页岩气藏表观渗透率和综合渗流模型建立
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摘要
页岩储层结构复杂,多尺度效应明显,存在黏性流动、滑脱效应、Knudsen扩散以及表面扩散等多重运移机制。利用Knudsen数划分流态,绘制了考虑真实气体效应的流态图版。考虑多重运移机制,建立了页岩气藏表观渗透率模型;在此基础上综合考虑吸附解吸以及溶解气扩散影响,建立了页岩气藏多重介质不稳定渗流数学模型,明确了不同运移机制对页岩气藏非稳态产能的影响。结果表明:不同运移机制之间既相互联系又相互制约;Knudsen扩散和表面扩散均通过改变表观渗透率大小,对生产中期阶段的气体流动能力产生重要影响;溶解气和吸附气均是页岩气的重要赋存形式,是开发过程中自由气的补充,对气井生产中晚期非稳态产能具有显著影响;溶解气与吸附气能够增加气藏的累产气量,减缓气藏压力的下降速度。
Multi-scaled effects of gas seepage behavior,such as slippage effect,Knudsen diffusion and surface diffusion,can lead to non-Darcy flow in shale formation. A flow chart considering real gas effects was plotted according the value of Knudsen number,and a comprehensive apparent permeability model was established considering different flow mechanisms. Flux contribution of slip viscous flow,Knudsen diffusion and surface diffusion were discussed under different pore radii and pressure conditions. Using the apparent permeability model,a comprehensive flow continual equation was built considering adsorption/desorption effect and dissolved gas diffusion in Kerogen. The results show that nonlinear flow effect is obvious in low pressure and small pore conditions. The main mass transfer mechanism is different under different conditions. Knudsen and surface diffusion mainly affect the middle flow period through changing the apparent permeablity. Dissolved gas in Kerogen and adsorbed gas are important occurrence of shale gas and supplement of free gas during reservoir development,and they have a significant influence on unstable productivity during middle-later flow period. Dissolved gas and adsorbed gas can increase the cumulative gas production,slow down gas reservoir pressure drop.
Multi-scaled effects of gas seepage behavior,such as slippage effect,Knudsen diffusion and surface diffusion,can lead to non-Darcy flow in shale formation. A flow chart considering real gas effects was plotted according the value of Knudsen number,and a comprehensive apparent permeability model was established considering different flow mechanisms. Flux contribution of slip viscous flow,Knudsen diffusion and surface diffusion were discussed under different pore radii and pressure conditions. Using the apparent permeability model,a comprehensive flow continual equation was built considering adsorption/desorption effect and dissolved gas diffusion in Kerogen. The results show that nonlinear flow effect is obvious in low pressure and small pore conditions. The main mass transfer mechanism is different under different conditions. Knudsen and surface diffusion mainly affect the middle flow period through changing the apparent permeablity. Dissolved gas in Kerogen and adsorbed gas are important occurrence of shale gas and supplement of free gas during reservoir development,and they have a significant influence on unstable productivity during middle-later flow period. Dissolved gas and adsorbed gas can increase the cumulative gas production,slow down gas reservoir pressure drop.
引文
[1]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.天然气地球科学,2014,25(6):934-939.JIANG R Z,WANG Y,JIA J F,et al.The new model for matrix and fracture permeability in shale reservoir.Natural Gas Geoscience,2014,25(6):934-939.
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[11]郭肖,任影,吴红琴.考虑应力敏感和吸附的页岩表观渗透率模型.岩性油气藏,2015,27(4):109-112.GUO X,REN Y,WU H Q.Apparent permeability model of shale gas considering stress sensitivity and adsorption.Lithologic Reservoirs,2015,27(4):109-112.
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[13]WU K L,CHEN Z X,LI X F,et al.A model for multiple transport mechanisms through nanopores of shale gas reservoirs with real gas effect-adsorption-mechanic coupling.International Journal of Heat and Mass Transfer,2016,93:408-426.
[14]WU K L,LI X F,WANG C C,et al.Apparent permeability for gas flow in shale reservoirs coupling effects of gas diffusion and desorption.Unconventional Resources Technology Conference,Denver,Colorado,2014.
