A general model for convection-dispersion-dynamic adsorption in porous media with stagnant volume

Abstract

A convection-dispersion model that encompasses first-order reversible kinetic adsorption as well as dead-end pore volume is presented. These phenomena, which characterize the flow of miscible fluids through porous media are described by a set of four differential equations. The system of equations has six parameters: Peclet number, stagnant volume, Stanton number which involves the mass transfer between stagnant and mobile fluid, Langmuir number which measures the adsorptive capacity of the rock, kinetic adsorption number which relates desorption and adsorption rates, and finally, flow rate number which relates convection and adsorption rates. The system of coupled partial differential equations is solved numerically by finite differences, applying an extension of the Crank-Nicolson scheme and an iterative procedure. To assess the accuracy of the numerical algorithm, solutions of this general model are compared with solutions of simpler models which are limiting cases of this one: (a) the exact solution for the linear adsorption case, (b) the exact solution of the capacitance Coats' model, and (c) the results of numerical models previously published. The influence of parameter values on concentration profiles is carefully analyzed. For a given concentration profile experimentally determined, either from field tests or laboratory displacements, some parameters are important. They determine the miscible fluid flow. On the contrary, other parameters can be disregarded. For example, the asymmetric tailing of effluent concentration distributions, the early or late breakthroughs respond to different mechanisms. They can be simulated by varying different parameters. Consequently, a general model that considers several mechanisms simultaneously is a useful tool to simulate different types of flow of miscible fluids through porous media.