横观各向同性地层井壁应力分析
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摘要
目前关于实钻井壁应力分布计算大都基于岩石的各向同性,在实际工况分析中存在误差。该文应用各向异性材料力学理论,将层状地层简化为横观各向同性岩石材料,建立了各向异性地层井孔周围应力计算模型。应用弹性力学广义平面应变问题的复变函数解法,结合井孔周围受力边界条件及相关坐标转换,得到横观各向同性地层斜井壁围岩应力解析解。对井壁围岩主应力影响因素的分析表明,层理面弹性参数、层理面倾角、水平原地应力比和井斜角方位角对井壁应力分布均会造成影响。在进行层理性地层井壁稳定分析时,应格外注意层理面倾角、原地应力比以及井斜参数的影响。该结果对现场施工设计有很好的指导意义。
Most of the existing models for borehole wall stress are based on isotropic rock. Thus, some errors may be generated under actual working conditions. In this research, according to the theory of mechanics of anisotropic materials, the bedded formation is simplified as transversely isotropic rock material, and a calculation model for stress around the borehole in anisotropic formations is developed. Based on the complex function solution of generalized plane strain elasticity problems, the circular-hole boundary conditions of the stress distribution, and the coordinate transformation, the stress distribution at the borehole wall in a transverse isotropic formation is investigated. A parametric study is carried out to investigate the effect of the elastic parameters, bedding plane inclination and orientation, ratio of horizontal in-situ stress, borehole deviation, and azimuth angle on the principal stress distribution. Results indicate that in the analysis of wellbore stability in bedding shale, special attention should be paid to the effect of bedding plane inclination, the in-situ stress ratio, and the borehole deviation parameters. The results are useful to construction site design before drilling.
Most of the existing models for borehole wall stress are based on isotropic rock. Thus, some errors may be generated under actual working conditions. In this research, according to the theory of mechanics of anisotropic materials, the bedded formation is simplified as transversely isotropic rock material, and a calculation model for stress around the borehole in anisotropic formations is developed. Based on the complex function solution of generalized plane strain elasticity problems, the circular-hole boundary conditions of the stress distribution, and the coordinate transformation, the stress distribution at the borehole wall in a transverse isotropic formation is investigated. A parametric study is carried out to investigate the effect of the elastic parameters, bedding plane inclination and orientation, ratio of horizontal in-situ stress, borehole deviation, and azimuth angle on the principal stress distribution. Results indicate that in the analysis of wellbore stability in bedding shale, special attention should be paid to the effect of bedding plane inclination, the in-situ stress ratio, and the borehole deviation parameters. The results are useful to construction site design before drilling.
引文
[1]陈勉,金衍.深井井壁稳定技术研究进展与发展趋势[J].石油钻探技术,2005,33(5):28―34.Chen Mian,Jin Yan.Advances and developmental trend of the wall stability technique[J].Petroleum Drilling Techniques,2005,33(5):28―34.(in Chinese)
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[6]Gaede O,Karpfinger F,Jocker J,et al.Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock[J].International Journal of Rock Mechanics and Mining Sciences,2012,51(4):53―63.
[7]Amader B.Rock anisotropy and theory of stress measurements[C]//Brebbia C,Orszag S.Lecture Notes in Engineering.Berlin:Springer Verlag,1983:87-116.
[8]Aadn?y B S.Continuum mechanics analysis of the stability of inclined boreholes in anisotropic rock formations[D].Trondheim:The Norwegian Institute of Technology,1987.
[9]Ong S H.Borehole stability[D].Norman OK:University of Oklahoma,1994.
[10]Gupta D J,Zaman M.Stability of boreholes in a geologic medium including the effects of anisotropy[J].Applied Mathematics and Mechanics,1999,20(8):837―866.
[11]崔杰,焦永树,曹维勇,蔡宗熙,各向异性地层中井孔周围应力场的研究[J].工程力学,2011,28(7):31―36.Cui Jie,Jiao Yongshu,Cao Weiyong,Cai Zongxi.A study on the stress field around a borehole in anisotropic formation[J].Engineering Mechanics,2011,28(7):31―36.(in Chinese)
[12]卢运虎,陈勉,袁建波,等.各向异性地层中斜井井壁失稳机理[J].石油学报,2013,34(3):563―568.Lu Yunhu,Chen Mian,Yuan Jianbo,et al.Borehole instability mechanism of a deviated well in anisotropic formations[J].Acta Petrolei Sinica,2013,34(3):563―568.(in Chinese)
[13]Kreyszig Z.Advanced engineering mathematics[M].6th ed.New York:John Wiley&Sons,Inc.,1988:337―339.
[14]Lekhnitskii S G.Theory of Elasticity of an anisotropic body[M].Moscow:Mir Publishers,1981:113―117.
