深部煤体采动应力下双曲函数型渗透率模型
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摘要
深部资源开采中,采动应力下煤体渗透率演化规律成为煤炭开采理论研究的热点之一。通过对煤体常规三轴渗流实验和采动应力路径下渗流实验对比分析,发现深部含瓦斯煤体在采动应力路径下其渗透率-体积应变异于常规三轴渗透实验。煤体常规三轴实验主要以三向应力加载为路径,而煤体在不断采出过程中其应力路径主要表现为特定方向加载其他方向卸荷的过程,可凝练为加轴压卸围压的应力路径,而应力-应变分析的起始点为静水压力状态,这必然引起煤体力学物理性质异于三向加载条件的行为。在采动应力条件下的渗透率-体应变空间内,以煤体体应变扩容点为界,当体应变达到扩容点后,随着体应变从压缩变形转换为膨胀变形,渗透率呈现出降低、稳态、增加的过程。为了定量地描述深部煤体渗透率在采动破坏或流变失稳过程中先减小后增大的行为,基于在体积应变空间内真实渗透网络是所有可能渗透网络中最优演化形式的假设,建立以渗透率、体积应变为变量的泛函关系,从而得出由体积应变表示的渗透率表达式。考虑深部煤体流变过程,将分数阶微积分理论推导的煤体体积蠕变方程代入渗透率函数中,得出以轴向应变为自变量的渗透率表达式。根据已有的实验数据对渗透率模型进行验证,结果表明:基于最优渗透网络得出的渗透率模型能很好地描述煤体渗透率在破坏过程中的演化规律,同时也可拟合流变过程中渗透率的变化趋势。
In the exploitation of deep resources,the permeability evolution of coal under mining stress has become one of the fundamental research topics in coal mining theory.It is found that through the comparative analysis of two kinds of seepage tests under different stress paths the permeability evolution with volumetric strain under mining stress path is different from that of conventional triaxial seepage test in deep gas-infiltrated coal.To the contrast of conventional triaxial compression test,the stress path of coal in the process of continuous mining is mainly the unloading process of a specific direction and loading at other directions.It can be simplified as the stress path of unloading confining pressure meanwhile loading axial stress,thus making hydrostatic pressure state as the starting point of stress-strain analysis and inevitably resulting in the behavior of the mechanical and physical properties of coal body different from the loading conditions.In the permeability-volume strain space under mining stress,when the volume strain reaches the dilation point,the permeability shows a process of decreasing,steady-state and increasing with the volume strain transforming from compression deformation to expansion deformation.In order to quantitatively describe the process that the permeability first decreases and then increases in the process of mining failure or rheological instability,based on the hypothesis that real permeable network is the best evolution form of all possible permeable networks in volume strain space,the permeability is expressed by volumetric strain through building the functional relationship with permeability and volumetric strain as variables.Considering the volume rheological process of deep coal,the volumetric creep equation of coal derived from fractional calculus theory is substituted into the developed permeability equation,and the permeability function with axial strain as independent variable is obtained.It is verified that through the existing experimental data the permeability model based on the hypothesis of the optimal permeable network can well describe the permeability evolution of deep coal in the process of failure or creep.
In the exploitation of deep resources,the permeability evolution of coal under mining stress has become one of the fundamental research topics in coal mining theory.It is found that through the comparative analysis of two kinds of seepage tests under different stress paths the permeability evolution with volumetric strain under mining stress path is different from that of conventional triaxial seepage test in deep gas-infiltrated coal.To the contrast of conventional triaxial compression test,the stress path of coal in the process of continuous mining is mainly the unloading process of a specific direction and loading at other directions.It can be simplified as the stress path of unloading confining pressure meanwhile loading axial stress,thus making hydrostatic pressure state as the starting point of stress-strain analysis and inevitably resulting in the behavior of the mechanical and physical properties of coal body different from the loading conditions.In the permeability-volume strain space under mining stress,when the volume strain reaches the dilation point,the permeability shows a process of decreasing,steady-state and increasing with the volume strain transforming from compression deformation to expansion deformation.In order to quantitatively describe the process that the permeability first decreases and then increases in the process of mining failure or rheological instability,based on the hypothesis that real permeable network is the best evolution form of all possible permeable networks in volume strain space,the permeability is expressed by volumetric strain through building the functional relationship with permeability and volumetric strain as variables.Considering the volume rheological process of deep coal,the volumetric creep equation of coal derived from fractional calculus theory is substituted into the developed permeability equation,and the permeability function with axial strain as independent variable is obtained.It is verified that through the existing experimental data the permeability model based on the hypothesis of the optimal permeable network can well describe the permeability evolution of deep coal in the process of failure or creep.
