基于单井敏感性局域化EnKF的油藏辅助历史拟合方法
|
摘要
常用的油藏自动历史拟合算法多数存在梯度计算不准确、产生伪相关性等问题,导致参数修正错误、模型反演失真。通过建立一种基于单井动态敏感性的局域化集合卡尔曼滤波(FMM-CL-EnKF)历史拟合方法,解决了传统距离截断方法处理伪相关性时与实际地层状况不匹配的问题。基于程函方程,根据地质模型静态参数场信息,快速追踪压力波从井点到地层网格的传播时间确定各单井动态最大敏感性区域,从而构建局域化矩阵。同时,结合集合卡尔曼滤波(EnKF)方法,实现数据同化方法梯度的矫正,减弱伪相关,通过逐步拟合生产动态达到更新油藏模型和获取最优估计的目的。概念算例和矿场算例的计算结果表明,FMM-CLEnKF方法在模型集合生产动态拟合效果及反演模型参数场准确性等方面均优于标准EnKF方法。
At present,the commonly used reservoir automatic history matching algorithms have problems such as inaccurate gradient calculation and pseudo-correlation,resulting in incorrect modification of geological parameter and model inversion distortion.The history matching method of ensemble Kalman filter with localization based on single-well dynamic sensitivity region(FMM-CL-EnKF)is newly established to solve the problem that the pseudo-correlation treated using the traditional distance truncation method may not conform to real geological characteristics.Based on Eikonal equation,according to the static parameter information of geological model,the propagation time of pressure wave from well point to a grid is rapidly calculated to determine the maximum sensitivity region of single well,so as to construct the localization matrix.In combination with EnKF,this study realizes the correction of spurious gradient information using data assimilation method,weakens the pseudo-correlation,and achieves the purposes of updating reservoir model and acquiring optimal estimate by gradually matching dynamic production data.The applications of synthetic and real examples show that the proposed FMM-CL-EnKF method is superior to the standard EnKF method in the matching effect of dynamic production data and the inversion accuracy of model parameter.
At present,the commonly used reservoir automatic history matching algorithms have problems such as inaccurate gradient calculation and pseudo-correlation,resulting in incorrect modification of geological parameter and model inversion distortion.The history matching method of ensemble Kalman filter with localization based on single-well dynamic sensitivity region(FMM-CL-EnKF)is newly established to solve the problem that the pseudo-correlation treated using the traditional distance truncation method may not conform to real geological characteristics.Based on Eikonal equation,according to the static parameter information of geological model,the propagation time of pressure wave from well point to a grid is rapidly calculated to determine the maximum sensitivity region of single well,so as to construct the localization matrix.In combination with EnKF,this study realizes the correction of spurious gradient information using data assimilation method,weakens the pseudo-correlation,and achieves the purposes of updating reservoir model and acquiring optimal estimate by gradually matching dynamic production data.The applications of synthetic and real examples show that the proposed FMM-CL-EnKF method is superior to the standard EnKF method in the matching effect of dynamic production data and the inversion accuracy of model parameter.
引文
[1]陈兆芳,张建荣,陈月明,等.油藏数值模拟自动历史拟合方法研究及应用[J].石油勘探与开发,2003,30(4):82-84.CHEN Zhaofang,ZHANG Jianrong,CHEN Yueming,et al.Automatic historical matching method and its application in reservoir simulation[J].Petroleum Exploration and Development,2003,30(4):82-84.
[2]邓宝荣,袁士义,李建芳,等.计算机辅助自动历史拟合在油藏数值模拟中的应用[J].石油勘探与开发,2003,30(1):71-74.DENG Baorong,YUAN Shiyi,LI Jianfang,et al.Applying computeraided history matching to the numerical simulation of reservoirs[J].Petroleum Exploration and Development,2003,30(1):71-74.
[3]闫霞,张凯,姚军,等.油藏自动历史拟合方法研究现状与展望[J].油气地质与采收率,2010,17(4):69-73.YAN Xia,ZHANG Kai,YAO Jun,et al.Review on automatic history matching methods for reservoir simulation[J].Petroleum Geology and Recovery Efficiency,2010,17(4):69-73.
[4]赵辉,曹琳,康志江,等.油藏开发闭环生产优化控制理论与方法[M].北京:科学出版社,2016:64-100.ZHAO Hui,CAO Lin,KANG Zhijiang,et al.Theoretical research on reservoir closed-loop production optimization[M].Beijing:Science Press,2016:64-100.
[5]闫霞.基于梯度逼真算法的油藏生产优化理论研究[D].青岛:中国石油大学(华东),2013.YAN Xia.Theoretical research of reservoir production optimization based on gradient approximation methods[D].Qingdao:China University of Petroleum,2013.
