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. Plain Language Summary Transport of dissolved substances in rocks and soils are controlled by the intricacies of the pore space. In short time scales, brief bursts of fast flow in otherwise slow-moving water lead to intense spreading. In long time scales and/or distances, this burst effect is drowned out and spreading behavior becomes weak and constant. The long time behavior is well understood and predictable, but not the short time behavior and their transition. We study the processes responsible for this transition from intense to weak spreading behavior. In the laboratory, we track how small particles in water move through the pore spaces of a transparent, synthetic soil. These measurements show us how long the fast flow bursts last, how fast they are, and how frequently they occur. Statistical analysis of the particle behavior reveals that flow has a short term memory, and we build a predictive model that captures this effect. Our novel model allows predictions of the changeover from intense to weak spreading, and demonstrates that it captures fundamental transport processes in naturally-occurring porous media. Therefore, this new model can be used to make better predictions for important applications such as groundwater contamination assessments or oil recovery.