水平井压裂水泥环应力分析
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摘要
为获取准确的井筒应力分布,根据弹性平面应变力学理论,考虑套管-水泥环-地层系统各部分的应力加载过程和水力裂缝产生的诱导应力场,建立了水平井压裂时套管-水泥环-地层系统应力分布的计算模型。利用该模型,分析了水力裂缝形成前后的系统应力分布,以及裂缝诱导应力场、水泥石杨氏模量、套管壁厚对水泥环内壁应力分布的影响。分析结果表明:随着与裂缝的距离增大,水泥环内壁受到的径向压缩应力逐渐降低,环向应力逐渐由压缩应力变为拉伸应力;优化裂缝间距、降低水泥石杨氏模量、增加套管壁厚可以降低水泥环内壁受力,缓解水泥环内壁的应力集中程度。本文所建模型可为水力压裂水平井的固井设计以及裂缝间距设计提供理论指导。
In order to obtain the accurate stress distribution of wellbore, according to the plane theory of elasticity, considering the stress loading process of casing-cement sheath-formation system and the stress field induced by hydraulic fractures, a calculation model of stress distribution in casing-cement sheath-formation system is established. Using this model, the stress distribution of the system before and after the formation of fractures, and the influences of the induced stress field, the Young's modulus of cement stone and the casing thickness on the stress distribution of cement sheath are analyzed. The results show that the radial compressive stress of the inner wall of the cement sheath decreases gradually with the distance from the fracture, and the circumferential stress gradually changes from the compressive stress to the tensile stress. Optimizing the fracture spacing, reducing the Young's modulus of cement stone and increasing the casing thickness can reduce the stress and relieve the stress concentration on the inner wall of the cement sheath. The model provided in this paper supplies a theoretical guidance for cementing design and fracture spacing design of horizontal well that will conduct hydraulic fracturing.
In order to obtain the accurate stress distribution of wellbore, according to the plane theory of elasticity, considering the stress loading process of casing-cement sheath-formation system and the stress field induced by hydraulic fractures, a calculation model of stress distribution in casing-cement sheath-formation system is established. Using this model, the stress distribution of the system before and after the formation of fractures, and the influences of the induced stress field, the Young's modulus of cement stone and the casing thickness on the stress distribution of cement sheath are analyzed. The results show that the radial compressive stress of the inner wall of the cement sheath decreases gradually with the distance from the fracture, and the circumferential stress gradually changes from the compressive stress to the tensile stress. Optimizing the fracture spacing, reducing the Young's modulus of cement stone and increasing the casing thickness can reduce the stress and relieve the stress concentration on the inner wall of the cement sheath. The model provided in this paper supplies a theoretical guidance for cementing design and fracture spacing design of horizontal well that will conduct hydraulic fracturing.
引文
[1]尹虎,李黔,李建涛,等.利用套管变形量进行地应力反演[J].石油钻探技术,2012,40(3):54-57.(YIN Hu,LI Qian,LI Jiantao,et al.Inversion of in-situ stress with the amount of casing deformation[J].Petroleum drilling technology,2012,40(3):54-57(in Chinese)).
[2]秦杜,楼一珊,翟晓鹏,等.非均匀地应力下套管挤压变形的有限元分析[J].石油地质与工程,2011,25(5):109-111.(QIN Du,LOU Yishan,ZHAI Xiaopeng,et al.Finite element analysis on non-uniform ground stress casing running extrusion deformation[J].Petroleum geology and engineering,2011,25(5):109-111(in Chinese)).
[3]张景富,张德兵,张强,等.水泥环弹性参数对套管-水泥环-地层固结体结构完整性的影响[J].石油钻采工艺,2013,35(5):43-46.(ZHANG Jingfu,ZHANG Debing,ZHANG Qiang,et al.Impact of elastic parameters of cement ring on structural integrity of casing-cement ring-strata cementing combination[J].Oil drilling&production technology,2013,35(5):43-46(in Chinese)).
[4]房军,赵怀文,岳伯谦,等.非均匀地应力作用下套管与水泥环的受力分析[J].石油大学学报(自然科学版),1995,19(6):52-57.(FANG Jun,ZHAO Huaiwen,YUE Boqian,et al.Analysis of sheath loading property of casing and cement under nonuniform geologic stress[J].Journal of China university of petroleum(natural science edition),1995,19(6):52-57(in Chinese)).
[5]曾德智,林元华,李双贵,等.非均匀地应力下水泥环界面应力分布规律研究[J].石油钻探技术,2007,35(1):32-34.(ZENG Dezhi,LIN Yuanhua,LI Shuanggui,et al.Study of stress distribution of cement sheath section under non-uniform formation stress[J].Petroleum drilling technology,2007,35(1):32-34(in Chinese)).
[6]王耀锋,李军强,杨小辉.套管-水泥环-地层系统应力分布规律研究[J].石油钻探技术,2008,36(5):7-11.(WANG Yaofeng,LI Junqiang,YANG Xiaohui.Stress distribution in casing-cement-stratum[J].Petroleum drilling technology,2008,36(5):7-11(in Chinese)).
