Estudo de ondas viajantes em um modelo de escoamento de espuma com partição de surfactante

Abstract

The efficiency of enhanced oil recovery (EOR) is often compromised by the high mobility of injected gases and the heterogeneity of reservoirs, which favor phenomena such as fingering and gravitational segregation. In this context, the use of foams, generated through the injection of surfactants, emerges as a promising alternative to improve the sweep efficiency of the reservoir. However, when the injected gas is CO2, the partial solubility of certain surfactants in the gas phase can significantly affect foam dynamics. This work is motivated by the need to understand the impact of surfactant partitioning between aqueous and gas phases on foam propagation in porous media. To this end, a simplified model of foam displacement is analyzed, consisting of mass balance equations for water and surfactant conservation, with initial data of Riemann type. Assuming the existence of traveling wave solutions, the partial differential equations are reduced to a system of ordinary differential equations. The qualitative analysis of this system, based on dynamical systems theory and fractional flow, enables the identification and classification of equilibrium points in the phase space. The formulation incorporates effects such as capillary pressure, foam mobility factor, and surfactant partition coefficient. The study also explores the existence of heteroclinic orbits connecting stable states of the solution. The theoretical results are complemented by numerical simulations that present the traveling wave profiles associated with the model. The analysis shows that a model accounting for surfactant partitioning between phases can exhibit different solution structures, depending on the position of the equilibria in phase space. The presence of multiple equilibrium points and the nature of their classifications highlight the system’s complexity and the sensitivity of the solutions to changes in initial conditions and physical parameters. These findings contribute to a better understanding of mobility control mechanisms in EOR processes involving foams.