SOLUTE TRANSPORT IN POROUS MEDIA USING SPATIAL FRACTIONAL ADVECTION-DIFFUSION EQUATION

Abstract

The problem of solute transport associated with fluid flow in porous media has become increasingly important in geophysical applications. The heterogeneity variations in a porous medium can have significant effects on the transport process. The main soul of this dissertation is to examine the potential of advection-diffusion equation (ADE) and spatial advection-diffusion equation (sFADE) to depict the behavior of solute transport in homogeneous as well as heterogeneous porous media. Conservative solute transport processes in heterogeneous media do not follow Fick’s Law of diffusion and shows several anomalous behaviors such as early arrival of tracer particles, long tailing of concentration profiles, and scale dependency of dispersion coefficient. The classical ADE, which follows Fick’s law, cannot precisely describe a transport process which is non-Fickian in nature. Such non-Fickian transport processes in porous media is characterized by various nonlocal space methods, such as sFADE. Moreover, this study attempts to inspect the deviations of coefficients of dispersion of sFADE with transport distance and to use the inverse problem method to estimate the parameters of sFADE at every distance. The inverse problem method was found to be very effective approach to estimate the parameters of solute transport of the sFADE.