考虑应力敏感的稠油热采试井模型研究
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摘要
基于稠油热采的物理过程,利用渗流力学基本原理,建立考虑应力敏感的稠油热采试井解释数学模型,通过Laplace变换和摄动变换法求解得到模型在拉氏空间的解析解,再利用Stehfest数值反演方法得到实空间的数值解,绘制无因次井底压力及压力导数与无因次时间的特征曲线,并进行影响因素分析。研究表明:该试井模型曲线可划分为5个流动阶段;考虑应力敏感影响时,内区与外区径向流阶段压力导数曲线都表现出不同程度的"上翘",外区径向流阶段压力导数曲线高于斜率为(1-n)/(3-n)的直线,应力敏感系数越大,偏离幅度越大;幂律指数越小,外区径向流阶段压力导数曲线"上翘"幅度越大。利用该模型可以分析储层的应力敏感特征,指导存在应力敏感效应的稠油热采试井资料的解释与研究。
Based on the physical process of heavy oil thermal recovery,the well test interpretation mathematical model of heavy oil thermal recovery well was established under considering stress sensitivity using the basic principle of percolation mechanics. The analytical solution of the model in Lagrangian space was obtained through Laplace transformation and perturbation transformation,then its numerical solution of real space was obtained using Stehfest numerical inversion,the dimensionless bottom-hole pressure and pressure derivative curves of the model were drawn,and the influence factors of the curves were analyzed. It is shown that,the dimensionless bottomhole pressure and pressure derivative curves of the model can be divided into five flow stages according to the characteristics of the pressure derivative curve. When stress sensitivity is considered,the pressure derivative curves will show " upwarping" in different degrees in the radial flow stage of non-Newtonian power law fluid area and Newtonian power law fluid area; in the radial flow stage of non-Newtonian fluid area,the pressure derivative curve is higher than the straight line with a slope of( 1-n)/( 3-n),the greater the stress sensitivity coefficient,the greater the deviation,and the less the power law index,the greater the " upwarping" degree of the pressure derivative curve. The model can be used for analyzing the stress sensitivity characteristics of reservoirs and guiding the interpretation of the well test data of heavy oil thermal recovery wells considering stress sensitivity.
Based on the physical process of heavy oil thermal recovery,the well test interpretation mathematical model of heavy oil thermal recovery well was established under considering stress sensitivity using the basic principle of percolation mechanics. The analytical solution of the model in Lagrangian space was obtained through Laplace transformation and perturbation transformation,then its numerical solution of real space was obtained using Stehfest numerical inversion,the dimensionless bottom-hole pressure and pressure derivative curves of the model were drawn,and the influence factors of the curves were analyzed. It is shown that,the dimensionless bottomhole pressure and pressure derivative curves of the model can be divided into five flow stages according to the characteristics of the pressure derivative curve. When stress sensitivity is considered,the pressure derivative curves will show " upwarping" in different degrees in the radial flow stage of non-Newtonian power law fluid area and Newtonian power law fluid area; in the radial flow stage of non-Newtonian fluid area,the pressure derivative curve is higher than the straight line with a slope of( 1-n)/( 3-n),the greater the stress sensitivity coefficient,the greater the deviation,and the less the power law index,the greater the " upwarping" degree of the pressure derivative curve. The model can be used for analyzing the stress sensitivity characteristics of reservoirs and guiding the interpretation of the well test data of heavy oil thermal recovery wells considering stress sensitivity.
引文
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[2]IKOKU C U,RAMEY H J.Transient flow of non-newtonian power-law fluids in porous media[C].SPE 7139-PA,1979.
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[11]贾智淳,闫术,董晓芳,等.剪切变稀作用对聚驱试井分析影响的数值研究[J].西南石油大学学报(自然科学版),2016,38(5):108-113.JIA Zhichun,YAN Shu,DONG Xiaofang,et al.Numerical study on the impact of shear thinning behavior in well test analysis for polymer flooding[J].Journal of Southwest Petroleum University(Science&Tecnology Edition),2016,38(5):108-113.
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[15]宁正福,廖新维,高旺来,等.应力敏感裂缝性双区复合气藏压力动态特征[J].大庆石油学院学报,2004,28(2):34-36.NING Zhengfu,LIAO Xinwei,GAO Wanglai,et al.Pressure transient response in deep-seated geothermal stresssensitive fissured composite gas reservoir[J].Journal of Daqing Petroleum Institute,2004,28(2):34-36.
[16]刘启国,唐伏平,冯国庆,等.开关井不同程度应力敏感效应对井底压力动态的影响[J].石油与天然气地质,2007,28(4):523-525.LIU Qiguo,TANG Fuping,FENG Guoqing,et al.Influence of different stress sensitivities on bottom hole pressure behaviors during well opening and shut-in[J].Oil&Gas Geology,2007,28(4):523-525.
