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

International audience ; When performing upscaling of transport phenomena in multiscale systems it is not uncommon that terms ofdifferent physical nature than those present at the underlying scale arise in the resulting averaged differentialequations. 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 discardedby 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 termis exactly zero using Green’s formula. This conclusion is shown to also be applicable when using the periodichomogenization 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, thecontribution 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 performingnumerical simulations in a non-symmetric unit cell.