Inertial Effects and Interface Dynamics during Rapid Fluid Reconfigurations

Abstract:

Inertial effects are generally neglected when modeling flow through porous media owing to the low flow rate. In case of multiphase flow, however, the presence of interfaces greatly complicates the dynamics of fluid displacement, leading to abrupt and spontaneous fluid redistribution (e.g., Haines jumps). We use numerical simulations (based on the solution of the Navier Stokes equation and on the Volume-Of-Fluid method) to investigate the role of inertia during these events and assess their impact on macroscopic quantities.

We demonstrate that the characteristic velocity of the reconfiguration events is in general unaffected by the injection rate: it is solely determined by the released amount of surface energy. Local velocities largely exceed typical injection velocity. We performed an energy-based analysis of this process and we demonstrate that inertia dominates the reconfiguration dynamics, leading to damped oscillations with their own timescale. In complex media, the oscillations are so frequent and so persistent that they affect the fluid distribution and, consequently, the work done by the external forces, which is related to macroscopic quantities such as relative and unsaturated permeabilities.