Journal of Natural Gas Science and Engineering 57 (2018) 45–51 Contents lists available at ScienceDirect Journal of Natural Gas Science and Engineering journal homepage: www.elsevier.com/locate/jngse Eﬀect of moisture on the desorption and unsteady-state diﬀusion properties of gas in low-rank coal T Haijun Guoa,b, Liang Yuana, Yuanping Chengc,∗, Kai Wanga,d, Chao Xua,b, Aitao Zhoua,b, Jie Zanga,b, Jiajia Liue a Beijing Key Laboratory for Precise Mining of Intergrown Energy and Resources, China University of Mining and Technology, Beijing, Beijing, 100083, People's Republic of China b State Key Laboratory Cultivation Base for Gas Geology and Gas Control, Henan Polytechnic University, Jiaozuo, 454000, People's Republic of China c National Engineering Research Center for Coal Gas Control, China University of Mining and Technology, Xuzhou, 221116, People's Republic of China d Hebei State Key Laboratory of Mine Disaster Prevention, North China Institute of Science and Technology, Beijing, 101601, China e College of Safety Science and Engineering, Henan Polytechnic University, Jiaozuo, 454000, People's Republic of China A R T I C LE I N FO A B S T R A C T Keywords: Low-rank coal CBM development Moisture Unsteady-state diﬀusion Non-constant diﬀusion coeﬃcient (non-CDC) model Currently, resource integration in coal-burning facilities and clean energy reconstruction are being strongly pushed forward in China. As a clean fossil energy, unconventional natural gas, such as coalbed methane (CBM), exhibits promise as an energy development strategy. In China, there are abundant CBM resources in the considerable reserves of low-rank coal. Therefore, the study of low-rank coal is the key to realize the high-yield and high-eﬃciency development of CBM resources in China. In this paper, a new water injection device was designed to prepare coal samples with a variety of moisture contents, and a novel method to measure the gas desorption properties in coal containing water was introduced. On this basis, the gas desorption law in low-rank coal with diﬀerent moisture contents was tested, and the eﬀect of moisture on the gas diﬀusion properties in low-rank coal was analyzed. The results indicate that the initial gas desorption volume of low-rank coal is extremely large and that the gas desorption law in the moisture-containing low-rank coal can be described by Airey's empirical equation. It is also observed that the ultimate gas desorption volume, initial gas desorption rate and initial eﬀective gas diﬀusion coeﬃcient all shift toward the direction that is beneﬁcial to CBM development. Therefore, reducing the moisture content in low-rank coals through certain techniques can dramatically enhance the gas migration behavior and achieve the purpose of high-yield CBM development. 1. Introduction In China, coal was always the main energy resource for the urban modernization in the past few decades. However, this has led to severe environmental pollution. Thus, all over the country, especially in large and medium-sized cities, resource integration in coal-burning facilities and clean energy reconstruction have been strongly pushed forward. As a clean fossil energy, unconventional natural gas, such as coalbed methane (CBM), will certainly become a bright spot for energy development strategies. The total CBM volume is approximately 3.68 × 1013 m3 in China, of which the CBM volume in low-rank coal seam is around 1.6 × 1013 m3, which accounts for 43% of the total (Wang et al., 2016). For a long time, most of the research (He et al., 2010; Xu et al., 2014; Zhao et al., 2013, 2016) was concentrated on medium-rank and high-rank coals in China. In the 21st century, CBM in the low-rank coal seam from the Powder River basin of USA, Surat basin ∗ Corresponding author. E-mail address: cyp620924@hotmail.com (Y. Cheng). https://doi.org/10.1016/j.jngse.2018.06.045 Received 13 January 2018; Received in revised