Dynamic Foam Behavior in the Entrance Region of a Porous Medium

In foam EOR, complex dynamics of bubble creation and destruction controls foam properties. Here we focus on the entrance region, where injected gas and liquid are transformed into foam. We solve for water saturation and foam texture in the entrance region using the population-balance foam model of Kam (2008), which features three steady states (no foam, strong foam, and an unstable intermediate state) at some injection rates, as seen in experiments. If foam is not pre-generated, and capillary-pressure gradients are neglected, as in many published simulation studies, the final steady state downstream is the one with highest water saturation - the weakest foam. In some cases, in the presence of capillary pressure, analysis of the asymptotic dynamic behavior in the vicinity of possible downstream steady states may rule out some possible steady states. We show that the apparent length of entrance region can be quit different if one measures water saturation or pressure gradient. Finally, we fit foam kinetic parameters to the length of the entrance region seen in some experiments; a companion paper (Ashoori et al., 2010b) investigates the effect of these parameters on the traveling wave at the shock front downstream.