Simplifications of macroscopic models for heat and mass transfer in porous media

Abstract

When performing upscaling of transport phenomena in multiscale systems it is not uncommon that terms of different physical nature than those present at the underlying scale arise in the resulting averaged differential equations. For diffusive species mass transfer with heterogeneous reaction and conductive heat transfer, additional terms result from upscaling using the volume averaging method, which are classically discarded by means of orders of magnitude estimates. In this work, these two cases are revisited and it is shown that, for single and two-species diffusive mass transfer with heterogeneous nonlinear reaction, the additional term is exactly zero using Green’s formula. This conclusion is shown to also be applicable when using the periodic homogenization method. Nevertheless, for heat conduction, with and without considering interfacial resistance, only the dominant conduction-corrective terms are shown to be zero also using Green’s formula. In contrast, the contribution of the co-conduction-corrective terms may be relevant depending on the systems characteristics, the properties of the phases and the macroscopic boundary conditions. This is exemplified by performing numerical simulations in a non-symmetric unit cell.