We investigated dispersion in homogeneous porous media (grain packs) by nuclear magnetic resonance (NMR) measurements and random walk simulations in pore networks. We measured water molecules displacements during a time interval tΔ by NMR measurements, which allows us to obtain propagators and charateristic cumulants of displacements such as the mean square displacement σ. The evolution of the cumulant σ as a function of time tΔ (σ2 ∝ taΔ) is a very sensitive test of Gaussian behaviour compared to the analysis of the shape of propagators. In a homogeneous 30μm grain pack and low Peclet numbers (15 < Pe < 45), we observed weak super dispersion in saturated conditions (a = 1.17) and gradually stronger super-dispersionas the water saturation decreases (up to a = 1.5 for 42 %) during steady-state oil-water two phase flow. Insaturated conditions, propagators and breakthrough curves are Gaussian or nearly Gaussian, whereas in two phase conditions, propagators are non symmetric and breakthrough curves show thick tails at long time. Weshow that the anomalous dispersion observed is better explained by Lévy stable laws (asymetric for longitudina ldispersion, and symetric for transverse dispersion) than by Gaussian laws. Random walk simulations were performed in a pore network constructed using high resolution images of the grain pack. They allow us to obtain the same informations than the NMR, with walkers submitted to diffusive and advective effects. The simulations show the existence of an anomalous stagnation not observed in experiments, highlighting the oversimplification of the pore network that prevent reproducing some aspects of the velocity field detected by NMR. However, the simulations indicate similarly a super-dispersion at long time in saturated conditions
