基于Skempton有效应力原理的岩石压缩系数研究
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摘要
基于适用于岩石的Skempton有效应力原理,系统地推导了岩石表观压缩系数、颗粒压缩系数、孔隙压缩系数在3种不同应力条件下的关系式,得到一组岩石各压缩系数的定量计算式,并进行了实例论证。研究表明:恒总应力下的岩石表观压缩系数、孔隙压缩系数分别为恒流压下的岩石表观压缩系数、孔隙压缩系数与颗粒压缩系数之差,封闭条件下的岩石压缩系数关系式与Gassmann方程认识一致;在相同应力条件下,岩石的孔隙压缩系数远大于表观压缩系数,表观压缩系数又大于颗粒压缩系数,不同压缩系数之间差距可达2~3个数量级;新计算式基于岩石的应力应变原理,厘清了各压缩系数之间的相互关系,计算简便,实用性好。
Based on the Skempton effective stress principle suitable for rocks,the expressions of the apparent compress on coefficient,particle compression coefficient and pore compression coefficient of rock under three stress conditions were derived,and they were verified by an example. The results show that the apparent compression coefficient and pore compression coefficient under constant total stress condition are respectively the difference between the corresponding compression coefficient and particle compression coefficient under constant pore pressure condition. The expressions of the compression coefficients of rock under the closed condition are consistent with those based on Gassmann equation. Under the same stress condition,the pore compression coefficient is far greater than the apparent compression coefficient,and the apparent compression coefficient is bigger than the particle compression coefficient. The difference between different compression coefficients of rock is up to 2 ~ 3 orders of magnitude. The calculation formulas are based on the stressstrain principle of rock,and the relationships between different compression coefficients of rock are clarified. They are simple and practical.
Based on the Skempton effective stress principle suitable for rocks,the expressions of the apparent compress on coefficient,particle compression coefficient and pore compression coefficient of rock under three stress conditions were derived,and they were verified by an example. The results show that the apparent compression coefficient and pore compression coefficient under constant total stress condition are respectively the difference between the corresponding compression coefficient and particle compression coefficient under constant pore pressure condition. The expressions of the compression coefficients of rock under the closed condition are consistent with those based on Gassmann equation. Under the same stress condition,the pore compression coefficient is far greater than the apparent compression coefficient,and the apparent compression coefficient is bigger than the particle compression coefficient. The difference between different compression coefficients of rock is up to 2 ~ 3 orders of magnitude. The calculation formulas are based on the stressstrain principle of rock,and the relationships between different compression coefficients of rock are clarified. They are simple and practical.
引文
[1]TERZAGHI K.Die berechnung der curchlassigkeitziffer des tones aus dem verlauf der hydrodynamischen spannungserscheinumgen[J].Sber Akad Wiss Wien,1923,132(2):125-138.
[2]TERZAGHI K.The shearing resistance of saturated soils and the angle between the planes of shear[C].Proceedings of First International Soil Mechanics and Foundation Engineering:Volume 1.Cambridge,Massachusetts:Graduate School of Engineering,Harvard University,1936:54-56.
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[4]李传亮.再谈岩石的压缩系数:回应高有瑞博士[J].中国海上油气,2011,25(4):85-87.LI Chuanliang.A more discussion on the compressibility of reservoir rocks:in reply to Dr.GAO Yourui[J].China Offshore Oil and Gas,2011,25(4):85-87.
[5]李传亮.再谈岩石的压缩系数:回应王厉强博士[J].新疆石油地质,2012,33(1):125-127.LI Chuanliang.The formulae of rock compressibility of reservoirs:reply to Dr WANG Liqiang[J].Xinjiang Petroleum Geology,2012,33(1):125-127.
[6]李传亮.实测岩石压缩系数偏高的原因分析[J].大庆石油地质与开发,2005,24(5):53-54.LI Chuanliang.Results interpretation of higher measured rock compressibility[J].Petroleum Geology&Oilfield Development in Daqing,2005,24(5):53-54.
[7]王厉强,李正科,申红,等.实测岩石孔隙压缩系数偏高原因再分析:与李传亮教授商榷[J].新疆石油地质,2012,33(3):379-381.WANG Liqiang,LI Zhengke,SHEN Hong,et al.A discussion on results interpretation again of higher measured rock compressibility[J].Xinjiang Petroleum Geology,2012,33(3):379-381.
[8]张津宁,张金功.柴西地区变围压条件下储层物性变化规律[J].特种油气藏.2016,23(5):114-118.ZHANG Jinning,ZHANG Jingong.Reservoir properties under variable confining pressure in Western Qaidam Basin[J].Special Oil and Gas Reservoirs,2016,23(5):114-118.
[9]高有瑞,刘艳,时付更.基质型灰岩储层岩石压缩系数的确定[J].中国海上油气,2011,23(4):247-250.GAO Yourui,LIU Yan,SHI Fugeng.Determining rock compressibility for matrix limestone reservoir[J].China Offshore Oil and Gas,2011,23(4):247-250.
