A Novel Analytical Model of Solute Transport in an Aquifer-Aquitard System with Mixing Processes in the Reservoirs

Analytical models have been widely used to aid understanding the physical and chemical processes of tracer (or chemicals) in an aquifer-aquitard system in the laboratory-controlled experiment, when the observation data is few or not available during the experiment. When injecting tracer into (or extracting them from) the aquifer-aquitard system during experiments, the pre-inlet and after-outlet reservoirs are indispensable. However, the concentration variation in the reservoirs was not treated properly in previous analytical models, resulting in poor performance in interpreting experimental data. In this study, new mathematical models describing the concentration variation in the pre-inlet and the after-outlet reservoirs are proposed, and they are integrated into the novel analytical model. The novel analytical model is developed under the mobile-immobile (MIM) framework in the aquifer-aquitard system, considering the longitudinal and vertical dispersion, the advection, and the first-order chemical reaction in both aquifer and aquitard. A finite-difference solution is developed and the experimental data are employed to test the new analytical model. Results indicate that the concentration variation in the reservoirs is important to solute transport in the aquifer-aquitard system in the laboratory-controlled experiment, and the new analytical model outperforms the previous models in interpreting experimental data. The global sensitivity analysis demonstrates that the output concentration of solute transport in the aquifer-aquitard system is most sensitive to the volume of water in the pre-inlet reservoir. The contribution of the diffusion effect to the total mass flux of tracer crossing the aquifer-aquitard interface is much smaller than the contribution of the dispersive and advective effects.