ABSTRACT
In the simulation of fluid flow and geomechanics, Mendel’s problem is one of the fundamental issues in describing the behavior of fluid pressure in a porous deformable medium in response to loading and also changing applied stresses conditions. Solving this problem involves solving equations for the fluid mass balance equation, Darcy law for fluid velocity, and the equation for momentum balance for the solid phase framework. These equations have been derived from the Biot consolidation theory. In this paper, Mandel’s problem for a fully saturated elastic porous medium is modeled using coupled finite volume-finite element technique and the results were compared with the analytical and exact solutions. Fluid pore pressure and displacement of solid phase were selected as the primary variable in the equations in this model. The proposed model provides a good match to the analytical solutions as well as the solutions provided by other researchers, which indicates the accuracy of the model designed in this paper. In this model, the Mendel’s effect is clearly visible in parts of medium that are far from the drainage boundaries. At the last, we have tried to study the impact of various physical, geometric and numerical parameters on this issue.
