Numerical derivation of dispersion coefficients for flow through three-dimensional randomly packed beds of monodisperse spheres

The longitudinal (D_L) and transverse (D_T) dispersion coefficients for flow through randomly packed beds of discrete monosized spherical particles are studied. The three-dimensional (3-D) porous-medium model consists of thousands of spherical particles that are divided into cells using Voronoi diagrams. The relationship between the variation of the dual stream function and the vorticity between neighboring particles is derived using Laurent series. The whole flow pattern at low particle Reynolds number is then obtained by minimization of the dissipation rate of energy with respect to the dual stream function. The D_L is obtained by fitting the resulting effluent curve to a 1-D solution of a continuous model. The D_T is obtained by fitting the numerical concentration profile to an approximate 2-D solution. The derived D_L and D_T values are in agreement with 3-D experimental data from the literature enabling a study of the effects of pore structure and porosity on D_L and D_T.