The simulation of multi-phase flow at low capillary numbers (Ca) remains a challenge. Approximate computations of the capillary forces tend to induce parasitic currents (PC) around the interface. These PC induce additional viscous dissipation and shear forces that potentially lead to wrong calculations of the general flow dynamics. Here, we focus on the case of spontaneous imbibition in a microchannel of Hele-Shaw cell symmetry with capillarity being the only driving force. We extend the Lucas-Washburn equation to account for arbitrary viscosity ratios and assess four volume-of-fluid (VOF) formulations against the analytical solution. More specifically, we evaluate the continuum surface force (CSF) formulation, the sharp surface force (SSF) formulation, the filtered surface force (FSF) formulation and the piecewise linear interface calculation (PLIC) formulation extended by a higher order discretisation of the interface curvature through a height function with respect to accuracy, performance and heuristic parameters. We quantify PC for each formulation and investigate their impact on flow with Ca < 10 −2. The magnitude of PC are largest for CSF and are reduced two fold by SSF. FSF reduces PC considerably more but shows periodic short bursts in the velocity field. PLIC shows no PC for the studied Ca and viscosity ratios. However, it fails when a denser fluid displaces a lighter fluid. Despite PC, all formulations are accurate within 10%. PLIC is suited to serve as a reference but relies on a structured mesh and is computationally expensive. FSF requires more heuristic parameters. Together with periodic bursts, this prevents a conclusive statement on the best choice between SSF and FSF.

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Imbibition is an important process encountered in many porous media applications. At the pore scale, pore network models (PNM) are computationally efficient and can model drainage accurately. However, using PNM to model imbibition still remains a challenge due to the complexities encountered in understanding pore-scale flow phenomena related to pore body filling (PBF) and snap-off along with the relative competition between these events. In this work, we use direct numerical simulations (DNS) to revisit the basic principles of PBF in a two-dimensional synthetic pore geometry. We notice that PBF during spontaneous imbibition is dependent on several parameters such as shape of the transition zone, contact angle and the fluid properties like density. The interactions between these parameters are investigated in a quantitative manner. We demonstrate the existence of a critical contact angle θ c and a barrier contact angle θ b . θ c depends on the shape of the pore geometry, whereas θ b depends on the pore geometry, contact angle and fluid properties. For a system comprising of light fluids, θ b is only slightly larger than θ c ; whereas for a system occupied by dense fluids, θ b is notably larger than θ c . The contact angle of the wetting phase θ in relation to θ c and θ b decides if the wetting phase can imbibe a pore body. Imbibition always occurs if θ < θ c . For θ > θ c , we observe capillary barrier zones in which capillary forces accompany viscous forces to resist spontaneous imbibition. For this case, we observe smooth transition of the meniscus curvature while the meniscus enters and exits capillary barrier zones. For θ c ≤ θ ≤ θ b , inertia assists the wetting phase to overcome resisting forces and imbibe the pore space. For θ > θ b , the resisting forces dominate over inertia so that the wetting phase cannot imbibe the pore space. For the synthetic pore geometries investigated, we provide analytical and semi-analytical expressions to determine θ c and the position of capillary barrier zones respectively. The barrier contact angle θ b is computed numerically for several inertial systems and for various shapes of the synthetic pore geometry. The results of this quantitative analysis can be utilised to improve the existing pore filling rules and predictive capabilities of PNM used for two-phase flows.

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Reactive transport modelling has established itself as a key player to analyze sophisticated hydrogeochemical interactions that occur over spatio-temporal scales on par with subsurface applications. In this paper, we benchmarked a new reactive transport package -porousMedia4Foam at the continuum-scale considering complex and well established cases available in the reactive transport modelling community.porousMedia4Foam was born by the successful coupling of two open-source packages -OpenFOAM ® and PHREEQC. The flow governing equations, transport of species and the evolution of porous media properties are handled by OpenFOAM ® whereas, the geochemistry is exclusively handled by PHREEQC. We further demonstrated the capability of using porousMedia4Foam to investigate reactive transport processes considering unstructured meshes. As porousMedia4Foam is an open-source package with included benefits to account for reactive transport processes occurring at various scales -pore-, hybrid-, and, Darcy-scales, we believe that porousMedia4Foam opens a new dimension to analyze reactive transport physics for various intriguing subsurface applications.