# An algorithmic procedure for the synthesis of distillation sequences with bypass

journal contribution

posted on 1986-01-01, 00:00 authored by Richard R. Wehe, Arthur W. Westerberg, Carnegie Mellon University.Engineering Design Research Center.Abstract: "When a separation system is to produce multicomponent products, it is frequently not necessary to separate a feed mixture completely into pure components. Instead, column bypasses can reduce both capital and operating costs by reducing mass load on the columns. This paper presents an algorithmic procedure for the synthesis of a sequence of simple, sharp split distillation columns with both bypasses and mixers that minimizes annualized costs. This procedure can solve problems in which a single feed is to be separated into two or more multicomponent products. We use models that are linear except for stream splitters. Unfortunately, superstructures developed from these models and simply optimized can display multiple local optima; a better approach is needed. We present an analysis of the problem structure that suggests a decomposition which allows significant reductions both in the problem search space and nonlinearities caused by splitters.""The decomposition permits one to solve any three component problem for its global optimum as two linear programs. Four and five componenet problems require six and twenty-four nonlinear programs, respectively, each of which models a structurally different flowsheet for the process. For each flowsheet, one can establish a lower bound for the corresponding nonlinear program by using a relaxation that allows the splitters to be treated linearly; giving a linear program which is readily solved. For two example problems, we first produced lower bounds for each structural alternative (a linear program for each). Solving the nonlinear program for the most promising structure eliminated the need for solving the nonlinear program for all remaining alternatives. Upper and lower bounds within 1% of each other strongly imply the solutions were globally optimal."