A Combinatorial Method for the Automatic Generation of Multiple, Near-Optimal Heat Exchanger Networks

0263–8762/01/$10.00+0.00# Institution of Chemical Engineers

Trans IChemE, Vol 79, Part A, September 2001

A COMBINATORIAL METHOD FOR THE AUTOMATICGENERATION OF MULTIPLE, NEAR-OPTIMAL

HEAT EXCHANGER NETWORKSJ. MIKKELSEN1 and B. QVALE2

1dk-TEKNIK ENERGY AND ENVIRONMENT, Søborg, Denmark.2Department of Energy Engineering, Technical University of Denmark, Lyngby, Denmark.

A method for the automatic synthesis of heat-exchanger networks (HENs) is describedhere. The method, named COMBINET, is based on combinatorial procedures, nopinch rules are used. The main idea is to � nd economic HENs. The procedure,

however, is well suited for optimizing energy recovery, minimizing heat-exchanger area,minimizing number of matches, etc., The program is capable of storing a speci� ed number ofthe best HENs from the screening procedure, thereby allowing the user to evaluate which onesbest satisfy other requirements. A number of cases from the open classical literature have beenstudied and the results compared. The studies have shown that in each case a number ofdifferent con� gurations exist that are almost equally good concerning economics, indicatingthe presence of a � at economic optimum. In six out of a total of nine cases investigated,COMBINET did � nd several networks which all were better than the hitherto best networkreported.

Keywords: HENS; combinatorial method; � at economic optimum.

INTRODUCTION

General Background

A milestone in the research area of heat exchanger networksynthesis (HENS) has been the appearance of the pinch-point method1. The pinch-point method does not give astraight-forward procedure for designing HENs. Instead, themethod provides a set of rules that give guidance forreaching the minimum utility target that corresponds to aheat-recovery approach-temperature (HRAT). HRAT is thelink to an economic optimization, and can be optimizedseparately with respect to total heat-transfer area andnumber of heat exchangers (units).

Many procedures use pinch-point type techniques whenderiving close-to-optimal solutions of HENs. A centralassumption is that HENs that satisfy minimum utilityconsumption, according to an optimized value of HRAT,and furthermore satisfy (or almost satisfy) targets for areaand number of units determined from optimization ofHRAT, are close-to-optimal solutions. One thing thesemethods have in common, is decomposition of the overalloptimization problem into optimization of sub-problems.The solutions of these sub-problems are used for settingup restrictions for an acceptable solution in order to limit thesearch domain for optimal solutions. In other words: thecombinatorial problem of investigating all network con� g-urations, which even in problems with a modest number ofstreams implies a vast number, is surmounted by eliminatinginvestigations of the vast majority of the possible networks.This characteristic of a methodology for optimizing HENSis essential. Gundersen and Naess2 have made an extensive

review of previously published work on cost optimizingHENS.

Another problem or aspect is that most methods for thedesign of HENs involve a high degree of complexity, mean-ing that a person has to be highly skilled and experienced inusing these methods in order to produce good results. Veryfew methods capable of producing solutions of high qualitycan be characterized as straight-forward methods.

The method presented in this paper (COMBINET), is a socalled ‘straight-forward’ procedure, meaning that a user ofthis method is most likely to � nd good solutions even withonly very limited expertise in this � eld. Networks aredesigned by combining heat exchangers, individually opti-mized with respect to economics. When dealing with largestream problems, only the most economically important heatexchangers are combined. The claim is: when dealing with alarge number of possible stream matches, only a small partof the combinations need be investigated in order to � ndgood and practical solutions. This method exhibits somesimilarity to a method of Victorov3, the differences arediscussed in this paper.

One of the purposes of this paper is to demonstrate thatthe COMBINET method is a tool that in most cases willproduce good HENs. In order to do this, results from anadditional eight cases are reported. The selected cases haveall been used in a comparison presented by Zheljew et al.4

between different methods for optimization of HENs. Thereasons why these cases are chosen are: the cases havecomplete sets of data that make economic optimizationpossible and the cases have already been used for compar-ison between different methods for HENS, so these results

663

can be re-used in testing the present method. The results4 arereported in tables together with results from the applicationof COMBINET to the selected cases. Not all of the cases4

(15) are used. The cases that consist of very few processstreams have not been included as they only generate a smallnumber of alternative con� gurations to be evaluated, andthus, do not constitute a test of the ef� ciency of thecombinatorial method COMBINET. Other cases have beenexcluded because of inconsistencies in reported results4.

COMBINET has been applied to a signi� cant number ofcases and has, in general, shown very good results. Thismethod is capable of � nding good solutions even whendealing with problems with a large number of streams, andcan always provide a solution in a reasonable amount oftime, as the user decides the extent of the combinatorialsearch domain. The case studies have proven the method tobe a strong and very practical tool for synthesis of HENs.

The present article represents modi� cation and extensionof a previously published paper5.

