A rapid and accurate direct measurement method of underground coal seam gas content based on dynamic diffusion theory

Yanwei Liu,Yang Du ,Zhiqiang Li ,Fajun Zhao ,Weiqin Zuo ,Jianping Wei ,Hani Mitri

a School of Safety Science and Engineering,Henan Polytechnic University,Jiaozuo 454000,China

b The Collaborative Innovation Center of Coal Safety Production of Henan Province,Jiaozuo 454000,China

c Department of Mining and Materials Engineering,McGill University,Montreal H3A0E8,Canada

d School of Civil Engineering,Henan Polytechnic University,Jiaozuo 454000,China

ABSTRACT Coal seam gas content is frequently measured in quantity during underground coal mining operation and coalbed methane (CBM) exploration as a significant basic parameter.Due to the calculation error of lost gas and residual gas in the direct method,the efficiency and accuracy of the current methods are not inadequate to the large area multi-point measurement of coal seam gas content.This paper firstly deduces a simplified theoretical dynamic model for calculating lost gas based on gas dynamic diffusion theory.Secondly,the effects of various factors on gas dynamic diffusion from coal particle are experimentally studied.And sampling procedure of representative coal particle is improved.Thirdly,a new estimation method of residual gas content based on excess adsorption and competitive adsorption theory is proposed.The results showed that the maximum error of calculating the losing gas content by using the new simplified model is only 4%.Considering the influence of particle size on gas diffusion law,the particle size of the collected coal sample is below 0.25 mm,which improves the measurement speed and reflects the safety representativeness of the sample.The determination time of gas content reduced from 36 to 3 h/piece.Moreover,the absolute error is 0.15–0.50 m3/t,and the relative error is within 5%.A new engineering method for determining the coal seam gas content is developed according to the above research.

Keywords:Coal seam gas content Dynamic diffusion model Determination method Lost gas content Desorption characteristics

1.Introduction

Coal mine gas disaster is always the most dangerous in the process of coal mining[1].The determination of coal seam gas content is one of the fundamental key works involving the regional prediction of coal and gas outburst,validity check of outburst prevention,prediction of coal mine gas emission and designing gas drainage systems[2,3].According to the Regulations on Prevention and Control of Coal and Gas Outbursts in China,when the longwall length is less than 120 m,this criterion requires at least one point measuring coal seam gas content every 30–50 m in mining region along stopping direction after gas drainage.On the other hand,at least two points should be measured when the working face length is more than 120 m.If the requirements are not completed in time,it will affect the normal production of coal mines,so the efficiency and accuracy of determining the coal seam gas content are particularly important.In the development of coalbed methane (CBM),the content of CBM has guiding significance for the estimation of CBM reserves,the formulation of CBM development plan and the prediction of its production capacity [4].Therefore,the rapid and accurate determination of gas content is of great practical significance for coal mine safety production and CBM development.

Gas diffusion law and model of coal particles are the fundamental theoretical bases for determining gas content.At present,the semi-empirical formula based on the classic diffusion model is commonly employed in coal mine and CBM industry to calculate the gas content.The gas diffusion model based on Fick’s law of homogeneous coal particles was proposed by Crank [5].Ruckenstein et al.[6] regarded coal particles as a double-porosity structure composed of macropores and micropores,and established a gas diffusion model of double-porosity coal particles.Liu [7] proposed a new constitutive model for gas diffusion from coal particles with tri-disperse pore structure by considering the difference in characteristics between soft coal and hard coal.Li et al.[8]constructed a new mathematical model for gas diffusion in coal particles,then analyzed and discussed the influences of particle size and the adsorption equilibrium pressure on the methane gas diffusion rate,gas diffusion quantity,and diffusion coefficient.Other empirical/semi-empirical models,such as Barrer type[9],Bolt type[10],Winter type [11],and Wang type [12],are also applicable.Among these models,the Barrer type is one of the most widely adopted conventional methods for directly determining the gas content.

Although these theories and models meet the needs of engineering to some extent,there are still deficiencies in some aspects.Even though some models can accurately describe the initial stage of gas desorption,they cannot predict the entire desorption process.Others can exactly predict the final desorption amount,but cannot match the trend of the process.Especially for coal seams that have experienced tectonic deformation,the pore structure parameters and connectivity of deformed coal are highly different from that of un-deformed coal.Furthermore,the initial desorption rate of the deformed coal particles is faster,and the proportion of the lost gas content to the total gas content is higher than that of the un-deformed coal [13],so the classical diffusion model is not suitable for deformed coal that is strongly damaged [14].The current diffusion model of coal particle cannot accurately calculate the lost gas content,resulting in a large error.Although some scholars have put forward an empirical formula for calculating the gas loss in deformed coal,due to the lack of theoretical basis,universality of the empirical formula needs to be verified in specific mining areas [15].The diffusion model based on the dynamic diffusion coefficient proposed by Li et al.[16]can accurately describe the diffusion process of the deformed coal,but it is not sufficient to determine the on-site gas content directly.

