Superdispersion in homogeneous unsaturated porous media using NMR propagators

The NMR propagator technique allows the measurements of the variance σ²=(ξ-ξ)² of the displacements as a function of time t when flowing in a porous media. The time dependence of {σ} is a very sensitive test of Gaussian behavior compared to the analysis of the shape of the propagators. Superdispersion occurs when σ²∝t^α with the exponent {α} larger than 1. In a homogeneous 30-{μ}m grain pack and 10 Pe 35, we observed weak superdispersion in saturated conditions ({α} = 1.17) and gradually strong superdispersion as the water saturation decreases (up to {α} = 1.5) during steady-state oil-water two-phase flow. In saturated conditions, the corresponding longitudinal propagators and breakthrough curves are Gaussian or nearly Gaussian, whereas in two-phase conditions, the longitudinal propagators are nonsymmetric and the breakthrough curves show a tail at long times.