页岩气藏微裂缝表观渗透率动态模型研究
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摘要
为研究页岩气藏开发过程中介质变形和滑脱效应对微裂缝表观渗透率动态变化的影响规律,分析有效应力和多孔介质结构参数等对气体渗流影响机制,采用光滑平板模型,结合分形及气体微观渗流理论,建立了介质变形和滑脱效应耦合作用下的微裂缝表观渗透率动态模型,并对模型进行可靠性验证和参数敏感性分析。研究表明,页岩气藏降压开采过程中受介质变形和滑脱效应"一负一正"耦合影响,微裂缝表观渗透率呈先减小后增大趋势,且临界压力值约为5 MPa;不同有效应力状态下,由于介质变形和滑脱效应耦合机制的差异性,导致表观渗透率变化规律不同,从微观作用机制角度对实验中不同加载条件下页岩应力敏感性的差异做出了理论解释;微裂缝最大开度越小,表观渗透率曲线"凹槽"越深,同时微裂缝孔隙度及开度分形维数越高、迂曲度分形维数越低,表观渗透率值越大。
The object of this paper is to study the coupled impacts of medium deformation and slippage effect on variation of apparent permeability for micro fractures, and to investigate the mechanism of effective stress condition and pore structure parameters on gas flow in shale gas reservoirs. A dynamic apparent permeability model for micro fractures is presented, which accounts for the coupled effects of medium deformation and gas slippage simultaneously based on the smooth plate model and combined with the fractal theory, as well as microscopic gas flow mechanism. Then the reliability verification and sensitivity analysis of the established model are performed. The results show that: The apparent permeability decreases firstly and then increases slowly as pore pressure reduces, and the critical pressure is about 5 MPa. The huge difference between the two coupled mechanism(medium deformation and slippage effect), resulting in the variation of apparent permeability curve with different effective stress states, which also explained the variation of stress sensitivity for shale with different loading modes in testing from microscopic perspective. The deeper "groove" of the apparent permeability curve when the maximum aperture is smaller. In addition, the higher the porosity and fractal dimension of the aperture, and the lower the tortuosity fractal dimension, the greater the apparent permeability is.
The object of this paper is to study the coupled impacts of medium deformation and slippage effect on variation of apparent permeability for micro fractures, and to investigate the mechanism of effective stress condition and pore structure parameters on gas flow in shale gas reservoirs. A dynamic apparent permeability model for micro fractures is presented, which accounts for the coupled effects of medium deformation and gas slippage simultaneously based on the smooth plate model and combined with the fractal theory, as well as microscopic gas flow mechanism. Then the reliability verification and sensitivity analysis of the established model are performed. The results show that: The apparent permeability decreases firstly and then increases slowly as pore pressure reduces, and the critical pressure is about 5 MPa. The huge difference between the two coupled mechanism(medium deformation and slippage effect), resulting in the variation of apparent permeability curve with different effective stress states, which also explained the variation of stress sensitivity for shale with different loading modes in testing from microscopic perspective. The deeper "groove" of the apparent permeability curve when the maximum aperture is smaller. In addition, the higher the porosity and fractal dimension of the aperture, and the lower the tortuosity fractal dimension, the greater the apparent permeability is.
引文
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[9]郭为,熊伟,高树生.页岩气藏应力敏感效应实验研究[J].特种油气藏,2012,19(1):95-97.GUO Wei,XIONG Wei,GAO Shu-sheng.Experimental study on stress sensitivity of shale gas reservoirs[J].Special Oil and Gas Reservoirs,2012,19(1):95-97.
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[14]曲冠政,曲占庆,HAZLETT Randy Dolye,等.页岩拉张型微裂缝几何特征描述及渗透率计算[J].石油勘探与开发,2016,43(1):115-120.QU Guan-zheng,QU Zhan-qing,HAZLETT Randy Dolye,et al.Geometrical description and permeability calculation about shale tensile micro-fractures[J].Petroleum Exploration and Development,2016,43(1):115-120.
[15]SONG Zhi-yong,SONG Hong-qing,MA Dong-xu,et al.Morphological characteristics of microscale fractures in gas shale and its pressure-dependent permeability[J].Interpretation,2016,5(1):SB25-SB31.