[17]李顺初,任丽,郑鹏社,等.基于应力敏感的天然裂缝性页岩气藏双孔模型解的结构[J].应用数学和力学,2017,38(2):233-242.LI Shunchu,REN Li,ZHENG Pengshe,et al.Similar structure of the solution to the dual-porosity model for naturally fractured shale gas reservoirs based on stress sensitivity[J].Applied Mathematics and Mechanics,2017,38(2):233-242.
[18]王璐,姚约东,黄山,等.裂缝性致密油藏非稳态窜流规律[J].断块油气田,2016,23(3):329-333.WANG Lu,YAO Yuedong,HUANG Shan,et al.Transient cross flow law for fractured tight oil reservoirs[J].FaultBlock Oil&Gas Field,2016,23(3):329-333.
[19]刘国勇,刘阳,张刘平.压实作用对砂岩储层物性的影响[J].西安石油大学学报(自然科学版),2006,21(4):24-28.LIU Guoyong,LIU Yang,ZHANG Liuping.Experimental study on the effects of compaction on the properties of sandstone reservoir[J].Journal of Xi’an Shiyou University(Natural Science Edition),2006,21(4):24-28.
[20]杨东东,戴卫华,张迎春,等.渤海砂岩油田岩石压缩系数经验公式研究[J].中国海上油气,2010,22(5):317-319.YANG Dongdong,DAI Weihua,ZHANG Yingchun,et al.Studying on an empirical formula of rock compressibility for sandstone oilfields in Bohai sea[J].China Offshore Oil and Gas,2010,22(5):317-319.
[21]熊钰,李航,耿站立,等.压实与出砂双重作用下疏松砂岩稠油油藏产能变化实验[J].中国海上油气,2015,27(6):63-68.XIONG Yu,LI Hang,GENG Zhanli,et al.Experimental study on productivity change of unconsolidated standstone heavy oil reservoir under the dual effect of compaction and sand production[J].China Offshore Oil and Gas,2015,27(6):63-68.
[22]RAGHAVAN R,CHIN L Y.Productivity changes in reservoirs with stress-dependent permeability[C].SPE 77535,2002.
[23]STEHFEST H.Numercial inversion of laplace transform[J].Communication of ACM,1970,13:47-49.
[2]IKOKU C U,RAMEY H J.Transient flow of non-newtonian power-law fluids in porous media[C].SPE 7139-PA,1979.
[3]VONGVUTHIPORNCHA S,RAGHAVAN R.Well test analysis of data dominated by storage and skin:non-newtonian power-law fluids[C].SPE 14454-PA,1987.
[4]栾志安.双重介质非牛顿液不稳定渗流解析解[J].石油学报,1981,2(4):75-79.LUAN Zhian.Analytical solution of unsteady seepage flow in non-newtonian fluid[J].Acta Petrolei Sinica,1981,2(4):75-79.
[5]宋考平,王雷,计秉玉.非牛顿-牛顿复合油藏渗流试井解释方法[J].石油学报,1996,17(1):82-86.SONG Kaoping,WANG Lei,JI Bingyu.Well test analysis of a compound reservoir with non-Newtonian and Newtonian fluid flow[J].Acta Petrolei Sinica,1996,17(1):82-86.
[6]宋考平,祝俊峰,刘泽俊,等.多区复合油藏非牛顿幂律流体试井解释[J].石油学报,1997,18(2):78-83.SONG Kaoping,ZHU Junfeng,LIU Zejun,et al.Well test analysis for a compound reservoir with non-newtonian power law fluids flow[J].Acta Petrolei Sinica,1997,18(2):78-83.
[7]梁光跃,廖新维,万光芬,等.非牛顿幂律流体试井模型的有效半径解及其曲线特征[J].科技导报,2010,28(13):58-61.LIANG Guangyue,LIAO Xinwei,WAN Guangfen,et al.Effective wellbore radius and typical curve characteristics of well test analysis of non-newtonian power-law fluids[J].Science&Technology Review,2010,28(13):58-61.
[8]李元媛,蔡睿贤.非牛顿幂律流体试井模型的一种简明解析解[J].科技导报,2010,28(18):32-35.LI Yuanyuan,CAI Ruixian.A concise analytical solutions of well test analysis:non-newtonian power-law fluids[J].Science&Technology Review,2010,28(18):32-35.
