On the Bimodal Radial Solute Transport in Dual-Permeability Porous Media

Porous media usually exhibit distinct transport properties of a dual domain, which is attributed to layering, fracturing, or aggregation. In this study, a mobile-mobile (MM) model of radial solute transport consisting of two advection-dispersion equations (ADEs) is presented to describe the bimodal (or double-peaked) breakthrough curves (BTCs) through two distinct pore domains consisting of interrelated fast-flow and slow-flow domains. Transport processes, including advection, dispersion, and first-order mass transfer between the two domains, were considered in the model. Semi-analytical solutions were derived using a Laplace transform, matrix diagonalization and numerical Laplace inversion method, and the solutions were verified against the existing analytical solution for the mobile-immobile (MIM) model under the special case of zero velocity in the slow-flow domain. In addition, Markov Chain Monte Carlo is applied to estimate the MM model parameters using the experimental data. The results indicate that a larger transfer coefficient between the fast-flow and the slow-flow domains resulted in a weaker bimodal phenomenon for concentration distribution curves, which was notably more apparent when there was a greater variation in pore flow velocities between the two domains. Also, the MM model can be used to investigate other types of abnormal transport features such as late arrival and early arrival. Finally, the ADE, MIM, and MM models were used to interpret the experimental data conducted by Fernandez-Garcia et al. (2004, ), and it was found that the proposed MM model can explain the bimodal feature of BTCs while the ADE and MIM models fail to do so.