[15]罗祖道,李思简.各向异性材料力学[M].上海:上海交通大学出版社,1994:12―14.Luo Zudao,Li Sijian.Mechanics of anisotropy material[M].Shanghai:Shanghai Jiaotong University Press,1994:12―14.(in Chinese)
[16]Lee H,Ong S H,Azeemuddin M,et al.A wellbore stability model for formations with anisotropic rock strengths[J].Journal of Petroleum Science and Engineering,2012,96(10):109―119.
[17]杨雪强,李子生,燕全会,孙汉芳.横观各向同性岩石类材料的破坏准则[J].工程力学,2012,29(12):328―333.Yang Xueqiang,Li Zisheng,Yan Quanhui,Sun Hanfang.Failure criterion for transversely isotropic rock materials[J].Engineering Mechanics,2012,29(12):328―333.(in Chinese)
[18]Gao Z,Zhao J,Yao Y.A generalized anisotropic failure criterion for geomaterials[J].International Journal of Solids and Structures,2010,47(22):3166―3185.
[2]Bradley W B.Failure of inclined boreholes[J].Journal of Energy Resources Technology,1979,101(12):232―239.
[3]陈勉,金衍,张广清,等.石油工程岩石力学[M].北京:科学出版社,2008:103―116.Chen Mian,Jin Yan,Zhang Guangqing,et al.Petroleum related rock mechanics[M].Beijing:Science Press,2008:103―116.(in Chinese)
[4]Zhang W,Gao J,Lan K,et al.Analysis of borehole collapse and fracture initiation positions and drilling trajectory optimization[J].Journal of Petroleum Science and Engineering,2015:129(5):29―39.
[5]胡秀章,王肖均,李永池.层状岩石中井孔稳定性的数值分析[J].石油勘探与开发,2004,31(4):89―94.Hu Xiuzhang,Wang Xiaojun,Li Yongchi.Numerical analysis of borehole stability in the bedded formation[J].Petroleum Exploration and Development,2004,31(4):89―94.(in Chinese)
[6]Gaede O,Karpfinger F,Jocker J,et al.Comparison between analytical and 3D finite element solutions for borehole stresses in anisotropic elastic rock[J].International Journal of Rock Mechanics and Mining Sciences,2012,51(4):53―63.
[7]Amader B.Rock anisotropy and theory of stress measurements[C]//Brebbia C,Orszag S.Lecture Notes in Engineering.Berlin:Springer Verlag,1983:87-116.
[8]Aadn?y B S.Continuum mechanics analysis of the stability of inclined boreholes in anisotropic rock formations[D].Trondheim:The Norwegian Institute of Technology,1987.
[9]Ong S H.Borehole stability[D].Norman OK:University of Oklahoma,1994.
[10]Gupta D J,Zaman M.Stability of boreholes in a geologic medium including the effects of anisotropy[J].Applied Mathematics and Mechanics,1999,20(8):837―866.
[11]崔杰,焦永树,曹维勇,蔡宗熙,各向异性地层中井孔周围应力场的研究[J].工程力学,2011,28(7):31―36.Cui Jie,Jiao Yongshu,Cao Weiyong,Cai Zongxi.A study on the stress field around a borehole in anisotropic formation[J].Engineering Mechanics,2011,28(7):31―36.(in Chinese)
[12]卢运虎,陈勉,袁建波,等.各向异性地层中斜井井壁失稳机理[J].石油学报,2013,34(3):563―568.Lu Yunhu,Chen Mian,Yuan Jianbo,et al.Borehole instability mechanism of a deviated well in anisotropic formations[J].Acta Petrolei Sinica,2013,34(3):563―568.(in Chinese)
[13]Kreyszig Z.Advanced engineering mathematics[M].6th ed.New York:John Wiley&Sons,Inc.,1988:337―339.
[14]Lekhnitskii S G.Theory of Elasticity of an anisotropic body[M].Moscow:Mir Publishers,1981:113―117.
[15]罗祖道,李思简.各向异性材料力学[M].上海:上海交通大学出版社,1994:12―14.Luo Zudao,Li Sijian.Mechanics of anisotropy material[M].Shanghai:Shanghai Jiaotong University Press,1994:12―14.(in Chinese)
[16]Lee H,Ong S H,Azeemuddin M,et al.A wellbore stability model for formations with anisotropic rock strengths[J].Journal of Petroleum Science and Engineering,2012,96(10):109―119.
[17]杨雪强,李子生,燕全会,孙汉芳.横观各向同性岩石类材料的破坏准则[J].工程力学,2012,29(12):328―333.Yang Xueqiang,Li Zisheng,Yan Quanhui,Sun Hanfang.Failure criterion for transversely isotropic rock materials[J].Engineering Mechanics,2012,29(12):328―333.(in Chinese)
[18]Gao Z,Zhao J,Yao Y.A generalized anisotropic failure criterion for geomaterials[J].International Journal of Solids and Structures,2010,47(22):3166―3185.