We study the dynamics of nonwetting liquid blobs during immiscible two-phase flows in stochastically reconstructed porous domains predominantly saturated by a wetting fluid. The flow problem is solved explicitly using a Lattice-Boltzmann model that captures both the bulk phase and interfacial dynamics of the process. We show that the nonwetting blobs undergo a continuous life cycle of dynamic breaking up and coalescence producing two populations of blobs, a mobile and a stranded one, that exchange continuously mass between them. The process reaches a “steady state” when the rates of coalescence and breaking up become equal, and the macroscopic flow variables remain practically constant with time. At steady state, mass partitioning between mobile and immobile populations depends strongly on the applied Bond number $\mathrm{Bo}$ and the initial nonwetting phase distributions. Three flow regimes are identified: a single-phase flow Darcy-type regime at low $\mathrm{Bo}$ numbers, a non-Darcy two-phase flow regime at intermediate values of $\mathrm{Bo}$, where the capillary number scales as $\mathrm{Ca}\propto {\mathrm{Bo}}^2$, and a Darcy-type two-phase flow regime at higher values of $\mathrm{Bo}$. Our numerical results are found to be in good agreement with recent experimental and theoretical works.

• Received 30 October 2012

DOI:https://doi.org/10.1103/PhysRevE.87.033001