Theory for the Phase Behavior of Microemulsions
Authors: Robbins Max L. 
Published: December 2007

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This paper was prepared for the Improved Oil Recovery Symposium of the Society of Petroleum Engineers of AIME, to be held in Tulsa, Okla., March 22–24, 1976. Permission to copy is restricted to an abstract of not more than 300 words. Illustrations may not be copied. The abstract should contain conspicuous acknowledgment of where and by whom the paper is presented. Publication elsewhere after publication in the JOURNAL paper is presented. Publication elsewhere after publication in the JOURNAL OF PETROLEUM TECHNOLOGY or the SOCIETY OF PETROLEUM ENGINEERS JOURNAL is usually granted upon request to the Editor of the appropriate journal provided agreement to give proper credit is made. provided agreement to give proper credit is made. Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and with the paper, may be considered for publication in one of the two SPE magazines.

Introduction
It is well-known that microemulsions* or micellar solutions* can exist in equilibrium with excess oil, water or both. Winsor referred to these respective equilibria as Types I, II and III. He showed qualitatively that the transitions I III II are dependent on the hydrophilic vs. lipophilic character of the surfactants (HLB), salinity, oil composition and temperature. Shinoda and coworkers experimentally defined these transitions as functions of temperature and ethylene oxide content for cosolubilized oil and water systems prepared with non-ionic surfactants. They described the single/2 phase boundaries for Type I and Type II systems on temperature-compositio n diagrams. They studied the shift in these boundaries with variation in HLB (ethylene oxide content, hydrocarbon chain length and added anionic surfactant), oil type and added salts. Similar effects were noted by Kon-no and Kitahara for the solubilization of water and aqueous salt solutions in non-aqueous media (Type II systems) by cationic, non-ionic and anionic surfactants.
Robbins quantized Type II systems by the saturation water uptake defined as the volume ratio of water to surfactant (V /V) in a microemulsion saturated with water. This quantity was shown both experimentally and theoretically to be a function of the volume fraction of heads in the surfactant (HLB). Saturation water uptake by ethoxylated octyl phenols was shown to depend on oil type. This author extended the treatment to Type I systems defining saturation oil uptake (V /V) as a function of the volume fraction of chains. His model predicts an inverse correlation between interfacial tension and V /V in Type II systems and V /V in Type I systems.
* The terms microemulsion and micellar solution are considered interchangeable for the present discussion. Reference (18) gives a review of the area. The position that micellar solutions are identical with microemulsions is given in references (19–21). References (22–24) differentiate between the two terms.