Multiperiod Optimisation

For single separation duty, Diwekar et al. (1989) considered the multiperiod optimisation problem and for each individual mixture selected the column size (number of plates) and the optimal amounts of each fraction by maximising a profit function, with a predefined conventional reflux policy. For multicomponent mixtures, both single and multiple product options were considered. The authors used a simple model with the assumptions of equimolal overflow, constant relative volatility and negligible column holdup, then applied an extended shortcut method commonly used for continuous distillation and based on the assumption that the batch distillation column can be considered as a continuous column with changing feed (see Type II model in Chapter 4). In other words, the bottom product of one time step forms the feed of the next time step. The pseudo-continuous distillation model thus obtained was then solved using a modified Fenske-Underwood-Gilliland method (see Type II model in Chapter 4) with no plate-to-plate calculations. The... 

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

For single separation duty Farhat et al. (1990) presented multiple criteria decisionmaking (MCDM) NLP based problem formulations for multiperiod optimisation. This involves either maximisation (Problem 1) of specified products (main-cuts) or minimisation (Problem 2) of unspecified products (off-cuts) subject to interior point constraints. These two optimisation problems are described below. 

Table 7.6. Multiperiod Optimisation of Design and Operation [Adopted from Logsdon et al., 1990]...

Thus the multiperiod optimisation problem is formulated as a sequence of two independent dynamic optimisation problems (PI and P2), with the total time minimised by a proper choice of the off cut variables in an outer problem (PO) and the quasi-steady state conditions appearing as a constraint in P2. The formulation is very similar to those presented by Mujtaba and Macchietto (1993) discussed in Chapter 5. For each iteration of PO, a complete solution of PI and P2 is required. Thus, even for an intermediate sub-optimal off cut recycle, a feasible quasi-steady state solution is calculated. The gradients of the objective function with respect to each decision variable (Rl or xRl) in problem PO were evaluated by a finite difference scheme (described in previous chapters) which again requires a complete solution of problem PI and P2 for each gradient evaluation (Mujtaba, 1989). 

In this chapter, a decomposition strategy considered by Mujtaba (1989) and Mujtaba and Macchietto (1992) is presented in which the whole multiperiod optimisation problem is divided into a series of independent dynamic optimisation problems. This is presented in the next section. 

Also with these assumptions and specifications the whole multiperiod optimisation problem shown in Figure 8.12 will now be decomposed into a series of independent dynamic optimisation problems (Figure 8.13). Referring to Figure 8.12 and Figure 8.13 the optimisation problem for Recycle Loop 1 may now be described as follows ... 

First, two examples using both problems OP1 and OP2 are presented to explain the effects of different solvent feeding modes and path constraint on the operation. In these examples only Task 1 of Figure 10.6 is carried out where component 1 is recovered at a given purity. Then, example 3 using Multiperiod Optimisation Problem (OP) is presented, where all three Tasks of Figure 10.6 are carried out. 

Example 3 Multiperiod Optimisation with Azeotropic Mixture... 

For single separation duty, Mujtaba and Macchietto (1993) proposed a method, based on extensions of the techniques of Mujtaba (1989) and Mujtaba and Macchietto (1988, 1989, 1991, 1992), to determine the optimal multiperiod operation policies for binary and general multicomponent batch distillation of a given feed mixture, with several main-cuts and off-cuts. A two level dynamic optimisation formulation was presented so as to maximise a general profit function for the multiperiod operation, subject to general constraints. The solution of this problem determines the optimal amount of each main and off cut, the optimal duration of each distillation task and the optimal reflux ratio profiles during each production period. The outer level optimisation maximises the profit function by... 

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 reflux ratio is discretised into two time intervals for task 1 and one time interval for task 2. Thus a total of 3 reflux ratio levels and 3 switching times are optimised for the whole multiperiod operation. Three cases are considered, corresponding to different values of the main-cut 1 product. For each case the... 

Multiperiod Campaign Operation Optimisation - Industrial Case Study... 

Logsdon et al. (1990) formulated multiperiod multiple separation duties design and operation optimisation problem for two binary mixtures. Only one distillate product per mixture was considered according to the operation shown in Figure 7.7. 

For a fixed column design, Bonny et al. (1996) considered multiperiod operation optimisation but with multiple separation duties. That is why this is presented in this chapter rather than in Chapter 6. The optimisation problem can be stated as ... 

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. 

General Multiperiod Dynamic Optimisation (MDO) Problem Formulation... 

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