Nonlinear Reactive Solute Transport: A Practical and Fast Solution Method

Abstract

Mixing cell models have been used frequently to model solute transport coupled with reactions. The main advantage of these models is their conceptual simplicity. This allows them to be solved sequentially with chemical speciation models to predict chemical concentrations in combined reaction/transport problems. Mixing cell models are actually just explicit finite-difference solutions of the governing advection-dispersion equation. It can be shown that the inclusion of reactions in the “standard” mixing cell model degrades its second-order accuracy. We propose, therefore, an improved model which maintains second-order accuracy regardless of whether reactions are included. In addition, the improved model is unconditionally stable, unlike the standard scheme. We show that nonequilibrium reactions can also be included without difficulty. Next, we show that different boundary conditions can be incorporated into the mixing cell models. In particular, a third-type surface condition is considered. For this case, to maintain second-order accuracy of the improved model, it is necessary to dispense with the explicit nature of the scheme on the boundary. At other locations the scheme is still explicit. Other conditions, e.g., a finite mass of solute available at the surface, as would be the situation if a landfill was considered, can be handled in the same way. The method can be extended to cater for multilayered porous media. The method can also be extended easily to simulate multispecies transport. Laboratory data on the precursor effect has been used to demonstrate the use of the multispecies transport model. Our results demonstrate that nonlinear reactions and transport can be modelled very efficiently and quickly.