Improving energy recovery in heat exchanger network with intensified tube-side heat transfer

Transcription

1 CHEMICAL ENGINEERING TRANSACTIONS Volume Editors Jiří. Jaromír Klemeš Petar Sabev Varbanov Hon Loong Lam Copyright 011 AIDIC Servizi S.r.l. ISBN ISSN DOI: 10.0/CET Improving energy recovery in heat changer network with intensified tube-side heat transfer Ming Pan 1 Igor Bulatov 1 Robin Smith 1 Jin-Kuk Kim 1 Centre for Process Integration The University of Manchester Sackville Street M1 9PL Manchester United Kingdom Department of Chemical Engineering Hanyang University 17 Haengdang-dong Seongdong-gu Seoul Republic of Korea igor.bulatov@manchester.ac.uk Implementing tube-inserts namely tube-side enhancement is an efficient way to increase the heat transfer coefficients of shell and tube heat changers which can achieve substantial energy saving in heat changer network (HEN) if suitable retrofit strategies are used (Pan et al. 011). In this paper a new optimization method is proposed to consider more details of tube-side enhancement for HEN retrofitting such as multiple tube passes logarithmic mean temperature difference (LMTD) LMTD correction factor (FT). Even though LMTD and FT will lead to compl nonlinear terms in mathematical programming the proposed approach can deal with the relevant computational difficulties efficiently. The validity of new optimization approach is illustrated with solving a literature ample (Li and Chang 010). 1. Introduction Nowadays heat transfer enhancement (HTE) techniques have been widely studied for retrofitting heat changer network (HEN) as low capital cost for network modifications is required to increase significant energy saving. To intensify heat transfer in shell and tube heat changer there are several options available for ample tube-side enhancements (twisted-tape inserts coiled-wire inserts hitran ) and shell-side enhancements (helical baffles EM baffles). Compared to shell-side enhancements implementation of tube-inserts is a relative simple task that can be easily achieved within a normal maintenance period when physical size modifications of changers are avoided. It is very common to use mathematical programming methods for HEN retrofit. But with the nonlinear characteristics in heat transfer logarithmic mean temperature difference (LMTD) and LMTD correction factor (FT) HEN retrofit must be formulated as a mixed integer nonlinear programming (MINLP) problem. Yee and Grossmann (1991) used arithmetic mean temperature difference (AMTD) to simplify nonlinear pression in heat transfer equations which might overestimate the driving force if the temperature difference approach of one changer side is significantly different than the other side. Sorsak and Kravana (00) and Ponce-Ortega et al. (008) used LMTD and FT approximate equations to avoid the numerical difficulties thus will Please cite this article as: Pan M. Bulatov I. Smith R.. and Kim J.K. 011 Improving energy recovery in heat changer network with intensified tube-side heat transfer Chemical Engineering Transactions DOI: 10.0/CET11506

2 76 lead to infeasible solutions in some cases. Smith et al. (009) further improved the network pinch method by considering multi-segmented stream data and combined structural modifications and cost optimisation in a single step to achieve cost-effective design. Recently Pan et al. (011) proposed a novel MILP-based optimization method to solve HEN retrofit problems concerning act LMTD. It is the first work to use LMTD act equations for optimizing HEN retrofit but the FT values of all changer are assumed to be fixed. Based on the work of Pan et al. (011) this paper presents an updated MILP-based optimization method for HEN retrofit with HTE where more details of tube-side enhancement are considered and the values of LMTD and FT for each changer can be calculated actly.. MILP-based approach of HEN retrofit with tube-side HTE.1 LMTD and FT In this work LMTD and FT are calculated based on the act equations (Serth 007) which are shown respectively in the following formulations where EX is the set of all changers NS is the number of shell-side passes in changer and HTO are inlet and outlet temperatures of hot stream in changer while CTI and CTO are inlet and outlet temperatures of cold stream in changer. For LMTD: LMTD ln CTO HTO CTI CTO / HTO CTI For FT (assume that hot stream is located in shell side): EX (1) R HTO CTO CTI P CTO CTI EX CTI ( ) If R <>1: 1/ NS 1 R P 1 P FT If R =1: S R 1ln S 1 EX R 1 S 1 R S S R 1 R 1 R 1 ln S R 1 R 1 P NS NS 1P S 1 S ln S ( 5) EX (6) S FT EX (7 8). Tube-side HTE To select suitable tube-side enhancements for changers one set of binary variables (EEX ) is used. EEX = 1 if the th kind of tube geometry is implemented in changer ; otherwise it is 0. One changer only has one kind of tube geometry as

