Dynamic Simulations With an Improved Model for Foam Generation

Abstract

We present the first 1D simulations of dynamic foam displacements with a population-balance model incorporating bubble creation controlled by pressure gradient. For the first time, a population-balance model is fit to steady-state experimental data for both the three foam states (coarse foam, intermediate, and strong foam) and the two strong-foam regimes (low-quality and high-quality) observed in laboratory studies. Simulations confirm the stability of the coarse-foam and strong-foam states to small perturbations, and the instability of the intermediate state, at fixed injection rates.In dynamic displacements, the model shows foam generation as injection rates increase, or as liquid fraction of injected fluids increases, in agreement with laboratory observations. When coarse foam is created instead of strong foam, there is a narrow region of finer foam predicted near the gas displacement front. This region appears to play a role in foam generation. However, in the limited cases examined here, foam generation occurs at roughly the same injection rate as predicted by local-steady-state theory. Because of this narrow region of finer-textured foam, fronts can be sharper than estimated from fractional-flow theory assuming a constant effective gas viscosity at its steady-state value behind the displacement front.If a strong foam forms in the low-quality regime, the kinetics of foam generation and destruction affects the length of the entrance region in which foam forms. Therefore, the length of the entrance region can be used to calibrate the kinetic parameters in the model. The displacement front and the bank behind it, however, are essentially what one would have predicted from local-steady-state modeling. The complexities of population-balance modeling are not necessary, if it is known that strong foam will be created.

Stability Analysis of Uniform Equilibrium Foam States for EOR Processes

“…This and related models (cf. Kam and Rossen 2003;Kam et al 2007;Kam 2008;Afsharpoor et al 2010) are the only ones available now that describe multiple foam states and the phenomenon of foam generation with increasing superficial velocity. Moreover, Kam developed his model to remedy an instability in an earlier version.…”

“…There are two main approaches to modeling complex mechanisms governing foam texture: population-balance modeling Friedmann et al 1991;Kovscek et al 1995;Kam et al 2007;Kam 2008;Chen et al 2010) and local-equilibrium (LE) modeling (Fisher et al 1990;de Vries and Wit 1990;Persoff et al 1991;Ettinger and Radke 1992;Vassenden and Holt 2000;Computer Modeling Group 2009;Chen et al 2010;Ashoori et al 2010). For simplicity, LE foam models assume that foam reaches the LE bubble texture corresponding to its water saturation very fast.…”

“…Friedmann et al (1991) fit the jump to strong foam with a population-balance model where lamella creation requires exceeding a minimum ∇P: the model is discontinuous at this value of ∇P. More recently, the only foam models to represent the multiple LE states for foam are variants of the population-balance model of Kam and Rossen (2003) (Kam et al 2007;Kam 2008;Afsharpoor et al 2010), where creation of lamellae depends on pressure gradient ∇P. (In this article, ∇P represents the magnitude of pressure gradient, not a vector quantity.)…”

“…For an alternate approach, see Chen et al (2010). Kam et al (2007) examined the stability of the strong-, weak-foam, and intermediate states numerically by checking the growth or decay of an arbitrary perturbation in foam texture (inversely related to bubble size) and water saturation using numerical simulation on one LE state from each group. The low-quality strong-and weak-foam states appeared stable, and the intermediate state unstable.…”

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

“…Population-balance (PB) models (e.g. Friedmann et al;1991;Kovscek et al, 1995;Kam et al, 2007;Chen et al, 2010) attempt to describe the processes that create and destroy the lamellae that separate gas bubbles, as well as the effect of bubble size on gas mobility. The second group of models represents the effect of bubble size implicitly, through a mobility-reduction factor that depends on saturations, superficial velocities and other factors (e.g.…”