[16]CHEN Dong,PAN Zhe-jun,YE Zhi-hui.Dependence of gas shale fracture permeability on effective stress and reservoir pressure:Model match and insights[J].Fuel,2015,383-392.
[17]WONG R C K,ALFARO M C.Fractal dimension analysis of shales using X-ray computer tomography[C].International Workshop on X-Ray CT for Geomaterials Soils,Concrete,Rocks.Kumamoto,JP:[s.n.].2004:239-243.
[18]曹涛涛,宋之光,刘光祥,等.氮气吸附法-压汞法分析页岩孔隙、分形特征及其影响因素[J].油气地质与采收率,2016,23(2):1-8.CAO Tao-tao,SONG Zhi-guang,LIU Guang-xiang,et al.Characteristics of shale pores,fractal dimension and their controlling factors determined by nitrogen adsorption and mercury injection methods[J].Petroleum Geology and Recovery Efficiency,2016,23(2):1-8.
[19]LI Bo,LIU Ri-cheng,JIANG Yu-jing.A multiple fractal model for estimating permeability of dual-porosity media[J].Journal of Hydrology,2016,540:659-669.
[20]YU Bo-ming,CHENG Ping.A fractal model for permeability of bi-dispersed porous media[J].International Journal of Heat&Mass Transfer,2002,45(14):2983-2993.
[21]何更生.油层物理学[M].北京:石油工业出版社,1994:297,43.HE Geng-sheng.Fundamental of petrophysics[M].Beijing:Petroleum Industry Press,1994:43,297.
[22]AMOS NUR,J.D.B YERLEE.An exact effective stress law for elastic deformation of rock with fluids[J].Journal of Geophysical Research,1971,76(26):6414-6419.
[23]ROY S,RAJU R,CHUANG H F,et a1.Modeling gas flow through microchannels and nanopores[J].Journal of Applied Physics,2003,93(8):4870-4879.
[24]BESKOK A,KARNIADAKIS G E.A model for flows in channels,pipes,and ducts at micro and nano scales[J].Microscale Thermophysical Engineering,1999,3(1):43-77.
[25]FINK R,KROOSS A B M,GENSTERBLUM Y,et al.Apparent permeability of gas shales-Superposition of fluid dynamic and poro-elastic effects[J].Fuel,2017:1930-1937.
[2]张东晓,杨婷云,吴天昊,等.页岩气开发机理和关键问题[J].科学通报,2016,61(1):62-71.ZHANG Dong-xiao,YANG Ting-yun,WU Tian-hao,et al.Recovery mechanisms and key issues in shale gas development[J].Chinese Science Bulletin,2016,61(1):62-71.
[3]张宏学,刘卫群.页岩气开采的相关实验、模型和环境效应[J].岩土力学,2014,35(增刊2):85-100.ZHANG Hong-xue,LIU Wei-qun.Relevant experiments,models and environmental effect of shale gas production[J].Rock and Soil Mechanics,2014,35(Supp.2):85-100.
[4]WU Ke-liu,CHEN Zhang-xing,LI Xiang-fang,et al.A model for multiple transport mechanisms through nanopores of shale gas reservoirs with real gas effectadsorption-mechanic coupling[J].International Journal of Heat and Mass Transfer.2016,93:408-426.
[5]WANG F P,REED R M,JOHN A et al.Pore networks and fluid flow in gas shales[C]//SPE Annual Technical Conference and Exhibition.[S.l.]:Society of Petroleum Engineers,2009.
[6]邹才能,董大忠,王社教,等.中国页岩气形成机理、地质特征及资源潜力[J].石油勘探与开发,2010,37(6):641-653.ZOU Cai-neng,DONG Da-zhong,WANG She-jiao,et al.Geological characteristics,formation mechanism and resource potential of shale gas in China[J].Petroleum Exploration and Development,2010,37(6):641-653.
[7]LI Jing,LI Xiang-fang,WANG Xiang-zeng,et al.Water distribution characteristic and effect on methane adsorption capacity in shale clay[J].International Journal of Coal Geology,2016,159(4):135-154.
[8]郑忏.分形多孔介质中气体流动与扩散的输运特性研究[博士学位论文D].武汉:华中科技大学,2012.ZHENG Chan.Study of some transport properties for gas flow and diffusion through fractal porous media[Ph.D.Thesis D].Wuhan:Huazhong University of Science and Technology,2012.