3 77 shown in Equation (9) where J is the set of all kinds of tube geometry (such as single/multiple tube passes or single/multiple tube passes with tube inserts). EEX 1 EX ij (9) The heat transfer coefficients of changers with different kinds of tube geometry can be formulated as: EEU M EEX EEU M EEX U 1 U 1 (10 11) EEU EEU min EEU EEU EX J (1 1) max In Equations (10)-(1) M is a sufficiently large positive number EEU is the heat transfer coefficient of changer if the th kind of tube geometry is implemented max EEU and min EEU are the upper and lower bounds of EEU.. HEN retrofit The model of HEN retrofit includes energy balance temperature constraints and energy assumptions. Equation (1) presents the energy balance for each changer where HFCP and CFCP are heat-flow capacities (the multiplication between heat capacity and flow-rate) of hot stream and cold stream in changer. HFCP HTO CFCP CTI CTO EX (1) The temperatures constraints of processing streams are shown in Equations (15)-(18) where CS and HS are the set of all cold streams and hot streams respectively; EX i cs EX o cs EX i hs and EX o hs describe the set of all changers located in the stream inlet or outlet; CMF and HMF are flow fraction of cold and hot streams in changer ; CSTI cs and CSTO cs are inlet and outlet temperatures of cold stream cs while HSTI hs and HSTO hs are inlet and outlet temperatures of hot stream hs. CTI CSTI cs CMF CTO CSTOcs o EXcs HSTI hs HMF HTO HSTOhs o EXhs i EX cs cs CS (15 16) i EX hs hs HS (17 18) In addition the minimum temperature difference approach ( T min ) in each changer is restricted in equations (19) and (0). CTO T min HTO CTI Tmin EX (19 0) Equation (1) presents the increased energy saving (QS) in HEN where EX hu and EX cu are the set of all changers consuming hot and cold utility CTI and are the initial inlet temperatures of cold stream and hot stream in changer before retrofit. CFCP CTI CTI HFCP QS (1) EXhu EX cu In Equations () and () the heat transfer in each changer is estimated based on the initial LMTD and FT which can be calculated with the stream initial temperatures ( HTO CTI and CTO ) in Equations (1)-(8). HBA and HBB are positive

4 78 variables and present the difference of energy change between streams and changers. For energy balance between streams and changers HBA and HBB should be small and the obective function has been formulated to minimize infeasible energy balances. HBA HBB HTO EXA U LMTD FT HFCP EX () EXA U LMTD FT HFCP HTO EX () Since the tube geometry of some changers change there might be some differences between initial stream temperatures and updated stream temperatures which are formulated in Equations () and (5). DA DB EX ( 5) DA and DB are positive variables and present the difference between initial and updated temperatures of hot stream inlet. Meanwhile the differences between initial and updated temperatures for hot stream outlet (DAHTO and DBHTO ) cold stream inlet and outlet (DACTI DBCTI DACTO and DBCTO ) are formulated in the same way. Equation (6) restricts that FT has to be considered if multiple tube passes are implemented where J m is the set of all kinds of tube geometry with multiple tube passes and MT is a set of 0-1 parameters that describes whether multiple tube passes are used in changer. MT EX (6) EEX J m In practice it is inefficient if FT is less than 0.8 in counter-flow changer which means that when multiple tube passes are used in an changer its FT value has to be larger than 0.8 and less than 1 while FT is equal to 1 only in one-tube-pass changer. The obective of the new MILP-based method is to minimize the differences of heat transfers and stream temperatures under the restriction of an estimated energy saving value (QS ) as shown in Equations (7) and (8). QS QS (7) Ob DACTI DBCTI DACTO DBCTO HBA HBB EX EX DA DB DAHTO DBHTO EX (8) The new MILP optimization framework model consists of obective function given in Equation (8) and other model constraints given from Equations (9)-(7). The iteration algorithm is mainly based on the work proposed by Pan et al. (011) where two iteration loops are proposed to find the optimal solution for HEN retrofit based on the MILP model. The first iteration loop is to find the solution for HEN retrofit under certain energy saving while the second iteration loop is to find the maximum energy saving for HEN retrofit.

