Stochastic dynamics of intermittent pore-scale particle motion in three-dimensional porous media: Experiments and theory

We study the evolution of velocity in time, which fundamentally controls the way dissolved substances are transported and spread in porous media. Experiments are conducted that use tracer particles to track the motion of substances in water, as it flows through transparent, 3-D synthetic sandstones. Particle velocities along streamlines are found to be intermittent and strongly correlated, while their probability density functions are lognormal and nonstationary. We demonstrate that these particle velocity characteristics can be explained and modeled as a continuous time random walk that is both Markovian and mean reverting toward the stationary state. Our model accurately captures the fine-scale velocity fluctuations observed in each tested sandstone, as well as their respective dispersion regime progression from initially ballistic, to superdiffusive, and finally Fickian. Model parameterization is based on the correlation length and mean and standard deviation of the velocity distribution, thus linking pore-scale attributes with macroscale transport behavior for both short and long time scales