Constraints Considered in the Formulation

The synthesis model is based on the zero effluent scheduling formulation with the addition of design specific constraints. The scheduling constraints used in the synthesis formulation are identical to those used in the scheduling formulation and the mass balance constraints are virtually identical except for a few minor changes in the limiting capacities, amount of water and amount of product. These changes will be discussed below. 

The first constraints that are added in the synthesis formulation are existence constraints. In the synthesis formulation an existence binary variable is defined for each processing unit and each storage vessel. If a storage vessel exists the binary variable will assume the value of 1, if it does not exist the binary variable will assume the value of 0. This is the same for a processing unit. If a processing unit is used at any point within the time horizon, than unit must then exist. This is dealt 

The capacity of each processing unit and storage vessel is an optimisation variable that must be bound to a minimum and maximum. The capacity of each processing unit and each storage vessel is limited to their respective maximum and minimum using constraints (8.57) and (8.58), respectively. 

The first minor change to the mass balance constraints from the scheduling formulation is found in constraint (8.2), which defines the size of a batch. In the synthesis formulation, the batch size is determined by the optimal size of the processing unit. Due to this being a variable, constraint (8.2) is reformulated to reflect this and is given in constraint (8.59). The nonlinearity present in constraint (8.59) is linearised exactly using Glover transformation (1975) as presented in Chapter 4. 

The amount of water used for a cleaning operation is also now variable and is dependent on the size of the processing unit. Constraint (8.6) is reformulated to account for this and takes the form of constraint (8.60). Constraint (8.60) shows that the amount of water used is related to the size of the processing unit through a proportionality factor. Once again there is a nonlinear term present in constraint 

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