Desorption-diffusion model and lost gas quantity estimation of coalbed ...

SCIENCE CHINA Earth Sciences • RESEARCH PAPER •

Apirl 2010 Vol.53 No.4: 626–632 doi: 10.1007/s11430-010-0027-x

Desorption-diffusion model and lost gas quantity estimation of coalbed methane from coal core under drilling fluid medium YANG ZhaoBiao1*, QIN Yong1, WANG ZhaoFeng2, Geoff WANG3 & WU CaiFang1 1

School of Mineral Resources and Geoscience, China University of Mining & Technology, Xuzhou 221008, China; 2 Safety College, Henan Polytechnic University, Jiaozuo 454000, China; 3 School of Engineering, University of Queensland, ST Lucia QLD 4072, Australia Received January 4, 2009; accepted September 1, 2009; published online February 5, 2010

The differences of coalbed methane (CBM) desorption-diffusion from coal drilling-core under various drilling fluid medium are not considered in the present calculating methods of lost CBM quantity, which leads possibly to the inaccuracy of CBM quantity in coal seam. Here we took the desorption of CBM from coal core under drilling fluid medium as a pressure-swing process, and based on the Langmuir equation and Fick-first law, established the desorption-diffusion model and numerical modeling method of lost gas (including free CBM) calculation in coal core under various drilling fluid mediums through physical simulation test and by considering comprehensively primary factors. The results showed that the physical simulated t-Qt curves can be rightly fitted by the numerical modeling data, which indicated the ultimate desorption quantity from the numerical modeling was adjacent to that from the physical simulation as a whole. It was found that the lost CBM quantity from the modeling method was generally higher than that from the direct method when lost time was relatively long. Thus, we suggest that it is necessary to emend the active China national standard through further investigation, since the lost CBM quantity from coal drilling-core was generally underestimated using the method in the current standard. drilling fluid, CBM, lost gas quantity, desorption-diffusion model, numerical modeling method Citation:

Yang Z B Qin Y, Wang Z F, et al. Desorption-diffusion model and lost gas quantity estimation of coalbed methane from coal core under drilling fluid medium. Sci China Earth Sci, 2010, 53: 626–632, doi: 10.1007/s11430-010-0027-x

CBM content is one of the important parameters for coal mine safety and CBM geology, and the accurate calculation of lost gas quantity is a key to estimate CBM content. Now, inaccuracy of CBM content determination is a basic science problem that is in dire need of resolution [1]. At present, the active methods for evaluating the lost quantity of CBM from coal drilling-core take the desorptive law under air medium as a basis of calculating the lost CBM quantity under drilling liquid medium without considering the differentia of the desorptive behaviors under various mediums [2–4]. However, the calculating results from these methods are *Corresponding author (email: [email protected]) © Science China Press and Springer-Verlag Berlin Heidelberg 2010

only approximate compensation to the lost quantity of CBM from coal core under actual medium condition with certain unavoidable error. Substantially, the desorption-diffusion of CBM from coal core is an isotonic process under air medium but a variable pressure one under drilling fluid medium [5], which both are fully different and cannot be substituted by each other. As for the desorption’s beginning time of CBM from coal core, it is assumed that the CBM begins to be desorbed if the direct method is used when coal core is hoisted to the half depth of borehole. In fact, the desorption-diffusion of CBM from coal core under drilling liquid is related to CBM pressure and drilling fluid pressure rested with the height of the fluid column covering on the coal core. Hence, the abovementioned hypothesis is not earth.scichina.com

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YANG ZhaoBiao, et al.

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reasonable because the CBM from coal core begins to be desorbed only when the CBM pressure is higher than the drilling fluid pressure [5, 6]. At the same time, the traditional methods for evaluating CBM content such as the direct method of American Mine Bureau and China National Standard (GB/T19559-2004) were established all on the basis of the theoretical assumption that CBM exists in coal seam mostly as adsorbed phase without including free and water-dissolved phases [7]. Free gas is little in middle- and high-rank coal seams with generally less than 10% [8], and, however, is commonly more than 50% in low-rank coal seam [7, 9]. Pratt et al. [10] discussed the data of CBM content from the coal cores in Triton basin, America, and suggested an underestimation of 22% because the free and water-dissolved gases were not included. Herein, it is necessary to discuss the theory of lost CBM evaluation during the coal coring, and establish a new CBM desorption-diffusion model including free gas under drilling fluid medium.