[9]郭为,熊伟,高树生.页岩气藏应力敏感效应实验研究[J].特种油气藏,2012,19(1):95-97.GUO Wei,XIONG Wei,GAO Shu-sheng.Experimental study on stress sensitivity of shale gas reservoirs[J].Special Oil and Gas Reservoirs,2012,19(1):95-97.
[10]糜利栋,姜汉桥,李俊健,等.页岩储层渗透率数学表征[J].石油学报,2014,35(5):929-934.MI Li-dong,JIANG Han-qiao,LI Jun-jian,et al.Mathematical characterization of permeability in shale reservoirs[J].Acta Petrolei Sinica,2014,35(5):929-934.
[11]姜瑞忠,汪洋,贾俊飞,等.页岩储层基质和裂缝渗透率新模型研究[J].天然气地球科学,2014,25(6):934-939.JIANG Rui-zhong,WANG Yang,JIA Jun-fei,et al.The new model for matrix and fracture permeability in shale reservoirs[J].Natural Gas Geoscience,2014,25(6):934-939.
[12]WU Ke-liu,LI Xiang-fang,WANG Chen-chen,et al.A model for gas transport in microfractures of shale and tight gas reservoirs[J].AICh E Journal,2015,61(6):2079-2088.
[13]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):720-729.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):720-729.
[14]曲冠政,曲占庆,HAZLETT Randy Dolye,等.页岩拉张型微裂缝几何特征描述及渗透率计算[J].石油勘探与开发,2016,43(1):115-120.QU Guan-zheng,QU Zhan-qing,HAZLETT Randy Dolye,et al.Geometrical description and permeability calculation about shale tensile micro-fractures[J].Petroleum Exploration and Development,2016,43(1):115-120.
[15]SONG Zhi-yong,SONG Hong-qing,MA Dong-xu,et al.Morphological characteristics of microscale fractures in gas shale and its pressure-dependent permeability[J].Interpretation,2016,5(1):SB25-SB31.
[16]CHEN Dong,PAN Zhe-jun,YE Zhi-hui.Dependence of gas shale fracture permeability on effective stress and reservoir pressure:Model match and insights[J].Fuel,2015,383-392.
[17]WONG R C K,ALFARO M C.Fractal dimension analysis of shales using X-ray computer tomography[C].International Workshop on X-Ray CT for Geomaterials Soils,Concrete,Rocks.Kumamoto,JP:[s.n.].2004:239-243.
[18]曹涛涛,宋之光,刘光祥,等.氮气吸附法-压汞法分析页岩孔隙、分形特征及其影响因素[J].油气地质与采收率,2016,23(2):1-8.CAO Tao-tao,SONG Zhi-guang,LIU Guang-xiang,et al.Characteristics of shale pores,fractal dimension and their controlling factors determined by nitrogen adsorption and mercury injection methods[J].Petroleum Geology and Recovery Efficiency,2016,23(2):1-8.
[19]LI Bo,LIU Ri-cheng,JIANG Yu-jing.A multiple fractal model for estimating permeability of dual-porosity media[J].Journal of Hydrology,2016,540:659-669.
[20]YU Bo-ming,CHENG Ping.A fractal model for permeability of bi-dispersed porous media[J].International Journal of Heat&Mass Transfer,2002,45(14):2983-2993.
[21]何更生.油层物理学[M].北京:石油工业出版社,1994:297,43.HE Geng-sheng.Fundamental of petrophysics[M].Beijing:Petroleum Industry Press,1994:43,297.
[22]AMOS NUR,J.D.B YERLEE.An exact effective stress law for elastic deformation of rock with fluids[J].Journal of Geophysical Research,1971,76(26):6414-6419.
[23]ROY S,RAJU R,CHUANG H F,et a1.Modeling gas flow through microchannels and nanopores[J].Journal of Applied Physics,2003,93(8):4870-4879.
[24]BESKOK A,KARNIADAKIS G E.A model for flows in channels,pipes,and ducts at micro and nano scales[J].Microscale Thermophysical Engineering,1999,3(1):43-77.
[25]FINK R,KROOSS A B M,GENSTERBLUM Y,et al.Apparent permeability of gas shales-Superposition of fluid dynamic and poro-elastic effects[J].Fuel,2017:1930-1937.