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Experimental study on gas diffusion dynamics in fractured coal: A better understanding of gas migration in in-situ coal seam
Energy 195 (2020) 117005
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Experimental study on gas diffusion dynamics in fractured coal: A better understanding of gas migration in in-situ coal seam Ting Liu a, b, *, Baiquan Lin a, Xuehai Fu b, Yabin Gao c, **, Jia Kong a, Yang Zhao a, Haoran Song a a
School of Safety Engineering, China University of Mining and Technology, Xuzhou, 221116, China Key Laboratory of CBM Resources and Dynamic Accumulation Process, China University of Mining and Technology, Ministry of Education, Xuzhou, Jiangsu province, 221008, China c College of Safety and Emergency Management Engineering, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 September 2019 Received in revised form 15 January 2020 Accepted 18 January 2020 Available online 20 January 2020
In-situ coal seam is generally under the stress constraint condition. However, the powder coal is often adopted to study gas diffusion dynamics in the laboratory, in this case, the stress cannot be imposed on the coal sample. So the question is, can the laboratory test results with the powder coal reflect the gas diffusion behaviors in the in-situ coal seam? Does the confining stress affect the gas diffusion behaviors in fractured coal? To address these questions, in this work, we first investigated the effect of coal size on gas diffusion dynamics with powder coal and lump coal under unconstrained conditions. The results show that there exists an obvious scale effect for gas diffusion in coal, and a critical value of coal size has been found for the scale effect. When the coal particle size is smaller than the critical value, the effective diffusivity decreases with an increase of the particle size; and when the particle size is larger than the critical value, no obvious change can be found in the effective diffusivity. The critical value for gas diffusion corresponds to the size of the coal matrix. The essential reason for the existence of the scale effect is the differences among the pore structures of coals with various sizes. Based on the research results under the unconstrained conditions, a coal core was selected to study the effect of confining stress and pore pressure on gas diffusion under constraint condition. The results indicated that the confining stress and pore pressure have significant impact on gas diffusion in fractured coal. With an increase of the confining stress and a decrease of the pore pressure, the effective diffusivity reduces gradually. Therefore, to get an accurate understanding of the gas diffusion behavior in in-situ coal seam, during the test in the lab, both the scale effect and confining stress should be considered. The research results obtained in this work have important guiding significance to reveal gas migration in in-situ coal seams during CBM depletion, CO2-ECBM and geological sequestration of CO2. © 2020 Elsevier Ltd. All rights reserved.
Keywords: Gas diffusion Scale effect Granular coal Fractured coal core In-situ coal seam
1. Introduction During coalbed methane (CBM) depletion, the gas migration in coal seam generally can be divided into three steps, namely desorption, diffusion and seepage [1,2]. At the initial stage, the gas is mainly from the fractures, and the process is dominated by the seepage. But as the gas pressure in the coal seam becomes depleted, the gas mainly comes from the matrix later, and the diffusion plays
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected], [email protected] (T. Liu). https://doi.org/10.1016/j.energy.2020.117005 0360-5442/© 2020 Elsevier Ltd. All rights reserved.
an increasingly important role in this stage [3]. In addition, the CO2 enhanced coalbed methane (CO2-ECBM) recovery and geological sequestration of CO2 also involve the diffusion of CH4 and CO2 in the coals seams. In these processes, the diffusion plays as a bridge connecting the desorption and seepage, and affects the CBM production and CO2 injection [4,5]. Therefore, a comprehensive understanding of the diffusion process in the in-situ coal seam contributes to the questions [3]: At what pressure should the CBM well be abandoned? When does the restimulation measure need to be taken? How long should the CO2 injection last? For the great importance of the diffusion process, a series of research, including modelling and laboratory test, was conducted to explore the gas diffusion behaviors in the coal [6e10]. Zhao et al.
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(2019) [11] presented a comprehensive review on the mathematical models for gas diffusion in coal particles and the applications in environment, energy and mining safety areas. To avoid the duplication of review effort, the mathematical models for gas diffusion in coal particles will not be included here. Because the main method used in our study is the laboratory test, here we put our emphasis on the review of the diffusion study by lab test. Keshavarz et al. (2017) [12] studied the effects of maceral composition and coal rank on gas diffusion in Australian coals. In their study, 18 bituminous and sub-bituminous coal samples were ground into coal particle with size of 0.5e1.0 mm. Then both CO2 and CH4 kinetic sorption tests were performed to calculate the diffusion rate. Du et al. (2018) [13] conducted experiments on gas diffusion under negative pressure environments. Coal samples from Duanshi Coal Mine in the Qinshui Basin were collected and ground into particles with size of 1e3 mm. Then diffusion tests with the initial pore pressure of 0.5 MPa, 1.5 MPa and 2.5 MPa were performed under various negative pressures. In order to reveal the effect of pore structure on gas diffusion in coal, Yang and Liu (2019) [14] performed a series of gas desorption and pore size distribution tests. In the study, coal particles with size of 0.177e0.250 mm was adopted to conducted the desorption test, and they believed that pulverization of the coal samples wouldn’t affect the accuracy of diffusion measurements. In addition, other researchers also conducted a series of studies to investigate the gas diffusion in coal particles under different conditions. In their studies, coal particles with sizes of 0.149e0.425 mm [9], 0e3.2 mm [7], 1e3 mm [15], 0.2e3 mm [16], 0.18e0.25 mm [17], were adopted. Up to date, the granular coal is often adopted to investigate the gas diffusion in coal, and in different studies, the size of the particles used varies greatly. Although obvious differences exist, the particle size used in previous research is generally less than 5 mm, and in most cases, it is less than 1 mm. However, as we know, the in-situ coal seams contain complex pore-fracture structures. The crushing process during coal particle preparation may damage the pore structure of the coal [18e20]. Unlike the granular coal adopted in the lab, in-situ coal seam generally contains a lot of fractures and is confined by crustal stress. However, the effects of fracture and confining stress on gas diffusion behaviors in coal have rarely been reported so far. Xu et al. (2015) [23] investigated the effects of gas pressure, coal rank and moisture content on gas diffusion in coal matrix. In their research, instead of the coal particles, a coal matrix flake (20 mm 15 mm 3 mm) was adopted. With this method, the damage of the pore structure can be avoided, but a confining stress cannot be imposed on this sample. In addition, a series of lab test results indicated that the adsorption equilibrium pressure had great impact on gas diffusion. Xu et al. (2015) [23] demonstrated that with an increase of the pore pressure, the diffusivity decreased gradually. The test result of Wang and Liu (2016) [3] indicated that with an increase of the pore pressure, the diffusivity increased first and followed by a reduction. While Pillalamarry et al. (2011) [9] concluded that the diffusivity of coal decreased with an increase of the pore pressure. By now, there is no consistent understanding on the effect of pore pressure on gas diffusion. Therefore, more lab tests should be conducted on this issue. For a porous medium, when the scale is very small, its attributes fluctuate randomly in space, which is related to the heterogeneity of pore structure in porous media. When the medium scale reaches a critical value, with a further increase of the scale, no obvious change on its attributes can be found. The element corresponding to the critical scale is called representative element volume (REV). For the heterogeneous medium, because of the existence of the fractures, the attributes on macroscale show great uncertainty in
space [21,22]. The in-situ coal seam is generally viewed as a dual porosity medium, which contains a complex pore-fracture structure, and its scale is far greater than that of the samples adopted in the lab. Therefore, to reveal the in-situ gas diffusion behavior in the laboratory, a REV, which can reflect the internal structure of the coal, must be determined first. And the external condition, such as confining stress and pore pressure, should be considered as well. Aiming at the research gaps, in this work, we first investigated the scale effect of gas diffusion in coal particles. Based on the results, the critical size of the REV was determined. Then, based on the critical size of the coal, a coal core was adopted to study the effects of confining stress and pore pressure on gas diffusion behaviors. Finally, the mechanisms of scale effect and the influence of confining stress and pore pressure on diffusion were discussed. 2. Experimental samples and apparatus 2.1. Coal samples In this work, two types of coal with different metamorphic degrees were selected to study the gas diffusion dynamics. These coals are from Gansu Yanbei (GSYB) and Guizhou Linhua (GZLH). Table 1 shows the results of proximate analysis and vitrinite reflectance. The Volatile Matter of coal GSYB is significantly higher than that of coal GZLH, while its Fixed Carbon is greatly lower than that of coal GZLH. The average maximum vitrinite reflectance of coals GSYB and GZLH are 0.58% and 2.86%, meaning that they are a bituminous coal with low metamorphic degree and an anthracite (according the Standards for Coal Industry in China, MT/T11582011). The T2 spectrum (by Nuclear Magnetic Resonance) and pore image (by Ar ion polishing-assisted SEM) (See Fig. S1 in supplementary material) of the coal samples show that for coal GSYB, the pore size distributes in a triple peak pattern. The distribution of pores with different size is relatively uniform in this coal. The results of Ar ion polishing-assisted SEM shows that the coal GSYB contains a lot of micron-scale pores and some nano-scale pores. The pore size curve of coal GZLH presents a bimodal distribution, although the second peak is not obvious. It can be deduced that the micropores dominate in coal GZLH, and this can be verified by the imaging results by Ar ion polishing-assisted SEM that limited pores can be found with a resolution of 20 mm, but a large number of nanopores can be detected with a resolution of 300 nm. To investigate the scale effect of gas diffusion in coal, powder coals were produced with the size of less than 0.075 mm, 0.075e0.12 mm, 0.12e0.18 mm, 0.18e0.25 mm, 0.25e0.38 mm, 0.38e0.83 mm, 0.83e1.70 mm, 10e15 mm, 15e30 mm. Moreover, cylindrical coal samples with a size of F 50 100 mm were adopted to study the effects of confining stress and pore pressure on gas diffusion behaviors (See Fig. S2 in supplementary material). 2.2. Experimental apparatus and method The experimental system used in this work is depicted in Fig. 1. The system in Fig. 1(a) is used for investigating the gas diffusion in coal without stress constraint, and it includes the degassing module, adsorption/desorption module, control module and data acquisition module. After the tests of gas diffusion in powder coal are completed, the adsorption cell in Fig. 1(a) is replaced by the cell in Fig. 1(b). With this cell, the samples can be stressed in both axial and radial directions. Integrating the cell in Fig. 1(b) with the system in Fig. 1 (a), the effect of external stress on gas diffusion behaviors can be investigated. The main procedures for the test of gas diffusion in coal are as follows:
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Table 1 Results of proximate analysis and vitrinite reflectance. Code
Moisture/Mad
Ash/Ad
Volatile Matter/Vdaf
Fixed Carbon/FCd
Average maximum vitrinite reflectance/Romax%
GSYB GZLH
2.51 2.41
9.70 11.04
38.54 5.81
55.49 83.79
0.58 2.86
Fig. 1. Experimental system for investigating gas diffusion in coal. (a) System for investing gas diffusion in powder coal under unconstraint condition; (b) Cell for investigating gas diffusion in cylindrical coal core under constraint condition.
