Distillation Sequencing Using Optimization of a Superstructure

Consider now ways in which the best arrangement of a distillation sequence can be determined more systematically. Given the possibilities for changing the sequence of simple columns or the introduction of prefractionators, side-strippers, side-rectifiers and fully thermally coupled arrangements, the problem is complex with many structural options. The problem can be addressed using the optimization of a superstructure. As discussed in Chapter 1, this approach starts by setting up a grand flowsheet in which all structural features for an optimal solution are embedded. 

However, before sizing and costing calculations can be carried out, the pressure must be also specified. Pressure is a critically important optimization variable, and the appropriate pressure is not known until optimization calculations have been carried out. If the pressure is allowed 

It is important to note that in formulating the problem in this way, it is a linear formulation, guaranteeing (within the bounds of the assumptions made) a global optimum solution. The potential problems associated with nonlinear optimization have been avoided. Even though the models are nonlinear, the problems associated with nonlinear optimization have been avoided. The approach can use either shortcut models or detailed models and the linearity of the optimization is maintained. 

Example 11.4 The mixture of alkanes given in Table 11.2 is to be separated into relatively pure products. Using the Underwood 

Equations, determine sequences of simple and complex columns that minimize the overall vapor load. The recoveries will be assumed to be 100%. Assume the actual to minimum reflux ratio to be 1.1 and all the columns, with the exception of thermal coupling and prefractionator links, are fed with saturated liquid. Neglect pressure drop through columns. Relative volatilities can be calculated from the Peng-Robinson Equation of State with interaction parameters set to zero. Pressures are allowed to vary through the sequence with relative volatilities recalculated on the basis of the feed composition for each column. Pressures of each column are allowed to vary to a minimum such that the bubble point of the overhead product is 10°C above the cooling water return temperature of 35°C (i.e. 45°C) or a minimum of atmospheric pressure. 

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