[15]岳陈军,张烈辉,赵玉龙,等.考虑表面扩散的页岩气渗透率两区复合解析模型.水动力学研究与进展:A辑,2016,31(3):362-371.YUE C J,ZHANG L H,ZHAO Y L,et al.A dual-zone composite analytic model for shale gas permeability considering surface diffusion.Chinese Journal of Hydrodynamics,2016,31(3):362-371.
[16]盛茂,李根生,黄中伟,等.考虑表面扩散作用的页岩气瞬态流动模型.石油学报,2014,35(2):347-352.SHENG M,LI G S,HUANG Z W,et al.Shale gas transient flow model with effects of surface diffusion.Acta Petrolei Sinica,2014,35(2):347-352.
[17]查文舒,李道伦,王磊,等.不同滑移边界下的页岩渗透率修正模型.力学学报,2015,47(6):923-931.ZHA W S,LI D L,WANG L,et al.Shale permeability correction models under different slip boundary conditions.Chinese Journal of Theoretical and Applied Mechanics,2015,47(6):923-931.
[18]张梦黎,郭肖,刘洪.多尺度孔隙介质视渗透率模型.石油化工应用,2016,35(4):18-22.ZHANG M L,GUO X,LIU H.The model for apparent permea-bility in multi-scale porous medium.Petrochemical Industry Application,2016,35(4):18-22.
[19]宋付权,刘禹,王常斌.微纳米尺度下页岩气的质量流量特征分析.水动力学研究与进展:A辑,2014,29(2):150-156.SONG F Q,LIU Y,WANG C B.Analysis of mass flow rate characteristics of the shale gas in micro/nano scale.Chinese Journal of Hydrodynamics,2014,29(2):150-156.
[20]ZAMIRIAN M,AMINIAN K,FATHI E,et al.A fast and robust technique for accurate measurement of the organic-rich shales characteristics under steady-state conditions.SPE 171018,2014.
[21]JAVADPOUR F.Nanopores and apparent permeability of gas flow in mudrocks(shales and siltstone).Journal of Canadian Petroleum Technology,2009,48(8):16-21.
[22]JAVADPOUR F,FISHER D,UNSWORTH M.Nanoscale gas flow in shale gas sediments.Journal of Canadian Petroleum Technology,2007,46(10):55-61.
[23]CIVAN F.Effective correlation of apparent gas permeability in tight porous media.Transport in Porous Media.2010,82(2):375-384.
[24]MICHEL G G,SIGAL R,CIVAN F,et al.Parametric investigation of shale gas production considering nano-scale pore size distribution,formation factor,and non-darcy flow mechanisms.SPE147438,2011.
[25]KLINKENBERG L J.The permeability of porous media to liquids and gases.Socar Proceeding,1941,2(2):200-213.
[26]JONES F O,OWENS W W.A laboratory study of low-permeability gas sands.Journal of Petroleum Technology,1980,32(9):1631-1640.
[27]SAMPATH K,KEIGHIN C W.Factors affecting gas slippage in tight sandstones of Cretaceous age in the Ninta Basin.Journal of Petroleum Technology,1982,34(11):2715-2720.
[28]ERTEKIN T,KING G R,SCHWERER F C.Dynamic gas slippage:a unique dual-mechanism approach to the flow of gas in tight formations.SPE Formation and Evaluation,1986,1(1):43-52.
[29]FLORENCE F,RUSHING J,NEWSHAM K E,et al.Improved permeability prediction relations for low permeability sands.SPE107954,2007.
[30]AUBERT C,COLIN S.High-order boundary conditions for gaseous flow in rectangular microdusts.Microscale Thermalphysical Engineering,2001,5(1):41-54.
[31]谢翀,樊菁.Navier-Stokes方程二阶速度滑移边界条件的检验.力学学报,2007,39(1):1-6.XIE C,FAN J.Assessment of second-order velocity-slip boundary conditions of the Navier-Stokes equations.Chinese Journal of Theoretical and Applied Mechanics,2007,39(1):1-6.
[32]BESKOK A,KARNIADAKIS G E.A model for flows in channels,pipes,and ducts at micro and nano scales.Microscale Thermalphysical Engineering,1999,3(1):43-77.
[33]MAXWELL J C.On stresses in rarified gases arising from inequalities of temperature.Philosophical Transactions of the Royal Society of London,1879,170:231-256.
[34]HSIA Y T,DOMOTO G A.An experimental investigation of molecular rarefaction effects in gas lubricated bearing at ultralow clearances.Journal of Lubrication Technology,1983,105(1):120-129.
