油藏渗流–应力耦合分析的FEM-FVM混合方法的改进  

Improvement of a mixed FEM-FVM method for reservoir simulation coupling fluid flow and mechanics

作　　者：邸元[1] 吴大卫 WU Yushu DI Yuan;WU Dawei;WU Yushu(College of Engineering,Peking University,Beijing 100871,China;Department of Petroleum Engineering,Colorado School of Mines,Golden,CO80401,USA)

机构地区：[1]北京大学工学院,北京100871 [2]科罗拉多矿业学院石油工程系,美国戈尔登CO80401

出　　处：《岩石力学与工程学报》2020年第S01期2645-2654,共10页Chinese Journal of Rock Mechanics and Engineering

基　　金：国家自然科学基金资助项目(U19B6003);国家科技重大专项资助项目(2016ZX05014)。

摘　　要：在油藏开采过程中,岩石应力场变化的波及范围远大于发生渗流的储层区域,因而现有渗流–应力全耦合方法数值模拟的计算量往往十分巨大。为了提高数值模拟的计算效率,考虑渗流计算区域和应力计算区域的差异,对FEM-FVM(有限元–有限体积)混合方法进行了改进。对储层渗流区域采用细密的网格进行计算,以获得地下流体较为准确的分布情况;对应力计算区域则采用粗网格进行计算,从而降低计算耗时。全耦合理论中的力学平衡方程采用有限元法在粗网格上进行离散;质量守恒方程则在细网格上采用有限体积法进行离散。对Terzaghi一维固结问题和Mandel二维固结问题的数值模拟表明,该方法的计算结果与解析解吻合较好。通过对一个二维单相流单井开采问题和一个三维两相流五点井网开采问题的数值计算,分析了油藏数值模拟中渗流–应力耦合效应的影响。For the practical procedure of oil production,stress field affects a much larger area than the reservoir domain,which requires a large amount of computation to simulate using recent approaches for fully coupled fluid flow-mechanics reservoir simulation.In order to increase numerical simulation efficiency,a hybrid method mixing finite element method(FEM)and finite volume method(FVM)is improved to consider the differences of computational domain between fluid flow and mechanics.A fine mesh is used for the computation of seepage in the reservoir domain to catch the detail distribute of fluids,whereas a coarse mesh for stress computation to reduce computational cost.The equilibrium equation of fully coupled approaches is discretized on the coarse grid by finite element method,and the mass balance equation is discretized on the fine grid by finite volume method.Numerical results of both Terzaghi′s and Mendal′s consolidation problems show great consistency with their analytical solutions,which verifies the proposed method.In order to analyze the fluid flow-mechanics coupling effect to reservoir simulation,the numerical results of a two dimensional single-phase flow problem with constant pressure pumping and a three dimensional two-phase flow case in five-spot scheme are carried out.

关 键 词：岩石力学 油藏数值模拟 渗流–应力耦合 有限体积法 有限元法 耦合问题 

分 类 号：TU45[建筑科学—岩土工程]