Representation of Design, Operations and Separations Duties

Fraction of Total Plant Time Allocated to each Mixture 2  

A name and a set of input and output states (Sf and SOh respectively) characterise each distillation task i. Each task is modelled by an associated set of DAEs of the form f(t,xi(t),xi(t),ui(t),v) = 0, where uft) is a vector of time 

Mujtaba and Macchietto (1996) assumed that the structure of each operation (a specific sequence of tasks and states and choice of main and off-cut states) is given a priori but the operating control variables, ttt- (in particular reflux ratio profile) and termination conditions for each task are to be optimised. It is usually best to operate at the maximum available energy input rate, unless hydraulic problems are encountered. For this reason, the vapour load is assumed to be always at its design value V during operation (Diwekar et al., 1989, 1991) and is dropped from the optimisation variables vector. 

Thus with given B0m and V, specification of the set of operations decision variables D°m = d°j, i = 1, NTm] (a total of 2 NTm decision variables) and control variables Um = t-, i = 1,NTm for all distillation tasks in operation m, it will be possible to calculate the overall performance measures for the batch (total distillation time, overall separation, products and intermediates amounts, recoveries, energy, etc.)- The same decision variables may be optimised to achieve some overall objective for the operation, (e.g. overall profit) subject to overall constraints (e.g. overall time, energy, etc.). 

The multiple separation duty specifications can be made in several ways. Two of which are  

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