Numerical Modeling of Fluid-Saturated Porous Sample Loading Based on Thermodynamically Compatible System Theory

A quasi-static approximation of a thermodynamically compatible system of PDEs is presented to model the loading test for a two-phase (solid-fluid) sample. To numerically solve the resulting PDEs written in terms of displacements, we use a second-order finite-difference scheme on a staggered grid. Numerical results demonstrate the application of the presented approach to estimate seismic attenuation in two-phase media on different scales, involving an effective porosity model of fractured media on the mesoscale or the geometry of a single pore directly at the microscale.