(374a) Distillation Boundaries in Four Component Mixtures

Residue curves, originally proposed by Ostwald and Schreinemakers around 1900, are an important tool in distillation design ? especially when the mixture to be separated is azeotropic. While the presence of azeotropes increases the complexity of any separation by giving rise to distillation boundaries, residue curves can often be used to guide understanding and to help identify those separations that are possible by distillation in the face of these boundaries.

Distillation boundaries for four component mixtures that exhibit azeotropy are studied. The contributions of this work to the state-of-the-art include 1) The first rigorous demonstration that distillation boundaries for four component mixtures correspond to local maxima in surface areas under conditions of Levi-Civita parallelism. 2) A novel triangulation procedure for measuring surface areas. 3) A rigorous optimization formulation for finding local maxima in surface areas subject to residue curve, stable node, and Levi-Civita constraints. 4) A numerical optimization algorithm for determining 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. 5) An outline of a rigorous proof that distillation boundaries for four component mixtures correspond to local maxima in surface area subject to conditions of Levi-Civita parallelism. 6) A description of the way in which theoretical and algorithmic results for four component mixtures can be extended to mixtures with five or more components.

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. Finally we show that this work is also strongly related to energy efficient process synthesis and optimization for pinched and non-pinched distillations that are possibly part of multi-unit processes like multiple column configurations, hybrid separations, and reaction-separation-recycle processes.