(445c) Considering Isothermal Streams in the Minlp Synthesis of Heat Exchanger Networks

A good number of works have been developed on the synthesis of heat exchanger networks, as reported in the recent review paper by Furman and Sahinidis (2002). However, most of the methodologies proposed to solve the heat exchangers network problem have not considered isothermal streams with phase change (i.e. streams that transfer their latent heat). Isothermal streams are very common in the chemical process industries; they arise for instance as part of many separation processes and refrigeration sections. Methodologies reported for the synthesis of heat exchanger networks for isothermal streams, and more generally with phase change, have typically oversimplified the problem, for instance by assuming 1 K drop or increase in the temperature of these streams. Hence, no rigorous model has been reported to handle this kind of problem.

In this work a new MINLP model for heat exchanger network synthesis that includes streams with phase change is proposed. The model considers every possible combination of process streams that may arise within a chemical process: streams with sensible heat, streams with latent heat, and streams with both latent and sensible heat. A superstructure based on the stage-wise representation by Yee and Grossmann (1990) is formulated. The proposed MINLP model provides the network structure that minimizes the total yearly cost, which includes the capital cost of the exchangers and the utility costs. A critical part of the optimization strategy is the development of logical conditions that ensure a proper placement of heat integration for process streams with change of phase within the superstructure. To accomplish this task, a set of disjunctions are formulated. The disjunctions are then reformulated using the convex hull transformation (Raman and Grossmann, 1994) to provide the set of constraints for the model implementation. Additional disjunctions are formulated to handle other numerical problems associated with the treatment of isothermal streams, for instance for the calculations of logarithmic mean temperature differences. Several examples that reflect different types of problems with isothermal streams have been solved to illustrate the application of the proposed model. No convergence problems were observed for any of the case studies that were analyzed, and the computational requirements were small.

References

Furman, K.C., Sahinidis, N.V. (2002). A critical review and annotated bibliography for heat exchanger network synthesis in the 20th century. Industrial and Engineering Chemistry research. 41, 2335-2370. Raman, R., Grossmann, I.E. (1994). Modeling and computational techniques for logic based integer programming. Computers and Chemical Engineering. 18, 563-578. Yee, T.F., Grossmann, I.E. (1990). Simultaneous optimization model for heat integration ?II Heat exchanger network synthesis. Computers and Chemical Engineering. 14, 1165-1184.