Influence of metamorphism degree on coal gas desorption characteristics and dynamics models

Influence of metamorphism degree on coal gas desorption characteristics and dynamics models | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Influence of metamorphism degree on coal gas desorption characteristics and dynamics models Huigang Xu, Xuyao Qi, Haidong Wang, Zhongqiu Liang, Tao Yang, and 3 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-5182181/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Elucidating the characteristics of desorption and diffusion of coal seam gas is essential for the prevention of gas disasters in coal mines. In this study, constant-temperature gas dispersion tests were conducted on lignite, fiery coal, and anthracite to unveil the intricate dynamics of gas diffusion in coal samples under the influence of coal metamorphism. The primary focus was to determine their gas desorption and diffusion characteristics and analyze the mathematical expressions of gas dispersion for coal samples with varying levels of metamorphism during different periods. The findings revealed that coal samples with high metamorphism could attain the desorption limit relatively swiftly, while low-rank lignite required a longer duration to reach the limit. Notably, the gas desorption diffusion rate exhibited significant sensitivity to the coal's metamorphism level. The gas desorption rate within the first 10 minutes was observed to be stable for lignite and fiery coal, while anthracite displayed a faster desorption rate in the initial 4 minutes followed by stability in the subsequent 6 minutes. Furthermore, the effective gas diffusion coefficient demonstrated a robust negative linear correlation with the degree of metamorphism, signifying a decrease in gas diffusion ability with an increase in metamorphism level. Empirical formulas employed to fit anthracite yielded relatively stable correlation indices, with Formula 3 deemed more suitable for depicting the gas desorption processes of lignite and fiery coal. Physical sciences/Engineering Physical sciences/Energy science and technology/Fossil fuels Coalbed methane (CBM) Desorption Diffusion Degree of metamorphism Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 1. Introduction China's energy is characterized by its 'rich coal, poor oil, and little gas'. Its proven coal reserves account for 33.8% of the world's coal reserves. With the increase in mining depth, the ground stress and gas pressure of coal seams increase, and dynamic gas disasters in coal mines become more and more serious [3–5] . Studying the desorption and diffusion characteristics of gas not only has an important impact on the development of coalbed methane resources but also is the theoretical basis for the prevention of gas disasters in coal mines. Gas desorption and adsorption are mutually reversible processes that can also be called mass transfer processes [6–8] . In the process of coal adsorption and desorption, there are some complex mechanisms of change, such as the effects of temperature and pressure, which also affect the adsorption and desorption performance of coal [9, 10] . Different ranks of coal have different structures, and their desorption capacity is also different. The Langmuir adsorption constant of coal can be determined by measuring and analyzing the pore distribution characteristics in it, and this can be used to predict the gas content and pressure in coal seams more accurately [11–14] . In addition, it can be used to study the risk of coal and gas outbursts and predict the possibility thereof. The adsorption constant is an important parameter for characterizing the surface adsorption capacity of coal, which is affected by a variety of internal factors, including the degree of coal metamorphism, the composition of coal rock, the conditions of the test, and the setting of parameters [15–17] . In coal that contains gas, free and adsorbed gases are in a state of dynamic equilibrium, and a new state of equilibrium is produced after changes in the gas pressure and temperature or shocks and oscillations [18, 19] . Yang et al. [20] suggested that the initial effective diffusion coefficient in the process of gas desorption is related to the pressure, the temperature of the adsorption equilibrium, and the particle size of the coal samples. Pores have an important impact on the adsorption, desorption, seepage, and diffusion of gas, which can affect the diffusion rate, adsorption capacity, and desorption capacity of gas, thus affecting its production efficiency. Li et al. [21] found that with a gradual increase in the degree of damage in structural coal, the pore volume and specific surface area also change. The pore volume ratio of large and mesoporous pores gradually increases, but the pore volume ratio of micropores gradually decreases. When the damage degree of structural coal reaches a certain degree, the volume ratios of large pores and mesopores also change, while the volume ratio of micropores remains unchanged. In addition, the structure of large and medium pores can also reduce the osmotic pressure of gas and reduce its diffusion rate, thus effectively improving the efficiency of gas desorption [22] . Gasparik,M. et al [23] . conducted a comprehensive examination of the impact of coal rank on the desorption characteristics of coalbed methane, delving into the alterations in saturation adsorption capacity and adsorption curve throughout the desorption process. Kusuma, M.I., et al. [24] employed molecular dynamics simulation to probe the influence of coal rank on coalbed methane desorption, furnishing theoretical elucidation of the impact of coal rank on adsorbent-gas interaction and desorption rate during the desorption process. Gregory, N. et al. [25] found that the shorter the micropore length of coal, the shorter the migration distance of gas in the coal body, the shorter the transport time, and the greater the adsorption capacity in the initial stage. Hu et al. [26] found that the greater the degree of coal metamorphism, the smaller the influence of large pores on the laws of gas desorption and diffusion, while there is a greater influence of micropores. So far, scholars have compared and tested the adsorption and desorption laws of coal in different mining areas and with different coal ranks and determined the relationships between them. These experiments include studying factors such as the degree of coal metamorphism, reservoir pressure, reservoir temperature, and type and content of water in the coal. Among these factors, the coal grade has an important effect on the adsorption and desorption capacity, as the adsorption capacity decreases with the increase in the coal grade. However, at present, there are few studies on the gas desorption and diffusion characteristics of coals with different degrees of metamorphism, and no unified mathematical expression of gas desorption has been formed. In view of this, desorption tests were carried out on coals with different degrees of metamorphism, a more extensive mathematical formula was adopted to fit the gas desorption curve, and the gas release rules of coals with different degrees of metamorphism were obtained. This will provide a reference for coal mine safety. 2. Methodology 2.1 Sample preparation The experimental samples included lignite from Anjialing Coal Mine, fiery coal from Yusshuling Coal Mine, and anthracite from Xinyuan Coal Mine, as shown in Figure 1. After sampling, the coal samples to be measured were broken, crushed, and screened, respectively. Experimental coal samples with a particle size of 0.20–0.3 mm were screened and put into the oven for 6 hours, and the drying temperature was 70 °C. Then, the samples were allowed to stand and cool down to 21 °C, sealed, and stored until use. According to the parameters obtained through an industrial analysis, all experimental coal samples were reduced to a 1–3 mm particle size for use, dried in a drying oven at 70 °C for 6 hours, cooled to 21 °C, and sealed until use. The related gas parameters and maximum vitrinite reflectance of the selected coal samples are shown in Table 1. Table 1. Coal quality analysis and related gas parameters of the mine Coal mine Coal variety M ad /% A d /% V daf /% Porosity /% a /(m 3 ·t -1 ) b /MPa R 0, max /% Anjialing Lignitic 1.09 16.34 34.25 3.83 8.975 1.146 0.308 Yushuling Fiery coal 1.10 5.31 41.13 3.82 13.914 1.258 0.721 Xinyuan Anthracite 1.76 13.09 7.02 0.13 40.546 1.147 2.382 M ad is moisture, A d is ash, V daf is volatile, a and b are the Langmuir adsorption constant, R 0,max is maximum vitrinite reflectance. The N 2 GA test was carried out with a Quantachrome NOVA-4200e specific area and pore size analyzer, which is designed for static physical adsorption-high-purity (99.999%) nitrogen adsorption-desorption in a liquid nitrogen environment (77.3 K), and is applicable to pores between 0.35 and 500 nm in diameter. It can be seen from figure 2 that the gas adsorption volumes of the three coal samples are 2.04 cm 3/ g, 3.87 cm 3 /g and 5.85 cm 3 /g, respectively. The adsorption capacity of anthracite is higher than that of fiery coal and lignite, and the adsorption capacity of fiery coal is higher than that of lignite, indicating that the adsorption capacity of coal increases with the increase of coal metamorphism. There are hysteresis loops in all three kinds of coal, indicating that all coal contains open pores. Lignitic has the smallest hysteresis loop and is not closed, and the inflection points of adsorption and desorption curves are not obvious, and the adsorption isotherms and desorption isotherms basically coincide. This phenomenon indicates that a cylindrical shape with one end closed and a slit shape with four sides open are common in this type of coal. Fiery coal has large hysteresis loops, many open and breathable pores, and good pore connectivity. The adsorption and desorption curves roughly coincide, and the adsorption and desorption curves basically coincide with the higher and lower sections of relative pressure, indicating that there are many semi-closed pores and open and breathable pores in its interior. The adsorption isotherm and desorption isotherm of anthracite show a separate state, and do not close at the stage of relatively low relative pressure, which indicates that anthracite has a high degree of micropore development, and is dominated by cylindrical micropores with one end closed, and the pore connectivity is poor. As one of the important observation indicators of pore structure characteristics in coal, pore size distribution can directly reflect the pore structure characteristics. The pore size distribution of coal based on BJH method analysis is shown in Table 2. Table 2. Pore size distribution of test coal sample Coal variety diameter /nm Cumulative pore volume /(cm 3 ·g -1 ) percentage /% lignitic 100 0.0006 15.8% fiery coal 100 0.0000860 14.7% anthracite 100 0.000665 6.3% 2.2 Experimental apparatus This experiment was carried out using an independently developed isothermal adsorption and desorption system that consisted of six main parts: a gas supply and gas control system, adsorption and desorption system, pressure collection system, vacuum degassing system, temperature measurement system, and desorption gas collection system. Test pressure range was 0-6 MPa, as shown in Figure 3. 