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Energy 36 (2011) 2381e2391
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Energy
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Heat exchanger networks retrofit with considering pressure drop by couplinggenetic algorithm with LP (linear programming) and ILP (integer linearprogramming) methods
Hadi Soltani a,b, Sirous Shafiei a,b,*a Faculty of Chemical Engineering, Sahand University of Technology, PO Box 51335/1996, Tabriz, Iranb Environmental Engineering Research Center (EERC), Sahand University of Technology, PO Box 51335/1996, Tabriz, Iran
a r t i c l e i n f o
Article history:Received 18 August 2010Received in revised form13 December 2010Accepted 12 January 2011Available online 26 February 2011
Keywords:Heat exchanger networks (HENs)RetrofitPressure dropGenetic algorithm (GA)Linear programming (LP)Integer linear programming (ILP)
* Corresponding author. Faculty of Chemical EnginTechnology, PO Box 51335/1996, Tabriz, Iran. Tel.: þ93444355.
E-mail address: [email protected] (S. Shafiei).
0360-5442/$ e see front matter Crown Copyright � 2doi:10.1016/j.energy.2011.01.017
a b s t r a c t
This research is trying to develop a new procedure for retrofit of HENs including pressure drop usinggenetic algorithm (GA) coupled with linear programming (LP) and integer linear programming (ILP)methods. The GA is used to produce structural modifications whereas continuous variables are handledusing a converted NLP formulation for Maximum Energy Recovery (MER). The converted NLP consists ofan LP for MER with adding a search loop to find the best minimum approach temperature and split ratioswhich are easier to solve.
To prevent complexity and ensure optimum solution, the pressure drops of streams are calculatedfrom the results of LP and then a modified ILP problem is solved to determine the maximum profit ofretrofit of HENs. The motivation of the ILP is decision making for elimination or reuse of currentexchangers and pumps and/or introducing new ones to the network. Results show that the proposedmethod often finds better solutions than those reported in the literature.
Crown Copyright � 2011 Published by Elsevier Ltd. All rights reserved.
1. Introduction
The study of retrofit procedures for heat exchanger networkshas been subject of numerous research works, due to the largesavings that can be achieved in utility and also electricalconsumption costs especially after the 1990s.
It is obvious that early works done in literature on networksretrofit focused on the cost and area estimation of the additionalexchangers required to achieve the new process conditions,without considering the layout of the existing network. One of thefirst works of this kind was proposed by Tjoe and Linnhoff [1,2] inwhich two steps were considered for HENs retrofit. Retrofit tar-geting is determined in the first step and modifications are carriedout next. The drawback of this method is that there is no generalrule for area distribution within a network in the design stepespecially in larger networks.
Mathematical programmingmethods by Yee and Grossmann [3]and combination of pinch and optimization methods [4e6] wereused for retrofit of HENs. Yee and Grossmann [3] developed a two
eering, Sahand University of8 412 3459142; fax: þ98 412
011 Published by Elsevier Ltd. All
step approach in which the first step was a mixed integer linearprogramming (MILP) prescreening for determination of theeconomic feasibility of the retrofit project and a mixed integernonlinear programming (MINLP) formulation was then applied tofind the optimized network. Because of the incorporation of addi-tional details, different types of binary variables are needed in theirMINLP formulation which only complicates the model. Meanwhilein the method of Asante and Zhu [4,5] and Zhu and Asante [6],sequential MILPs are solved until a desired energy recovery isobtained. After finding the final structure, a nonlinear program-ming (NLP) model is solved to minimize the total annual cost of thenetwork and to determine the best configuration of streams.
Refs. [7,8] combined pinch technology and exergy analysis tosolve the retrofit of HENs Problems. Panjeshahi et al. [7] used thistechnique to perform a retrofit study of an ammonia plant, toimprove energy efficiency whereas Wang et al. [8] applied it tosolve the heat pocket on the grand composite curve of a process’sHEN Problems to improve its efficiency. The main strategy was toreplace the higher quality process hot streams with a lower qualityutility in the pocket to exchange heat with the cold streams, and touse disengaged streams to generate high quality utilities. Thereforewhen energy in the pocket is large, the temperature difference ofthe hot and cold streams in the pocket is large, and there are twolevels of utilities available in the temperature interval, the energy
rights reserved.
Finding opt. y and ΔTmin
Solving the modified LP
For MER
No
No
G.A.
Calculating pressure
drops of streams from
the results of LP
Maximum Profit?
Termination?
Yes
Yes
Solving the modified
ILP for Assignment
Fig. 1. The overall algorithm for HENs retrofit.
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e23912382
recovery in the pocket can be implemented to improve the energyperformance of the system. Kralj [9] applied the stage-wise modelof superstructure representation, as proposed by Yee and Gross-mann for retrofit of HENs. This method is general so it can be usedin new designs as well as during existing process integration.
Since solving HENs either sequentially or with simultaneousformulations is NP-hard [10] it limits the usefulness of determin-istic methods such as GBD, OA and etc. thus stochastic methods likeSimulated Annealing, Swarm Algorithms, Ant Colony Optimization,tabu search and genetic algorithms are more useful approaches fortackling such problems.