[6]ALIREZA K,STEPHEN K D.油藏数值模拟自动历史拟合方法——以Nelson油田为例[J].石油勘探与开发,2012,39(3):326-337.ALIREZA K,STEPHEN K D.Schemes for automatic history matching of reservoir modeling:a case of Nelson oilfield in the UK[J].Petroleum Exploration and Development,2012,39(3):326-337.
[7]王鸣川,段太忠,孙红军,等.油藏自动历史拟合研究进展[J].科技导报,2016,34(18):236-245.WANG Mingchuan,DUAN Taizhong,SUN Hongjun,et al.Research progress in reservoir automatic history matching[J].Science&Technology Review,2016,34(18):236-245.
[8]ZHANG Kai,LU Ranran,ZHANG Liming,et al.A two-stage efficient history matching procedure of non-Gaussian fields[J].Journal of Petroleum Science and Engineering,2016,138:189-200.
[9]赵辉,谢鹏飞,曹琳,等.基于井间连通性的油藏开发生产优化方法[J].石油学报,2017,38(5):555-561.ZHAO Hui,XIE Pengfei,CAO Lin,et al.Reservoir production optimization method based on inter-well connectivity[J].Acta Petrolei Sinica,2017,38(5):555-561.
[10]鲍敬伟,李丽,叶继根,等.高含水复杂断块油田加密井井位智能优选方法及其应用[J].石油学报,2017,38(4):444-452.BAO Jingwei,LI Li,YE Jigen,et al.Well location intelligent optimization method and its application for infill wells in high water cut complex fault-block oilfields[J].Acta Petrolei Sinica,2017,38(4):444-452.
[11]崔传智,李松,杨勇,等.特高含水期油藏平面分区调控方法[J].石油学报,2018,39(10):1155-1161.CUI Chuanzhi,LI Song,YANG Yong,et al.Planar zoning regulation and control method of reservoir at ultra-high water cut stage[J].Acta Petrolei Sinica,2018,39(10):1155-1161.
[12]孙贺东,欧阳伟平,张冕.基于数值模型的气井现代产量递减分析及动态预测[J].石油学报,2017,38(10):1194-1199.SUN Hedong,OUYANG Weiping,ZHANG Mian.Advanced production decline analysis and performance forecasting of gas wells based on numerical model[J].Acta Petrolei Sinica,2017,38(10):1194-1199.
[13]GEIR N,JOHNSEN L M,AANONSEN S I,et al.Reservoir monitoring and continuous model updating using ensemble Kalman filter[R].SPE84372,2003.
[14]GAO Guohua,ZAFARI M,REYNOLDS A C.Quantifying uncertainty for the PUNQ-S3 problem in a Bayesian setting with RML and EnKF[R].SPE93324,2006.
[15]GU Yaqing,OLIVER D S.An iterative ensemble Kalman filter for multiphase fluid flow data assimilation[J].SPE Journal,2007,12(4):438-446.
[16]EVENSEN G,HOVE J,MEISINGSET H,et al.Using the EnKF for assisted history matching of a North Sea reservoir model[R].SPE106184,2007.
[17]ZHAO Yong,REYNOLDS A,LI Gaoming.Generating facies maps by assimilating production data and seismic data with the ensemble Kalman filter[R].SPE113990,2008.
[18]王玉斗,何健,李高明.基于离散余弦变换的集合Kalman滤波方法对河流相油藏渗透率场的反演[J].地球物理学报,2011,54(7):1900-1911.WANG Yudou,HE Jian,LI Gaoming.Inverse of the fluvial channel reservoir permeability field using ensemble Kalman filter based on discrete cosine transform[J].Chinese Journal of Geophysics,2011,54(7):1900-1911.
[19]闫霞,李阳,姚军,等.基于流线EnKF油藏自动历史拟合[J].石油学报,2011,32(3):495-499.YAN Xia,LI Yang,YAO Jun,et al.Automatic history matching of reservoirs using the streamline-based EnKF method[J].Acta Petrolei Sinica,2011,32(3):495-499.
[20]梁晓东.基于超球体变换EnKF方法的油藏动态历史拟合研究[D].重庆:重庆科技学院,2017.LIANG Xiaodong.Research of the dynamic historical matching of reservoir based on super-sphere transform EnKF method[D].Chongqing:Chongqing University of Science and Technology,2017.
[21]SETHIAN J A.Level set methods and fast marching methods:evolving interfaces in computational geometry,fluid mechanics,computer vision,and materials science[M].Cambridge,UK:Cambridge University Press,1999.
[22]SHARIFI M,KELKAR M,BAHAR A,et al.Dynamic ranking of multiple realizations by use of the fast-marching method[J].SPE Journal,2014,19(6):1069-1082.
