Characteristics of Methane (CH4) Diffusion in Coal and Its Influencing

Dec 24, 2017 - ... strategy supplement for conventional oil and natural gas, coalbed methane (CBM) has been paid more attention by China, America, Aus...
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Characteristics of Methane (CH4) Diffusion in Coal and Its Influencing Factors in the Qinshui and Ordos Basins Junlong Zhao,*,†,‡ Dazhen Tang,§ Yong Qin,†,‡ Hao Xu,§ Yulong Liu,§ and Haiyong Wu§ †

Key Laboratory of Coalbed Methane Resource and Reservoir Formation Process, Ministry of Education, China University of Mining and Technology, Xuzhou, Jiangsu 221008, China ‡ School of Resources and Earth Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China § School of Energy Resources, China University of Geosciences (Beijing), Beijing 100083, China ABSTRACT: Diffusion coefficient is usually used to evaluate the methane (CH4) diffusion properties in the coal matrix and is vital to coalbed methane (CBM) development. Although extensive literature on the CH4 diffusion coefficient can be obtained, most of them aim at the whole coal or coal rank instead of the macrolithotype. Additionally, the primary structure of coal was destroyed with the common determination technologies (e.g., the particle, steady-state, and inverse diffusion methods) which could result in great errors. In this work, to avoid the shortcomings of the above methods, nine flake coal samples from six coal mines in the Qinshui and Ordos Basins were prepared to determine the CH4 diffusion coefficient with the slab calculation model. Meanwhile, the effects on the diffusion from the gas pressure, temperature, water saturability, and coal pore structure, and the gas adsorption capacity controlled by the coal rank and macrolithotype, were analyzed to reveal the diffusion mechanism (mode) at the CBM reservoir and laboratory conditions. Results show that the CH4 diffusion coefficient, at an order of magnitude of 10−10 m2/s measured with the flake coal sample, is more truthful. High temperature and gas pressure, low water saturability, developed pore structure, and high gas adsorption capacity contribute to large CH4 diffusion coefficient. Although the higher rank coal has the larger gas adsorption capacity, the CH4 diffusion coefficient exhibits a “U” shape (first decreasing and then increasing) with the increase of coal rank due to more micropores in low- and high-rank coals than the middle-rank coal. From the bright to dull coals at the same coal rank, the decreasing development of pore structure and gas adsorption capacity causes the decreasing CH4 diffusion coefficient. But compared to the coal rank, the influence of coal macrolithotype on CH4 diffusion coefficient is weaker. In addition, the CH4 diffusion modes in coal mainly are transitional and Fick diffusions in the CBM reservoir and laboratory. methods are commonly used.7,8,16−21 The analysis model of the above methods is the unipore or bidisperse diffusion model at spherical symmetric flow.22−24 However, all these methods have some deficiency (e.g., the primary structure of coal was destroyed) and the results are various since the test principles or conditions are different.25,26 In addition, two types of factors could influence the CH4 diffusion coefficient measurement: one is the experimental conditions (such as the gas component, gas pressure, temperature, and water saturability) and the other is the coal itself (pore structure and gas adsorption capacity determined by the coal rank and macrolithotype).2,7,14,17,26−36 However, all of the previous work omits the coal heterogeneity, especially the coal macrolithotype.36−38 Different from the coal rank, determined by various physical and chemical properties and used to describe the carbonification degree,39 the coal macrolithotype refers to the nature of the ingredient matter, conditions of deposition, and the extent of operation of the first or biochemical process of coal making, which could be restricted by maceral composition,38 and maybe determine how to optimize the CBM favorable reservoir and developmental approaches.40−44 In a word, because of the coal complexity, the current measurement methods and the analysis of the influencing factors cannot meet the demand of CBM industry development.

