Abstract:

Simulating reactive transport in groundwater is computationally expensive because solute transport and chemical reactions are coupled and must be solved simultaneously. The Water Mixing Approach (WMA) offers an alternative that decouples these two processes. Rather than solving everything together, WMA represents transport as a sequence of mixing operations involving neighbouring waters. Concentrations at each point are calculated as a weighted mixture of nearby waters plus the contribution from reactions. Transport and reactions are thus separated, reducing computational cost and allowing reactions to be solved independently at each node or cell.

The aim of this work is to evaluate and improve the implicit WMA so that transport and reactions remain decoupled in reactive transport simulations. The original version of WMA was explicit in time, making it unstable for large time steps. Here, it is extended to an implicit formulation, which is unconditionally stable. However, making the formulation implicit couples transport and reactions again. To keep them separate, two variants are proposed: the “lumped” variant, which aggregates reaction contributions from neighbouring waters at the computation point, and the “consistent” variant, which approximates these contributions using reaction rates already computed upstream and estimates of those downstream.
Both variants are compared with the Direct Substitution Approach (DSA) and analytical solutions for two problems: a single mineral at equilibrium, and two adjacent mineral zones at equilibrium as well. For problems with smooth solutions, all methods converge well. However, when chemical conditions change abruptly, as in the two-mineral-zone problem, all methods fail, including DSA.

This leads to an important conclusion: numerical methods have been designed to ensure convergence in concentrations, but not in reaction rates. In the presence of sharp geochemical fronts, the computed reaction rates are inaccurate regardless of the method used. This suggests a need to develop new numerical methods that also ensure convergence in reaction rates.