279571 A New Approach to Heat Exchanger Network Synthesis Problem
Introduction
Heat exchanger networks (HENs) bring several fluid streams into their desired temperatures by using available heat in the process. Since water and energy that are wasted to produce utility streams such as superheated steam and cooling water cause environmental and economic costs, processing a fluid to be heated with the one to be cooled is better than producing utility streams for efficient usage of energy.
In this study, we present a new solution approach for HEN synthesis problem. Our aim is to provide a complete network design coupled with a detailed equipment design for heat exchangers (HEs). We generate all possible HE alternatives instead of structuring the HEN at the very beginning as done in Yee and Grossmann (1990). Alternatives are generated by discretizing the inlet and outlet temperatures for hot and cold stream pairs. A mixed-integer nonlinear programming (MINLP) model is solved to design each HE alternative in detail. The model decides on the number of shell-and-tube passes and tubes, diameter of shell, inner/outer tube diameters, and tube pattern while minimizing HE area or the total construction and operation cost.
The Yee-Grossmann approach, based on developing a MINLP formulation for a proposed superstructure of the design of network, dominates the HEN design literature since 1990 (see Furman & Sahinidis, 2002; Morar & Agachi, 2010; and references therein). Related studies that keep the superstructure mostly focus on reviewing viability of the formulation assumptions, improving the methodology for solving the MINLP, and/or extending the framework. Mizutani et al. (2003), an example of those who extend the Yee-Grossmann approach, combine detailed HE design with HEN superstructure. Our study is pretty different than all these studies in the literature because we produce a detailed design for every network alternative, abandon using a superstructure, and evaluate all possible alternatives on a shortest-path network problem in which each path represents a HEN design alternative. Considering all thermo-physical and transport properties, the heat transfer coefficients are calculated for every stream at the environment temperature and pressure. Plus, one can also control the solution quality by deciding on the minimum temperature difference between inlet and outlet streams as the main parameter.
Problem Formulation and Solution Approach
Our goal for the HEN synthesis problem is to achieve maximum heat transfer between streams and to use utility streams minimally. The decisions are:
- Which cold and hot streams meet in a HE?
- How much heat will transfer in HEs?
- What should be the design properties for every HE?
- How many HEs should be in the network?
- How should HEs be arranged in the network?
The main idea behind our problem formulation is to generate all possible HE alternatives, each of which can be represented a node on a network. We call a stream ‘hot (cold) stream' if that would be cooled (heated) during the process. ‘System inlet (target) temperature' refers to the temperature of a stream at the beginning (after being processed) in the system. Start and end nodes of the network represent the initial and target status of the streams, respectively. Arcs between nodes, having associated costs, are generated by considering the inlet and outlet temperatures and energy requirements of the streams. The minimum-cost path on the network gives the final HEN design (Figure-1).
Figure-1. General representation of the whole network, where the selected HEN is shown in bold.
Note that nodes (i.e. alternatives HE designs) are generated for all hot and cold stream pairs and for every step change of their temperatures. For example, assume that there are 3 hot (H1, H2, H3) and 2 cold (C1, C2) streams and their system inlet and target temperatures are given. If the minimum temperature difference α is selected as 10°C by discretization, the system inlet and target temperatures are set as represented in Table-1. Table-2 shows some possible alternatives of HEs for this example. At each node on the graph, we keep the temperature information for all streams so that we can keep track of them along the network. Figure-2 shows what data is stored at a node if there are m hot streams (i=1,…,m) and n cold streams (j=1,…,n).
Table-1. Data for a HEN synthesis problem
Streams | System inlet temp. (°C) | Target temp. (°C) | System inlet temp. after discretization | Target temp. after discretization |
H1 | 300 | 150 | 15α | 0 |
H2 | 260 | 150 | 11α | 0 |
H3 | 340 | 240 | 10α | 0 |
C1 | 30 | 60 | 0 | 3α |
C2 | 50 | 130 | 0 | 8α |
Table-2. Several HE alternatives generated for the example
Hot stream | Cold stream | Hot inlet | Cold inlet | Hot outlet | Cold outlet |
H1 | C1 | 15α | 14α | 0 | 2α |
H1 | C1 | 6α | 2α | 0 | 3α |
H2 | C1 | 11α | 9α | 0 | α |
H2 | C2 | 5α | 2α | 6α | 8α |
H3 | C2 | 8α | 5α | α | 4α |
Figure-2. Content of a node in the network.
