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.

Channeling: a new class of dissolution in complex porous media

“…Since GeoChemFoam uses steadystate formulations of flow and transport, it can be applied with very large time-steps (CF L ≈ 1000), allowing for large speed-ups in computation time. Details of the numerical method are presented in [28] and in the supplementary information. The original geometries and output files can be downloaded from our Zenodo dataset archive, the geometry creation scripts are on github and an example input deck is on the GeoChemFoam wiki.…”

“…The numerical model, including meshing, time-stepping and convergence, is presented in detail in the supplementary information. A simplified chemical model is employed representing dissolution of calcite mineral during acid injection, with one fluid component and one reaction component [20,24,28]. The molecular diffusion is the constant D = 10 −9 m 2 .s −1 .…”

“…2). A series of 26 numerical simulations was performed on each of the geometries by injecting acid at different flow and reactive conditions using our new highly efficient open source numerical solver GeoChemFoam [25][26][27][28], which is based on the Open Source Computational Fluid Dynamics toolbox OpenFOAM [29]. We observe that many of the model scenario results do not fit the conceptual model of the three traditional dissolution regimes and have fundamentally categorically distinct porosity-permeability relationships.…”

On the Role of Gravity in Dissolving Horizontal Fractures

“…This may be attributed to the local estimate of the reactive surface area embedded in the DBS approach, in which the VoS-ψ formulation was implemented using a diffuse interface localization function ψ = 4ε f (1−ε f ). Maes et al (2022) showed that the VoS-ψ formulation would underestimate the overall dissolution rate and proposed two improved VoS formulations. We think that the improved VoS formulations proposed by Maes et al (2022) would not change the overall conclusions or conceptual model, but only improve the local accuracy.…”

“…Maes et al (2022) showed that the VoS-ψ formulation would underestimate the overall dissolution rate and proposed two improved VoS formulations. We think that the improved VoS formulations proposed by Maes et al (2022) would not change the overall conclusions or conceptual model, but only improve the local accuracy. In addition, the parameter of the dissolution rate is not matched in this work, but directly from the NaCl physical properties.…”