Polynomial Based Optimisation Framework - A New Approach

Mujtaba and Macchietto (1997) proposed a new and an alternative technique that permits very efficient solution of the maximum profit problem using the solutions of the maximum conversion problem already calculated. This is detailed and explained in the following using again the ethanol esterification example presented in the previous section. 

Maximum Conversion C = gift) Optimum Amount of Distillate Dj = g2(t) Optimum Reflux Ratio r = g3(t) Total Reboiler Heat Load QR = g4(t) 

The dynamic optimisation problem P2 now results in a single variable algebraic optimisation problem. The only variable to be optimised is the batch time t. The solution of the problem does no longer require full integration of the model equations. This method will solve the maximum profit problem very cheaply under frequently changing market prices of (CD/, CB0, C ) and will thus determine new optimum batch time for the plant. The optimal values of C, Dh r, QR, etc. can now be determined using the functions represented by Equations 9.2-9.5. 

For a given product purity of x D = 0.70, Mujtaba and Macchietto (1997) solved the maximum profit problem for a number of cost parameters using the method described above. The results are presented in Table 9.3. For each case, Table 9.3 also shows the optimal batch time, amount of product, reflux ratio, total reboiler duty and maximum conversion (calculated using the polynomial equations). 

0 Reprinted with permission from (Mujtaba, I.M. and Macchietto, S., Ind. Eng. Chem. Res. 36 (6), 2287-2295). Copyright (1997). American Chemical Society. 

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