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This article presents a three-dimensional numerical framework for the simulation of fluid-fluid immiscible compounds in complex geometries, based on the multiple-relaxation-time lattice Boltzmann method to model the fluid dynamics and the color-gradient approach to model multicomponent flow interaction. New lattice weights for the lattices D3Q15, D3Q19, and D3Q27 that improve the Galilean invariance of the color-gradient model as well as for modeling the interfacial tension are derived and provided in the Appendix. The presented method proposes in particular an approach to model the interaction between the fluid compound and the solid, and to maintain a precise contact angle between the two-component interface and the wall. Contrarily to previous approaches proposed in the literature, this method yields accurate solutions even in complex geometries and does not suffer from numerical artifacts like nonphysical mass transfer along the solid wall, which is crucial for modeling imbibition-type problems. The article also proposes an approach to model inflow and outflow boundaries with the color-gradient method by generalizing the regularized boundary conditions. The numerical framework is first validated for three-dimensional (3D) stationary state (Jurin's law) and time-dependent (Washburn's law and capillary waves) problems. Then, the usefulness of the method for practical problems of pore-scale flow imbibition and drainage in porous media is demonstrated. Through the simulation of nonwetting displacement in two-dimensional random porous media networks, we show that the model properly reproduces three main invasion regimes (stable displacement, capillary fingering, and viscous fingering) as well as the saturating zone transition between these regimes. Finally, the ability to simulate immiscible two-component flow imbibition and drainage is validated, with excellent results, by numerical simulations in a Berea sandstone, a frequently used benchmark case used in this field, using a complex geometry that originates from a 3D scan of a porous sandstone. The methods presented in this article were implemented in the open-source PALABOS library, a general C++ matrix-based library well adapted for massive fluid flow parallel computation.

Magma degassing fundamentally controls the Earth's volatile cycles. The large amount of gas expelled into the atmosphere during volcanic eruptions (i.e., volcanic outgassing) is the most obvious display of magmatic volatile release. However, owing to the large intrusive:extrusive ratio, and considering the paucity of volatiles left in intrusive rocks after final solidification, volcanic outgassing likely constitutes only a small fraction of the overall mass of magmatic volatiles released to the Earth's surface. Therefore, as most magmas stall on their way to the surface, outgassing of uneruptible, crystal‐rich magma storage regions will play a dominant role in closing the balance of volatile element cycling between the mantle and the surface. We use a numerical approach to study the migration of a magmatic volatile phase (MVP) in crystal‐rich magma bodies (“mush zones”) at the pore scale. Our results suggest that buoyancy‐driven outgassing is efficient over crystal volume fractions between 0.4 and 0.7 (for mm‐sized crystals). We parameterize our pore‐scale results for MVP migration in a thermomechanical magma reservoir model to study outgassing under dynamical conditions where cooling controls the evolution of the proportion of crystal, gas, and melt phases and to investigate the role of the reservoir size and the temperature‐dependent viscoelastic response of the crust on outgassing efficiency. We find that buoyancy‐driven outgassing allows for a maximum of 40–50% volatiles to leave the reservoir over the 0.4–0.7 crystal volume fractions, implying that a significant amount of outgassing must occur at high crystal content (>0.7) through veining and/or capillary fracturing.