5 79. A case study An ample presented by Li and Chang (010) is used for a case study. In this section the techniques of multiple tube passes and tube inserts are implemented in isting HEN to improve energy recovery. The isting HEN includes three hot streams (-S) and two cold streams (S and ). The heat-flow capacity of each stream is 8.5 kw/k () 0. kw/k (S) 5.8 kw/k (S) 9. kw/k (S) and kw/k () respectively. Table 1 shows the heat transfer limits of changers in different tube geometries. The original and retrofitted HENs proposed by Li and Chang (010) are presented in Figure 1. Figure presents the original and retrofitted HENs optimized with the new approach. By comparing Figures 1 and the new method can save up to 1% and 9.% utility consumptions for Cases 1 and respectively. The details for changers in each case are given in Tables. The case study shows that the new approach considering act LMTD and FT can find optimal solutions for practical HEN retrofit and increase energy saving without heavy topology modifications. Table 1: Heat transfer coefficients of changers in different tube geometries (kw/m K) EXs Tube passes (no tube-side enhancement) Tube passes (tube-side enhancement) 1 (N) (N) (N) 6 (N) 1 (E) (E) (E) 6 (E) 1 0 ~ ~ ~.00 0 ~ ~ ~ ~ ~ ~ ~ ~ 0. 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~.00 0 ~ ~ ~ 0. 0 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~.00 K 50K S.K 6K S 1 00K 6K 99K 58K 8.K 01.K H 1 S 91K kw (a) Case 1: Original HEN (base case) Figure 1: The base case and retrofitted HENs proposed by Li and Chang (010) K 50K S 09.9K K 0.6K 178 kw 50K 0.7K 10 kw 5K C 1.8K S 1 00K.9K 58K 58.5K 05.K H kw Enhanced changers 1695 kw 50K 1815 kw 5K C 6K 99K S 91K (a) Case : HTE-based retrofit of base case HEN K 50K S S 00K 58K 7.7K H 111 kw K 50K S S 00K 58K 80.1K H 1157 kw Figure : The optimal solutions with tube-side HTE K (b) Case : Retrofitted HEN (Li and Chang 010) K 1 1K 1 5 F s = K 18.1K 1 1K 5 1K 8.8K 5 1.1K 1 5 F s = 0.18 Enhanced changers (b) Case : HTE-based retrofit of Case 88K 871 kw 50K 161 kw 5K C 6K F s = K S 91K 79 kw 50K 18 kw 5K C 6K F s = K S 91K

6 80 Table : The details for changers in each case Case Exchanger 1 Exchanger Exchanger Exchanger Exchanger 5 A U TP A U TP A U TP A U TP A U TP (N) (N) (N) (N) (E) (N) (E) (N) (N) (N) (N) (N) (N) 0.8 1(E) (N) (E) (E) (N) A: area (m ) U: overall heat transfer coefficient (kw/m K) TP: tube passes.. Conclusions Nonlinear terms in LMTD and FT usually lead to a compl MINLP model for HEN retrofit. To reduce the corresponding computational difficulties a new MILP model has been built up and an iteration algorithm is utilized to guarantee the global optimization. Unlike isting design methods the new method can maintain its practicability and reliability for HEN retrofitting as LMTD and FT are both from act calculations. Acknowledgement Financial support from Research Councils UK Energy Programme (EP/G0607/1 Intensified Heat Transfer for Energy Saving in Process Industries) and EC Proect INTHEAT (FP7-SME INTHEAT) are gratefully acknowledged. References Li B.H. and Chang C.T. 010 Retrofitting heat changer networks based on simple pinch analysis Industry and Engineering Chemistry Research Pan M. Bulatov I. Smith R. and Kim J.K. 011 Novel optimization method for retrofitting heat changer networks with intensified heat transfer 1st European Symposium on Computer Aided Process Engineering ESCAPE 1 (Submitted). Ponce-Ortega J.M. Jiménez-Gutiérrez A. and Grossmann I.E. 008 Optimal synthesis of heat changer networks involving isothermal process streams Computers and Chemical Engineering Serth R.W. Eds. 007 Process Heat Transfer Principles and Applications. Elsevier Amsterdam. Smith R. Jobson M. and Chen L. 009 Recent development in the retrofit of heat changer networks Chemical Engineering Transactions Sorsak A. and Kravana Z. 00 MINLP retrofit of heat changer networks comprising different changer types. Computers and Chemical Engineering Yee T.F. and Grossmann I.E A screening and optimization approach for the retrofit of heat changer networks Industry and Engineering Chemistry Research 0 (1)