开采扰动下考虑损伤破裂的深部煤体渗透率模型研究
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摘要
为了研究深部煤体在开采扰动影响下的渗透率演化规律,以三向应力条件下的煤体渗透率模型为基础,从吸附解吸作用引起裂隙变形和损伤破裂造成煤基质弹性模量劣化的角度进行理论推导,引入内膨胀应变系数的概念,同时基于Drucker-Prager破坏准则的损伤本构关系建立了两种考虑煤体损伤破裂的渗透率演化模型——指数型和立方型,并且对常规三轴加载、开采扰动加卸载和改变气体压力下的瓦斯渗透试验结果进行了拟合分析。结果表明:所构建的两种模型可以较好地反映常规三轴加载和开采扰动加卸载下煤体渗透率的分区段变化特征,也可以描述有效围压恒定条件下煤体渗透率随气体压力升高而降低的规律。在开采扰动加卸载和改变气体压力的试验中,指数型的拟合效果略优于立方型。研究结果可为深部煤炭开采及瓦斯抽采的工作提供指导。
To investigate the permeability evolution of deep coal under the influence of mining disturbance, two forms of permeability model including the damage and fracture effect were established. These two forms were exponential form and cubic form, respectively. These two permeability models were based on the previous coal permeability model in three-dimensional(3 D) stress state. The derivation process included two aspects, i.e., the fracture deformation caused by adsorption and the deterioration of elastic modulus from matrix caused by damage. Meanwhile, the internal swelling ratio and the damage constitutive based on Drucker-Prager failure criterion were introduced into the models. According to permeability tests under conventional triaxial compression, loading-unloading under mining disturbance and changing the gas pressure, the permeability of coal in the tests were analyzed in detail. The results show that these two models can reflect the permeability evolution in the conventional triaxial compression and loading-unloading tests. Moreover, these two models can represent the decrease of coal permeability with the increase of gas pressure under the constant effective confining pressure condition. In the loading-unloading and changing the gas pressure tests, the fitted results in exponential form are slightly better than those in cubic form. This study provides a useful reference for developing the technology of deep coal mining and gas extraction.
To investigate the permeability evolution of deep coal under the influence of mining disturbance, two forms of permeability model including the damage and fracture effect were established. These two forms were exponential form and cubic form, respectively. These two permeability models were based on the previous coal permeability model in three-dimensional(3 D) stress state. The derivation process included two aspects, i.e., the fracture deformation caused by adsorption and the deterioration of elastic modulus from matrix caused by damage. Meanwhile, the internal swelling ratio and the damage constitutive based on Drucker-Prager failure criterion were introduced into the models. According to permeability tests under conventional triaxial compression, loading-unloading under mining disturbance and changing the gas pressure, the permeability of coal in the tests were analyzed in detail. The results show that these two models can reflect the permeability evolution in the conventional triaxial compression and loading-unloading tests. Moreover, these two models can represent the decrease of coal permeability with the increase of gas pressure under the constant effective confining pressure condition. In the loading-unloading and changing the gas pressure tests, the fitted results in exponential form are slightly better than those in cubic form. This study provides a useful reference for developing the technology of deep coal mining and gas extraction.
引文
[1]谢和平,周宏伟,薛东杰,等.煤炭深部开采与极限开采深度的研究与思考[J].煤炭学报,2012,37(4):535-542.XIE He-ping,ZHOU Hong-wei,XUE Dong-jie,et al.Research and consideration on deep coal mining and critical mining depth[J].Journal of China Coal Society,2012,37(4):535-542.
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[5]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):1-16.
[6]亓宪寅,李家卓,王威.基于不同方向模量损失率的含瓦斯煤各向异性渗透模型[J].岩土力学,2018,39(2):635-643.QI Xian-Yin,LI Jia-zhuo,WANG Wei.An anisotropic permeability model of coal containing methane based on different directional modulus reduction ratios[J].Rock and Soil Mechanics,2018,39(2):635-643.
