Comparison of implicit-Texture and population-balance foam models

Simulation models for foam enhanced oil recovery are of two types: Those that treat foam texture or bubble size explicitly (population-balance models) and those that treat the effects of foam texture implicitly through a gas mobility-reduction factor. The implicit-Texture models all implicitly assume local equilibrium (LE) between the processes of foam creation and destruction. In published studies most populationbalance models predict rapid attainment of local-equilibrium as well, and some have been recast in LE versions. In this paper we compare population-balance and implicit-Texture (IT) models in two ways. First, we show the equivalence of the two approaches by deriving explicitly the foam texture and foam-coalescencerate function implicit in the IT models, and then show its similarity to that in population-balance models. Second, we compare the models based on their ability to represent a set of N₂ and CO₂ steady-state foam experiments and discuss the corresponding parameters of the different methods. Each of the IT models examined was equivalent to the LE formulation of a population-balance model with a lamella-destruction function that increases abruptly in the vicinity of the limiting capillary pressure Pc∗, as in current population-balance models. The relation between steady-state foam texture and water saturation or capillary pressure implicit in the IT models is essentially the same as that in the populationbalance models. The IT and population-balance models match the experimental data presented equally well. The IT models examined allow for flexibility in making the abruptness of the coalescence rate near Pc an adjustable parameter. Some allow for coarse foam to survive at high capillary pressure, and allow for a range of power-law non-Newtonian behavior in the low-quality regime. Thus the IT models that incorporate an abrupt change in foam properties near a given water saturation can be recast as LE versions of corresponding population-balance models with a lamella-destruction function similar to those in current PB models. The trends in dimensionless foam texture implicit in the IT models is similar to that in the PB models. In other words, both types of model, at least in the LE approximation, equally honor the physics of foam behavior in porous media.