Capturing Non‐Fickian Mesoscale Solute Transport in Porous Media: The Role of Transient Storage and Mass Exchange

Solute transport in porous media at the mesoscale, whose characteristic dimension is in the range of tens to hundreds of grain diameters, is governed by disordered pore-scale velocity fields, often producing a non-Fickian behavior that cannot be described by the classical Advection–Dispersion Equation (ADE) with constant dispersivity. We investigate this behavior using transport experiments in hydrogel bead media, combining planar laser-induced fluorescence and refractive index matching to obtain high-resolution tracer concentration data across a control plane. The resulting breakthrough curves (BTCs) exhibit long tailing, a sign of non-Fickian transport. To interpret the experimental results, we developed a stochastic model of the BTC at the control plane, considering both constant (Fickian) and time-varying dispersivity derived from theory. For the time-varying case, we used the macrodispersion stochastic model developed for heterogeneous formations. The Fickian limit was set using the analytical expression for spherical inclusions in uniform fluid flow, which was also applied to the constant dispersivity model. Both parameterizations capture the bulk of the BTC but fail to reproduce the tail. By incorporating a mobile–immobile mass exchange model to account for solute retention in low-velocity and stagnant zones, we achieved excellent agreement across the entire BTC with the analytical expressions of dispersivity. The fitted exchange parameters resulted in low Damköhler numbers, which confirm significant delay of a small portion of the injected mass as epitomized by slow exchange. These results underscore the importance of including transient storage processes in mesoscale transport models to predict BTC tailing and retention accurately.