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CHEMICAL ENGINEERING TRANSACTIONS

VOL. 39, 2014

A publication of

The Italian Association

of Chemical Engineering

www.aidic.it/cet
Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Peng Yen Liew, Jun Yow Yong

ISBN 978-88-95608-30-3; ISSN 2283-9216 DOI: 10.3303/CET1439240

Please cite this article as: Pan M., Bulatov I., Smith R., 2014, Recent methods for retrofitting heat exchanger networks with

heat transfer intensifications, Chemical Engineering Transactions, 39, 1435-1440 DOI:10.3303/CET1439240

1435

Recent Methods for Retrofitting Heat Exchanger Networks

with Heat Transfer Intensifications

Ming Pan*, Igor Bulatov, Robin Smith

Centre for Process Integration, The University of Manchester, Sackville street, Manchester, M13 9PL, UK

ming.pan@manchester.ac.uk

This paper presents an overview of recent optimization approaches for retrofitting heat exchanger

networks (HENs) with heat transfer intensified techniques. The developed methods includes the heuristic

rules for finding suitable enhanced exchangers in HENs, and the SA-based optimization method and

MILP-based iterative mathematical programming method for optimizing HEN retrofit problems. An

industrial case is investigated with the different optimization methods in several typical retrofit scenarios,

providing a better understanding of implementing intensification techniques in suitable exchangers to

achieve the best energy saving in a whole retrofitted HEN.

1. Introduction

The most efficient way to decrease energy consumption and the release of greenhouse gases from the

process industries is to increase heat recovery. The cleanest energy is the energy saved by improved

efficiency. In major process industries including oil refining, petrochemical processes, food, cement, steel,

pulp and paper, where very substantial energy savings can be made. Calculations indicate that the energy

consumption could be decreased by 30 % purely by using intensification technology in the critical parts of

the heat recovery system (Pan et al., 2012). Various new ways have recently been developed to

significantly enhance heat exchanger performance. These techniques do not need to be applied through

the whole heat recovery system, but mainly at those critical parts that limit the system performance.

Recently, the approaches of implementing heat transfer intensification techniques have be considered in

more details. Pan et al. (2011) firstly proposed a novel MILP-based method to solve HEN retrofit problems

with intensified heat transfer techniques. Wang et al. (2012a) proposed a detailed model for predicting

exchanger performances and developed five heuristic rules to identify suitable heat exchangers for

intensification. For modelling detailed intensified techniques, Pan et al. (2013a) focused on the recent

achievements of tube-side and shell-side enhancement techniques, considered different techniques in the

same cases to compare their performances, and investigated their combinations. Intensified heat transfer

techniques are also considered to reduce fouling effect in enhanced exchangers (Pan et al., 2013b). To

combine the advantages of intensification and the conventional retrofit methods, Pan et al. (2013c)

successfully found valid retrofitted structures for retrofitting HEN with heat transfer intensification, which

can achieve significant energy saving without expensive cost from too many modifications. Sreepathi and

Rangaiah (2014) proposed several exchanger reassignment strategies for HEN retrofitting. One of those

was developed and used in multi-objective optimization. Liu et al. (2014) applied hybrid genetic algorithm

to obtain the optimal retrofitted HEN with full utilization of the existing heat exchangers and structures.

Kang and Liu (2014) presented a retrofitting approach for heat exchanger networks (HENs) for single-

period and multiple-period operations, aiming at the improvement of operation flexibility of HENs.

Based on the aforementioned researches, this paper provides an overview of recent optimization

approaches for retrofitting heat exchanger networks (HENs) with heat transfer intensified techniques. The

conventional approaches (heuristic based, simulated annealing based and MILP-based) are investigated

in an industrial case study to illustrate their efficiencies of solving HEN retrofit problems with heat transfer

intensification.

1436

2. Conventional approaches of retrofitting HENs with heat transfer intensification

The existing methods for retrofitting HENs can be divided into three categories, thermodynamic analysis

(e.g. Heuristic Rules), stochastic optimization methods (e.g. Simulated Annealing), and deterministic

programming methods (e.g. MILP). The optimization procedures and required models of the most efficient

approaches based on the above categories are briefly introduced in this section. More details of these

methods have been reported by Wang et al. (2012a), Wang et al. (2012b) and Pan et al. (2012).

2.1 Heuristic rule approach
The heuristic rules proposed by Wang et al. (2012a) are used to consider aspects of the reduction in the

use of utilities, and the selection of suitable heat exchangers to be enhanced. Retrofit problems can be

dealt without involving complex calculations. The optimization procedure includes five steps (namely five

rules):

 Rule 1: searching for exchangers in utility path. The candidates for intensification should be on

utility path. The exchangers on the same stream with a utility exchanger can affect the duty of the utility

exchanger directly.