HENs retrofit using stochastic methods was first suggested byAthier et al. [11] in which simulated annealing (SA) was coupledwith an NLP method where structural parameters were modifiedby SA and continuous ones were handled in the NLP section. ThenBochenek and Jezowski [12] and Jezowski et al. [13] proposeda method based on the GA and the network pinch concept andoptimized both integer and continuous parameters by the GA. Itseems that genetic algorithm is suitable for structural optimizationbecause of its discrete nature and strong ability for complete searchof the solution space without being trapped at local optima.Therefore Rezaei and Shafiei [14] considered a new method toretrofit HENs using this concept by coupling GA, NLP and ILP. In thismethod the GA produces different networks during the optimiza-tion process and finds the best structural modifications. The NLP isformulated based on maximum energy recovery (MER) anddetermines the heat loads of exchangers and finally an ILP is addedto the algorithm to find out which one of the current units must beeliminated, reused or relocated. Also decision to purchase newexchangers is justified in this section. Themajor objective of retrofitproblems is the reduction of the utility consumption, electricalcharges, full utilization of the existing exchangers and pumps andidentification of the required structural modifications. The maindrawback of these methods is that they ignore the pressure dropeffects and pumping cost of streams during the retrofit process.
Ignoring pressure drop relation with heat transfer coefficientand exchanger area leads to the networks which are not feasibleeventually. Thus for the first time Polley et al. [15] incorporated therelationship between pressure drop, film coefficient and area intothe retrofit procedure. However, during the targeting stage, theyconsidered only the existing network area and not its distributionamong the existing exchangers, thus leaving out an importantconstraint. Nie and Zhu [16] proposed a method in which aftermodifications to recover a certain amount of heat, the exchangersare classified into two groups. The first group needs no extra areawhile the second one needs extra area or shell. Therefore twoseparate models were used for each.
For the first group, pressure drop is ignored and for the secondone a hyper structure to optimize the pressure drop is considered.The exchangers are regrouped after optimization and the calcula-tions continue until no change in members of each group isobserved. Silva and Zemp [17] considered the distribution of heattransfer area and pressure drop with variable heat transfer coeffi-cients in retrofit. In this work, the traditional HEN retrofit proce-dure was modified so that the problem was described asa nonlinear model, and the additional area required for the newnetwork condition and available pressure drop were estimatedbased on economic optimization. Panjeshahi and Tahouni [18] usedpinch technology with considering pressure drop to solve thedebottlenecking of the HEN problems. Their concept was to studythe association of pumps and compressors cost together with therequired additional area and operational cost. The overall optimi-zation was targeted at increasing plant throughput.
Since simultaneous involvement of pressure drop, heat transfercoefficient and exchanger area converts the problem to the MINLP
and/or NLP Problems which is too difficult to solve or converge [19],so in this paper a method based on the work of Ref. [14] is proposedin which cost of pump of streams is introduced into the optimiza-tion and retrofit of HENs.
This paper addresses the problem of the revamping of HENsconsidering pressure drop costs using combination of geneticalgorithm, LP and integer linear programming (ILP) methods inwhich GA produces different networks during the optimizationprocess and finds the best structural modifications. The LP isformulated based on maximum energy recovery (MER) anddetermines heat loads of exchangers. One is able to calculate thearea of new units and stream pressure drop knowing exchangerarea and other required parameters after utilization of the LP.
To consider pumps in the current network and using those inthe optimized network, some new constraints are added to theprocedure of Ref. [14]. These constraints are used so that all pumpsare used in the revamped network and if necessary new pumps areadded to compensate for the additional pressure drop.
This paper is organized in the following manner: problemstatement is first presented in Section 2 while Section 3 brieflydescribes the proposed methodology that has been used by Ref.[14]. Modified Structural optimization, LP and ILP models areexplained in Sections 4 and 5 and application of the approach isillustrated by three examples in Section 6. Section 7 concludes andgives some suggestions for improving the method.
2. Problem statement
In the retrofit of heat exchanger networks, inlet and outlettemperatures of process and utility streams, heat capacity flowrates and heat transfer coefficients of the streams are known. Hotand cold utilities are available as external sources for cooling andheating of the process streams.
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e2391 2383
In order to calculate the pressure drops, four physical propertiesare needed. These are specific heat capacity (Cp), density (r),viscosity (m), and thermal conductivity (k). In addition, some char-acteristics related to the exchanger structures and a set of cost datashould be included. Finally the structure of an existing network isgiven while the objective is to achieve the maximum heat recovery(MHR) for the minimum investment for structural modifications.The best tradeoff between MHR and minimum investment cost isequal tomaximumprofit of the retrofit project. The investment costcan be considered for purchasing of new exchangers and pumps,relocation of the existing units (exchangers and pumps), addition ofarea to the current exchangers and piping aspects.
To avoid complexity of the problem and ensure convergence, inILP section piping cost is ignored.
3. Methodology
The overall algorithm of the proposed method is shown in Fig. 1inwhich themain objective is themaximization of the profit. In thisfigure, optimization is started with an initial population which isproduced by the GA. In the next step, networks are evaluated by theLP and using the results the pressure drop of streams is calculated.Then using ILP the network is modified to achieve maximum profitby balancing investment cost and operating cost.
