“MITIGATION OF SPURIOUS CURRENTS IN MULTIPHASE FLOW SIMULATION AT LOW CAPILLARY NUMBERS”

One of the most challenging issues in computational modelling of multiphase flow is spurious currents. Spurious currents arise by the errors in the interface curvature computations between two fluids in the computational domain. Being predominant in porous media at small capillary numbers, they might cause numerical instabilities and compromise the quality of the results in terms of fluid velocity and capillary pressure within the numerical simulation. In this work, as an attempt to fix this issue, we investigate and implement the solutions proposed in the literature to develop a set of optimal computational settings that mitigate their impact. First, we provide numerical simulations for the classical case of a circular stationary droplet of oil relaxing from an initial square shape surrounded by water using the open-source finite-volume computational fluid dynamics (CFD) code OpenFOAM. The investigation is conducted setting the interfacial compression coefficient (Cα) equal to zero (no interface compression) and higher than zero. Then, in order to reduce spurious currents, the volume of fluid (VOF) index function is smoothed by applying the so-called smoother ‘Laplacian filter’ aiming to decrease the curvature computation errors. It was proved that applying the Laplacian filter twice smooths sufficiently the index function. Since this filter is not implemented in the OpenFOAM library, an external code found in the literature is used and linked to the VOF solver. Furthermore, an error analysis on the accuracy of the numerical solution of the Laplace pressure for a stationary droplet with respect to the exact (analytical) solution of the Laplace pressure for a sphere has been performed. The obtained results show that introducing the interface compression has led to a sharp (thinner) interface, but increased the magnitude of spurious currents which has been reduced later by almost one order of magnitude when the smoother was applied. The error in the Laplace pressure calculations has also decreased by almost 36%. Finally, this work was extended to model both drainage/imbibition experiments and a steadily moving droplet in capillary tubes. This work demonstrates the potential and stability of the proposed computational rules to adequately reduce the magnitude of spurious currents when simulating multiphase flow phenomena in real porous media.