Improvement of remeshed Lagrangian methods for the simulation of dissolution processes at pore-scale

• Published in: Advances in water resources 2020-12, Vol.146, p.103780, Article 103780
• Main Authors: Etancelin, Jean-Matthieu, Moonen, Peter, Poncet, Philippe
• Format: Article
• Language: English
• Subjects: Analysis of PDEs; Computer Science; Digital rock physics; Dissolution process; Distributed, Parallel, and Cluster Computing; Earth Sciences; Engineering Sciences; Environmental Engineering; Environmental Sciences; Geochemistry; Lagrangian methods; Mathematics; Numerical Analysis; Porous media; Reactive flows; Reactive fluid environment; Sciences of the Universe; Three-dimensional flows
• ISSN: 0309-1708; 1872-9657
• DOI: 10.1016/j.advwatres.2020.103780

•Focus on hybrid methods using grids and Lagrangian tracking, to reconcile accurate remeshing and sign-preservation.•How to choose a remeshing kernel, and how to adapt diffusion to adjust the discrepency introduced by the remeshing.•Various two-scale porous media are investigated at rocks pore scale. This article shows how to consistently and accurately manage the Lagrangian formulation of chemical reaction equations coupled with the superficial velocity formalism introduced in the late 80s by Quintard and Whitaker. Lagrangian methods prove very helpful in problems in which transport effects are strong or dominant, but they need to be periodically put back in a regular lattice, a process called remeshing. In the context of digital rock physics, we need to ensure positive concentrations and regularity to accurately handle stagnation point neighborhoods. These two conditions lead to the use of kernels resulting in extra-diffusion, which can be prohibitively high when the diffusion coefficient is small. This is the case especially for reactive porous media, and the phenomenon is reinforced in porous rock matrices due to Archie’s law. This article shows how to overcome this difficulty in the context of a two-scale porosity model applied in the Darcy-Brinkman-Stokes equations, and how to obtain simultaneous sign preservation, regularity and accurate diffusion, and apply it to dissolution processes at the pore scale of actual rocks.