A THEORETICAL-MODEL OF COLLISION AND COALESCENCE OF GANGLIA IN POROUS-MEDIA

The problem of collision and coalescence of nonwetting ganglia is central to understanding the mechanics of bank formation during immiscible two-phase flow in porous media. Here we present a theoretical model of the process of collision and coalescence of a pair of mobilized ganglia in porous media, and we investigate the conditions under which coalescence is prompt or difficult. The porous medium is modeled as a three-dimensional network of randomly sized unit cells of the constricted-tube type, pertaining to consolidated porous materials. The problem of simultaneous flow of the two ganglia in the porous medium is solved using the network approach. The details of the flow near and between the two colliding menisci are analyzed with a film drainage model, which takes into account the presence of the constraining pore wall, the wetting film which surrounds the ganglia by occupying roughness features on the pore wall, and the hydrodynamic interactions of the three liquid bodies. The factors controlling film drainage in a single throat are investigated. While the film is draining, the colliding ganglia are moving within the pore network, and for this reason the entire problem has to be solved on two different time scales: that of the motion of ganglia, and that of the film drainage. The model is used to evaluate the probability of coalescence between pairs of colliding ganglia. Using this model, the dependence of the probability of coalescence given a collision, C11, on the parameters that affect the flow (capillary number Ca, viscosity ratio κ, and dynamic contact angles) is investigaged. The simulations indicate that wettability is a more important parameter than Ca or κ, and that C11 decreases as the ocntact angle increases. In most cases considered the value of C11 is in the range from 0.03 to 0.15. © 1991.