An adaptive multi-scale iterative scheme for a phase-field model for precipitation and dissolution in porous media

TL;DR

This paper introduces an adaptive multi-scale iterative scheme for a phase-field model that simulates mineral precipitation and dissolution in porous media, addressing geometric changes and non-linearities for improved simulation accuracy.

Contribution

It develops a robust, convergent two-scale phase-field scheme with an adaptive strategy to enhance efficiency in modeling dynamic pore structure changes.

Findings

The scheme accurately captures anisotropies and heterogeneities.

Adaptive strategy improves computational efficiency.

Numerical tests validate the scheme's accuracy and robustness.

Abstract

Mineral precipitation and dissolution processes in a porous medium can alter the structure of the medium at the scale of pores. Such changes make numerical simulations a challenging task as the geometry of the pores changes in time in an apriori unknown manner. To deal with such aspects, we here adopt a two-scale phase-field model, and propose a robust scheme for the numerical approximation of the solution. The scheme takes into account both the scale separation in the model, as well as the non-linear character of the model. After proving the convergence of the scheme, an adaptive two-scale strategy is incorporated, which improves the efficiency of the simulations. Numerical tests are presented, showing the efficiency and accuracy of the scheme in the presence of anisotropies and heterogeneities.