Anomalous transport of colloids in heterogeneous porous media: A multi-scale statistical theory

Transport of suspended colloids in heterogeneous porous media is a multi-scale process that exhibits anomalous behavior and cannot be described by the Fickian dispersion theory. Although many studies have documented colloids' transport at different length scales, a theoretical basis that links pore- to core-scale observations remains lacking. It is hypothesized that a recently proposed pore-scale statistical kinetic theory is able to capture the results observed experimentally.

We implement a multi-scale approach via conducting core-flooding experiments of colloidal particles in a sandstone sample, simulating particles flowing through a sub-volume of the rock's digital twin, and developing a core-scale statistical theory for particles' residence times via upscaling the pore-scale kinetic theory. Experimental and computational results for solute transport are used as benchmark.

Based on good agreement across the scales achieved in our investigation, we show that the macroscopically observed anomalous transport is particle-type dependent and stems from particles' microscopic dispersion and deposition in heterogeneous flow fields. In particular, we reveal that residence-time distributions (i.e., breakthrough curve) obey a closed-form function that encompasses particles' microscopic dynamics, which allows investigations of a whole transition from pre-asymptotic to asymptotic behavior. The physical insights attained could be useful for interpreting experimental data and designing colloidal tracers.