1. INTRODUCTION As a booming clean energy and important strategy supplement for conventional oil and natural gas, coalbed methane (CBM) has been paid more attention by China, America, Australia, etc.1 At the in situ state, most of the CBM is adsorbed onto inner surfaces of matrixes in the naturally fractured coal,2 and the network of cleats providing the main flow paths for gas/water are water-saturated.3 Therefore, the drainage decompression is the unique CBM development method. After the CBM desorption, the concentration and pressure gradients would form successively, which results in the CH4 diffusion and seepage, respectively.4 The CBM production integrates the CH4 desorption, diffusion, and seepage behaviors,5,6 where both the CH4 diffusion in the coal matrix and seepage in the cleats (reservoir permeability) could affect the gas well productivity, especially for the former which even has an effect on the CBM reserve evaluation.7,8 The phenomenon of “CH4 molecules migrate in the form of the random thermal motion from the high- to low-concentration areas” is known as diffusion,9,10 and is usually represented by the diffusion coefficient.11 On the basis of the pore size (diameter) and gas molecule mean free path, the diffusion modes could be divided into the Fick, transitional, and Knudsen diffusions.12−14 Meanwhile, the diffusion modes also include surface and crystal diffusions with a small amount.15 At present, three determination technologies for the CH4 diffusion coefficient including the particle, steady-state, and inverse diffusion © XXXX American Chemical Society

Received: October 9, 2017 Revised: December 11, 2017 Published: December 24, 2017 A

DOI: 10.1021/acs.energyfuels.7b03032 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels

(or electric voltage) was converted. The slab model is described as follows:

Thus, to avoid the shortcomings of existing methods, the flake sample and slab diffusion model were used in this work to measure and solve the CH4 diffusion coefficient, respectively. Moreover, the effects on the CH4 diffusion from gas pressure, temperature, water saturability, and pore structure and also gas adsorption capacity controlled by the coal rank and macrolithotype were investigated to reveal the gas diffusion mechanism (mode) at the CBM reservoir and laboratory conditions, which is helpful to understand the CBM diffusion effect deeply and provide the theoretical and technical support for CBM high-efficiency development.

⎛ 4q 2Dt ⎞ 2a(1 + a) ⎜− n ⎟ exp ⎜ 2 2 + + 1 a a q L2 ⎟⎠ ⎝ n=1 n (5) where p is the gas pressure at time t, p0 is the initial gas pressure, p∞ is the gas pressure when the coal is saturated by gas, D is the gas diffusion coefficient, a = α−1Vg/Vsa is the ratio of total gas volume Vg in the vessel to the coal sample volume Vsa [α is the partition coefficient (α = 1), Vsa = AL, A is the largest face area of the flake coal sample, and L is the sample thickness], and qn is the consecutive nonzero positive roots of equation tan(q) + aq = 0. Equation 5 could be further simplified as p − p∞ Mt =1− =1− M∞ p0 − p∞

2. METHODS AND EXPERIMENTS 2.1. Diffusion Model Review. Most of the CH4 in the coal matrix is adsorbed on the inner surface while a small quantity of gas exists in the free state in the cleats. The CBM production experiences the pseudosteady and nonequilibrium gas adsorption/desorption, diffusion, and seepage processes. To describe the three complex stages, the Langmuir equation for the adsorbed state gas, the ideal gas state equation for free gas, the Fick’s Second Law for gas diffusion, and the Darcy’s Law for gas seepage could be approached, respectively.26 For the gas diffusion, Crank22 derived the unipore diffusion model at spherical symmetric flow on the basis of Fick’s Second Law, which is described by

Mt 6 =1− 2 M∞ π

∞

∑ n−1

⎛ D′n2π 2t ⎞ 1 exp⎜− ⎟ 2 ⎝ n R2 ⎠

p − p∞ p0 − p∞

Ma 6 =1− 2 Ma ∞ π

∞

∑ n−1

⎛ D ′n2π 2t ⎞ 1 ⎜− a 2 ⎟ exp n2 Ra ⎠ ⎝

(1)

