Dimensionless Equation of State to Predict Microemulsion Phase Behavior Soumyadeep Ghosh and Russell T. Johns* Department of Energy and Mineral Engineering, College of Earth and Mineral Sciences, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ABSTRACT: Prediction of microemulsion phase behavior for changing state variables is critical to formulation design of surfactant-oil-brine (SOB) systems. SOB systems find applications in various chemical and petroleum processes, including enhanced oil recovery. A dimensional equation-of-state (EoS) was recently presented by Ghosh and Johns 1 that relied on estimation of the surfactant tail length and surface area. We give an algorithm for flash calculations for estimation of three-phase Winsor regions that is more robust, simpler, and noniterative by making the equations dimensionless so that estimates of tail length and surface area are no longer needed. We predict phase behavior as a function temperature, pressure, volume, salinity, oil type, oil-water ratio, and surfactant/alcohol concentration. The dimensionless EoS is based on coupling the HLD-NAC (Hydrophilic Lipophilic Difference-Net Average Curvature) equations with new relationships between optimum salinity and solubility. An updated HLD expression that includes pressure is also used to complete the state description. A significant advantage of the dimensionless form of the EoS over the dimensional version is that salinity scans are tuned based only on one parameter, the interfacial volume ratio. Further, stability conditions are developed in a simplified way to predict whether an overall compositions lies within the single, two-, or three- phase regions. Important new microemulsion relationships are also found, the most important of which is that optimum solubilization ratio is equal to the harmonic mean of the oil and water solubilization ratios in the type III region. Thus, only one experimental measurement is needed in the three-phase zone to estimate the optimum solubilization ratio, a result which can aid experimental design and improve estimates of optimum from noisy data. Predictions with changing state variables are illustrated by comparison to experimental data using standard diagrams including a new type of dimensionless fish plot. The results show that the optimum solubilization ratio and salinity using the tuned dimensionless EoS are within average errors of 2.44% and 1.17% of experimental values for the fluids examined. We then use the dimensionless equations and thermodynamic first- principles to derive the constant in Huh’s equation for interfacial tension prediction. ■ INTRODUCTION AND BACKGROUND Microemulsions are homogeneous solutions consisting of surfactant, oil, and brine (SOB). The term was first introduced by Hoar and Schulman who found that, by titration of a milky emulsion containing potassium oleate (a soap) with a medium- chain alcohol (pentanol or hexanol), a stable oil-in-water emulsion was produced. 2 Winsor later described micro- emulsions as swollen micellar solutions. 3 Broadly, micelles (surfactant aggregates in aqueous solution), macroemulsions (or simple emulsions), and microemulsions (also known as micellar solutions) can be categorized by the dimensions of the dispersed phase. Microemulsions can have low interfacial tensions that result in negative Gibbs free energy of emulsion formation, which implies microemulsions are formed sponta- neously and are thermodynamically stable. 4 The affinity of a surfactant toward the oil or water phase is a function of the surfactant type, composition, and state of the system. Winsor introduced the concept of the R-ratio to explain the balance between the surfactant’s oil and water affinity. 5 Three distinct regions near the interface are defined: an aqueous region (W), a nonpolar oleic region (O), and an amphiphilic or bridging region (C). The interfacial zone (C) is of a fixed thickness separating the oil and water bulk phases. 6 The R-ratio is the ratio of molecular interaction energies on the oil to the water side of the C-layer. For an R-ratio equal to unity, the surfactant has equal affinity toward the oil and water regions. This occurs at optimum conditions, where the surfactant solubilizes oil and water equally. However, the use of R-ratio is not practical, as interaction energies at the molecular level are not known. Several attempts have been made to predict optimum conditions, which are of special interest to chemical enhanced oil recovery applications. Salager and coauthors presented an empirical equation valid at optimum conditions for oil-water- brine systems in the presence of an anionic surfactant. 7 That relationship was extended to include the effect of pressure, Received: July 18, 2016 Published: August 9, 2016 Article pubs.acs.org/Langmuir © 2016 American Chemical Society 8969 DOI: 10.1021/acs.langmuir.6b02666 Langmuir 2016, 32, 8969-8979