引文
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[7]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.
[8]李世平,李玉寿,吴振业.岩石全应力应变过程对应的渗透率-应变方程[J].岩土工程学报,1995,17(2):13-19.Li Shiping,Li Yushou,Wu Zhenye.Permeability-strain equation for corresponding stress-strain process of rock[J].Chinese Journal of Geotechnical Engineering,1995,17(2):13-19.
[9]李晓泉,尹光志.含瓦斯煤的有效体积应力与渗透率关系[J].重庆大学学报,2011,34(8):103-108.LI Xiaoquan,YIN Guangzhi.Relationship between effective volumetric stress and permeability of gas-filled coal[J].Journal of Chongqing University,2011,34(8):103-108.
[10]祝捷,姜耀东,孟磊,等.载荷作用下煤体变形与渗透性的相关性研究[J].煤炭学报,2012,37(6):984-988.ZHU Jie,JIANG Yaodong,MENG Lei,et al.Pertinence study on deformation and permeability of coal containing methane during loading process[J].Journal of China Coal Society,2012,37(6):984-988.
[11]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 Heping,ZHOU Hongwei,LIU Jianfeng,et al.Mining-induced mechanical behavior in coal seams under different mining layouts[J].Journal of China Coal Society,2011,36(7):1067-1074.
[12]谢和平,张泽天,高峰,等.不同开采方式下煤岩应力场-裂隙场-渗流场行为研究[J].煤炭学报,2016,41(10):2405-2417.XIE Heping,ZHANG Zetian,GAO Feng,et al.Stress-fracture-seepage field behavior of coal under different mining lay-outs[J].Journal of China Coal Society,2016,41(10):2405-2417.
[13]ZHOU H W,LIU J F,XUE D J,et al.Numerical simulation of gas flow process in mining-induced crack network[J].International Journal of Mining Science and Technology,2012,22(6):793-799.
[14]XUE D J,ZHOU H W,CHEN C F,et al.A combined method for evaluation and prediction on permeability in coal seams during enhanced methane recovery by pressure-relieved method[J].Environmental Earth Sciences,2015,73(10):5963-5974.
[15]ZHOU H W,ZHONG J C,REN W G,et al.Characterization of pore-fracture networks and their evolution at various measurement scales in coal samples using X-rayμCT and a fractal method[J].International Journal of Coal Geology,2018,189:35-49.
[16]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 Tenglong,ZHOU Hongwei,WANG Lujun,et al.Coal permeability model for gas movement under the three-dimensional stress[J].Journal of China Coal Society,2018,43(7):1930-1937.
[17]尹光志,王浩,张东明.含瓦斯煤卸围压蠕变试验及其理论模型研究[J].煤炭学报,2011,36(12):1963-1967.YIN Guangzhi,WANG Hao,ZHANG Dongming.Creep experimental and theory model on coal containing gas under the condition of unloading confining pressure[J].Journal of China Coal Society,2011,36(12):1963-1967.
[18]许江,彭守建,陶云奇,等.蠕变对含瓦斯煤渗透率影响的试验分析[J].岩石力学与工程学报,2009,28(11):2273-2280.XU Jiang,PENG Shoujian,TAO Yunqi,et al.Experimental analysis of influence of creep on permeability of gas-bering coal[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(11):2273-2280.
[19]蒋长宝,黄滚,黄启翔.含瓦斯煤多级式卸围压变形破坏及渗透率演化规律实验[J].煤炭学报,2011,36(12):2039-2042.JIANG Changbao,HUANG Gun,HUANG Qixiang.Experiment on deformation failure and permeability evolution law of gas-containing coal under multi-stage unloading confining pressure[J].Journal of China Coal Society,2011,36(12):2039-2042.
[20]YANG Y,ZOBACK M D.The effects of gas adsorption on swelling,visco-plastic creep and permeability of sub-bituminous coal[A].The 45th US Rock Mechanics/Geomechanics Symposium[C].San Francisco,2011:433-440.
[21]DANESH N N,CHEN Z,AMINOSSADATI S M,et al.Impact of creep on the evolution of coal permeability and gas drainage performance[J].Journal of Natural Gas Science&Engineering,2016,33:469-482.
[22]YIN G,LI M,WANG J G,et al.Mechanical behavior and permeability evolution of gas infiltrated coals during protective layer mining[J].International Journal of Rock Mechanics&Mining Sciences,2015,80:292-301.