[23]ARROYO E,DEVEGOWDA D,DATTA-GUPTA A,et al.Streamline-assisted ensemble Kalman filter for rapid and continuous reservoir model updating[J].SPE Reservoir Evaluation&Engineering,2008,11(6):1046-1060.
[24]EMERICK A,REYNOLDS A.Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications[J].Computational Geosciences,2011,15(2):251-269.
[25]张黎明,周建人,张凯,等.协方差局地化方法在自动历史拟合中的应用[J].断块油气田,2017,24(1):46-50.ZHANG Liming,ZHOU Jianren,ZHANG Kai,et al.Application of covariance localization method in automatic history matching[J].Fault-Block Oil&Gas Field,2017,24(1):46-50.
[26]LEEM J,LEE K,KANG J M,et al.History matching with ensemble Kalman filter using fast marching method in shale gas reservoir[R].SPE176164,2015.
[27]KULKARNI K N,DATTA-GUPTA A,VASCO D W.A streamline approach for integrating transient pressure data into high-resolution reservoir models[J].SPE Journal,2001,6(3):273-282.
[28]SHARIFI M,KELKAR M.Novel permeability upscaling method using fast marching method[J].Fuel,2014,117:568-578.
[29]HOUTEKAMER P L,MITCHELL H L.Data assimilation using an ensemble Kalman filter technique[J].Monthly Weather Review,1998,126(3):796-811.
[30]QIN Fuhao,LUO Yi,OLSEN K B,et al.Finite-difference solution of the Eikonal equation along expanding wavefronts[J].Geophysics,1992,57(3):478-487.
[2]邓宝荣,袁士义,李建芳,等.计算机辅助自动历史拟合在油藏数值模拟中的应用[J].石油勘探与开发,2003,30(1):71-74.DENG Baorong,YUAN Shiyi,LI Jianfang,et al.Applying computeraided history matching to the numerical simulation of reservoirs[J].Petroleum Exploration and Development,2003,30(1):71-74.
[3]闫霞,张凯,姚军,等.油藏自动历史拟合方法研究现状与展望[J].油气地质与采收率,2010,17(4):69-73.YAN Xia,ZHANG Kai,YAO Jun,et al.Review on automatic history matching methods for reservoir simulation[J].Petroleum Geology and Recovery Efficiency,2010,17(4):69-73.
[4]赵辉,曹琳,康志江,等.油藏开发闭环生产优化控制理论与方法[M].北京:科学出版社,2016:64-100.ZHAO Hui,CAO Lin,KANG Zhijiang,et al.Theoretical research on reservoir closed-loop production optimization[M].Beijing:Science Press,2016:64-100.
[5]闫霞.基于梯度逼真算法的油藏生产优化理论研究[D].青岛:中国石油大学(华东),2013.YAN Xia.Theoretical research of reservoir production optimization based on gradient approximation methods[D].Qingdao:China University of Petroleum,2013.
[6]ALIREZA K,STEPHEN K D.油藏数值模拟自动历史拟合方法——以Nelson油田为例[J].石油勘探与开发,2012,39(3):326-337.ALIREZA K,STEPHEN K D.Schemes for automatic history matching of reservoir modeling:a case of Nelson oilfield in the UK[J].Petroleum Exploration and Development,2012,39(3):326-337.
[7]王鸣川,段太忠,孙红军,等.油藏自动历史拟合研究进展[J].科技导报,2016,34(18):236-245.WANG Mingchuan,DUAN Taizhong,SUN Hongjun,et al.Research progress in reservoir automatic history matching[J].Science&Technology Review,2016,34(18):236-245.
[8]ZHANG Kai,LU Ranran,ZHANG Liming,et al.A two-stage efficient history matching procedure of non-Gaussian fields[J].Journal of Petroleum Science and Engineering,2016,138:189-200.
[9]赵辉,谢鹏飞,曹琳,等.基于井间连通性的油藏开发生产优化方法[J].石油学报,2017,38(5):555-561.ZHAO Hui,XIE Pengfei,CAO Lin,et al.Reservoir production optimization method based on inter-well connectivity[J].Acta Petrolei Sinica,2017,38(5):555-561.
[10]鲍敬伟,李丽,叶继根,等.高含水复杂断块油田加密井井位智能优选方法及其应用[J].石油学报,2017,38(4):444-452.BAO Jingwei,LI Li,YE Jigen,et al.Well location intelligent optimization method and its application for infill wells in high water cut complex fault-block oilfields[J].Acta Petrolei Sinica,2017,38(4):444-452.