The LP section consists of an LP and a search loop. The LP is usedfor MER and the search loop is used to find the best minimumapproach temperature (DTmin) and split ratios (yi) within thenetwork. In this work split ratios are bounded to [0.1e0.9] whereasthe search range for DTmin is set to [0.1, 30 �C].
After solving the LP, heat loads of each match and area of newexchangers are available so at this step pressure drop in both tubeside and shell side can be calculated knowing exchanger area andassumption of constant heat transfer coefficients (h).
Taking (h) to be constant, may affect the cost of final network intwo ways. If the real (h) is larger than assumed, calculated area ismore but pressure drop is less than real area and pressure drop.Accordingly the two effects neutralize each other to some extentand the effect of assuming constant (h) on the overall cost isreduced since both have nearly the same order of magnitude.
The next step is using pumps and exchangers in the newnetwork so that less investment cost is needed and maximumprofit can be obtained. To do this a modified ILP method is used. It
E1
1st gene 2nd gene 3r
H1
H2
H3
E2
E3
E4
E5
E6
a
Fig. 2. (a) HEN with seven e
determines whether for a match within the network, a newexchanger must be purchased or an existing one can be reassignedand also weather pumps are sufficient to supply required pressureor new pumps must be purchased.
In fact the ILP calculates the minimum modification cost for thenetworks which are produced by the GA. These costs are used asa criterion for the optimization of the (DTmin) and split ratios (yi).They are also utilized in the calculation of the profit of HENs duringthe structural optimization.
After determination of the fitness of the first generation, thesecond one is produced using genetic algorithm operators whichare reproduction, crossover and mutation. The overall algorithmmay be repeated for a specified number of generations or stoppedwhen the desired solution is obtained. The next section explainsthe method for HEN retrofit.
4. Structural optimization
In the present method an HEN is treated as a chromosome andexchangers are considered as a sequence of genes. Therefore eachgene includes the address of one ormore exchangers. For addressingthe location of the exchangers, node representation is used.
This kind of addressing is usual and Asante and Zhu [4,5], Zhuand Asante [6], Bochenek and Jezowski [12], Jezowski et al. [13],Rezaei and Shafiei [14] and Lewin et al. [20], have used it.
The number of splitters and their branches are function of anexisting structure and the size of the problem. Some modificationshave made it possible to produce networks with different config-urations. It is to be noted that as number of branches increases theconfiguration gets more complex and the run time increases.
For showing the location of exchangers in the network anexchanger address matrix (EAM) is defined in which each row is anaddress of an exchanger. Fig. 2 shows a network and its EAM withthree genes, three hot and two cold streams.
In the EAM the first column is the hot stream, the 2nd onerepresents the gene number of the hot stream and the 3rd is thenode number of the hot stream. The 4th, 5th and the 6th are similarnumbers for cold streams.
As observed in Fig. 2, if splitting occurs in a gene, the nodes ofa splitter are numbered from 2 to the one more than the number ofbranches otherwise the number of each node will be 2. Thisrepresentation is specially suited for GA operators and always
C2
d gene
C1
E7
E1 : 1 1 2 1 1 2
E2 : 2 2 2 2 2 4
E3 : 3 2 2 2 2 3
E4 : 1 2 2 2 2 2
E5 : 2 3 3 2 3 2
E6 : 2 3 2 1 3 3
E7 : 3 3 2 1 3 2
b
xchangers; (b) its EAM.
Table 1Stream data for case study 1.
Stream Tin (�C) Tout (�C) h (kW/m2 �C) MCp (kW/K)
H1 175 45 0.2 10H2 125 65 0.2 40C1 20 155 0.2 20C2 40 112 0.2 15CU 15 25 1.5HU 180 179 2.5
Table 3Economic data for case study 1.
Items Cost data Remarks
Heat exchanger capital cost ($) 30,000þ 750A0.81 A in m2
Pump capital cost ($) 2000þ 5(MDP/r)0.68 DP in Pa, r inkg/m3, M¼ kg/s
Reassignment cost of anexisting pump or exch. ($)
300
Plan lifetime (yr) 2 yearUnit cost for hot utility ($) 120 per kW yearUnit cost for cold utility ($) 10 per kW yearCost of power ($/kW h) 0.05Pump efficiency 70%Plant operation (h/yr) 8000Interest rate (%) 10
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e23912384
creates feasible structures. Three operators are considered to reachmaximum profit: reproduction, crossover and mutation.
5. LP and ILP procedures
5.1. LP formulation
Amulti objective functionwas defined to relax some exchangersfrom pinching atDTminwhile achievingMER. The objective functionof the LP is:
MaximizeXno: of exch:
i¼1
qi þ X2ðno: of exch:Þ
i¼1
DT
!,S:F: (1)
where qi is the heat load of exchangers and DT is the approachtemperature in hot or cold end of the exchangers. S.F. is a scalingfactor and must be large enough to ensure that the second term inequation (1) does not affect the main objective which is MER.
The constraints for the above objective function are:
a) Energy balance for each exchanger on hot and cold streams.(Nonlinear if splitting occurs)
b) Energy balance for hot and cold utilities. Heaters and coolersare included in the formulation and if they are not needed, theoptimization sets their loads to zero. (Linear)
c) Mass balance for splitters. (Linear)d) Monotonic decrease or increase of temperatures on streams.
