The fully implicit water mixing approach for the efficient simulation of reactive transport

Reactive transport is a phenomenon resulting from the interaction and coupling of solute transport and chemical reactions. A new method to solve reactive transport known as Water Mixing Approach (WMA) was introduced by Soler-Sagarra et al. (2022). The idea is to interpret solute transport as water mixing and advection, where diffusion and dispersion are simulated as water exchange instead of Fickian solute flux. The WMA has the advantage of decoupling transport and chemistry. Transport computations are restricted to the evaluation of mixing ratios. This way, reactive transport computations are restricted to reactive mixing calculations, which can be performed separately for every target (node, cell, or particle, depending on the approach adopted to simulate transport). This facilitates parallelisation. However, the original work only considered the explicit case, which is conditionally stable and therefore requires artificial values of the dispersion coefficient to avoid numerical instabilities. We present a formulation of the WMA that is implicit both in transport, to ensure stability, and in chemical reactions to be able to simulate fast reactions. The implicit formulation requires lumping the reactive term. We test the validity of the approach by comparison with analytical solutions and the Direct Substitution Approach (DSA) method in a case with 2 adjacent mineral zones in equilibrium, and in a denitrification case with two redox reactions. We find that the proposed approach is extremely efficient and accurate for small dispersion cases.