form 20 June 2018; Accepted 29 June 2018 Available online 30 June 2018 1875-5100/ © 2018 Elsevier B.V. All rights reserved. of Australia and Alberta basin of Canada has achieved commercial development (Beaton et al., 2006; Busch and Gensterblum, 2011; Stricker et al., 1998). By comparison, the study of CBM in the low-rank coal, especially lignite, still stays in the stage of scientiﬁc research and experimental development. In general, coal with a vitrinite reﬂectance R0 < 0.65% is called low-rank coal in China (Guo et al., 2015; Wang et al., 2016). The porosity of low-rank coal is high, its speciﬁc surface area is large and it has many polar functional groups, such as hydroxy and carboxyl; therefore, it can absorb more water than coals of other ranks (Crosdale et al., 2008; Fu et al., 2005, 2012; Wang et al., 2011). The statistical data show that in China, the moisture content of long ﬂame coal is mostly in the range of 3%–12% and the moisture content of lignite is typically 10%–28% (Guo et al., 2015; Qiao, 2009). There are four existing forms of moisture in the low-rank coal (Allardice et al., 2003; Crosdale et al., 2008): 1) In the macropores and fractures in the form of Journal of Natural Gas Science and Engineering 57 (2018) 45–51 H. Guo et al. remove the moisture in coal. The density (ρ) of the coal sample was measured using an Ultrapyc 1200e Automatic Gas Pycnometer for Density from Quantachrome; the instrument has a resolution and accuracy of 0.0001 g/mL and 0.02%, respectively. Then, the coal samples (weighing mcoal) were placed in the coal sample tank. The volume of gas molecules adsorbed onto the pore surfaces of coal matrices is extremely small, so it can be ignored. Thus, the volume of the coal sample in the coal sample tank can be calculated using Eq. (1): free water; 2) in the capillary channel of low-rank coal; 3) adsorbed in the coal pores in the form of multimolecular layer; 4) adsorbed in the coal pores in the form of monomolecular layer. Moisture in the low-rank coal matrix has signiﬁcant impact on the gas ad-desorption properties and plays an important role in gas migration in coal (Gensterblum et al., 2013; Pan et al., 2010). In the past, studies on water-containing coal by most scholars (Day et al., 2008; Gensterblum et al., 2013; Krooss et al., 2002; Liu et al., 2012) have mainly focused on equilibrium water coals, and the inﬂuence of the variation of moisture content in coal on the CBM development is rarely taken into account. In addition, some scholars (Crosdale et al., 2008; Joubert et al., 1974; Moore and Crosdale, 2006; Xie and Chen, 2007; Zhang et al., 2009) have also studied the gas adsorption properties in coal with diﬀerent moisture contents; however, due to limits of the experimental device, it was diﬃcult to uniformly humidify the experimental coal sample and ensure accurate moisture content when coal samples with diﬀerent moisture contents were prepared via artiﬁcial addition of humidity. In this paper, a water injection device that can uniformly humidify the experimental coal samples was developed to prepare coal samples with diﬀerent moisture contents, and the new device and method to measure the gas desorption properties in coal containing water were introduced. On this basis, the eﬀect of moisture on the gas migration mechanism in low-rank coal is studied to provide a theoretical basis for the CBM development in low-rank coal reservoirs. Vcoal = mcoal ρ (1) 2) Combining with the volume (V01) of the coal sample tank, the volume (Vf ) of the free gas in the coal sample tank at adsorption equilibrium can be obtained using the following equation: Vf = V01 − Vcoal (2) Thus, the free gas volume (Vf0 ) under the standard conditions can be obtained using the following equation (Guo et al., 2016b): Peq Vf Teq = P0 Vf0 T0 (3) where Peq is the adsorption equilibrium pressure in the coal sample tank, MPa; Teq is the temperature of the coal samples within the coal sample tank, K; P0 and T0 are the standard pressure (0.101325 MPa) and temperature (273.15 K), respectively. 