Design and optimization of recycle policies for multicomponent azeotropic distillation processes with bifurcation analysis

Abstract:
Many azeotropic mixtures exhibit distillation boundaries and corresponding distillation regions that limit the reachable products of simple distillation columns. Such mixtures cannot be separated by a sequential series of columns. Instead, special separation schemes in which the columns are coupled by one or more recycle streams must be utilized. Two common process types are pressure-swing distillation and the exploitation of highly curved distillation boundaries. For ternary mixtures the mass balance lines of the splits are designed by graphical analysis of the residue curve map. The distillation boundaries are usually approximated by the residue curves connecting the azeotropes and the pure component vertices. However, graphical analysis is impossible for quaternary or higher dimensional mixtures since comprehensive methods for visualization of such phase diagrams are missing. Mathematical formulations for the design of sequences with feasible and economically at! tractive splits often suffer from the fact that points on a simple distillation boundary cannot be obtained by evaluation of a function of the form f(x)=0. Instead, feasibility can only be assessed by integration of residue curves starting from the desired distillate and bottom product compositions. Davydian, Malone and Doherty (Theo. Found. Chem. Eng., 31 (1997), 327-338) introduce a formulation of the split feasibility problem that is based on the detection of a pitchfork bifurcation of the pinch equation system. This geometric criterion offers the advantage that points on the resulting pinch distillation boundary (PDB) can be obtained from a system of equations of the form f(x)=0 which can easily be solved if suitable initial values are known. In this contribution the applicability of a bifurcation-theoretic formulation of split feasibility for the design of recycle policies for azeotropic distillation processes is investigated. First, a robust homotopy-continuation algorithm for the determination of the pinch distillation boundary is presented that allows to asses whether a split specification given by the concentrations of the distillate and bottom products is feasible. The algorithm also determines the point of intersection between the mass balance line of the separation and the closest distillation boundary. Thus the distance of the desired product to the distillation boundary is known and can be used as a measure of feasibility. Using the assessment of split feasibility from the bifurcation analysis the design of recycle policies for azeotropic distillation processes can be formulated as a nonlinear optimization problem (NLP) where the feasibility of each split is formulated as a nonlinear constraint. The objective function aims at minimizing the overall recycle stream of the process. In addition, the application of methods for the determination of the minimum separation energy in order to directly minimize the operating cost of the sequence will be discussed. The ternary pressure-swing distillation of an ethanol-water mixture using acetone as an entrainer is used as an illustrative example for the optimization and the assessment of split feasibility. The application of the method to mixtures with more than three components is highlighted by adding isopropanol to the feed of the pressure-swing distillation process.

Keywords:
Multicomponent azeotropic distillation, Bifurcation analysis, Split feasibility, Shortcut Method, Rectification body method, RBM