Simulation of fluid flow in a porous medium is essential for predicting the complex behavior of materials and distribution of stress for many applications, such as fluid injection, soil liquefaction, and simulation of biological structures. In this work, we propose an energy-based continuum mechanics framework to simulate fluid flow in porous deformable media. A general approach is presented for defining the total strain energy density of the porous medium, based on the free energy model of the components. We derive the momentum and transport balances based on the total strain energy density of the porous medium. A Finite Element model is presented to analyze the behavior of saturated and unsaturated porous medium in the large deformation regime, using a nonlinear constitutive model for the solid skeleton. Therefore, the proposed model can be applied for modeling complicated behavior of saturated and unsaturated porous mediums containing compressible fluid and solid constituents. Moreover, the developed model allows for the simulation of porous media containing single and multiple immiscible fluid phases. As a specific application of the proposed model, we investigate the CO2 injection into geological formations. The results show that this model can predict the injection process, including the phase change of the CO2 gas under pressure. 

Energetic Formulation of Large-Deformation Poroelasticity for Fluid Injection Simulation into Deep Underground Formations

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