(163f) Temperature Collocation Method for Design of Complex Distillation Column

Zhang, L., University of Illinois at Chicago
Linninger, A. A., University of Illinois at Chicago

Mathematical models of complex distillation problems are challenging for two reasons. First, problem size increases as the number of stages approximates infinity close to singular points of the composition space (e.g. saddle, pinch points). Secondly, in column design problems it is not known aprior whether a set of desired specifications has a feasible solution. In case of an infeasible specification, all direct solution methods don't converge. Hence, we have developed a set of collocation based methods specially for its use in column design including simple and complex column configuration. The method proposes variable transformations which enable it to successfully solve columns design problems even near pinch and saddle points with acceptable accuracy. We also present a new algorithm to test the feasibility of a distillation design. The key novelty of our procedure exploits a view of physically meaningful design variable to distinguish between feasible region and unattainable composition range. The method is shown to be effective in constant relative volatility, idea and even non-ideal equilibrium models. The presentation will introduce our new algorithm for the complex column configuration.

The new design method features a quick feasible test, design of ideal and nonideal complex distillation column. When defining the polynomials in terms of stage location, it is impossible to model an infinite column section because the polynomials can not be well behaved as the number of stages increase to infinity. The method based the new method can deal with pinch and sharp as well as sloppy split problem. Our algorithm allows us to compute the column section profiles and also can calculate number of trays in each section and the feed tray for each of the separations task. The new collocation method with the help of the column section model reduced significantly the numbers of equations, no matter what the actual number of trays in the complex column is.

This approach also provides means to for determining the minimum reflux ratio with the floppy and sharp split in complex column configuration. Two cases of the separation distillations design about ideal and nonideal mixtures will be discussed.

The new robust feasibility and design algorithm is a necessary component in an optimal complex column sequencing tool. With a very inexpensive feasibility test as proposed by our algorithm, we come one step closes to a fully automated globally convergent column sequencing procedure. This computational approach will be helpful in designing distillation based solvent recovery systems for the pharmaceutical and special chemical industry. In addition, we see the potential of the proposed method in support of plant-wide heat integration in which many feasible test subproblems need to be solved repeatedly.