[35]YIN-KWEE N E,LIU N Y.A multicoefficient slip-corrected reynolds equation for micro-thin film gas lubrication.International Journal of Rotating Machinery,2005,2:105-111.
[36]寇雨,周文,赵毅楠,等.鄂尔多斯盆地长7油层组页岩吸附特征与类型及吸附气量影响因素.岩性油气藏,2016,28(6):52-57.KOU Y,ZHOU W,ZHAO Y N,et al.Adsorption characteristics,types and influencing factors of Chang 7 shale of Triassic Yanchang Formation in Ordos Basin.Lithologic Reservoirs,2016,28(6):52-57.
[37]DARABI H,ETTEHAD A,JAVADPOUR F,et al.Gas flow in ultra-tight shale strata.Journal of Fluid Mechanics,2012,710(12):641-658.
[38]CAO C,LI T T,ZHAO Y P,et al.Multi-field coupling permeability model in shale gas reservoir.SPE 184033,2017.
[39]ZHAO Y L,ZHANG L H,XIONG Y,et al.Pressure response and production performance for multi-fractured horizontal wells with complex seepage mechanism in box-shaped shale gas reservoir.Journal of Natural Gas Science and Engineering,2016,32:66-80.
[40]IGWE G J I.Gas transport mechanism and slippage phenomenon in porous media.SPE 16479,1987.
[41]RUTHVEN D M.Principles of adsorption&adsorption processes.New York:John Wiley and Sons,1984:80-109.
[42]何映颉,杨洋,张廷山,等.石墨狭缝吸附页岩气的分子模拟.岩性油气藏,2016,28(6):88-94.HE Y J,YANG Y,ZHANG T S,et al.Molecular simulation of shale gas adsorption in graphite slit-pores.Lithologic Reservoirs,2016,28(6):88-94.
[43]段永刚,曹廷宽,杨小莹,等.页岩储层纳米孔隙流动模拟研究.西南石油大学学报(自然科学版),2015,37(3):63-68.DUAN Y G,CAO T K,YANG X Y,et al.Simulation of gas flow in nano-scale pores of shale gas deposits.Journal of Southwest Petroleum University(Science&Technology Edition),2015,37(3):63-68.
[44]BRUNAUER S,EMMETT P H,TELLER E.Adsorption of gases in multimolecular layers.Journal of American Chemical Society,1938,60(29):309-319.
[2]于荣泽,张晓伟,卞亚南,等.页岩气藏流动机理与产能影响因素分析.天然气工业,2012,32(9):10-15.YU R Z,ZHANG X W,BIAN Y N,et al.Flow mechanism of shale gas reservoirs and influential factors of their productivity.Natural Gas Industry,2012,32(9):10-15.
[3]李勇明,姚锋盛,赵金洲,等.页岩气藏纳米孔隙微观渗流动态研究.科学技术与工程,2013,13(10):2657-2661.LI Y M,YAO F S,ZHAO J Z,et al.Shale gas reservoir nanometerpore microscopic seepage dynamic research.Science Technology and Engineering,2013,13(10):2657-2661.
[4]SWAMI V,SETTARI AT.A numerical model for multi-mechanism flow in shale gas reservoirs with application to laboratory scale testing.SPE 164840,2013.
[5]SWAMI V,SETTARI A T.A pore scale gas flow model for shale gas reservoir.SPE 155756,2012.
[6]SHABRO V,TORRES-VERDIN C,SEPEHRNOORI K.Forecasting gas production in organic shale with the combined numerical simulation of gas diffusion in Kerogen,Langmuir desorption from surfaces,and advection in nanopores.SPE 159250,2012.
[7]郭为,熊伟,高树生,等.页岩纳米级孔隙气体流动特征.石油钻采工艺,2012,34(6):57-60.GUO W,XIONG W,GAO S S,et al.Gas flow characteristics in shales nanopores.Oil Drilling&Production Technology,2012,34(6):57-60.
[8]夏阳,金衍,陈勉.页岩气渗流过程中的多场耦合机理.中国科学:物理学力学天文学,2015,45(9):30-43.XIA Y,JIN Y,CHEN M.The coupling of multi-physics for gas flow in shale reservoirs.Scientia Sinica:Physica,Mechanica,Astronomica,2015,45(9):30-43.
