Thermodynamically equivalent configurations for thermally coupled distillation

In this work a systematic way of generating all the thermodynamically equivalent structures for a given sequence of separation task in N‐1 distillation columns (N is the number of components to be separated) is presented first. The problem is represented through a set of symbolic relations that can be written as propositional logic expressions. Alternatives from fully thermally coupled systems (only one reboiler and one condenser) to conventional columns (each column with a reboiler and a condenser), plus all the intermediate possibilities, are considered. Then all the thermodynamically equivalent structures that do not have control problems associated with the flow transfer among columns are generated. Again the problem is formulated as a set of symbolic relations written as propositional logic expressions. A formula with a detailed derivation to calculate the number of alternatives for a given sequence of tasks is also presented. Logic expressions in propositional logic form or translated into algebraic expressions in terms of binary variables can be integrated in the framework of Disjunctive Programming to extract the best solution for a given objective function. Several results are presented with systems involving mixtures of 4 and 5 components.