At present,the most frequently used method for determining gas content is the direct method,and the gas composition varies with different kinds of measurements,while the sum of the desorption gas,the lost gas and the residual gas is the gas content[3].Based on different measurement methods of the residual gas content,the direct method can be divided into two types,i.e.the degassing method (in negative pressure) and the natural desorption method (in normal atmosphere pressure) [17].The degassing method first degases the coal sample under vacuum and measures the degassing amount of the coal sample before and after pulverizing.The sum of the two is the residual gas content,and the measurement result is relatively veracious.The latter is used to measure the desorption amount of the coal sample before and after pulverizing at normal pressure and the formula is used to calculate the un-desorbed gas content at normal atmosphere.The sum of the three is the residual gas content,and the measurement time of the natural desorption method is shorter than that of the degassing method.In China,the Chongqing Branch of the Coal Science Research Institute has developed a set of DGC gas content measuring device,which is suitable for directly measuring gas content in coal mines by natural desorption method.It has been widely popularized in China,and has improved the efficiency of measuring gas content of coal seams to a certain degree.However,the following problems still exist in the application of determination technology of gas content in coal mine.

(1) The measurement time of the degassing method generally requires more than two days.Moreover,it takes about 8 h to determine the content of desorbed gas by natural desorption method at atmospheric pressure,while the nondesorbed gas content at atmospheric pressure is taken into account.This results in longer processing time,which is challenging to satisfy the demands of current mining sites.

(2) The calculation accuracy of gas loss needs to be improved ulteriorly,especially for deformed coal that affected by tectonic deformation.

(3) The measurement efficiency of residual gas content at normal atmosphere is low.The un-desorbed gas content at normal atmosphere was calculated by the Langmuir equation,which significantly deviated from the actual values,especially when the CH4component is lower than 80%.

The on-site measurement results by using the degassing method and natural desorption method are different.This paper selected 37 coal samples for the determination of gas content by degassing method and natural desorption method.The measurement results of the natural desorption tend to be generally low,which is about 75% on average compared to that of the degassing method.The maximum error between the two results is 50%,the error is irregular and cannot be corrected by coefficient.The gas content measured by natural desorption method did not accord with the requirements of national standards or coal mine gas control standards.The test results are shown in Fig.1.The main difference between these two methods lies in the different methods for determination of residual gas content.In order to gain the residual gas content under natural desorption,it is essential to calculate the un-desorbed gas content by using the Langmuir equation,which is the primary source of error [18].

Based on the dynamic gas diffusion model of coal and considering various factors comprehensively,this paper puts forward the calculation model of gas content loss in engineering,which improves the calculation accuracy of residual gas content and optimizes the measurement process of gas content.The precision and efficiency of determining the gas content has been significantly improved,especially for the deformed coal which has experienced tectonic deformation.

2.Dynamic diffusion theory and simplified mathematical model of gas loss

Classical diffusion models include homogeneous spherical coal gas diffusion model,dual-porosity diffusion model,and triple pore structure diffusion model.The homogeneous spherical coal particle model assumes a complex porous medium as a single pore system.The model is simple and widely used.At present,the empirical formulas used in the determination of coal seam gas content and coal and gas outburst prediction parameters are derived from the model.However,because it does not reflect the difference in pore structure and has poor adaptability,it is only suitable for the initial gas emission law of low-damage coal.For the tectonic soft coal that has been severely damaged,large deviations result in inaccurate measurement of coal seam gas content and desorption index of the drilling cuttings,and prediction of coal and gas outbursts and detection of extraction effects are not reliable.

The dual-porosity diffusion model [6,19,20] contains a parallel diffusion model and a continuity model.The parallel model has a simple structure and is convenient for mathematical calculations,so it is widely used.However,the model has the following two shortcomings:(1) Derivation of a faster diffusion rate based on assumptions will become the dominant diffusion,but this is contrary to the actual situation;(2)The model requires that gas molecules maintain a balance between micropores and macropores.On the other hand,it is believed that the diffusion rate of molecules in micropores is slow.The continuity model can better describe the entire process of coal particle gas diffusion.The dual-porosity diffusion model has a better performance,and it is generally used in the experimental diffusion modelling,but much too complicated to be applied in practice [21].The main disadvantages of the dualporosity diffusion model are:(1)The actual situation of coal particle gas diffusion is not considered in the modeling process,nor can the reason for the difference in the desorption rules of soft coal and hard coal be explained;(2)The gas adsorption process of coal particles is assumed to be a linear Henry isothermal adsorption process,which is significantly different from the Langmuir equation;(3)The model considers the emission of free gas as a diffusion process,which is not in line with the actual situation.A large number of experimental studies have shown that the free gas in the coal particles will be released at the instant of desorption,and there is still a pressure difference between the inside and the outside of the coal particles during the process of releasing.

