CALCULATING BINARY AND TERNARY MULTIPHASE EQUILIBRIA - THE TANGENT PLANE INTERSECTION METHOD

The background and capabilities of a recently developed phase equilibr ium calculation method (Tangent Plane Intersection method) are discuss ed. The method is based on an alternative interpretation of the tangen t plane concept, such that the section of the tangent plane constraine d within the Gibbs energy surface (tau) provides an indication of how close the search is to the minimum Gibbs energy solution. The T.P.I. m ethod has been used to calculate binary liquid-liquid, vapour-liquid-l iquid and vapour-liquid equilibria, and also a range of ternary vapour -liquid-liquid equilibrium behaviour. Three solution techniques (discr ete, hybrid1, hybrid2), two of which are based on the Nelder-Mead simp lex method, are proposed for the calculation of the ternary multiphase equilibria. These alternatives utilise the available variables by gro uping them together in different ways, and are compared in terms of th eir reliability and efficiency. Unusually, the methods are initialised using compositions near the pure components. This means that multipha se regions distributed throughout the available composition space can be determined using a single, non-arbitrary set of initial phase estim ates. Both hybrid methods were found to be sensitive to the position o f the overall mixture composition and shape of the multiphase region i n question, but, for the systems examined, the hybrid1 solution method was found to be both the most reliable and widely applicable of the t hree studied. (C) 1998 Elsevier Science B.V. All rights reserved.