(1) Procedures for the test of gas diffusion in granular coal ① Put coal particle with a given size in drying oven with a constant temperature of 60 C for 24 h. ② The dried sample with a weight of mc is put into the adsorption cell placed in the water bath with a constant temperature of 30 C. ③ Run the vacuum pump to degas the system for 12 h. ④ Inject He into the reference cell with a given pressure of pHe, then open the valve between the adsorption and reference cells to inject the He into adsorption cell, after equilibrium is achieved, record the gas pressure as p’He. ⑤ Degas the system, and inject CH4 into the system just as the procedure of He injection, record the gas pressure as pCH4 and p’CH4. ⑥ During desorption, the gas volume is continuously recorded. Due to the high gas desorption amount, the initial interval is set as 5 s, and it is expanded properly with the decay of the gas volume. The desorption time lasts for 120 min according to the standard of GBT 23250e2009 (direct method to measure gas content in coal mines) [25]. ⑦ Repeat the above steps for another sample until all the samples are tested. (2) Procedures for the test of gas diffusion in fractured coal In this part, gas diffusion in a cylindrical fractured coal with size of F50 100 mm under constraint condition is tested. The procedure is the same with that of powder coal, and the scheme is as follows: Case 1: The adsorption equilibrium pressure is set as 2 MPa, then the gas diffusion is tested with the confining stress (axial stress is equal to radial stress) of 4 MPa, 8 MPa, 12 MPa, 16 MPa, 20 MPa. Case 2: Both the confining stress and axial stress are set as 8 MPa, then the gas diffusion is tested with the pore pressure of 1 MPa, 2 MPa, 3 MPa, 4 MPa, 5 MPa. Notice that due to the possible existence of fractures in the coal
cores, it should be ensured that before the start of the diffusion, no free gas exists in the fractures, and this can be achieved by opening the exhaust valve until the gas pressure in the holder indicates zero. In addition, gas migration velocity in fracture is much higher than that in matrix pore, therefore, during diffusion, the process of gas migration in fracture can be ignored. (3) Procedures for data processing ① First the gas adsorption amount in equilibrium is calculated as Q∞ with the pressure monitored; ② The ratio of gas desorption amount Qt at time t to Q∞ is called desorption ratio, and the curve Qt =Q∞ t is the characteristic curve of gas desorption; ③ Further, we can get the curve lnð1 Qt =Q∞ Þ t. ④ Eq. (1) shows the unipore diffusion mode for describing gas diffusion porous media. By giving 1 to n, Eq. (1) can be simplified as Eq. (2) [35,36].
∞ Qt 6 X 1 ¼1 2 exp Q∞ p n¼1 n2
n2 p2 D t r 20
! (1)
where, Qt is the total amount of gas diffused at time t, mL/g, Q∞ is the total amount of gas adsorbed on coal at equilibrium pressure, mL/g, D is the diffusivity, m2/s, r0 is the radius of coal particles, m, and n means the nth level of the series.
Qt p2 D p2 ln 1 ¼ 2 t þ ln Q∞ 6 r0
(2)
⑤ From Eq. (2), we can see that the tangent slope at any point of the curve lnð1 Qt =Q∞ Þ t is D=r 20 ,p2 . In this work, the expression D=r 20 is defined as the effective diffusivity De, further we can get the curve De ~ t.
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3. Results and analyses 3.1. Results and analyses of gas diffusion in coal with various sizes The characteristic curves of gas diffusion in coal with various sizes (Fig. S3 in supplementary material) shows that with an increase of the time, the desorption ratio increases rapidly first and then tends to equilibrium gradually. In addition, with an increase of the coal size, the maximum desorption ratio in 2 h reduces rapidly at the initial stage, and later, it gradually stabilizes to a fixed value. For example, for the coal GSYB, the maximum desorption ratio in 2 h is 0.760 when the particle size is less than 0.075 mm, and the desorption ratio decreases to 0.250 for coal with size of 0.25e0.38 mm. With a further increase of the coal size, no obvious change can be found on the maximum desorption ratio, and it finally stabilizes around 0.20. For coal GZLH, the maximum desorption ratio corresponding to coal particle less than 0.075 mm is 0.880, and it decreases to 0.409 with the coal size increases to 0.83e1.70 mm. With a further increase of the coal size, the maximum desorption ratio fluctuates around 0.40. The decrease of the maximum desorption ratio with the particle size is mainly because that with an increase of the particle size, the pore structure in the particles becomes more complex, therefore, the resistance for gas diffusion in big coal particle is greater than that of the small particles. With the characteristic curves, we can further calculate the effective diffusivity of the coal samples. In Fig. 2 (a) and (b), for coal
samples with different sizes, the effective diffusivity decreases with the time on the whole, although a slight fluctuation exists. For example, the initial effective diffusivity of coal GSYB with a size less than 0.075 mm is 0.0146, and after 7200 s, it decays to 1.81 106. In our previous study, we developed a time-dependent model to describe the phenomenon that the effective diffusivity decreases with the time [26]. Reasons for the time-dependence of diffusivity includes three parts: 1) during the diffusion, the decrease of the pore pressure leads to a shrinkage of the matrix, which results in a decrease of the diffusivity [24]; 2) at the initial stage, the desorbed gas mainly comes from pores with large diffusivity, later it is dominantly from pores with small diffusivity; 3) in a given pore, there exists multiple diffusion modes, including molecular diffusion, transition diffusion and Knudesen diffusion, and the apparent diffusivity of coal particles can be obtained by adding up the diffusivities of the three diffusion modes proportionally [27]. The high pore pressure at the initial stage determines the small mean free path of gas molecules, thus in this stage, the molecular diffusion dominates the diffusion process, and the diffusivity is relatively large; with a decrease of the pore pressure, the mean free path of gas molecules increases gradually, and the diffusion mode gradually transits to the transition diffusion and Knudesen diffusion, therefore, the diffusivity decreases gradually [28]. Under the same external conditions, the diffusion behaviors of coal are mainly determined by the pore structures. The characteristic curves show that there exists limit scales for different coals, and the diffusion dynamics of coal beyond this scale is independent
Fig. 2. Change of effective diffusivity with time and coal size. (a) and (b) show the relation between effective diffusivity and time of GSYB and GZLH, respectively; (c) and (d) show the relation between effective diffusivity and coal size of GSYB and GZLH, respectively.