2. Coal samples and experimental methods 2.1. Coal samples 3) The temperature of the thermostatic oil bath was adjusted to (60 ± 0.1) °C, and the coal sample tank and coal samples were outgassed for approximately 48 h under high vacuum to remove air and other impurities in them. Then, the valve of the coal sample tank and the switch of the vacuum pump were closed successively. 4) The temperature of the thermostatic oil bath was changed to (30 ± 0.1) °C, and then the constant-ﬂux pump and the stirring apparatus were opened to inject the distilled water into the coal samples in the coal sample tank. The volume of injected water was calculated in advance according to the requirement for the experiment. After the water injection was completed, the switch of the constant-ﬂux pump and the corresponding valve of the coal sample tank were closed. It should be noted that to uniformly humidify the experimental coal sample, the stirring apparatus should keep continuous stirring for 45–50 min before it is closed (Guo et al., 2016b). The coal sample in the coal sample tank was equilibrated for 48 h after the stirring apparatus being closed to allow the injected water to fully humidify the coal sample. 5) The coal sample tank was ﬁlled with methane (> 99.9% purity) and the gas intake valve was adjusted to let the gas pressure stabilize at 2 MPa when the gas adsorption equilibrium state was achieved. It was considered that adsorption equilibrium had been reached after 6 h of unchanged pressure in the coal sample tank. 6) To test the gas desorption law in coal, the ﬁrst step was pressure relief when the gas desorption law in coal was tested. As shown in Fig. 1, the valve (m) was opened to link the gas sample bag to the coal sample tank, making the pressure reduce to the atmospheric pressure. Then, the valve (m) was turned to connect the coal sample tank with the gas desorption measuring cylinder as soon as possible. The coal samples were collected from the northern China mining area. The samples were sealed in a package from the site and prepared for the proximate analysis, petrographic analysis and porosity tests. The basic physical parameters of the low-rank coal samples are shown in Table 1. 2.2. Experimental methods In general, coal sampled from the mining area is in a pulverized or broken state; that is, most coal samples are in particulate form. Therefore, the gas desorption and diﬀusion properties in coal samples are usually measured via desorption or sorption methods (Guo et al., 2016b; Zhang, 2008). In this paper, the desorption method was used. To prepare coal samples with diﬀerent moisture contents, a water injection device that can uniformly humidify experimental coal samples was developed. Using the device, we can inject water into the coal sample after vacuum degassing or achieving gas adsorption equilibrium and then stir the experimental coal sample to humidify it uniformly. Meanwhile, in this paper, the new experimental device and method to measure the gas desorption properties were introduced to accurately obtain experimental results. The schematic diagram of the experimental device is shown in Fig. 1. The experimental steps and methods for the analysis are as follows: 1) The coal sample was crushed in a pulverizer and screened to obtain the desired sample size of 1–3 mm. Then, the specimens were placed in a vacuum drying oven at 50 °C to completely dry for 72 h to Table 1 Basic physical parameters of the low-rank coal samples. Proximate analysis (wt%) Petrographic composition (vol %) Aad Vdaf Fcad Vitrinite content Inertinite content Liptinite content Mineral content 9.28 49.53 32.47 95.17 0.59 0 4.24 Maximum vitrinite reﬂectance (Ro)/% Porosity/% 0.41 17.82 Aad = ash content on air-dried basis; Vdaf = volatile matter content on dry ash-free basis; Fcad = ﬁxed carbon content on air-dried basis. 