Thermodynamic Modeling of Quaternary Systems: Oil/Brine/Surfactant/Alcohol

Surfactant flooding for EOR results in multiphase oil/brine/surfactant/alcohol mixtures. Because alcohol and surfactant do not partition among the phases in constant proportion, thermodynamic modeling phases in constant proportion, thermodynamic modeling of quaternary systems is necessary in an accurate treatment of phase equilibria in these systems. We describe here the quaternary version of a free-energy-based equation of state (EOS). The systematic computation of phase equilibria in a quaternary system begins on the phase equilibria in a quaternary system begins on the binary edges and ternary faces and proceeds by numerical continuation through the higher dimensional composition space. We expedite the computation with knowledge of the limits of thermodynamic stability the spinodal surfaces and all critical points that lie on those surfaces. This preliminary calculation indicates those regions in which solution of the nonlinear equations of phase equilibria will suffer from slow numerical convergence. phase equilibria will suffer from slow numerical convergence. Multiphase equilibria are searched out by both parametric and compositional continuation. The results provide the basis for understanding the trends of three- and four-phase equilibria in oil/brine/surfactant/alcohol mixtures. Introduction At completion of secondary oil recovery, most of the residual petroleum is held in place in the reservoir pore space by capillary forces. The strength of these forces is dictated by the magnitude of the interfacial tension (IFT) between coexisting oleic and aqueous phases. In one method of tertiary oil recovery, the capillary forces are reduced by injection of formulations containing surfactant and alcohol, which with oil and brine form a microemulsion phase having, under the right conditions, ultralow (approximately 10–3 dyne/cm [10–3 mN/m]) IFT's against coexisting oil-rich and water-rich phases. When there axe ultralow tensions, flooding with the surfactant and alcohol formulation can result in substantial oil recovery. Whether ultralow tensions occur depends crucially on the equilibrium phase behavior of the surfactant and alcohol mixtures with the reservoir oil and brine. Although reservoir oil, brine, and commercial surfactant are multicomponent substances, it is common to treat the oil/brine/surfactant/alcohol system as a pseudoternary mixture in which the surfactant and alcohol, pseudoternary mixture in which the surfactant and alcohol, the oil, and the brine partition as pseudocomponents. This approach has been quite useful for qualitatively understanding the general patterns of phase behavior, but it suffers the disadvantage that alcohol and surfactant partition quite differently between oil-rich and water-rich partition quite differently between oil-rich and water-rich phases and are, therefore, poor pseudocomponents. Our phases and are, therefore, poor pseudocomponents. Our purpose here is to improve the situation by modeling purpose here is to improve the situation by modeling oil/brine/surfactant/alcohol systems as quaternary mixtures in which surfactant and alcohol are independent components. The preferred modeling technique is to fit limited data to the parameters of a free-energy-based EOS. The benefits of such a description are many:the free energy of the model dictates the number of phases and composition regions of metastable states, some possibly long-lived;the parameters of the model link directly the phase behavior and the molecular forces between constituent molecules; andthe topography of the free energy function in composition space is the primary determinant of IFT and wettability behavior. Rossen et al. used this approach to model pseudoternary oil/brine/surfactant mixtures with a modified version of the Flory-Huggins EOS. We describe here the quaternary version of this model, which should prove useful for quantitative predictions of phase splits and compositions. predictions of phase splits and compositions. The computational strategy for extracting phase equilibria from a quaternary thermodynamic model relies on known equilibria for binary edges and ternary faces, which serve as termini of and initial approximations for quaternary equilibria. As quaternary phase equilibria are computed by projecting from the edges and faces, the calculation is guided by supplementary determinations of the limit of thermodynamic stability or spinodal and the lines of critical points that fall on this limit. It is near the critical points that the iteration schemes for solving the nonlinear equations of phase equilibria begin to fail. Moreover, the computation of critical points is a simpler task requiring less effort than the points is a simpler task requiring less effort than the calculation of phase equilibria. Once the location of all critical points and their stability have been determined, the pattern of phase behavior with the quaternary compositional tetrahedron is determined easily. SPEJ p. 330