电缆地层测试器测量的油水两相有限元模型

The finite element simulation of formation wireline testing for oil-water two-phase flow

在电缆地层测试器的测量过程中,油水两相共渗的情况普遍存在,此时其测量过程的数学模型是非线性的耦合场问题,无法用解析方法求解.加上测量中存在抽吸探针与地层、井筒接触面几何形状复杂、探针与地层尺寸相差悬殊等问题,使得应用渗流力学中较为成熟的有限差分方法求解数学模型也不能获得理想的结果.本文应用适合于处理复杂几何形状计算的有限元方法,根据地层测试器测试过程中油水两相渗流的数学模型,首次建立了地层测试器测量油水两相渗流的有限元模型,给出了验证和求解的实例.运用本文所建立的计算模型可以更准确地模拟测试过程中压力和饱和度随时间和空间变化的情况,为正确使用地层测试器提供指导.

Under reservoir condition, oil-water two-phase flow in porous rocks is the most common fluid movement pattern. The mathematic model of wireline formation testing under such a condition poses a nonlinear and coupled fields problem with no analytical solution. The finite difference method could not give satisfactory solutions to this problem due to the complex shapes of the interface between sink probe and formation on borehole wall, and the extreme size difference between probe and formation. In this paper, we developed the first finite element model to dynamically simulate the oil-water two phase formation testing, based on our mathematic model for formation testing of oil-water two phase fluid flow in porous media and the finite element theory. With this model, we can find out the distributions of pressure and saturation fields in time and space during the testing, which can provide the foundation on adequate application of wireline formation tester. Theoretical verification and numerical examples of the model are presented.