基于不同方向模量损失率的含瓦斯煤各向异性渗透模型
|
摘要
煤是自然界中一种常见的沉积岩,它具有显著的各向异性特征。然而目前针对煤体渗透特性研究,多数学者为了简化问题,多假设煤体为各向同性材料,提出了相应的各向同性渗透模型。这类模型并不能完全反映含瓦斯煤气-固耦合真实工程和室内试验的实际情况。假设煤体为横观各向同性,推导出以不同方向模量损失率为关键参数的煤体各向异性渗透模型,在此基础上,推导出含瓦斯煤的气-固耦合控制方程,并植入Comsol计算平台,系统研究煤体各向异性对气体扩散和渗透的影响。理论和数值研究结果表明:不同方向的模量损失率R_i反映出煤体结构各向异性变化程度,若R_i不同,其煤体各方向渗透特性也不相同;煤体渗透率的改变主要受解吸附效应和有效应力作用双重影响,R_i反映了这两种效应对于渗透率的影响程度;单轴应变或位移控制边界条件下,水平方向的模量损失率R_1对于垂直方向的煤体渗透率改变量△k_z的影响程度大于对水平方向的煤体渗透率改变量△k_x的影响程度,垂直方向模量损失率R_3对△k_z的影响则弱于对于△k_x的影响。
Coal, as a typical sedimentary rock, has a naturally anisotropic feature. For simplicity, coal is considered as an isotropic material in the study of coal permeability, and the corresponding isotropic permeability models have been proposed. However, the actual situation of gas-solid coupling in the field and laboratory tests cannot be well reflected by these models. In this paper, coal is treated as transversely isotropic, and an anisotropic permeability model is developed by using different directional modulus reduction ratios as the key parameters. The developed model is further implemented in COMSOL multiphysics software to comprehensively investigate the effect of coal anisotropy on gas diffusion and penetration. Theoretical and numerical results show that different directional modulus reduction ratios(R_i) reflect the degree of anisotropy of the coal structure. When R_i is different, the coal permeability is also not the same. Coal permeability is mainly governed by mechanical effects and desorption effects, and meanwhile, these two effects on each direction of the permeability of coal are controlled by boundary conditions. R_i is a reflection of these two effects. Under the uniaxial strain or displacement control boundary condition, the horizontal modulus reduction ratio(R_1) has more significant effect on the amount of permeability change in the vertical direction(△k_z) than on that in the horizontal direction(△k_x). However, the vertical modulus reduction ratio(R_3) has less effect on△k_x than on△k_z.
Coal, as a typical sedimentary rock, has a naturally anisotropic feature. For simplicity, coal is considered as an isotropic material in the study of coal permeability, and the corresponding isotropic permeability models have been proposed. However, the actual situation of gas-solid coupling in the field and laboratory tests cannot be well reflected by these models. In this paper, coal is treated as transversely isotropic, and an anisotropic permeability model is developed by using different directional modulus reduction ratios as the key parameters. The developed model is further implemented in COMSOL multiphysics software to comprehensively investigate the effect of coal anisotropy on gas diffusion and penetration. Theoretical and numerical results show that different directional modulus reduction ratios(R_i) reflect the degree of anisotropy of the coal structure. When R_i is different, the coal permeability is also not the same. Coal permeability is mainly governed by mechanical effects and desorption effects, and meanwhile, these two effects on each direction of the permeability of coal are controlled by boundary conditions. R_i is a reflection of these two effects. Under the uniaxial strain or displacement control boundary condition, the horizontal modulus reduction ratio(R_1) has more significant effect on the amount of permeability change in the vertical direction(△k_z) than on that in the horizontal direction(△k_x). However, the vertical modulus reduction ratio(R_3) has less effect on△k_x than on△k_z.
引文
[1]POMEROY C D,ROBINSON D J.The effect of applied stresses on the permeability of a middle rank coal to water[J].International Journal of Rock Mechanics and Mining Sciences&Geomechanics Abstracts,1967,4(3):329-343.
[2]KOENIG R A,STUBBS P B.Interference testing of a coalbed methane reservoir[C]//SPE unconventional gas technology symposium.Louisville,Kentucky:Society of Petroleum Engineers,1986.
[3]GASH B W,RICHARD F V,POTTER G,et al.The effects of cleat orientation and confining pressure on cleat porosity,permeability and relative permeability in coal[J].Paper,1992,9321:17-21.
[4]DAY S,FRY R,SAKUROVS R.Swelling of Australian coals in supercri-tical CO2[J].International Journal of Coal Geology,2008,74(1):41-52.
[5]SEIDLE J R,HUITT L G.Experimental measurement of coal matrix shrinkage due to gas desorption and implications for cleat permeability increases[C]//International Meeting on Petroleum Engineering.Beijing:Society of Petroleum Engineers,1995.
[6]SHI J Q,DURUCAN S.Drawdown induced changes in permeability of coalbeds:A new interpretation of the reservoir response to primary recovery[J].Transport in Porous Media,2004,56:1-16.
[7]PALMER I,MANSOORI J.How permeability depends on stress and pore pressure in coalbeds:a new model[C]//Annual Technical Conference&Exhibition.Denver:Society of Petroleum Engineers,1996.
[8]张宏学,刘卫群,朱立.页岩储层裂隙渗透率模型和试验研究[J].岩土力学,2015,36(3):719-729.ZHANG Hong-xue,LIU Wei-qun,ZHU Li.Fracture permeability model and experiments of shale gas reservoirs[J].Rock and Soil Mechanics,2015,36(3):719-729.