[9]夏阳,金衍,陈勉,等.页岩气渗流数学模型.科学通报,2015,60(24):2259-2271.XIA Y,JIN Y,CHEN M,et al.Gas flow in shale reservoirs.Chinese Science Bulletin,2015,60(24):2259-2271.
[10]刘圣鑫,钟建华,刘晓光,等.致密多孔介质气体运移机理.天然气地球科学,2014,25(10):1520-1528.LIU S X,ZHONG J H,LIU X G,et al.Gas transport mechanism in tight porous media.Natural Gas Geoscience,2014,25(10):1520-1528.
[11]郭肖,任影,吴红琴.考虑应力敏感和吸附的页岩表观渗透率模型.岩性油气藏,2015,27(4):109-112.GUO X,REN Y,WU H Q.Apparent permeability model of shale gas considering stress sensitivity and adsorption.Lithologic Reservoirs,2015,27(4):109-112.
[12]朱维耀,马千,邓佳,等.纳微米级孔隙气体流动数学模型及应用.北京科技大学学报,2014,36(6):709-715.ZHU W Y,MA Q,DENG J,et al.Mathematical model and application of gas flow in nano-micron pores.Journal of University of Science and Technology Beijing,2014,36(6):709-715.
[13]WU K L,CHEN Z X,LI X F,et al.A model for multiple transport mechanisms through nanopores of shale gas reservoirs with real gas effect-adsorption-mechanic coupling.International Journal of Heat and Mass Transfer,2016,93:408-426.
[14]WU K L,LI X F,WANG C C,et al.Apparent permeability for gas flow in shale reservoirs coupling effects of gas diffusion and desorption.Unconventional Resources Technology Conference,Denver,Colorado,2014.
[15]岳陈军,张烈辉,赵玉龙,等.考虑表面扩散的页岩气渗透率两区复合解析模型.水动力学研究与进展:A辑,2016,31(3):362-371.YUE C J,ZHANG L H,ZHAO Y L,et al.A dual-zone composite analytic model for shale gas permeability considering surface diffusion.Chinese Journal of Hydrodynamics,2016,31(3):362-371.
[16]盛茂,李根生,黄中伟,等.考虑表面扩散作用的页岩气瞬态流动模型.石油学报,2014,35(2):347-352.SHENG M,LI G S,HUANG Z W,et al.Shale gas transient flow model with effects of surface diffusion.Acta Petrolei Sinica,2014,35(2):347-352.
[17]查文舒,李道伦,王磊,等.不同滑移边界下的页岩渗透率修正模型.力学学报,2015,47(6):923-931.ZHA W S,LI D L,WANG L,et al.Shale permeability correction models under different slip boundary conditions.Chinese Journal of Theoretical and Applied Mechanics,2015,47(6):923-931.
[18]张梦黎,郭肖,刘洪.多尺度孔隙介质视渗透率模型.石油化工应用,2016,35(4):18-22.ZHANG M L,GUO X,LIU H.The model for apparent permea-bility in multi-scale porous medium.Petrochemical Industry Application,2016,35(4):18-22.
[19]宋付权,刘禹,王常斌.微纳米尺度下页岩气的质量流量特征分析.水动力学研究与进展:A辑,2014,29(2):150-156.SONG F Q,LIU Y,WANG C B.Analysis of mass flow rate characteristics of the shale gas in micro/nano scale.Chinese Journal of Hydrodynamics,2014,29(2):150-156.
[20]ZAMIRIAN M,AMINIAN K,FATHI E,et al.A fast and robust technique for accurate measurement of the organic-rich shales characteristics under steady-state conditions.SPE 171018,2014.
[21]JAVADPOUR F.Nanopores and apparent permeability of gas flow in mudrocks(shales and siltstone).Journal of Canadian Petroleum Technology,2009,48(8):16-21.
[22]JAVADPOUR F,FISHER D,UNSWORTH M.Nanoscale gas flow in shale gas sediments.Journal of Canadian Petroleum Technology,2007,46(10):55-61.
[23]CIVAN F.Effective correlation of apparent gas permeability in tight porous media.Transport in Porous Media.2010,82(2):375-384.
[24]MICHEL G G,SIGAL R,CIVAN F,et al.Parametric investigation of shale gas production considering nano-scale pore size distribution,formation factor,and non-darcy flow mechanisms.SPE147438,2011.