[7]尹光志,蒋长宝,许江,等.煤层气储层含水率对煤层气渗流影响的试验研究[J].岩石力学与工程学报,2011,30(增刊2):3401-3406.YIN Guang-zhi,JIANG Chang-bao,XU Jiang,et al.Experimental study of influences for water content in coalbed gas reservoirs on methane seepage[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Supp.2):3401-3406.
[8]陈金刚,徐平,赖永星,等.煤储层渗透率动态变化效应研究[J].岩土力学,2011,32(8):2512-2516.CHEN Jin-gang,XU Ping,LAI Yong-xing,et al.Research on dynamic variation effect of coal reservoirs permeability[J].Rock and Soil Mechanics,2011,32(8):2512-2516.
[9]CONNELL L D,LU M,PAN Z J.An analytical coal permeability model for triaxial strain and stress conditions[J].International Journal of Coal Geology,2010,84(2):103-114.
[10]PERERA M S A,RANJITH P G,CHOI S K.Coal cleat permeability for gas movement under triaxial,non-zero lateral strain condition:a theoretical and experimental study[J].Fuel,2013,109:389-399.
[11]LU S Q,CHENG Y P,LI W.Model development and analysis of the evolution of coal permeability under different boundary conditions[J].Journal of Natural Gas Science and Engineering,2016,31:129-138.
[12]XIE J,GAO M Z,YU B,et al.Coal permeability model on the effect of gas extraction within effective influence zone[J].Geomechanics and Geophysics for GeoEnergy and Geo-Resources,2015,1(1-2):15-27.
[13]ZHANG N,LI X R,CHENG H M,et al.A coupled damage-hydro-mechanical model for gas drainage in low-permeability coalbeds[J].Journal of Natural Gas Science and Engineering,2016,35:1032-1043.
[14]JU Y,WANG J G,WANG H J,et al.CO2 permeability of fractured coal subject to confining pressures and elevated temperature:experiments and modeling[J].Science China Technological Sciences,2016,59(12):1931-1942.
[15]薛熠,高峰,高亚楠,等.采动影响下损伤煤岩体峰后渗透率演化模型研究[J].中国矿业大学学报,2017,46(3):521-527.XUE Yi,GAO Feng,GAO Ya-nan,et al.Research on mining-induced permeability evolution model of damaged coal in post-peak stage[J].Journal of China University of Mining&Technology,2017,46(3):521-527.
[16]XUE Y,GAO F,LIU X G,et al.Theoretical and numerical simulation of the mining-enhanced permeability model of damaged coal seam[J].Geotechnical&Geological Engineering,2016,34(5):1425-1433.
[17]XUE Y,GAO F,LIU X G,et al.Permeability and pressure distribution characteristics of the roadway surrounding rock in the damaged zone of an excavation[J].International Journal of Mining Science and Technology,2017,27(2):211-219.
[18]荣腾龙,周宏伟,王路军,等.三向应力条件下煤体渗透率演化模型研究[J].煤炭学报,2018,43(7):1930-1937.RONG Teng-long,ZHOU Hong-wei,WANG Lu-jun,et al.Coal permeability model for gas movement under the three-dimensional stress[J].Journal of China Coal Society.2018,43(7):1930-1937.
[19]LIU H H,RUTQVIST J.A new coal-permeability model:internal swelling stress and fracture-matrix interaction[J].Transport in Porous Media,2010,82(1):157-171.
[20]ZANG J,WANG K,ZHAO Y X.Evaluation of gas sorption-induced internal swelling in coal[J].Fuel,2015,143:165-172.
[21]WANG K,ZANG J,WANG G D,et al.Anisotropic permeability evolution of coal with effective stress variation and gas sorption:model development and analysis[J].International Journal of Coal Geology,2014,130(4):53-65.
[22]LIU J S,ELSWORTH D.Three-dimensional effects of hydraulic conductivity enhancement and desaturation around mined panels[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(8):1139-1152.
[23]ZHANG J C,ROEGIERS J C,SPETZLER H A.Influence of stress on permeability around a borehole in fractured porous media[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(3):496-501.