Liu [7] established a triple-pore gas diffusion model using Dw,Dz,and Ddto represent the diffusion coefficients of micropores,mesopores (transition pores),and macropores in coal particles.In the diffusion process,the gas in the micropores diffuses to the surface of the coal particles through the mesopores and macropores,the gas in the mesopores diffuses to the surface of the coal particles through the macropores,and the gas in the macropores directly diffuses to the surface of the coal particles,that is,Dw≠Dz≠Dd.The general solution of heterogeneous coal particle gas diffusion model with triple-pore structure is still an infinite series solution,which is basically consistent with the experimental data fitting results.However,it involves many parameters and is not easy to apply in engineering practice.

Coal is a porous medium with a large pore size span and complex structure,whose pore characteristics are the physical bases of gas adsorption,desorption,diffusion,and seepage [22].Therefore,the pore structure and pore size distribution of coal are fatal factors affecting the gas diffusion [23].According to the diffusion theory of gas in porous media,there are three modes of gas diffusion in porous media i.e.micropore diffusion,surface diffusion,and crystal diffusion.These three diffusion modes can all occur during the coal gas diffusion process,but the main mode is the micropore diffusion.The pore structure of actual coal particles is very intricate,and the diffusion path is zigzag.Lots of experimental results show that the gas diffusion coefficient continuously decays with time,especially the attenuation rate of the deformed coal is more obvious,which is mainly caused by the uneven distribution of gas adsorption positions in coal particles [16,24].Different pore sizes and irregular distribution in coal particles lead to the fact that the gas adsorbed on different pore surfaces must be desorbed through diverse diffusion paths [25].The diffusion path is composed of pores with different sizes and different diffusion coefficient,which makes their resistance to gas diffusion different.The gas with shorter path and small diffusion resistance will be released in priority,while the gas with long diffusion path and high diffusion resistance is released slowly.Macroscopically,it shows that the gas diffusion coefficient changes continuously with the diffusion time [7,16,26].

A schematic diagram of a multi-scale pore diffusion model is shown in Fig.2[1]to illustrate its pore model.In Fig.2,M1 denotes a series of particle clusters;M2denotes the secondary coal particle clusters,and so on.These are the analogous to n-grade coal particle clusters Mn,similar to a multi-sphere containing structure.P1represents the first-order diffusion pores between a series of particle clusters M2; P2is the secondary diffusion pore between a series of particle clusters M3; P3is analogized up to several nanometersized pores Pn,with each stage of a series of particle clusters and inter-granular pores having similar structures.

The path in which the gas passed through the inter-particle pores was curved and consecutive.The curved pores shown in Fig.2 were further abstracted into the tandem multi-scale pore structure illustrated in Fig.3 so as to analyze the diffusion of gas.In Fig.3,the parameter d denotes the pore diameter;D1is the diffusion coefficient corresponding to the first-order pore P1;D2is the diffusion coefficient corresponding to the second-order pore P2;and D3and D4are successively analogized to the diffusion coefficient Dnof the n-order pores.

Based on the relationship between multi-scale pore distribution and multi-stage distribution of diffusion coefficient shown above,a new hypothesis for the physical model of gas diffusion was raised on the basis of the undermentioned requirements:(1) Coal particles are isotropic spheres; (2) Heterogeneous multi-scale pores form the coal particle porosity system,and pores of different sizes are distributed from large to small in succession;(3)The gas diffusion law in coal particles follows the continuum mechanics assumption.The above three points are the physical bases for establishing the mathematical model of this research.

The mathematical model for the dynamic diffusion coefficients of gas diffusion in coal particles with multi-scale pores was established by using the formula shown in Eq.(1) [16].

where Qtis the cumulative gas desorption amount in cm3; t the cumulative desorption time,including exposure time and downhole desorption time; Q∞the cumulative gas desorption in cm3as diffusion time approaches infinity; β the attenuation coefficient;D0the initial diffusion coefficient in cm2/s;and r the radius of a coal particle in cm.

The new model with the dynamic diffusion coefficients is adequate to accurately describe the entire gas diffusion process.Therefore,it could be applied to estimate the potential loss in the determination processes of gas content,and then to solve the fundamental theoretical problems for accurate determination of the gas content.However,this model is challenging to apply to engineering,so the authors simplified the dynamic diffusion coefficient model to obtain a new model for calculating the gas loss applied in engineering.

Fig.3.The diffusion coefficients corresponding to multi-scale pores in diffusion model.

First,a simplified formula of the dynamic diffusion coefficient was obtained as follows.

where D is the dynamic diffusion coefficient attenuated with time and Dt can be obtained by

By substituting Eq.(3) into Eq.(2),the following Eq.(4) was obtained.

Eq.(4) could be simplified to Eq.(5) as follows.

where t′is the actual desorption time; and t0the loss time from exposing the coal sample to loading the coal sample canister.

