基于单井敏感性区域的油藏模拟辅助历史拟合
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摘要
针对当前历史拟合中单井敏感性区域难以确定和反演参数变量维数大的问题,建立了一种快速有效计算单井敏感性区域的方法,并提出了一种模型参数化方法。利用Fast-Marching Method(FMM)求解油藏压力传播过程中的程函方程,计算压力波从井点到达每个网格的飞行时间,依据飞行时间确定油藏三维单井敏感性区域。以单井敏感性区域内网格的模型参数平均值作为参数变量来降低求解维数,并通过近似扰动梯度升级优化算法来提高拟合效率。实例证明,此方法对油藏动态生产指标的拟合取得了较好的效果,整体过程计算代价小,满足工程应用的要求。
In view of the limitations that sensitivity region of single well cannot be accurately estimated and the dimension of inversion model parameter vector in objective function is huge for assisted history matching, this study establishes a novel method to calculate sensitivity region of single well fast and efficiently, and proposes a simple method for model parameterization. We use the Fast-Marching Method(FMM) to solve the pressure-diffusivity equation of Eikonal equation form and calculate the arrival time from well point to each grid of reservoir model. The sensitivity region of single well is determined according to the arrival time in 3 D space. Based on the sensitivity region of single well, we take the average of model parameter of the grids in the region as the elements of inversion model parameter vector to reduce its dimension, and use an upgraded perturbation gradient approximation algorithm to improve the computational efficiency. With the proposed method for calculation of sensitivity region of single well and model parameterization, the application case shows a good matching result and low computational cost for historical dynamic production data, and can meet the engineering requirements.
In view of the limitations that sensitivity region of single well cannot be accurately estimated and the dimension of inversion model parameter vector in objective function is huge for assisted history matching, this study establishes a novel method to calculate sensitivity region of single well fast and efficiently, and proposes a simple method for model parameterization. We use the Fast-Marching Method(FMM) to solve the pressure-diffusivity equation of Eikonal equation form and calculate the arrival time from well point to each grid of reservoir model. The sensitivity region of single well is determined according to the arrival time in 3 D space. Based on the sensitivity region of single well, we take the average of model parameter of the grids in the region as the elements of inversion model parameter vector to reduce its dimension, and use an upgraded perturbation gradient approximation algorithm to improve the computational efficiency. With the proposed method for calculation of sensitivity region of single well and model parameterization, the application case shows a good matching result and low computational cost for historical dynamic production data, and can meet the engineering requirements.
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.
[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.
[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.
[4]赵辉.油藏开发闭合生产优化理论研究[D].青岛:中国石油大学(华东),2011.
[5]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.
[6]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.
[7] ARROYO E,DEVEGOWDA D,DATTA-GUPTA A,et al. Streamlineassisted ensemble kalman filter for rapid and continuous reservoir model updating[J]. SPE Reservoir Evaluation&Engineering,2008, 11(6):1046-1060.
[8] 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.
[9] ABDASSAH D, MUCHARAM L, SOENGKOWO I, et al. Coupling seismic data with simulated annealing method improves reservoir characterization[R]. SPE 36968,1996.
[10] ROMERO C E,CARTER J N. Using genetic algorithms for reservoir characterisation[J]. Journal of Petroleum Science&Engineering,2001,31(2):113-123.
[11] GAO G,LI G,REYNOLDS A C. A stochastic optimization algorithm for automatic history matching[J]. SPE Journal,2007,12(2):196-208.
[12] EVENSEN G, HOVE J, MEISINGSET H, et al. Using the enkf for assisted history matching of a north sea reservoir model[R].SPE 106184,2007.
[13] BRUN B,GOSSELIN O,BARKER J W. Use of Prior Information in gradient-based history matching[J]. SPE Journal,2004,9(1):67-78.
[14] SARMA P,DURLOFSKY L J,AZIZ K,et al. A new approach to automatic history matching using kernel pca[R]. SPE 106176,2007.
[15] JAFARPOUR B, MCLAUGHLIN D B. History matching with an ensemble Kalman filter and discrete cosine parameterization[J].Computational Geosciences,2008,12(2):227-244.
[16] 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.
[17] KULKARNI K N,KHIL D G,VASCO D W. A streamline approach for integrating transient pressure data into high resolution reservoir nodels[J]. SPE Journal,2001,6(6):273-282.
[18]赵辉,唐乙玮,康志江,等.油藏开发生产优化近似扰动梯度升级算法[J].中国石油大学学报(自然科学版),2016,40(2):99-104.
[19]袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,1999:219-339.
[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.
[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.
[4]赵辉.油藏开发闭合生产优化理论研究[D].青岛:中国石油大学(华东),2011.
[5]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.
[6]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.
[7] ARROYO E,DEVEGOWDA D,DATTA-GUPTA A,et al. Streamlineassisted ensemble kalman filter for rapid and continuous reservoir model updating[J]. SPE Reservoir Evaluation&Engineering,2008, 11(6):1046-1060.
[8] 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.
[9] ABDASSAH D, MUCHARAM L, SOENGKOWO I, et al. Coupling seismic data with simulated annealing method improves reservoir characterization[R]. SPE 36968,1996.
[10] ROMERO C E,CARTER J N. Using genetic algorithms for reservoir characterisation[J]. Journal of Petroleum Science&Engineering,2001,31(2):113-123.
[11] GAO G,LI G,REYNOLDS A C. A stochastic optimization algorithm for automatic history matching[J]. SPE Journal,2007,12(2):196-208.
[12] EVENSEN G, HOVE J, MEISINGSET H, et al. Using the enkf for assisted history matching of a north sea reservoir model[R].SPE 106184,2007.
[13] BRUN B,GOSSELIN O,BARKER J W. Use of Prior Information in gradient-based history matching[J]. SPE Journal,2004,9(1):67-78.
[14] SARMA P,DURLOFSKY L J,AZIZ K,et al. A new approach to automatic history matching using kernel pca[R]. SPE 106176,2007.
[15] JAFARPOUR B, MCLAUGHLIN D B. History matching with an ensemble Kalman filter and discrete cosine parameterization[J].Computational Geosciences,2008,12(2):227-244.
[16] 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.
[17] KULKARNI K N,KHIL D G,VASCO D W. A streamline approach for integrating transient pressure data into high resolution reservoir nodels[J]. SPE Journal,2001,6(6):273-282.
[18]赵辉,唐乙玮,康志江,等.油藏开发生产优化近似扰动梯度升级算法[J].中国石油大学学报(自然科学版),2016,40(2):99-104.
[19]袁亚湘,孙文瑜.最优化理论与方法[M].北京:科学出版社,1999:219-339.