Modeling the Effect of Oil on Foam for EOR

The effectiveness of foam for mobility control in the presence of oil is key to foam EOR. A fundamental property of foam EOR is the existence of two steady-state flow regimes: the high-quality regime and the low-quality regime. Experimental studies have sought to understand the effect of oil on foam through its effect on these two regimes. Here we explore the existence of multiple steady states for one widely used foam model. The widely used STARS foam model includes two algorithms for the effect of oil on foam: in the "wet-foam" model, oil changes the mobility of full-strength foam in the low-quality regime; in the "dry-out" model, oil alters the limiting water saturation at which foam collapses. We examine their effect on the two flow regimes, using Corey relative permeabilities for oil. Specifically, we plot the pressure-gradient contours that define the two flow regimes as a function of superficial velocities of water, gas and oil and show how oil shifts behavior in the regimes. There are two ways to study the effect of oil on steady-state foam: 1) at fixed oil saturation. This is the way a simulator represents the effect, but it is difficult if not impossible to fix this condition in a laboratory coreflood. 2) at fixed superficial velocities. In both kinds of plots, the wet-foam model shifts behavior in the low-quality regime with no direct effect on the high-quality regime. The dry-out model shifts behavior in the high-quality regime but not the low-quality regime. At fixed superficial velocities, both models predict multiple steady states at some injection conditions. We investigate these states using a simple 1D simulator with and without incorporating capillary diffusion. The steady-state attained after injection depends on the initial state. In some cases, it appears that the steady state at intermediate pressure gradient is inherently unstable as represented in the model. In some cases introduction of capillary diffusion is required to attain a uniform steady-state in the medium. The existence of multiple steady states, with the middle one unstable, is reminiscent of catastrophe theory and of studies of foam generation without oil.