[9]GU F,CHALATURNYK R.Permeability and porosity models considering anisotropy and discontinuity of coalbeds and application in coupled simulation[J].Journal of Petroleum Science and Engineering,2010,74(3-4):113-131.
[10]祝捷,姜耀东,赵毅鑫,等.考虑吸附作用的各向异性煤体有效应力[J].中国矿业大学学报,2010,39(5):699-704.ZHU Jie,JIANG Yao-dong,ZHAO Yi-xin,et al.Effective stress of anisotropic coal considering adsorption[J].Journal of China University of Mining&Technology,2010,39(5):699-704.
[11]ROBERTSON E P.Measurement and modeling of sorption-induced strain and permeability changes in coal[D].State of Colorado,United States:Colorado School of Mines,2005.
[12]吕闰生.受载瓦斯煤体变形渗流特征及控制机制研究[D].北京:中国矿业大学(北京),2014.LüRun-sheng.Research on deformation-seepage characteristics and mechanism of gassy coal under load[D].Beijing:China University of Mining&Technology(Beijing),2014.
[13]LIU J S,ELSWORTH D,BRADY B H.Linking stressdependent effective porosity and hydraulic conductivity fields to RMR[J].International Journal of Rock Mechanics and Mining Sciences,1999,36:581-596.
[14]魏明尧.含瓦斯煤体气固耦合渗流机制及应用研究[D].徐州:中国矿业大学,2013.WEI Ming-yao.Study of gas-solid coupling seepage flow in coal containing methane and its application[D].Xuzhou:China University of Mining&Technology,2013.
[15]OLIVIER COUSSY.Poromechanics[M].Chichester,West Sussex:John Wiley&Sons Ltd,2004:71-112.
[16]HARPALANI S,SCHRAUFNAGEL R A.Shrinkage of coal matrix with release of gas and its impact on permeability of coal[J].Fuel,1990,69(5):551-556.
[2]KOENIG R A,STUBBS P B.Interference testing of a coalbed methane reservoir[C]//SPE unconventional gas technology symposium.Louisville,Kentucky:Society of Petroleum Engineers,1986.
[3]GASH B W,RICHARD F V,POTTER G,et al.The effects of cleat orientation and confining pressure on cleat porosity,permeability and relative permeability in coal[J].Paper,1992,9321:17-21.
[4]DAY S,FRY R,SAKUROVS R.Swelling of Australian coals in supercri-tical CO2[J].International Journal of Coal Geology,2008,74(1):41-52.
[5]SEIDLE J R,HUITT L G.Experimental measurement of coal matrix shrinkage due to gas desorption and implications for cleat permeability increases[C]//International Meeting on Petroleum Engineering.Beijing:Society of Petroleum Engineers,1995.
[6]SHI J Q,DURUCAN S.Drawdown induced changes in permeability of coalbeds:A new interpretation of the reservoir response to primary recovery[J].Transport in Porous Media,2004,56:1-16.
[7]PALMER I,MANSOORI J.How permeability depends on stress and pore pressure in coalbeds:a new model[C]//Annual Technical Conference&Exhibition.Denver:Society of Petroleum Engineers,1996.
[8]张宏学,刘卫群,朱立.页岩储层裂隙渗透率模型和试验研究[J].岩土力学,2015,36(3):719-729.ZHANG Hong-xue,LIU Wei-qun,ZHU Li.Fracture permeability model and experiments of shale gas reservoirs[J].Rock and Soil Mechanics,2015,36(3):719-729.
[9]GU F,CHALATURNYK R.Permeability and porosity models considering anisotropy and discontinuity of coalbeds and application in coupled simulation[J].Journal of Petroleum Science and Engineering,2010,74(3-4):113-131.
[10]祝捷,姜耀东,赵毅鑫,等.考虑吸附作用的各向异性煤体有效应力[J].中国矿业大学学报,2010,39(5):699-704.ZHU Jie,JIANG Yao-dong,ZHAO Yi-xin,et al.Effective stress of anisotropic coal considering adsorption[J].Journal of China University of Mining&Technology,2010,39(5):699-704.
[11]ROBERTSON E P.Measurement and modeling of sorption-induced strain and permeability changes in coal[D].State of Colorado,United States:Colorado School of Mines,2005.
[12]吕闰生.受载瓦斯煤体变形渗流特征及控制机制研究[D].北京:中国矿业大学(北京),2014.LüRun-sheng.Research on deformation-seepage characteristics and mechanism of gassy coal under load[D].Beijing:China University of Mining&Technology(Beijing),2014.
[13]LIU J S,ELSWORTH D,BRADY B H.Linking stressdependent effective porosity and hydraulic conductivity fields to RMR[J].International Journal of Rock Mechanics and Mining Sciences,1999,36:581-596.
[14]魏明尧.含瓦斯煤体气固耦合渗流机制及应用研究[D].徐州:中国矿业大学,2013.WEI Ming-yao.Study of gas-solid coupling seepage flow in coal containing methane and its application[D].Xuzhou:China University of Mining&Technology,2013.
[15]OLIVIER COUSSY.Poromechanics[M].Chichester,West Sussex:John Wiley&Sons Ltd,2004:71-112.
[16]HARPALANI S,SCHRAUFNAGEL R A.Shrinkage of coal matrix with release of gas and its impact on permeability of coal[J].Fuel,1990,69(5):551-556.