[9]郭辉,程时清,于海洋,等.聚合物驱复合模型试井分析方法[J].断块油气田,2014,21(4):504-508.GUO Hui,CHENG Shiqing,YU Haiyang,et al.Well test analysis method of composite model by polymer flooding[J].Fault-Block Oil&Gas Field,2014,21(4):504-508.
[10]程时清,聂向荣.聚合物驱复合油藏试井模型与典型曲线[J].华中科技大学学报(自然科学版),2012,40(4):110-113.CHENG Shiqing,NIE Xiangrong.Well test model and type curives of composite reservoirs with polymer flooding[J].Hua Zhong University of Science&Technology(Natural Science Edition),2012,40(4):110-113.
[11]贾智淳,闫术,董晓芳,等.剪切变稀作用对聚驱试井分析影响的数值研究[J].西南石油大学学报(自然科学版),2016,38(5):108-113.JIA Zhichun,YAN Shu,DONG Xiaofang,et al.Numerical study on the impact of shear thinning behavior in well test analysis for polymer flooding[J].Journal of Southwest Petroleum University(Science&Tecnology Edition),2016,38(5):108-113.
[12]RAGHAVAN R,SCORER J D T,MILLIER F G.An investigation by numerical methods of the effect of pressure-dependent rock and fluid properties on well flow tests[C].SPE 2617-PA,1972.
[13]PEDROSA O A.Pressure transient response in stress-sensitive formations[C].SPE 15115,1986.
[14]廖新维,冯积累.超高压低渗气藏应力敏感试井模型研究[J].天然气工业,2005,25(2):110-112.LIAO Xinwei,FENG Jilei.Well test model of stress sensitive gas reservoirs with super high pressure and low permeability[J].Natural Gas Industry,2005,25(2):110-112.
[15]宁正福,廖新维,高旺来,等.应力敏感裂缝性双区复合气藏压力动态特征[J].大庆石油学院学报,2004,28(2):34-36.NING Zhengfu,LIAO Xinwei,GAO Wanglai,et al.Pressure transient response in deep-seated geothermal stresssensitive fissured composite gas reservoir[J].Journal of Daqing Petroleum Institute,2004,28(2):34-36.
[16]刘启国,唐伏平,冯国庆,等.开关井不同程度应力敏感效应对井底压力动态的影响[J].石油与天然气地质,2007,28(4):523-525.LIU Qiguo,TANG Fuping,FENG Guoqing,et al.Influence of different stress sensitivities on bottom hole pressure behaviors during well opening and shut-in[J].Oil&Gas Geology,2007,28(4):523-525.
[17]李顺初,任丽,郑鹏社,等.基于应力敏感的天然裂缝性页岩气藏双孔模型解的结构[J].应用数学和力学,2017,38(2):233-242.LI Shunchu,REN Li,ZHENG Pengshe,et al.Similar structure of the solution to the dual-porosity model for naturally fractured shale gas reservoirs based on stress sensitivity[J].Applied Mathematics and Mechanics,2017,38(2):233-242.
[18]王璐,姚约东,黄山,等.裂缝性致密油藏非稳态窜流规律[J].断块油气田,2016,23(3):329-333.WANG Lu,YAO Yuedong,HUANG Shan,et al.Transient cross flow law for fractured tight oil reservoirs[J].FaultBlock Oil&Gas Field,2016,23(3):329-333.
[19]刘国勇,刘阳,张刘平.压实作用对砂岩储层物性的影响[J].西安石油大学学报(自然科学版),2006,21(4):24-28.LIU Guoyong,LIU Yang,ZHANG Liuping.Experimental study on the effects of compaction on the properties of sandstone reservoir[J].Journal of Xi’an Shiyou University(Natural Science Edition),2006,21(4):24-28.
[20]杨东东,戴卫华,张迎春,等.渤海砂岩油田岩石压缩系数经验公式研究[J].中国海上油气,2010,22(5):317-319.YANG Dongdong,DAI Weihua,ZHANG Yingchun,et al.Studying on an empirical formula of rock compressibility for sandstone oilfields in Bohai sea[J].China Offshore Oil and Gas,2010,22(5):317-319.
[21]熊钰,李航,耿站立,等.压实与出砂双重作用下疏松砂岩稠油油藏产能变化实验[J].中国海上油气,2015,27(6):63-68.XIONG Yu,LI Hang,GENG Zhanli,et al.Experimental study on productivity change of unconsolidated standstone heavy oil reservoir under the dual effect of compaction and sand production[J].China Offshore Oil and Gas,2015,27(6):63-68.
[22]RAGHAVAN R,CHIN L Y.Productivity changes in reservoirs with stress-dependent permeability[C].SPE 77535,2002.
[23]STEHFEST H.Numercial inversion of laplace transform[J].Communication of ACM,1970,13:47-49.