2.3 Experimental scheme and procedure In order to study the adsorption-desorption kinetic characteristics of three coal samples under different gas pressures, 99.99% CH 4 was used to carry out the test, and three different gas pressures were set up, which were 0.74MPa, 1.06MPa and 1.46MPa respectively. In order to avoid the chance of the test results, three groups of experiments were carried out in each scheme, and one group of data was selected for analysis when there was no large error in the experimental results. The specific test steps were as follows: (1)In the preparation stage of the experiment, an air tightness test was carried out first. (2)Then, 300 g of the coal sample was placed in an adsorption tank. Turn on the constant temperature water bath system and vacuum pump at the same time, degassing the sample to be tested in the constant temperature water bath at 60℃ for 12 hours, and remove the water and gas in the coal sample until the air in the coal sample reaches the vacuum degree of 4 Pa; (3)Gas was injected into the tank with the coal sample at a preset pressure, constant-pressure adsorption was maintained for 24 h, and it was ensured that the internal temperature of the adsorption tank was less than room temperature. (4)Tests were conducted according to the GBT19560-2004 standard, and desorption data were continuously recorded every 5 s for more than 100 minutes. 3. Results 3.1 Influence of the degree of metamorphism on the amount of gas desorption in coal Figure 4 illustrates the Q-t isothermal gas desorption curve of coal samples with varying degrees of metamorphism under different gas equilibrium pressures over a time period of 100 minutes. It is evident that, under identical external environmental conditions, the cumulative gas desorption of coal increased gradually with the prolongation of desorption time. Once the desorption time reached a certain threshold, the cumulative gas desorption exhibited small fluctuations around a stable value. Interestingly, it was observed that regardless of the desorption time, the curve obtained under high pressure consistently surpassed the curve obtained under low pressure. This observation implies that an increase in equilibrium pressure corresponded to a higher cumulative gas desorption. In the initial phase of gas desorption, the amount of gas desorbed increased with the degree of coal metamorphism. Coal samples with high metamorphism exhibited a relatively significant increase in gas desorption. For lignite, the gas desorption increased as the pressure increased. The first 10 minutes of desorption were characterized by the highest amount and rate of gas desorption, representing a rapid desorption stage. Subsequently, the desorption rate gradually stabilized, and the gas desorption volume exhibited a slow increase. This stage marked the onset of stable desorption, which occurred approximately after 80 minutes. Similarly, fiery coal demonstrated an increase in gas desorption with increasing pressure. The highest desorption amount was observed within the first 5 minutes, accompanied by a relatively high desorption rate. This period corresponded to the rapid desorption stage. After 5 minutes, while the desorption amount continued to gradually increase, the gas desorption rate slightly decreased, indicating the onset of a stable desorption stage. The desorption capacity of anthracite also varied with changes in pressure, exhibiting an increase with increasing pressure. The highest amount of gas desorption occurred within the first 10 minutes, accompanied by the highest desorption rate, representing the rapid desorption stage. After 10 minutes, the desorption rate gradually stabilized, and the gas desorption volume exhibited a slow increase. Subsequently, a stable desorption stage was reached. Overall, these findings provide insights into the desorption behavior of different coal samples under varying pressures and highlight the distinct stages of rapid and stable desorption. The gas desorption characteristics of the coal were most pronounced within the first 3 minutes . Based on the degrees of metamorphism, the total amounts of desorption in these three coal samples within the first 10 minutes accounted for 76.1%, 45.2%, and 36.7% of the total desorption, respectively. It can be observed that coal samples with a higher degree of metamorphism reached the limiting value relatively quickly, while low-rank lignite required a longer duration to reach the limit value. However, as the desorption time increased, the gas desorption rate of the highly metamorphic coal samples exhibited a progressively faster decline, resulting in a subsequent deceleration of the desorption rate. 3.2 Effect of the metamorphic degree on the gas desorption rate of coal The changes in the desorption rates of the three coals over time are depicted in Figure 5. It is evident that the trends in the changes in desorption velocities differed among the three coal types. However, the initial gradient of the curve under high pressure was greater than that under low pressure, indicating a higher initial gas desorption velocity under high equilibrium pressure compared to low equilibrium pressure. Additionally, the maximum gas desorption rate under different pressures and the rate of decline in the desorption rate varied with the degree of coal metamorphism. Among the three coal samples, anthracite, which had the highest coal rank, exhibited the smallest initial gas desorption velocity when the equilibrium pressure ranged from 1.36 to 1.46 MPa. However, as the desorption process progressed, its desorption velocity decreased and became the slowest within the same time frame. The initial desorption rate of the low metamorphic fiery coal was low, and it gradually decreased as the desorption process continued. Among the three coal samples, lignite, with the lowest degree of metamorphism, exhibited the highest initial gas desorption rate, but it also experienced the fastest subsequent decline. Specifically, when the equilibrium pressure was 1.06 MPa, low-rank lignite displayed the fastest initial gas desorption rate, which swiftly decreased as the desorption progressed. On the other hand, gassy coal, with a metamorphic degree intermediate to the other coal samples, demonstrated a relatively faster initial gas desorption rate, which gradually decreased over time. Anthracite had the lowest initial gas desorption rate, and its desorption speed decreased the slowest over the same duration. When the equilibrium pressure was 0.74 MPa, the intermediate metamorphic fiery coal exhibited the smallest initial desorption rate. As the desorption process continued, the desorption rate slowly decreased over the same duration. Remarkably, the initial desorption rate of anthracite, with a high degree of metamorphism, did not differ greatly from that of lignite, which had the lowest degree of metamorphism. However, as the desorption process continued, anthracite experienced the least decrease in desorption rate over the same duration, while lignite exhibited the greatest decline. Data were collected at half-minute intervals during the initial 10 minutes, and a curve was plotted based on the difference between the former and latter groups. The ratio of the former group's desorption rate to the latter group's is presented in Figures 6 and 7. It is evident from the figures that the desorption rate curves for the three experimental coals exhibited distinct trends. The difference in desorption rate within the first 10 minutes under varying pressures was more pronounced for lignite compared to fiery coal and anthracite, implying a greater decline in desorption rate for lignite. Furthermore, the difference in desorption rate for lignite within the initial 10 minutes showed no significant variation between the first 4 minutes and the last 6 minutes, while the difference in desorption rate for fiery coal did not significantly differ from that of the last 6 minutes. The linear correlation between the ratio of differences in the desorption rate within the first 4 minutes was stronger than that of the last 6 minutes, and the linear correlation coefficient increased with the increase in gas pressure. 