The calculations of dispersion coefficients inside two-dimensional randomly packed beds of circular particles

The longitudinal (D_L) and transverse (D_T) dispersion coefficients in two-dimensional (2-D) randomly packed beds of circular particles in a laminar flow regime are derived. A 2-D discrete system of particles is divided into cells using modified Voronoi diagrams. The relationship between the variation of the stream function and the averaged vorticity is obtained from computational fluid dynamics (CFD) simulations. The whole flow pattern is then obtained by using the principle of energy dissipation rate minimization. The obtained values of D_L agree well with 3-D experimental data for all velocities investigated. At very high velocities, D_T in 2-D appears to be higher than 3-D experimental data. In addition, the effects of particle-size distributions, packing structure, and porosity on the D_L and D_T were studied. One result was that an increase in the width of the particle-size distribution resulted in higher values of D_L and D_T at high velocities.