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of coal sample size. Therefore, it is reasonable to presume that a scale effect also exists on coal diffusivity. Fig. 2 (c) and (d) presents the effect of coal size on the diffusivity. Overall, the diffusivity decreases with an increase of the coal size. But we also find a critical value, if the coal size is greater than the critical value, the diffusivity is independent of the coal size. Based on the critical size, the effect of coal size on diffusivity in Fig. 2 (c) and (d) can be divided into significant influence zone and insignificant influence zone. For coal GSYB, when the coal size is smaller than 0.25e0.38 mm, the diffusivity decreases with an increase of the particle size, and when the coal size is greater than 0.25e0.38 mm, no obvious reduction can be found. Taking the desorption time of 300 s as an example, when the increase of coal size from less than 0.075 mm to 0.25e0.38 mm, the effective diffusivity reduces from 4.74 105 to 4.19 106 with a decrease of 91.2%. While from 0.25 to 0.38 mm to f50 100 mm (cylindrical coal core), the diffusivity fluctuates slightly, and no obvious reduction can be found. The analysis indicates that the critical value of coal GSYB is 0.25e0.38 mm. With the same method, the critical value of coal GZLH can be determined as 0.45e2 mm. In addition, from Fig. 2 (c) and (d), we can also find that at the initial stage, the scale effect is not obvious, but with the increase of time, the influence of coal size on the effective diffusivity becomes more significant. The variation of the effective diffusivity of coal particles with the size can be attributed to the change of the pore structures. The detailed mechanism will be discussed in section 4.1. 3.2. Effect of external conditions on gas diffusion in fractured coal The above analyses indicate that only when the coal size is larger than the critical value, the lab test results can reflect the gas diffusion in situ coal seam more accurately. In addition, for the insitu coal seam, it is generally under the constraint condition, and investigating the effects of confining stress and pore pressure is of great importance to the better understanding of gas diffusion dynamics in in-situ coal seam. To the best of our knowledge, this issue has rarely been experimentally investigated before, therefore, in this section, the effects of confining stress and pore pressure on gas diffusion in lump coals are systematically discussed. 3.2.1. Effect of confining stress The characteristic curves of gas diffusion in coal core under different confining stress (Fig. S4 in supplementary material) shows that the desorption ratio increases sharply at the initial stage, but later it tends to increase gently. Although the overall variation trends of the characteristic curves for different coal are similar, difference still can be found. For example, under the same confining stress, the desorption ratio of coal GSYB at the equilibrium is obviously higher than that of coal GZLH. This phenomenon is mainly determined by the difference between pore structures of the coal cores. From Fig. S1, we can see that there exists a fairly high proportion of meso- and macro-pores in coal GSYB, therefore, the gas migration in coal GSYB is relatively easy. While for coal GZLH, it is dominated by the micro-pores, the migration resistance of gas in this coal is relatively high, therefore, the gas diffusion is more difficult in this case. For a given coal core, its desorption ratio decreases with an increase of the confining stress. For the coal GSYB, its desorption ratio corresponding to the confining stress of 4 MPa is 0.35, while when the confining stress increases to 20 MPa, the desorption ratio decreases to 0.08, with a decrease of 77.1%. For the coal GZLH, the desorption ratio corresponding to the confining stress of 4 MPa is 0.17, and when the confining stress increases to 20 MPa, it decreases to 0.07, with a decrease of 58.8%. This experimental phenomenon implies that the external confining stress can significantly reduce
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the gas desorption ratio of the fractured coal. The main reason may be that the existence of the confining stress changes the pore structure of the fractured coal, which further influences the gas diffusion process in coal. Fig. 3 shows the variation of effective diffusivity of fractured coals under different confining stress with the time. During the diffusion process, the diffusivity decreases sharply at the initial stage and later gradually tends to be stable. This indicates that for the fractured coal, the diffusion process is also time dependent, which is consistent with that of the granular coal. And the reasons for the time dependence of the diffusion in fractured coal are the same with those in the granular coal. There exists obvious difference between the diffusivities of coals GSYB and GZLH. Taking the confining stress of 4 MPa as an example, the effective diffusivities at the initial time are 7.54 104 and 3.05 104 for coals GSYB and GZLH, respectively. In addition, at the initial stage, the decay of the diffusivity of coal GZLH is sharper than that of GSYB. The reason is that for the coal GZLH, the proportion of meso- and macro-pores is lower than that of GSYB. Besides, the poor pore connectivity of GZLH also contributes to the fast decay of its diffusivity. For the same coal, the diffusivity decreases with an increase of the confining stress. Taking the time 100 s as an example, the effective diffusivities of coal GSYB with confining stresses of 4, 8, 12, 16 and 20 MPa are 1.36 104, 0.85 104, 0.48 104, 0.33 104 and 0.26 104, respectively. The increase of confining stress from 4 MPa to 20 MPa leads to a decrease of 80.9% of the diffusivity. For coal GZLH, the effective diffusivities corresponding to confining stresses of 4, 8, 12, 16 and 20 MPa are 0.63 104, 0.51 104, 0.30 104, 0.22 104 and 0.23 104, respectively. The increase of confining stress from 4 MPa to 20 MPa leads to a decrease of 63.5% of the diffusivity. 3.2.2. Effect of pore pressure The characteristic curves of gas diffusion in coal core under different pore pressure (Fig. S5 in supplementary material) shows that with an increase of the time, the desorption ratio increases sharply at the initial stage, and followed by a gentle increase. We can see that the time corresponding to the turning point when the diffusion of different coal samples tends to be stable is different. For the coal GSYB, it tends to equilibrium in a very short time (less than 200 s), while coal GZLH tends to be stable at the time of 800e1600 s. In addition, under the same pore pressure, the maximum desorption ratio of coal GSYB is greater than that of GZLH. The major reason for these phenomena is the difference between the pore structures of the two coals. For the same coal, the maximum desorption ratio increases with the pore pressure. For coal GSYB, its maximum desorption ratio corresponding to the pore pressure of 1 MPa is 0.21, while that corresponding to the pore pressure of 5 MPa is 0.42. The increase of pore pressure from 1 MPa to 5 MPa results in an increase of 100% of the maximum desorption ratio. For coal GZLH, the maximum desorption ratio relating to the pore pressure of 1 MPa is 0.14, and that relating to the pore pressure of 5 MPa is 0.31. The increase of pore pressure from 1 MPa to 5 MPa results in an increase of 121.4% of the maximum desorption ratio. The above analyses indicate that the increase of the pore pressure can significantly improve the desorption ratio of the coal. Fig. 4 shows the variation of the effective diffusivity during diffusion process under different pore pressures. Overall, with an increase of the time, the effective diffusivity reduces sharply initially and followed by a gentle decrease. In addition, the effective diffusivity increases with the pore pressure on the whole. Taking the diffusivity at 100 s as an example, for the coal GSYB, the effective diffusivities corresponding to the pore pressures of 1, 2, 3,
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Fig. 3. Effective diffusivity of fractured coal under different confining stress. (a) GSYB; (b) GZLH.
Fig. 4. Effective diffusivity of fractured coal with different pore pressures. (a) GSYB; (b) GZLH.
4 and 5 MPa are 0.53 104, 0.64 104, 1.19 104, 1.44 104 and 1.511 104, respectively. When the pore pressure increases from 1 MPa to 5 MPa, the effective diffusivity increases by 183.5%. For coal GZLH, when the pore pressures are set as 1, 2, 3, 4 and 5 MPa, the effective diffusivities at 100 s are 0.24 104, 0.56 104, 0.48 104, 0.48 104 and 1.01 104, respectively. And the increase of pore pressure from 1 MPa to 5 MPa leads to an increase of 320.8% of the effective diffusivity. 4. Discussions 4.1. Discussion on scale effect of diffusion dynamics The analyses above indicate that the gas diffusion behaviors are significantly affected by coal size, which means that the diffusion process has obvious scale effect. With an increase of the coal size, both the maximum desorption ratio and effective diffusivity decrease first and then gradually tend to be a constant. Coal diffusivity, reflecting the velocity of gas migration in coal matrix, is mainly determined by the diffusion dynamics of gas molecular and pore structure of coal. Under a constant pore pressure and temperature, the diffusivity is dominated by the coal structure itself [14]. In order to explore the essential reason for the size dependence of gas diffusion in coal, a schematic diagram has been depicted in Fig. 5. It is generally believed that coal is a complicated dual-porosity medium, which is consisted of coal
matrices and fractures, and the matrix is composed of coal skeleton and pores [29]. From Fig. 5, we can see that when the coal particle is very small (for example, less than 0.075 mm), which is only a small part of the completed coal matrix (part of REV ①). In this case, the topology of the pores in the coal particle is very simple, which corresponds to a low resistance of the gas migration in coal particle and a resultant large effective diffusivity. With an increase of coal particle size (for example, 0.075e0.12 mm), there are more pores in the coal particle, and the structure of the coal particle becomes more complex (part of REV ②). The gas migration path in the coal particle becomes longer and the resistance increases, which leads to a decrease of the effective diffusivity. When the particle size reaches the size of a complete coal matrix (complete REV ③), the pore structure of coal particles is extremely complex. From the topology of the pore structure, we can see that the complete matrix contains multistage pores, which is naturally corresponds to a high resistance of gas migration. Therefore, the effective diffusivity will be reduced to a fairly low level. With the further increase of the coal size, the gas diffusion dynamic doesn’t change any more. This is because that in this case, the coal particle is made up of several matrices and the fractures between the matrices. The topology of the pores is composed of multiple repetitive units in parallel. During the desorption, the gas migrates from the pores to the fractures, and no interactions among the gas migration in different units. Therefore, in this case the effective diffusivity is only determined by the pore structure of coal matrix. If we assume that the
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Fig. 5. Schematic diagram of the scale effect of gas diffusion in coal.