[24]曹文贵,赵明华,刘成学.基于Weibull分布的岩石损伤软化模型及其修正方法研究[J].岩石力学与工程学报,2004,23(19):3226-3231.CAO Wen-gui,ZHAO Ming-hua,LIU Cheng-xue.Study on the model and its modifying method for rock softening and damage based on Weibull random distribution[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(19):3226-3231.
[25]杨明辉,赵明华,曹文贵.岩石损伤软化统计本构模型参数的确定方法[J].水利学报,2005,36(3):345-349.YANG Ming-hui,ZHAO Ming-hua,CAO Wen-gui.Method for determining the parameters of statistical damage softening constitutive model for rock[J].Journal of Hydraulic Engineering,2005,36(3):345-349.
[26]李文璞.采动影响下煤岩力学特性及瓦斯运移规律研究[D].重庆:重庆大学,2014.LI Wen-pu.Research on mechanical characteristics and gas migration law of coal influenced by mining[D].Chongqing:Chongqing University,2014.
[27]袁镭.中高煤级煤孔隙结构特征及其主控因素[D].焦作:河南理工大学,2014.YUAN Lei.Research on the pore structure of the middle and high rank coal and its controlling factors[D].Jiaozuo:Henan Polytechnic University,2014.
[28]谢和平,周宏伟,刘建锋,等.不同开采条件下采动力学行为研究[J].煤炭学报,2011,36(7):1067-1074.XIE He-ping,ZHOU Hong-wei,LIU Jian-feng,et al.Mining-induced mechanical behavior in coal seams under different mining layouts[J].Journal of China Coal Society,2011,36(7):1067-1074.
[29]张泽天.不同开采方式煤岩应力场-裂隙场-渗流场行为研究[D].成都:四川大学,2016.ZHANG Ze-tian.Multiphysics fields behavior of coal under different mining layouts[D].Chengdu:Sichuan University,2016.
[30]朱红青,刘星魁.采空区非间隔性注氮防火效果及施工参数[J].辽宁工程技术大学学报(自然科学版),2011,30(5):706-712.ZHU Hong-qing,LIU Xing-kui.Fire prevention effects and construction parameters of continuous nitrogen injection in gob area[J].Journal of Liaoning Technical University(Natural Science),2011,30(5):706-712.
[31]薛东杰,周宏伟,王子辉,等.不同加载速率下煤岩采动力学响应及破坏机制[J].煤炭学报,2016,41(3):595-602.XUE Dong-jie,ZHOU Hong-wei,WANG Zi-hui,et al.Failure mechanism and mining-induced mechanical properties of coal under different loading rates[J].Journal of China Coal Society,2016,41(3):595-602.
[32]许江,曹偈,李波波,等.煤岩渗透率对孔隙压力变化响应规律的试验研究[J].岩石力学与工程学报,2013,32(2):225-230.XU Jiang,CAO Jie,LI Bo-bo,et al.Experimental research on response law of permeability of coal to pore pressure[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(2):225-230.
[33]MAZUMDER S,SIEMONS N,WOLF K H.Differential swelling and permeability change of coal in response to CO2 injection for enhanced coalbed methane[J].International Journal of Coal Geology,2008,74(2):123-138.
[2]薛东杰,周宏伟,彭瑞东,等.基于应力降的非连续支承压力强扰动特征研究[J].岩石力学与工程学报,2018,37(5):1080-1095.XUE Dong-jie,ZHOU Hong-wei,PENG Rui-dong,et al.Stress drop on strong disturbance of discontinuous abutment pressure[J].Chinese Journal of Rock Mechanics and Engineering,2018,37(5):1080-1095.
[3]谢和平,高峰,周宏伟,等.煤与瓦斯共采中煤层增透率理论与模型研究[J].煤炭学报,2013,38(7):1101-1108.XIE He-ping,GAO Feng,ZHOU Hong-wei,et al.On theoretical and modeling approach to mining enhanced permeability for simultaneous exploitation of coal and gas[J].Journal of China Coal Society,2013,38(7):1101-1108.
[4]PAN Z J,CONNELL L D.Modelling permeability for coal reservoirs:a review of analytical models and testing data[J].International Journal of Coal Geology,2012,92:1-44.
