Abstract: The widely used Cartesian grid has some disadvantages in the description of geologically complex reservoirs.In addition,finite difference method based on Cartesian grid causing significant orientation effects.PEBI grid takes advantages of finite elements of flexible approximation of reservoir geometry,and reduced orientation effects by using window techniques.It is easy to be refined and be applied in finite differente simulators.This paper presents the differente equation of control volume finite elements,with a method of automatic triangulation and PEBI grid generation.2-D single-phase model and two-phase model were designed to test the feasibility of the PEBI grid.The numerical results indicated that PEBI grid could simulate radial flow near the well bore with high accuracy.The results are consistent with the analysis solution and PEBI grid reduces grid orientation effects greatly comparing with 5-point finite-difference method.

Key words: PEBI grid, Cartesian grid, two-phase flow, numerical simulation, grid orientation effects, difference equation, automatic generation

摘要： 油藏数值模拟中广泛采用的笛卡尔网格在描述地质条件复杂的油藏时存在很大的局限,并且笛卡尔网格有限差分法数值模拟存在严重的网格取向效应.文中采用PEBI网格,吸取了有限元方法的优点,可以逼近任意油藏形状,便于局部加密和应用窗口技术,可以减小网格取向效应;同时吸取有限差分的正交性特点,便于计算机实现.文中给出了控制体有限元方法的差分方程,提出一种三角形划分和PEBI网格自动生成的方法,设计两个模型进行了二维单相流、二维油水两相流数值模拟.计算结果表明,PEBI网格模拟近井问题用较少的网格取得了较高的精度,与解析解吻合较好;在油水流度比较大的情况下,PEBI网格的取向效应比有限差分五点格式明显小.

关键词: PEBI网格, 笛卡尔网格, 两相流, 数值模拟, 网格取向效应, 差分方程, 自动生成