Internal Research Project I-10

1 October 2024 to 31 December 2024

The Vision Topic of SFB 1313 on carbonate dissolution/precipitation is formulated in the proposal of the second funding period. Beyond the porous-media flow applications, carbonate dissolution and precipitation is particularly relevant for higher Re-number, where Stokes flow or Navier-Stokes flow more adequately represents the flow regime. The main challenge to address relevant spatial and temporal scales is the highly increased computational demand in comparison to Darcy-flow types of equations.

For that reason, we propose a small internal project that allows for investigating, testing, and if possible improving solution efficiency of the Stokes solver in Dumux with respect to the implementation of coupled hydraulic and reactive processes.

A challenge arises for the use of the current staggered grid implementation of the Dumux simulator, which is used to model a problem with flow of water with CO2 and reacting with the boundary consisting of calcium carbonate. The primary variable for the concentrations is located in the center of the cell at the boundary, which means that for the calculation of the reaction rate, the reactive source term is currently calculated at the not exactly correct location at the wall but shifted by half a discretization length. Assuming that the concentrations of dissolved carbonates are even higher at the boundary, this leads to an overestimation of the reaction rate. The significance of this is dependent on the discretization length, or in other words, dependent on the computational effort to be invested.

The work plan for this small project includes the testing of a few ideas to deal with that challenge or to overcome it.

Firstly, it is planned to discretized the domain with aspect ratio different from unity, such that the discretization length is smaller towards the reactive boundary, while the computational effort remains feasible.

Second, we plan to test an approach to extrapolate the concentrations inside the domain to the respective locations at the reactive wall. Dependent on the strength of advective flows and their directions, or in other words dependent on the two Damköhler numbers (diffusive and advective), this approach may work or not. For strong advection parallel to the wall which dilutes the concentrations, an extrapolation of the concentration gradient towards the reactive wall will overestimate the concentrations there, and therefore underestimate the reaction rate or even lead to precipitation instead of dissolution.

We want to implement that, test it, and analyse it to determine appropriate future steps.