3.Factors affecting the law of gas desorption

Several momentous factors affecting the gas diffusion law include particle size,deformation degree,gas adsorption equilibrium pressure,moisture,and temperature,which result in the law of gas desorption to present differently under different conditions [26–31].This paper studied the variation of gas desorption characteristics under different conditions to verify the accuracy,reliability and applicability of the new simplified model,and to determine the most suitable coal sample particle size in the rapid determination theory.Since laboratory testing processes are more standard than on-site testing,the gas loss can be measured more exactly.The new simplified model is based on dynamic diffusion coefficient(Eq.(6));and the most widely used Barrer formula were adopted to fit the measured data with Origin 9.0.The results show that the fitness of the new simplified model to the data of gas desorption is far higher than that of the Barrer formula under any conditions; and the results are more suitable for describing the gas desorption characteristics of coal particles.The new model estimates the lost gas content more accurately and reliably,with a maximum relative error of only 4%,which has a distinct advantage over the Barrer formula.

The experimental system for studying the gas diffusion law of coal particles was designed and processed based on the experimental devices in China’s standard MT/T 752-1997,GB/T 19560-2004,and AQ/T 1065-2008.The specific principle is described in the document [7].

3.1.Effect of particle size of coal on gas desorption

Particle size is one of the essential factors to study the gas desorption characteristics of coal particles[23].The experimental conditions of gas desorption experiment were as follows:the adsorption equilibrium pressure was 0.74±0.01 MPa,and the temperature was 30 ± 1 °C; the gas desorption characteristics of coal particles with different particle sizes at different times were investigated.The particle sizes of coal samples were 3.00–6.00,1.00–3.00,0.50–1.00,0.25–0.50,and <0.25 mm.

The results are shown in Fig.4 and Table 1.It can be seen from the Fig.4 that the value of Qt/Q∞increases with the decrease of particle size,and the smaller the particle size is,the shorter the time to reach the ultimate desorption amount.These show that the coal sample with particle size less than 0.25 mm has the highest desorption capacity,which mainly shows the diffusion and desorption characteristics of the coal sample.The new simplified model and the cylinder formula are used to fit the experimental data of gas desorption of two kinds of coal particles.The fitting results show that the new simplified model has an excellent fitting effect.When the loss time is 2 min,the fitting coefficient of deformed coal is between 0.98856 and 0.99955,and that of undeformed coal is between 0.99291 and 0.99956.The fitting coefficient of Barrer formula is relatively low,especially for deformed coal,the correlation coefficient is 0.15771–0.89540,which is inconsistent with the experimental data.The results show that the classical Barrer model cannot accurately reveal the gas desorption law of structural coal,which is also the reason why larger coal samples were used in previous measurement.

3.2.Effect of deformation degree of coal on gas desorption

According to the Regulations on Prevention and Control of Coal and Gas Outburst,the deformation degree is one of the crucial indexes for identifying coal and gas outburst.The gas desorption characteristics of deformed and un-deformed coal are quite different.The experimental conditions for the gas adsorption and desorption experiments were as follows:the adsorption equilibrium pressure was 0.74 ± 0.01 MPa,and the temperature was 30 ± 1 °C.The gas desorption characteristics of coal particles with different degrees of deformation were studied to fit the new model.

The experimental results are shown in Fig.5 and Table 2.At the same time,the more severe the coal deformation,the higher the cumulative gas diffusion rate Qt/Q∞.The new simplified model has a better fit for coal with a higher degree of deformation,with a fitting coefficient between 0.99598 and 0.99973.The Barrer formula has a higher fitting degree to the gas desorption characteristics of coal with lower deformation degree,but the fitting degree is still lower than that of the new simplified model.The initial velocity of gas desorption in deformed coal is higher than that of un-deformed coal,which may cause the gas loss of deformed coal in the first 2 min to be higher than that of un-deformed coal.When calculating the gas content of coal seam,if the formula cannot accurately estimate the gas loss,the measurement error will increase.The new simplified model is very accurate for calculating the gas loss of coals with different degrees of deformation.

3.3.Effect of equilibrium pressure on gas desorption

The adsorption equilibrium pressure has an immense impact on gas desorption characteristics[28].To verify the applicability of the new simplified model under different equilibrium pressure,coal samples with particle size of 1–3 mm are selected with adsorption equilibrium pressures of 0.50±0.01,0.74±0.01,1.50±0.01,and 2.50 ± 0.01 MPa,respectively.After adsorption equilibrium,the entire desorption process of coal sample was recorded at a constant ambient temperature.During the desorption process,atmospheric pressure P0was considered to be a constant,and the diffusion parameters were calculated using experimental data.

Fig.4.Gas loss comparison of deformed and un-deformed coal between new simplified model and Barrer model under different particle size (loss time is 2 min).

Table 1Data fitted by the new model and the Barrer model.

Fig.5.Gas loss comparison of coal particles with different degrees of deformation based on the new simplified model and Barrer model (loss time is 2 min).

The results are shown in Fig.6 and Table 3.The results show that when the loss time is 2 and 5 min,the cumulative gas loss increases with the increase of the equilibrium pressure.Through the laboratory loss amount verification,using the measured gas desorption data within 120 min,the loss amount with the loss time of 2 and 5 min is calculated,which proves that the fitting result of the new model is far more reliable than that of Barrer model,with the error only between 0.68% and 0.84%,and the correlation coefficient of above 0.97819.Therefore,the new simplified model has better applicability for describing gas desorption characteristics and can describe the whole process of coal desorption more accurately.