[23]许江,李波波,周婷,等.加卸载条件下煤岩变形特性与渗透特征的试验研究[J].煤炭学报,2012,37(9):1493-1498.XU Jiang,LI Bobo,ZHOU Ting,et al.Experimental study of coal deformation and permeability characteristics under loadingunloading conditions[J].Journal of China Coal Society,2012,37(9):1493-1498.
[24]ZHOU H W,WANG C P,HAN B B,et al.A creep constitutive model for salt rock based on fractional derivatives[J].International Journal of Rock Mechanics and Mining Sciences,2011,48(1):116-121.
[25]何明明,李宁,朱才辉,等.岩石分数阶体积变形模型及其试验研究[J].岩土力学,2016,37(11):3137-3144.HE Mingming,LI Ning,ZHU Caihui,et al.The volume deformation behavior of rock based on fractional calculus and its experimental study[J].Rock and Soil Mechanics,2016,37(11):3137-3144.
[26]霍丙杰,范张磊,路洋波,等.保护层开采被保护层体积应变与渗透特性相似模拟研究[J].煤炭科学技术,2018,46(7):19-25.HUO Bingjie,FAN Zhanglei,LU Yangbo,et al.Similarity simulation study on permeability of protected coal seam volumetric strain during mining protective coal seam[J].Coal Science and Technology,2018,46(7):19-25.
[27]李祥春,张良,赵艺良.常规三轴压力下含瓦斯煤蠕变-渗流演化规律[J].工程科学与技术,2018,50(4):55-62.LI Xiangchun,ZHANG Liang,ZHAO Yiliang.Evolution of gasfilled coal creep-seepage under conventional triaxial compression[J].Advanced Engineering Sciences,2018,50(4):55-62.
[2]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 Heping,ZHOU Hongwei,XUE Dongjie,et al.Research and consideration on deep coal mining and critical mining depth[J].Journal of China Coal Society,2012,37(4):535-542.
[3]谢和平,高峰,鞠杨,等.深部开采的定量界定与分析[J].煤炭学报,2015,40(1):1-10.XIE Heping,GAO Feng,JU Yang,et al.Quantitative definition and investigation of deep mining[J].Journal of China Coal Society,2015,40(1):1-10.
[4]周宏伟,谢和平,左建平.深部高地应力下岩石力学行为研究进展[J].力学进展,2005,35(1):91-99.ZHOU Hongwei,XIE Heping,ZUO Jiangping.Developments in researches on mechanical behaviors of rocks under the condition of high ground pressure in the depths[J].Advances in Mechanics,2005,35(1):91-99.
[5]PALMER I.Permeability changes in coal:Analytical modeling[J].International Journal of Coal Geology,2009,77(1):119-126.
[6]WANG G X,ZHANG X D,WEI X R,et al.A review on transport of coal seam gas and its impact on coalbed methane recovery[J].Frontiers of Chemical Science and Engineering,2011,5(2):139-161.
[7]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.
[8]李世平,李玉寿,吴振业.岩石全应力应变过程对应的渗透率-应变方程[J].岩土工程学报,1995,17(2):13-19.Li Shiping,Li Yushou,Wu Zhenye.Permeability-strain equation for corresponding stress-strain process of rock[J].Chinese Journal of Geotechnical Engineering,1995,17(2):13-19.
[9]李晓泉,尹光志.含瓦斯煤的有效体积应力与渗透率关系[J].重庆大学学报,2011,34(8):103-108.LI Xiaoquan,YIN Guangzhi.Relationship between effective volumetric stress and permeability of gas-filled coal[J].Journal of Chongqing University,2011,34(8):103-108.
[10]祝捷,姜耀东,孟磊,等.载荷作用下煤体变形与渗透性的相关性研究[J].煤炭学报,2012,37(6):984-988.ZHU Jie,JIANG Yaodong,MENG Lei,et al.Pertinence study on deformation and permeability of coal containing methane during loading process[J].Journal of China Coal Society,2012,37(6):984-988.
[11]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 Heping,ZHOU Hongwei,LIU Jianfeng,et al.Mining-induced mechanical behavior in coal seams under different mining layouts[J].Journal of China Coal Society,2011,36(7):1067-1074.
[12]谢和平,张泽天,高峰,等.不同开采方式下煤岩应力场-裂隙场-渗流场行为研究[J].煤炭学报,2016,41(10):2405-2417.XIE Heping,ZHANG Zetian,GAO Feng,et al.Stress-fracture-seepage field behavior of coal under different mining lay-outs[J].Journal of China Coal Society,2016,41(10):2405-2417.
