CHEMICAL ENGINEERING TRANSACTIONS VOL. 61, 2017 A publication of The Italian Association of Chemical Engineering Online at www.aidic.it/cet Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš Copyright © 2017, AIDIC Servizi S.r.l. ISBN 978-88-95608-51-8; ISSN 2283-9216 Optimal Heat Exchanger Network Synthesis with Detailed Shell and Tube Heat Exchanger Design Based on Superstructure Model Lin Sun*, Bo-Shi Zhao, Xiong-Lin Luo Department of Automation, China University of Prtroleum, Beijing, 102249, China sunlin@cup.edu.cn The shell and tube heat exchanger (SHE) is the most common type of heat transfer equipment used in heat exchanger networks (HENs) in the field of chemical process industries. Both counter-current flow and co- current flow may be involved in the shell and tube heat exchangers. To calculate the temperature difference, the correction factor FT is generally used for multi-pass heat exchanger optimization. For synthesis of heat exchanger networks, a lot of researchers use the correction factor FT as a constraint condition, and the HEN with minimum number of shells is optimized by iterative calculation based on a stage-wise superstructure model. However, in these studies the heat transfer temperature difference correction factor FT are used to avoid temperature crossing without considering the optimization of shell and tube number. In this paper, a method of HEN synthesis with the optimization of the number of shells and tubes for each SHE based on superstructure model is presented. Firstly, the heat transfer process of counter-current and co-current flow in SHE is studied. The correction factor of heat transfer temperature difference FT is calculated based on the mechanism of heat transfer process. Then, each tube of heat exchanger instead of a SHE is defined as a single unit and the energy balance function is established for each unit to minimize the total cost of HEN in the proposed superstructure model of HEN. By using the methodology of mixed integer nonlinear program (MINLP), the HEN synthesis and the correction factor of heat transfer temperature difference FT are optimized simultaneously. The proposed methodology allows for proper handling of the trade-offs involving energy consumption, number of units, number of shells and tubes, and network area to provide a network with the minimum total annual cost. Finally, the case study results demonstrate the effectiveness of this proposed method, and the total cost of HEN are lowered as well as the number of tubes and shells for each SHE is optimized simultaneously. 1. Introduction The shell and tube heat exchanger (SHE) is the most common type of heat transfer equipment used in heat exchanger networks in the field of chemical process industries. Different methods for optimization and design of the SHE have been used for the economic factors. Some scholars (Selbas et al., 2006) took the allowable pressure drop as the constraint and designed shell and tube heat exchanger based on the genetic algorithm. Patel et al. (2010) applied particle swarm optimization to design shell-and-tube heat exchangers from the perspective of economics. In recent years, the generalized disjunctive programming (GDP) was used for optimization problem formulation and the mixed-integer nonlinear programming (MINLP) was used for its solution (Mizutaniet and Pessoa, 2003). However, all of these studies were focused on the design of heat exchangers without considering the optimization of the tubes and shells for multi-pass SHE. In terms of the multi-pass heat exchangers, the flow arrangement involves part counter-current and part co- current flow. The effective temperature difference for heat exchanger is reduced compared with a counter- current device, which is accounted for in design by the introduction of the FT factor into the basic heat exchanger design equation. Ahmad et al. (1988) proposed a non-interactive algebraic solution for the number of shell side passes and the XP parameter. As an alternative approach, some equations were reported to estimate XP for different values of R (Shenov, 1996). Although Moita (2014) proposed approaches to solve this DOI: 10.3303/CET1761030 Please cite this article as: Sun L., Zhao B.-S., Luo X.-L., 2017, Optimal heat exchanger network synthesis with detailed shell and tube heat exchanger design based on superstructure model, Chemical Engineering Transactions, 61, 193-198 DOI:10.3303/CET1761030 193 problem, the algorithm could sometimes lead to suboptimal designs and was difficult to use for optimum HEN synthesis. Though these researchers have proposed various methods to optimize the design of heat exchanger, it does not involve the effect of a single heat exchanger for the heat exchanger network (HEN) optimal integration. Recently, there are also a lot of studies which presented about the synthesis of the HEN with multi-pass SHE. Kravanja et al. (2002) considered different types of the heat exchangers in the superstructure model and optimized the HENs and the heat exchangers simultaneously. Scholars computed the number of shells in a HEN firstly and the design began by assuming a specific number of shells, then the FT value was evaluated (Wang and Sundén, 2001). A mixed integer non-linear programming formulation for this optimization problem which used the correction factor as a constraint to calculate the minimum shell number was proposed (Ponce- Ortega et al., 2006). Sun et al. (2011) proposed a methodology to analysis the number of tube passes and the minimum temperature difference by using the composite curves and problem table. These studies focused on the synthesis of HEN with the shell and tube optimization as a constraint to avoid temperature cross. Polley and Shahi (1991) took