3.3 Effect of the metamorphic degree on the gas diffusion characteristics of coal After undergoing the processes of adsorption and desorption, gas permeates the pores of the coal matrix. By utilizing desorption data and applying Fick's second law of diffusion, it is possible to calculate a physical parameter that characterizes the gas diffusion capacity within coal, known as the effective diffusion coefficient. Through linear regression analysis between the effective diffusion coefficient and the maximum reflectance of vitrinite, the impact of the degree of metamorphism on gas diffusion performance can be examined. The diffusion coefficient signifies the ability of coal to facilitate gas diffusion and its numerical value reflects the rate at which gas migrates through coal pores. In this study, the effective diffusion coefficient was introduced as a means to quantify the gas diffusion capacity. The relevant expressions are provided below: where Q t is the amount of gas desorption from coal at time t (mL/g); Q ∞ is the limiting gas desorption capacity of coal (mL/g); t is the desorption time (s); D e is the effective diffusion coefficient ( s -1 ); p 0 is the gas pressure during the test (MPa); M ad and A ad are moisture and ash in coal (%). The direct determination of the effective gas diffusion coefficient using the formula mentioned above is not feasible. To address this, we set n=1 in Eq. (1) and performed a logarithmic transformation of both sides of the equation, thus converting it into a linear fitting formula for calculation. Table 3. Effective gas diffusion coefficients of the coal samples. Coal samples Lignite Fiery coal Anthracite D e /s -1 9.32×10 -5 6.18×10 -5 0.36×10 -5 The effective diffusion coefficients of the coal samples, as shown in Table 3, followed a descending order: lignite, fiery coal, and anthracite. This observation markedly contrasts with the pre-desorption amount and adsorption constant of the coal samples mentioned earlier, suggesting that the impact of metamorphism on gas diffusion capacity differs significantly from its influence on adsorption and desorption capacity. Based on the measured results of the maximum reflectivity of vitrinite and the effective gas diffusion coefficients of the coal samples, the relationship between the effective gas diffusion coefficient and the metamorphic degree in the samples was calculated, as demonstrated in Figure 8. As can be observed in Figure 8, the linear fitting coefficient between the effective gas diffusion coefficient and the maximum reflectance of vitrinite was 0.947, indicating a strong negative linear correlation with metamorphism for the effective gas diffusion coefficients of the three coal samples. This correlation suggests that the ability of gas to diffuse in coal decreases as the metamorphic degree increases. The different effective gas diffusion coefficients of the coal samples with varying degrees of metamorphism can be primarily attributed to the maceral components of the coal itself, as well as compaction and dehydration during the coalification process. In coals with a lower degree of metamorphism, there is a higher content of inertinite and chitinite at the maceral level, which results in abundant large pores within these macerals. These pores provide a wide space for gas diffusion, thereby facilitating gas diffusion processes. 4. Gas desorption dynamics models Numerous studies by domestic and foreign scholars have focused on the mathematical modeling of gas desorption in coal, resulting in the proposal of various formulas. However, some of these formulas have limitations. To investigate the gas desorption behavior of the three coal samples and identify suitable mathematical expressions, a commonly employed formula was utilized to fit the desorption process under different pressures. The mathematical expressions employed are presented in Table 4 . Table 4 Mathematical expression for gas desorption fitting NO . - Formula 1 \({Q_{\text{t}}}=a{t^i}\) Formula 2 \({Q_{\text{t}}}={{{v_0}\left[ {{{\left( {1+t} \right)}^{1 - n}} - 1} \right]} \mathord{\left/ {\vphantom {{{v_0}\left[ {{{\left( {1+t} \right)}^{1 - n}} - 1} \right]} {\left( {1 - n} \right)}}} \right. \kern-0pt} {\left( {1 - n} \right)}}\) Formula 3 \({Q_{\text{t}}}={Q_\infty }\sqrt {1 - {e^{ - kbt}}}\) It can be seen from Fig. 10 that the fitting correlation coefficients of the three equations are all above 0.9, indicating a good fitting effect. In terms of the R 2 correlation index, when the desorption equilibrium pressure was 0.74 MPa, Formula 1 displayed a lower R 2 value compared to the other two empirical formulas, suggesting a weaker fitting correlation. Conversely, the other two formulas exhibited better fitting effects. As the equilibrium pressure increased, the correlation coefficients for all formulas also increased, albeit less noticeably for Formula 2 and Formula 3. When Formula 1 reached 1.46 MPa, its R 2 value increased to 0.977, significantly improving the fitting degree. However, Formula 2 had an R 2 value of 0.987, and Formula 3 had an R 2 value of 0.990, indicating even better fitting results. Overall, the correlation coefficient ( R 2 ) increased with increasing equilibrium pressure for all empirical formulas. Formula 2 showed a correlation coefficient range of 0.971–0.989, while Formula 1 had a range of 0.949–0.977. Formula 3 exhibited the smallest range of variation for its correlation coefficient, ranging from 0.979 to 0.990, resulting in the best fitting effect among the empirical formulas. The fitting results indicated that the regression coefficients of all three formulas changed with variations in the equilibrium pressure. However, the changes were significant for Formula 1, while relatively minor for Formulas 2 and 3. It can be seen from Fig. 11 that the fitting results for the fiery coal samples were satisfactory across the three different equilibrium pressures. At an equilibrium pressure of 0.74 MPa, Formula 3 exhibited some deviation during the middle stage of gas release, while Formula 1 displayed significant deviation in the middle and late stages. Conversely, Formula 2 demonstrated the highest degree of fitting. At an equilibrium pressure of 1.06 MPa, Formula 2 exhibited the best fitting results, although Formulas 3 and 1 showed some deviation during the early and middle stages of gas dispersion. Under an equilibrium pressure of 1.46 MPa, both Formulas 3 and 1 deviated during the middle and late stages of gas release, while Formula 2 continued to display the highest degree of fitting. This suggests that Formula 2 provided a good fitting effect. Throughout the entire desorption process, the correlation coefficient of Formula 2 varied only between 0.993 and 0.998. Additionally, Formula 1 had a fitting correlation coefficient of 0.993–0.997, indicating its ability to accurately describe the diffusion process of coal samples. Considering the fitting regression coefficient, Formula 3 exhibited the smallest range of variation, implying that using Formula 3 data in different equilibrium pressure segments to calculate gas loss would result in minimal differences and greater stability. It can be seen from Fig. 12 that the empirical formula displayed a good fitting effect in the early stage for the anthracite coal samples. The correlation coefficient ( R 2 ) of the fitting equation gradually increased with increasing equilibrium pressure and then gradually decreased after reaching a certain point. The correlation coefficients obtained using Formulas 2, 1, and 3 were all greater than 0.95. However, Formula 2 consistently yielded correlation coefficients above 0.99 for the entire desorption process, reflecting a strong fitting effect. At an equilibrium pressure of 0.74 MPa, Formula 2 exhibited some deviation in the early stage, while Formula 3 showed the highest degree of fitting, and Formula 1 displayed deviations during the early, middle, and late stages of gas dispersion. Under an equilibrium pressure of 1.06 MPa, Formula 2 demonstrated the highest degree of fitting, while Formulas 3 and 1 exhibited certain deviations in the early and middle stages. Similarly, under an equilibrium pressure of 1.46 MPa, Formula 2 again had the highest degree of fitting, while Formula 1 deviated during the middle and late stages of gas dispersion. The fitting results indicated that the overall applicability of the three empirical formulas was relatively good, especially at an equilibrium pressure of 1.46 MPa. Formulas 2, 1, and 3 all obtained high correlation index values, indicating a relatively good fitting effect. In the experiment, different classical empirical formulas were adopted to conduct a regression analysis on the experimental data obtained for desorption in three groups of coal samples under different equilibrium pressures. The three empirical fitting formulas used for anthracite yielded relatively stable correlation index values, indicating a good fitting effect. The fitting results of Formulas 2, 3, and 1 under an equilibrium pressure of 1.46 MPa were relatively ideal. For lignite, Formula 3 exhibited a relatively large correlation coefficient ( R 2 ) with a small range of variation, indicating the best fitting effect compared to the other two empirical formulas. Additionally, for fiery coal, Formula 3 accurately described the gas release process of the coal samples. 5. Conclusions Coal samples with a higher degree of metamorphism exhibited a faster attainment of the desorption limit value, whereas low-rank lignite required a longer period to reach this limit. However, as the desorption time increased, the desorption rate of highly metamorphic coal samples gradually declined, resulting in a progressively slower desorption rate. As coal metamorphism increased, the rate of decline in the gas desorption rate slowed down, and the higher the degree of coal metamorphism, the greater the amount of gas desorption. The effective gas diffusion coefficient of the coal samples exhibited a strongly negative linear correlation with the degree of metamorphism, indicating that the ability of the coal samples to facilitate gas diffusion decreased as the degree of metamorphism increased. Among the three empirical fitting formulas applied to anthracite, a relatively stable correlation index was obtained, and the fitting effect was satisfactory. For an equilibrium pressure of 1.46 MPa, the fitting results of Formulas 2, 3, and 1 were relatively ideal. Formula 3 yielded a relatively high correlation coefficient ( R 2 ) and exhibited a smaller range of coefficient variation for lignite, making it the most effective fitting formula compared to the other two. For fiery coal, Formula 3 was deemed more suitable for describing the gas desorption process of the coal samples. Declarations Author Contributions Huigang Xu: Conceptualization, Data curation, Writing - original draft. Xuyao Qi: Data curation, Formal analysis. Haidong Wang: Funding acquisition, Methodology. Zhongqiu Liang: Formal analysis. Tao Yang: Formal analysis,Visualization. Yongming Zou: Formal analysis. Qi Jiang: Formal analysis. Lei Jin: Formal analysis,Visualization. Funding This research was funded by the Natural Science Foundation of Hebei Province (E2024508006), the National Natural Science Foundation of China (52274200). 