1 Mathematical modeling 1.1

Description of methods

Based on the further understanding of the desorption, diffusion and seepage of CBM from coal core, using the fluid mechanics, thermodynamics, engineering mathematics, mathematical modeling and drilling engineering knowledge, referring to the CBM reservoir modeling method, synchronously combining with the factors influencing the CBM desorption-diffusion behaviors such as raw CBM pressure, coal adsorptivity and porosity, coal-body structure (granularity), moisture content, core-hoisting velocity and drilling liquid column pressure and temperature, physical simulation experiment of CBM desorption during core-hoisting was performed. CBM desorption-diffusion model in which free gas was considered also was established based on the Langmuir’s equation and Fick’s law. Finally, the model and equation for evaluating the lost quantity of CBM from coal core were established. 1.2

Preconditions

For assuring the maneuverability of model on basis of rational logical correlation, some conditions during mathematical modeling were simplified as follows: (1) Taking ideally coal seam as an assembly composed of the regular coal matrix blocks with micro-pore and fissures, or a fissure-micropore system. Coal matrix block might be a tabular, columnar or spherical body. (2) Ignoring the impact of stress on coal permeability and Klinkenberg’s effect [11] during the desorption of CBM from coal matrix block. In other words, the matrix shrinking

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effect was ignored and the diffusion coefficient was treated as a constant. (3) Regarding the desorption-diffusion process of CBM from coal core as an isothermal one. This is because the drilling fluid is always flowing circularly during the hoisting of coal core so that the temperature of the environment around coal core is almost unchanged. (4) Gas in coal matrix block occurs mainly in adsorbed and free phases. Adsorbed phase obeys the Langmuir’s equation the free phase obeys ideal gas equation, and diffusion behavior obeys the Fick-first law. Thus, the diffusion includes bulk diffusion, Knudsen’s diffusion, and surface diffusion of adsorbed layer. All the desorption-diffusion process is an imbalanced and para-steady one. (5) Coal core is hoisted at a uniform velocity so that the pressure-drop per second is constant. (6) Before coal core is drilled, the CBM pressure in the fissure-micropore system of coal seam is in balance, and there exists no desorption-diffusion behavior. (7) Ignoring the effect of the medium trap and the adsorption from the chemical and clay minerals in drilling fluid to effective pressure-drop of coal core, by assuming that those factors will not influence normal desorption of CBM from coal core. (8) Desorption of CBM from coal core begins to occur only when the medium pressure overlain on coal core is less than critical desorption pressure. In other words, there exists no free gas diffusion and migration in the period during which the gas pressure drops from raw coal reservoir pressure to critical desorption pressure during the hoisting of coal core. (9) Ignoring the effect of the moisture in coal core to CBM desorption and there is no two-phase flow when CBM diffuses in coal core. The seepage of CBM in fissure system can be ignored because the desorption of CBM from coal core during the hoisting corresponds with the desorption and diffusion of CBM to the surface of coal grain with larger desorptive surface area and shorter desorptive time. 1.3

Mathematical model

Adsorption-desorption balance of CBM in the micro-pore system of coal matrix obeys the Langmuir’s equation: Cp =

VL P , PL + P

(1)

where: P, the fluid pressure in fissure of coal matrix block, in MPa; Cp, the concentration of adsorbed gas in the micro-pore system of coal matrix block under balance condition, in cm3/g; VL, the Langmuir volume, cm3/g; PL, Langmuir pressure, in MPa. Free gas in the micropore-fissure system of coal matrix obeys ideal-gas equation: PV=ZnRT,

(2)

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where: Z, methane compression factor; n, amount of gas substance, in mol; R, constant; P, gas pressure intensity, in MPa; V, gas volume, in cm3; T, gas temperature, in K. Because the gas volume is affected by both temperature and pressure, gas volume should be revised to standard state (0℃ and 101.33 kPa)so that it can be compared and calculated in the same standard: VSTP =