The solution approach consists of 5 steps summarized below:
a) Node Enumeration: Generate all necessary nodes by enumerating all possible inlet and outlet temperatures for every stream in the system. The temperature enumeration would be performed as explained above. Note that at a node (HE), the inlet temperature of a processed hot stream should be higher than its outlet temperature, and inverse is also true for a processed cold stream. For each unprocessed stream, the outlet temperature should be equal to its inlet temperature.
b) Eliminating Nodes: Calculate the thermo-physical properties for every processed stream for each HE. Eliminate the node if energy balance is not satisfied. The heat load required by the cold fluid should be equal to the heat load generated by the hot fluid.
c) Connecting Nodes
a. Dummy nodes: There are 2 dummy nodes (Start, End) in the graph. Every node v should be directly connected to the starting and ending dummy nodes.
b. Connecting HE Nodes: For any two nodes u and v, u and v would be connected if the following condition holds:
- For all hot streams and cold streams:
outlet temperature of hot stream i in node v = inlet temperature of hot stream i in node u
AND
outlet temperature of cold stream j in node v = inlet temperature of cold stream j in node u
d) Individual HE Design and Costs: For every node in the network, solve a cost-minimizing MINLP model for the detailed design of shell-and-tube heat exchangers with TEMA standards. The MINLP model consists of necessary design (Geankoplis, 2003) and cost equations (Turton et. al., 2003) for each HE (i.e. node), and gives the cost of each incoming arc to that node. The costs on the arcs from the start to the end nodes are calculated by solving a MINLP model for every stream that is not at the system inlet temperature and has not reached its desired temperature, respectively. Utilities such as cold water for cooling and superheated steam for heating are assumed to be used. The utility costs are added to the cost of that specific arc. If the streams are at the system inlet temperature, the cost of an arc from the starting node to that node should be 0. Similarly, if the streams have reached their target temperatures, then the cost of an arc from that node to the ending node should be 0.
e) Shortest Path: Solve the shortest-path problem on the whole network to find the best HEN with detailed design.
Computational Results and Conclusion
For implementation of our solution approach we use MATLAB. For solving the MINLP models, MATLAB calls GAMS/BARON solver. We solve the shortest-path problem by using the Dijkstra's algorithm. Our approach is flexible and successfully finds the required number of heat exchangers and their connections. Note that the decision maker can change the parameter α to manage the HEN synthesis achieved at the end.
Several HEN examples from the literature are solved to assess the performance of our approach and comparative results are obtained. We observed that our approach outperform the superstructure approach.
References
Furman, K.C. & Sahinidis, N.V. (2002). A critical review and annotated bibliography for heat exchanger network synthesis in the 20^{th} century. Ind. Eng. Chem. Res., 41, 2335-2370.
Geankoplis, C.J. (2003). Transport Processes and Separation Process Principles (4^{th} ed.). New Jersey: Prentice Hall.
Mizutani, F.T., Pessoa, F.L.P., Queiroz, E.M., Hauan, S. & Grossmann, I.E. (2003). Mathematical programming model for heat exchanger network synthesis including detailed heat-exchanger designs. 2. Network synthesis. Ind. Eng. Chem. Res., 42, 4019-4027.
Morar, M. & Agachi, P.S. (2010). Review: Important contributions in development and improvement of the heat integration techniques, Comput. Chem. Eng., 34, 1171-1179.
Turton, R., Bailie, R.C., Whiting, W.B. & Shaeiwitz, J.A. (2003). Analysis, Synthesis, and Design of Chemical Processes (2^{nd} ed.). New Jersey: Prentice Hall.
Yee, T.F. & Grossmann, I.E. (1990). Simultaneous optimization models for heat integration – II. Heat exchanger network synthesis. Comput. Chem. Eng., 14, 1165-1184.
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