Temporal and Spatial Evolution of Pore Scale Pdfs of Solute Concentrations to Study Incomplete Mixing in Porous Media

Knowing local concentration distributions is important for transport and mixing in particular in porous media, yet a comprehensive understanding of them remains a challenge. Computing advancements have enabled high-resolution pore-scale simulations, offering an opportunity for unprecedentedly in-depth investigation of mixing. In this study we use simulation data to examine concentration distributions at the pore scale in the context of longitudinal (pseudo-one-dimensional) solute transport through a porous column. In order to perform the measurements, we first devise a semi-analytical approach to estimate the mean effective transport velocity profile under non-uniform Darcy-scale fluid velocity, which unavoidably occur due to the presence of lateral boundaries. This development allows sampling micro-scale concentrations over a moving surface that possesses a well defined Darcy-scale mean concentration, hence enabling computation of the local concentration distribution which is induced by pore-scale fluctuations. The implemented approach involves inverse modeling of the transverse dispersion coefficient, which allows us to measure this parameter in the unlikely setting of a longitudinal column experiment. The estimated transverse dispersion coefficient values closely agree with previously published experimental data. We find that the measured pore-scale concentration pdfs are best represented by a beta distribution, thus validating this longstanding hypothesis with direct evidence. Furthermore, we fully describe the temporal and spatial evolution of the local concentration pdf, as well as its Péclet number dependence.