油、水二相流固耦合渗流的数学模型

The fully coupled mathematical model of fluids solid for oil and water biphase seepage.

为了正确模拟油藏中流体流动的动态过程，必须考虑由于注水和开采而引起的多相流体的流动、应力状态的变化和储集层变形之间复杂的相互作用。但由于这种问题的控制方程是三维非线性耦合方程，因此，很难模拟这种耦合作用。利用广义的Ｂｉｏｔ理论建立了一个完全耦合的数学模型，它描述可变形油藏中岩石变形和油水流动的这种相互作用。模型中假设岩石骨架具有弹塑性特性，流体是可压缩的。以岩石骨架位移和油水压力为未知变量所建立的控制方程，包括岩石骨架的平衡方程和流体（油、水）的连续性方程。所建立的流固耦合模型在石油工程，特别是在油藏数值模拟中有广泛的应用。

In order to correctly simulated the dynamic process of the fluids flow in oil reservoirs, it must be consider that the complex interaction among multiphase fluid flow, changes in stress state, and formation deformation as a result of injection and production operations. Modeling the interaction is made difficult by the fact that the governing equations are nonlinear and coupled, and the problems to be solved are three dimensional. A fully coupled mathematical model to describe the complex interaction of two immiscible fluids (oil and water) within a deforming saturated oil reservoirs is developed on the basis of the generalized Biot's theory. The rock skeleton is assumed to have an elastoplastic behavior, and the fluids are assumed to be compressible. The final governing equations in terms of rock displacements, fluids pressure consist of the equilibrium of rock skeleton and continuity equations for two immiscible fluids flowing in a porous medium. This model has a wide range of applications in the field of petroleum engineering, especially in the numerical simulation of oil reservoir.