煤体双重孔隙瓦斯双渗流模型及无因次解算
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摘要
考虑瓦斯在煤层中的解吸、放散与渗流,利用达西定律分别描述煤基质与裂隙内的瓦斯运移,以煤基质与裂隙之间的传质通量为桥梁,发展煤体双重孔隙瓦斯双渗流模型,推导无因次模型,并运用有限差分法进行编程解算。结果表明:瓦斯压力、含量在裂隙内的下降速度要远大于煤基质;基质空间内瓦斯压力及含量的分布具有非均匀性及非稳态性;增大裂隙渗透性或煤层瓦斯压力,或减小煤壁表面瓦斯压力,均能导致瓦斯涌出速度的增大;煤体游离瓦斯含量对瓦斯涌出速度影响较小。结合潘一矿煤层瓦斯参数,对比模拟结果和实测数据,验证了煤体双重孔隙瓦斯双渗流模型的正确性。
Considering the three stages of methane flow in coalseam including desorption,migration and seepage,Darcy?s law was employed to describe gas migration in coal matrix and fracture,and the gas mass transfer flux between coal matrix and fracture was served as a coupling term to develop a mathematical model of methane flow in a dual-porosity,dual-permeability coal seam and its dimensionless model. The finite difference method was applied to develop a numerical solution for the model. The numerical results show that the decline rate of gas pressure and content in fracture is much faster than that in coal matrix. The gas pressure distribution and gas content in coal matrix are heterogeneous and unsteady over time. A higher permeability of fracture,a higher original gas pressure in coal,or a lower gas pressure outside coal wall,lead to a higher gas emission rate. The dual-porosity and dual-permeability model for methane flow in coal seam is validated to be correct by comparing the simulated results and the field data from Panyi mine.
Considering the three stages of methane flow in coalseam including desorption,migration and seepage,Darcy?s law was employed to describe gas migration in coal matrix and fracture,and the gas mass transfer flux between coal matrix and fracture was served as a coupling term to develop a mathematical model of methane flow in a dual-porosity,dual-permeability coal seam and its dimensionless model. The finite difference method was applied to develop a numerical solution for the model. The numerical results show that the decline rate of gas pressure and content in fracture is much faster than that in coal matrix. The gas pressure distribution and gas content in coal matrix are heterogeneous and unsteady over time. A higher permeability of fracture,a higher original gas pressure in coal,or a lower gas pressure outside coal wall,lead to a higher gas emission rate. The dual-porosity and dual-permeability model for methane flow in coal seam is validated to be correct by comparing the simulated results and the field data from Panyi mine.
引文
[1]BUMB A C,MCKEE C R.Gas-well testing in the presence of desorption for coalbed methane and devoian shale[J].SPE Formation Evaluation,1988,3(1):179–185.
[2]MANIK J,ERTEKIN T,KOHLER T E,et al.Development and validation of a compositional coalbed simulator[J].Journal of Canadian Petroleum Technology,2002,41(4):39–45.
[3]高建良,侯三中.掘进工作面动态瓦斯压力分布及涌出规律[J].煤炭学报,2007,32(11):1 127–1 131.(GAO Jianliang,HOU Sanzhong.Dynamic distribution of gas pressure and emission around a diving roadway[J].Journal of China Coal Society,2007,32(11):1 127–1 131.(in Chinese))
[4]尹光志,李铭辉,李生舟,等.基于含瓦斯煤岩固气耦合的钻孔抽采瓦斯三维数值模型[J].煤炭学报,2013,38(4):535–541.(YIN Guangzhi,LI Minghui,LI Shengzhou,et al.3D numerical simulation of gas drainage from boreholes based on solid-gas coupling model of coal containing gas[J].Journal of China Coal Society,2013,38(4):535–541.(in Chinese)).
[5]秦跃平,刘鹏,郝永江,等.钻孔瓦斯涌出的有限差分模型及数值模拟[J].辽宁工程技术大学学报:自然科学版,2014,33(10):1 297–1 231.(QIN Yueping,LIU Peng,HAO Yongjiang,et al.Finite difference model of borehole gas emission and numerical simulation[J].Journal of Liaoning Technical University:Natrual Science,2014,33(10):1 297–1 231.(in Chinese))
[6]ERTKEIN T,KING G A,SCHWREER F C.Dynamic gas slippage:a unique dual-mechanisum approach to the flow of gas in tight formations[J].SPE Formation Evaluation,1986,1(1):43–52.
