Effects of fractal trajectory on gas diffusion in porous media

Abstract

AbstractA mathematical model was developed to represent the effect of tortuous trajectory and irregular step length on gas diffusion in porous media, and then it was conformed by analyzing the experimentally determined flux with respect to 19 groups of binary gas mixtures in a porous catalyst pellet. Based on the analysis of actual diffusing distance within porous media, the diffusing trajectory of gas molecules was characterized into fractal curves, leading to a novel flux equation of binary gas mixtures. The established model represented the tortuous structure by the only model parameter the fractal dimension of diffusion trajectories dF. A yardstick was devised to account for the influence of pore size, diffusing species, temperature and pressure on the trajectory length of gas diffusion. The size of the yardstick δ could be found after diffusing species, temperature and pressure were specified for a given porous medium. The fitting between the experimentally determined flux and the model equation resulted in a fractal dimension of 1.102. It was evident that the model prediction was in fairly good agreement between the experimental results in the literature and those of the study, and the irregular degree of diffusing trajectory is much less than that of the pore surface. Detailed comparison with the traditional treatment by the tortuosity factor demonstrated that the methodology established here would be especially significant for very tortuous pore systems.