Numerical Analysis of Fluid Flow in a Deformable Porous Medium Using Finite Element Method

Document Type : Research Paper

Authors

1 Assistant Professor, Faculty of Petroleum, Gas and Petrochemical Engineering, Persian Gulf University, Bushehr, Iran

2 Faculty of Petroleum, Gas and Petrochemical Engineering, Persian Gulf University, Bushehr, Iran

Abstract

In this paper, a coupled fluid flow-geomechanical simulation in a deformable porous medium using finite element numerical method is presented. This model includes solving conservation of mass and momentum balance equations for solid framework and fluid phases. These equations are based on the Biot consolidation theory. Fluid pore pressure and solid-phase displacement have been selected as the primary variables in these equations. The governing equations are discretized using finite element method. The final equation system is then solved in a fully coupled process which was conducted by using MATLAB software. In this process, convergence and stability of results are guaranteed. Then, Mendel’s problem is solved using a proposed model and the results are compared with the analytical solution of the problem. The proposed model shows a very good agreement with the analytical solution, which indicates the accuracy of the model proposed in this article. Finally, this model is used to simulate the discharge of water from a sand column with a two phase saturation approach. The main priority of this study is providing precise formulations, applicability, and the ability of finite element in modeling coupled fluid flow and deformation in a porous medium.

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