFGA) and the no-mining influence area (CDEFIHC). The radius of the broken area around the drilling hole is five times the borehole radius, and the influence area distance GF induced by roadway excavation is expressed as [65] hΘ λ γ H tan φ þ C GF ¼ ð21Þ ln C 2tg φ where h is the mining height of the coal seam, H is the buried depth of the mining roadway, C is the cohesion of coal, φ is the internal friction angel of coal, γ is the bulk density of overburden strata, λ is the stress concentration factor of the vertical direction in front of the coal wall,and Θ is the coefficient of side pressure coal wall defined as Θ ¼ 1 sin φ = 1 þ sin φ . In the test place h¼3.8 m, H¼ 320 m, γ ¼ 25 kN/m3, C ¼98 kPa, ϕ ¼151 and λ ¼ 2.2, the affected zone’s distance of excavation GF¼ 16 m can be calculated. The initial pressure in the coal is p0 ¼1.42 MPa, the borehole sealing length is AB ¼8 m, and the effective drainage length is BC¼ 72 m. The model boundary conditions are implemented in the modelling as follows: (a) For solid deformation: the model top border has the stress boundary q ¼ γ H and free boundary condition, the left border has free boundary condition and no stress, and the other borders have the normal displacement constraint and no stress; (b) for the CH4 flow in the coal matrix and the fracture: all borders have no flow boundary condition in the matrix; however, the pressure boundary condition p0CH4 ¼ 9350 Pa is imposed on BC, and the remaining borders have no flow boundary conditions in the fracture; (c) for the air flow in the fracture: AG has the pressure boundary condition p0Air ¼ 101,350 Pa, BC is regarded as the export flow boundary N0, which is estimated according to the measured leakage amount, and the remaining borders have no flow boundary condition. 3.3. Validation Grid generation of the model, including 3000 elements and 85,827 degrees of freedom, is through mapped mesh method as shown in Fig. 3b. Most parameters of the model (as listed in Table 1) are chosen from the experimental results, whereas the unreported parameters are substituted from the contemporary literature [28,53,59]. The parameters of different boreholes are shown in Table 2, in which the fracture aperture b2 of the affected zone is obtained from the history matching of gas drainage and the numerical parameter inversion. In order to better understand the gas drainage processes and the coal gas–air mixing mechanisms, the contours of gas
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Fig. 3. Model boundary conditions and mesh generation. Table 1 Modelling parameters for the numerical simulation. Parameter
Value
Parameter
Value
Young’s modulus of coal, E (MPa) Young’s modulus of coal grains, Es (MPa) Fracture stiffness, Kn (MPa) Poisson’s ratio of coal (υ) Density of coal, ρs (kg/m3) Initial porosity of matrix (ϕm) Initial permeability of matrix, km0 (m2) Fracture width of original coal b1, (m) Fracture spacing of coal, a (m) Gas dynamic viscosity μ, (N s/m2)
2823 8469 4800 0.339 1250 0.05 2.8 10 16 5 10 6 0.005 1.84 10 5
Bulk density of coal and rock, μ (kN/m3) Vertical depth of the roadway mining, H (m) Standard atmospheric pressure, pa (MPa) CH4 Langmuir pressure constant, PL (MPa) CH4 Langmuir volume constant, VL (m3/kg) CH4 Langmuir volumetric strain constant (εL) Molar gas constant, R (J/(mol K) Coal temperature, T (K) CH4 diffusion coefficient, D1 (m2 s) Air diffusion coefficient, D2 (m2 s)
2.5 320 0.101325 2.45 0.016 0.0128 8.3143 300 3.6 10 12 5.8 10 12
Table 2 Simulation parameters for the different boreholes. Borehole Fracture spacing of coal, a (m)
Fracture width Initial fracture of original width of coal, b1 (m) disturbed coal, b2 (m)
Leakage rates of BC segment, N0, (mol/(m2 s))
No. 1 No. 2 No. 3
5 10 6 5 10 6 5 10 6
8 10 5 2 10 4 5 10 5
0.001 0.005 0.005
6 10 5 8 10 4 6 10 5
concentration in coal fractures during the gas drainage processes of the borehole No. 1 are shown in Fig. 4a, and the dynamic evolutions of matrix/fracture permeability and gas pressure in the matrix at point I (90, 1) are shown in Fig. 4b. It observed from Fig. 4 that the excavation-induced fractures around drainage boreholes accelerate the release of gas in the vicinity of a drainage borehole. As the gas in this region is released, these fractures widen further due to coal matrix shrinkage, which responds to the increase of fracture permeability and the decrease of matrix permeability. Through these widened fractures, a large amount
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Fig. 4. Dynamic evolution of gas concentration, gas pressure and dual-permeability. (a) The contours of gas concentration in the coal fracture with time, (b) the dynamic evolutions of matrix/fracture permeability and gas pressure in the matrix.
