Dispersion of a passive solute in two phase flow through porous media has been studied by combining three tools, namely reconstruction of porous media, Immiscible Lattice Boltzmann algorithm and random walks. Plane Poiseuille flow has been solved analytically and it provides a useful comparison for the random walk code. The influence of the Peclet number, of the water saturation and of the partition coefficient has been determined for two different samples. Overall correlations are proposed to cover the variations of the two first parameters. (C) 2002 Elsevier Science Ltd. All rights reserved.