[7]罗新荣.双重孔隙可压密煤层瓦斯运移的数值模拟[J].重庆大学学报,1998,21(6):29–34.(LUO Xinrong.Study on transport equation and numeric simulation equation of gas migration in coal seam with dual-porosity[J].Journal of Chongqing University,1998,21(6):29–34.(in Chinese))
[8]刘珊,同登科.变形双重介质煤层气拟稳态渗流问题[J].天然气科学,2004,15(6):669–672.(LIU Shan,TONG Dengke.The pseudo steady state flow problem of coalbed gas in deformed media with double porosity[J].Natural Gas Geoscience,2004,15(6):669–672.(in Chinese))
[9]PROB T,ZULEIMA T.K,TURGAY E.Development of a multi-mechanistic,dual-porosity,dual-permeability,numerical flow model for coalbed methane reservoirs[J].Journal of Natural Gas Science and Engineering,2012,8:121–131.
[10]赖枫鹏,李治平,刘晓燕,等.拟稳态扩散的煤层气井动态模型及应用[J].煤炭学报,2014,39(9):1 820–1 825.(LAI Fengpeng,LI Zhiping,LIU Xiaoyan,et al.Dynamic model of coalbed methane well under pseudo-steady diffusion and its application[J].Journal of China Coal Society,2014,39(9):1 820–1 825.(in Chinese))
[11]ANECELL K L,LAMBER S,JOHNSON F S.Analysis of the coalbed degasification process at a seventeen well pattern in the warrior basin of Alabama[C]//SPE Unconventional Gas Recovery Symposium.Pennsylvania.[S.l.]:[s.n.],1980:18–21.
[12]PAUL,G W,SAWYER W K,DEAN R H.Validation of 3D coalbed simulators[C]//The 65th SPE Annual Technical and Exhibition of the Society of Petroleum Engineers.New Orleans,LA:[s.n.],1990:203–210.
[13]张群.煤层气储层数值模拟模型及应用的研究[博士学位论文][D].北京:煤炭科学研究总院,2003.(ZHANG Qun.Study of coal seam gas reservoir simulation numerical model and application[Ph.D.Thesis][D].Beijing:China Coal Research Institute,2003.(in Chinese))
[14]REEVES S,PEKOT L.Advanced reservoir modeling in desorptioncontrolled reservoirs[C]//Proceeding of the SPE Rocky Mountain Petroleum Technology Conference.Keystone:SPE,2001:1–14.
[15]ZOU M,WEI C,YU H,et al.Modeling and application of coalbed methane recovery performance based on a triple porosity/dual permeability model[J].Journal of Natural Gas Science and Engineering,2015,22:679–688.
[16]谭云亮,尹延春,滕桂荣,等.基于Lattice Boltzmann方法的瓦斯渗流模拟研究[J].煤炭学报,2014,39(8):1 446–1 454.(TAN Yunliang,YI Yanchun,TENG Guirong,et al.Simulation research of gas seepage based on Lattice Boltzmann method[J].Journal of China Coal Society,2014,39(8):1 446–1 454.(in Chinese))
[17]滕桂荣,谭云亮,高明.基于lattice Boltzmann方法对裂隙煤体中瓦斯运移规律的模拟研究[J].岩石力学与工程学报,2007,26(增1):3 503–3 508.(TENG Guirong,TAN Yunliang,GAO Ming.Simulation of gas seepage in fissured coal based on Lattice Boltzmann method[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Supp.1):3 503–3 508.(in Chinese))
[18]秦跃平,郝永江,王亚茹,等.基于两种数学模型的煤粒瓦斯放散数值解算[J].中国矿业大学学报,2013,42(6):923–928.(QIN Yueping,HAO Yongjiang,WANG Yaru,et al.Numerical solution of gas emission in coal particle based on two kinds of mathematical models[J].Journal of China University of Mining and Technology,2013,42(6):923–928.(in Chinese))
[19]秦跃平,郝永江,刘鹏,等.封闭空间内煤粒瓦斯解吸实验与数值模拟[J].煤炭学报,2015,40(1):87–92.(QIN Yueping,HAO Yongjiang,LIU Peng,et al.Coal particle gas desorption experiment and numerical simulation in enclosed space[J].Journal of China Coal Society,2015,40(1):87–92.(in Chinese))