(2)

where Ma is the total amount of gas adsorbed/desorbed in the macropores at time t, Ma∞ is the total amount of gas adsorbed/desorbed at indefinite time in the macropores, Ra is the macrosphere radius, and Da′ is the macropore effective diffusivity. micropore:

Mi 6 =1− 2 Mi∞ π

∞

∑ n−1

⎛ D ′n2π 2t ⎞ 1 ⎜− i a ⎟ exp Ri ⎠ n2 ⎝

(3)

where Mi is the total amount of gas adsorbed/desorbed in the micropores at time t, Mi∞ is the total amount of gas adsorbed/desorbed at an indefinite time in the micropores, Ri is the microsphere radius, and Di′ is the micropore effective diffusivity. Hence, the over uptake is Mt Ma + M i M M = = β a + (1 − β) i M∞ Ma ∞ + M i ∞ Ma ∞ Mi∞

⎛ 4q 2Dt ⎞ 2a(1 + a) exp⎜⎜− 1 2 ⎟⎟ 2 2 1 + a + a q1 L ⎠ ⎝

(6)

where q1 is the first consecutive nonzero positive roots of equation tan(q) + aq = 0. Therefore, by fitting of the pressure difference (p − p∞) and time t, the CH4 diffusion coefficient D could be obtained. 2.2. Samples and Methods. To reveal the CH4 diffusion characteristics, the fresh bulk coal samples (∼15 × 15 × 15 cm3) with different coal ranks were collected from the following: (1) Duanshi (DS) and Houcun (HC) mines, high-rank coal from Jincheng mining area, southern of the Qinshui Basin; (2) Xiangshan (XS) and Yuchang (YC) mines, middle-rank coal from Hancheng mining area, east of the Ordos Basin; (3) Dafosi (DFS) and Tingnan (TN) mines, low-rank coal from Binchang mining area, west of the Ordos Basin, respectively (Figure 1). These samples were obtained directly from the working faces in the Permian Shanxi Formation and Jurassic Yan’an Formation in the Qinshui and Ordos Basins (Figure 2). Table 1 summarizes the coal sample information used for the CH4 diffusion. Figure 3 shows the experimental setup, flake sample, and the corresponding schematic illustrations. The experimental setup is the coal matrix gas diffusion coefficient determinator located in the National Engineering Research Center of CBM Development and Utilization (Figure 3a), which is mainly composed by diffusion, counting, evacuating, temperature, and pressure devices (Figure 3b). The functions of these devices have been described in our previous work in detail.26,36 The reasons why this method in this work could obtain more truthful diffusion coefficients are, on the one hand, the primary pore structure of the coal could be maintained by the test method; on the other hand, the experimental setup measures the voltage change by the pressure sensor instead of gas adsorption capacity.26,36 Before the diffusion measurement, the flake coal samples should be prepared first from the bulk coal samples. The sample size is ∼20 mm × 15 mm × 3 mm in length, width, and thickness, and the maximum fracture width is less than 3 μm (Figures 3c−e). Then these flake samples were put in the sonicleaning pool for cleaning. The sample volumes and thicknesses were measured by a drainage method and a vernier caliper, respectively. Here, the samples for CH4 diffusion coefficient measurement should be completely dried and the temperature of the dryer was set at 110 °C. In this work, the gas injection pressure for all the samples was from 1 to 5 MPa (the interval is 1 MPa) and the temperature was set to be 40 °C. The inter-record gap by the experimental instrument is 1 s and the measurement is ongoing until the gas pressure changes no longer. To analyze the effects of the temperature, water saturability, and coal macrolithotype on the CH4 diffusion coefficient, the middlerank YC sample was further measured at 20 and 30 °C. The high-rank HC sample was further measured at the moist conditions when the dry samples were finished. Here, the standard brine with a mineralization degree of 8% (the mass ratio of NaCl:CaCl2:MgCl2·6H2O is 70:6:4) was adopted to simulate formation of water. The water saturability was processed for only 24 h to ensure that the samples would not be damaged. Moreover, the middle-rank XS samples were further divided into four subtypes (bright, semibright, semidull, and dull coals) according to the overall relative luster and percentage of bright

