The convective heat transfer of fractal porous media under stress condition

Abstract

The study of coupled convective heat transfer and deformation behavior in porous media is still a major scientific and engineering challenge, despite major technological advances in both theoretical and computational thermodynamics in the past two decades. Specifically, essential controls on convective heat transfer of porous media under stress condition are not yet definitive. In this paper, meaningful and reasonable quantitative models that manifest the most important fundamental controls on convective heat transfer of porous media under stress condition are proposed. Predictions of the normalized permeability using the theoretical models, derived from Hertzian contact theory and fractal geometry, agree well with available experimental data. The proposed model design specifically accounts for multiple key variables, including the influence of the microstructural parameters of porous media, including elastic modulus and Poisson's ratio, and as functions of rock lithology. The results presented here include (1) the heat transfer rate decreases with the increase of effective stress, and increases with the increased porous media elastic modulus or the increased power law index for a specific effective stress, (2) the heat transfer rate increases with the increase of pore fractal dimension Df0 or the increased ratio rmin0/rmax0 for a specific effective stress. However, the relationship between the convective heat transfer coefficient and effective stress with different pore fractal dimension Df0 is complicated and not monotonic, (3) The heat transfer rate and convective heat transfer coefficient increase as expected with the increase of Nusselt number (i.e. the parameter represents the convective heat transfer in the pore) for a specific effective stress. In general, fractal convective heat transfer models illustrate mechanisms that affect coupled convective heat transfer and deformation behavior of porous media. And, the model proposed here is intended to increase efficacy of reservoir development strategies.