[5]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):1-16.
[6]亓宪寅,李家卓,王威.基于不同方向模量损失率的含瓦斯煤各向异性渗透模型[J].岩土力学,2018,39(2):635-643.QI Xian-Yin,LI Jia-zhuo,WANG Wei.An anisotropic permeability model of coal containing methane based on different directional modulus reduction ratios[J].Rock and Soil Mechanics,2018,39(2):635-643.
[7]尹光志,蒋长宝,许江,等.煤层气储层含水率对煤层气渗流影响的试验研究[J].岩石力学与工程学报,2011,30(增刊2):3401-3406.YIN Guang-zhi,JIANG Chang-bao,XU Jiang,et al.Experimental study of influences for water content in coalbed gas reservoirs on methane seepage[J].Chinese Journal of Rock Mechanics and Engineering,2011,30(Supp.2):3401-3406.
[8]陈金刚,徐平,赖永星,等.煤储层渗透率动态变化效应研究[J].岩土力学,2011,32(8):2512-2516.CHEN Jin-gang,XU Ping,LAI Yong-xing,et al.Research on dynamic variation effect of coal reservoirs permeability[J].Rock and Soil Mechanics,2011,32(8):2512-2516.
[9]CONNELL L D,LU M,PAN Z J.An analytical coal permeability model for triaxial strain and stress conditions[J].International Journal of Coal Geology,2010,84(2):103-114.
[10]PERERA M S A,RANJITH P G,CHOI S K.Coal cleat permeability for gas movement under triaxial,non-zero lateral strain condition:a theoretical and experimental study[J].Fuel,2013,109:389-399.
[11]LU S Q,CHENG Y P,LI W.Model development and analysis of the evolution of coal permeability under different boundary conditions[J].Journal of Natural Gas Science and Engineering,2016,31:129-138.
[12]XIE J,GAO M Z,YU B,et al.Coal permeability model on the effect of gas extraction within effective influence zone[J].Geomechanics and Geophysics for GeoEnergy and Geo-Resources,2015,1(1-2):15-27.
[13]ZHANG N,LI X R,CHENG H M,et al.A coupled damage-hydro-mechanical model for gas drainage in low-permeability coalbeds[J].Journal of Natural Gas Science and Engineering,2016,35:1032-1043.
[14]JU Y,WANG J G,WANG H J,et al.CO2 permeability of fractured coal subject to confining pressures and elevated temperature:experiments and modeling[J].Science China Technological Sciences,2016,59(12):1931-1942.
[15]薛熠,高峰,高亚楠,等.采动影响下损伤煤岩体峰后渗透率演化模型研究[J].中国矿业大学学报,2017,46(3):521-527.XUE Yi,GAO Feng,GAO Ya-nan,et al.Research on mining-induced permeability evolution model of damaged coal in post-peak stage[J].Journal of China University of Mining&Technology,2017,46(3):521-527.
[16]XUE Y,GAO F,LIU X G,et al.Theoretical and numerical simulation of the mining-enhanced permeability model of damaged coal seam[J].Geotechnical&Geological Engineering,2016,34(5):1425-1433.
[17]XUE Y,GAO F,LIU X G,et al.Permeability and pressure distribution characteristics of the roadway surrounding rock in the damaged zone of an excavation[J].International Journal of Mining Science and Technology,2017,27(2):211-219.
[18]荣腾龙,周宏伟,王路军,等.三向应力条件下煤体渗透率演化模型研究[J].煤炭学报,2018,43(7):1930-1937.RONG Teng-long,ZHOU Hong-wei,WANG Lu-jun,et al.Coal permeability model for gas movement under the three-dimensional stress[J].Journal of China Coal Society.2018,43(7):1930-1937.
[19]LIU H H,RUTQVIST J.A new coal-permeability model:internal swelling stress and fracture-matrix interaction[J].Transport in Porous Media,2010,82(1):157-171.
[20]ZANG J,WANG K,ZHAO Y X.Evaluation of gas sorption-induced internal swelling in coal[J].Fuel,2015,143:165-172.