[7]王宴滨,高德利,房军.套管-水泥环-地层多层组合系统受力特性分析[J].应用力学学报,2014,31(3):387-389.(WANG Yanbin,GAO Deli,FANG Jun.Mechanical characteristics analysis of casing-cement ring-formation multilayer composite system[J].Chinese journal of applied mechanics,2014,31(3):387-389(in Chinese)).
[8]李子丰.油气井杆管柱力学研究进展与争论[J].石油学报,2016,37(4):531-556.(LI Zifeng.Research advances and debates on tubular mechanics in oil and gas wells[J].Acta petrolei sinica,2016,37(4):531-556(in Chinese)).
[9]BRADLEY W B.Failure of inclined boreholes[J].Journal of energy resources technology,1979,101(4):232-239.
[10]唐志强.基于井壁崩落的定向井坍塌压力计算模型[D].成都:西南石油大学,2015.(TANG Zhiqiang.Collapse pressure calculation model of directional well based on wellbore breakout[D].Chengdu:Southwest Petroleum University,2015(in Chinese)).
[11]LV Z,HE S,GU D,et al.Hydraulic fracture initiation while staged fracturing for horizontal wells[C]//Proceedings of International Petroleum Technology Conference.Beijing:Internation Petroleum Technology Conference,2013.
[12]郭天魁,张士诚,刘卫来,等.页岩储层射孔水平井分段压裂的起裂压力[J].天然气工业,2013,33(12):87-93.(GUO Tiankui,ZHANG Shicheng,LIU Weilai,et al.Initiation pressure of multi-stage fracking for perforated horizontal wells of shale gas reservoirs[J].Natural gas industry,2013,33(12):87-93(in Chinese)).
[13]曾顺鹏,张国强,韩家新,等.多裂缝应力阴影效应模型及水平井分段压裂优化设计[J].天然气工业,2015,35(3):55-59.(ZENG Shunpeng,ZHANG Guoqiang,HAN Jiaxin,et al.Model ofmulti-fracture stress shadow effect model and optimization design for staged fracturing of horizontal wells[J].Natural gas industry,2015,35(3):55-59(in Chinese)).
[14]李勇明,陈曦宇,赵金洲,等.水平井分段多簇压裂缝间干扰研究[J].西南石油大学学报(自然科学版),2016,38(1):76-83.(LI Yongming,CHEN Xiyu,ZHAO Jinzhou,et al.The effects of crack interaction of multi-stage horizontal fracture[J].Journal of southwest petroleum university(natural science edition),2016,38(1):76-83(in Chinese)).
[15]SNEDDON I N.The distribution of stress in the neighbourhood of a crack in an elastic solid[J].Proceedings,royal society of London,series A,1946,187(1009):229-260.
[16]WARPINSKI N R,BRANAGAN P T.Altered-stress fracturing[J].Journal of petroleum technology,1989,41(9):990-997.
[17]郭辛阳,步玉环,李娟,等.固井封固系统初始作用力及其影响[J].中国石油大学学报(自然科学版),2011,35(3):79-83.(Guo Xinyang,BU Yuhuan,LI Juan,et al.Initial forces on cementing isolation system and its effect on isolation system[J].Journal of China university of petroleum(edition of natural science),2011,35(3):79-83(in Chinese)).
[18]MUSKHELISHVILI N I.Some basic problems of the mathematical theory of elasticity[M].Berlin:Springer Science&Business Media,2013.
[19]THIERCELIN M J,DARGAUD B,BARET J F,et al.Cement design based on cement mechanical response[J].SPE drilling&completion,1998,13(4):266-273.
[20]ZOBACK M D.Reservoir geomechanics[M].Cambridge:Cambridge University Press,2010.
[21]谢贻权.弹性力学[M].杭州:浙江大学出版社,1988.(XIE Yiquan.Elastic mechanics[M].Hangzhou:Zhejiang University Press,1988(in Chinese)).
[22]EL-SAYED A A H,KHALAF F.Resistance of cemented concentric casing strings under nonuniform loading[J].SPE drilling engineering,1992,7(1):59-64.
[2]秦杜,楼一珊,翟晓鹏,等.非均匀地应力下套管挤压变形的有限元分析[J].石油地质与工程,2011,25(5):109-111.(QIN Du,LOU Yishan,ZHAI Xiaopeng,et al.Finite element analysis on non-uniform ground stress casing running extrusion deformation[J].Petroleum geology and engineering,2011,25(5):109-111(in Chinese)).
[3]张景富,张德兵,张强,等.水泥环弹性参数对套管-水泥环-地层固结体结构完整性的影响[J].石油钻采工艺,2013,35(5):43-46.(ZHANG Jingfu,ZHANG Debing,ZHANG Qiang,et al.Impact of elastic parameters of cement ring on structural integrity of casing-cement ring-strata cementing combination[J].Oil drilling&production technology,2013,35(5):43-46(in Chinese)).