(Linear)e) Hot and cold end approach temperatures must be equal or
greater than DTmin in each exchanger including utilityexchangers. (Linear)
f) Energy balance at mixing points. (Linear)
H1175
45E2
5.2. Pressure drop effect
Polley et al. [15] developed a general relationship betweenfractional pressure drop and convective film heat transfer coeffi-cient as follows:
DP ¼ KAhm (2)
where DP is the exchanger pressure drop, A is the heat transfer areaand h is the film heat transfer coefficient. It has been shown that,although different exchanger geometries give relationships of thisform, the value ofm varies from geometry to geometry. In this work
Table 2Physical properties for case study 1.
Stream r (kg/m3) m (kg/m s) k (W/m �C) Cp (J/kg �C)
H1 716 2.40E�04 0.11 1658H2 777 2.30E�04 0.11 2684C1 700 2.30E�04 0.12 2456C2 680 2.30E�04 0.13 2270
we assume that all the exchangers of the network are of the samegeometry and type (counter flow single-pass shell single-pass tubeexchangers). Shenoy [21] developed equations of the type of Eq. (2)based on the detailed BelleDelaware method. The equationsderived by Ref. [21] are used in this paper. Hence, for turbulent flowin shell and tube exchangers, the equation for the tube side is:
DPt ¼ KtAh3:5t (3)
and for the shell is:
DPs ¼ KsAh5:1s (4)
where t and s stand for tube and shell respectively. The parametersKt and Ks depend on the geometry and the physical properties ofthe streams. Typical expressions for these parameters are [21]:
Kt ¼ 1=ð0:023Þ2:5�D1=2 � m11=6t � 1
Mtrtk7=3t Cp7=6t
� DDt
���
mtmtw
��0:14�4:5ð5Þ
Ks ¼67�Ltp�
�Ltp�Dt
��D1:1e �m1:3s
Dt�Ms�rs�k3:4s �Cp1:7s
���
msmsw
��0:14�6:2(6)
The equivalent diameter can be calculated as [21]:For triangular pitch:
De ¼ 4�30:5=4$L2tp � p=8$D2
t
.ðp=2$DtÞ (7)
and for square pitch:
De ¼ 4�L2tp � p=4$D2
t
.ðp$DtÞ (8)
In the above equations Ltp is the tube pitch,M is the mass flow, Dis the internal diameter of the tubes, Dt is the external diameter ofthe tubes and De is the equivalent diameter of the tubes.
H2
C1
C2
CU2125
65
20
40112
HU1155
1320
1400
E1E4
E3
1080
85
1300
98
Fig. 3. Initial network of case study 1.
H1
H2
C1
C2
CU2
17545
12565
20
40112
HU1155
805
885
E new3
110.75 51.9
515
E2
E 1E 4
E 3
108.8
662
77.65
828.4
E new1E new2 98
251.6
638
Fig. 4. Resulting network by Shenoy [21].
Fig. 6. Average (below) and best solution (above) Profit vs. generation for case study 1.
Table 4Exchanger reassignment and area distribution in case study 1.
Matchno.
Exchangerassignment
Retrofitarea (m2)
Existingarea (m2)
Additionalarea (m2)
1 Enew 213.69 217.2 e
2 E3 287.24 268.7 18.543 E4 256.2 256.2 e
4 E1 707.4 358.9 348.55 Enew 34.74 e 34.746 Enew 5.9 e 5.97 E2 57.33 e 57.33
Table 5Pump reassignment in case study 1.
Matchno.
Pumpassignment
Retrofit pres.drop (Pa)
Existing pres.drop (Pa)
Additional pres.drop (Pa)
1 Pu1 74 35 392 Pu2 21 31 e
3 Pu3 81 43 384 Pu4 52 34 18
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e2391 2385
After obtaining dependence of the exchanger pressure drop tothe area and heat transfer coefficient of the exchanger, pressuredrop of each stream must be determined. While pressure drop ofa series of exchangers can be obtained by summing up individualpressure drops, overall pressure drop for parallel configuration ismore complex. This is because flow rate in parallel brancheschanges until the pressure drop equalizes in all branches. Shenoy[21] approximation can be utilized to overcome this problem. Inthis approximation it is assumed that pressure drop is dividedlinearly between each step proportional to the available area ateach step. So in this paper the similar approximations were used.
The area of each exchanger between hot streams i and/or hotutility and cold streams j and/or cold utility is given by:
Aij ¼qij
LMTD
1hi
þ 1hj
!; ci˛NH; j˛NC (9)
Aicu ¼ qicuLMTD
�1hi
þ 1hcu
�; ci˛NH (10)
Ahuj ¼qhujLMTD
1hhu
þ 1hj
!; cj˛NC (11)
Since above relations are not valid for exchangers with phasechange, heat transfer coefficients of cold and hot utilities should beconsidered as known. In this way equations can be developed fortotal area of hot and cold streams.