T0 × Pm × Vm , Z × P0 × T

(3)

where: VSTP, gas volume in standard state, in cm3; Vm, pore volume, in cm3; T0, absolute temperature, 273.15 K; P0, standard atmospheric pressure, 101.33 kPa; Pm, medium pressure, in MPa. Based on the porosity and volume equations, it can be deduced:

where V0, the volume of coal matrix block, in cm3; ϕ, porosity, in %; m, mass of coal matrix block, in g; ρ′, the density of coal, in g/cm3. So, the correlation of free gas concentration to pressure can be obtained: VSTP T × P ×φ = 0 m , m Z × P0 × T × ρ ′

(4)

where Cr, free gas concentration, in cm3/g. The impact of compression factor Z can be ignored as to simplifying the calculation. Diffusion of gas from coal matrix system to fissure system obeys the Fick-first law: dC = Dσ [C ( p) − C ], dt C ( p) = C p + Cr =

(5)

(7)

where: C, average concentration of gas in coal matrix unit, in cm3/g; t, diffusion time, in min; C(p), concentration of gas at the margin of coal matrix uint under balance state, in Table 1

VL Pc T Pφ + 0 c . PL + Pc P0 T ρ ′

VL Pm T × P × φ VL ( Pc − ρ gvt × 10 −3 ) + 0 m = PL + Pm P0 × T × ρ ′ PL + Pc − ρ gvt × 10 −3 +

T0 × ( Pc − ρ gvt × 10 −3 ) × φ , P0 × T × ρ ′

(9) where: Pc, critical desorption pressure, in MPa; ρ, drilling fluid density, in g/cm3; v, core-hoisting velocity, in m/min; g, accelerational gravity, 9.81 m/s2; other symbols are same to the former. Taking step length as Δt=t/N, thus, for the period within the step n to n+1, the gas concentration C(P) can be expressed as follows: C ( p n +1/ 2 ) =

C ( p n +1 ) + C ( p n ) . 2

Transforming and integrating to the eq. (5), it can be got:

∫

Cn

1 C ( p n +1/ 2 ) − C

dC = Dσ

t n+1

∫

dt ,

tn

so that: C ( p n +1/ 2 ) − C n +1 C ( p n +1/ 2 ) − C n

= e − DσΔt .

Differencing result is C ( p n +1 ) + C ( p n ) 2 [1 − exp(− DσΔt )] .

C n +1 = C n exp(− DσΔt ) +

Geometric and form factors of micro-pore coal matrix unit [12]

Geometry of coal matrix unite Cube Clyinder Spheroid

Characteristic parameter Half of unit thickness hi Radius Ri Radius Ri

(8)

The boundary condition is:

(6)

Exchange ratio of CBM between coal matrix unite and fissure system can be described by the formula as follows [12–15]: dC , dt

C0 = C ( p0 ) = C p ( Pc ) + Cr ( Pc ) =

C n+1

T × P ×φ VL P + 0 m . PL + P P0 × T × ρ ′

q = −Fg

cm3/g; D, diffusion coefficient; σ, form factor; Fg, geometric factor (Table 1); other symbols are same to the former. There exists a gas average concentration C in coal matrix system at each time during CBM desorption so that the differentia of the concentration C to the concentration of gas at the margin of matrix unit, which can be described with the Fick-first law. Boundary conditions are variational under drilling fluid medium so that there is no analytical solution. So, the solution can be obtained only with numerical modeling method. Initial condition of the modeling is as follows:

C ( p) =

Vm = φV0 , m = V0 × ρ ′ ,

Cr =


Geometric factor (Fg) 2 4 6

Form factor (σ) (π/2hi)2 (2.4082/Ri)2 (π/Ri)2

(10)


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Then, average desorptive velocity of gas from coal matrix to fissure system in the time gap from n to n+1 is defined as follows: q n +1 = −Fg × +

Fg C n +1 − C n = − {C n [exp(− DσΔt ) − 1] Δt Δt

C ( p n +1 ) + C ( p n ) [1 − exp(− DσΔt )]}. 2

(11) So, cumulative amount of desorption-diffusion can be expressed as follows: Qt =

N +1

∑ q n +1Δt = Fg (C0 − C n +1 ).

(12)

n =0

Eq. (12) is just numerical desorption-diffusion model under the conditions of drilling fluid medium.

