Thermal dispersion in porous media as a function of the solid–fluid conductivity ratio

Abstract

Thermal dispersion in porous media is an import phenomenon in combustion and in steam injection systems for Enhanced Oil Recovery methods, among several others engineering applications. In this work, thermal dispersion tensors were calculated within an infinite porous medium formed by a spatially periodic array of longitudinally-displaced elliptic rods. Two different thermal conductivity ratios between the solid and fluid phases were used for analyzing their effect on the thermal dispersion tensor, following a systematic analysis of several porous media modeled by different unit-cell geometry. As such, just one unit-cell, together with periodic boundary conditions for mass, momentum and energy equations, was used to represent the medium. The numerical methodology herein employed is based on the control-volume approach. Turbulence was assumed to exist within the fluid phase and a low Reynolds k– ε closure was used to model it. The flow equations at the pore-scale were numerically solved using the SIMPLE method on a non-orthogonal boundary-fitted coordinate system. Cell-integrated results for the longitudinal dispersion coefficient showed little sensitiveness on porosity, boundary condition type, medium morphology and solid–fluid conductivity ratio, whereas for the transversal direction, all of these parameters modified the numerical value obtained for the dispersion coefficient.