Essay On Optimization Problem

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Optimization problem
After having defined the structure of the extractive distillation process, the optimal values of the design and operating variables can be determined based on an optimization problem whose details will be discussed as follows.
Decision variables
Due to the fact that the parameters specified as the (design/operating) degrees of freedom can be used as the decision variables, the decision variables can be divided into two categories including: design and operating decision variables. The design variables include the total stage number of each column, feed and solvent stages of the extractive distillation column and feed plate of the recovery column. However, it is easier to assume that the extractive distillation column is …show more content…

Accordingly, the resulting optimization problem is a mixed-integer nonlinear problem and a mixed-integer nonlinear programming (MINLP) optimization problem should be handled. Here, the MINLP capability of the NOMAD optimization package (Audet and Dennis Jr, 2006) has been used to solve the formulated MINLP problems.
Constraints
Two constraints regarding the minimum product specifications (i.e., purity of the products) in columns were considered. The mole fraction of the acetone product in the distillate of the column C1 and the mole fraction of the produced chloroform as the distillate of the column C2 should be equal or greater than the desired product purity of 99.5mol%.
Objective function
For the combined optimization of the design and operation of the acetone/chloroform/DMSO extractive distillation process, the objective was the minimization of the total annual cost (TAC) of the plant. TAC is calculated as the sum of the operating costs (i.e., utility costs) and annual capital investment (i.e., investment for column shell, trays and heat exchangers) as shown in Eq. (1), where the annual capital investment is defined as the capital investment divided by a three year payback

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