(380a) A Global Terrain Approach to Distillation Design Feasibility
Design feasibility is often one of the first issues addressed in any synthesis activity. In distillation, Underwood's method is still a widely used and valuable tool in the early stages of column synthesis and design. For feasible design specifications of bottoms and distillate composition and reflux (or reboil) ratio, it provides a simple algebraic methodology for determining the number of rectifying and stripping stages needed to make the desired separation. However, when Underwood's method fails, it is unclear if failure is due to numerical difficulties or infeasible design specifications. Thus a more robust approach to design feasibility is needed.
In this work, we consider the following problem: determine with certainty if a single distillation column is feasible or infeasible for specified given specified bottoms and distillate compositions. The proposed approach is based on the combined use of a reduced space optimization formulation, the minimum bubble point distance function of Zhang and Linninger (2004), and the terrain method of Lucia and Yang (2003). In our approach, the reflux ratio is a key optimization variable and the Underwood design equations are solved in an inner loop of the computations. The resulting methodology always yields a three-dimensional master global optimization problem in the unknown variables (i.e., the number of rectifying stages, the number of stripping stages, and reflux ratio) and thus provides valuable visualization. Once a feasible design is determined, other optimization studies can be conducted (e.g., minimizing energy consumption or total annualized costs). Numerical studies show that the terrain method can find feasible designs as well as all physically meaningful stationary points of the minimum bubble point distance function. Several numerical examples are used to illustrate the existence of curious multiple solutions and therefore the need for a robust and efficient global optimization approach. Geometric illustrations are used to elucidate key points and to show that the methodology proposed in this work always provides valuable geometric insight, regardless of the number of components in the mixture. No equations are presented. We also briefly describe ways in which the proposed methodology can be applied to other problems.