46 Journal of Natural Gas Science and Engineering 57 (2018) 45–51 H. Guo et al. Fig. 1. Schematic diagram of the water injection and desorption device. 1- High pressure CH4 cylinder; 2- Pressure reducing valve; 3- Reference tank; 4- Vacuum pump; 5Compound vacuum gauge; 6- Constant-ﬂux pump; 7Blender motor; 8- Stirring apparatus; 9-Water inlet and gas intake; 10- Gas outlet; 11- Thermostatic oil bath; 12- Coal sample tank; 13- Agitating vane; 14Gas desorption measuring cylinder; 15- Gas sample bag; a-e− Pressure gauge; f-i- Valve; j- Four-way joint; k- Three-way joint; m- Controllable three-way joint. considered the coal as an aggregation of separated “blocks” having diﬀerent sizes and containing fractures. Thus, on the basis of Darcy's law, the coal gas emission theory was established and the empirical Eq. (5) revealing the relationship between the gas desorption volume in coal and the time was put forward. The desorbed gas volume at diﬀerent times (t) was measured by recording the liquid level in the gas desorption measuring cylinder. The total gas desorption time was determined according to the gas desorption volume per unit time. The gas desorption volumes could be converted into volumes (Vt) at STP based on the atmospheric pressure and temperature outside the coal sample tank. The gas volume in the gas sample bag was measured and converted into the volume (Vco) at STP, and then the revised volume (Qt) of the desorbed gas per unit mass at diﬀerent times t could be obtained using the following equation (Guo et al., 2016b): Qt = (Vco − Vf0) + Vt mcoal n Qt − t = 1 − e ( t0 ) Q∞ (5) where Q∞ is the ultimate gas desorption volume, mL/g; t0 is the time constant, s; n is the constant related to the fracture development in coal. Based on the data in Fig. 2, Eq. (5) was applied to ﬁt the gas desorption volume in low-rank coal with diﬀerent moisture, and results are shown in Fig. 3 and Table 2. From Fig. 3 and Table 2, it is found that the correlation coeﬃcients of the ﬁtting to the gas desorption volume in low-rank coal with different moisture contents using Airey's empirical equation are all greater than 0.99, which indicates that the Airey's empirical equation can be used to quantitatively describe the gas desorption law in low-rank coal. The variation of the ultimate gas desorption volume with the moisture content was plotted in Fig. 4. As can be seen, there is a linear relationship between the ultimate gas desorption volume and the moisture content, which can be expressed as follows: (4) 7) When the desorption experiment ended, the coal sample tank was opened quickly and coal samples from the upper, middle and lower portions of the coal sample tank were collected, respectively. Three coal samples were collected from every portion. Then, the proximate analysis of the collected coal samples was immediately performed. The results indicated that the moisture content of every collected coal sample was basically identical and consistent with that calculated in advance. Thus, the average moisture content of the nine collected coal samples was considered as the moisture content of the coal sample in the coal sample tank (Guo et al., 2016b). Q∞= − 0.62Mad + 21.08 (6) According to the property of the geometric curve, the slope of a certain point in the gas desorption curve is the gas desorption rate at that point. Thus, the Airey's empirical equation is derived over time, with the result shown below: 3. Experimental results and analysis 3.1. Eﬀect of moisture on the isothermal desorption properties During the gas desorption experiment on low-rank coal, the gas adsorption equilibrium pressure and temperature were set as 2 MPa and 30 °C, respectively. The gas desorption experimental results of coal samples with diﬀerent moisture contents are shown in Fig. 2. From Fig. 2, it is found that the initial