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

Abstract

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.

Morphogen gradients are regulated by porous media characteristics of the developing tissue

“…Since the gradients are also sensitive to changes in the molecular diffusion constant and in transient HSPG binding, this suggests that diffusive hindrance may be a core mechanism in morphogen gradient emergence, maintenance, and robustness. Diffusive hindrance is a core concept of transport in porous media [3, 10, 14, 34, 38, 45, 100, 105, 106, 112, 123]. In the present system, diffusive hindrance results from the joint effect of geometric tortuosity, transient HSPG binding in the ECS and at the cell surfaces, receptor complex formation, and the finite molecular diffusion constant of the morphogen.…”

On the Deviation of Computed Permeability Induced by Unresolved Morphological Features of the Pore Space

“…While the latter allow a gain in accuracy, the use of collocated grids easily aligns the computational points to the experimental datasets. Optimized grid-based methods may be coupled to other methods dedicated to the flow features to be investigated: transport based on particle methods [54,55], anisotropic diffusion for space-variable medium [56,57], phase-field description of multi-phase flows [58,59] and its upscaling [8,60], complex fluid and rheology [61,57], etc...…”

Editorial: Recent developments in upscaling and characterization of flow and transport in porous media

“…Dissolution mechanisms during saturated or unsaturated flow were investigated at the pore-scale by Esteves et al (2020) who studied reactive transport by means of pore-network modeling taking into account changes in porosity and permeability due to calcite dissolution reactions at the mineral surface. Still at the pore-scale, Etancelin et al (2020) studied dissolution and diffusive transport processes by coupling a Lagrangian formulation with the superficial velocity used in the volume averaging method. This approach takes advantage of the quality of particle tracking for transport, the quality of particle distributions from remeshing and the computation of diffusion by adaptation of the remeshing kernel.…”