Improved Volume-of-Solid formulations for micro-continuum simulation of mineral dissolution at the pore-scale

Abstract

We present two novel Volume-of-Solid (VoS) formulations for micro-continuum simulation of mineral dissolution at the pore-scale. The traditional VoS formulation (VoS-ψ) uses a diffuse interface localization function ψ to ensure stability and limit diffusion of the reactive surface. The main limitation of this formulation is that accuracy is strongly dependent on the choice of the localization function. Our first novel improved formulation (iVoS) uses the divergence of a reactive flux to localize the reaction at the fluid-solid interface, so no localization function is required. Our second novel formulation (VoS-ψ') uses a localization function with a parameter that is fitted to ensure that the reactive surface area is conserved globally. Both novel methods are validated by comparison with experiments, numerical simulations using an interface tracking method based on the Arbitrary Eulerian Lagrangian (ALE) framework, and numerical simulations using the VoS-ψ. All numerical methods are implemented in GeoChemFoam, our reactive transport toolbox and three benchmark test cases in both synthetic and real pore geometries are considered: (1) dissolution of a calcite post by acid injection in a microchannel and experimental comparison, (2) dissolution in a 2D polydisperse disc micromodel at different dissolution regimes and (3) dissolution in a Ketton carbonate rock sample and comparison to in-situ micro-CT experiments. We find that the iVoS results match accurately experimental results and simulation results obtained with the ALE method, while the VoS-ψ method leads to inaccuracies that are mostly corrected by the VoS-ψ' formulation. In addition, the VoS methods are significantly faster than the ALE method, with a speed-up factor of between 2 and 12.

Improved micro-continuum approach for capillary-dominated multiphase flow with reduced spurious velocity

“…They found the micro-continuum DBS framework is significantly faster than the Arbitrary Lagrangian Eulerian (ALE) method for simulations of calcite dissolutions, since the ALE method requires additional treatment for interface displacement. 36 Ashrafizadeh et al solved the Stokes-Brinkman and the Poisson-Nernst_Planck equations simultaneously to explore the effect of nanochannel shape on the ion transfer behavior. 37,38 Xu et al 31 extended the pore-scale microcontinuum model to non-isothermal reactive flow through a multiscale porous medium.…”