(188b) Multi-Objective Optimization of Dividing Wall Columns
However, the optimization of distillation columns is a multi-objective problem. This means there are typically several competing objective functions like the number of stages N, the reboiler duty Q and the product purities. Accordingly, the result of the optimization is not a single working point but a high number of non-dominated solutions called Pareto-optimal. Pareto-optimal points are characterized by the fact that they represent best compromises of the objective functions. If an objective function is to be improved by moving from one Pareto-optimal point to another, at least one other function deteriorates at the same time 5. To obtain Pareto-optimal points, optimization variables influencing those have to be chosen and constraints are optional. In the case of dividing wall columns, the optimization variables are for example the feed and side draw stage, the liquid and vapor split above and below the dividing wall or the outlet streams.
A common way to optimize distillation setups is to minimize total annualized costs TAC 6,7. The objective functions are combined to one cost function by using heuristic weighting factors and exponents. This limits the solution space significantly before the calculation and in most cases, only one optimal point is calculated being a very problem specific value. Like that, the results of a TAC minimization is barely applicable for another user since it represents only a very small part of the optimal solution space. To obtain a universally usable result, the whole solution space could be calculated first. Afterwards the user would be able to choose one of the possible, optimal operation points depending on the specific problem at hand. Like that, the calculation has to be performed only once and different operators can use the results several times.
Therefore, this works aims to achieve universal results of the optimization of distillation setups. The focus is on dividing wall columns and their comparison to conventional distillation setups.
For the optimization, an adaptive scalarization scheme is used 4. In a first step it combines the multiple objective functions to one by using the weighted sum method. The single objective problem is then solved as for the TAC calculation, too. Unlike as for the TAC determination, the weights are changed after the calculation of an optimal point. This is done by an adaptive scalarization method called sandwiching. Like that, the minimum necessary number of optimal points is calculated to describe the Pareto-optimal solution space. For the process simulation data Aspen Plus® is coupled with the optimization tool.
After the optimization, the visualization of the multi-dimensional solution space is a big challenge. To overcome this problem, self-organizing patch plots are used 8. In those plots, the exact solutions of the optimization are presented without any interpolation. Another advantage is that not only the objective functions can be shown but also the corresponding optimal variables. After the representation, filtering of the results is possible. Thus, the results can be adapted for each rectification setup of the same kind that is to be operated with the same feed and for the specific problems of the user. This method offers a much more all-purpose way of optimization.
In this contribution, the solution space of a dividing wall column will be presented in self-organizing patch plots. For that, only one optimization run had to be performed. With the help of different case studies, the universal applicability of the method will be presented.
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