各向异性油藏渗流的有限元数值模拟

为使模拟计算更加接近实际情况,将油水井作为油藏的内边界处理,建立各向异性油藏单相流体渗流问题的有限元方程。在此基础上利用八节点四边形等参元,结合伽辽金有限元方法对渗流方程在空间域上离散,采用全隐式时步格式在时间域上离散。对单相流体的平面单向流、各向异性油藏平面径向流的有限元解和解析解进行对比,得到了地层中不同位置处的压力变化和产量变化规律。研究结果表明,有限元模拟的结果与解析解相比很接近,这充分说明所建立的模型和计算程序是正确的。该研究成果可用来指导油井的实际生产,对预测油井的产能变化具有重要意义。

FINITE ELEMENT NUMERICAL SIMULATION OF SEEPAGE IN AN ANISOTROPIC RESERVOIR

Finite element method is widely used to numerically simulate the seepage and the coupling of flow and stress in geotechnical engineering.In present,the finite difference method is the main numerical method of fluid flowing in porous media.Compared with the finite difference method,the finite element method is a valid numerical method and has more advantages than the finite difference method,but it is not deeply studied in solving reservoir problems.The flow equations for a single phase in an anisotropic reservoir and the equations of finite element method are established.Those equations are discretized in space by using Galerkin finite element method and in time by using backward difference method.Finally the linear equations are solved by Gauss-Seidel method.On base of the finite element equations and relative theory,eight-node quadrilateral elements are used,and a finite element simulating software is developed.For the unstable state flow of single phase fluid,the finite element method is compared with analytical solution for one-dimensional plane flow.And the radial flow in an anisotropic reservoir is simulated with the software package.The distribution of fluid pressure in formation and the production of the oil well in an anisotropic reservoir are obtained.It is shown that the finite element solution is precise enough compared with the analytical method,which proves that the provided method and program are correct,and that it is precise and reliable to solve reservoir problems with the finite element method.These researches can be used to guide the oil wells production,and present an important method to forecast the production output in oil reservoirs.