2 Physical and numerical modeling 2.1

Physical simulating experiment

Physical simulating experiment in the paper was done using a device named as the auto-simulating and auto-measuring instrument for CBM desorption during hoisting of coal core under drilling fluid medium. Figure 1 shows the sketch of the apparatus designed by Wang [5]. The whole simulating process was divided into three main steps: the first step, degassing of coal sample in vacuum state; the second, CBM balanceable adsorption of coal sample filled with high purity methane according to CBM pressure of simulation; and the third, hoisting simulation of

Figure 1

Sketch of apparatus for simulating experiment.


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coal core under drilling fluid medium, with the measurement of methane-desorbed quantity. The key among the steps is the simulation for the linear drop of drilling fluid pressure during the hoisting of coal core. Drilling fluid pressure overlain on coal core was indirectly modeled with nitrogen-gas pressure. Simulating parameters (such as the buried depth of coal seam, density of drilling fluid, and core-hoisting velocity) were inputted into the special simulating software. Simulation of core-hoisting process was actualized with the linear drop of nitrogen-gas pressure, which was controlled jointly by the cyber-program and digital valve. Observing whether or not air bubbles occurred in the burette of simulating device, once air bubbles appeared, which means the start of CBM desorption, the log for noting the cumulative quantity of CBM desorption per minute. End of the cyber-program run indicated that coal core had been hoisted to ground where: the pressure around coal core was equal to atmospheric pressure. Then, the quantity of CBM desorption had been continually measured for 15 min. Description of the coal samples used to simulating experiment in the paper was given in Table 2. The samples are lean coal in coal rank and very fragmentized in structure with the typical characteristics of tectonically-deformed coal. 2.2

Numerical modeling

Numerical simulation was performed using the Matlab programme. The solution was acquired with iterative method, which is comparatively easy and accurate. The details of simulating process are as follows: (1) Inputting the parameter needed, including VL, Pc, PL,

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Table 2


Description of basic properties of coal sample used to simulation

Sample No. SQ1 SQ3

Table 3

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Occurrence of coal sample Location Seam No. Depth (m) Anyang, China 21 689–692 Anyang, China 21 856–858

Structure of coal-body

Ad 10.68 15.37

Mylonitic Mylonitic

Primary analysis (%) Wd CF 2.14 88.34 1.34 67.29

Vdaf 11.66 16.72

Ro,max (%) 2.49 2.27

Numerical simulating parameter of the coal samples Sample No. SQ1 SQ3

Porosity (%) 4.05 4.00

Apparent density (g/cm3) 1.51 1.48

T0, P0, T, t, ϕ, ρ, ρ′, g (gravitational acceleration) and the measured desorptive data(t, Qt)in air medium condition. The simulating parameters of the coal samples are been seen in Table 3. (2) Calculating Dσ with the data of initial desorption under air medium according to the formula −ln(1-Qt/ Q∞)=Dσt, where: Q∞ is the sum of the measured quantity of desorbed and remnant gas under the condition of ground, in cm3/g; Qt is the initial accumulative quantity of desorbed gas from t time on ground, in cm3/g. (3) Calculating C0 and C(p0) with the data form the steps abovementioned, and ensuring the length of time step. The simulating results showed that, when time step Δt is equal to 0.01 min, the calculating results are comparatively accurate. Then, the concentration and quantity of desorbed gas at every time could be obtained by the formula. (4) Plotting t-Qt curve from the calculated results, and process of numerical simulation ended. The results showed that the numerical simulated curve can fit truly to the t-Qt curve from the physical simulation, and total quantity of desorbed gas from the numerical simulation during the hoisting of coal core was close to that from the physical simulation (Figures 2 and 3). Simulating conditions in Figure 2 were as follows: raw coal sample SQ1,

PL,daf (MPa) 1.63 1.66

Figure 3 Plots of gas-desorbed quantity from raw coal sample SQ3 simulated under mud slurry medium.

CBM pressure with 1.6 MPa, water density with 1 g/cm3, core-hoisting velocity with 44.4 m/min, buried depth of coal seam with 400 m, and desorption under water medium for 3 min. Those in Figure 3 included: raw coal sample SQ3, CBM pressure with 1.17 MPa, mud slurry density with 1.17 g/cm3, core-hoisting velocity with 44.4 m/min, buried depth of coal seam with 400 m, and desorption under mud slurry medium for 5 min.