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Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Xuyao","middleName":"","lastName":"Qi","suffix":""},{"id":373696487,"identity":"a2a979b2-5cf4-460b-a3ab-f659cfb23f95","order_by":2,"name":"Haidong Wang","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAnklEQVRIiWNgGAWjYDACCQbDByASwiZSi7EBiOQhRYsZWCXxWgxuN2+rLqixsLdnYD54m4coLXeOld2ecUwisYeBLdmaKC1mN3LMbvM2SCTwMPCYSROtpRioxZ6Hgf8b8VqYgVoYexh42IjTYn8jrViaB+SXw2zGlnOI0SI5I3njZ56aOnv29uaHN94QowUBmElTPgpGwSgYBaMAHwAA3+4nqJ7uWpIAAAAASUVORK5CYII=","orcid":"","institution":"North China Institute of Science \u0026 Technology","correspondingAuthor":true,"submittingAuthor":false,"prefix":"","firstName":"Haidong","middleName":"","lastName":"Wang","suffix":""},{"id":373696488,"identity":"f2273c4d-88c7-4e1d-a02e-6feb82109f99","order_by":3,"name":"Zhongqiu Liang","email":"","orcid":"","institution":"CCTEG Shenyang Research 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Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Qi","middleName":"","lastName":"Jiang","suffix":""},{"id":373696492,"identity":"540d41e7-d9c1-4646-beaf-63a32fd57ace","order_by":7,"name":"Lei Jin","email":"","orcid":"","institution":"North China Institute of Science \u0026 Technology","correspondingAuthor":false,"submittingAuthor":false,"prefix":"","firstName":"Lei","middleName":"","lastName":"Jin","suffix":""}],"badges":[],"createdAt":"2024-09-30 15:53:15","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-5182181/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-5182181/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":71025619,"identity":"2048b511-34d6-4da2-97ec-c1264b42cc18","added_by":"auto","created_at":"2024-12-10 10:27:48","extension":"png","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":314895,"visible":true,"origin":"","legend":"\u003cp\u003eGeographical locations of the coal samples\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/8cd1df56f4f62ab7b4b8aa15.png"},{"id":71024848,"identity":"038d3623-ebbd-448c-8e82-e7c6276adc44","added_by":"auto","created_at":"2024-12-10 10:19:48","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":91715,"visible":true,"origin":"","legend":"\u003cp\u003eN\u003csub\u003e2\u003c/sub\u003eGA adsorption and desorption isotherms of coal samples\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/5fdcc61d0ecd287ac533f54c.png"},{"id":71025910,"identity":"a0b01942-a013-4c65-9987-fb1b4d366c64","added_by":"auto","created_at":"2024-12-10 10:35:48","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":532438,"visible":true,"origin":"","legend":"\u003cp\u003eIsothermal adsorption desorption system\u003c/p\u003e\n\u003cp\u003e1-Computer acquisition system; 2-Reference tank; 3-Vacuum pump; 4-Gas cylinders; 5-Coal sample tank; 6-Vacuum pump\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/a26c903601bb705472ef9897.png"},{"id":71025911,"identity":"d2b9bcfd-7b0c-48a0-9d06-e13ebcf4c55c","added_by":"auto","created_at":"2024-12-10 10:35:48","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":136062,"visible":true,"origin":"","legend":"\u003cp\u003eCoal desorption curve.\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/fa0843b8b21f7574fc6738ec.png"},{"id":71024846,"identity":"34bc863f-e9d2-4f50-be22-5b4fc12203b2","added_by":"auto","created_at":"2024-12-10 10:19:48","extension":"png","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":123632,"visible":true,"origin":"","legend":"\u003cp\u003eChanges in the desorption rate of coal under various gas equilibrium pressures were examined\u003c/p\u003e","description":"","filename":"5.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/694a7b605140505efee99710.png"},{"id":71026563,"identity":"12d1a6b6-6ee4-4847-bcb3-25d1333e787f","added_by":"auto","created_at":"2024-12-10 10:43:48","extension":"png","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":133463,"visible":true,"origin":"","legend":"\u003cp\u003eProportionality of the desorption rate of coal under different gas pressures.\u003c/p\u003e","description":"","filename":"6.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/e476700c6b11d05591e3d532.png"},{"id":71025621,"identity":"5c25d4fc-227a-4e7d-b425-5797a9b3fbae","added_by":"auto","created_at":"2024-12-10 10:27:48","extension":"png","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":87246,"visible":true,"origin":"","legend":"\u003cp\u003eSummary of the desorption rates of coal under different pressures.\u003c/p\u003e","description":"","filename":"7.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/1dde7d74d5a631980ec091f3.png"},{"id":71025622,"identity":"a2e00a6f-d084-4abf-aa3a-00bd75d156cd","added_by":"auto","created_at":"2024-12-10 10:27:48","extension":"png","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":29484,"visible":true,"origin":"","legend":"\u003cp\u003eRelationship between the effective diffusion coefficient and the degree of metamorphism of coal.\u003c/p\u003e","description":"","filename":"8.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/b4dd0923419a48a86746a440.png"},{"id":71024855,"identity":"8affe72c-b540-4ca6-95f0-bfbaa2db77a1","added_by":"auto","created_at":"2024-12-10 10:19:48","extension":"png","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":153127,"visible":true,"origin":"","legend":"\u003cp\u003eFitting curve of the amount of desorption in lignite.\u003c/p\u003e","description":"","filename":"9.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/2efb6febd494ba6202f0f159.png"},{"id":71024853,"identity":"3b7174f2-a98c-4fb9-8e81-72e6c28b19b6","added_by":"auto","created_at":"2024-12-10 10:19:48","extension":"png","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":156808,"visible":true,"origin":"","legend":"\u003cp\u003eDesorption fitting curve for fiery coal.\u003c/p\u003e","description":"","filename":"10.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/a2f623ca72f07f55ee6fada1.png"},{"id":71024856,"identity":"019c6860-95ef-4fdf-babe-d5c9989743ef","added_by":"auto","created_at":"2024-12-10 10:19:48","extension":"png","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":135678,"visible":true,"origin":"","legend":"\u003cp\u003eDesorption fitting curve of anthracite\u003c/p\u003e","description":"","filename":"11.png","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/2089345964c1cf1df2dfeeb0.png"},{"id":71026913,"identity":"887d49ae-0b1e-4637-ad52-a509cc04ac3d","added_by":"auto","created_at":"2024-12-10 10:51:50","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2258235,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-5182181/v1/f0489476-9e65-481c-880e-b30073072e59.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Influence of metamorphism degree on coal gas desorption characteristics and dynamics models","fulltext":[{"header":"1. Introduction","content":"\u003cp\u003eChina's energy is characterized by its 'rich coal, poor oil, and little gas'. Its proven coal reserves account for 33.8% of the world's coal reserves. With the increase in mining depth, the ground stress and gas pressure of coal seams increase, and dynamic gas disasters in coal mines become more and more serious\u003csup\u003e[3\u0026ndash;5]\u003c/sup\u003e. Studying the desorption and diffusion characteristics of gas not only has an important impact on the development of coalbed methane resources but also is the theoretical basis for the prevention of gas disasters in coal mines. Gas desorption and adsorption are mutually reversible processes that can also be called mass transfer processes\u003csup\u003e[6\u0026ndash;8]\u003c/sup\u003e. In the process of coal adsorption and desorption, there are some complex mechanisms of change, such as the effects of temperature and pressure, which also affect the adsorption and desorption performance of coal\u003csup\u003e[9, 10]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eDifferent ranks of coal have different structures, and their desorption capacity is also different. The Langmuir adsorption constant of coal can be determined by measuring and analyzing the pore distribution characteristics in it, and this can be used to predict the gas content and pressure in coal seams more accurately\u003csup\u003e[11\u0026ndash;14]\u003c/sup\u003e. In addition, it can be used to study the risk of coal and gas outbursts and predict the possibility thereof. The adsorption constant is an important parameter for characterizing the surface adsorption capacity of coal, which is affected by a variety of internal factors, including the degree of coal metamorphism, the composition of coal rock, the conditions of the test, and the setting of parameters\u003csup\u003e[15\u0026ndash;17]\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eIn coal that contains gas, free and adsorbed gases are in a state of dynamic equilibrium, and a new state of equilibrium is produced after changes in the gas pressure and temperature or shocks and oscillations \u003csup\u003e[18, 19]\u003c/sup\u003e. Yang et al.\u003csup\u003e[20]\u003c/sup\u003e suggested that the initial effective diffusion coefficient in the process of gas desorption is related to the pressure, the temperature of the adsorption equilibrium, and the particle size of the coal samples. Pores have an important impact on the adsorption, desorption, seepage, and diffusion of gas, which can affect the diffusion rate, adsorption capacity, and desorption capacity of gas, thus affecting its production efficiency. Li et al.\u003csup\u003e[21]\u003c/sup\u003e found that with a gradual increase in the degree of damage in structural coal, the pore volume and specific surface area also change. The pore volume ratio of large and mesoporous pores gradually increases, but the pore volume ratio of micropores gradually decreases. When the damage degree of structural coal reaches a certain degree, the volume ratios of large pores and mesopores also change, while the volume ratio of micropores remains unchanged.\u003c/p\u003e \u003cp\u003eIn addition, the structure of large and medium pores can also reduce the osmotic pressure of gas and reduce its diffusion rate, thus effectively improving the efficiency of gas desorption\u003csup\u003e[22]\u003c/sup\u003e. Gasparik,M. et al\u003csup\u003e[23]\u003c/sup\u003e. conducted a comprehensive examination of the impact of coal rank on the desorption characteristics of coalbed methane, delving into the alterations in saturation adsorption capacity and adsorption curve throughout the desorption process. Kusuma, M.I., et al.