3.4.Effect of temperatures on gas desorption

With the increase of mining depth,the underground ambient temperature gradually increases due to the influence of the geothermal gradient.Besides,the spontaneous combustion of coal and the drilling process of underground drilling will increase the temperature of coal samples,and the temperature also has a significant influence on the gas desorption characteristics [30].Coal samples with the particle size of 1–3 mm were selected and set at 10 ± 1,20 ± 1,30 ± 1,and 40 ± 1 °C under the adsorption equilibrium pressure of 0.74±0.01 MPa to investigate the applicability of the new model for gas desorption at different temperatures.

The experimental data are shown in Fig.7 and Table 4.With the increase of temperature,the gas diffusion rate(Qt/Q∞) of coal particle increases,and the final desorption increases significantly.The new model is used to fit the experimental data of coal particle gas diffusion under different temperatures.The fitting results show that the new model can fit the experimental data well,and the accuracy and reliability of calculating the loss at different temperatures are very high.The fitting coefficient of the new model is between 0.98480 and 0.99418,the calculation result is accurate,the error is 0.64%–1.32%; the fitting coefficient of the Barrer formula is between 0.66302 and 0.82750,the error is between 14.0% and 17.6%,and the calculated loss is obviously small.Theresults show that the new simplified model is more suitable for coal particle gas desorption at different temperatures.

Table 2Data fitted by the new model and the Barrer model respectively.

Fig.6.Comparison of the gas losses of coal particles based on the new simplified model and the Barrer model under different equilibrium pressure conditions at different loss time.

Table 3Data fitted by the new model and the Barrer model at loss time of 2 and 5 min,respectively.

Fig.7.Gas loss comparison of coal particles based on the new simplified model and Barrer model at different temperatures (loss time is 2 min).

3.5.Effect of moisture of coal on gas desorption

The gas desorption ability of coal can vary due to diverse natural and human factors such as groundwater,coal seam injection,hydraulic punching,and the inner water of coal [31].With the increase of water content,the cumulative diffusion amount and diffusion coefficient of gas emission of coal particle decrease.The conditions for the adsorption equilibrium pressure of gas desorption experiment were 0.74 ± 0.01 MPa,the temperature was 30 ± 1 °C,and the coal sample size was between 1 and 3 mm.The applicability of the new model in the case of the same particle size and different moisture content(dry coal sample,raw coal sample,wet coal sample,and equilibrium water coal sample) was investigated.

The experiment results are shown in Fig.8 and Table 5.The experimental results show that,during the same desorption time,the gas diffusion rate of coal particles decreases with the increase of water content,and water has a significant effect of inhibiting gas diffusion.The new model can accurately describe the gas diffusion law of coal particles with different water content and has a high degree of fitting.The calculation of gas loss in the first 2 min is more accurate,but the fitting degree of the Barrer formula is low,especially when the coal sample is relatively dry.The error will be greater.

4.A new method for rapid and accurate determination of gas content

The degassing method is applied to determine the gas content of coal seams with high correctness,but the defect is that the method takes a long time.The accuracy of the measurement results of the natural desorption method is low.Both methods have their drawbacks.Especially in the determination of some deformedcoal,the error between the two methods will be greater.Based on the dynamic gas diffusion model,this paper proposes a method that can quickly and accurately determining the coal seam gas content.This method is more suitable for deformed coal.The flow chart of the new method is shown in Fig.9.

Table 4Data fitted by the new simplified model and the Barrer model at different temperatures,respectively.

Fig.8.Gas loss comparison of coal particles with different moistures based on the new simplified model and Barrer model (loss time is 2 min).

4.1.Sampling process requirements

At present,in China,the method of coal sampling underground is generally the method of coal sampling in pressure tuyere,and the method of coal sampling in threaded hole.The sampling time must be within 5 min.However,the friction between the drill pipe and the coal wall during the sampling of these two methods will cause the coal to fall from the coal wall,and it is easy to mix the samples,especially in soft coal seam that has been subjected to tectonic deformation,so it is impossible to realize the fixed-point sampling truly,which will affect the accuracy of the results.For the sake of calculating the gas loss,a double air duct drill pipe sampling device was used.Its main feature was that it has a nonretractable drill pipe and is able to achieve continuous fixedpoint sampling.With a sampling depth more than 100 m,more than 3 kg coal could be sampled in 2 min.

