Coupled fluid flow and solid deformation in porous media modelling is essential in a wide variety of applications. It is also crucial to provide an appropriate discretization for these coupled problems. Therefore, in this study, we provide comparisons between a classical continuous Galerkin (CG), and a new approach, enriched Galerkin (EG) to solve such problem. Even though both the EG and CG methods deliver approximately the same solution for the Terzaghi's 1-D model, the CG method may produce spurious pressure and volumetric strain oscillations where a vast difference of conductivity property is observed. On the contrary, the EG method results demonstrate a smooth transition across the mentioned interfaces. These phenomena lead to different reservoir compaction and conductivity effects, which are induced by volumetric strain, on flux approximation in heterogeneous, both porosity and permeability, materials. These impacts are exemplified, and the differences between the EG and CG methods grow larger in softer materials. Although both methods maintain global mass conservation, the EG method guarantees a local mass conservation property by the construction. The EG method, however, demands more computational resources in terms of both degrees of freedom and number of iterations than the CG method.

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