Numerical Analysis of Mass Transfer Around a Sphere Buried in Porous Media: Concentration Contours and Boundary Layer Thickness

Abstract

The mass transfer process between a moving fluid and a slightly soluble or fast reacting sphere buried in a packed bed, with “uniform velocity”, was obtained numerically, for solute transport by both advection and diffusion. Fluid flow in the granular bed around the sphere was assumed to follow Darcy’s law and the elliptic Partial Differential Equations (PDE), resulting from a differential material balance on the solute in an elementary control volume, was studied and solved numerically over the “whole range” of values of the relevant parameters (Peclet number and Schmidt number). The numerical solutions gave the concentration contour plots and concentration boundary layer thickness as a function of the relevant parameters. For each concentration level, the width and downstream length of the corresponding contour surface were determined. General expressions are presented to predict contaminant “plume” size downstream of the polluting source. An important feature of this work is the detailed discussion of the finite differences method adopted, with emphasis on the High-Resolution Schemes (HRS) used in the discretization of the convection term of the PDE.