[25]KLINKENBERG L J.The permeability of porous media to liquids and gases.Socar Proceeding,1941,2(2):200-213.
[26]JONES F O,OWENS W W.A laboratory study of low-permeability gas sands.Journal of Petroleum Technology,1980,32(9):1631-1640.
[27]SAMPATH K,KEIGHIN C W.Factors affecting gas slippage in tight sandstones of Cretaceous age in the Ninta Basin.Journal of Petroleum Technology,1982,34(11):2715-2720.
[28]ERTEKIN T,KING G R,SCHWERER F C.Dynamic gas slippage:a unique dual-mechanism approach to the flow of gas in tight formations.SPE Formation and Evaluation,1986,1(1):43-52.
[29]FLORENCE F,RUSHING J,NEWSHAM K E,et al.Improved permeability prediction relations for low permeability sands.SPE107954,2007.
[30]AUBERT C,COLIN S.High-order boundary conditions for gaseous flow in rectangular microdusts.Microscale Thermalphysical Engineering,2001,5(1):41-54.
[31]谢翀,樊菁.Navier-Stokes方程二阶速度滑移边界条件的检验.力学学报,2007,39(1):1-6.XIE C,FAN J.Assessment of second-order velocity-slip boundary conditions of the Navier-Stokes equations.Chinese Journal of Theoretical and Applied Mechanics,2007,39(1):1-6.
[32]BESKOK A,KARNIADAKIS G E.A model for flows in channels,pipes,and ducts at micro and nano scales.Microscale Thermalphysical Engineering,1999,3(1):43-77.
[33]MAXWELL J C.On stresses in rarified gases arising from inequalities of temperature.Philosophical Transactions of the Royal Society of London,1879,170:231-256.
[34]HSIA Y T,DOMOTO G A.An experimental investigation of molecular rarefaction effects in gas lubricated bearing at ultralow clearances.Journal of Lubrication Technology,1983,105(1):120-129.
[35]YIN-KWEE N E,LIU N Y.A multicoefficient slip-corrected reynolds equation for micro-thin film gas lubrication.International Journal of Rotating Machinery,2005,2:105-111.
[36]寇雨,周文,赵毅楠,等.鄂尔多斯盆地长7油层组页岩吸附特征与类型及吸附气量影响因素.岩性油气藏,2016,28(6):52-57.KOU Y,ZHOU W,ZHAO Y N,et al.Adsorption characteristics,types and influencing factors of Chang 7 shale of Triassic Yanchang Formation in Ordos Basin.Lithologic Reservoirs,2016,28(6):52-57.
[37]DARABI H,ETTEHAD A,JAVADPOUR F,et al.Gas flow in ultra-tight shale strata.Journal of Fluid Mechanics,2012,710(12):641-658.
[38]CAO C,LI T T,ZHAO Y P,et al.Multi-field coupling permeability model in shale gas reservoir.SPE 184033,2017.
[39]ZHAO Y L,ZHANG L H,XIONG Y,et al.Pressure response and production performance for multi-fractured horizontal wells with complex seepage mechanism in box-shaped shale gas reservoir.Journal of Natural Gas Science and Engineering,2016,32:66-80.
[40]IGWE G J I.Gas transport mechanism and slippage phenomenon in porous media.SPE 16479,1987.
[41]RUTHVEN D M.Principles of adsorption&adsorption processes.New York:John Wiley and Sons,1984:80-109.
[42]何映颉,杨洋,张廷山,等.石墨狭缝吸附页岩气的分子模拟.岩性油气藏,2016,28(6):88-94.HE Y J,YANG Y,ZHANG T S,et al.Molecular simulation of shale gas adsorption in graphite slit-pores.Lithologic Reservoirs,2016,28(6):88-94.
[43]段永刚,曹廷宽,杨小莹,等.页岩储层纳米孔隙流动模拟研究.西南石油大学学报(自然科学版),2015,37(3):63-68.DUAN Y G,CAO T K,YANG X Y,et al.Simulation of gas flow in nano-scale pores of shale gas deposits.Journal of Southwest Petroleum University(Science&Technology Edition),2015,37(3):63-68.
[44]BRUNAUER S,EMMETT P H,TELLER E.Adsorption of gases in multimolecular layers.Journal of American Chemical Society,1938,60(29):309-319.