Homogenization of non-Darcy flow in porous media containing spheroidal impervious inclusions
Vincent Monchiet · International Journal of Solids and Structures · 2024
The aim of the present study is to determine the nonlinear filtration law of a porous medium containing spheroidal impervious inclusions through a homogenization framework. At the local scale, it is assumed that the fluid flow through the porous solid surrounding the inclusions obeys the Forchheimer equation . The macroscopic law is derived in the field of nonlinear variational approach applied to some representative cell, namely a porous spheroid containing a single centered spheroidal inclusion confocal to the outer. Both a static and kinematical approach are developed to bound the overall filtration properties of the heterogeneous solid. Appropriate trial fields are considered to determine closed-form estimates and are obtained from the solution of a linear problem replacing the Forchheimer law in the porous solid at the microscopic scale by the Darcy law . The analytic estimates are calculated through some approximations and lead to accurate solutions of the nonlinear problems . Finally, the analytic models are compared with FFT solutions in the case of a regular array of spheroidal impervious inclusions.