非正交坐标系统下斜井泥浆侵入数值模拟

THE APPLICATION OF NONORTHOGONAL COORDINATE SYSTEMS IN NUMERICAL SIMULATION OF MUD-FILTRATE INVASION IN DEVIATED WELLS

针对斜井剖分过程中采用传统的直角坐标系,矩形网格剖分地层,采用梯形近似处理斜井边界时出现的要达到精确模拟就只能缩小网格尺寸而引起计算量急剧增加这一矛盾问题,根据实际模型引入了非正交坐标系,在非正交坐标系中,存在两种基矢,它们相互之间以及与直角坐标系统之间的转化关系具备一套完整的理论体系,简化了对斜井水平地层以及直井倾斜地层等模型的模拟。实际数值模拟结果表明,采用非正交坐标系在保证精度的同时,极大地减少了运算量,取得了很好的效果。

FDM (finite difference method) is the most commonly used method in the simulation of water-base mud-filtrate invasion, which is on the basis of the filtration theory of oil-water two-phase flow. The 'mesh ladders' are used to approximate the boundary of the deviated wells in conventional orthogonal coordinate system. The mesh size must be diminished to get accurate results, which will extremely increase the computation. The nonorthogonal coordinate systems are introduced to solve the problem. The two kinds of unitary vectors in nonorthogonal coordinate systems can be transformed mutually to orthogonal forms with a set of self-contained theoretical methods. It is convenient to simulate the models of deviated well or deviated formation in nonorthogonal coordinate systems. The simulation results also approve that the method will get better results with less computation.