pore structure in each coal matrix is the same, then the resistance of the pore structure does not change with the increase of the coal size, thus the effective diffusivity keeps constant in this condition. The above analyses show that there exists an obvious scale effect of gas diffusion in coal, and a critical value has been found for this scale effect. When the coal particle size is smaller than this critical value, the effective diffusivity decreases gradually with the increase of coal particle size; when the coal particle size is larger than this critical value, the effective diffusivity does not change obviously. Based on the theoretical analysis above, we conclude that the critical coal size for gas diffusion corresponds to the size of the complete coal matrix. The above results imply that for the laboratory tests of gas adsorption/desorption and diffusion, only when the size of the coal particles used is larger than coal matrix size, the obtained results can more accurately reflect the gas storage and migration properties in the in-situ coal reservoir.
4.2. Discussion on influence of external conditions on diffusion dynamics In the above section, we investigated the effects of confining stress and pore pressure on gas diffusion dynamics of the fractured coal cores. The results show that both the confining stress and pore pressure have obvious influence on desorption ratio and diffusivity. The experimental results above indicate that with an increase of the confining stress, both the desorption ratio and diffusivity of the
fractured coals decrease gradually. And with an increase of the pore pressure, both the desorption ratio and diffusivity of the fractured coals rise gradually. The diffusion resistance of gas transport in coal matrix is dominated by the pore size and the mean free path of gas molecules [30]. During the CBM depletion, the pore size is controlled by the matrix deformation. And the matrix strain can generally be expressed by Eq. (3) [31].
εm ¼ aT DT þ εl
p p0 p þ pl p0 þ pl
Dse Kc
(3)
where aT is the thermal expansion coefficient, DT is the increment of the temperature, εl is the Langmuir-type volumetric strain constant, p, p0 and pl are gas pressure, initial gas pressure and Langmuir-type pressure constant, Dse is the increment of the effective stress, and Kc is the bulk modulus of coal matrix. The mean free path of gas molecules is mainly controlled by the gas pressure, temperature and the pore size through Eq. (4) [32].
KT L ¼ pffiffiffi 2pd2 p
(4)
where L is the mean free path of gas molecules, d is the collision diameter of the gas molecule, p indicates the gas pressure, K means the Boltzmann constant and T is the temperature. From Eqs. (3) and (4), we can see that the diffusion process is
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only controlled by the confining stress, when the temperature and pore pressure are set as constants. Fig. 6 (a) shows the diagram of the influence of confining stress on gas diffusion process. It is assumed that in the matrix, only pores are included, and during the diffusion process, the gas is directly released to the atmosphere through the pores. While for the fractured coal, it not only contains a large number of pores, but also contains some fractures. In this case, there are two paths for gas migration in coals. The first one is from the pores to the atmosphere directly, which is the same with the gas migration in coal matrix. And the other is the gas diffuses from the pores to the fractures, and then further migrates to the atmosphere. Compared with the gas migration in the pores, the velocity of gas migration in fracture is very high. As far as the whole diffusion process is concerned, the process of gas migration in fracture can be ignored. Therefore, the process of gas migration in fractured coal can still be viewed as the diffusion process. Compared with the gas migration in matrix, in the fractured coal, the existence of the fractures only increases the exposure area of the coal to the atmosphere. We can deduce that under the same conditions, the more fractures in coal, the more favorable for gas diffusion. The effects of confining stress on gas diffusion behavior are reflected as follows: 1) the increase of the confining stress leads to an increase of the effective stress and a decrease of the pore size, which further results in an increase of the diffusion resistance and a decrease of the effective diffusivity [33,34]; 2) with an increase of the confining stress, the effective stress imposed on the coal core increases, which leads to a decrease of the fracture aperture and
closure of some fractures, thus further results in a decrease of the effective area for the diffusion and a decrease of the diffusivity. Both the reasons above lead to a decrease of the diffusivity and desorption ratio with the increase of confining stress imposed on the fractured coal core. From Eqs. (3) and (4) we can see that when the temperature and confining stress keep constant, the diffusion is only affected by the pore pressure. And the equations show that both the pore size and mean free path of gas molecules change with the variation of the pore pressure. In the following section, we will discuss how the pore size and mean free path of gas molecules change with the pore pressure, and how they affect the diffusivity of fractured coal. Fig. 6 (b) depicts the diagram of influence of pore pressure on gas diffusion in fractured coal. The influences of pore pressure on gas diffusion dynamics are reflected as follows: 1) the increase of the pore pressure leads to a decrease of the effective stress and an increase of the pore size, which further results in a decrease of the diffusion resistance and an increase of the effective diffusivity; 2) the decrease of the effective stress imposed on the coal core can also lead to an increase of the fracture aperture, thus further results in an increase of the effective area for the diffusion and a resultant increase of the diffusivity. Both the reasons above lead to an increase of the diffusivity and desorption ratio with the increase of pore pressure in the fractured coal core. In addition, from Eq. (4), we can see that the mean free path of gas molecules decreases with an increase of the pore pressure. For a certain pore size in coal matrix, the dominant diffusion resistance will transit from gas molecules colliding with pore walls to intermolecular collisions,
Fig. 6. Diagram of influence of confining stress and pore pressure on gas diffusion in fractured coal.
T. Liu et al. / Energy 195 (2020) 117005
9
meaning that the diffusion mode will transit from Knudsen diffusion to Fick diffusion [30] (l < 0.1 dp, Fick diffusion; 0.1 dp < l < 10 dp, Transition diffusion; l > 10 dp, Knudsen diffusion, where dp is the pore diameter). Accordingly, the diffusivity manifests an increasing trend with the increasing pore pressure.
Acknowledgement
5. Conclusions
Appendix A. Supplementary data
Aiming at the problem that the gas diffusion dynamics in in-situ coal seam is not clear, we systematically investigated the scale effect of the gas diffusion in granular coal and attempted to clarify the gas diffusion behavior in in-situ coal seam with fractured coals under constraint condition. The research results are expected to advance the understanding of gas diffusion behavior in in-situ coal seam. The major conclusions obtained are as follows.
Supplementary data to this article can be found online at https://doi.org/10.1016/j.energy.2020.117005.
(1) There exists an obvious scale effect for gas diffusion in coal, and a critical value has been found for the scale effect. When the coal particle size is smaller than the critical value, the effective diffusivity decreases gradually with the increase of particle size; and when the particle size is larger than the critical value, no obvious change can be found in the effective diffusivity. It is concluded that the critical value for gas diffusion corresponds to the size of the coal matrix. This means that only when the coal particle is larger than the complete coal matrix, the research results can reflect the gas diffusion in coal more accurately. (2) The essential reason for the existence of the scale effect is the differences among the pore structures of coals with various sizes. Small coal particle corresponds to a simple pore topology and low diffusion resistance, and a larger coal particle relates to a complex pore topology and high diffusion resistance. When the coal particle is larger than a complete coal matrix, the pore topology will not become more complex, this is the reason for the existence of the critical value for gas diffusion. (3) The confining stress and pore pressure have significant impact on gas diffusion in fractured coal. With an increase of the confining stress and a decrease of the pore pressure, the effective diffusivity reduces gradually. This is because that the increase of the confining stress and decrease of the pore pressure lead to an increase of the effective stress imposed on the coal core, which reduces pore size and the effective diffusion area of the coal. Moreover, the increase of the pore pressure can also reduce the mean free path of gas molecules, which contributes to the increase of the effective diffusivity as well. (4) In-situ coal seam is generally under constraint condition with complex internal structures. In order to get an accurate understanding of the gas diffusion behaviors in in-situ coal seam during CBM depletion, CO2-ECBM and geological sequestration of CO2, a representative elementary volume including complete internal structure of coal should be determined, and the confining stress should be considered during the test in the laboratory. Therefore, in the future research, lump coal with complete internal structure under constraint condition is suggested to study gas diffusion behavior in in-situ coal seam.
Declaration of competing interest On behalf of all authors, the corresponding author states that there is no conflict of interest.
This work was supported by National Postdoctoral Program for Innovative Talents (BX20190369), China Postdoctoral Science Foundation (2019M661996) and National Natural Science Foundation of China (51804212).