gas desorption volume of lowrank coal is extremely large, and the gas desorption volume of the lowrank coal from the ﬁrst 3 min is approximately equal to 80%–90% of the total gas desorption volume. Then, the desorption curve suddenly slows down and quickly ﬂattens. Moreover, the gas desorption volume of coal samples at the same time t decreases signiﬁcantly with increasing moisture content. n−1 n ⎛t⎞ Q′t = Q∞ ⎡ ⎢ t0 ⋅ t0 ⎣ ⎝ ⎠ ⎜ ⎟ ⋅e n − t t0 ⎤ ( )⎥ ⎦ (7) Combining the gas desorption data in Fig. 3 and the ﬁtting parameters in Table 2, Eq. (7) was applied to obtain the gas desorption rate of low-rank coal with diﬀerent moisture contents. The results are shown in Fig. 5. Fig. 5 indicates that under the conditions of the same moisture content, the gas desorption rate in low-rank coal decreases over time. At the initial stage of gas desorption in coal, the decreasing trend of the gas desorption rate is extremely rapid; as time goes on, the decreasing trend gradually slows down; in the late period, the gas desorption rate almost no longer changes. From Fig. 5, it is also found that at the initial stage of gas desorption in coal, the gas desorption rate decreases with increasing moisture content in coal; as time goes on, the diﬀerences among the gas desorption rates of low-rank coal samples with diﬀerent moisture 3.2. Eﬀect of moisture on the ultimate gas desorption volume and the gas desorption rate During the investigation of coal gas emission, Airey (Airey, 1968) 47 Journal of Natural Gas Science and Engineering 57 (2018) 45–51 H. Guo et al. Fig. 2. Gas desorption experimental results of low-rank coal samples with diﬀerent moisture contents. Fig. 3. Results of the ﬁtting to the gas desorption volume in low-rank coal with diﬀerent moisture contents using Airey's empirical equation. Fig. 4. Relationship between the ultimate gas desorption volume and the moisture content. Table 2 Parameters and correlation coeﬃcients of the ﬁtting to the gas desorption volume in low-rank coal with diﬀerent moisture contents using Airey's empirical equation. Mad/% Q∞/(mL·g−1) t0 /s n R2 0.00 5.13 9.97 15.22 20.46 26.38 21.64 17.12 15.26 10.98 8.98 4.67 3.07 14.97 12.84 17.13 33.59 38.66 0.14 0.17 0.16 0.16 0.17 0.15 0.9949 0.9991 0.9989 0.9942 0.9957 0.9973 contents become smaller and smaller, even showing an irregular change. The authors believe that it is mainly caused by the anisotropy of coal. 3.3. Eﬀect of moisture on the unsteady-state diﬀusion properties of gas in low-rank coal Fig. 5. Gas desorption rate of low-rank coal with diﬀerent moisture contents. 3.3.1. Evaluation of the diﬀusion coeﬃcient Coal is a porous material, and the pore and fracture system in it is not only the storage space of CBM but also the channel for CBM transportation (Zhao et al., 2014, 2016). The gas migration in coal is a very complex behavior. From the viewpoint of molecular movement, it is thought that the gas adsorption and/or desorption on the coal pore surface is completed instantaneously (Guo et al., 2016b). However, due to the resistance caused by gas diﬀusion out of various types of pores in the coal matrices and the gas ﬂow through the fractures in coal, it usually takes some time for the gas to migrate in coal. In general, the type of gas migration in coal matrices features as unsteady-state gas diﬀusion (Guo et al., 2014, 2016b). 