[4]房军,赵怀文,岳伯谦,等.非均匀地应力作用下套管与水泥环的受力分析[J].石油大学学报(自然科学版),1995,19(6):52-57.(FANG Jun,ZHAO Huaiwen,YUE Boqian,et al.Analysis of sheath loading property of casing and cement under nonuniform geologic stress[J].Journal of China university of petroleum(natural science edition),1995,19(6):52-57(in Chinese)).
[5]曾德智,林元华,李双贵,等.非均匀地应力下水泥环界面应力分布规律研究[J].石油钻探技术,2007,35(1):32-34.(ZENG Dezhi,LIN Yuanhua,LI Shuanggui,et al.Study of stress distribution of cement sheath section under non-uniform formation stress[J].Petroleum drilling technology,2007,35(1):32-34(in Chinese)).
[6]王耀锋,李军强,杨小辉.套管-水泥环-地层系统应力分布规律研究[J].石油钻探技术,2008,36(5):7-11.(WANG Yaofeng,LI Junqiang,YANG Xiaohui.Stress distribution in casing-cement-stratum[J].Petroleum drilling technology,2008,36(5):7-11(in Chinese)).
[7]王宴滨,高德利,房军.套管-水泥环-地层多层组合系统受力特性分析[J].应用力学学报,2014,31(3):387-389.(WANG Yanbin,GAO Deli,FANG Jun.Mechanical characteristics analysis of casing-cement ring-formation multilayer composite system[J].Chinese journal of applied mechanics,2014,31(3):387-389(in Chinese)).
[8]李子丰.油气井杆管柱力学研究进展与争论[J].石油学报,2016,37(4):531-556.(LI Zifeng.Research advances and debates on tubular mechanics in oil and gas wells[J].Acta petrolei sinica,2016,37(4):531-556(in Chinese)).
[9]BRADLEY W B.Failure of inclined boreholes[J].Journal of energy resources technology,1979,101(4):232-239.
[10]唐志强.基于井壁崩落的定向井坍塌压力计算模型[D].成都:西南石油大学,2015.(TANG Zhiqiang.Collapse pressure calculation model of directional well based on wellbore breakout[D].Chengdu:Southwest Petroleum University,2015(in Chinese)).
[11]LV Z,HE S,GU D,et al.Hydraulic fracture initiation while staged fracturing for horizontal wells[C]//Proceedings of International Petroleum Technology Conference.Beijing:Internation Petroleum Technology Conference,2013.
[12]郭天魁,张士诚,刘卫来,等.页岩储层射孔水平井分段压裂的起裂压力[J].天然气工业,2013,33(12):87-93.(GUO Tiankui,ZHANG Shicheng,LIU Weilai,et al.Initiation pressure of multi-stage fracking for perforated horizontal wells of shale gas reservoirs[J].Natural gas industry,2013,33(12):87-93(in Chinese)).
[13]曾顺鹏,张国强,韩家新,等.多裂缝应力阴影效应模型及水平井分段压裂优化设计[J].天然气工业,2015,35(3):55-59.(ZENG Shunpeng,ZHANG Guoqiang,HAN Jiaxin,et al.Model ofmulti-fracture stress shadow effect model and optimization design for staged fracturing of horizontal wells[J].Natural gas industry,2015,35(3):55-59(in Chinese)).
[14]李勇明,陈曦宇,赵金洲,等.水平井分段多簇压裂缝间干扰研究[J].西南石油大学学报(自然科学版),2016,38(1):76-83.(LI Yongming,CHEN Xiyu,ZHAO Jinzhou,et al.The effects of crack interaction of multi-stage horizontal fracture[J].Journal of southwest petroleum university(natural science edition),2016,38(1):76-83(in Chinese)).
[15]SNEDDON I N.The distribution of stress in the neighbourhood of a crack in an elastic solid[J].Proceedings,royal society of London,series A,1946,187(1009):229-260.
[16]WARPINSKI N R,BRANAGAN P T.Altered-stress fracturing[J].Journal of petroleum technology,1989,41(9):990-997.
[17]郭辛阳,步玉环,李娟,等.固井封固系统初始作用力及其影响[J].中国石油大学学报(自然科学版),2011,35(3):79-83.(Guo Xinyang,BU Yuhuan,LI Juan,et al.Initial forces on cementing isolation system and its effect on isolation system[J].Journal of China university of petroleum(edition of natural science),2011,35(3):79-83(in Chinese)).
[18]MUSKHELISHVILI N I.Some basic problems of the mathematical theory of elasticity[M].Berlin:Springer Science&Business Media,2013.
[19]THIERCELIN M J,DARGAUD B,BARET J F,et al.Cement design based on cement mechanical response[J].SPE drilling&completion,1998,13(4):266-273.
[20]ZOBACK M D.Reservoir geomechanics[M].Cambridge:Cambridge University Press,2010.
[21]谢贻权.弹性力学[M].杭州:浙江大学出版社,1988.(XIE Yiquan.Elastic mechanics[M].Hangzhou:Zhejiang University Press,1988(in Chinese)).
[22]EL-SAYED A A H,KHALAF F.Resistance of cemented concentric casing strings under nonuniform loading[J].SPE drilling engineering,1992,7(1):59-64.
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