Liu and Liu [26] studied the gas desorption characteristics of coal samples with different particle sizes and found that the coal particle is the most representative when the particle size is less than 0.25 mm.The accuracy of coal seam gas content determination results is also related to the adsorption performance of coal samples.This paper also studies the adsorption capacity of coal samples with different particle sizes.The experiment selected coal samples with different particle sizes and used the WY-98B adsorption apparatus developed by Shenyang Coal Research Institute to measure the adsorption constant.The results are shown in Fig.10.It can be seen that the coal sample with a particle size of 0.20–0.25 mm has a immensely improved adsorption capacity compared with that of coal with particle size of 1.00–3.00 mm;and the adsorption capacity of the coal sample with a particle size of<0.10 mm is substantially the same as that with a particle size of 0.20–0.25 mm.Moreover,according to the research of Hou et al.[32] and Mastalerz et al.[33],from the analysis of the differences between different particle size of pore structure,the smaller the particle size,the larger the specific surface area,and the particle size of 0.25 mm below the coal particle can more precisely represent the actual pore structure of coal.Therefore,if the coal particle size is less than 0.25 mm,the more representative the results of the actual situation of coal seam gas content,the more accurate the measurement.However,in the previous methods,coal samples with larger particle size were generally selected because the models used to describe the gas desorption characteristics,such as the Barrer formula,have an inferior fitting degree of coal particles with the proper particle size<0.25 mm,which basically cannot describe the gas desorption characteristics.Furthermore,the direct selection of coal samples with a particle size <0.25 mm during downhole sampling also reduces the subsequent process of pulverizing coal samples,shortens the time that coal samples exposed to the air,reduces the loss of gas,and improves the accuracy.Therefore,the new method will select coal samples with particle size<0.25 mm when sampling.

Fig.9.The basic principle and procedure of the new method for gas content measurement.

Fig.10.The adsorption law of coal samples fitted by Langmuir equation.

Table 5Data fitted by the new simplified model and the Barrer model with different moistures,respectively.

4.2.Estimation of losing gas content

The determination of the desorption amount and desorption speed of coal samples is mainly for estimating the amount of loss.The key to estimating the amount of loss is to find a suitable model and method for estimation.Laboratory research found that the new model is more applicative than the Barrer formula to describe the law of soft coal gas desorption,especially in terms of loss estimation,the new model has distinct advantages.In order to verify the field applicability of the loss calculation method,the newly proposed model(Eq.(6))and the Barrer formula were used to compare the content of lost gas.The results were as follows:(1)The fitting index of the new simplified model was between 0.98987 and 0.99733,while that of the Barrer formula was between 0.91766 and 0.96955.Consequently,the new simplified model showed a higher degree of correlation; (2) The gas quantity calculated by the new simplified model was larger than the calculated value of the Barrer formula,which means that the new simplified model has higher accuracy; (3) The discrepancy between the degassing method and the natural desorption method had increased when using the new model relative to the Barrer formula.As shown in Figs.11 and 12,the difference in the volume of gas loss between the degassing method and natural desorption method increased from 61 to 112 cm3and from 15 to 131 cm3,respectively.and the error of the degassing method and natural desorption method was minished.The absolute error of the natural desorption method for the determination gas content was reduced by 0.17 and 0.28 cm3/g,respectively.No matter which sampling method is used,the new model can get better fitting results than Barrer model.

4.3.Estimation of residual gas content

The results of the determination of the same kind of coal sample by degassing method and atmospheric natural desorption method are quite different.The main reason is that there is an error between the residual gas content calculated by the formula and the actual measurement value of the instrument used for the degassing method.The results of the degassing process are accurate,but the measuring period is correspondingly long,and the time of natural desorption method is faster,but the error of the results is too large.Therefore,it is essential to optimize the calculation method of atmospheric natural desorption method for calculating the residual gas amount.

Fig.11.Determination resulted of degassing method and natural desorption method in the Xin’an Coal Mine.

Fig.12.Determination resulted of degassing method and natural desorption method in the Xin’an Coal Mine 14211 tunnel.

4.3.1.Excess adsorption

The first method to obtain Xb(excess adsorption quantity,cm3/g) is given in the standard method—the Direct Method of Determining Coalbed Gas Content in the Mine (GB/T23250-2009),as shown in Eq.(7)[34].The second method used a high-pressure volumetric method (MT/T752) to determine the natural pressure adsorption capacity.It was determined that the sum of the natural pressure adsorption amount and the free gas content in the standard state was Xb(the free gas content was obtained through a calculation process).It was revealed by Eq.(11) that the second Xbobtaining method was to replace the first part of Eq.(7) with a high-pressure volumetric method (the principle of the highpressure volumetric method was the Langmuir model).

where a and b are the Langmuir constants in cm3/g and MPa,respectively; Adand Madthe percentages of ash and moisture in the coal,respectively; k the porosity in cm3/cm3; and γ the weight of the coal in g/cm3.

Theoretically speaking,both Xbacquisition methods were based on the Langmuir equation of single-component gas (Eq.(8)).The classical adsorption models use the surface Gibbs margin instead of the actual experimental variables.The adsorption capacity of this study’s method is shown in Eq.(9).

where p is the adsorption pressure in MPa; nabsolutethe absolute adsorption amount of the Langmuir equation in mol/kg; nexcessthe excess adsorption amount in mol/kg; ntotalthe amount of the adsorbed gas in mol; ρgasthe density of the adsorbate in mol/m3;Vkthe adsorption of the pores and gaps in m3in the experimental unit(including the pores of the coal and unfilled spaces in the unit);and msorbentthe mass of experimental coal sample in kg.

