Concentration and temperature transients in heterogeneous porous media: Part II: Radial transport

Abstract

Being the most commonly used model of transport of solute and heat in porous media, analytical solutions of the convection–dispersion equation are of great importance for both interpretative and numerical model validation purposes. As in the linear case, the use of two different concentration variables namely resident and flux concentrations are equally common in radial transport; while the former is used in deriving the governing equations, the latter is the one measured in experiments. Therefore, description of transport processes in terms of dependent variables must be relevant to the way tracer experiments are to be performed. In addition, the common assumption of velocity and scale dependence of dispersion coefficient also leads to modification in governing differential equations whether they are expressed in resident or flux concentrations. This work presents a detailed classification of the solutions of convection–dispersion equation in radial coordinates based on velocity- and/or scale-dependent forms of dispersion coefficient and also on the physical meanings of the solutions with respect to two different concentrations. The classification of solutions includes guidelines for selection of appropriate solution to be employed in field experiments and numerical validation as well. This classification has led to the development of several new solutions in this work that are of great importance for interpreting and designing field experiments.