Unveil the influence of porous media heterogeneity on fluid flow and solute transport

Abstract

Heterogeneity in porous mediums is a common occurrence in natural rock formations, impacting the movement of fluids and solutes within them. This research systematically explores the influence of such heterogeneity on fluid flow and solute transport. An analytical solution is developed for fluid flow within a dual-porous mediums system by integrating the Darcy-Brinkman equation coupled with shear stress and velocity continuity conditions at the porous media interface. Utilizing asymptotic analysis and perturbation methods, analytical solutions for the dispersion coefficient of both porous media are derived and validated against existing literature. Furthermore, advection-diffusion equations are numerically solved to obtain the solute concentration profile, shedding light on its transport within heterogeneous porous mediums.

The simulations reveal intriguing behaviors: as the permeability factor, λ_D, approaches 100, velocities in both mediums tend towards zero, contrasting with a parabolic velocity profile when λ_D reaches 0.01. The impact of the surrounding porous medium permeability factor, λ_2D, on the dispersion coefficient of main porous medium, $D_{1D}^{\ast }$, is negligible when the Péclet number (Pe) is below 1, yet it exhibits variability with λ_2D for Pe greater than 1. The concentration difference between the two porous mediums is minimal at x_D < 2 for most instances but notably pronounced around x_D = 4 initially, followed by rapid attenuation. This highly generalized model not only captures solute transport in the presence of porous mediums heterogeneity but also can be simplified to represent scenarios such as a permeable channel surrounded by impermeable mediums or even the classical Taylor-Aris model.