Development of a three-scale homogenization method for flow in porous media

In this study, we develop a three-scale homogenization method that can analyze steady flow in porous media with hierarchically multiscale internal structures. To this end, first, a porous medium is modeled with respect to three scales by considering the porous medium as a macro-structure, a base material and a flow path as a meso-structure, and a micro flow path inside the base material as a micro-structure. Then, we formulate a three-scale homogenization method by dually applying the mathematical homogenization method to not only the meso/micro but also the macro/meso scales. Using the present method, we analyze micro/meso flow fields and meso/macro permeabilities of a three-scale porous medium.