of air flows into the coal seam and mixes with the desorbed gas, resulting in the low gas drained concentration. Furthermore, the theoretical model is verified against the actual gas drainage data as shown in Fig. 5.
4. The simulation of leakage sealing effect
Fig. 5. The comparison between the simulation results and the field data of gas drainage.
The effect of gas drainage is closely related to the basic properties of coal such as the porosity, the permeability and the adsorption characteristics. In this paper, we mainly focus on the gas drainage quality under different sealing effects, and the coal properties that affect the gas drainage quality will be discussed in another paper. Practice has proved that increasing the length of the sealing segment AB can improve the gas drainage concentration. The numerical simulation of the gas drainage quality is shown in Fig. 6 for different sealing lengths AB and leakage rates N0. It is observed from Fig. 6 that the smaller leakage rate corresponds to the higher gas concentration for the same sealing borehole length AB, whereas the effect of the leakage rate on the
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Fig. 6. Gas drainage quality for different sealing lengths and leakage rates.
pure CH4 flow is sufficiently weak to be negligible. For example, when AB ¼ 20 m, the trends of the CH4 flow with time are basically corresponding under the leakage rates N0 ¼ 2 10 5 mol/(m2 s) and N0 ¼ 1 10 6 mol/(m2 s) in the gas drainage. However, the concentrations of gas drainage are significantly different: the average gas concentration is 30%, and the lowest gas concentration is 7% for 115.7 d when N0 ¼ 2 10 5 mol/(m2 s), whereas the average gas concentration is 82.2%, and the lowest gas concentration is 59.3% when N0 ¼ 1 10 6 mol/(m2 s). When N0 changes from 2 10 5 mol/(m2 s) to 1 10 6 mol/(m2 s), the average gas concentration increases by 174%. For the same leakage rate, the longer sealing length of the borehole corresponds to the higher concentration of gas drainage. For example, for the borehole sealing length AB ¼8 m, the average concentration of gas drainage is 24.2% for 115.7 d under N0 ¼ 2 10 5 mol/(m2 s), whereas the concentration is 27.3% and 30% for AB ¼16 m and AB ¼20 m, respectively. Thus, when AB ¼16 m and 20 m, the concentration increases by only 12.8% and 24%, respectively, comparing with that for AB ¼8 m. However, it is also observed from Fig. 6a that there is no linear relationship between the sealing length and the pure CH4 flow. In addition, increasing the sealing length can enhance the gas concentration at the expense of less pure CH4 flow because the increase in sealing length reduces the effective drainage length, which may reduce the total amount of pure CH4 flow. For example, for the sealing lengths AB ¼ 8 m, AB ¼16 m and AB ¼20 m, the pure CH4 flow are 0.0032 m3/s, 0.0045 m3/s and 0.0043 m3/s, respectively, at the
Fig. 7. The influence of changing the leakage fracture characteristics on the gas drainage concentration (in the figures, I and II are the drainage stage before and after the change of leakage permeability, respectively).
beginning of the gas drainage. Thus, the low gas concentration essentially results from the leakage fractures around the drilling borehole. If the characteristics of the leakage fractures can be improved, the gas effect will increase. To better illustrate this problem, the simulation with reference to the gas drainage quality is performed for different leakage characteristics as shown in Fig. 7. It is observed from Fig. 7(a) and (b) that both the gas concentration and the pure CH4 flow are closely related to the leakage fracture width b2. When the permeability of the mining
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Fig. 8. The process of sealing the air-leakage fractures around the borehole using particles. (a) Schematic diagram of the borehole plugging-up stage, (b) schematic diagram of fracture sealing using particles.
