Thermodynamic Modeling of Pseudoternary Phase Behavior

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Abstract
Phase behavior is the fulcrum at which the chemistry and physics of surfactant and solvent systems govern the engineering and economics of chemical flooding. Salient behavior is represented by pseudoternary diagrams that account for polar, nonpolar, and amphiphilic components. The common 2_,3,2¯, phase-split progression—induced, for example, by salinity change in microemulsion systems—is required by thermodynamic principles. Although such progressions can be simulated semiempirically, modeling them with a suitable free-energy function or an equation of mixture state is more reliable for interpolating and extrapolating limited data on phase splits and coexisting phase compositions for use in mechanism-based computer simulation of laboratory experiments and field applications. Simple equations of mixture state prove inadequate but lead to the promising new linearly screened Flory-Huggins (LSFH) equation, which accounts for simultaneous association of amphiphile with oil and water and aggregation of surfactant amphiphile into curved sheetlike structures that separate water-rich from oil-rich regions. From this equation for a ternary mixture are calculated representative sets of diagrams with continuous progressions of tielines and binodals, plait points, tie-triangles, and three-phase regions with their critical endpoints. Several overlapping regions of metastable one- and two-phase equilibria are identified. Free-energy surfaces are pictured, and the free-energy factor that jointly controls interfacial tension (IFT) is computed. Ultralow tensions are favored by low-relief free-energy surfaces; so also are long-lived metastable states. The exponentially screened Flory-Huggins (ESFH) equation, superior in some ways to the linearly screened version, also is discussed briefly. Computational methods are described for fitting the six parameters of the ternary equation to data as well as for predicting phase behavior from given parameters.