For hot streams:
ATi ¼Xj
Aij þ Aicu; ci˛NH (12)
And for cold streams:
ATj ¼Xi
Aij þ Ajhu; cj˛NC (13)
Assuming hot and cold streams flow through tubes and shellsrespectively and flow is turbulent single phase and single-pass shell
H1
H2
175
125
112
HU1155
566.8361.7
136.9 111.9
Enew E3
E2
125 6
112
112500
y1=0.23
y2=0.52
Fig. 5. Best network for case s
and single-pass tube exchangers, the equations for overall pressuredrop are as follows:
Pressure drop for hot streams:
DPi ¼ KtiATih3:5i ; ci˛NH (14)
Pressure drop for cold streams:
DPj ¼ KsjATjh5:1j ; cj˛NC (15)
These equations relate the film heat transfer coefficients to thepressure drop for each hot and cold streams. Besides, these values
C1
C2
CU1 45
65
20
40
512
233.2E1
74
1838.3
65.4
E4
Enew8.3
CU2
49.7
66.2 Enew
5
tudy 1 with DT¼ 13.1 �C.
Table 6Comparison of the results for case study 1.
Units Additionalarea (m2)
HU(kW)
CU(kW)
Paybacktime (yrs)
Saving(k$/yr)
Profit at twoyears ($)
Shenoy [21] 7 309 885 805 1.95 66.95 3347.5This work 7 465 361.7 282.9 1.014 134.82 132970
Table 7Stream data for case study 2.
Stream Tin (�C) Tout (�C) MCp (kW/K) h (kW/m2 �C)
H1 165 95 148 0.45H2 240 65 86.4 0.55C1 125 220 139 0.35C2 61 192 54 0.4C3 70 185 62 0.64
Table 8Physical property data for case study 2.
Stream r (kg/m3) m (cPs) k (W/m �C) Cp (J/kg �C)
H1 165 95 148 0.45H2 240 65 86.4 0.55C1 125 220 139 0.35C2 61 192 54 0.4C3 70 185 62 0.64
H1
H2
C1
C2
CU1165
95
24065
125
61192
HU1220
3460
8485
E4
C3HU3
CU2
5807
2790
18570
E3
E2
E1
2160 2560
7153
4340
Fig. 7. Initial network of case study 2.
H1
H2
C1
C2
CU1165
95
24065
125
61192
HU1220
2888
3408
E2
C3HU3
CU2
3283
18570
E4
Enew1 E3
7324
4513.1
1445.7
2473
3553.5HU2
2153.4
E5
E1
E6
E8
E7
Enew2
2616.9
Fig. 9. Best network for case study 2 with DT¼ 12.44 �C.
Table 9Exchanger reassignment and area distribution in case study 2.
Matchno.
Exchangerassignment
Retrofitarea (m2)
Existingarea (m2)
Additionalarea (m2)
1 E5 347.9 272.8 69.12 Enew 1361 e 13613 E3 724 724 e
4 E4 968.2 742 266.25 E2 596.1 588 8.16 E7 109.9 128.84 e
7 E8 146.9 218.2 e
8 E1 131.6 133 e
9 Enew 54 e 5410 E6 43.4 45.8 e
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e23912386
of pressure drop have to be less or equal to the maximum allowablevalues for the pressure drop of each stream (given). In the aboveequations DPi and DPj are the pressure drops for hot and coldstreams, ATi and ATj are the total contact area for hot and cold
H1
H2
165
240
192
HU1220
7108
HU3
128
185
E2
E1 EA E
1610
26
1927 2560
HU2
2158
Fig. 8. Final network by
streams, correspondingly. In this paper we assumed that the heattransfer coefficient, h in these equations is constant.
Since relations used for calculating pressure drop in the networkare nonlinear and non convex [19], if they are directly entered to theobjective function and the constraints, they convert the LP problemto a non convex NLP. Therefore to avoid complexity of the problemthe pressure drop is calculated after solving LP problem and it iscompared with allowable pressure drop. If pressure drop is greaterthan allowable one, a penalty term is added to the objective func-tion. This causes the probabilities of occurrence of structureshaving larger pressure drops to be reduced in the next generations.
5.3. ILP formulation
To consider the pumps required to overcome the pressure drop inthe retrofit problem, the followingobjective function and constraints
C1
C2
CU1 95
65
125
61
3460
E4
C3
CU2
3925
70
E3B
64
4994
4340
Silva and Zemp [17].
Table 10Pump reassignment in case study 2.
Matchno.
Pumpassignment
Retrofit pres.drop (kPa)
Existing pres.drop (kPa)
Additional pres.drop (kPa)
1 Pu4 62.65 29 33.652 Pu3 289.57 7.5 282.073 Pu5 184.6 141.2 43.44 Pu1 399.8 45.2 354.65 Pu2 137.55 139.5 e
Table 11Comparison of the results for case study 2.
Units Additionalarea (m2)
HU consumption(kW)
CU consumption(kW)
Silva andZemp [17]
11 410 9400 7385
This work 10 1758.4 8178.3 6171
Table 12Stream data for case study 3.
Stream no. Tin (�C) Tout (�C) MCp (kW/K) h (kW/m2 �C)
H1 180 30 72.8 0.511H2 270 40 137.8 0.497H3 350 30 41.6 0.463H4 380 50 174.2 0.489H5 150 100 790.4 0.577H6 290 190 462.8 0.470C1 20 390 624 0.373
Table 13Physical property data for case study 3.