[20]秦跃平,刘鹏.煤粒瓦斯吸附规律的实验研究及数值分析[J].煤炭学报,2015,40(4):749–753.(QIN Yueping,LIU Peng.Experimental study on gas adsorption law in coal particle and its numerical analysis[J].Journal of China Coal Society,2015,40(4):749–753.(in Chinese))
[21]王健.煤粒瓦斯放散数学模型及数值模拟[J].煤炭学报,2015,40(4):781–785.(WANG Jian.The mathematical model of gas emission in coal particles and the numerical solution[J].Journal of China Coal Society,2015,40(4):781–785.(in Chinese))
[22]杨其銮,王佑安.煤屑瓦斯扩散理论及其应用[J].煤炭学报,1986,9(3):87–93.(YANG Qiluan,WANG Youan.Diffusion theory and application of coal gas[J].Journal of China Coal Society,1986,9(3):87–93.(in Chinese))
[23]杨其銮.关于煤屑瓦斯放散规律的试验研究[J].煤矿安全,1987,18(2):9–16.(YANG Qiluan.Experimental research on coal gas diffusion[J].Safety in Coal Mines,1987,18(2):9–16.(in Chinese))
[24]刘彦伟,魏建平,何志刚,等.温度对煤粒瓦斯扩散动态过程的影响规律与机理[J].煤炭学报,2013,38(1):100–105.(LIU Yanwei,WEI Jianping,HE Zhigang,et al.Influence rules and mechanisms of temperature on dynamic process of gas diffusion from coal particles[J].Journal of China Coal Society,2013,38(1):100–105.(in Chinese))
[25]刘彦伟.煤粒瓦斯放散规律、机理与动力学模型研究[博士学位论文][D].焦作:河南理工大学,2011.(LIU Yanwei.Study on gas emission rules,mechanism and dynamic model from coal particle[Ph.D.Thesis][D].Jiaozuo:Henan Polytechnic University,2011.(in Chinese))
[26]秦跃平,王健,罗维,等.定压动态瓦斯解吸规律实验[J].辽宁工程技术大学学报:自然科学版,2012,31(5):581–585.(QIN Yueping,WANG Jian,LUO Wei,et al.Experiment of dynamic gas desorption under constant pressure[J].Journal of Liaoning Technical University:Natural Science,2012,31(5):581–585.(in Chinese))
[27]胡守涛.顺层长钻孔区域预抽瓦斯工艺参数优化及应用[硕士学位论文][D].焦作:河南理工大学,2011.(HU Shoutao.Optimization of process parameters and application of along seam long drilling used for pre-pumping coal seam gas[M.S.Thesis][D].Jiaozuo:Henan Polytechnic University,2011.(in Chinese))
[28]刘兵昌.潘集深部煤层瓦斯解吸特征及影响因素分析[硕士学位论文][D].淮南:安徽理工大学,2014.(LIU Bingchang.Study on gas desorption characteristics and influence factors in in Panji deep mining area[M.S.Thesis][D].Huainan:Anhui University of Science and Technology,2014.(in Chinese))
[29]曹垚林.潘一矿综掘巷道煤壁瓦斯涌出规律分析[J].煤矿安全,2009,40(1):19–23.(CAO Yaolin.Study of gas emission law of comprehensive mechanized coal mining wall in Panyi mine[J].Safety in Coal Mines,2009,40(1):19–23.(in Chinese))
[2]MANIK J,ERTEKIN T,KOHLER T E,et al.Development and validation of a compositional coalbed simulator[J].Journal of Canadian Petroleum Technology,2002,41(4):39–45.
[3]高建良,侯三中.掘进工作面动态瓦斯压力分布及涌出规律[J].煤炭学报,2007,32(11):1 127–1 131.(GAO Jianliang,HOU Sanzhong.Dynamic distribution of gas pressure and emission around a diving roadway[J].Journal of China Coal Society,2007,32(11):1 127–1 131.(in Chinese))
[4]尹光志,李铭辉,李生舟,等.基于含瓦斯煤岩固气耦合的钻孔抽采瓦斯三维数值模型[J].煤炭学报,2013,38(4):535–541.(YIN Guangzhi,LI Minghui,LI Shengzhou,et al.3D numerical simulation of gas drainage from boreholes based on solid-gas coupling model of coal containing gas[J].Journal of China Coal Society,2013,38(4):535–541.(in Chinese)).
