A Solution for Mixing-Limited Equilibrium Reactions in Idealized Radial Flow

Analytical solutions of field-scale reactive transport are needed for testing numerical codes and for design of injection-based remediation schemes. Aquifer injection via a well induces a reaction zone limited to the mixing fringe between injected and ambient solutions, and thus a mixing-limited reactive transport. Here we develop a quasi-analytical model for multicomponent equilibrium reactive transport in idealized 2-D radial flow in a homogeneous aquifer. We combine a classical model of the dynamics of the mixing zone geometry with a scalar dissipation representation of the mixing-limited reaction to develop a quasi-analytical solution for reaction extent. Our formulation accommodates the spatial variation of the hydrodynamic dispersion coefficient in a radial flow. This scenario is investigated first for a single bimolecular equilibrium reaction and then extended to multiple equilibrium reactions. The results compare well to explicit numerical simulation. Finally, we provide again a quasi-analytical solution for the case where dispersive spreading is not contemporaneous with mixing, treated via a mobile-mobile irreversible mass transfer from unmixed to mixed phases following Ginn (2018, https://doi.org/10.1002/2017WR022120).