  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-psi) uses a diffuse interface localization function psi 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-psi') 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-psi. 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
\textit{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-psi method leads to inaccuracies that are mostly
corrected by the VoS-psi' formulation. In addition, the VoS methods are
significantly faster than the ALE method, with a speed-up factor of between 2
and 12.