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Experimental study on gas diffusion dynamics in fractured coal: A better understanding of gas migration in in-situ coal seam Ting Liu a, b, *, Baiquan Lin a, Xuehai Fu b, Yabin Gao c, **, Jia Kong a, Yang Zhao a, Haoran Song a a
School of Safety Engineering, China University of Mining and Technology, Xuzhou, 221116, China Key Laboratory of CBM Resources and Dynamic Accumulation Process, China University of Mining and Technology, Ministry of Education, Xuzhou, Jiangsu province, 221008, China c College of Safety and Emergency Management Engineering, Taiyuan University of Technology, Taiyuan, Shanxi, 030024, China b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 27 September 2019 Received in revised form 15 January 2020 Accepted 18 January 2020 Available online 20 January 2020
In-situ coal seam is generally under the stress constraint condition. However, the powder coal is often adopted to study gas diffusion dynamics in the laboratory, in this case, the stress cannot be imposed on the coal sample. So the question is, can the laboratory test results with the powder coal reflect the gas diffusion behaviors in the in-situ coal seam? Does the confining stress affect the gas diffusion behaviors in fractured coal? To address these questions, in this work, we first investigated the effect of coal size on gas diffusion dynamics with powder coal and lump coal under unconstrained conditions. The results show that there exists an obvious scale effect for gas diffusion in coal, and a critical value of coal size has been found for the scale effect. When the coal particle size is smaller than the critical value, the effective diffusivity decreases with an increase of the particle size; and when the particle size is larger than the critical value, no obvious change can be found in the effective diffusivity. The critical value for gas diffusion corresponds to the size of the coal matrix. The essential reason for the existence of the scale effect is the differences among the pore structures of coals with various sizes. Based on the research results under the unconstrained conditions, a coal core was selected to study the effect of confining stress and pore pressure on gas diffusion under constraint condition. The results indicated that the confining stress and pore pressure have significant impact on gas diffusion in fractured coal. With an increase of the confining stress and a decrease of the pore pressure, the effective diffusivity reduces gradually. Therefore, to get an accurate understanding of the gas diffusion behavior in in-situ coal seam, during the test in the lab, both the scale effect and confining stress should be considered. The research results obtained in this work have important guiding significance to reveal gas migration in in-situ coal seams during CBM depletion, CO2-ECBM and geological sequestration of CO2. © 2020 Elsevier Ltd. All rights reserved.
Keywords: Gas diffusion Scale effect Granular coal Fractured coal core In-situ coal seam
1. Introduction During coalbed methane (CBM) depletion, the gas migration in coal seam generally can be divided into three steps, namely desorption, diffusion and seepage [1,2]. At the initial stage, the gas is mainly from the fractures, and the process is dominated by the seepage. But as the gas pressure in the coal seam becomes depleted, the gas mainly comes from the matrix later, and the diffusion plays
* Corresponding author. ** Corresponding author. E-mail addresses: [email protected], [email protected] (T. Liu). https://doi.org/10.1016/j.energy.2020.117005 0360-5442/© 2020 Elsevier Ltd. All rights reserved.
an increasingly important role in this stage [3]. In addition, the CO2 enhanced coalbed methane (CO2-ECBM) recovery and geological sequestration of CO2 also involve the diffusion of CH4 and CO2 in the coals seams. In these processes, the diffusion plays as a bridge connecting the desorption and seepage, and affects the CBM production and CO2 injection [4,5]. Therefore, a comprehensive understanding of the diffusion process in the in-situ coal seam contributes to the questions [3]: At what pressure should the CBM well be abandoned? When does the restimulation measure need to be taken? How long should the CO2 injection last? For the great importance of the diffusion process, a series of research, including modelling and laboratory test, was conducted to explore the gas diffusion behaviors in the coal [6e10]. Zhao et al.
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(2019) [11] presented a comprehensive review on the mathematical models for gas diffusion in coal particles and the applications in environment, energy and mining safety areas. To avoid the duplication of review effort, the mathematical models for gas diffusion in coal particles will not be included here. Because the main method used in our study is the laboratory test, here we put our emphasis on the review of the diffusion study by lab test. Keshavarz et al. (2017) [12] studied the effects of maceral composition and coal rank on gas diffusion in Australian coals. In their study, 18 bituminous and sub-bituminous coal samples were ground into coal particle with size of 0.5e1.0 mm. Then both CO2 and CH4 kinetic sorption tests were performed to calculate the diffusion rate. Du et al. (2018) [13] conducted experiments on gas diffusion under negative pressure environments. Coal samples from Duanshi Coal Mine in the Qinshui Basin were collected and ground into particles with size of 1e3 mm. Then diffusion tests with the initial pore pressure of 0.5 MPa, 1.5 MPa and 2.5 MPa were performed under various negative pressures. In order to reveal the effect of pore structure on gas diffusion in coal, Yang and Liu (2019) [14] performed a series of gas desorption and pore size distribution tests. In the study, coal particles with size of 0.177e0.250 mm was adopted to conducted the desorption test, and they believed that pulverization of the coal samples wouldn’t affect the accuracy of diffusion measurements. In addition, other researchers also conducted a series of studies to investigate the gas diffusion in coal particles under different conditions. In their studies, coal particles with sizes of 0.149e0.425 mm [9], 0e3.2 mm [7], 1e3 mm [15], 0.2e3 mm [16], 0.18e0.25 mm [17], were adopted. Up to date, the granular coal is often adopted to investigate the gas diffusion in coal, and in different studies, the size of the particles used varies greatly. Although obvious differences exist, the particle size used in previous research is generally less than 5 mm, and in most cases, it is less than 1 mm. However, as we know, the in-situ coal seams contain complex pore-fracture structures. The crushing process during coal particle preparation may damage the pore structure of the coal [18e20]. Unlike the granular coal adopted in the lab, in-situ coal seam generally contains a lot of fractures and is confined by crustal stress. However, the effects of fracture and confining stress on gas diffusion behaviors in coal have rarely been reported so far. Xu et al. (2015) [23] investigated the effects of gas pressure, coal rank and moisture content on gas diffusion in coal matrix. In their research, instead of the coal particles, a coal matrix flake (20 mm 15 mm 3 mm) was adopted. With this method, the damage of the pore structure can be avoided, but a confining stress cannot be imposed on this sample. In addition, a series of lab test results indicated that the adsorption equilibrium pressure had great impact on gas diffusion. Xu et al. (2015) [23] demonstrated that with an increase of the pore pressure, the diffusivity decreased gradually. The test result of Wang and Liu (2016) [3] indicated that with an increase of the pore pressure, the diffusivity increased first and followed by a reduction. While Pillalamarry et al. (2011) [9] concluded that the diffusivity of coal decreased with an increase of the pore pressure. By now, there is no consistent understanding on the effect of pore pressure on gas diffusion. Therefore, more lab tests should be conducted on this issue. For a porous medium, when the scale is very small, its attributes fluctuate randomly in space, which is related to the heterogeneity of pore structure in porous media. When the medium scale reaches a critical value, with a further increase of the scale, no obvious change on its attributes can be found. The element corresponding to the critical scale is called representative element volume (REV). For the heterogeneous medium, because of the existence of the fractures, the attributes on macroscale show great uncertainty in
space [21,22]. The in-situ coal seam is generally viewed as a dual porosity medium, which contains a complex pore-fracture structure, and its scale is far greater than that of the samples adopted in the lab. Therefore, to reveal the in-situ gas diffusion behavior in the laboratory, a REV, which can reflect the internal structure of the coal, must be determined first. And the external condition, such as confining stress and pore pressure, should be considered as well. Aiming at the research gaps, in this work, we first investigated the scale effect of gas diffusion in coal particles. Based on the results, the critical size of the REV was determined. Then, based on the critical size of the coal, a coal core was adopted to study the effects of confining stress and pore pressure on gas diffusion behaviors. Finally, the mechanisms of scale effect and the influence of confining stress and pore pressure on diffusion were discussed. 2. Experimental samples and apparatus 2.1. Coal samples In this work, two types of coal with different metamorphic degrees were selected to study the gas diffusion dynamics. These coals are from Gansu Yanbei (GSYB) and Guizhou Linhua (GZLH). Table 1 shows the results of proximate analysis and vitrinite reflectance. The Volatile Matter of coal GSYB is significantly higher than that of coal GZLH, while its Fixed Carbon is greatly lower than that of coal GZLH. The average maximum vitrinite reflectance of coals GSYB and GZLH are 0.58% and 2.86%, meaning that they are a bituminous coal with low metamorphic degree and an anthracite (according the Standards for Coal Industry in China, MT/T11582011). The T2 spectrum (by Nuclear Magnetic Resonance) and pore image (by Ar ion polishing-assisted SEM) (See Fig. S1 in supplementary material) of the coal samples show that for coal GSYB, the pore size distributes in a triple peak pattern. The distribution of pores with different size is relatively uniform in this coal. The results of Ar ion polishing-assisted SEM shows that the coal GSYB contains a lot of micron-scale pores and some nano-scale pores. The pore size curve of coal GZLH presents a bimodal distribution, although the second peak is not obvious. It can be deduced that the micropores dominate in coal GZLH, and this can be verified by the imaging results by Ar ion polishing-assisted SEM that limited pores can be found with a resolution of 20 mm, but a large number of nanopores can be detected with a resolution of 300 nm. To investigate the scale effect of gas diffusion in coal, powder coals were produced with the size of less than 0.075 mm, 0.075e0.12 mm, 0.12e0.18 mm, 0.18e0.25 mm, 0.25e0.38 mm, 0.38e0.83 mm, 0.83e1.70 mm, 10e15 mm, 15e30 mm. Moreover, cylindrical coal samples with a size of F 50 100 mm were adopted to study the effects of confining stress and pore pressure on gas diffusion behaviors (See Fig. S2 in supplementary material). 2.2. Experimental apparatus and method The experimental system used in this work is depicted in Fig. 1. The system in Fig. 1(a) is used for investigating the gas diffusion in coal without stress constraint, and it includes the degassing module, adsorption/desorption module, control module and data acquisition module. After the tests of gas diffusion in powder coal are completed, the adsorption cell in Fig. 1(a) is replaced by the cell in Fig. 1(b). With this cell, the samples can be stressed in both axial and radial directions. Integrating the cell in Fig. 1(b) with the system in Fig. 1 (a), the effect of external stress on gas diffusion behaviors can be investigated. The main procedures for the test of gas diffusion in coal are as follows:
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Table 1 Results of proximate analysis and vitrinite reflectance. Code
Moisture/Mad
Ash/Ad
Volatile Matter/Vdaf
Fixed Carbon/FCd
Average maximum vitrinite reflectance/Romax%
GSYB GZLH
2.51 2.41
9.70 11.04
38.54 5.81
55.49 83.79
0.58 2.86
Fig. 1. Experimental system for investigating gas diffusion in coal. (a) System for investing gas diffusion in powder coal under unconstraint condition; (b) Cell for investigating gas diffusion in cylindrical coal core under constraint condition.