[5]秦跃平,刘鹏,郝永江,等.钻孔瓦斯涌出的有限差分模型及数值模拟[J].辽宁工程技术大学学报:自然科学版,2014,33(10):1 297–1 231.(QIN Yueping,LIU Peng,HAO Yongjiang,et al.Finite difference model of borehole gas emission and numerical simulation[J].Journal of Liaoning Technical University:Natrual Science,2014,33(10):1 297–1 231.(in Chinese))
[6]ERTKEIN T,KING G A,SCHWREER F C.Dynamic gas slippage:a unique dual-mechanisum approach to the flow of gas in tight formations[J].SPE Formation Evaluation,1986,1(1):43–52.
[7]罗新荣.双重孔隙可压密煤层瓦斯运移的数值模拟[J].重庆大学学报,1998,21(6):29–34.(LUO Xinrong.Study on transport equation and numeric simulation equation of gas migration in coal seam with dual-porosity[J].Journal of Chongqing University,1998,21(6):29–34.(in Chinese))
[8]刘珊,同登科.变形双重介质煤层气拟稳态渗流问题[J].天然气科学,2004,15(6):669–672.(LIU Shan,TONG Dengke.The pseudo steady state flow problem of coalbed gas in deformed media with double porosity[J].Natural Gas Geoscience,2004,15(6):669–672.(in Chinese))
[9]PROB T,ZULEIMA T.K,TURGAY E.Development of a multi-mechanistic,dual-porosity,dual-permeability,numerical flow model for coalbed methane reservoirs[J].Journal of Natural Gas Science and Engineering,2012,8:121–131.
[10]赖枫鹏,李治平,刘晓燕,等.拟稳态扩散的煤层气井动态模型及应用[J].煤炭学报,2014,39(9):1 820–1 825.(LAI Fengpeng,LI Zhiping,LIU Xiaoyan,et al.Dynamic model of coalbed methane well under pseudo-steady diffusion and its application[J].Journal of China Coal Society,2014,39(9):1 820–1 825.(in Chinese))
[11]ANECELL K L,LAMBER S,JOHNSON F S.Analysis of the coalbed degasification process at a seventeen well pattern in the warrior basin of Alabama[C]//SPE Unconventional Gas Recovery Symposium.Pennsylvania.[S.l.]:[s.n.],1980:18–21.
[12]PAUL,G W,SAWYER W K,DEAN R H.Validation of 3D coalbed simulators[C]//The 65th SPE Annual Technical and Exhibition of the Society of Petroleum Engineers.New Orleans,LA:[s.n.],1990:203–210.
[13]张群.煤层气储层数值模拟模型及应用的研究[博士学位论文][D].北京:煤炭科学研究总院,2003.(ZHANG Qun.Study of coal seam gas reservoir simulation numerical model and application[Ph.D.Thesis][D].Beijing:China Coal Research Institute,2003.(in Chinese))
[14]REEVES S,PEKOT L.Advanced reservoir modeling in desorptioncontrolled reservoirs[C]//Proceeding of the SPE Rocky Mountain Petroleum Technology Conference.Keystone:SPE,2001:1–14.
[15]ZOU M,WEI C,YU H,et al.Modeling and application of coalbed methane recovery performance based on a triple porosity/dual permeability model[J].Journal of Natural Gas Science and Engineering,2015,22:679–688.