48 Journal of Natural Gas Science and Engineering 57 (2018) 45–51 H. Guo et al. diﬀusion coeﬃcients in coal are usually not constant, especially when the eﬀect of moisture content and temperature is taken into account (Guo et al., 2016b). Thus, it has become a conundrum for researchers to obtain the analytical solution of the diﬀusion equation under the condition of non-constant diﬀusion coeﬃcients. Recently, some investigators (Jian et al., 2012; Zhang, 2008) have proposed a non-CDC model by analogy, in which the diﬀusion coeﬃcient depends on the time t. According to their ideas, if the gas diﬀusion coeﬃcient D is only t related to the time t, we can deﬁne αgas = ∫0 Ddt . Then, Eq. (9) can be converted as follows (Guo et al., 2016b): From a mathematical point of view, Fick's law is widely used by scholars to quantify the gas diﬀusion process in a porous medium (Charrière et al., 2010; Guo et al., 2016a; Yang and Wang, 1986; Zhang, 2008): J = −D ∂cgas (8) ∂lh where J is the diﬀusive ﬂux, kg/(m2·s); D is the diﬀusion coeﬃcient, which reﬂects the diﬀusion “rate”, m2/s; cgas is the concentration of the diﬀusion medium, kg/m3; lh is the diﬀusion distance, m; and ∂cgas ∂lh is the concentration gradient (a vector). The negative sign reﬂects that the direction of the concentration gradient is opposite to the direction of the diﬀusive ﬂux (i.e., the concentration gradient goes from low to high concentration, but the diﬀusive ﬂux is from high to low concentration) (Guo et al., 2016b; Zhang, 2008). To apply Fick's law for solving engineering problems, based on Fick's law, the continuity principle of ﬂuids ﬂow and the mass conservation equation, some scholars (Yang and Wang, 1986; Zhang, 2008) have derived the diﬀusion equation (i.e., Fick's second law). If the diﬀusion coeﬃcient D is independent of the concentration cgas , the onedimensional diﬀusion equation can be obtained: ∂cgas ∂t =D ∂cgas ∑ n=1 (15) Assuming the following, ∫t Ddt ⎧ ⎪x = 0 rc ⎨ Qt F = ⎪ Q∞ ⎩ (16) Then, Eq. (15) can be converted into a unary quadratic equation as follows: 6 x+F=0 π 3x 2 − 2 2t 1 − Dnr 2π c e n2 (14) t (9) ∞ ∂lh2 t 6 ∫0 Ddt 3∫ Ddt Qt = − 0 2 Q∞ π rc rc The structure of coal is extremely complex. To study the gas migration law in coal, the coal particle is considered as a uniform sphere. Based on this assumption, the following analytical solution for the gas diﬀusion coeﬃcient of a spherical coal particle was obtained (Yang and Wang, 1986; Zhang, 2008): Qt 6 =1− 2 Q∞ π ∂2cgas The above equation is equivalent to Eq. (9) by making αgas equivalent to t and D equal to 1. Therefore, solutions obtained for constant D may be applied to non-constant D. Thus, the following equation is obtained (Guo et al., 2016b): ∂2cgas ∂lh2 = ∂αgas (10) (17) Solving the above equation yields the following solution: where Qt is the gas desorption ratio in coal; and rc is the radius of the Q∞ spherical coal particle, m. However, the above equation is an inﬁnite series equation, which is diﬃcult to be applied to engineering practice (Guo et al., 2016b). Thus, by introducing the error function, some scholars (Yang and Wang, 1986; Zhang, 2008) solved the analytical solution of the gas diﬀusion equation, as presented below: 6 π x= − 36 π − 12F 6 Assuming that y = 1 y = rc2 x 2 = rc2 ⎛⎜ − ⎝ π = 1 − π 1 F − π 3 (18) t 0 ∫ Ddt , thus, 2 1 F − ⎞⎟ π 3⎠ (19) ∞ Qt 6 Dt ⎡ 1 nr ⎤ 3Dt + 2 ∑ ierfc ⎛ c ⎞ ⎥ − 2 = Q∞ rc ⎢ π rc Dt ⎠ ⎦ ⎝ n=1 ⎣ ⎜ From Eq. (19), it is found that y is a function of F , and F is obtained by recording the gas desorption volume in coal at the diﬀerent times t . Thus, y is also a function of t . Given the value of y , the diﬀusion coeﬃcient D can be calculated as follows: ⎟ (11) ( ) nr where ierfc Dtc is the integrated error function. In terms of engineering applications (such as coal mining), it still meets the requirements of engineering accuracy if the error function is ignored. Therefore, the above equation can be expressed as follows (Guo et al., 2016b): Qt 6 Dt 3Dt = − 2 Q∞ π rc rc D= Qt Q∞ (20) Based on the non-CDC model, the value of y at the diﬀerent times t is obtained by the gas desorption experiment ﬁrst; then, the functional relationship between y and t can be obtained by the function ﬁtting; ﬁnally, the gas diﬀusion coeﬃcient D at the diﬀerent time can be obtained by deriving the function of y for t (Guo et al., 2016b). (12) When the fraction desorbed is less than 0.5, the diﬀusion equation can be simpliﬁed as Eq. (13) to give an estimate of the