(1) Procedures for the test of gas diffusion in granular coal ① Put coal particle with a given size in drying oven with a constant temperature of 60 C for 24 h. ② The dried sample with a weight of mc is put into the adsorption cell placed in the water bath with a constant temperature of 30 C. ③ Run the vacuum pump to degas the system for 12 h. ④ Inject He into the reference cell with a given pressure of pHe, then open the valve between the adsorption and reference cells to inject the He into adsorption cell, after equilibrium is achieved, record the gas pressure as p’He. ⑤ Degas the system, and inject CH4 into the system just as the procedure of He injection, record the gas pressure as pCH4 and p’CH4. ⑥ During desorption, the gas volume is continuously recorded. Due to the high gas desorption amount, the initial interval is set as 5 s, and it is expanded properly with the decay of the gas volume. The desorption time lasts for 120 min according to the standard of GBT 23250e2009 (direct method to measure gas content in coal mines) [25]. ⑦ Repeat the above steps for another sample until all the samples are tested. (2) Procedures for the test of gas diffusion in fractured coal In this part, gas diffusion in a cylindrical fractured coal with size of F50 100 mm under constraint condition is tested. The procedure is the same with that of powder coal, and the scheme is as follows: Case 1: The adsorption equilibrium pressure is set as 2 MPa, then the gas diffusion is tested with the confining stress (axial stress is equal to radial stress) of 4 MPa, 8 MPa, 12 MPa, 16 MPa, 20 MPa. Case 2: Both the confining stress and axial stress are set as 8 MPa, then the gas diffusion is tested with the pore pressure of 1 MPa, 2 MPa, 3 MPa, 4 MPa, 5 MPa. Notice that due to the possible existence of fractures in the coal
cores, it should be ensured that before the start of the diffusion, no free gas exists in the fractures, and this can be achieved by opening the exhaust valve until the gas pressure in the holder indicates zero. In addition, gas migration velocity in fracture is much higher than that in matrix pore, therefore, during diffusion, the process of gas migration in fracture can be ignored. (3) Procedures for data processing ① First the gas adsorption amount in equilibrium is calculated as Q∞ with the pressure monitored; ② The ratio of gas desorption amount Qt at time t to Q∞ is called desorption ratio, and the curve Qt =Q∞ t is the characteristic curve of gas desorption; ③ Further, we can get the curve lnð1 Qt =Q∞ Þ t. ④ Eq. (1) shows the unipore diffusion mode for describing gas diffusion porous media. By giving 1 to n, Eq. (1) can be simplified as Eq. (2) [35,36].
∞ Qt 6 X 1 ¼1 2 exp Q∞ p n¼1 n2
n2 p2 D t r 20
! (1)
where, Qt is the total amount of gas diffused at time t, mL/g, Q∞ is the total amount of gas adsorbed on coal at equilibrium pressure, mL/g, D is the diffusivity, m2/s, r0 is the radius of coal particles, m, and n means the nth level of the series.
Qt p2 D p2 ln 1 ¼ 2 t þ ln Q∞ 6 r0
(2)
⑤ From Eq. (2), we can see that the tangent slope at any point of the curve lnð1 Qt =Q∞ Þ t is D=r 20 ,p2 . In this work, the expression D=r 20 is defined as the effective diffusivity De, further we can get the curve De ~ t.
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3. Results and analyses 3.1. Results and analyses of gas diffusion in coal with various sizes The characteristic curves of gas diffusion in coal with various sizes (Fig. S3 in supplementary material) shows that with an increase of the time, the desorption ratio increases rapidly first and then tends to equilibrium gradually. In addition, with an increase of the coal size, the maximum desorption ratio in 2 h reduces rapidly at the initial stage, and later, it gradually stabilizes to a fixed value. For example, for the coal GSYB, the maximum desorption ratio in 2 h is 0.760 when the particle size is less than 0.075 mm, and the desorption ratio decreases to 0.250 for coal with size of 0.25e0.38 mm. With a further increase of the coal size, no obvious change can be found on the maximum desorption ratio, and it finally stabilizes around 0.20. For coal GZLH, the maximum desorption ratio corresponding to coal particle less than 0.075 mm is 0.880, and it decreases to 0.409 with the coal size increases to 0.83e1.70 mm. With a further increase of the coal size, the maximum desorption ratio fluctuates around 0.40. The decrease of the maximum desorption ratio with the particle size is mainly because that with an increase of the particle size, the pore structure in the particles becomes more complex, therefore, the resistance for gas diffusion in big coal particle is greater than that of the small particles. With the characteristic curves, we can further calculate the effective diffusivity of the coal samples. In Fig. 2 (a) and (b), for coal
samples with different sizes, the effective diffusivity decreases with the time on the whole, although a slight fluctuation exists. For example, the initial effective diffusivity of coal GSYB with a size less than 0.075 mm is 0.0146, and after 7200 s, it decays to 1.81 106. In our previous study, we developed a time-dependent model to describe the phenomenon that the effective diffusivity decreases with the time [26]. Reasons for the time-dependence of diffusivity includes three parts: 1) during the diffusion, the decrease of the pore pressure leads to a shrinkage of the matrix, which results in a decrease of the diffusivity [24]; 2) at the initial stage, the desorbed gas mainly comes from pores with large diffusivity, later it is dominantly from pores with small diffusivity; 3) in a given pore, there exists multiple diffusion modes, including molecular diffusion, transition diffusion and Knudesen diffusion, and the apparent diffusivity of coal particles can be obtained by adding up the diffusivities of the three diffusion modes proportionally [27]. The high pore pressure at the initial stage determines the small mean free path of gas molecules, thus in this stage, the molecular diffusion dominates the diffusion process, and the diffusivity is relatively large; with a decrease of the pore pressure, the mean free path of gas molecules increases gradually, and the diffusion mode gradually transits to the transition diffusion and Knudesen diffusion, therefore, the diffusivity decreases gradually [28]. Under the same external conditions, the diffusion behaviors of coal are mainly determined by the pore structures. The characteristic curves show that there exists limit scales for different coals, and the diffusion dynamics of coal beyond this scale is independent
Fig. 2. Change of effective diffusivity with time and coal size. (a) and (b) show the relation between effective diffusivity and time of GSYB and GZLH, respectively; (c) and (d) show the relation between effective diffusivity and coal size of GSYB and GZLH, respectively.