where Mt is the total amount of gas adsorbed/desorbed at time t, M∞ is the total amount of gas adsorbed/desorbed at an indefinite time, t is time, R is the sphere radius, and D′ is the effective diffusion coefficient and is defined as D′ = D/(1 + HS/ε), in which D is the diffusion coefficient, H is the Henry’s constant for adsorption, S is the pore surface area, and ε is the porosity. However, this model could be applied only to some bright coals rather than all the coal macrolithotypes.2 Ruckenstein et al.23 considered the heterogeneous pore structures of coal and the CH4 diffusion was divided into two stages: one is the fast diffusion in the macropores and the other is the slow diffusion in the micropores. Then the bidisperse diffusion model at spherical symmetric flow was developed as macropore:

≈

∞

∑

(4)

where β = Ma/(Ma∞+ Mi∞) is the ratio of macropore adsorption/ desorption to the total adsorption/desorption. Although the data matching the bidisperse diffusion model is satisfying,7,26,45 it is inconsistent with the actual adsorption because it assumes the adsorption isotherm is linear. Thus, Xu et al.26 and Zhao et al.36 measured the more precise CH4 diffusion coefficient with flake coal sample and computed the value by the slab model where the relationship between the amount of gas adsorbed and gas pressure B

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Figure 1. Maps of the Qinshui and Ordos Basins and sampling point distributions.

Figure 2. Coal-bearing strata and sampling seams in the Qinshui and Ordos Basins. equilibrium treatment is ∼100−125 g. Every sample was treated more than 4 days at 97% humidity for moisture equilibrium. Then, with IS-100, the CH4 adsorption isotherm measurement could be carried out after inserting the coals into the sample cell. Here, the experimental temperature (30 °C) and equilibrium pressure (up to 10 MPa) were set, respectively.4,44 Finally, the Langmuir volume and pressure could

components, namely, the vitrain and clarain.43,44 All the samples could be used to discuss the influence from the coal rank. Additionally, the broken samples were collected for the tests of CH4 isothermal adsorption, random vitrinite reflectance, proximate, and maceral analysis. The particle size for the CH4 isothermal adsorption is 60−80 mesh (0.18−0.25 mm) and the sample weight for the moistureC

DOI: 10.1021/acs.energyfuels.7b03032 Energy Fuels XXXX, XXX, XXX−XXX

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reservoir needs a long period of time to reach the maximum gas production, but the production capacity is stable; the smaller the Langmuir pressure, the more difficult the gas desorption, and the lower the desorption efficiency.35 A Leitz MPV-3 photometer microscope was used to measure the coal random vitrinite reflectance and maceral analyses (500 points) according to ISO 7404.3-1994 and ISO 7404.5-1994,47,48 respectively. These measurements were performed on the same polished section of the coal sample. The proximate analysis was analyzed with a 5E-MAC III infrared fast coal analyzer following ISO 562-2010, ISO1171-2010, and ISO11722-2013.49−51

Table 1. Coal Sample Information Used for CH4 Diffusion sample number DFS TN XS YC HC DS

coal rank

coal seam

coal mining area

coal mine

low

4

Binchang

middle

3

Hancheng

high

3

Jingcheng

Dafosi Tingnan Xiangshan Yuchang Houcun Duanshi

be computed by data matching with the Langmuir sorption model.46 The Langmuir model is given as p V = VL p + pL (7)

3. RESULTS AND DISCUSSION 3.1. Properties of Coal Petrology and CH4 Isothermal Adsorption. Table 2 shows the results of proximate analysis and coal composition. Overall, the moisture content is between 0.21% and 5.23%, ash yield ranges from 8.16% to 27.93%, volatile matter is 3.68%−26.18%, and fixed carbon range is from 40.66% to 85.69%. Of all the samples, the vitrinite content is 34.55%−81.22%, inertinite accounts for between 14.30% and 62.57%, liptinite content is less than 3.00%, and mineral matter content ranges from 0.48% to 9.28%. The high-rank sample has the highest vitrinite content and lowest ash yield, while the lowrank sample has the highest inertinite and liptinite contents as well as ash yield. The middle-rank coals are between them.