Stream r (kg/m3) m (cPs) k (W/m �C) Cp (J/kg �C)
H1 700 0.3 0.12 2600H2 700 0.4 0.12 2600H3 750 0.5 0.12 2600H4 750 0.5 0.12 2600H5 630 0.2 0.12 2600H6 750 0.4 0.12 2600C1 800 1 0.12 2600
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e2391 2387
are defined. The objective function is to achieve theminimumcost ofmodifications for a specified level of energy recovery in a givenstructure and can be expressed as:
minXNm
j¼1
mj � Cn;j þXNex
i¼1
XNm
j¼1
zij � Ci;j þXNHþNC
i¼1
XNHþNC
j¼1
zpij
� Cpi;j; m; z; zp˛f0;1g (16)
In this formulation mj is used for purchasing a new heat exchangerfor the jth match and zij indicates the reassignment of the ithexisting exchanger to the jth match. zpij is a binary variable indi-cating use of pump of ith stream in the current network in jthstream in the optimized network, Cn,j is the purchase cost of thenew exchanger for jth match, Cpi,j is the purchase cost of the newpump to be connected in series with the jth stream pump and Ci,j isthe purchase cost of additional area required in using ith exchangerin jth match. Also Nm, Nex, NH and NC are the number of matches ofnew network, the number of existing exchangers in the initialnetwork and the number of hot and cold streams respectively.
H1
H2
H3
H4
H5
H6
180
270
350
380
150
290
390 HU1
144.7
231.6
172674553825894101656
E6
E5
E4
84.9112.6185.6227.09
191.6
Fig. 10. Initial network of case study
Four constraints are used for this model:
XNm
j¼1
zij � 1; i ¼ 1;.;Nex (17)
XNex
i¼1
zij þmj ¼ 1; j ¼ 1;.;Nm (18)
XNHþNC
i¼1
zpij ¼ 1; j ¼ 1;.;NHþ NC (19)
XNHþNC
j¼1
zpij ¼ 1; i ¼ 1;.;NHþ NC (20)
C1
30
40
30
50
100
190
20
CU2
CU3
88.9
139.4
30.6
662825134
4292
14426
4549
E2
E3
CU1
CU4
CU5
CU6
31591
14385
745.1
8762
70.9
E1
118.2
3 after increasing throughput.
Table 14Economic data for case study 3.
Items Cost data Remarks
Heat exchanger capital cost ($) 8600þ 670A0.83 A in m2
Cost capital cost ($) 8600þ 7310(qH0.5)0.2 H liquid head,m, q in m3/kg
Reassignment cost of an existingpump or exch. ($)
300
Plan lifetime (yr) 20Unit cost for hot utility ($/kW yr) 70Unit cost for cold utility ($/kW yr) 7Power cost ($/kWyr) 60Pump efficiency 70%Annualisation factor i(1þ i)N/[(1þ i)N� 1] N plant
lifetime, yrInterest rate (%) 15
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e23912388
The first constraint causes each exchanger to be assigned to only onematch. Second constraintmeans either purchase a newexchanger oruse an existing one. The third and the fourth constraints ensure usingthe existing pumps on only one stream of the new configuration.
As mentioned before, the best tradeoff between the cost ofmodifications and utility and electricity saving is used as a termi-nation criterion for finding the best DTmin and split ratios in the LPmodel. In addition, it is also utilized in the calculation of the fitnessof each network in the GA.
When Sections 4 and 5 are coupled together, one can carry outthe optimization algorithm shown in Fig. 1. This method was testedwith three case studies described in the next section.
6. Illustrative examples
Three examples from the literature were considered to validatethe proposed approach. The first and the second examples are fromShenoy [21] and Silva and Zemp [17] in order to compare thecurrent method and the retrofit method based on pinch technologyand combining mathematical programming and pinch technology,
H1
H2
H3
H4
H5
H6
180
270
350
380
150
290
390HU1
169
321.9
1395442506
E 5
E6
1
169
358
153.4166.4
447.3
208.1
461.3
8079
36803
46280
E 11
E 8
E 10
y1=0.264
y2=0.2
Fig. 11. Best network for case study 3 with
respectively. The third is crude pre-heat train and belongs to Pan-jeshahi and Tahouni [18] that deals with the problem of optimaldebottlenecking of HENs considering minimum total cost.
Programming was done in MATLAB which contains some of theoptimization functions and a number of codes for the process of theGA and decoding of the exchanger address matrices to form theconstraints of the optimization. Although MATLAB is easy and userfriendly, it is too slow for handling these types of problems. So theoriginal codes were compiled to C language and final codes wereloaded on Sahand University of Technology (SUT) computer centerin which five parallel computers having 2 GB of ram memory and3.4 GHz processor with a master one were used. The optimizationtime that corresponds to each case study was about 20, 35, 90 minwhich may be reduced by increasing the number of slavecomputers and improving their characteristics.
For all case studies counter current heat exchangers wereconsidered and possibility of up to four split on a stream wasprovided. In the following figures the heat loads of exchangers areshown by underlined numbers.
6.1. Example 1
This example has two hot and two cold streams witha maximum payback period of two years and no cost for exchangerreassignments. Stream data, physical properties and cost data areshown in Tables 1e3 respectively. (Note that the reassignment costof an existing pump and exchanger has not been considered inShenoy’s work [21]). The original network is shown in Fig 3.