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of coal sample size. Therefore, it is reasonable to presume that a scale effect also exists on coal diffusivity. Fig. 2 (c) and (d) presents the effect of coal size on the diffusivity. Overall, the diffusivity decreases with an increase of the coal size. But we also find a critical value, if the coal size is greater than the critical value, the diffusivity is independent of the coal size. Based on the critical size, the effect of coal size on diffusivity in Fig. 2 (c) and (d) can be divided into significant influence zone and insignificant influence zone. For coal GSYB, when the coal size is smaller than 0.25e0.38 mm, the diffusivity decreases with an increase of the particle size, and when the coal size is greater than 0.25e0.38 mm, no obvious reduction can be found. Taking the desorption time of 300 s as an example, when the increase of coal size from less than 0.075 mm to 0.25e0.38 mm, the effective diffusivity reduces from 4.74 105 to 4.19 106 with a decrease of 91.2%. While from 0.25 to 0.38 mm to f50 100 mm (cylindrical coal core), the diffusivity fluctuates slightly, and no obvious reduction can be found. The analysis indicates that the critical value of coal GSYB is 0.25e0.38 mm. With the same method, the critical value of coal GZLH can be determined as 0.45e2 mm. In addition, from Fig. 2 (c) and (d), we can also find that at the initial stage, the scale effect is not obvious, but with the increase of time, the influence of coal size on the effective diffusivity becomes more significant. The variation of the effective diffusivity of coal particles with the size can be attributed to the change of the pore structures. The detailed mechanism will be discussed in section 4.1. 3.2. Effect of external conditions on gas diffusion in fractured coal The above analyses indicate that only when the coal size is larger than the critical value, the lab test results can reflect the gas diffusion in situ coal seam more accurately. In addition, for the insitu coal seam, it is generally under the constraint condition, and investigating the effects of confining stress and pore pressure is of great importance to the better understanding of gas diffusion dynamics in in-situ coal seam. To the best of our knowledge, this issue has rarely been experimentally investigated before, therefore, in this section, the effects of confining stress and pore pressure on gas diffusion in lump coals are systematically discussed. 3.2.1. Effect of confining stress The characteristic curves of gas diffusion in coal core under different confining stress (Fig. S4 in supplementary material) shows that the desorption ratio increases sharply at the initial stage, but later it tends to increase gently. Although the overall variation trends of the characteristic curves for different coal are similar, difference still can be found. For example, under the same confining stress, the desorption ratio of coal GSYB at the equilibrium is obviously higher than that of coal GZLH. This phenomenon is mainly determined by the difference between pore structures of the coal cores. From Fig. S1, we can see that there exists a fairly high proportion of meso- and macro-pores in coal GSYB, therefore, the gas migration in coal GSYB is relatively easy. While for coal GZLH, it is dominated by the micro-pores, the migration resistance of gas in this coal is relatively high, therefore, the gas diffusion is more difficult in this case. For a given coal core, its desorption ratio decreases with an increase of the confining stress. For the coal GSYB, its desorption ratio corresponding to the confining stress of 4 MPa is 0.35, while when the confining stress increases to 20 MPa, the desorption ratio decreases to 0.08, with a decrease of 77.1%. For the coal GZLH, the desorption ratio corresponding to the confining stress of 4 MPa is 0.17, and when the confining stress increases to 20 MPa, it decreases to 0.07, with a decrease of 58.8%. This experimental phenomenon implies that the external confining stress can significantly reduce
5
the gas desorption ratio of the fractured coal. The main reason may be that the existence of the confining stress changes the pore structure of the fractured coal, which further influences the gas diffusion process in coal. Fig. 3 shows the variation of effective diffusivity of fractured coals under different confining stress with the time. During the diffusion process, the diffusivity decreases sharply at the initial stage and later gradually tends to be stable. This indicates that for the fractured coal, the diffusion process is also time dependent, which is consistent with that of the granular coal. And the reasons for the time dependence of the diffusion in fractured coal are the same with those in the granular coal. There exists obvious difference between the diffusivities of coals GSYB and GZLH. Taking the confining stress of 4 MPa as an example, the effective diffusivities at the initial time are 7.54 104 and 3.05 104 for coals GSYB and GZLH, respectively. In addition, at the initial stage, the decay of the diffusivity of coal GZLH is sharper than that of GSYB. The reason is that for the coal GZLH, the proportion of meso- and macro-pores is lower than that of GSYB. Besides, the poor pore connectivity of GZLH also contributes to the fast decay of its diffusivity. For the same coal, the diffusivity decreases with an increase of the confining stress. Taking the time 100 s as an example, the effective diffusivities of coal GSYB with confining stresses of 4, 8, 12, 16 and 20 MPa are 1.36 104, 0.85 104, 0.48 104, 0.33 104 and 0.26 104, respectively. The increase of confining stress from 4 MPa to 20 MPa leads to a decrease of 80.9% of the diffusivity. For coal GZLH, the effective diffusivities corresponding to confining stresses of 4, 8, 12, 16 and 20 MPa are 0.63 104, 0.51 104, 0.30 104, 0.22 104 and 0.23 104, respectively. The increase of confining stress from 4 MPa to 20 MPa leads to a decrease of 63.5% of the diffusivity. 3.2.2. Effect of pore pressure The characteristic curves of gas diffusion in coal core under different pore pressure (Fig. S5 in supplementary material) shows that with an increase of the time, the desorption ratio increases sharply at the initial stage, and followed by a gentle increase. We can see that the time corresponding to the turning point when the diffusion of different coal samples tends to be stable is different. For the coal GSYB, it tends to equilibrium in a very short time (less than 200 s), while coal GZLH tends to be stable at the time of 800e1600 s. In addition, under the same pore pressure, the maximum desorption ratio of coal GSYB is greater than that of GZLH. The major reason for these phenomena is the difference between the pore structures of the two coals. For the same coal, the maximum desorption ratio increases with the pore pressure. For coal GSYB, its maximum desorption ratio corresponding to the pore pressure of 1 MPa is 0.21, while that corresponding to the pore pressure of 5 MPa is 0.42. The increase of pore pressure from 1 MPa to 5 MPa results in an increase of 100% of the maximum desorption ratio. For coal GZLH, the maximum desorption ratio relating to the pore pressure of 1 MPa is 0.14, and that relating to the pore pressure of 5 MPa is 0.31. The increase of pore pressure from 1 MPa to 5 MPa results in an increase of 121.4% of the maximum desorption ratio. The above analyses indicate that the increase of the pore pressure can significantly improve the desorption ratio of the coal. Fig. 4 shows the variation of the effective diffusivity during diffusion process under different pore pressures. Overall, with an increase of the time, the effective diffusivity reduces sharply initially and followed by a gentle decrease. In addition, the effective diffusivity increases with the pore pressure on the whole. Taking the diffusivity at 100 s as an example, for the coal GSYB, the effective diffusivities corresponding to the pore pressures of 1, 2, 3,
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Fig. 3. Effective diffusivity of fractured coal under different confining stress. (a) GSYB; (b) GZLH.
Fig. 4. Effective diffusivity of fractured coal with different pore pressures. (a) GSYB; (b) GZLH.
4 and 5 MPa are 0.53 104, 0.64 104, 1.19 104, 1.44 104 and 1.511 104, respectively. When the pore pressure increases from 1 MPa to 5 MPa, the effective diffusivity increases by 183.5%. For coal GZLH, when the pore pressures are set as 1, 2, 3, 4 and 5 MPa, the effective diffusivities at 100 s are 0.24 104, 0.56 104, 0.48 104, 0.48 104 and 1.01 104, respectively. And the increase of pore pressure from 1 MPa to 5 MPa leads to an increase of 320.8% of the effective diffusivity. 4. Discussions 4.1. Discussion on scale effect of diffusion dynamics The analyses above indicate that the gas diffusion behaviors are significantly affected by coal size, which means that the diffusion process has obvious scale effect. With an increase of the coal size, both the maximum desorption ratio and effective diffusivity decrease first and then gradually tend to be a constant. Coal diffusivity, reflecting the velocity of gas migration in coal matrix, is mainly determined by the diffusion dynamics of gas molecular and pore structure of coal. Under a constant pore pressure and temperature, the diffusivity is dominated by the coal structure itself [14]. In order to explore the essential reason for the size dependence of gas diffusion in coal, a schematic diagram has been depicted in Fig. 5. It is generally believed that coal is a complicated dual-porosity medium, which is consisted of coal
matrices and fractures, and the matrix is composed of coal skeleton and pores [29]. From Fig. 5, we can see that when the coal particle is very small (for example, less than 0.075 mm), which is only a small part of the completed coal matrix (part of REV ①). In this case, the topology of the pores in the coal particle is very simple, which corresponds to a low resistance of the gas migration in coal particle and a resultant large effective diffusivity. With an increase of coal particle size (for example, 0.075e0.12 mm), there are more pores in the coal particle, and the structure of the coal particle becomes more complex (part of REV ②). The gas migration path in the coal particle becomes longer and the resistance increases, which leads to a decrease of the effective diffusivity. When the particle size reaches the size of a complete coal matrix (complete REV ③), the pore structure of coal particles is extremely complex. From the topology of the pore structure, we can see that the complete matrix contains multistage pores, which is naturally corresponds to a high resistance of gas migration. Therefore, the effective diffusivity will be reduced to a fairly low level. With the further increase of the coal size, the gas diffusion dynamic doesn’t change any more. This is because that in this case, the coal particle is made up of several matrices and the fractures between the matrices. The topology of the pores is composed of multiple repetitive units in parallel. During the desorption, the gas migrates from the pores to the fractures, and no interactions among the gas migration in different units. Therefore, in this case the effective diffusivity is only determined by the pore structure of coal matrix. If we assume that the
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Fig. 5. Schematic diagram of the scale effect of gas diffusion in coal.
