Water Mixing Approach (WMA) for reactive transport modeling

We describe a formulation to solve reactive transport (RT) problems. The basic idea is to represent transport as mixing water instead of individual solute concentrations, hence the Water Mixing Approach (WMA) name. This conceptual representation simplifies RT calculations as it decouples transport from chemistry. Transport is first solved in terms of water mixing ratios (lambda), which we show is feasible for any transport formulation. Chemical calculations can then be written as a set of reactive mixing calculations, which are local, so that they do not need to iterate with transport. We have implemented the WMA for a mixed Eulerian-Lagrangian transport solver with streamline-oriented grid and constant travel time between sequential cells (isochronal grid), which is free of numerical dispersion. We test the WMA on three RT cases. First, a binary system case is used to test the accuracy of the method. Second, a calcite dissolution case is used to compare the WMA to the Direct Substitution Approach to test both accuracy and computational cost (CPU). Third, the accuracy and simplicity of the proposed approach is tested on a reactive pulse injection case, solved in 2D on a spreadsheet. Results confirm the accuracy, simplicity and efficiency (low CPU cost) that result from decoupling transport and chemical steps. Transport through highly heterogeneous media remains a challenge, but the definite separation and simplification of mixing processes in WMA opens a new path for reactive transport modeling in general, and for the search of an effective transport equation.