[16]谭云亮,尹延春,滕桂荣,等.基于Lattice Boltzmann方法的瓦斯渗流模拟研究[J].煤炭学报,2014,39(8):1 446–1 454.(TAN Yunliang,YI Yanchun,TENG Guirong,et al.Simulation research of gas seepage based on Lattice Boltzmann method[J].Journal of China Coal Society,2014,39(8):1 446–1 454.(in Chinese))
[17]滕桂荣,谭云亮,高明.基于lattice Boltzmann方法对裂隙煤体中瓦斯运移规律的模拟研究[J].岩石力学与工程学报,2007,26(增1):3 503–3 508.(TENG Guirong,TAN Yunliang,GAO Ming.Simulation of gas seepage in fissured coal based on Lattice Boltzmann method[J].Chinese Journal of Rock Mechanics and Engineering,2007,26(Supp.1):3 503–3 508.(in Chinese))
[18]秦跃平,郝永江,王亚茹,等.基于两种数学模型的煤粒瓦斯放散数值解算[J].中国矿业大学学报,2013,42(6):923–928.(QIN Yueping,HAO Yongjiang,WANG Yaru,et al.Numerical solution of gas emission in coal particle based on two kinds of mathematical models[J].Journal of China University of Mining and Technology,2013,42(6):923–928.(in Chinese))
[19]秦跃平,郝永江,刘鹏,等.封闭空间内煤粒瓦斯解吸实验与数值模拟[J].煤炭学报,2015,40(1):87–92.(QIN Yueping,HAO Yongjiang,LIU Peng,et al.Coal particle gas desorption experiment and numerical simulation in enclosed space[J].Journal of China Coal Society,2015,40(1):87–92.(in Chinese))
[20]秦跃平,刘鹏.煤粒瓦斯吸附规律的实验研究及数值分析[J].煤炭学报,2015,40(4):749–753.(QIN Yueping,LIU Peng.Experimental study on gas adsorption law in coal particle and its numerical analysis[J].Journal of China Coal Society,2015,40(4):749–753.(in Chinese))
[21]王健.煤粒瓦斯放散数学模型及数值模拟[J].煤炭学报,2015,40(4):781–785.(WANG Jian.The mathematical model of gas emission in coal particles and the numerical solution[J].Journal of China Coal Society,2015,40(4):781–785.(in Chinese))
[22]杨其銮,王佑安.煤屑瓦斯扩散理论及其应用[J].煤炭学报,1986,9(3):87–93.(YANG Qiluan,WANG Youan.Diffusion theory and application of coal gas[J].Journal of China Coal Society,1986,9(3):87–93.(in Chinese))
[23]杨其銮.关于煤屑瓦斯放散规律的试验研究[J].煤矿安全,1987,18(2):9–16.(YANG Qiluan.Experimental research on coal gas diffusion[J].Safety in Coal Mines,1987,18(2):9–16.(in Chinese))
[24]刘彦伟,魏建平,何志刚,等.温度对煤粒瓦斯扩散动态过程的影响规律与机理[J].煤炭学报,2013,38(1):100–105.(LIU Yanwei,WEI Jianping,HE Zhigang,et al.Influence rules and mechanisms of temperature on dynamic process of gas diffusion from coal particles[J].Journal of China Coal Society,2013,38(1):100–105.(in Chinese))
[25]刘彦伟.煤粒瓦斯放散规律、机理与动力学模型研究[博士学位论文][D].焦作:河南理工大学,2011.(LIU Yanwei.Study on gas emission rules,mechanism and dynamic model from coal particle[Ph.D.Thesis][D].Jiaozuo:Henan Polytechnic University,2011.(in Chinese))
[26]秦跃平,王健,罗维,等.定压动态瓦斯解吸规律实验[J].辽宁工程技术大学学报:自然科学版,2012,31(5):581–585.(QIN Yueping,WANG Jian,LUO Wei,et al.Experiment of dynamic gas desorption under constant pressure[J].Journal of Liaoning Technical University:Natural Science,2012,31(5):581–585.(in Chinese))
[27]胡守涛.顺层长钻孔区域预抽瓦斯工艺参数优化及应用[硕士学位论文][D].焦作:河南理工大学,2011.(HU Shoutao.Optimization of process parameters and application of along seam long drilling used for pre-pumping coal seam gas[M.S.Thesis][D].Jiaozuo:Henan Polytechnic University,2011.(in Chinese))
[28]刘兵昌.潘集深部煤层瓦斯解吸特征及影响因素分析[硕士学位论文][D].淮南:安徽理工大学,2014.(LIU Bingchang.Study on gas desorption characteristics and influence factors in in Panji deep mining area[M.S.Thesis][D].Huainan:Anhui University of Science and Technology,2014.(in Chinese))
[29]曹垚林.潘一矿综掘巷道煤壁瓦斯涌出规律分析[J].煤矿安全,2009,40(1):19–23.(CAO Yaolin.Study of gas emission law of comprehensive mechanized coal mining wall in Panyi mine[J].Safety in Coal Mines,2009,40(1):19–23.(in Chinese))