[21]WANG K,ZANG J,WANG G D,et al.Anisotropic permeability evolution of coal with effective stress variation and gas sorption:model development and analysis[J].International Journal of Coal Geology,2014,130(4):53-65.
[22]LIU J S,ELSWORTH D.Three-dimensional effects of hydraulic conductivity enhancement and desaturation around mined panels[J].International Journal of Rock Mechanics and Mining Sciences,1997,34(8):1139-1152.
[23]ZHANG J C,ROEGIERS J C,SPETZLER H A.Influence of stress on permeability around a borehole in fractured porous media[J].International Journal of Rock Mechanics and Mining Sciences,2004,41(3):496-501.
[24]曹文贵,赵明华,刘成学.基于Weibull分布的岩石损伤软化模型及其修正方法研究[J].岩石力学与工程学报,2004,23(19):3226-3231.CAO Wen-gui,ZHAO Ming-hua,LIU Cheng-xue.Study on the model and its modifying method for rock softening and damage based on Weibull random distribution[J].Chinese Journal of Rock Mechanics and Engineering,2004,23(19):3226-3231.
[25]杨明辉,赵明华,曹文贵.岩石损伤软化统计本构模型参数的确定方法[J].水利学报,2005,36(3):345-349.YANG Ming-hui,ZHAO Ming-hua,CAO Wen-gui.Method for determining the parameters of statistical damage softening constitutive model for rock[J].Journal of Hydraulic Engineering,2005,36(3):345-349.
[26]李文璞.采动影响下煤岩力学特性及瓦斯运移规律研究[D].重庆:重庆大学,2014.LI Wen-pu.Research on mechanical characteristics and gas migration law of coal influenced by mining[D].Chongqing:Chongqing University,2014.
[27]袁镭.中高煤级煤孔隙结构特征及其主控因素[D].焦作:河南理工大学,2014.YUAN Lei.Research on the pore structure of the middle and high rank coal and its controlling factors[D].Jiaozuo:Henan Polytechnic University,2014.
[28]谢和平,周宏伟,刘建锋,等.不同开采条件下采动力学行为研究[J].煤炭学报,2011,36(7):1067-1074.XIE He-ping,ZHOU Hong-wei,LIU Jian-feng,et al.Mining-induced mechanical behavior in coal seams under different mining layouts[J].Journal of China Coal Society,2011,36(7):1067-1074.
[29]张泽天.不同开采方式煤岩应力场-裂隙场-渗流场行为研究[D].成都:四川大学,2016.ZHANG Ze-tian.Multiphysics fields behavior of coal under different mining layouts[D].Chengdu:Sichuan University,2016.
[30]朱红青,刘星魁.采空区非间隔性注氮防火效果及施工参数[J].辽宁工程技术大学学报(自然科学版),2011,30(5):706-712.ZHU Hong-qing,LIU Xing-kui.Fire prevention effects and construction parameters of continuous nitrogen injection in gob area[J].Journal of Liaoning Technical University(Natural Science),2011,30(5):706-712.
[31]薛东杰,周宏伟,王子辉,等.不同加载速率下煤岩采动力学响应及破坏机制[J].煤炭学报,2016,41(3):595-602.XUE Dong-jie,ZHOU Hong-wei,WANG Zi-hui,et al.Failure mechanism and mining-induced mechanical properties of coal under different loading rates[J].Journal of China Coal Society,2016,41(3):595-602.
[32]许江,曹偈,李波波,等.煤岩渗透率对孔隙压力变化响应规律的试验研究[J].岩石力学与工程学报,2013,32(2):225-230.XU Jiang,CAO Jie,LI Bo-bo,et al.Experimental research on response law of permeability of coal to pore pressure[J].Chinese Journal of Rock Mechanics and Engineering,2013,32(2):225-230.
[33]MAZUMDER S,SIEMONS N,WOLF K H.Differential swelling and permeability change of coal in response to CO2 injection for enhanced coalbed methane[J].International Journal of Coal Geology,2008,74(2):123-138.