3

Figure 2 Plots of gas-desorbed quantity from raw coal sample SQ1 simulated under water medium.

VL,daf (cm3/g) 34.14 29.63

Case analyses

Lost gas quantity of four coal samples S1, S2, S3, and S4 in Anyang mining district, Henan province, was evaluated with both direct and numerical simulating methods respectively (Table 4). It is found that the lost gas quantity from numerical simulation is generally higher than that from direct method, which is distinct when lost time is relatively long (Table 4). Seidle and Metcalfe [16] and Yee et al. [17] suggested that the lost gas quantity would be always underestimated with direct method when lost gas quantity is very large or the lost time is very long, which is consistent with the results in the paper. It was further found that the lost gas quantities from


Table 4

S2

S3

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Estimated data of lost gas quantity with various methodsa) Lost gas quantity (cm3/g)

Lost time (min)

Depth (m)

Quantity of desorbed- and remnant-gas (cm3/g)

Mud slurry

Air

Direct method

Numerical simulating

SQ1-2

688.5

5.69

63

13

0.03

13.2

SQ1-3

689.0

13.18

5.5

3

0.05

1.53

SQ1-4

689.5

15.64

5.5

3

0.06

1.27

SQ1-5

691.3

20.06

5.5

3

2.05

1.37

SQ1-6

692.3

14.50

5.5

2

0.05

1.21

Mean

−

13.81

−

−

0.45

3.72

SQ2-2

1104.2

10.82

8.5

2

0.53

0.54

SQ2-3

1105.1

11.08

7.5

2

0.94

0.82

SQ2-4

1106.8

6.97

150

6

5.17

6.58

SQ2-5

1107.5

7.45

121

6

4.35

5.19

SQ2-6

1109.0

6.53

105

8

5.22

6.88

Mean

−

8.57

−

−

3.24

4.00

SQ3-2

856.5

8.69

130.5

4

8.3

11.28

SQ3-3

857.0

11.62

4.5

5

1.07

1.28

SQ3-4

857.6

10.64

4

8

1.48

1.69

SQ3-5

858.0

10.17

4

8

1.06

1.26

SQ3-6

859.0

10.00

9

5

0.91

1.12

Mean

−

10.22

−

−

2.56

3.33

Well No. Sample No.

S1

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LS-2

636.4

15.52

4.5

4

2.23

1.73

LS-3

636.9

22.03

4

6

0.87

0.40

LS-4

638.4

20.37

4.5

2

2.45

1.1

Mean 19.31 − − − a) Gas content is in air-dry basis, and gas volume is in standard condition (0°C, 101.325 kPa).

1.85

1.08

S4

direct method is very consistent with that from numerical simulating method when the lost time is shorter (t75 min) (Figure 4). It is regulated by China National Standard (GB/T 19559-2004), which was established on the basis of the American-Mine-Bureau’s direct method that it must take less than 10 min to hoist coal core from underground coal seam to ground. In contrast, the lost gas quantity with the active method of China is generally on the low side, which is possibly resulted in the underestimation the CBM content of coal seam in China. The deduction is consistent with the fact that the mined CBM resources from China were commonly larger than the exploring CBM resources in some given areas [18].

Figure 4

Comparison of lost gas quantities with two methods.

4

Conclusions

The active methods for estimating lost CBM quantity from coal core are not considering the differentia of CBMdesorbed process under air and drilling fluid medium, which leads possibly to the inaccuracy of the measured CBM content. Desorption-diffusion of CBM from coal core is a isotonic process under air medium but a variable pressure one under drilling fluid medium, which is just the reason resulted in the inaccuracy. Considering comprehensively primary factors that influence the desorption of CBM from coal core under drilling fluid medium, we discussed the theory of lost gas estimation with physical simulating experiment, and established the desorption-diffusion model and numerical modeling method of lost gas (including free CBM) calculation from coal core under various drilling fluid mediums on the basis of the Langmuir’s equation and Fick-first law. The results showed that the data from the numerical modeling can fit accurately the t-Qt curves from the physical simulation, and total desorbed-gas quantity from the former method is close to that from the latter. Ultimately, the desorbed-gas quantity from the direct method is consistent with that from the numerical modeling results when lost time is shorter than 25 min, but the latter is generally larger than the former when lost time is longer than 75 min. In

