The permeability effect on the diffusion and correlation process of fluid flow in porous media

Abstract

This study numerically examines the fluid flow in porous media used in desalination. This topic is of significant current interest in the fields of science, engineering and technology, particularly in the process of water filtration. Moreover, in this work, we are attracted to correlation and diffusion process of the porous medium below the effect of permeability, dynamic pressure and friction coefficient. These parameters characterized the fluid flow in porous medium. To study numerically this phenomenon, many models have been proposed. However, we developed our investigation by using the Langevin dynamics model. Furthermore, this dynamic framework is based on Newton’s second law and Darcy’s law. Hence, we modeled the medium as a set of random diameters pores, which are dispersed randomly. The obtained results indicate that the average velocity time evolution presents an exponential profile with two different states: the first is transient and the second is permanent. The two regimes are separated by a cross-over time. Furthermore, time evolution exhibits an increasing profile versus the permeability, then it presents a decreasing profile versus the friction coefficient. Likewise, the diffusion process and correlation are tested for different parameters, especially the permeability and the dynamic pressure. We remark that the effective diffusion coefficient decreases exponentially with permeability and increases linearly with dynamic pressure. Hence, the fluid flow correlation in porous media presents a Gaussian function profile, with standard deviation function which increases exponentially with permeability.