储层流固耦合的数学模型及其有限元方程

利用有限元方法,建立了一个描述可变形饱和储层中流体流动的数值模型。该模型由一组完全耦合的控制方程组成,包括岩石骨架的平衡方程和流体在多孔介质中流动的连续性方程,模型中采用了基于Mohr-Coulomb屈服面的弹塑性本构关系。利用有限元方法得到了控制方程中未知的位移和流体压力在几何域上的耦合解。用全隐式数值格式对上述方程在时间域上进行求解,得到了完全耦合的有限元离散方程,并研究了该数值模型的稳定条件。该模型在石油工程中有广泛的应用,为可变形饱和油藏流固耦合渗流的数值模拟奠定了理论基础。

THE FULLY COUPLED MATHEMATICAL MODEL OF THE FLUID-SOLID IN AN OIL RESERVOIR AND ITS FINITE ELEMENT EQUATIONS

A numerical model, based on the finite element method, is established to describe a fluid flow in a deforming saturated oil reservoir.The mathematical formulation describes a fully coupled governing equation system which consists of the equilibrium of rock skeleton and continuity for a fluid flow in a porous medium.An elasto-plastic model is utilized on a basis of Mohr-Coulomb yield surface.The Galerkin finite element method is applied to obtain simultaneous solutions in the space domain to the governing equations where the displacements and the fluid pressures are the primary unknowns.The final discretized equations are sovled in the time domain by using a fully implicit numerical scheme and the fully coupled finite element equations are obtained.A linear analysis is used to study the stability conditions of the present model.This model has a wide range of applications in the field of oil reservoir engineering and provides a theoretical basis for numerial simulation of a fluid flow in a deforming saturated oil reservoir.