Tuesday, November 6, 2007 - 10:30 AM

Optimal Synthesis of Para-Xylene Separation Processes Based on Crystallization

Ricardo M. Lima and Ignacio E. Grossmann. Department of Chemical Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213

This paper addresses the synthesis and optimization of crystallization processes for p-xylene recovery. Crystallization is a well known technology for p-xylene recovery from a mixture containing the three xylene isomers:¬ m-xylene, o-xylene and p-xylene,¬ and ethylbenzene. 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 different operation ranges of feed solid concentrations), melting stages with slurry drums and heat exchangers, and a final stage of purification involving centrifuges with wash streams with high p-xylene concentration. The design of crystallization processes has been the subject of several US patents in the last decades (Eccli and Fremuth, 1996; Hubbell and Rutten, 1998; Lammers, 1965; Laurich, 1969; Lindley and McLeod, 1976; Mikitenko and MacPherson, 2000; Wilsak, 2003). The more recent trend in these patents has been to design energy efficient processes by minimizing the energy consunption through the minimization of the number of melting stages and refrigeration loads that are required. To accomplish this objective these works have proposed different operating conditions but also different process configurations for the all p-xylene recovery process. A systematic treatment, however, is lacking because the synthesis and optimization of crystallization processes is an area where little work has been reported.

We propose in this paper a superstructure that considers feasible flowsheet alternatives for the all process configurations and model it as a Mixed-Integer Nonlinear Programming (MINLP) problem in order to identify optimum configurations for the crystallization process. This superstructure is a generalization of the flowsheets studied by Mendez et al. (2005). In this work we have embedded all the flowsheets studied by these authors and considered new connections between stages. The superstructure includes a sub-superstructure for the first crystallization stage and a new sub-superstructure for the set of centrifuges with wash, which allowed establishing new connections between the different process stages so as to consider flowsheets that have been proposed in US patents.

The proposed MINLP model includes several nonlinearities, mainly in the solubility correlations and heat balances, as well as discontinuities in the solubility correlations, giving rise to a nonlinear nonconvex MINLP problem of a large dimension. In order to cope with the complexity of this MINLP model and to avoid its direct solution, we propose a two-level decomposition consisting of the iterative solution of an aggregated and a detailed model. The two key ideas in the aggregated model are: a) merging the units in centrifuge blocks and slurry drums into single input-output blocks so that the aggregated model is defined in the space of interconnection of major blocks; b) elimination of the constraints that set an upper bound on the inlet flowrate of each centrifuge unit. In this way a large number of equations and variables are eliminated because groups of individual units are replaced by a single equivalent unit. However, in order to meet the same production targets, the constraints that impose operating ranges for the centrifuges are relaxed in the aggregated model. For the definition of the detailed model, the number of units in each aggregated block is calculated by the ceiling of the ratio between the calculated capacity of the block and the upper bound of the size for each unit. As an example, for the first stage of centrifuges the number of units is determined by the ceiling of the ratio between the individual feed flowrate of solid p-xylene in the aggregated block divided by the maximum individual feed flowrate of solid p-xylene treated for each centrifuge. In each iteration of the two-level decomposition an integer cut is added to the aggregated model to eliminate previous combinations of number of units. Therefore, this requires the introduction of binary variables in the aggregated model in order to calculate the number of units associated with each aggregated block. The solution of the aggregated model is used to initialize the detailed model as well as to define a reduced superstructure for the detailed model. While the proposed approach has the advantage of providing an effective solution method, its limitation is that convergence cannot be guaranteed in terms of lower and upper bounds. Therefore, the approach we take is to simply iterate over a fixed number of major iterations.

The results obtained show that the aggregated MINLP model is easier to initialize and and to solve than the MINLP model of the overall superstructure. Furthermore, the solution from the aggregated model provides a good initial point for the detailed model. The optimum flowsheet that was obtained yields a new design alternative compared to previous flowsheets studied by Mendez et al (2005). Comparing the configuration of the optimum flowsheet obtained by these authors with the one obtained in this work, the latter has three fewer slurry drums, one less melting stage, four fewer centrifuges, but one more crystallizer. This led to a reduction of 12% in the total annualized investment cost but at the expense of a small increase in the total annual operating cost, resulting in a modest net improvement in the total annual profit.


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Hubbell D., Rutten P. (1998). Crystallization process for purification of paraxylene. United States Patent No. 5,811,629.

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Lindley J., McLeod A. (1976). Separation process by fractional crystallization. United States Patent No. 3,959,978.

Mikitenko P., MacPherson S. (2000). Process for separating paraxylene comprising at least two crystallization stages at high temperature. United States Patent No. 6,147,272. 3

Mendez, C.A., J. Myers, S. Roberts, J. Logsdon, A. Vaia and I. E. Grossmann, “MINLP model for synthesis of Paraxylene Separation Processes based on Crystallization Technology,” Proceedings ESCAPE-15, pp. 829-834, Barcelona, Spain (2005).

Wilsak R. (2003). Energy efficient process for producing high purity paraxylene. United States Patent No. 6,565,653.