\u003csup\u003e[24]\u003c/sup\u003e employed molecular dynamics simulation to probe the influence of coal rank on coalbed methane desorption, furnishing theoretical elucidation of the impact of coal rank on adsorbent-gas interaction and desorption rate during the desorption process. Gregory, N. et al.\u003csup\u003e[25]\u003c/sup\u003e found that the shorter the micropore length of coal, the shorter the migration distance of gas in the coal body, the shorter the transport time, and the greater the adsorption capacity in the initial stage. Hu et al.\u003csup\u003e[26]\u003c/sup\u003e found that the greater the degree of coal metamorphism, the smaller the influence of large pores on the laws of gas desorption and diffusion, while there is a greater influence of micropores.\u003c/p\u003e \u003cp\u003eSo far, scholars have compared and tested the adsorption and desorption laws of coal in different mining areas and with different coal ranks and determined the relationships between them. These experiments include studying factors such as the degree of coal metamorphism, reservoir pressure, reservoir temperature, and type and content of water in the coal. Among these factors, the coal grade has an important effect on the adsorption and desorption capacity, as the adsorption capacity decreases with the increase in the coal grade. However, at present, there are few studies on the gas desorption and diffusion characteristics of coals with different degrees of metamorphism, and no unified mathematical expression of gas desorption has been formed. In view of this, desorption tests were carried out on coals with different degrees of metamorphism, a more extensive mathematical formula was adopted to fit the gas desorption curve, and the gas release rules of coals with different degrees of metamorphism were obtained. This will provide a reference for coal mine safety.\u003c/p\u003e"},{"header":"2. Methodology","content":"\u003cp\u003e2.1 Sample preparation\u003c/p\u003e\n\u003cp\u003eThe experimental samples included lignite from Anjialing Coal Mine, fiery coal from Yusshuling Coal Mine, and anthracite from Xinyuan Coal Mine, as shown in Figure 1. After sampling, the coal samples to be measured were broken, crushed, and screened, respectively. Experimental coal samples with a particle size of 0.20\u0026ndash;0.3 mm were screened and put into the oven for 6 hours, and the drying temperature was 70 \u0026deg;C. Then, the samples were allowed to stand and cool down to 21 \u0026deg;C, sealed, and stored until use.\u003c/p\u003e\n\u003cp\u003eAccording to the parameters obtained through an industrial analysis, all experimental coal samples were reduced to a 1\u0026ndash;3 mm particle size for use, dried in a drying oven at 70 \u0026deg;C for 6 hours, cooled to 21 \u0026deg;C, and sealed until use. The related gas parameters and maximum vitrinite reflectance of the selected coal samples are shown in Table 1.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 1.\u003c/strong\u003e Coal quality analysis and related gas parameters of the mine\u003c/p\u003e\n\u003cdiv align=\"Left\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"544\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCoal\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003emine\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCoal variety\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 54px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eM\u003csub\u003ead\u003c/sub\u003e/%\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eA\u003csub\u003ed\u003c/sub\u003e/%\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 45px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eV\u003csub\u003edaf\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e/%\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 69px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ePorosity\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e/%\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 63px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ea\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e/(m\u003csup\u003e3\u003c/sup\u003e\u0026middot;t\u003csup\u003e-1\u003c/sup\u003e)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 50px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eb\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e/MPa\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 56px;\"\u003e\n \u003cp\u003e\u003cstrong\u003e\u003cem\u003eR\u003c/em\u003e\u003c/strong\u003e\u003cstrong\u003e\u003csub\u003e0, max\u003c/sub\u003e\u003c/strong\u003e\u003c/p\u003e\n \u003cp\u003e\u003cstrong\u003e/%\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003eAnjialing\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eLignitic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 54px;\"\u003e\n \u003cp\u003e1.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e16.34\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 45px;\"\u003e\n \u003cp\u003e34.25\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 69px;\"\u003e\n \u003cp\u003e3.83\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 63px;\"\u003e\n \u003cp\u003e8.975\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 50px;\"\u003e\n \u003cp\u003e1.146\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 56px;\"\u003e\n \u003cp\u003e0.308\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003eYushuling\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eFiery coal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 54px;\"\u003e\n \u003cp\u003e1.10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e5.31\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 45px;\"\u003e\n \u003cp\u003e41.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 69px;\"\u003e\n \u003cp\u003e3.82\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 63px;\"\u003e\n \u003cp\u003e13.914\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 50px;\"\u003e\n \u003cp\u003e1.258\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 56px;\"\u003e\n \u003cp\u003e0.721\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 80px;\"\u003e\n \u003cp\u003eXinyuan\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 82px;\"\u003e\n \u003cp\u003eAnthracite\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 54px;\"\u003e\n \u003cp\u003e1.76\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 47px;\"\u003e\n \u003cp\u003e13.09\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 45px;\"\u003e\n \u003cp\u003e7.02\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 69px;\"\u003e\n \u003cp\u003e0.13\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 63px;\"\u003e\n \u003cp\u003e40.546\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 50px;\"\u003e\n \u003cp\u003e1.147\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 56px;\"\u003e\n \u003cp\u003e2.382\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eM\u003csub\u003ead\u003c/sub\u003e is moisture, A\u003csub\u003ed\u003c/sub\u003e is ash, V\u003csub\u003edaf\u003c/sub\u003e is volatile, a and b are the\u0026nbsp;Langmuir adsorption constant, \u003cem\u003eR\u003c/em\u003e\u003csub\u003e0,max\u003c/sub\u003e is maximum vitrinite reflectance.\u003c/p\u003e\n\u003cp\u003eThe N\u003csub\u003e2\u003c/sub\u003eGA test was carried out with a Quantachrome NOVA-4200e specific area and pore size analyzer, which is designed for static physical adsorption-high-purity (99.999%) nitrogen adsorption-desorption in a liquid nitrogen environment (77.3 K), and is applicable to pores between 0.35 and 500 nm in diameter.\u003c/p\u003e\n\u003cp\u003eIt can be seen from figure 2 that the gas adsorption volumes of the three coal samples are 2.04 cm\u003csup\u003e3/\u003c/sup\u003eg, 3.87 cm\u003csup\u003e3\u003c/sup\u003e/g and 5.85 cm\u003csup\u003e3\u003c/sup\u003e/g, respectively. The adsorption capacity of anthracite is higher than that of fiery coal and lignite, and the adsorption capacity of fiery coal is higher than that of lignite, indicating that the adsorption capacity of coal increases with the increase of coal metamorphism. There are hysteresis loops in all three kinds of coal, indicating that all coal contains open pores. Lignitic has the smallest hysteresis loop and is not closed, and the inflection points of adsorption and desorption curves are not obvious, and the adsorption isotherms and desorption isotherms basically coincide. This phenomenon indicates that a cylindrical shape with one end closed and a slit shape with four sides open are common in this type of coal. Fiery coal has large hysteresis loops, many open and breathable pores, and good pore connectivity. The adsorption and desorption curves roughly coincide, and the adsorption and desorption curves basically coincide with the higher and lower sections of relative pressure, indicating that there are many semi-closed pores and open and breathable pores in its interior. The adsorption isotherm and desorption isotherm of anthracite show a separate state, and do not close at the stage of relatively low relative pressure, which indicates that anthracite has a high degree of micropore development, and is dominated by cylindrical micropores with one end closed, and the pore connectivity is poor. As one of the important observation indicators of pore structure characteristics in coal, pore size distribution can directly reflect the pore structure characteristics. The pore size distribution of coal based on BJH method analysis is shown in Table 2.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e2.