Eq.(8) represents the Langmuir absolute adsorption equilibrium (indicating it satisfies monolayer adsorption,no adsorption interaction,adsorbent structure,chemically homogenous surface,etc).Eq.(9)represents the excess adsorption equilibrium (indicating possible multilayer adsorption,adsorbate interactions,adsorbent heterogeneity,etc.).Thus,when measuring the gas content in coal seams,there will be an unavoidable error between these two methods.The error will be the result of the excess adsorption equilibrium caused by the difference between the excess adsorption amount and the Langmuir model’s adsorption amount.Therefore,it is required to determine whether the error still meets the requirements of engineering precision.

4.3.2.Competitive adsorption

When the volume fraction of CH4is less than 80%,the singlecomponent Langmuir equation cannot represent the true adsorption and desorption processes of the mixed gas due to the influences of the competitive adsorption between gases.For this reason,the adsorption and desorption should be represented by the Langmuir extension equation,as shown in Eq.(10).

where i is the gas of natural composition in the coal seam.

In the measurement of coal seam gas content,when the gas pressure of a coal sample varied from atmospheric pressure to absolute pressure,the amount of the desorbed gas could be calculated using Eq.(10),which had the ability to correct some errors calculated in Eq.(7) (taking into account the interactions of the adsorbates).It was found that the pressure of the mixed desorbed gas during the calculation satisfies the mixed gas equation,as shown in Eq.(11) [18].

where K is the Boltzmann constant; T the temperature of the system; nithe amount of moles of the constituent gas in mol; and pithe pressure in Pa.

In the gas weathered zones,the coal seam gas content tends to be low and the distribution is irregular.Nevertheless,this was not the focus of current research.Near the gas weathered zones,the gas composition of coal was mainly CH4,but it also contained other gases.It was necessary to study the effect of the competitive gas adsorption and desorption on the examination of gas content.

Ruthven [35] introduced a separation factor to express the selectivity of mixed gas adsorption.When the molar fractions of the adsorbed phases of gases i and j were xiand xj,respectively,and the molar fractions of the free phase were yiand yj,then xi+xj=1 and yi+yj=1.The separation factor α could then be expressed by Eq.(12).

The free gas concentration was obtained by measuring the gas content of coal seam (gas chromatographic analysis and calculation of the natural gas composition).And then the concentration of the adsorbed phase can be calculated on grounds of the separation coefficient.

4.3.3.Residual gas content calculations

The three gases that determine the gas content of coal seams are mainly CH4,N2and CO2; and a considerable part of coal samples only contain the first two gas components.When the gas in the coal samples contained two natural components,the gas content of coal seams was measured employing the two methods shown in Table 6.The coal samples in the Table 6 contained two gases (CH4and N2),and the natural components were the results of the atmospheric pressure method.In Table 6,the M coal samples were from Maling Mountain,and the J coal samples were from Jiaozuo.The numbers (1 to 3) behind the ‘‘M” and ‘‘J” represent the experimental number of each sample.

Table 7 lists some characteristic parameters of the coal in the experimental mine areas.The separation factors in the Table 7 were calculated according to Eq.(12).The adsorption constants indicated that the adsorption order of the three gases in the coal samples from the two mining areas was CO2> CH4> N2,and the maximum separation factor was αCO2/N2.

After calculating the gas partial pressure according to the natural components of each coal sample in Table 6,the separation factor in Table 7,and the Eq.(12),then the gas partial pressure can be calculated by using Eq.(11).For the gas partial pressure of CH4and N2,Eq.(10)and Table 7 are used to calculate the adsorption quantity of CH4and N2.The sum of the adsorption quantity of the two gases is the residual gas volume corrected by the extended Langmuir equation.See Table 8 for the calibration results and parameters.However,it can be found that the corrected result by the natural desorption method is smaller.In order to make the result of the natural desorption method consistent with the result of the degassing method,the residual gas content in the normal atmosphere calculated by the Eq.(7) is corrected by a coefficient of 1.45.And the gas content is calculated (Table 8).The data in Tables 6 and 8 indicate that when the coal sample contains two natural components (CH4and N2),the gas content measured by the degassing method is generally larger than the natural desorption method,and it is revised by the Langmuir expansion equation.The error increases from 5.1%–17.3%to 5.4%–18.3%,indicating that when the coal sample contains CH4and N2,the main cause that affects the natural desorption method is the adsorbed quantity of gas in micropores and the adsorbed quantity of gas in closed pores,but they have a competitive adsorption.After the residual gas content in the normal atmosphere is corrected by the coefficient of 1.45,the error of the measurement result by the atmospheric pressure method is 0.8%–4.8%,and the consistency of the gas content in the degassing method and the atmospheric pressure desorption method is basically realized.