[11]崔传智,李松,杨勇,等.特高含水期油藏平面分区调控方法[J].石油学报,2018,39(10):1155-1161.CUI Chuanzhi,LI Song,YANG Yong,et al.Planar zoning regulation and control method of reservoir at ultra-high water cut stage[J].Acta Petrolei Sinica,2018,39(10):1155-1161.
[12]孙贺东,欧阳伟平,张冕.基于数值模型的气井现代产量递减分析及动态预测[J].石油学报,2017,38(10):1194-1199.SUN Hedong,OUYANG Weiping,ZHANG Mian.Advanced production decline analysis and performance forecasting of gas wells based on numerical model[J].Acta Petrolei Sinica,2017,38(10):1194-1199.
[13]GEIR N,JOHNSEN L M,AANONSEN S I,et al.Reservoir monitoring and continuous model updating using ensemble Kalman filter[R].SPE84372,2003.
[14]GAO Guohua,ZAFARI M,REYNOLDS A C.Quantifying uncertainty for the PUNQ-S3 problem in a Bayesian setting with RML and EnKF[R].SPE93324,2006.
[15]GU Yaqing,OLIVER D S.An iterative ensemble Kalman filter for multiphase fluid flow data assimilation[J].SPE Journal,2007,12(4):438-446.
[16]EVENSEN G,HOVE J,MEISINGSET H,et al.Using the EnKF for assisted history matching of a North Sea reservoir model[R].SPE106184,2007.
[17]ZHAO Yong,REYNOLDS A,LI Gaoming.Generating facies maps by assimilating production data and seismic data with the ensemble Kalman filter[R].SPE113990,2008.
[18]王玉斗,何健,李高明.基于离散余弦变换的集合Kalman滤波方法对河流相油藏渗透率场的反演[J].地球物理学报,2011,54(7):1900-1911.WANG Yudou,HE Jian,LI Gaoming.Inverse of the fluvial channel reservoir permeability field using ensemble Kalman filter based on discrete cosine transform[J].Chinese Journal of Geophysics,2011,54(7):1900-1911.
[19]闫霞,李阳,姚军,等.基于流线EnKF油藏自动历史拟合[J].石油学报,2011,32(3):495-499.YAN Xia,LI Yang,YAO Jun,et al.Automatic history matching of reservoirs using the streamline-based EnKF method[J].Acta Petrolei Sinica,2011,32(3):495-499.
[20]梁晓东.基于超球体变换EnKF方法的油藏动态历史拟合研究[D].重庆:重庆科技学院,2017.LIANG Xiaodong.Research of the dynamic historical matching of reservoir based on super-sphere transform EnKF method[D].Chongqing:Chongqing University of Science and Technology,2017.
[21]SETHIAN J A.Level set methods and fast marching methods:evolving interfaces in computational geometry,fluid mechanics,computer vision,and materials science[M].Cambridge,UK:Cambridge University Press,1999.
[22]SHARIFI M,KELKAR M,BAHAR A,et al.Dynamic ranking of multiple realizations by use of the fast-marching method[J].SPE Journal,2014,19(6):1069-1082.
[23]ARROYO E,DEVEGOWDA D,DATTA-GUPTA A,et al.Streamline-assisted ensemble Kalman filter for rapid and continuous reservoir model updating[J].SPE Reservoir Evaluation&Engineering,2008,11(6):1046-1060.
[24]EMERICK A,REYNOLDS A.Combining sensitivities and prior information for covariance localization in the ensemble Kalman filter for petroleum reservoir applications[J].Computational Geosciences,2011,15(2):251-269.
[25]张黎明,周建人,张凯,等.协方差局地化方法在自动历史拟合中的应用[J].断块油气田,2017,24(1):46-50.ZHANG Liming,ZHOU Jianren,ZHANG Kai,et al.Application of covariance localization method in automatic history matching[J].Fault-Block Oil&Gas Field,2017,24(1):46-50.
[26]LEEM J,LEE K,KANG J M,et al.History matching with ensemble Kalman filter using fast marching method in shale gas reservoir[R].SPE176164,2015.
[27]KULKARNI K N,DATTA-GUPTA A,VASCO D W.A streamline approach for integrating transient pressure data into high-resolution reservoir models[J].SPE Journal,2001,6(3):273-282.
[28]SHARIFI M,KELKAR M.Novel permeability upscaling method using fast marching method[J].Fuel,2014,117:568-578.
[29]HOUTEKAMER P L,MITCHELL H L.Data assimilation using an ensemble Kalman filter technique[J].Monthly Weather Review,1998,126(3):796-811.
[30]QIN Fuhao,LUO Yi,OLSEN K B,et al.Finite-difference solution of the Eikonal equation along expanding wavefronts[J].Geophysics,1992,57(3):478-487.