 Rule 2: sensitivity analysis. Based on the heat exchangers selected with Rule 1, sensitivity tables are

used to quantify impact of heat transfer intensity on utility consumption of the HEN. High sensitivity

exchanger can be a good candidate for intensification.

 Rule 3: checking pinching match. Pinching match is the bottleneck of heat recovery network.

Normally, the pinching match will have a very small heat transfer temperature difference.

 Rule 4: enhancing candidates in sequence. Once the best exchanger selected based on Rule 2 is

enhanced, sensitivity analysis (Rule 2) is applied again to all candidate exchangers to find the next

best one.

 Rule 5: enhancing pinching match. Enhancing pinching match can be considered in the situation of

no good candidate for the heat transfer enhancement, or the potential for energy savings from

enhancing promising candidates may be very low.

Based on the heuristic rules 1-5, suitable candidates in HEN are selected, and the optimal solution of HEN

retrofit can be obtained.

2.2 Stochastic optimization method
Stochastic optimization methods are optimization methods that generate and use random variables.

Simulated annealing (SA) is a generic probabilistic metaheuristic for the global optimization problem of

locating a good approximation to the global optimum of a given function in a large search space. The SA-

based optimization method adopted in this paper is based on the approach proposed by Wang et al.

(2012b).

In the SA method, continuous variables include exchanger duties, stream flowrates, stream temperatures,

and exchanger heat transfer coefficients; while discrete variables include adding intensification techniques,

deleting intensification techniques. Thus, adding intensification techniques and deleting intensification

techniques are described as the SA moves, which can create a network with a small random difference

from the trial situation as follows:

 Intensification is randomly added to tube side or shell side or both in an exchanger with an increasing

ratio of heat transfer coefficient.

 The maximum increasing ratio of heat transfer coefficient according to enhancement device is

described in constraints. Moreover, the maximum number of exchangers to be enhanced can be set as

too many modifications on exchangers are not common in practical industry.

 The objective function is to minimize the energy consumption or the total retrofit cost of networks.

 After a SA move is made, the new network will be accepted if the objective value is improved;

otherwise, the new network will be denied.

Repeat the above procedure in a sufficient long computing time, an optimal retrofitted network with heat

transfer intensification can be found.

Two calculation approaches (duty-based and area-based) are used for determining heat exchanger

performances. In duty-based approach, the inlet temperatures, stream capacities and heat load in an

exchanger are known, thus exchanger area can be calculated directly from Eq(1)-Eq(3), where EX is the

set of all exchangers, HTIex, HTOex, CTIex and CTOex are inlet and outlet temperatures of hot and cold

streams in exchanger ex, Qex is the duty of exchanger ex, HFCPex and CFCPex are heat-flow capacities

(the multiplication between heat capacity and flow-rate) of hot and cold streams in exchanger ex, LMTDex

is the logarithmic mean temperature difference of exchanger ex, EXAex is area of exchanger ex, and Uex is

the heat transfer coefficient of exchanger ex.

1437

ex
exex

HFCP

Q
HTIHTO 

, EXex 
(1)

ex
exex

CFCP

Q
CTICTO 

, EXex 
(2)

exex

ex
ex

LMTDU

Q
EXA




, EXex 
(3)

In area-based approach, exchanger area is known and fixed, but heat load (Qex) is unknown. The

calculation of heat load (Qex) requires a iterative procedure of Eq(1)-Eq(3), and an estimated value of heat

load is needed in the initial condition. Even though the area-based approach leads to a longer computing

time, it presents practical HEN retrofit process with heat transfer intensification directly, and avoids

minimum approach temperature violation.

2.3 Deterministic programming method
A deterministic algorithm is an algorithm which, given a particular input, will always produce the same

output, with the underlying machine always passing through the same sequence of states. MILP-based

iterative methods proposed by Pan et al. (2012) have been widely used for retrofitting HENs with heat

transfer intensification recently. The optimization approach includes an MILP-based model and an iteration

algorithm.

First of all, logarithmic mean temperature difference (LMTD) is initialized with initial stream temperatures,

as shown in Eq(4), where HTI’ex, HTO’ex, CTI’ex and CTO’ex are inlet and outlet initial temperatures of hot

and cold streams in exchanger ex.

   
    

exexexex

exexexex
ex

ICTOHT/OCTIHTln

ICTOHTOCTIHT
DLMT




 , EXex  (4)

Then, a set of binary variables is proposed: EEXex =1, if an intensification technique is implemented in

exchanger ex; otherwise, it is 0. Thus, the heat transfer coefficients of intensified exchangers can be

formulated as:

 
exexex

EEXMINUU  1 , EXex  (5)

 
exexex

EEXMAXUU  1 , EXex  (6)

where MAXUex and MINUex are the upper and lower bounds of heat transfer coefficient when a

intensification technique is implemented in exchanger ex.

