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. (c) 2013 American Institute of Chemical Engineers AIChE J 60: 749-761, 2014