diﬀusivity for short duration (t < 600s) (Charrière et al., 2010; Smith and Williams, 1984a; b). Qt 6 Dt = =B t Q∞ π rc dy dt 3.3.2. Eﬀect of moisture on the gas diﬀusion properties in low-rank coal Based on Fig. 2 and Table 2, Qt (i.e., the value of F ) can be calQ∞ culated. Thus, the value of y at the diﬀerent time can be obtained using Eq. (19). The results are shown in Fig. 6. It is found that the exponential formula as follows can describe the curves in Fig. 6. The ﬁtting results are shown in Table 3. (13) From Eq. (13), it is found that there is a linear relationship between and t if the gas desorption time in coal is very short. In the Car- y = y0 + A1 e−t / t1 + A2 e−t / t2 + A3 e−t / t3 tesian coordinate system, a linear ﬁt of Qt versus t yields a value of K; Q∞ this allows the calculation of the gas diﬀusion coeﬃcient D. However, the above method assumes a constant diﬀusion coeﬃcient and is only accurate for short desorption times, but in fact, the gas (21) where y0 , A1 , A2 , A3 , t1, t2, t3 are the ﬁtting parameters. Taking the derivative of Eq. (21), the following expression can be obtained: 49 Journal of Natural Gas Science and Engineering 57 (2018) 45–51 H. Guo et al. Fig. 6. Variation of y with time under the condition of diﬀerent moisture contents. D= dy A A A = − 1 e−t / t1 − 2 e−t / t2 − 3 e−t / t3 dt t1 t2 t3 Fig. 7. Variation of eﬀective diﬀusion coeﬃcients of the low-rank coal with diﬀerent moisture contents along with time. (22) In practical application, the eﬀective diﬀusion coeﬃcient De as follows is used widely. De = D / rc2 (23) From Table 3, it is found that the correlation coeﬃcients are all greater than 0.99 by ﬁtting the curves in Fig. 6 using Eq. (21), which indicates that the non-CDC model can quantitatively describe the gas diﬀusion characteristics in low-rank coal well. Substituting the data in Table 3 into Eq. s (22) and (23), the changes of eﬀective diﬀusion coeﬃcients of the low-rank coal with diﬀerent moisture contents along with time were obtained, as shown in Fig. 7. Fig. 7 indicates that under the condition of the same moisture content, the initial eﬀective diﬀusion coeﬃcients of low-rank coal are relatively larger; as time goes on, the eﬀective diﬀusion coeﬃcients drop sharply. It is also found that the lower the moisture content, the smaller the eﬀective gas diﬀusion coeﬃcients for low-rank coal, which indicates that the gas diﬀusibility in low-rank coal decreases with increasing moisture content. Fig. 8. Variation of the ultimate desorption volume, initial desorption rate and initial eﬀective diﬀusion coeﬃcient with the moisture content. with the moisture content were summarized and presented in Fig. 8. From Fig. 8, it is found that if the moisture content in low-rank coal decreases from 26.38% to 0%, the ultimate desorption volume, initial desorption rate and initial eﬀective diﬀusion coeﬃcient increase 363%, 309% and 367%, respectively. It is worth noting that all parameters will transform to the direction of enhancing CBM development when the moisture content in low-rank coal decreases. The pores in low-rank coal are well connected which provides a huge space for coal to adsorb moisture and gas (Guo et al., 2015). Moreover, there are many polar and hydrophilic functional groups in low-rank coal (Crosdale et al., 2008; Fu et al., 2005, 2012), which results in the water molecules being adsorbed by low-rank coal pores more easily than gas molecules. On the one hand, water in low-rank coal occupies the adsorption sites of gas molecules, which sharply reduces the gas adsorption and desorption volume in low-rank coal. On the other hand, water molecules block some pore channels in low-rank 4. Discussion CBM drainage is a process of diﬀusion and permeation of methane in the pores of the coal reservoir. During this process, the key parameters that have a great eﬀect on the CBM development are the effective diﬀusion coeﬃcient