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 c Foam can divert flow from higher- to lower-permeability layers and thereby improve vertical conformance in gas-injection enhanced oil recovery. Recently, Kapetas et al. (2015) measured foam properties in cores from four sandstone formations ranging in permeability from 6 to 1900 md, and presented parameter values for foam model fit to those data. Permeability affects both the mobility reduction of wet foam in the "low-quality" foam regime and the limiting capillary pressure at which foam collapses. Kapetas et al. showed how foam would divert injection between layers of these formations if all layers were full of foam injected at a given quality (gas fractional flow). Here we examine the effects of injection method on diversion in a dynamic foam process using fractional-flow modeling and the model parameters derived by Kapetas et al. Like them, we consider a hypothetical reservoir containing non-communicating layers with the properties of the four formations in their study. The effectiveness of diversion varies greatly with injection method. In a SAG (surfactant-alternatinggas) process, diversion of the first slug of gas depends on foam behavior at very high foam quality. Mobility in the foam bank during gas injection depends on the nature of a shock front that bypasses most foam qualities usually studied in the laboratory. The foam with the lowest mobility at fixed foam quality does not necessarily give the lowest mobility in a SAG process. In particular, diversion in SAG depends on how and whether foam collapses at low water saturation; this property varies greatly among the foams reported by Kapetas et al. Moreover, diversion depends on the size of the surfactant slug received by each layer before gas injection. This of course favors diversion away from high-permeability layers that receive a large surfactant slug, but there is an optimum surfactant slug size: too little surfactant and diversion from high-permeability layers is not effective; too much and mobility is reduced in lowpermeability layers, too. For a SAG process, it is very important to determine if foam collapses completely at irreducible water saturation. In addition, we show the diversion expected in a foam-injection process as a function of foam quality. The faster propagation of surfactant and foam in the higher-permeability layers aids in diversion, as expected. This depends on foam quality and non-Newtonian foam mobility and varies with time of injection. Injectivity is extremely poor with foam injection, but is not necessarily worse than waterflood in some effective SAG foam processes atastrophe theory and of studies of foam generation without oil. @en