\u003c/strong\u003e\u003cstrong\u003e\u0026nbsp;\u003c/strong\u003ePore size\u0026nbsp;distribution\u0026nbsp;of test coal sample\u003c/p\u003e\n\u003cdiv align=\"Left\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"539\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 95px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCoal variety\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e\u003cstrong\u003ediameter\u003c/strong\u003e\u003cstrong\u003e/nm\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCumulative pore volume\u0026nbsp;\u003c/strong\u003e\u003cstrong\u003e/(cm\u003csup\u003e3\u003c/sup\u003e\u0026middot;g\u003csup\u003e-1\u003c/sup\u003e)\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e\u003cstrong\u003epercentage\u003c/strong\u003e\u003cstrong\u003e/%\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" style=\"width: 95px;\"\u003e\n \u003cp\u003elignitic\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e\u0026lt;10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e0.0021\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e55.3%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e10-100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e0.0011\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e28.9%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e\u0026gt;100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e0.0006\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e15.8%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" style=\"width: 95px;\"\u003e\n \u003cp\u003efiery coal\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e\u0026lt;10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e0.003875\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e65.3%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e10-100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e0.001205\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e20%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e\u0026gt;100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e0.0000860\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e14.7%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd rowspan=\"3\" style=\"width: 95px;\"\u003e\n \u003cp\u003eanthracite\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e\u0026lt;10\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e0.0079\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e80%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e10-100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e0.00131\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e13.3%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd style=\"width: 125px;\"\u003e\n \u003cp\u003e\u0026gt;100\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 216px;\"\u003e\n \u003cp\u003e0.000665\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd style=\"width: 103px;\"\u003e\n \u003cp\u003e6.3%\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003e2.2 Experimental apparatus\u003c/p\u003e\n\u003cp\u003eThis experiment was carried out using an independently developed isothermal adsorption and desorption system that consisted of six main parts: a gas supply and gas control system, adsorption and desorption system, pressure collection system, vacuum degassing system, temperature measurement system, and desorption gas collection system. Test pressure range was 0-6 MPa, as shown in Figure 3.\u003c/p\u003e\n\u003cp\u003e2.3 Experimental scheme and procedure\u003c/p\u003e\n\u003cp\u003eIn order to study the adsorption-desorption kinetic characteristics of three coal samples under different gas pressures, 99.99% CH\u003csub\u003e4\u003c/sub\u003e was used to carry out the test, and three different gas pressures were set up, which were 0.74MPa, 1.06MPa and 1.46MPa respectively. In order to avoid the chance of the test results, three groups of experiments were carried out in each scheme, and one group of data was selected for analysis when there was no large error in the experimental results. The specific test steps were as follows:\u003c/p\u003e\n\u003cp\u003e(1)In the preparation stage of the experiment, an air tightness test was carried out first.\u003c/p\u003e\n\u003cp\u003e(2)Then, 300 g of the coal sample was placed in an adsorption tank. Turn on the constant temperature water bath system and vacuum pump at the same time, degassing the sample to be tested in the constant temperature water bath at 60℃ for 12 hours, and remove the water and gas in the coal sample until the air in the coal sample reaches the vacuum degree of 4 Pa;\u003c/p\u003e\n\u003cp\u003e(3)Gas was injected into the tank with the coal sample at a preset pressure, constant-pressure adsorption was maintained for 24 h, and it was ensured that the internal temperature of the adsorption tank was less than room temperature.\u003c/p\u003e\n\u003cp\u003e(4)Tests were conducted according to the GBT19560-2004 standard, and desorption data were continuously recorded every 5 s for more than 100 minutes.\u003c/p\u003e"},{"header":"3. Results","content":"\u003cp\u003e3.1 Influence of the degree of metamorphism on the amount of gas desorption in coal\u003c/p\u003e\n\u003cp\u003eFigure 4 illustrates the Q-t isothermal gas desorption curve of coal samples with varying degrees of metamorphism under different gas equilibrium pressures over a time period of 100 minutes. It is evident that, under identical external environmental conditions, the cumulative gas desorption of coal increased gradually with the prolongation of desorption time. Once the desorption time reached a certain threshold, the cumulative gas desorption exhibited small fluctuations around a stable value. Interestingly, it was observed that regardless of the desorption time, the curve obtained under high pressure consistently surpassed the curve obtained under low pressure. This observation implies that an increase in equilibrium pressure corresponded to a higher cumulative gas desorption.\u003c/p\u003e\n\u003cp\u003eIn the initial phase of gas desorption, the amount of gas desorbed increased with the degree of coal metamorphism. Coal samples with high metamorphism exhibited a relatively significant increase in gas desorption. For lignite, the gas desorption increased as the pressure increased. The first 10 minutes of desorption were characterized by the highest amount and rate of gas desorption, representing a rapid desorption stage. Subsequently, the desorption rate gradually stabilized, and the gas desorption volume exhibited a slow increase. This stage marked the onset of stable desorption, which occurred approximately after 80 minutes. Similarly, fiery coal demonstrated an increase in gas desorption with increasing pressure. The highest desorption amount was observed within the first 5 minutes, accompanied by a relatively high desorption rate. This period corresponded to the rapid desorption stage. After 5 minutes, while the desorption amount continued to gradually increase, the gas desorption rate slightly decreased, indicating the onset of a stable desorption stage. The desorption capacity of anthracite also varied with changes in pressure, exhibiting an increase with increasing pressure. The highest amount of gas desorption occurred within the first 10 minutes, accompanied by the highest desorption rate, representing the rapid desorption stage. After 10 minutes, the desorption rate gradually stabilized, and the gas desorption volume exhibited a slow increase. Subsequently, a stable desorption stage was reached. Overall, these findings provide insights into the desorption behavior of different coal samples under varying pressures and highlight the distinct stages of rapid and stable desorption.\u003c/p\u003e\n\u003cp\u003eThe gas desorption characteristics of the coal were most pronounced within the first 3 minutes . Based on the degrees of metamorphism, the total amounts of desorption in these three coal samples within the first 10 minutes accounted for 76.1%, 45.2%, and 36.7% of the total desorption, respectively. It can be observed that coal samples with a higher degree of metamorphism reached the limiting value relatively quickly, while low-rank lignite required a longer duration to reach the limit value. However, as the desorption time increased, the gas desorption rate of the highly metamorphic coal samples exhibited a progressively faster decline, resulting in a subsequent deceleration of the desorption rate.\u003c/p\u003e\n\u003cp\u003e3.2 Effect of the metamorphic degree on the gas desorption rate of coal\u003c/p\u003e\n\u003cp\u003eThe changes in the desorption rates of the three coals over time are depicted in Figure 5. It is evident that the trends in the changes in desorption velocities differed among the three coal types. However, the initial gradient of the curve under high pressure was greater than that under low pressure, indicating a higher initial gas desorption velocity under high equilibrium pressure compared to low equilibrium pressure. Additionally, the maximum gas desorption rate under different pressures and the rate of decline in the desorption rate varied with the degree of coal metamorphism. Among the three coal samples, anthracite, which had the highest coal rank, exhibited the smallest initial gas desorption velocity when the equilibrium pressure ranged from 1.36 to 1.46 MPa. However, as the desorption process progressed, its desorption velocity decreased and became the slowest within the same time frame.\u003c/p\u003e\n\u003cp\u003eThe initial desorption rate of the low metamorphic fiery coal was low, and it gradually decreased as the desorption process continued. Among the three coal samples, lignite, with the lowest degree of metamorphism, exhibited the highest initial gas desorption rate, but it also experienced the fastest subsequent decline. Specifically, when the equilibrium pressure was 1.06 MPa, low-rank lignite displayed the fastest initial gas desorption rate, which swiftly decreased as the desorption progressed. On the other hand, gassy coal, with a metamorphic degree intermediate to the other coal samples, demonstrated a relatively faster initial gas desorption rate, which gradually decreased over time. Anthracite had the lowest initial gas desorption rate, and its desorption speed decreased the slowest over the same duration.\u003c/p\u003e\n\u003cp\u003eWhen the equilibrium pressure was 0.74 MPa, the intermediate metamorphic fiery coal exhibited the smallest initial desorption rate. As the desorption process continued, the desorption rate slowly decreased over the same duration. Remarkably, the initial desorption rate of anthracite, with a high degree of metamorphism, did not differ greatly from that of lignite, which had the lowest degree of metamorphism. However, as the desorption process continued, anthracite experienced the least decrease in desorption rate over the same duration, while lignite exhibited the greatest decline.