pore structure in each coal matrix is the same, then the resistance of the pore structure does not change with the increase of the coal size, thus the effective diffusivity keeps constant in this condition. The above analyses show that there exists an obvious scale effect of gas diffusion in coal, and a critical value has been found for this scale effect. When the coal particle size is smaller than this critical value, the effective diffusivity decreases gradually with the increase of coal particle size; when the coal particle size is larger than this critical value, the effective diffusivity does not change obviously. Based on the theoretical analysis above, we conclude that the critical coal size for gas diffusion corresponds to the size of the complete coal matrix. The above results imply that for the laboratory tests of gas adsorption/desorption and diffusion, only when the size of the coal particles used is larger than coal matrix size, the obtained results can more accurately reflect the gas storage and migration properties in the in-situ coal reservoir.
4.2. Discussion on influence of external conditions on diffusion dynamics In the above section, we investigated the effects of confining stress and pore pressure on gas diffusion dynamics of the fractured coal cores. The results show that both the confining stress and pore pressure have obvious influence on desorption ratio and diffusivity. The experimental results above indicate that with an increase of the confining stress, both the desorption ratio and diffusivity of the
fractured coals decrease gradually. And with an increase of the pore pressure, both the desorption ratio and diffusivity of the fractured coals rise gradually. The diffusion resistance of gas transport in coal matrix is dominated by the pore size and the mean free path of gas molecules [30]. During the CBM depletion, the pore size is controlled by the matrix deformation. And the matrix strain can generally be expressed by Eq. (3) [31].
εm ¼ aT DT þ εl
p p0 p þ pl p0 þ pl
Dse Kc
(3)
where aT is the thermal expansion coefficient, DT is the increment of the temperature, εl is the Langmuir-type volumetric strain constant, p, p0 and pl are gas pressure, initial gas pressure and Langmuir-type pressure constant, Dse is the increment of the effective stress, and Kc is the bulk modulus of coal matrix. The mean free path of gas molecules is mainly controlled by the gas pressure, temperature and the pore size through Eq. (4) [32].
KT L ¼ pffiffiffi 2pd2 p
(4)
where L is the mean free path of gas molecules, d is the collision diameter of the gas molecule, p indicates the gas pressure, K means the Boltzmann constant and T is the temperature. From Eqs. (3) and (4), we can see that the diffusion process is
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only controlled by the confining stress, when the temperature and pore pressure are set as constants. Fig. 6 (a) shows the diagram of the influence of confining stress on gas diffusion process. It is assumed that in the matrix, only pores are included, and during the diffusion process, the gas is directly released to the atmosphere through the pores. While for the fractured coal, it not only contains a large number of pores, but also contains some fractures. In this case, there are two paths for gas migration in coals. The first one is from the pores to the atmosphere directly, which is the same with the gas migration in coal matrix. And the other is the gas diffuses from the pores to the fractures, and then further migrates to the atmosphere. Compared with the gas migration in the pores, the velocity of gas migration in fracture is very high. As far as the whole diffusion process is concerned, the process of gas migration in fracture can be ignored. Therefore, the process of gas migration in fractured coal can still be viewed as the diffusion process. Compared with the gas migration in matrix, in the fractured coal, the existence of the fractures only increases the exposure area of the coal to the atmosphere. We can deduce that under the same conditions, the more fractures in coal, the more favorable for gas diffusion. The effects of confining stress on gas diffusion behavior are reflected as follows: 1) the increase of the confining stress leads to an increase of the effective stress and a decrease of the pore size, which further results in an increase of the diffusion resistance and a decrease of the effective diffusivity [33,34]; 2) with an increase of the confining stress, the effective stress imposed on the coal core increases, which leads to a decrease of the fracture aperture and
closure of some fractures, thus further results in a decrease of the effective area for the diffusion and a decrease of the diffusivity. Both the reasons above lead to a decrease of the diffusivity and desorption ratio with the increase of confining stress imposed on the fractured coal core. From Eqs. (3) and (4) we can see that when the temperature and confining stress keep constant, the diffusion is only affected by the pore pressure. And the equations show that both the pore size and mean free path of gas molecules change with the variation of the pore pressure. In the following section, we will discuss how the pore size and mean free path of gas molecules change with the pore pressure, and how they affect the diffusivity of fractured coal. Fig. 6 (b) depicts the diagram of influence of pore pressure on gas diffusion in fractured coal. The influences of pore pressure on gas diffusion dynamics are reflected as follows: 1) the increase of the pore pressure leads to a decrease of the effective stress and an increase of the pore size, which further results in a decrease of the diffusion resistance and an increase of the effective diffusivity; 2) the decrease of the effective stress imposed on the coal core can also lead to an increase of the fracture aperture, thus further results in an increase of the effective area for the diffusion and a resultant increase of the diffusivity. Both the reasons above lead to an increase of the diffusivity and desorption ratio with the increase of pore pressure in the fractured coal core. In addition, from Eq. (4), we can see that the mean free path of gas molecules decreases with an increase of the pore pressure. For a certain pore size in coal matrix, the dominant diffusion resistance will transit from gas molecules colliding with pore walls to intermolecular collisions,
Fig. 6. Diagram of influence of confining stress and pore pressure on gas diffusion in fractured coal.
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meaning that the diffusion mode will transit from Knudsen diffusion to Fick diffusion [30] (l < 0.1 dp, Fick diffusion; 0.1 dp < l < 10 dp, Transition diffusion; l > 10 dp, Knudsen diffusion, where dp is the pore diameter). Accordingly, the diffusivity manifests an increasing trend with the increasing pore pressure.
Acknowledgement
5. Conclusions
Appendix A. Supplementary data
Aiming at the problem that the gas diffusion dynamics in in-situ coal seam is not clear, we systematically investigated the scale effect of the gas diffusion in granular coal and attempted to clarify the gas diffusion behavior in in-situ coal seam with fractured coals under constraint condition. The research results are expected to advance the understanding of gas diffusion behavior in in-situ coal seam. The major conclusions obtained are as follows.
Supplementary data to this article can be found online at https://doi.org/10.1016/j.energy.2020.117005.
(1) There exists an obvious scale effect for gas diffusion in coal, and a critical value has been found for the scale effect. When the coal particle size is smaller than the critical value, the effective diffusivity decreases gradually with the increase of particle size; and when the particle size is larger than the critical value, no obvious change can be found in the effective diffusivity. It is concluded that the critical value for gas diffusion corresponds to the size of the coal matrix. This means that only when the coal particle is larger than the complete coal matrix, the research results can reflect the gas diffusion in coal more accurately. (2) The essential reason for the existence of the scale effect is the differences among the pore structures of coals with various sizes. Small coal particle corresponds to a simple pore topology and low diffusion resistance, and a larger coal particle relates to a complex pore topology and high diffusion resistance. When the coal particle is larger than a complete coal matrix, the pore topology will not become more complex, this is the reason for the existence of the critical value for gas diffusion. (3) The confining stress and pore pressure have significant impact on gas diffusion in fractured coal. With an increase of the confining stress and a decrease of the pore pressure, the effective diffusivity reduces gradually. This is because that the increase of the confining stress and decrease of the pore pressure lead to an increase of the effective stress imposed on the coal core, which reduces pore size and the effective diffusion area of the coal. Moreover, the increase of the pore pressure can also reduce the mean free path of gas molecules, which contributes to the increase of the effective diffusivity as well. (4) In-situ coal seam is generally under constraint condition with complex internal structures. In order to get an accurate understanding of the gas diffusion behaviors in in-situ coal seam during CBM depletion, CO2-ECBM and geological sequestration of CO2, a representative elementary volume including complete internal structure of coal should be determined, and the confining stress should be considered during the test in the laboratory. Therefore, in the future research, lump coal with complete internal structure under constraint condition is suggested to study gas diffusion behavior in in-situ coal seam.
Declaration of competing interest On behalf of all authors, the corresponding author states that there is no conflict of interest.
This work was supported by National Postdoctoral Program for Innovative Talents (BX20190369), China Postdoctoral Science Foundation (2019M661996) and National Natural Science Foundation of China (51804212).
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