Static Capillary Pressure of Ganglion in Porous Media

Abstract:

Residual ganglia emerge in porous media as a result of incomplete fluid-fluid displacements, injection of emulsion or foam, or phase separation. Since a ganglion corresponds to a disconnected phase occupying a finite number of pores, the traditional Darcy-scale description of capillary pressure (P_c) for hydrodynamically connected fluids becomes invalid.

We propose a conceptual pore-scale model for P_c of a ganglion statically trapped in a two-dimensional regularly arranged disk pack (FIG.1.(a)). All possible metastable configurations are analytically identified. We find that the volume of a ganglion (V) alone is not adequate to determine P_c. At fixed pore geometry and wettability, P_c is also a function of pore occupancy, k, and a topological parameter, n. P_c can therefore be written as P_c(V, k, n). Counter-intuitively, all P_c, regardless of V, k and n, fall within a narrow range, if k>1, which agrees with previous experiments by Garing, et al. (AWR, 2017).

We further study the changes in P_c during the growth and subsequent shrinkage of the ganglion (FIG.1.(b)). Unlike P_c for a hydrodynamically connected phase, the ganglion P_c is non-monotonic and discontinuous with respect to V. The effect of hysteresis is strong. A growing ganglion always chooses a configuration of maximum possible P_c at any given V; while a shrinking ganglion chooses the configuration of minimum P_c. At infinitely large V, the P_c-V curve converges to that of a hydrodynamically connected phase at the Darcy scale. The impact of pore geometry and wettability are shown to be quantitative but not qualitative. The work provides useful insight into the equilibrium states of dispersed fluids in porous media.