The Geometry of Separation Boundaries: Four-Component Mixtures

The determination of distillation boundaries for four-component mixtures that exhibit azeotropy is studied. It is shown that these distillation boundaries correspond to local maxima in surface areas under conditions of Levi-Civita parallelism. An extension of the optimization methodology given in Lucia and Taylor is used to determine local maxima in surface areas by repeatedly computing maximum line integrals or distances in one spherical coordinate over a set of initial conditions that span the range of the second spherical coordinate. An optimization formulation that defines the determination of local maxima in surface areas subject to residue curve and stable node constraints is given. Numerical measurement of surface areas is accomplished using a triangulation procedure. Several numerical examples of varying complexity involving four-component mixtures that exhibit azeotropes are presented to show the efficacy of the proposed optimization methodology. Geometric illustrations are used throughout to highlight key features of our methodology for determining distillation boundaries in four-component mixtures. 2007 American Institute of Chemical Engineers AIChE J, 53: 1770–1778, 2007