An improved operator splitting method for accurate and efficient simulation of strong feedback of chemistry on hydrodynamics
Résumé
Reactive transport is a highly non-linear problem that requires solving with efficient algorithms. Two classes of formulation are usually found in the literature: the frontal global implicit approach, and the operator splitting method. Operator splitting, particularly in a sequential iterative approach, has been proven to be accurate and efficient for classical reactive transport problems. Mineral changes, due to dissolutions and precipitations, can modify the pore structure and in the end the hydrodynamic properties of the medium. The physical description of this feedback on a REV scale requires adding microscopic information on the pore structure evolution, usually with empirical relations on global parameters, for instance between porosity and permeability (e.g. Kozeny-Carman) or diffusion (e.g. Archie's law). This issue is not addressed here, where we focus on the added non-linearity of the feedback. The impact of chemistry on porosity is straightforward, with a simple balance on the mineral volume evolution. However, the degree of coupling between porosity change and its effect on transport and flow is less clear. An analytical solution on a simple 1D diffusive problem has been devised to check the accuracy of the sequential iterative approach. It is proven that porosity changes have to be strongly coupled with chemistry and mass transport, i.e. integrated into the sequential resolution, to achieve a correct solution. On the contrary, the effect on flow is smaller, so that an explicit coupling remains accurate, with the benefit of less required CPU. The strong iterative coupling between chemistry, transport and porosity changes can be CPU challenging, especially for clogging systems. In this case, small porosity combines with a slow income of mobile aqueous reagent; on the contrary, fixed species (minerals or surface compounds) display very high concentrations (compared to the low water content), and associated large variations. This leads to a 0 multiplied by infinity instability, which can be CPU consuming. The precise observation of a simple 1D advective/dispersive case brings some insight into the behaviour of the system, particularly near a reaction front. This allows for the devising of better estimates of the porosity and the fixed fractions, at the beginning of each new time step. The estimator can be perfect for the simplest cases, and retains a good accuracy for more complex problems. Thus, convergence is reached more rapidly, the problem stiffness is largely reduced, and larger time steps can be used, even keeping the number of coupling iterations low. An example of the improved behaviour of the system is given on a practical application: the carbonation of a cement paste in contact with a carbonated water. This problem is well-known to lead to a complete clogging at the interface: the calcium silicate hydrates are destabilized by the acidic calcium-poor water, so that calcium and the hydroxides are leached towards the interface, where they meet the carbonates, and precipitate as calcite. The system thus leads to a re-concentration of the calcium at the interface, which reduces drastically the porosity; a near complete clogging occurs which stops further reactions.