Semi-analytical Solution for Reactive Solute Transport in a Filled Macropore-Matrix System and Application to Laboratory Experiments

The macropore-matrix system plays a critical role in governing preferential flow under field conditions, and understanding solute transport within such a system forms the basis for investigating the complex fate of contaminants in heterogeneous porous media. Moreover, single macropores in the field are often partially or completely filled with sediments, yet the process of reactive transport in such filled macropore–matrix systems has received limited attention. A mobile–immobile (MIM) model is developed for sediment-filled macropore–matrix systems, representing solute transport as a three-domain process with advection, radial dispersion, reactions, sorption, and rate-limited mass exchange. The governing equations are solved using Laplace-domain analysis with numerical inversion and validated against numerical simulations. In addition, Markov Chain Monte Carlo (MCMC) is applied to estimate the MIM model parameters using the experimental data. Results from the semi-analytical solution show that pore filling strongly modifies solute transport and breakthrough behavior. A reduction in the porosity ratio between the mobile and immobile regions lowers the peak of the breakthrough curves (BTCs) and amplifies tailing. Likewise, a smaller mass-transfer coefficient produces higher pore concentrations and modifies BTC tailing by delaying mass exchange between the mobile and immobile regions. Analysis of diffusion fluxes further reveals that back-diffusion is an important mechanism responsible for the observed tailing behavior. Parameter inversion using the MCMC method based on the proposed model shows a marked improvement over existing approaches, reducing root mean square error (RMSE) by up to 55% in the column experiment. Overall, the proposed model effectively captures the solute transport characteristics in macropore–matrix systems and provides valuable theoretical and practical insights for groundwater pollution studies in heterogeneous aquifers.