\u003c/p\u003e\n\u003cp\u003eData were collected at half-minute intervals during the initial 10 minutes, and a curve was plotted based on the difference between the former and latter groups. The ratio of the former group\u0026apos;s desorption rate to the latter group\u0026apos;s is presented in Figures 6 and 7. It is evident from the figures that the desorption rate curves for the three experimental coals exhibited distinct trends. The difference in desorption rate within the first 10 minutes under varying pressures was more pronounced for lignite compared to fiery coal and anthracite, implying a greater decline in desorption rate for lignite. Furthermore, the difference in desorption rate for lignite within the initial 10 minutes showed no significant variation between the first 4 minutes and the last 6 minutes, while the difference in desorption rate for fiery coal did not significantly differ from that of the last 6 minutes. The linear correlation between the ratio of differences in the desorption rate within the first 4 minutes was stronger than that of the last 6 minutes, and the linear correlation coefficient increased with the increase in gas pressure.\u003c/p\u003e\n\u003cp\u003e3.3 Effect of the metamorphic degree on the gas diffusion characteristics of coal\u003c/p\u003e\n\u003cp\u003eAfter undergoing the processes of adsorption and desorption, gas permeates the pores of the coal matrix. By utilizing desorption data and applying Fick\u0026apos;s second law of diffusion, it is possible to calculate a physical parameter that characterizes the gas diffusion capacity within coal, known as the effective diffusion coefficient. Through linear regression analysis between the effective diffusion coefficient and the maximum reflectance of vitrinite, the impact of the degree of metamorphism on gas diffusion performance can be examined. The diffusion coefficient signifies the ability of coal to facilitate gas diffusion and its numerical value reflects the rate at which gas migrates through coal pores. In this study, the effective diffusion coefficient was introduced as a means to quantify the gas diffusion capacity. The relevant expressions are provided below:\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e\u003c/p\u003e\n\u003cp\u003ewhere\u0026nbsp;\u003cem\u003eQ\u003c/em\u003e\u003csub\u003et\u003c/sub\u003e is the amount of gas desorption from coal at time t (mL/g); \u003cem\u003eQ\u003c/em\u003e\u003csub\u003e\u0026infin;\u003c/sub\u003e is the limiting gas desorption capacity of coal (mL/g); \u003cem\u003et\u003c/em\u003e is the desorption time (s); \u003cem\u003eD\u003c/em\u003e\u003csub\u003ee\u003c/sub\u003e is the effective diffusion coefficient (\u003cem\u003es\u003c/em\u003e\u003csup\u003e-1\u003c/sup\u003e); \u003cem\u003ep\u003c/em\u003e\u003csub\u003e0\u003c/sub\u003e is the gas pressure during the test (MPa); \u003cem\u003eM\u003c/em\u003e\u003csub\u003ead\u003c/sub\u003e and \u003cem\u003eA\u003c/em\u003e\u003csub\u003ead\u003c/sub\u003e are moisture and ash in coal (%).\u003c/p\u003e\n\u003cp\u003eThe direct determination of the effective gas diffusion coefficient using the formula mentioned above is not feasible. To address this, we set n=1 in Eq. (1) and performed a logarithmic transformation of both sides of the equation, thus converting it into a linear fitting formula for calculation.\u003c/p\u003e\n\u003cp\u003e\u003cimg 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\"\u003e\u003cbr\u003e\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTable 3.\u0026nbsp;\u003c/strong\u003eEffective gas diffusion coefficients of the coal samples.\u003c/p\u003e\n\u003cdiv align=\"Left\"\u003e\n \u003ctable border=\"1\" cellspacing=\"0\" cellpadding=\"0\" width=\"461\"\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 99px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eCoal samples\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eLignite\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eFiery coal\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 111px;\"\u003e\n \u003cp\u003e\u003cstrong\u003eAnthracite\u003c/strong\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd valign=\"top\" style=\"width: 99px;\"\u003e\n \u003cp\u003e\u003cem\u003eD\u003c/em\u003e\u003csub\u003ee\u003c/sub\u003e/s\u003csup\u003e-1\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 117px;\"\u003e\n \u003cp\u003e9.32\u0026times;10\u003csup\u003e-5\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 133px;\"\u003e\n \u003cp\u003e6.18\u0026times;10\u003csup\u003e-5\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd valign=\"top\" style=\"width: 111px;\"\u003e\n \u003cp\u003e0.36\u0026times;10\u003csup\u003e-5\u003c/sup\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cp\u003eThe effective diffusion coefficients of the coal samples, as shown in Table 3, followed a descending order: lignite, fiery coal, and anthracite. This observation markedly contrasts with the pre-desorption amount and adsorption constant of the coal samples mentioned earlier, suggesting that the impact of metamorphism on gas diffusion capacity differs significantly from its influence on adsorption and desorption capacity.\u003c/p\u003e\n\u003cp\u003eBased on the measured results of the maximum reflectivity of vitrinite and the effective gas diffusion coefficients of the coal samples, the relationship between the effective gas diffusion coefficient and the metamorphic degree in the samples was calculated, as demonstrated in Figure 8. As can be observed in Figure 8, the linear fitting coefficient between the effective gas diffusion coefficient and the maximum reflectance of vitrinite was 0.947, indicating a strong negative linear correlation with metamorphism for the effective gas diffusion coefficients of the three coal samples. This correlation suggests that the ability of gas to diffuse in coal decreases as the metamorphic degree increases. The different effective gas diffusion coefficients of the coal samples with varying degrees of metamorphism can be primarily attributed to the maceral components of the coal itself, as well as compaction and dehydration during the coalification process. In coals with a lower degree of metamorphism, there is a higher content of inertinite and chitinite at the maceral level, which results in abundant large pores within these macerals. These pores provide a wide space for gas diffusion, thereby facilitating gas diffusion processes.\u003c/p\u003e"},{"header":"4. Gas desorption dynamics models","content":"\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eNumerous studies by domestic and foreign scholars have focused on the mathematical modeling of gas desorption in coal, resulting in the proposal of various formulas. However, some of these formulas have limitations. To investigate the gas desorption behavior of the three coal samples and identify suitable mathematical expressions, a commonly employed formula was utilized to fit the desorption process under different pressures. The mathematical expressions employed are presented in Table\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003e.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"gridtable\"\u003e\u0026nbsp;\u003ctable id=\"Tab4\" border=\"1\"\u003e\n \u003ccaption language=\"En\"\u003e\n \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e\n \u003cdiv class=\"CaptionContent\"\u003e\n \u003cp\u003eMathematical expression for gas desorption fitting\u003c/p\u003e\n \u003c/div\u003e\n \u003c/caption\u003e\n \u003ccolgroup cols=\"2\"\u003e\u003c/colgroup\u003e\n \u003cthead\u003e\n \u003ctr\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e\u003cem\u003eNO\u003c/em\u003e.\u003c/p\u003e\n \u003c/th\u003e\n \u003cth align=\"left\"\u003e\n \u003cp\u003e-\u003c/p\u003e\n \u003c/th\u003e\n \u003c/tr\u003e\n \u003c/thead\u003e\n \u003ctbody\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFormula 1\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q_{\\text{t}}}=a{t^i}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFormula 2\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q_{\\text{t}}}={{{v_0}\\left[ {{{\\left( {1+t} \\right)}^{1 - n}} - 1} \\right]} \\mathord{\\left/ {\\vphantom {{{v_0}\\left[ {{{\\left( {1+t} \\right)}^{1 - n}} - 1} \\right]} {\\left( {1 - n} \\right)}}} \\right. \\kern-0pt} {\\left( {1 - n} \\right)}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003ctr\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003eFormula 3\u003c/p\u003e\n \u003c/td\u003e\n \u003ctd align=\"left\"\u003e\n \u003cp\u003e\u003cspan class=\"InlineEquation\"\u003e\u003cspan class=\"mathinline\"\u003e\\({Q_{\\text{t}}}={Q_\\infty }\\sqrt {1 - {e^{ - kbt}}}\\)\u003c/span\u003e\u003c/span\u003e\u003c/p\u003e\n \u003c/td\u003e\n \u003c/tr\u003e\n \u003c/tbody\u003e\n \u003c/table\u003e\n\u003c/div\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eIt can be seen from Fig. 10 that the fitting correlation coefficients of the three equations are all above 0.9, indicating a good fitting effect. In terms of the \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e correlation index, when the desorption equilibrium pressure was 0.74 MPa, Formula 1 displayed a lower \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e value compared to the other two empirical formulas, suggesting a weaker fitting correlation. Conversely, the other two formulas exhibited better fitting effects. As the equilibrium pressure increased, the correlation coefficients for all formulas also increased, albeit less noticeably for Formula 2 and Formula 3. When Formula 1 reached 1.46 MPa, its \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e value increased to 0.977, significantly improving the fitting degree. However, Formula 2 had an \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e value of 0.987, and Formula 3 had an \u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e value of 0.990, indicating even better fitting results. Overall, the correlation coefficient (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) increased with increasing equilibrium pressure for all empirical formulas. Formula 2 showed a correlation coefficient range of 0.971\u0026ndash;0.989, while Formula 1 had a range of 0.949\u0026ndash;0.977. Formula 3 exhibited the smallest range of variation for its correlation coefficient, ranging from 0.979 to 0.990, resulting in the best fitting effect among the empirical formulas. The fitting results indicated that the regression coefficients of all three formulas changed with variations in the equilibrium pressure. However, the changes were significant for Formula 1, while relatively minor for Formulas 2 and 3.