Fig. 9. 2372 Roadway field test photos.
influence area is small, which corresponds to a low leakage rate, the flow and the concentration of pure CH4 drainage are high. For example, for b2 ¼8 10 6 m and N0 ¼ 8 10 7 mol/(m2 s), the amount of gas drainage is 36.5 m3, and the average concentration of gas drainage is 83.48% for 115.7 d. However, when b2 ¼ 8 10 4 m and N0 ¼ 2 10 4 mol/(m2 s), the amount of gas drainage is 34.5 m3, and the average concentration of gas drainage is 6.34% for 115.7 d. Thus, the change in leakage characteristics has little effect on the total amount of gas drainage, but it can significantly improve the gas drainage concentration. To clearly describe the relationship between the leakage fracture characteristics and the gas drainage concentration, we take the history data of the borehole No. 1 before and after the change of leakage permeability as an example, in which the borehole No. 1 is the same as 1♯ gas drainage drilling in Fig. 10. The simulation shows the effect of changing the leakage fracture characteristics on the gas drainage concentration when the gas concentration declines. It is observed from Fig. 7(c) that the gas drainage concentration is
significantly enhanced by changing the leakage characteristics. For example, when b2 ¼6 10 5 m and N0 ¼ 8 10 6 mol/(m2 s), the gas drainage concentration decreases from 100% (t¼ 0 d) to 20.8% after 12 d. If the leakage fracture width is changed, the gas drainage concentration will significantly increase, and the duration of gas production is also extended. For example, for b2 ¼ 2 10 6 m and N0 ¼ 5 10 7 mol/(m2 s), the highest gas concentration increases to 91.9%, and the average gas drainage concentration is 48.9% during 12–90 d, which increases by 15.1 times compared to the original natural drainage for b2 ¼ 6 10 5 m and N0 ¼ 8 10 5 mol/(m2 s).
5. A technology to control the gas quality When performing gas drainage, effectively sealing the leakage passages of roadway air into the borehole is the key to solve the engineering problems of low concentration and small flow. However, overall, the existing borehole sealing methods [66–71] are
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Fig. 10. Concentration variation curves before and after fracture sealing (in the figures, a and b are the drainage duration before and after fracture sealing, respectively).
only performed at the sealing stage inside the borehole, which does not address the problem of decreasing gas drainage concentration because of the evolution and development of the leakage fractures that are caused by the mining activities and the gas drainage. Therefore, a new approach of using particles to seal the leakage fractures around the boreholes is proposed in this paper. In this method, when the gas drainage concentration rapidly decreases, the fine expansive particles are injected into the borehole sealing section using high-pressure air, and the particles penetrate the leakage fractures in the coal seam. After a period of time, the particles will deposit/coagulate to block up the fracture channels. Hence, the size and the number of fractures will decrease, which increases the leakage resistance to resist the outside air that enters. Thus, the gas concentration substantially increases, and the duration of gas production is also extended. The process can be divided into two different stages: the borehole plugging-up stage and the fracture sealing stage. During the first stage (Fig. 8a), once the borehole is drilled to the expected length, the drainage pipe, which is twined with foam polymeric materials, is delivered into the borehole to plug up the outside air. The length of the plugging segment with foam polymeric materials is L1 (73 m), whereas the distance to the borehole outlet, which is filled with expansive cement, is L2 (77 m). Then, the drainage pipe is connected for gas drainage. As the drainage continues, the methane pressure in the coal will decrease, which causes the CH4 flow to slowly decrease.
Simultaneously, the outside air under the driven pressure is sucked into the drainage system and causes the concentration to decrease. When the concentration decreases to less than 30%, the fracture sealing stage is started as shown in Fig. 8b. To prevent the roadway air from infiltrating the borehole, the fine expansive particles seep into the air leakage fractures of the sealing segment (L1 þ L2) in the coal seam under the common effect of highpressure gas and negative drainage pressure. Then, the gas drainage concentration is increased, and the gas drainage period with a higher concentration (4 30%) is extended. It should be noted that the fine expansive particles to seal fractures [72] in the coal seam, which consist of bentonite, magnesium oxide, talc, polyacrylamide, super absorbent resin and additives, are specifically compounded for this technology. The particles are characterised by their easy conveyability, high volume expansibility and strong cohesive in moist atmosphere. The fine expansive particles, which transport in the fractures, can roll up more solid particles to improve the sealing effect and are not easily inhaled into the gas drainage system by the negative drainage pressure.
