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(430b) A New Heat Integration Model for Simultaneous Utility and Total Heat Exchanger Area Targeting

Authors: 
Kong, L., University of Wisconsin-Madison
Wu, Y., University of Wisconsin - Madison
Maravelias, C. T., University of Wisconsin-Madison
The heat integration between cold and hot process streams is beneficial because it minimizes the utility consumption and increases energy efficiency. There are two approaches to this problem, sequential/decomposition and simultaneous. In the sequential approaches, heat integration is performed after the chemical process has been designed (all the process stream conditions are determined), and it is performed in three sequential steps to determine (1) the minimum utilities for the entire system, (2) minimum number of heat exchangers, and (3) total heat exchanger area and total cost. The major limitations of the sequential approaches are that they neglect (1) the interactions between the chemical process and heat integration subsystems, and (2) the trade-off among utility consumption, number of exchangers, and area. To address the first limitation, simultaneous approaches have been proposed [1, 2], where process synthesis and utility targeting (i.e. minimize total unity consumption under variable stream conditions) are considered simultaneously. However, these approaches do not take into account the tradeoff between energy cost and capital investment (e.g. heat exchanger area) in the heat integration subsystem. Another approach that addresses both limitations is the formulation of rigorous mixed-integer nonlinear programming (MINLP) superstructure heat exchanger network synthesis (HENS) model in which the utility consumption, heat exchanger area, and network configurations are simultaneously optimized [3]. However, this approach can lead to suboptimal solutions and it is computationally expensive when adopted for simultaneous process synthesis and HEN optimization.

To address the aforementioned challenge, we propose a MINLP optimization model for simultaneous utility and area targeting. The model can handle process streams with variable temperatures and flow rates so that it can be integrated with process synthesis models. The model is based on a mathematical representation of the balanced composite curves (BCCs) in the pinch analysis. The cold and hot composite curves (including cold and hot utilities) are each constructed from the cumulative enthalpies from low to high temperatures using implicit orderings. The BCCs are then constructed by â??bringingâ? the two composite curves together but allowing the heat recovery approach temperature (HRAT) to vary. The BCCs are divided vertically into enthalpy intervals wherever the curves have slope changes, which corresponds to a process stream starting or finishing along the BCCs. Therefore, the total number of intervals needed is twice the amount of process streams. It is important to note that if any one of the two BCCs has a slope change (a â??kinkâ? in the graphic representation), we calculate the temperature of the other BCC at the same enthalpy. In each interval, it is assumed that the hot streams and cold streams transfer heat vertically. Using the boundary temperatures and enthalpies at each interval, we can calculate the mean temperature difference and the approximate heat exchanger area needed at each interval. Finally, the objective is to minimize total area cost and utility

The nonlinearities in this model come from either the bilinear [flow rates]*[temperature difference] terms, or the terms in the area cost calculation that appear in the objective function. If either the stream flow rates or temperatures are fixed, the feasible space will be defined strictly by linear constraints, and the only nonlinearities will be in the objective function. In the case that flow rates, temperatures, and HRAT are all fixed, the model reduces to the problem table algorithm in the pinch analysis.

The proposed model can be generalized to consider intermediate utilities. Further, we extend the model so that it handles process streams with unknown cold/hot classifications. In other words, the model can deal with streams that cannot be determined as cold/hot streams prior to solving the optimization problem, which is in particular useful when the proposed model is integrated with a chemical process superstructure model that involves the (de)activation of units.

We apply the proposed model on several examples that involve process streams with variable flow rates and temperatures. Finally, we illustrate its applicability by integrating it with a rigorous biofuel production superstructure model.

References

1. Duran, M.A. and I.E. Grossmann, Simultaneous-Optimization and Heat Integration of Chemical Processes. Aiche Journal, 1986. 32(1): p. 123-138

2. Grossmann, I.E., H. Yeomans, and Z. Kravanja, A rigorous disjunctive optimization model for simultaneous flowsheet optimization and heat integration. Computers & chemical engineering, 1998. 22: p. S157-S164

3. Yee, T.F. and I.E. Grossmann, Simultaneous optimization models for heat integrationâ??II. Heat exchanger network synthesis. Computers & Chemical Engineering, 1990. 14(10): p. 1165-1184