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contrast, the lost gas quantity resulted from active method of China is generally on the low side, which might induce the underestimation of CBM content in China. The deduction is consistent with the fact that the mined CBM resources in some given areas of China were commonly larger than the exploring CBM resources, so that it is necessary to review the current China National Standard on the basis of further investigation. We thank Hu Yisheng for the help of computer program design, and the reviewers for constructive comments. This work was supported by the Key Project of National Natural Science Foundation of China (Grant No. 40730422) and Young Project of National Natural Science Foundation of China (Grant No. 40802032). 1

2

3

4

5

Qin Y, Zhu W X. Some scientific problems faced to development of coalbed methane industry in China (in Chinese). Sci Found China, 2006, 20: 148–151 Kissell F N, Meculloc C M. The Direct Method of Determining Methane Content of Coalbeds for Ventilation Design. U.S. Bureau of Mines Report of Investigations. RI7767. 1981 Smith D M, Williams F L. A New Technique for Defermining the Methane Content of Coal. In: Proceedings of the 16th Intersociety Energy Conversion Engineering Conference. Atlanta: GA, 1981. 1267–1272 China National Standard Bureau. Measured Method of Coalbed Methane Content (GB/T 19559-2004) (in Chinese). Beijing: China Standard Press, 2004. 1–16 Wang Z F. Study on the gas desorption laws of coal in the media of air,water and drilling mud and their applications (in Chinese). Doctoral Dissertation. Xuzhou: China University of Mining and Technology, 2001. 24–82

6 7 8 9

10

11 12 13 14 15 16 17 18


Ning D Y, Yang S J. Study Mensuration Method of Geological Survey Coalbed Gas (in Chinese). Fushun: Fushun Branch of China Coal Research Institute, 1995. 12 Zhang X M, Han B S, Li J W. CBM occurrence and gas content estimate method in lignite (in Chinese). Coal Geol Explor, 2006, 34: 28–30 Zhang X M, Zhang S A, Zhong L W. Coalbed Methane of China (in Chinese). Xi’an: Shaanxi Science & Technology Press, 1991. 2–100 Bustin R M, Clarkson C R. Free gas storage in matrix porosity: A potentially significant coalbed resource in low rank coals. In: Proceedings of the 1999 International Coalbed Methane Symposium, 1999. Tuscaloosa: The University of Alabama, 1999. 197–214 Pratt T J, Mavor M J, DeBruyn R P. Coal gas resource and production potential of subbituminous coal in Powder River Basin. In: Proceedings of the 1999 International Coalbed Methane Symposium, 1999. Tuscaloosa: The University of Alabama, 1999. 23–24 Klinkenberg L J. The permeability of porous media to liquid and gases. In: Drilling and Production Practice. American Petroleum Institute, 1941. 200–213 Price H S, McCulloch R C, Edwards J C, et al. A computer model study of methane migration in coal beds. Can Min Metall Bull, 1973, 66: 103–112 Yue X Y. Coalbed Methane Exploration and Simulation Technology (in Chinese). Chengdu: Sichun University Press, 2000. 11–135 Shu X B, Chen J F. Coalbed Methane Geology and Exploration (in Chinese). Beijing: Science Press, 2001. 66–81 Zhang D L, Wang X H. Numerical simulation research on coalbed methane desorption mechanism (in Chinese). Nat Gas Ind, 2005, 25: 77–79 Seidle J P, Metcalfe R S. Development of coalbeds methane. SPE23025. Perth: The SPE Asia-Pacific Conference, 1991 Yee D, Seidle J P, Hanson W B. Gas Sorption on Coal and Measurement of Gas Content. In: Law B E, Rice D D, eds. Hydrocarbons from Coal. AAPG Stud Geol, 1993, 38: 203–218 Qin Y. Confronting position and challenge of Chinese coalbed methane industrialization (II): Scientifical & technological keys (in Chinese). Nat Gas Ind, 2006, 26: 4–8