Table 9 illustrates the results when the coal gas samples contained three components.It can be seen that the volume ratio of the CH4in the Table 9 was greater than 77%.However,the content of N2and CO2had not exceeded 15%.These findings indicated that there were competing adsorption between the three gases.During the measurement,the influence of external factors on the measurement results was excluded as much as possible.As can be seen in Table 9,the results measured by the degassing method are larger than those of the natural desorption method.The correction values of the extended Langmuir equation are obtained by using the data in Table 9 and the correction methods of the above two natural component gases,as shown in Table 10.The error before correction in the Table 10 was computed to be between 0.9% and 9.1%.However,the error had become smaller after the corrections with the post-correction error ranging from 0 to 1.6%.

It was observed that when the natural gas compositions of the coal seams contained N2,CH4,and CO2,the order of adsorption capacity was CO2> CH4> N2.It was found that CO2was always preferentially adsorbed,while N2was consistently at a disadvantage.The fractionation of the gaseous components due to competitive adsorption resulted in the decrease of the adsorption quantity of N2and the increase in CO2[36].Therefore,the competitive adsorption of the extended Langmuir equation is more suitable for the calculation of the residual gas content in the normal atmosphere.The calculated values obtained by using the extended Langmuir equation were larger than those of Langmuir equation and the error of the extended Langmuir model was found to be less than 5%,which successfully met the general engineering requirements.

When the natural gas compositions of the coal seams contained N2and CH4,the calculated values obtained using Eq.(10) were smaller than those obtained using Eq.(7).The measurement errors of some coal samples before and after the correction were observed to be relatively large.The errors were determined to be mainly caused by the excessive adsorption amount,which could be corrected using a coefficient method (coefficient=1.45).

Table 6Coal gas content of the two natural components.

Table 7Results of determination of the adsorption constants of the coal samples.

Table 8Corrected results (two natural components).

Table 9Coal seam gas content of the three natural components.

Table 10Corrected results (three natural components).

5.On-site verification

The sampling location of the comparison experiment is at 14211 face of Xinan Coal Mine of Yima Coal Industry Group,which belongs to 2-1 coal seam and is located in the outburst danger zone of the mine,and the coal rank is meager-mean.The maximum gas content and gas pressure of 14211 working face are up to 10.99 m3/t and 1.4 MPa,respectively,which has the coal and gas outburst hazard.

There are three coal lithotypes in 14211 working face:bright type,semi-bright type,and semi-dark type,and the degree of coal damage is up to Ⅳtype tectonic coal.The geographical structure ofthe 14211 working face is simple,it is monoclinic structure and interlayer slip structure.The geological conditions of the 14211 working face are simple,the folds are gentle,the thickness of the 2-1 coal seam is different and the change is obvious.

Table 11Comparison of the determination results of coal seam gas content in a mine face.

This study deduced a simplified model for estimating the gas loss content and improved the accuracy and efficiency of calculating the gas content in coal seams.A complete method for determining gas content in coal seams is proposed.The same set of samples were used to determine the gas content of the coal seam by the degassing method and the new method,respectively.Twenty representative samples were selected.

The comparison test results are shown in Table 11.Among the 20 comparison samples,the absolute error between the degassing method results and the natural desorption method results were between 0.15 and 0.5 m3/t,and the relative error was within 5%.The new method has the ability to complete the indoor testing of 5 to 6 coal samples in half a day.Thus,the required testing time for gas content has been effectually reduced from 36 to 3 h.The new method is used to quantify the gas content in the study area and significant effects are achieved in improving production efficiency.

6.Conclusions

The conclusions of this study are as follows.

(1) Based on the physical and mathematical models of gas dynamic diffusion,a calculation model for quickly calculating the gas loss is proposed.The accuracy of the model under various factors has been verified through experiments.The results show that compared with the classical model,the new model has the advantages of faster calculation of gas loss and higher fitting degree.It can accurately calculate the gas loss affected by different particle size,loss time and other factors,and can comprehensively describe the whole process of coal gas diffusion.

(2) The concept of competitive adsorption was introduced in the determination of residual gas content.The results show that when the volume fraction of CH4is less than 80%,the calculation error of residual gas content can be controlled within 5% by coefficient correction method,which improves the overall accuracy of measurement.

(3) The new method uses drilled powder with the particle size less than 0.25 mm.The coal sample of this particle size has larger gas adsorption capacity and faster desorption speed,which saves the pulverizing time of the coal sample and improves the accuracy of the subsequent measurement.The results of on-site verification show that the relative error of the new method is within 5%,and the measurement time of coal seam gas content is significantly reduced,which greatly improves production efficiency and safety.

Acknowledgements

Financial supports for this work,provided by the National Natural Science Foundation of China (51774119,51374095,and 51604092),the primary research projects of critical scientific research in Henan Colleges and Universities (19zx003),Program for Innovative Research Team in University of Ministry of Education of China (IRT_16R22) and State Key Laboratory Cultivation Base for Gas Geology and Gas Control (Henan Polytechnic University) (WS2018A02),are gratefully acknowledged.