Effect of Permeability on Foam-model Parameters and the Limiting Capillary Pressure

Accurate modelling of foam rheology on the field scale requires detailed understanding of the correlation between the fundamental properties of foam and the scalable parameters of the porous medium. It has been experimentally observed that foam experiences an abrupt coalescence when the capillary pressure in the porous medium approaches a certain value referred to as the “limiting capillary pressure”, Pc*. Current foam models that treat foam texture implicitly mimic this fundamental behaviour with a so-called dry-out function, which contains adjustable parameters like fmdry and epdry (in the STARS foam simulator). Parameter fmdry (called Sw* in other models) represents the water saturation corresponding to the limiting capillary pressure Pc* and epdry determines the abruptness of foam coalescence as a function of water saturation. In this paper, using experimental data, we examine the permeability-dependence of these parameters. We find that the value of fmdry decreases with increasing permeability. We also find that, for the data examined in this paper, the transition from high-quality regime to low-quality regime is more abrupt in lower-permeability rocks. This implies that in high-permeability rocks foam might not collapse abruptly at a single water saturation; instead there is range of water saturation over which foam weakens. In addition, we address the question of whether Pc* is dependent on formation permeability. We estimate Pc* from data for foam mobility in vs. foam quality, and find, as did Khatib et al. (1988), who introduced the limiting capillary pressure concept, that Pc* can vary with permeability. It increases as permeability decreases, but not enough to reverse the trend of increasing foam apparent viscosity as permeability increases.