Simplest deformation models of a fluid-saturated poroelastic medium

Under analysis is the model of two-phase flow in porous medium and deformation of the pore space. The model includes the equations of fluid transfer and porous matrix deformation, derived from the conservation laws. It is shown that the system of the constitutive equations contains a few small parameters, and the corresponding expansion allows obtaining a hierarchical sequence of models of certain deformation conditions. The zero approximation and first approximation models are written in explicit form. It is found that if fluids are incompressible, the first approximation equations go to the Buckley-Leverett model-like system with account for the change of the porous space. The zero approximation equations describe the porous medium behavior under condition of the unchanged volume. In this case, the equation of the pore pressure is separated from the equation of the elastic matrix. The analytical solutions obtained for the zero approximation model in cylindrical coordinates feature shear stresses capable to cause failure.