6. Field application This technology has been commercially applied to enhance the concentration of pre-mining gas drainage in the Huachu coal mine in China. The process is illustrated in Fig. 8. The MK-II particle
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conveyor [73] was used to transport the particles. The transport power is an underground high-pressure gas source. The particle transport pressure is controlled between 0.2 and 0.3 MPa. When the borehole is fully filled with fine expansive particles, the air source of the particle transport is cut off to use the quick-setting cement sealing borehole orifice. Then, the sealing stage of leakage fractures using solid particles is completed. The field test and the gas drainage results are shown in Figs. 9 and 10, respectively. Fig. 10 shows that the stage “a” represents the state of gas concentration decay, and when the gas concentration declines, the gas drainage concentration is significantly improved in the gas drainage stage “b” after the particles seal the drainage borehole. In addition, a gas drainage period of 2–3 months at a higher concentration is maintained. After solid particle sealing is performed in boreholes 1♯–6♯, the gas drainage concentrations quickly increase, whereas the concentrations in boreholes 7♯and 8♯ have a small delay effect. This result shows that fine expansive particle sealing for the leakage fractures is a complex dynamic process. It includes not only the deposition and agglomeration of particles under the negative drainage pressure, but also the water absorption-induced particle expansion. That may be the reason why the simulation result deviates from the field borehole data after particle injection as shown in Fig. 7c. However, the same conclusion can be easily found from the theoretical simulations and field experiments that reducing the width and the number of leakage fractures can significantly enhance the gas drainage concentration. The test shows that the gas drainage concentration can be improved by 10%–65% after the solid particles seal the leakage fractures in the coal seam. The higher-concentration gas production is also extended by 2–3 months. Thus, this method can greatly improve the amount of gas drainage for a single borehole by 2000 m3–3000 m3, where the average is 2500 m3.
7. Conclusions A fully coupled compositional (coal seam gas and air) model of coal deformation, coal gas flow and transport, and air flow in coal seams is developed to better understand the gas drainage processes, the coal gas–air mixing mechanisms, and their implications on the in-situ control of the pre-mining drained gas concentration. Based on the results of this study, the following conclusions can be drawn: (1) The excavation-induced fractures around drainage boreholes accelerate the release of gas in the vicinity of a drainage borehole. This is why the initial drained gas concentration is high. As the gas in this region is released, these fractures widen further due to coal matrix shrinkage. Through these widened fractures, air flows into the coal seam and mixes with the desorbed gas. This air–gas mixing decreases the drained gas concentration rapidly if the air flow channels were not sealed. (2) The quantification of complex interactions between binary gas mixtures (CH4 and air) and dual solid media (coal matrix and fracture), such as matrix shrinkage induced by gas desorption within the coal matrix, fracture dilation or compaction caused by the flow of free gas and air in the fracture, and coal effective stress alteration which results in the dynamic evolution of dual-porosity and dual-permeability, provides a practical tool to effectively control the air–gas mixing processes. (3) The successful application of the quantification tool to evaluate the effectiveness of a new in-situ control technology by injecting fine expansive particles into the leakage fractures around the borehole proves its feasibility. The field test shows that the characteristics of the leakage fractures are
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significantly changed after the technology was applied. For boreholes with an originally low gas concentration (0–30%), the new technology can increase the gas concentration by 10– 65% and extend the production time by approximately 2–3 months. The total amount of gas drainage increases to 2000– 3000 m³ per borehole.
Acknowledgements This work was supported by the National Natural Science Foundation of China (51174199). Jiangsu Province Outstanding Youth Scientific Fund (BK2012003), Jiangsu Natural Science Funds (SBK201021648), Fok Ying Tung Education Foundation, Center of Cooperative Innovation of CUMT (2014XT02), Colleges and Universities Young Teacher Fund for Basic Research Subject (131049) and the College Graduate Research and Innovation Program of Jiangsu (CXZZ130925) are gratefully acknowledged. This work was also a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
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