Radiation in Porous Media: an Upscaling Methodology

The radiative properties of any porous medium are statistically defined by a cumulated extinction distribution function, a cumulated absorption probability and a bidirectional phase function. These functions are obtained by a Monte Carlo technique, from both the medium morphology data, known or issued from a X or γ ray tomography, and the radiative properties at a scale lower than the tomography spatial resolution. At this local scale, the porous medium phases can be opaque, transparent or semi transparent. The RDFI method leads to the determination, with a precise accuracy criterion, of the extinction and absorption coefficients, as long as the porous medium can be homogenized by one (or two) equivalent semi transparent medium. Under precise conditions discussed here, a radiative conductivity tensor (or two coupled tensors associated with the two phases) can be deduced from these radiative properties for an optically thick REV. Actual cases of porous media involved in new energy technologies are discussed vs the scales involved in the applications.