The objectives of this project are to perform a novel fundamental study of the mechanism of dispersion, to develop an improved multiscale statistical model of dispersion, and to use this advance in understanding to optimize field scale displacements. A numerical experiment using particle tracking in large scale domains demonstrates that the large echo dispersion coefficients estimated in Mahadevan et al.(2003) are not unreasonable. It could be that irreversible mixing is occurring even in large-scale miscible displacements. For this case, the traditional definition of dispersivity does not apply because the dispersion coefficient does not scale linearly with velocity because of the unidirectional nature of the velocity field. With the use of a heterogeneous velocity field, a linear scaling is expected as demonstrated in particle tracking done on pore-network models(Bruderer and Bernabe 2001). Our grain-scale simulation studies show that the echo test in parallel layers is scale-dependent when there is transverse flow between layers. We also show that transverse dispersion is significant when velocity fluctuation in the transverse direction is high and that the transverse dispersion value depends on the medium configuration. In this study we calculated transversal and longitudinal dispersion in a 2D homogeneous configuration by applying an inverse fit method to match the simulation concentration data to the 2D analytical solution of the convection-dispersion equation. We show that, in the case of zero diffusion in pore-scale simulations, local mixing would be reversible when flow is at low Reynolds number. The progress to date is meeting the expectations laid out in the project description.