and permeability, which are seriously inﬂuenced by the moisture content in coal. As shown in the previous studies (Guo et al., 2015), the moisture content in low-rank coal is high, and especially, the moisture content of some lignite can even be as high as 40%–50%. Therefore, the inﬂuence of moisture must be considered during the development of CBM in low-rank coal seams. Based on the above experimental results, the variation of the ultimate desorption volume, initial desorption rate and initial eﬀective diﬀusion coeﬃcient Table 3 Fitting results of curves between y and time under the diﬀerent moisture contents. Mad/% y0/(10−8 m2) A1 /( × 10−8) t1 A2 /( × 10−8) t2 A3 /( × 10−7) t3 R2 0.00 5.13 9.97 15.22 20.46 26.38 3.02 2.84 2.63 2.44 2.29 1.91 −9.57 −9.69 −7.97 −7.54 −6.79 −6.68 14.70 18.71 18.60 19.20 42.46 49.61 −5.64 −5.47 −5.07 −4.83 −4.44 −3.57 275.91 335.04 342.64 371.88 421.12 459.69 −1.49 −1.52 −1.33 −1.21 −1.17 −0.89 4900.47 4826.05 4612.22 4496.33 4661.92 4677.47 0.9995 0.9998 0.9999 0.9999 0.9999 0.9999 50 Journal of Natural Gas Science and Engineering 57 (2018) 45–51 H. Guo et al. 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Conclusion In the paper, low-rank coal was studied as a subject. A water injection device was developed to prepare coal samples with a variety of moisture contents, and a novel method to measure the gas desorption properties in coal containing water were introduced. Then, the eﬀect of moisture on the gas desorption and diﬀusion properties in low-rank coal was tested. Conclusions are as follows: 1) The initial gas desorption volume of low-rank coal is relatively large; next, the desorption curve suddenly slows and quickly ﬂattens. Moreover, the gas desorption volume of coal samples at the same time t decreases signiﬁcantly with increasing moisture content. The Airey's empirical equation can be used to quantitatively describe the gas desorption law in low-rank coal. 2) Under the conditions of the same moisture content, the gas desorption rate in low-rank coal decreases over time. At the initial stage of gas desorption in coal, the decreasing trend of the gas desorption rate is extremely rapid, but over time, this decreasing trend gradually slows. In the late period, the gas desorption rate almost stay changed. At the initial stage of gas desorption in coal, the gas desorption rate decreases with increasing moisture content in coal, and over time, the diﬀerences among the gas desorption rates of lowrank coal samples with diﬀerent moisture contents are increasingly smaller, even showing an irregular change. 3) Under the condition of the same moisture content, the initial effective diﬀusion coeﬃcients of low-rank coal are relatively larger, and over time, the eﬀective diﬀusion coeﬃcients drop sharply. The lower the moisture content, the smaller are the eﬀective gas diﬀusion coeﬃcients in low-rank coal. 4) The ultimate desorption volume, initial desorption rate and initial eﬀective diﬀusion coeﬃcient will transform to the direction of enhancing CBM development when the moisture content in low-rank coal decreases. Therefore, to enhance the gas migration in CBM development, it is very important to reduce the moisture content in low-rank coal by applying certain technical measures. Notes The authors declare no competing ﬁnancial interest. Acknowledgments The authors are grateful to the ﬁnancial support from the State Key Laboratory Cultivation Base for Gas Geology and Gas Control (Henan Polytechnic University) (WS2018B06), the State Key Research Development Program of China (No. 2016YFC0600708), the Open Funds of Hebei State Key Laboratory of Mine Disaster Prevention (No. KJZH2017K02), the Yue Qi Distinguished Scholar Project, China University of Mining & Technology, Beijing, and the National Natural Science Foundation of China (No. 51474219, 51604278 and 51604101). 51

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