›› 2017, Vol. 38 ›› Issue (2): 1-1.doi: 10.7657/XJPG20170221

• 论文 •    

基于伴随模型的历史拟合参数敏感性分析方法

汪勇1,张璋2,孙业恒1,刘威2   

  1. (1.中国石化 胜利油田分公司 勘探开发研究院,山东 东营 257015;2.中国石油大学 石油工程学院,山东 青岛 266580)
  • 出版日期:2019-01-01 发布日期:1905-07-14

Methods of Parameter Sensitivity Analysis for History Matching Based on Adjoint Model

WANG Yong1, ZHANG Zhang2, SUN Yeheng1, LIU Wei2   

  1. (1.Research Institute of Exploration and Development, Shengli Oilfield Company, Sinopec, Dongying, Shangdong 257015, China; 2.School of Petroleum Engineering, China University of Petroleum, Qingdao, Shangdong 266580, China)
  • Online:2019-01-01 Published:1905-07-14

摘要: 针对目前油藏数值模拟参数敏感性分析方法存在运算量大、无法处理大规模油藏、计算精度达不到要求等缺陷,提出了基于伴随模型的历史拟合参数敏感性分析方法。依据伴随系统理论,建立伴随变量独立于模拟计算变量的伴随模型,避免直接求解梯度方程;根据油藏数值模拟器的渗流模型状态方程及求解方法,构建伴随模型的系数矩阵,求解伴随方程,得到伴随变量;建立敏感系数计算方程,利用所得到的伴随变量,求解目标函数关于控制变量的敏感系数矩阵。与常用的梯度模拟器法和试验设计法相比:伴随模型的系数矩阵易于构建,可直接来源于渗流模型状态方程的求解结果;求解梯度方程的计算量仅取决于观测数据的数量,而不取决于模型参数的数量,为求解某一观测数据对所有模型参数的导数,只需构建并求解一个相应的伴随方程;只需正演一次原模型以及反演一次伴随模型,就可以得到所有时间每一个网格参数的敏感系数,提高了参数敏感性分析效率。

Abstract: In view of the problems of huge computations, incapacity to deal with large scale reservoirs and unqualified computational accuracy of the current sensitivity analysis methods in numerical reservoir simulation, this paper proposes an adjoint model-based parameter sensitivity analysis method for history matching. Based on the adjoint system theory, an adjoint model with the adjoint variables independent of simulated variables is established and direct resolution of gradient equation can be avoided; coefficient matrices of the adjoint model are constructed according to the state equation of the reservoir percolation model and solving methods of the numerical reservoir simulator. Adjoint variables are acquired by solving the adjoint equations and sensitive coefficient calculation equations are established. The sensitive coefficient matrices of objective functions with respect to control variables are solved by using the adjoint variables. Compared with the commonly used gradient simulator methods and experimental design methods, the advantages of this method are as follows: the coefficient matrices of the adjoint model can be directly derived from the results of the state equation; the amounts of calculations to solve the gradient equation only depend on the quantity of the observation data rather than the number of model parameters. In order to obtain the derivatives of particular observation data with regard to all model parameters, it only needs to construct and solve one corresponding adjoint equation. With high calculation ability; the sensitive coefficients of all producing time for each grid parameter could be acquired simply by forward modeling an original model and inverting an adjoint model only once, thus the efficiency of parameter sensitivity analysis is greatly improved

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