Application of the Lattice-Boltzmann method to the modeling of population blob dynamics in 2D porous domains

In the present paper, the Lattice-Boltzmann method is employed for the simulation of immiscible two-phase flow through a 2D porous domain when the volume fraction of the non-wetting phase is relatively low and thus it flows in the form of disconnected blobs. The flow problem is solved using an immiscible two-phase LB model where interfacial forces are expressed in terms of the chemical potential through the Gibbs–Duhem equation. We study the population dynamics of the non-wetting fluid blobs, namely the temporal evolution of the average blob size, with respect to the applied body force and the wetting phase volume fraction. Our results show that the system reaches a “steady state” where the average values of the studied parameters, such as the superficial velocities of both phases, and the number and size distribution of the blobs remain practically constant in time, although the temporal fluctuations around average values may be significant. We show that the average volume of the blobs decreases (and the population of the blobs increases) as the body force increases, namely as the viscous forces become dominant over capillary forces. The effect of the wetting volume fraction on the number of the blobs is more complex; as the wetting volume fraction decreases at constant body force, the blobs cover larger areas within the pore space producing larger pressure gradients and the dynamic breakup of blobs intensifies resulting in increasing blob numbers. However, below a critical value of the wetting volume fraction, the number of blobs begins to decrease and the non-wetting phase begins to span the entire pore network.