有限元法油水两相油藏数值模拟研究

Simulation of the Oil and Water Two phase Flow Based on the Galerkin Finite Element Method

研究了利用迦利金有限元方法模拟油藏中油水两相渗流问题,提供一种油藏数值模拟方法。研究方法从数学模型出发,严格推导了油藏油水两相渗流方程的有限元弱形式,在井边界处理及上游权选择等非线性处理方面给出了可行的策略。采用商业性有限元代码生成平台FEPG,生成六面体八结点有限元软件代码,模拟三维两相油藏的油水渗流规律。为验证有限元方法及软件的正确性,与基于有限差分的商业软件进行对比,结果表明有限元方法模拟计算结果有效可靠,同时网格弥散现象有所控制。

This paper simulates the oil-water two-phase flow of oil and water based on the Galerkin finite element method, as an advanced reservoir simulation method. The finite element mathematical model in the weak form is derived for the oil-water two-phase flow, Then, a feasible strategy is adopted to deal with the nonlinearity terms in the well boundary processing and the upstream weight selection. Using the finite element code generation platform FEPG, the finite element software code based on hexahedral eight nodes is generated for the simulation of the three-dimensional two-phase oil-water percolation. To validate the finite element method and the software, the resuhs are compared with those obtained by the commercial software based on the finite difference, and it is shown that the finite element method is effective and reliable.