A new approach for the optimization of nonsharp distillation superstructures

Abstract

AbstractIn general, the optimization problem of the separation of a multicomponent feed stream into two or more multicomponent products with the use of nonsharp distillation columns is an MINLP with a nonlinear objective function. Due to the high number of variables and the high degree of nonlinearity, the presentation of a comprehensive and simple three‐phase approach was considered to solve the Mixed Integer Nonlinear Programming (MINLP) using the combination of mathematical and stochastic methods. In the method, the variables are classified into two groups: A set of variables are optimized by genetic algorithm as a stochastic algorithm; doing so converts MINLP to Linear Programming (LP), and the remaining variables are managed by solving an LP problem for known values of the former set by a regular and quick mathematical method such as simplex search. One advantage of this study is that it extracts some essential relationships between the first set of variables by the mathematical operations on the nonlinear constraints of the main problem as these variables are not optimized altogether; instead, some of them are optimized and the rest are obtained with the assistance of those relationships. Thus, the optimization workload (in both parts of GA and LP problem) is very low and the best structure can be obtained in a very short time (less than 2 min). Also, the study applies the lowest reduction on the main superstructure than previous works and therefore, the generalization of the problem is further preserved. Three published examples are used to verify the proposed method.