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eIt can be seen from Fig. 11 that the fitting results for the fiery coal samples were satisfactory across the three different equilibrium pressures. At an equilibrium pressure of 0.74 MPa, Formula 3 exhibited some deviation during the middle stage of gas release, while Formula 1 displayed significant deviation in the middle and late stages. Conversely, Formula 2 demonstrated the highest degree of fitting. At an equilibrium pressure of 1.06 MPa, Formula 2 exhibited the best fitting results, although Formulas 3 and 1 showed some deviation during the early and middle stages of gas dispersion. Under an equilibrium pressure of 1.46 MPa, both Formulas 3 and 1 deviated during the middle and late stages of gas release, while Formula 2 continued to display the highest degree of fitting. This suggests that Formula 2 provided a good fitting effect. Throughout the entire desorption process, the correlation coefficient of Formula 2 varied only between 0.993 and 0.998. Additionally, Formula 1 had a fitting correlation coefficient of 0.993\u0026ndash;0.997, indicating its ability to accurately describe the diffusion process of coal samples. Considering the fitting regression coefficient, Formula 3 exhibited the smallest range of variation, implying that using Formula 3 data in different equilibrium pressure segments to calculate gas loss would result in minimal differences and greater stability.\u003c/p\u003e\n\u003c/div\u003e\n\u003cdiv class=\"BlockQuote\"\u003e\n \u003cp\u003eIt can be seen from Fig.\u0026nbsp;12 that the empirical formula displayed a good fitting effect in the early stage for the anthracite coal samples. The correlation coefficient (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) of the fitting equation gradually increased with increasing equilibrium pressure and then gradually decreased after reaching a certain point. The correlation coefficients obtained using Formulas 2, 1, and 3 were all greater than 0.95. However, Formula 2 consistently yielded correlation coefficients above 0.99 for the entire desorption process, reflecting a strong fitting effect.\u003c/p\u003e\n\u003c/div\u003e\n\u003cp\u003eAt an equilibrium pressure of 0.74 MPa, Formula 2 exhibited some deviation in the early stage, while Formula 3 showed the highest degree of fitting, and Formula 1 displayed deviations during the early, middle, and late stages of gas dispersion. Under an equilibrium pressure of 1.06 MPa, Formula 2 demonstrated the highest degree of fitting, while Formulas 3 and 1 exhibited certain deviations in the early and middle stages. Similarly, under an equilibrium pressure of 1.46 MPa, Formula 2 again had the highest degree of fitting, while Formula 1 deviated during the middle and late stages of gas dispersion.\u003c/p\u003e\n\u003cp\u003eThe fitting results indicated that the overall applicability of the three empirical formulas was relatively good, especially at an equilibrium pressure of 1.46 MPa. Formulas 2, 1, and 3 all obtained high correlation index values, indicating a relatively good fitting effect.\u003c/p\u003e\n\u003cp\u003eIn the experiment, different classical empirical formulas were adopted to conduct a regression analysis on the experimental data obtained for desorption in three groups of coal samples under different equilibrium pressures. The three empirical fitting formulas used for anthracite yielded relatively stable correlation index values, indicating a good fitting effect. The fitting results of Formulas 2, 3, and 1 under an equilibrium pressure of 1.46 MPa were relatively ideal. For lignite, Formula 3 exhibited a relatively large correlation coefficient (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) with a small range of variation, indicating the best fitting effect compared to the other two empirical formulas. Additionally, for fiery coal, Formula 3 accurately described the gas release process of the coal samples.\u003c/p\u003e"},{"header":"5. Conclusions","content":"\u003col\u003e\n \u003cli\u003eCoal samples with a higher degree of metamorphism exhibited a faster attainment of the desorption limit value, whereas low-rank lignite required a longer period to reach this limit. However, as the desorption time increased, the desorption rate of highly metamorphic coal samples gradually declined, resulting in a progressively slower desorption rate.\u003c/li\u003e\n \u003cli\u003eAs coal metamorphism increased, the rate of decline in the gas desorption rate slowed down, and the higher the degree of coal metamorphism, the greater the amount of gas desorption. The effective gas diffusion coefficient of the coal samples exhibited a strongly negative linear correlation with the degree of metamorphism, indicating that the ability of the coal samples to facilitate gas diffusion decreased as the degree of metamorphism increased.\u003c/li\u003e\n \u003cli\u003eAmong the three empirical fitting formulas applied to anthracite, a relatively stable correlation index was obtained, and the fitting effect was satisfactory. For an equilibrium pressure of 1.46 MPa, the fitting results of Formulas 2, 3, and 1 were relatively ideal. Formula 3 yielded a relatively high correlation coefficient (\u003cem\u003eR\u003c/em\u003e\u003csup\u003e2\u003c/sup\u003e) and exhibited a smaller range of coefficient variation for lignite, making it the most effective fitting formula compared to the other two. For fiery coal, Formula 3 was deemed more suitable for describing the gas desorption process of the coal samples.\u003c/li\u003e\n\u003c/ol\u003e"},{"header":"Declarations","content":"\u003cp\u003eAuthor Contributions\u003c/p\u003e\n\u003cp\u003eHuigang Xu: Conceptualization, Data curation, Writing - original draft. Xuyao Qi: Data curation, Formal analysis. Haidong Wang: Funding acquisition, Methodology. Zhongqiu Liang: Formal analysis. Tao Yang: Formal analysis,Visualization. Yongming Zou: Formal analysis. Qi Jiang: Formal analysis. Lei Jin: Formal analysis,Visualization.\u003c/p\u003e\n\u003cp\u003eFunding\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;This research was funded by the Natural Science Foundation of Hebei Province (E2024508006), the National Natural Science Foundation of China (52274200).\u003c/p\u003e\n\u003cp\u003eData Availability Statement\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;The data used to support the findings of this study are available from the corresponding author upon request.\u003c/p\u003e\n\u003cp\u003eConflicts of Interest\u003c/p\u003e\n\u003cp\u003e\u0026nbsp;The data used to support the findings of this study are available from the corresponding author upon request.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n\u003cli\u003eBP. Statistical review of world energy. BP2020. \u003c/li\u003e\n\u003cli\u003eClarkson CR,BustinRM.The effect of pore structure and gas pressure upon the transport properties of coal: a laboratory and modeling study.2. 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Study on porous structure and gas diffusion characteristics of primary structure coal and tectonic coal, \u003cem\u003eCoal Science and Technology\u003c/em\u003e, 2018, 46(03): 103-107.\u003c/li\u003e\n\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":false,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Coalbed methane (CBM), Desorption, Diffusion, Degree of metamorphism","lastPublishedDoi":"10.21203/rs.3.rs-5182181/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-5182181/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003eElucidating the characteristics of desorption and diffusion of coal seam gas is essential for the prevention of gas disasters in coal mines.\u003cstrong\u003e \u003c/strong\u003eIn this study, constant-temperature gas dispersion tests were conducted on lignite, fiery coal, and anthracite to unveil the intricate dynamics of gas diffusion in coal samples under the influence of coal metamorphism. The primary focus was to determine their gas desorption and diffusion characteristics and analyze the mathematical expressions of gas dispersion for coal samples with varying levels of metamorphism during different periods. The findings revealed that coal samples with high metamorphism could attain the desorption limit relatively swiftly, while low-rank lignite required a longer duration to reach the limit. Notably, the gas desorption diffusion rate exhibited significant sensitivity to the coal's metamorphism level. The gas desorption rate within the first 10 minutes was observed to be stable for lignite and fiery coal, while anthracite displayed a faster desorption rate in the initial 4 minutes followed by stability in the subsequent 6 minutes. Furthermore, the effective gas diffusion coefficient demonstrated a robust negative linear correlation with the degree of metamorphism, signifying a decrease in gas diffusion ability with an increase in metamorphism level. Empirical formulas employed to fit anthracite yielded relatively stable correlation indices, with Formula 3 deemed more suitable for depicting the gas desorption processes of lignite and fiery coal.\u003c/p\u003e","manuscriptTitle":"Influence of metamorphism degree on coal gas desorption characteristics and dynamics models","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2024-12-10 10:19:43","doi":"10.21203/rs.3.rs-5182181/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"9d6432dd-aebc-4cc4-9a6e-8c68d0c1e663","owner":[],"postedDate":"December 10th, 2024","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":39769209,"name":"Physical sciences/Engineering"},{"id":39769210,"name":"Physical sciences/Energy science and technology/Fossil fuels"}],"tags":[],"updatedAt":"2024-12-10T10:19:46+00:00","versionOfRecord":[],"versionCreatedAt":"2024-12-10 10:19:43","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-5182181","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-5182181","identity":"rs-5182181","version":["v1"]},"buildId":"cBFmMYwuxLRRLfASyISRj","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}