This paper addresses the synthesis and optimization of crystallization processes for p-xylene recovery from streams of mixed xylenes. Crystallization based processes exploit the large freezing point difference between p-xylene and the remaining components in the mixture. Typical processes consist of one or two crystallization stages operating at different temperature levels, liquid/solid separation devices using different types of centrifuges (imposed by operation ranges of feed solid concentrations and of feed temperature), melting stages with slurry drums and heat exchangers, and a final stage of purification involving centrifuges with wash streams. The units are organized by stages in series and/or parallel configurations giving rise to complex flowsheets. Lima and Grossmann (2008) proposed a novel superstructure, a mixed integer nonlinear programming (MINLP) model, and a decomposition strategy to cope with the complexity of the model. The decomposition strategy developed by these authors allowed them to propose and study alternative flowsheets for the p-xylene separation from streams with high concentration of p-xylene. The size and complexity of their superstructure and respective model prevented the application of global optimization deterministic algorithms to solve the MINLP problems at each level of the decomposition approach proposed.

In this work we propose a generalized disjunctive programming (GDP) model to describe the superstructure proposed by Lima and Grossmann (2008). A specific feature of this superstrucutre that we try to explore is the existence of a network of crystallizers and three sets of centrifuges operating in parallel. The proposed GDP model involves disjunctions associated with the existence or not of each crystallizer and centrifuge. However, in each term of each disjunction, the equations of the downstream splitters and upstream mixers of each unit are also considered. Therefore, whenever a crystallizer is not selected the corresponding splitter and mixer are also not considered. Although, these sets of units in parallel may resemble trays of distillation columns, these sets represent a distinct case, since there are no connections between the units in the same set. A logic-based outer-approximation algorithm is proposed to solve the GDP problem, where the linearizations for the terms of the disjunctions are provided from the solutions of an aggregated model. In this aggregated model, the sets of units in parallel are replaced by a single equivalent unit, decreasing the size and complexity of the associated MINLP problems. Therefore, the solution of the full MINLP problem or the solution of a set-covering problem (Turkay and Grossmann, 1996) to define the sub-structures to provide the linearizations is not necessary. The main idea of this approach is to avoid the solution of large MINLP models where all the units in parallel are present, as it was implemented in the decomposition approach proposed by Lima and Grossmann (2008). The solution of smaller nonlinear programming (NLP) problems at each iteration of the logic-based approach should provide additional solutions in terms of flowsheets and operating conditions.

Optimum flowsheets for a wide range of p-xylene concentrations in the feed stream are presented and compared with flowsheets reported in the literature. In addition, numerical and algorithm performance indicators for comparing the two approaches (two-level decomposition and GDP) are also presented.

References

Lima, R. M. and Grossmann, I. E., (2008), Optimal synthesis of p-xylene separation processes based on crystallization technology, AIChE Journal, submitted.

Turkay, M. and Grossmann I.E., (1996), Logic-based MINLP algorithms for the optimal synthesis of process networks, Computers and Chemical Engineering, 20(8), 959-978.