Optimisation Problem Formulation

All the optimisation problem formulations presented above were aimed to achieve optimal operation policies for a variety of objective functions but for a single period operation (i.e. single distillation task). In single period operation only one product cut is made from both binary and multicomponent mixtures and optimal operation policy is restricted only to that period. 

In section 6.5, the multiperiod optimisation problem formulation considered by Farhat et al. (1990) is presented with typical example problems. 

The dynamic optimisation problem formulation is illustrated for representative multiperiod operations. The STNs in Figures 6.1 and 6.2 for binary and ternary mixtures undergoing single separation duty describe the multiperiod operations (see Chapter 3). For other networks, mixtures with larger number of components and other constraints the problem formulation requires only simple modifications of that presented in this section. 

The optimisation problem formulation for the multiperiod operation given in Figure 6.1 can now be written as follows ... 

The optimisation problem formulation for the operation shown in Figure 6.2 is presented in the following. Extension of the procedure illustrated to more components is a straightforward task. 

In this chapter first, the optimisation method of Al-Tuwaim and Luyben (1991) for single separation duty is presented. Then the optimisation problem formulation and solution considered by Mujtaba and Macchietto (1996) is explained. Finally, the optimisation problem formulations considered by Logsdon et al. (1990) and Bonny et al. (1996) are presented. 

Mujtaba and Macchietto (1996) presented a general design and operation optimisation problem formulation and solution for single and multiple separation duties. 

Therefore only two time periods are involved in the optimisation problem formulation, one for each mixture. Instantaneous switching occurs between batches and therefore set up time between the batches is ignored. The profit function does not include the allocation of time to each separation. For each mixture (m) individual profits (Pm) were maximised to maximise the overall profit. 

Classical Two-Level Optimisation Problem Formulation for Binary Mixtures... 

Mujtaba (1989) considered the separation of a binary mixture (Benzene-Toluene) with off-cut recycle. The optimal operating policy, computation time, etc. were determined using the two level and the one level optimisation problem formulations and the results were compared. 

This section presents the dynamic optimisation problem formulation of Mujtaba (1989) and Mujtaba and Macchietto (1992) to obtain optimal recycle policies in multicomponent batch distillation. Some special cases were identified where the methods used for the binary case could be applied fairly easily to multicomponent mixtures. The previously mentioned measure q of the degree of difficulty of separation was used to identify those special cases. A new operational strategy regarding the order of off-cuts recycle in a multicomponent environment was discussed. The Benefits of recycling were correlated against the measure q. 

The fractions of each off-cut (such as s, j, smu, s1, etc.) charged to subsequent batches are included in the decision variable list within the optimisation problem formulation by Bony et al. (presented in Chapter 7). 

Mujtaba (1999) considered the conventional configuration of BED processes for the separation of binary close boiling and azeotropic mixtures. Dynamic optimisation technique was used for quantitative assessment of the effectiveness of BED processes. Two distinct solvent feeding modes were considered and their implications on the optimisation problem formulation, solution and on the performance of BED processes were discussed. A general Multiperiod Dynamic Optimisation (MDO) problem formulation was presented to obtain optimal separation of all the components in the feed mixture and the recovery of solvent while maximising the overall profitability of the operation. 

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