[13]ZHOU H W,LIU J F,XUE D J,et al.Numerical simulation of gas flow process in mining-induced crack network[J].International Journal of Mining Science and Technology,2012,22(6):793-799.
[14]XUE D J,ZHOU H W,CHEN C F,et al.A combined method for evaluation and prediction on permeability in coal seams during enhanced methane recovery by pressure-relieved method[J].Environmental Earth Sciences,2015,73(10):5963-5974.
[15]ZHOU H W,ZHONG J C,REN W G,et al.Characterization of pore-fracture networks and their evolution at various measurement scales in coal samples using X-rayμCT and a fractal method[J].International Journal of Coal Geology,2018,189:35-49.
[16]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 Tenglong,ZHOU Hongwei,WANG Lujun,et al.Coal permeability model for gas movement under the three-dimensional stress[J].Journal of China Coal Society,2018,43(7):1930-1937.
[17]尹光志,王浩,张东明.含瓦斯煤卸围压蠕变试验及其理论模型研究[J].煤炭学报,2011,36(12):1963-1967.YIN Guangzhi,WANG Hao,ZHANG Dongming.Creep experimental and theory model on coal containing gas under the condition of unloading confining pressure[J].Journal of China Coal Society,2011,36(12):1963-1967.
[18]许江,彭守建,陶云奇,等.蠕变对含瓦斯煤渗透率影响的试验分析[J].岩石力学与工程学报,2009,28(11):2273-2280.XU Jiang,PENG Shoujian,TAO Yunqi,et al.Experimental analysis of influence of creep on permeability of gas-bering coal[J].Chinese Journal of Rock Mechanics and Engineering,2009,28(11):2273-2280.
[19]蒋长宝,黄滚,黄启翔.含瓦斯煤多级式卸围压变形破坏及渗透率演化规律实验[J].煤炭学报,2011,36(12):2039-2042.JIANG Changbao,HUANG Gun,HUANG Qixiang.Experiment on deformation failure and permeability evolution law of gas-containing coal under multi-stage unloading confining pressure[J].Journal of China Coal Society,2011,36(12):2039-2042.
[20]YANG Y,ZOBACK M D.The effects of gas adsorption on swelling,visco-plastic creep and permeability of sub-bituminous coal[A].The 45th US Rock Mechanics/Geomechanics Symposium[C].San Francisco,2011:433-440.
[21]DANESH N N,CHEN Z,AMINOSSADATI S M,et al.Impact of creep on the evolution of coal permeability and gas drainage performance[J].Journal of Natural Gas Science&Engineering,2016,33:469-482.
[22]YIN G,LI M,WANG J G,et al.Mechanical behavior and permeability evolution of gas infiltrated coals during protective layer mining[J].International Journal of Rock Mechanics&Mining Sciences,2015,80:292-301.
[23]许江,李波波,周婷,等.加卸载条件下煤岩变形特性与渗透特征的试验研究[J].煤炭学报,2012,37(9):1493-1498.XU Jiang,LI Bobo,ZHOU Ting,et al.Experimental study of coal deformation and permeability characteristics under loadingunloading conditions[J].Journal of China Coal Society,2012,37(9):1493-1498.
[24]ZHOU H W,WANG C P,HAN B B,et al.A creep constitutive model for salt rock based on fractional derivatives[J].International Journal of Rock Mechanics and Mining Sciences,2011,48(1):116-121.
[25]何明明,李宁,朱才辉,等.岩石分数阶体积变形模型及其试验研究[J].岩土力学,2016,37(11):3137-3144.HE Mingming,LI Ning,ZHU Caihui,et al.The volume deformation behavior of rock based on fractional calculus and its experimental study[J].Rock and Soil Mechanics,2016,37(11):3137-3144.
[26]霍丙杰,范张磊,路洋波,等.保护层开采被保护层体积应变与渗透特性相似模拟研究[J].煤炭科学技术,2018,46(7):19-25.HUO Bingjie,FAN Zhanglei,LU Yangbo,et al.Similarity simulation study on permeability of protected coal seam volumetric strain during mining protective coal seam[J].Coal Science and Technology,2018,46(7):19-25.
[27]李祥春,张良,赵艺良.常规三轴压力下含瓦斯煤蠕变-渗流演化规律[J].工程科学与技术,2018,50(4):55-62.LI Xiangchun,ZHANG Liang,ZHAO Yiliang.Evolution of gasfilled coal creep-seepage under conventional triaxial compression[J].Advanced Engineering Sciences,2018,50(4):55-62.
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