Upscaling Statistical Methodology for Radiative Transfer in Porous Media: New Trends

Abstract

The morphology of a porous medium is now generally known from X and γ ray tomography techniques. From these data and radiative properties at the pore scale, a homogenized medium associated with a porous medium phase is exhaustively characterized by radiative statistical functions, i.e., by a statistical cumulative extinction distribution function, absorption, and scattering cumulative probabilities and a general scattering phase function. The accuracy is only limited by the tomography resolution or the geometrical optics validity. When this homogenized medium follows the Beer’s laws, extinction, absorption, and scattering coefficients are identified from these statistical functions; a classical radiative transfer equation (RTE) can then be used. In all other cases, a generalized radiative transfer equation (GRTE) is directly expressed from the radiative statistical functions. When the homogenized medium is optically thick at a spatial scale such as it is practically isothermal, the radiative transfer can simply be modeled from a radiative Fourier’s law. The radiative conductivity is directly determined by a perturbation technique of the GRTE or RTE. An accurate validity criterion of the radiative Fourier’s law has recently been defined. Some paths for future research are finally given.