where p is the gas pressure (MPa), V is the volume of gas adsorbed (m3/t), VL is the Langmuir volume representing the maximum volume that can be adsorbed at infinite pressure (m3/t), and pL is the Langmuir pressure at which the adsorbed volume is half the Langmuir volume (MPa). The Langmuir volume is a parameter to measure the adsorption capacity of the coal reservoir and its values reflect the maximum adsorption capacity of the coal reservoir at this temperature. The Langmuir pressure is a parameter to influence the shape of the adsorption isotherm, which reflects the difficulty degree of CBM desorption: the higher the Langmuir pressure, the easier desorption of adsorbed gas in coal, and the more favorable the CBM development. The coal

Figure 3. Experimental setup, flake sample, and the corresponding schematic illustrations. D

DOI: 10.1021/acs.energyfuels.7b03032 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels Table 2. Results of Proximate Analysis and Coal Composition proximate analysis (wt %, air-dry basis)

coal composition (vol %)

sample number

moisture

ash yield

volatile matter

fixed carbon

vitrinite

inertinite

liptinite

mineral

DFS TN XS YC HC DS

5.23 2.73 0.94 0.87 0.22 0.21

27.93 18.88 13.38 12.15 8.16 10.42

26.18 23.83 16.73 12.33 6.04 3.68

40.66 54.56 68.95 74.65 85.58 85.69

34.55 39.34 75.37 77.93 81.22 80.58

62.57 57.54 14.30 15.58 15.77 14.98

2.40 1.29 1.05 0.44 0.00 0.00

0.48 1.83 9.28 6.05 3.01 4.44

3.2.1. Gas Pressure, Temperature, and Water Saturability. The experimental conditions in this work mainly include the gas pressure, temperature, and water saturability. Table 4 and Figure 4

Table 3 shows the results of random vitrinite reflectance and CH4 isothermal adsorption. It could be seen that the random Table 3. Results of Random Vitrinite Reflectance and CH4 Isothermal Adsorption isothermal adsorption (mineral matter containing basis) sample number

random vitrinite reflectance (%)

Langmuir volume (m3/t)

Langmuir pressure (MPa)

DFS TN XS YC DS HC

0.65 0.54 1.72 1.91 3.15 2.95

13.22 10.09 26.68 24.25 41.82 40.23

3.03 3.92 1.05 2.18 1.58 2.32

vitrinite reflectance is 0.54%−3.15%, Langmuir volume ranges from 10.09 to 41.82 m3/t, and Langmuir pressure is between 1.05 and 3.92 MPa. Since the Langmuir volume could be used to represent the CH4 adsorption capacity by coal, the high-rank coal has the largest Langmuir volume (>40 m3/t), the middlerank coal comes in second (20−30 m3/t), and the value of low-rank coal is the smallest (14.7

1.47 2.24 2.10 1.96 3.37 3.15 2.94 6.73 6.31 5.88

0.13∼12.6

>13.5

1.35 1.18 1.58

1.68

1.26

313.15 293.15 313.15 303.15 293.15

293.15

303.15

313.15

293.15

303.15

313.15

293.15

303.15

313.15

303.15

40 5 30 20 40 4 30 20 40 3

temperature (°C) temperature (K) CH4 mean free path (nm)

gas pressure (MPa)

30 20 40 40 30 20

20

30

2 1

Table 6. CH4 Molecule Mean Free Paths and Pore Size Ranges of Diffusion Types in Coal under Different Equilibrium Pressures (1−5 MPa) and Temperature (20−40 °C)a