The constraints of heat transfer (HBAex and HBBex) and energy balance (AEBex and BEBex) in an

exchanger are shown in Eq(7)-Eq(10).

 
exexexexexexex

DLMTUEXAHTOHTIPHFCHBA  , EXex  (7)

 
exexexexexexex

HTOHTIPHFCDLMTUEXAHBB  , EXex  (8)

   
exexexexexexex

CTOCTIPCFCHTOHTIPHFCAEB  , EXex  (9)

   
exexexexexexex

HTOHTIPHFCCTOCTIPCFCBEB  , EXex  (10)

The minimum temperature difference (∆Tmin) is restricted in Eq(11) and Eq(12).

min
TCTOHTI

exex
 , EXex  (11)

min
TCTIHTO

exex
 , EXex  (12)

The stream temperature differences (DAHTIex and DBHTIex) are presented in Eq(13) and Eq(14). Other

temperature differences, such as DAHTOex, DBHTOe, DACTIex, DBCTIex, DACTOex and DBCTOex are

formulated in the same way.

1438

exexex
IHTHTIDAHTI  , EXex  (13)

exexex
HTIIHTDBHTI  , EXex  (14)

Eq(15) presents energy saving (QS) after in the retrofit, where EXhu and EXcu are the set of all exchangers

consuming hot and cold utilities; OCTIex and OHTIex are the original inlet temperatures of cold stream and

hot stream in exchanger ex before retrofit.

     



cuhu EXex

exexex
EXex

exexex
HTIOHTIPHFCOCTICTIPCFCQS

(15)

The objective of the MILP-based method is to minimize the summation of difference in energy balances,

heat transfers and stream temperatures with the restrictions of an estimated energy saving value (QS’), as

shown in Eq(16) and Eq(17).

SQQS  (16)

   

   




















 



 



EXex EXex
exexexexexex

EXex
exex

EXex
exexexex

BEBAEBDBHTODAHTODBHTIDAHTI

HBBHBADBCTODACTODBCTIDACTIObj

(17)

The MILP-based model for maximum energy saving consists of an objective function given in Eq(17) and

model constraints given from Eq(4)-Eq(16).

Since the MILP-based model has been built, an iteration algorithm (two iteration loops) is used to find the

optimal solution for HEN retrofit problems. In the first loop, the MILP-based model is solved repeatedly to

obtain a feasible solution for HEN retrofit under certain energy saving. In the second loop, the maximum

value of energy saving is searched, and the feasible solution under the maximum energy saving can be

found by using the procedure proposed in the first loop.

3. Case study

Figure 1: An industrial scale HEN for the case study

H 9

H10

H11

H Hot stream: HU Hot utility: C Cold stream: CU Cold utility:

1439

The example investigated in this paper is an industrial scale HEN, as shown in Figure 1. The retrofit

objective is to reduce the hot utility (HU) consumption, namely, reduce the heat duty of heat exchanger 30

(target exchanger). The stream data and initial exchanger data can be found in Tables 1 and 2. Moreover,

the heat-flow capacities of hot utility and cold utility are 93 kW/ºC and 9,652.5 kW/ºC, the inlet

temperatures of hot utility and cold utility are 1,500 ºC and 12.45 ºC, the minimum temperature difference

approaches (∆Tmin) before and after heat transfer intensification are 19 ºC and 5 ºC.

Table 1: Stream details in case study

Stream C1 C2 C3 H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11

FCP

(kW/ºC)
323 358.5 474 14.2 181.5 113 100 22.2 39.5 28.0 176 24.5 25.0 69.6

Tin (ºC) 33.5 91.34 151 335 253.2 294 212 213 174 364 290 284 240 179

Tout (ºC) 95.6 157.3 352 69.4 116.1 130 156 61.7 43.3 65.6 211 65.6 57.8 69.3

Table 2: Exchanger details in original HEN

EXs
HTIex
(ºC)

HTOex

(ºC)

CTIex

(ºC)

CTOex

(ºC)

LMTDex

(ºC)

EXAex

(m
2
)

Uex

(kW/m
2
·ºC)

Duty

(kW)