[10]罗瑞兰.关于低渗致密储层岩石的应力敏感问题[J].石油钻采工艺,2010,32(2):126-130.LUO Ruilan.Discussion of stress sensitivity of low permeability and tight reservoir rocks[J].Oil Drilling&Production Technology,2010,32(2):126-130.
[11]SEMPTON A W.Effective stress in soils,concrete and rock[C].Pore Pressure and Suction in Soils.London:Butterworths,1961:4-16.
[12]秦积舜,李爱芬.油层物理学[M].东营:中国石油大学出版社,2003:121-123.
[13]BIOT M A.Theory of elasticity and consolidation for a porous anisotropic solid[J].Journal of Applied Physics,1955,26(2):182-185.
[14]GASSMANN F.Elastic waves through a Peaking of spheres[J].Geophysics,1951,16:673-682.
[15]GEERTSMA J.The effect of fluid pressure decline on volumetric changes of porous rocks[J].Petroleum Transactions,AIME,1957,210:331-340.
[16]BISHOP A W.The influence of an undrained change in stress on the pore pressure in porous media of low compressibility[J].Geotechnique,1973,23(3):435-442.
[2]TERZAGHI K.The shearing resistance of saturated soils and the angle between the planes of shear[C].Proceedings of First International Soil Mechanics and Foundation Engineering:Volume 1.Cambridge,Massachusetts:Graduate School of Engineering,Harvard University,1936:54-56.
[3]李传亮.岩石压缩系数与孔隙度的关系[J].中国海上油气(地质),2003,17(5):355-358.LI Chuanliang.Relationship between compression coefficient and porosity of rock[J].China Offshore Oil and Gas(Geology),2003,17(5):355-358.
[4]李传亮.再谈岩石的压缩系数:回应高有瑞博士[J].中国海上油气,2011,25(4):85-87.LI Chuanliang.A more discussion on the compressibility of reservoir rocks:in reply to Dr.GAO Yourui[J].China Offshore Oil and Gas,2011,25(4):85-87.
[5]李传亮.再谈岩石的压缩系数:回应王厉强博士[J].新疆石油地质,2012,33(1):125-127.LI Chuanliang.The formulae of rock compressibility of reservoirs:reply to Dr WANG Liqiang[J].Xinjiang Petroleum Geology,2012,33(1):125-127.
[6]李传亮.实测岩石压缩系数偏高的原因分析[J].大庆石油地质与开发,2005,24(5):53-54.LI Chuanliang.Results interpretation of higher measured rock compressibility[J].Petroleum Geology&Oilfield Development in Daqing,2005,24(5):53-54.
[7]王厉强,李正科,申红,等.实测岩石孔隙压缩系数偏高原因再分析:与李传亮教授商榷[J].新疆石油地质,2012,33(3):379-381.WANG Liqiang,LI Zhengke,SHEN Hong,et al.A discussion on results interpretation again of higher measured rock compressibility[J].Xinjiang Petroleum Geology,2012,33(3):379-381.
[8]张津宁,张金功.柴西地区变围压条件下储层物性变化规律[J].特种油气藏.2016,23(5):114-118.ZHANG Jinning,ZHANG Jingong.Reservoir properties under variable confining pressure in Western Qaidam Basin[J].Special Oil and Gas Reservoirs,2016,23(5):114-118.
[9]高有瑞,刘艳,时付更.基质型灰岩储层岩石压缩系数的确定[J].中国海上油气,2011,23(4):247-250.GAO Yourui,LIU Yan,SHI Fugeng.Determining rock compressibility for matrix limestone reservoir[J].China Offshore Oil and Gas,2011,23(4):247-250.
[10]罗瑞兰.关于低渗致密储层岩石的应力敏感问题[J].石油钻采工艺,2010,32(2):126-130.LUO Ruilan.Discussion of stress sensitivity of low permeability and tight reservoir rocks[J].Oil Drilling&Production Technology,2010,32(2):126-130.
[11]SEMPTON A W.Effective stress in soils,concrete and rock[C].Pore Pressure and Suction in Soils.London:Butterworths,1961:4-16.
[12]秦积舜,李爱芬.油层物理学[M].东营:中国石油大学出版社,2003:121-123.
[13]BIOT M A.Theory of elasticity and consolidation for a porous anisotropic solid[J].Journal of Applied Physics,1955,26(2):182-185.
[14]GASSMANN F.Elastic waves through a Peaking of spheres[J].Geophysics,1951,16:673-682.
[15]GEERTSMA J.The effect of fluid pressure decline on volumetric changes of porous rocks[J].Petroleum Transactions,AIME,1957,210:331-340.
[16]BISHOP A W.The influence of an undrained change in stress on the pore pressure in porous media of low compressibility[J].Geotechnique,1973,23(3):435-442.
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