Radial reactive solute transport in an aquifer–aquitard system

•New solutions of radial dispersion in an aquifer–aquitard system are presented.•The rates of mass change in the aquitard increase with time sub-linearly.•The RTDs follows the Maxwell–Boltzmann distribution in a semi-log plot.

Radial reactive transport is investigated in an aquifer–aquitard system considering the important processes such as advection, radial and vertical dispersions for the aquifer, vertical advection and dispersion for the aquitards, and first-order biodegradation or radioactive decay. We solved the coupled governing equations of transport in the aquifer and the aquitards by honoring the continuity of concentration and mass flux across the aquifer–aquitard interfaces and recognizing the concentration variation along the aquifer thickness. This effort improved the averaged-approximation (AA) model, which dealt with radial dispersion in an aquifer–aquitard system by excluding the aquitard advection. To compare with our new solution, we expanded the AA model by including the aquitard advection. The expanded AA model considerably overestimated the mass in the upper aquitard when an upward advection existed there. The rates of mass change in the upper aquitard from the new solution and the AA model solution increased with time following sub-linear fashions. The times corresponding to the peak values of the residence time distributions for the AA model, the expanded AA model, and the new model were almost the same. The residence time distributions seemed to follow the Maxwell–Boltzmann distribution closely when plotting the time in logarithmic scale. In addition, we developed a finite-element COMSOL Multiphysics simulation of the problem, and found that the COMSOL solution agreed with the new solution well.