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H

DOI: 10.1021/acs.energyfuels.7b03032 Energy Fuels XXXX, XXX, XXX−XXX

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Energy & Fuels first decreases rapidly and then tends to a certain value with the increase of gas pressure (Figure 9b). In the actual CBM field, with the increase of the coal seam burial depth, both the gas pressure and temperature increase, which results in the CH4 molecular average free path tending to a certain value. Considering the advantage diffusion mechanism of gas in the medium, the pore diameter ranges for different CH4 diffusion types in coal could be determined. In the laboratory, when the temperature is 20 °C and the gas pressure is 5 MPa, the threshold values for three diffusion types are 0.12 and 11.8 nm, respectively (Table 6). Nevertheless, since the effective molecular diameter of CH4 is 0.33 nm and the effective distance when the CH4 molecular experiences interactions with coal surface is about 0.55 nm (the corresponding pore diameter is more than 1.1 nm), the adsorption potential well distance is about 0.36 nm.63 In other words, in the pore diameter ranges of 0.33−1.1 nm, the CH4 molecule cannot move freely and exhibits in adsorbed phase because of the influence of the coal surface, which results in the diffusion type being surface diffusion. However, under the experimental conditions, the pore diameter ranges of Knudsen diffusion are all less than 0.7 nm (Table 6). Therefore, the dominant diffusion types under the experimental conditions are the Fick and transitional diffusions. Moreover, under the reservoir conditions (the temperature is usually between 20 and 40 °C and the average reservoir pressure is 4−6 MPa35,64), the Knudsen diffusion is also difficult to be found.

ORCID

Junlong Zhao: 0000-0002-8911-894X Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was financially supported by the Key Project of the National Science & Technology (Grant Nos. 2016ZX05042002 and 2016ZX05044-002), the National Natural Science Foundation Project (Grant Nos. 41530314 and 41772155), and the project funded by China Postdoctoral Science Foundation (Grant No. 2017M621871). The authors are grateful to anonymous reviewers and the editor Dr. Patrick Hatcher for their careful reviews and detailed comments that helped to substantially improve the manuscript.

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4. CONCLUSIONS (1) The flake sample could keep the primary structure of the coal, resulting in a more sufficient CH4 adsorption and more accurate diffusion coefficient. The experimental setup measures the voltage change by the pressure sensor instead of the gas adsorption capacity further improving the measurement accuracy. The CH4 diffusion coefficient is at an order of magnitude of 10−10 m2/s. (2) Both the experimental conditions (gas pressure, temperature, and water saturability) and coal properties (pore structure and gas adsorption capacity) could affect the CH4 diffusion coefficient measurement. High temperature and gas pressure, in addition to low water saturation, contribute to large CH4 diffusion coefficient. The more developed pore structure and larger gas adsorption capacity favor a larger CH4 diffusion coefficient. (3) Compared to the coal macrolithotype, the influence of coal rank on CH4 diffusion coefficient is more obvious. Although the higher rank coal has a larger gas capacity, the CH4 diffusion coefficient exhibits a “U” shape (first decrease and then increase) with the increase of coal rank because of more micropores existing in low- and high-rank coals compared to those in middle-rank coal. From the bight to dull coals at the same coal rank, the decreasing development of pore structure and gas capacity cause the decreasing CH4 diffusion coefficient. (4) By the relationship between the gas molecular average free path and coal pore diameter, the advantage diffusion mechanism of gas could be determined. In the CBM reservoir (the temperature is usually between 20 and 40 °C and the average reservoir pressure is 4−6 MPa) and laboratory (the temperature is usually between 20 and 40 °C and the average reservoir pressure is 1−5 MPa), CH4 diffusion modes in coal mainly are transitional and Fick diffusions.

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*E-mail: [email protected] (J.L.Z.). I

DOI: 10.1021/acs.energyfuels.7b03032 Energy Fuels XXXX, XXX, XXX−XXX

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DOI: 10.1021/acs.energyfuels.7b03032 Energy Fuels XXXX, XXX, XXX−XXX