1 117.220 66.284 33.510 40.523 51.660 174.990 0.12509 1130.8

2 131.237 130.000 14.194 14.208 116.416 11.666 0.10292 139.8

3 174.400 76.670 33.510 57.450 74.024 116.660 0.44702 3860.3

4 284.200 174.731 156.731 162.390 54.291 174.990 0.28230 2682.0

5 212.440 156.050 48.986 66.454 125.521 100.000 0.44880 5633.4

6 174.444 85.701 66.454 85.606 45.500 650.000 0.20884 6176.5

7 66.284 61.670 12.998 13.009 50.939 20.000 0.10054 102.4

8 76.670 62.200 12.527 12.586 56.573 30.000 0.33677 571.6

9 62.200 43.330 12.450 12.527 39.535 55.560 0.33933 745.4

10 171.093 57.780 12.586 12.880 90.200 277.800 0.11305 2832.8

11 85.701 69.300 12.880 12.998 64.218 55.560 0.31994 1141.5

12 169.050 117.220 85.606 89.174 52.070 22.224 0.99432 1150.6

13 221.101 147.201 89.174 95.590 87.473 38.060 0.62153 2069.2

14 147.201 65.560 13.009 13.246 86.996 85.720 0.30654 2285.9

15 109.340 69.440 13.246 13.304 74.344 42.860 0.17781 566.6

16 198.376 131.237 91.340 133.665 51.308 128.580 1.15000 7586.7

17 335.400 109.340 91.340 109.248 82.246 207.690 0.18792 3210.1

18 174.731 139.686 121.457 123.852 31.809 207.690 0.12996 858.6

19 139.686 65.560 13.304 13.492 83.862 138.460 0.15640 1816.1

20 206.228 141.852 123.852 156.444 31.243 1384.600 0.27010 11684.2

21 178.700 174.444 156.444 157.270 19.665 27.692 0.54395 296.2

22 212.680 169.050 151.050 153.093 34.741 83.076 0.33560 968.6

23 240.070 171.093 153.093 156.731 42.634 41.538 0.97373 1724.4

24 253.200 206.228 162.390 180.376 57.110 1038.450 0.14375 8525.4

25 222.747 210.900 13.978 14.194 202.682 66.660 0.15433 2085.1

26 293.700 198.376 180.376 203.101 44.923 299.970 0.79934 10771.6

27 248.975 221.101 203.101 204.747 29.175 233.310 0.11466 780.5

28 290.380 222.747 204.747 229.860 35.065 1020.000 0.33281 11903.4

29 364.260 248.975 229.860 236.670 57.142 240.000 0.23538 3228.0

30 1500.000 912.546 236.670 351.930 891.221 180.000 0.34056 54633.2

31 141.852 116.050 13.492 13.978 114.751 60.000 0.68018 4683.1

In this case study, three typical optimization approaches are used to solve the retrofit problem. They are

heuristic rule approach (Wang et al., 2012a), SA optimization approach (Wang et al., 2012b), and MILP-

based iterative approach (Pan et al., 2012). Intensified technique is implemented to directly increase the

overall heat transfer coefficients of enhanced exchangers. It is assumed that the maximum intensified

coefficient of each exchanger is two times of its original value. The optimal solutions based on the three

optimization approaches are shown in Table 3.

As presented in Table 3, heat transfer coefficients increase in the intensified exchangers, all exchangers

remain unchanged area, and the optimal solution based on the MILP-based approach requires less

1440

computing time and give the best solution. It is noted that the MILP-based method can quickly find the

most appropriate heat exchangers for intensification.

Table 3: Optimal solutions based on the three optimization approaches

Optimization approaches Intensified exchangers (U: kW/m
2
·°C)

Energy

saving (kW)

Computing

time

Heuristic rule approach

(Wang et al., 2012a)

EX20 (0.348), EX24 (0.155), EX26

(1.2), EX28 (0.448)
1904.2

optimization

approach

(Wang et al.,

2012b)

Duty-based
EX4 (0.407), EX20 (0.3), EX23

(1.444), EX28 (0.413)
1118.6 2~3 h

Partial area-

based

EX4 (0.367), EX6 (0.211), EX12

(1.092), EX18 (0.151), EX28 (0.407)
929.0 22~24 h

Area-based
EX20 (0.397), EX24 (0.195), EX26

(0.878), EX28 (0.425), EX29 (0.336)
2114.0 22~24 h

MILP-based iterative approach

(Pan et al., 2012)

EX20 (0.385), EX24 (0.192), EX26

(0.851), EX28 (0.442), EX29 (0.35)
2161.4 < 1 min

4. Conclusions

Many conventional optimization approaches have been widely studied for retrofitting HENs with heat

transfer intensification. However, most of the reported methods are still in the research stage and far from

being used in industrial application. In this paper, the existing typical optimization approaches are

compared and used to solve an industrial scale problem. The MILP-based iterative approach has been

demonstrated to be more efficient for the bottlenecking of HENs with the systematic application of

intensified heat transfer compared with the heuristic rule approach and SA optimization approach.

Acknowledgement

Financial support from EC ENERGY.2011.5.1-1 (282789) CAPSOL Design Technologies for Multi-scale

Innovation and Integration in Post-Combustion CO2 Capture: From Molecules to Unit Operations and

Integrated Plants are gratefully acknowledged.

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