Using pinch technology, Shenoy [21] reported a payback periodof 1.95 years and a profit of $3347.5 for an investment cost of$130,290 and a saving of 66,950 $/yr in the utility consumption. Thenetwork obtained by this method is shown in Fig. 4.
Using Shenoy’s [21] method heat transfer coefficients wereobtained to satisfy pressure drop constraints and so there was noneed to add extra pumps. Also somemodificationswere done in thearea of the networks to decrease pressure drop.
C1
30
40
30
50
100
190
20
CU1
CU2
CU3
49
1356
4249
5233
E3
E7
E1
56
68.5
.1
13491 9564
E 9
E 13
E 2
E4
71
39520 20683
46.7
97.6
95.5
y2=0.2 y2=0.427
3 split on cold stream with DT¼ 2.5 �C.
C1
H1153 30
H2
H3
H4
H5
H6
40
30
50
100
190
20
180
270
350
380
150
290
390
CU1
CU2
CU3
HU1
45
156
121
121181
40
122
95116
155
143148151176
283
357306
123567868
39520
10523
9529
19611568034607
46280
52556
1103
16029
3789
E 12
E 1
E 5
E 13
E 4
E 11
E 7
E 6
E10
E 3
E8
E9
E2
y=0.69 y=0.39 y=0.77
Fig. 12. The second best network for case study 3 with DT¼ 5.2 �C.
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e2391 2389
Using the method of this article, a network (Fig. 5) with sevenexchangers and two splitters was obtained with a profit of $132,970in two years. Fig. 6 shows the best solution and average profit ofpopulation vs. generation.
In this example all streams need extra pump except for hotstream no. 2. Tables 4 and 5 show uses of previous exchangers andpumps in the new configuration as well as added area andpurchased exchangers and pumps. Table 5 shows pressure drop ofexchangers which have been calculated assuming single-pass shellsand tubes and constant physical properties given in Ref. [21] andalso constant h.
Table 6 compares the results with two methods. This tableshows that although the heat transfer coefficients are assumedconstant but the obtained profit is much more than the profitreported in Ref. [21].
6.2. Example 2
This example was studied by Silva and Zemp [17]. In thisexample the retrofit procedure was applied to a five stream
Table 15Exchanger reassignment and area distribution in case study 3 for the best solution.
Match no. Exchangerassignment
Retrofitarea (m2)
Existingarea (m2)
Additionalarea (m2)
1 E11 8213 441.51 7771.492 E5 4103 2404.43 1698.573 E8 6199 746.67 5452.534 E10 939 955.52 e
5 E9 15,504 293.69 15,210.316 E13 3468 3015.15 452.857 E2 2031 1332.33 698.678 E4 866 823.64 42.369 E3 211 291.94 e
10 E7 372 372.45 e
11 E1 309 295.64 13.3612 E6 1743 1377.63 365.37
problem. Stream data are tabulated in Table 7. Table 8 gives thephysical properties for the streams. The existing network is shownin Fig. 7.
The objective is to reduce hot utility consumption from11,275 kW up to 9400 kW. The results obtained from the methodsuggested by Silva and Zemp [17] propose 353 m2 additional areasin targeting stage and in the final design require 410 m2 additionalareas and an extra exchanger for hot utility. Fig. 8 shows finalnetwork proposed by their method. In this example as in previousexample the heat transfer coefficients were obtained to satisfypressure drop constraints and with some modifications extra areawere added to reduce pressure drops.
To calculate utility exchanger’s area, some temperatures wereassumed for utility streams (300 �C and 299 �C for hot utilities and15 �C and 25 �C for cold utilities). Also constant heat transfercoefficients of 1.5 and 1 kW/m2 �C were used for hot and coldutilities respectively.
The final network generated by the present method (assumingno splitter) is shown in Fig. 9. This network uses two newexchangers of 1361 m2 and 54 m2 and also adds 343 m2 to theexisting area of the initial network exchanger. This amount of areareduces hot and cold utilities up to 8178.3 kW and 6171 kWrespectively (13% and 16.5% less than the amount obtained in Ref.[17]). To overcome pressure drop it needs purchase of additionalpumps detailed in Tables 9 and 10.
Table 16Pump reassignment in case study 3 for the best solution.
Matchno.
Pumpassignment
Retrofit pres.drop (kPa)
Existing pres.drop (kPa)
Additional pres.drop (kPa)
1 Pu1 246.1 152.7 93.42 Pu4 688.3 354.5 333.83 Pu2 190.9 102.4 88.54 Pu5 1231.4 69.6 1161.85 Pu6 599.8 189.9 409.96 Pu3 646.1 89.52 556.587 Pu7 1578.3 350.1 1228.2
Table 17Comparison of the results for case study 3.
Units Additionalarea (m2)
Areainvestment(k$)
Saving inutilities(k$/yr)
Investment(pump and area)þCost of power(k$/yr)
Panjeshahi andTahouni [18]
16 3818.85 969.653 1635.3 181.48
This work(best result)
12 31,705.51 4863.214 4554.6 940.15
This work(second result)
13 40,883.16 5677.630 3780.5 1093.48
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e23912390
If final values of heat transfer coefficients obtained by Silva andZemp [17] were used less areas could be obtained. Table 11compares the results obtained using two methods.
