Off-cut Recycle in Binary Separation

Dynamic optimisation of this type of periodic operation was first attempted and reported in the literature by Mayur et al. (1970), who considered the initial charge to the reboiler as a fresh feed stock mixed with the recycled off-cut material from the previous distillation task. Each batch cycle is then operated in two distillation tasks. During the Task 1, a quantity of overhead distillate meeting the light product specification is collected. The residue is further distilled off in Task 2 until it meets the bottom product specification. The overhead during Task 2 meets neither specifications (but the composition is usually kept close to the that of the initial charge for thermodynamic reasons) and is recycled as part of the charge for the next batch. As the batch cycle is repeated a quasi-steady state mode of operation is attained which is characterised by the identical amount and composition of the recycle (from the previous batch) and the off-cut (from the current batch). Luyben (1988) indicates that the quasi-steady state mode is achieved after three or four such cycles. 

Mayur et al. measured the benefits of recycling in terms of a potential reduction 

Reduction in hatch time For a given fresh feed and a given separation, the column performance is measured in terms of minimum batch time required to achieve a desired separation (specified top product purity (x D]) and bottom product purity (x B2) for binary mixture). Then an optimal amount and composition of recycle, subject to physical bounds (maximum reboiler capacity, maximum allowable purity of the off-cut) are obtained in an overall minimum time to produce the same separation (identical top and bottom products as in the 

The problem of choosing whether and when to recycle each off-cut and the size of the cut is a difficult one. Liles (1966) considered dynamic programming approach and Luyben (1988) considered repetitive simulation approach to tackle this problem. Mayur et al. (1970) and Christensen and Jorgensen (1987) tackled it as a dynamic optimisation problem using Pontryagin s Maximum Principle applied to very simplified column models as mentioned in Chapters 4 and 5. 

Mujtaba (1989) used the measure of the degree of difficulty of separation proposed by Christensen and Jorgensen (1987) to decide whether or not an off-cut is needed. The optimal control algorithm of Morison (1984) was then used to develop operational policies for reflux ratio profiles and amount and timing of off-cuts which minimise the total batch time. A more realistic dynamic column model (type IV as presented in Chapter 4) was used in the optimisation framework. 

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