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Description
This contribution describes an improved formulation for Volume-of-Fluid (VOF)-based modelling of mass transfer, providing a more robust basis for pore-scale simulations relevant to geological CO₂ sequestration and H₂ storage, including Ostwald ripening. VOF is an efficient, mass-conserving single-field method for simulating two-phase flow, that can be extended to mass transfer problem using the Continuous Species Transfer (CST) approach. However, the unified VOF-CST formulation introduces significant modelling challenges.
A first challenge concerns the definition of the diffusion coefficient in cells that contain both phases. The common approach blends gas and liquid diffusivities using their volume fractions [1]. For cases where the trapped gas is compositionally pure, simulations show that this blending leads to an incorrect interfacial diffusive flux and a spurious resistance at the interface, so that accurate results are obtained only on finer meshes. A second problem is that the VOF method does not represent the interface as a geometrically sharp surface but smears it over several cells. In standard formulations, the relative velocity between phases is assumed to be zero and is replaced by an artificial interface-compression term to limit this smearing. However, in mass-transfer problems the relative velocity between phases is physically non-negligible, and neglecting it leads to additional numerical diffusion, particularly when a compositionally pure trapped gas phase grows.
We revisit the VOF-CS equations under the assumption of a compositionally pure trapped gas with zero concentration gradient in the gas phase. This allows the derivation of a conservative effective diffusion coefficient for interfacial cells, for which the appropriate value is shown to be the liquid-phase diffusivity rather than a volume-fraction-weighted average. Implemented in GeoChemFoam [2] , this closure reduces interfacial mass-flux errors and, together with a suitable numerical scheme, matches an analytical dissolution solution on relatively coarse meshes. The interface-compression term is then modified to be consistent with the problem physics and boundary conditions, which keeps the interface sharper, reduces numerical diffusion, and improves the predicted evolution of trapped-gas volume and mass transfer. With these improvements, the model can now accurately capture diffusive exchange between neighbouring gas droplets, enabling the simulation of Ostwald ripening in which one droplet progressively dissolves into another.
[1] Maes, Julien, and Soulaine, Cyprien. "A unified single-field Volume-of-Fluid-based formulation for multi-component interfacial transfer with local volume changes." Journal of Computational Physics 402 (2020): 109024. https://doi.org/10.1016/j.jcp.2019.109024
[2] https://github.com/GeoChemFoam DOI:10.5281/zenodo.11354428
| Country | United Kingdom |
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