Multi-objective optimization of membrane separation modules using genetic algorithm

Abstract

Hollow fiber membrane separation modules are used extensively in industry for a variety of separation processes. In most cases, conflicting requirements and constraints govern the optimal choice of decision (or design) variables. In fact, these optimization problems may involve several objectives, some of which must be maximized, while the others minimized simultaneously. Often, a set of equally good (non-dominated or Pareto optimal) solutions exist. In this study, a membrane separation module for the dialysis of beer has been taken as an example system to illustrate the multi-objective optimization of any membrane module. A mathematical model is first developed and 'tuned' using some experimental results available in the literature. The model is then used to study a few simple multi-objective optimization problems using the non-dominated sorting genetic algorithm (NSGA). Two objective functions are used: the alcohol removal (%) from the beer is maximized, while simultaneously minimizing the removal of the 'extract' (taste chemicals). Pareto optimal solutions are obtained for this module. It was found that the inner radius of the hollow fiber is the most important decision variable for most cases. Another optimization problem using the cost as the third objective function is also solved, using a combination of the e-constraint method and NSGA. It is found that the Pareto solutions lie on a curve in the three-dimensional objective function space, and do not form a surface.