Dynamic Simulations With an Improved Model for Foam Generation

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Summary 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. Introduction Foam can improve sweep efficiency in gas-injection improved oil recovery (IOR) processes (Schramm 1994; Rossen 1996; Terdre 2003), redirect acid flow in matrix acid stimulation (Gdanski 1993; Cheng et al. 2002; Nguyen et al. 2003), and increase the efficiency of environmental remediation of aquifers (Hirasaki et al. 2000; Mamun et al. 2002). A continuing goal of foam research is the development of a fully mechanistic, predictive model. This paper describes efforts toward such a model and insights gained from application of the model to dynamic displacements. Before providing a detailed description of the model, it is worthwhile to review the mechanisms of foam in porous media and the experimental observations that the model attempts to reproduce.