6.3. Example 3
This case study of crude oil pre-heat train is taken from Panje-shahi and Tahouni [18] in which 6 hot streams heat the crudebefore entering the crude column. The objective of this example isthe reduction of hot utility load and is a debottlenecking problemafter % 20 increases in network throughput shown in Fig. 10.
Streamdata andphysical properties for the streamsare tabulatedin Tables 12 and 13 respectively. Also Table 14 includes cost data(Note that the reassignment cost of an existing pump or exchangerhas not been considered in Panjeshahi and Tahouni [18]).
The method of Panjeshahi and Tahouni [18] suggested use ofadditional 3818.75 m2 which reduces hot and cold utilities by21.238 MW and 21.2771 MW respectively.
The network suggested by the present method (with consid-ering at most 3 split) is shown in Fig. 11. It suggests a reduction of59.15 MWand 59.151 MW for hot and cold utilities respectively andit requires additional 31,705.51 m2 areas. The same heat transfercoefficients of Ref. [18] were used here.
One of the advantages of GA is that it does not produce only onesolution. The second best network is shown in Fig. 12.
Tables 15 and 16 show uses of previous exchangers and pumpsin the new configuration as well as added area and purchasedexchangers.
Table 16 shows pressure drops calculated assuming constant h(it includes pressure drops of utility exchangers). Note that retrofitareas of exchangers E8, E9, E11 are much more than the existingareas, therefore if necessary these exchangers can be used in otherlocations and new exchangers can be purchased for these matches.The investment costs were calculated assuming the above point.
Table 17 gives a comparison between two methods. Althoughextra area suggested by Panjeshahi and Tahouni [18] and its cost isless than the amount suggested by the present procedure, thepresent method reduced the utility loads much more (37.93 MWand 37.87 MW in hot and cold utilities respectively). Annual cost ofutility consumption is reduced about $2.92�106 less than the onein Ref. [18].
7. Conclusion
In this article a new effective method to consider pressure dropin retrofit problems is proposed based on GAeLPeILP method. Toreduce complexity, streams heat transfer coefficients (h) weretaken to be constant and for each potential solution the pressuredrop was calculated after reaching a feasible configuration.
The case studies show that the new method gives better resultsfor the networks previously studied in the literature. The new
method can be easily applied to the industrial cases and this is thesubject of the future research work.
The benefit of this kind of representation is that only feasiblenetworks are produced during the optimization process.
Taking (h) to be constant, may affect the cost of final network intwo ways. If the real (h) is larger than assumed, calculated area willbe more but pressure drop will be less than real area and pressuredrop. Accordingly the two effects nearly neutralize each other andthe effect of assuming constant (h) on the overall cost is reduced.However assuming constant (h) may not lead to the best solutionand further research may focus on effective methods to includevariable (h).
One of the advantages of this method is that it needs noinitialization because of the use of the GA in structural optimiza-tion, simplex method in the LP formulation and branch & boundmethod in the ILP section. The only variables that require initialguess are the minimum approach temperature (DTmin) and splitratios. In this article an initial value of 15 �C was considered forDTmin and all split ratios were initially set to 0.5.
It must be noted that the number of branches in each splitter isvery important because it controls the size of the superstructureand the search space. Application of the current approach to largescale industrial networks requires inclusion of more branches. Thenumber of branches can be set according to the structure of theexisting network and/or some heuristics proposed by Li and Hua[22] which is based on the ratio of the heat capacity flow rates ofthe hot and cold streams.
Acknowledgment
The authors would like to thank Sahand University of Tech-nology (SUT) and Environmental Engineering Research Center(EERC) for their support for this research work.
Nomenclature
A heat transfer area (m2)Ci,j cost of additional area for the reassignment of the ith
existing exchanger to the jth match, i¼ [1, ., Nex],j¼ [1, ., Nm]
Cn,j cost of purchasing a new exchanger for the jth matchCpi,j cost of purchasing a new pump to be connected in series
with the jth steam pump, j¼ [1, ., NHþNC]CUi cold utility load of the ith hot process stream,
i¼ [1, ., NH]Ei the ith exchanger of an HENh film heat transfer coefficient (kW/m2 �C)HUj hot utility load of the jth cold process stream,
j¼ [1, ., NC]LMTD the logarithmic mean of the temperature differenceMCp heat capacity flow rate (kW/K)M mass flow (kg/s)mj assignment of a new exchanger to the jth match,
j¼ [1, ., Nm]NC the number of cold process streamsNex the number of existing exchangersNH the number of hot process streamsNm the number of matches in a modified networkPui assignment of the pump of ith stream, i¼ [1,., NHþNC]DP pressure dropqi heat load of the ith exchanger of an HEN (kW)T temperature (�C)DT approach temperature difference in hot or cold end of
exchangers (�C)
H. Soltani, S. Shafiei / Energy 36 (2011) 2381e2391 2391
DTmin minimum approach temperature difference (�C)yi split ratio in the ith branch of splitterszij reassignment of the ith existing exchanger to the jth
matchzpij binary variable using for pump of ith stream in the
current network in jth stream in the optimized network,i¼ [1, ., NHþNC], j¼ [1, ., NHþNC]
Indicescu stand for cold utilityhu stand for hot utilityi stand for hot streamj stand for cold streamin stand for inletout stand for outlets stand for shellt stand for tubew stand for water
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