On Constrained Minimisation Techniques for Solving General Geochemical Reactive Transport Problems
Résumé
In the framework of reactive transport modelling several approaches have been proposed. Many research efforts are devoted to families of sequential operator-splitting and fully (or global) implicit methods coupling solute transport and geochemical equations solvers respectively. However, there is little works advocated to numerical solvers genuinely efficient for this task. We have developed a new geochemical engine based on robust non-linear optimisation technology for mixed algebraic-differential equations stemming from thermodynamic equilibrium and kinetic processes. It is shown how our constrained minimisation algorithm for solving thermodynamic equations eliminates the need for the search process of dissolved or non existing mineral phases, and how general geochemical constraints are fetched directly into it. In the paper we also discuss predictor-corrector techniques for solving the coupled set of geochemical equations. These techniques contribute significantly to the general efficiency of reactive transport simulations because the number of iterations is significantly reduced by comparison to the Newton-Raphson method. Another numerical advantage of this approach is guaranteeing total concentrations positivity of all species, even those present in small amounts. To exten d this feature globally, the geochemical engine is coupled with a higher-order Godunov method for finite volume computations in non-rectangular 3D grids. The C/C++ computer package featuring these new developments is designed in a flexible manner allowing it to be plugged with other available solute transport packages. It has gone through intensive benchmarks and comparisons with other reactive transport models. Finally, we close the paper by an application of the computer model to CO2 injection in a deep French geothermal reservoir surrounding Paris. The main aquifer strata known as the 'Dogger' has an active record of geothermal development since the seventies. Currently, it is one possible target for large scale injection of CO2 in its supercritical form. We guided two sets of simulations, near the wells for typical injection periods of 50 years, and in the far field for a few thousands years, to show the contrast in the flow and geochemical transport processes throughout. The contrasted behaviour suggests that it is possible to spatially decouple modelling near and far from the injection wells in the Dogger context.