account of the pressure drop in network while designing heat exchanger networks. Some scholars took account of the selection of heat exchanger and heat transfer enhancement equipment selection during the integration optimization of heat exchanger network. Ebert and Panchal (1995) used simulated annealing algorithm and MILP optimization methods to optimize the performance considerations of heat transfer enhancement of the HEN. In recent years, some researchers have carried out the design of heat exchanger based on the optimal synthesis of HENs (Ravagnani et al., 2005). In these studies, the pressure drop and the transfer coefficient are mainly considered. In this work, the synthesis of HEN with the optimum number of shells and tubes for each SHE based on superstructure model is presented. Firstly, the correction factor of heat transfer temperature difference FT is calculated based on the mechanism of heat transfer process. Then, to minimize the total cost based on the proposed superstructure model of a HEN, the heat transfer unit is represented as the heat transfer process in one tube and one shell of the SHE. Finally, the HEN synthesis and the correction factor of heat transfer temperature difference FT are optimized simultaneously. 2. Superstructure model for multi-pass HEN synthesis Based on the stage-wise superstructure model of heat exchanger network with no split streams proposed by (Yee and Grossmann, 1990), this paper builds a stage-wise superstructure model of multi-pass heat exchanger network with no split streams. Not only must the number of the shells and the tubes but also the optimization results of the HEN be calculated. At the same time, the proposed superstructure model is modified. The tubes are defined as the separate units instead of the heat exchangers, then the superstructure model is established. At last, this paper uses the formulation of MINLP to solve the model. As Figure 1 shows, the modified stage-wise superstructure, and it consists of k stages. In the Figure1, if the tubes are existed, they are showed as ' ', while they are showed as' ' when they are not existed. The number of tubes nt can be obtained by the optimization of the HEN. C1 C2 QC QC stage 1 stage 2 stage 3 stage 4 stage k Figure 1: Stage-wise superstructure of multi-pass HEN with no split streams Here, nt is the number of tubes, and ns is the number of shells. The note i indicates the ith heat flow while j indicates the jth cold flow. The number of stages is k. The specific heat capacity is Cp. The balance equations of the tube pass are,  oitinitpit TTCq ,,  (1) )( 1 ikikpiijk TTCq (2) Where, q means the heat loads, and T indicates the temperature for the inlet and outlet of the tube side. The energy balance equation of the multi-pass SHE is 194       s s tn s n s n t ijktijksijk qqq 1 1 1 ,, (3) Where, s indicates the shell and t indicates the tube. The qijk means the heat transfer loads for the ith heat flow and the jth cold flow in the kth stage. The heat transfer area A for each SHE is calculated by using following equation,     ijktn t ijkLMijk ijktijk ijk TK nq A , 1 , (4) Where, K notes the heat transfer coefficient. Where ijkTLM indicates the logarithmic mean temperature difference for the t-th tube with the s-th shell in the kth stage. For the counter-current flow,     in ijkc out ijkh out ijkc in ijkh in ijkc out ijkh out ijkc in ijkhcu ijkLM TT TT TTTT T ,, ,, ,,,, ln     (5) For the co-current flow,     out ijkc out ijkh in ijkc in ijkh out ijkc out ijkh in ijkc in ijkhco ijkLM TT TT TTTT T ,, ,, ,,,, ln     (6) Where, cu LM ijkT is the countercurrent flow logarithmic mean temperature difference for the t-th tube with the s- th shell in the k-th stage, and where in ijkhT , and out ijkhT , denote the inlet and outlet temperature of the tube; in ijkcT , and out ijkcT , are the shell inlet and outlet temperature. co LM ijkT is the co-current flow logarithmic mean temperature difference for the t-th tube with the s-th shell in the k-th stage. Use the binary system to show the existence of the tube, NKkNCjNHi q q z ijk ijk ijk        ,,, 0,0 0,1 (7) Based on this proposed superstructure model of the multi-pass HEN, the number of tubes and the HEN are synthesized simultaneously. By calculating the logarithmic mean temperature difference ijkTLM for co-current side and countercurrent side separately, the FT factor is also calculated. 3. Heat Exchanger Network synthesis with detailed equipment design Based on the provided superstructure model of multi-pass HEN, a two-stage strategy is used to resolve this problem. Firstly, the HEN is synthesized with the optimization of the number of tubes and shells based on the proposed superstructure model. In the second stage, the SHEs are designed in detail based on the TEMA standard. In order to calculate the FT of the heat exchangers and the heat transfer area of the heat exchangers, the main steps of the algorithm are as shown in Figure 2 based on the presented superstructure model and the energy balance. As shown in Figure 2 to synthesize the multi-pass HEN, an initial heat transfer coefficient K0 is defined, and then the superstructure model of HEN established. Based on this proposed model, the HEN is synthesized and the number of shells and tubes is calculated. The temperature difference correction factor FT is also calculated and verified. Based on this first stage, the detailed equipment design can be calculated based on the TEMA standards. Consequently, by the iterative calculation the optimal HEN with detailed equipment design is obtained. 195 Initialize the heat transfer coefficient K0 Establish the superstructure model of HEN Synthesize the HEN and optimize the number of tubes by using MINLP Calculate FT 0 .75