Limitations of the Present Investigation

In order to be able to compare the present procedure withthe results of other investigations, the documentation ofthese other investigations has to be complete. This excludesmost recent and extensive investigations, and, by coinci-dence, limits the comparisons to cases in which the possi-bility of stream splits and multiple matches are notconsidered.

Permitting stream splits and multiple (repeated) matchesbetween streams can lead to less utility consumption and/orfewer units. However, if it is deemed important to introducestream splits, these can be introduced manually in advance,as they are quite easily identi� able. Splitting streams orallowing for multiple matches, however, is not the primarygoal of the present procedure. On the contrary, the primarygoal is to develop a simple and practical method for thedevelopment of economic con� gurations of HEN’s, to beused in small- or medium sized process plants. Thecomparative studies described below, to a large extent,con� rm the success of the procedure.

DESCRIPTION OF THE COMBINET METHOD

In this return of the paper, a short background of themethod is given, followed by a detailed explanation of thealgorithm (illustrated with an example), and � nally,similarities and differences to the method3 are pointed out.

Background

The method presented here and a method calledGREEDY6, which was the predecessor of COMBINET,are based on direct economic optimization, meaning thatthere is no explicit optimization of heat recovery. No targetfor optimum heat recovery or any pinch rules are used forderiving heat exchanger networks. The reason for this is theassumption that the major incentive for implementing effec-tive HENs is the prospect of increasing the long-term netpro� t.

The GREEDY method derives a network by successivelyadding the most economically advantageous heat exchangerto the network, until all possibilities of � nding economical

heat exchangers have been exhausted. The area of each heatexchanger is optimized with respect to economics asdescribed in the next section.

The GREEDY procedure tends to favour and select � rstheat exchangers with a large temperature driving force(TDF). This often leads to rather bad economics of thelast incorporated heat exchangers in the completedGREEDY network.

Furthermore, and perhaps even more crucially heat-recovery potential might be lost. This irregular distributionof TDF often leads to simple (few number of units) buteconomically non-optimal networks. A special featureimplemented in this method made it possible to interruptthe incorporation of a suggested heat exchanger. Using thisfeature when heat exchangers with extremely high TDFswere suggested, networks superior to the ‘strictly’ GREEDYnetwork, with respect to economics and heat recovery,would often result. This fact led to the combining ofindividually optimized heat exchangers into a number ofdifferent networks7 and simply chosing the best one (orones). The number is speci� ed by the investigator, and islimited by the computational capacity, but can still be quitelarge. This forms the basis for the COMBINET method.

Economic Optimization of a Single Heat Exchange

In order to describe the operating principle behind theprocedure, a hot process stream (the stream has to becooled) and a cold process stream (the stream has to beheated) are to be considered. It is assumed that temperaturesof the hot and cold stream are such that an exchange of heatbetween the two streams is possible (see Figure 1).

The � rst step is to start with a very small heat-exchangerarea, and calculate the heat exchanged and the economics.The economic indicator could be net present value (NPV)of savings or pay-back time. Whether NPV of savings orpay-back time should be used depends on many factorsincluding political circumstances, � nancial climate and theabsolute magnitudes of the energy quantities involved. Inthe present study NPV of savings has been used as itcorresponds to minimizing total cost which is the sameobjective used in the cases that serve as comparison.

The NPV of savings, that arise from reduced utility costsfor this heat exchanger is calculated from cost functions forheat exchangers and costs for hot and cold utility. If norestrictions are violated, a small area is added to the initial

Figure 1. Initial heat exchanger (TDF: Temperature driving force).


664 MIKKELSEN and QVALE

one, and again the heat exchanged and NPV of savings arecalculated. If this increase of area has improved the NPV ofsavings, these steps will be continued until the economicscease to improve or at least one restriction is violated. Atthis point, the heat exchanger is said to be optimized in areawith respect to NPV of savings. The restrictions to respectare the EMAT and speci� ed � nal temperature of streams. Inprinciple, EMAT can be set equal to zero, but for somepractical and technical reasons it might be desirable to set aminimum allowable value.

Instead of maximizing NPV of savings, the optimizationcan be done by minimizing pay-back time for the heatexchanger. In that case, the optimization will only bemeaningful if the cost functions of the heat exchangersinclude a � xed charge term. Otherwise the pay-back timewill steadily increase and the optimized area will be zero.This is due to the fact that for each area increase after theinitial small area, the corresponding amount of additionalrecovered heat has been exchanged with steadily decreasingTDF (see Figure 1). A typical cost function for a heatexchanger is:

CostExchanger = FCT + CostArea . Areaexp (1)

Where FCT is a � xed charge term and the value of the areaexponent (exp) usually is between 0.5 and 1.

Strategy of the Design Procedure (Synthesis)

A simple example consisting of 2 hot and 3 cold processstreams is presented in this section, in order to illustrate thealgorithm followed when combining individual economic-ally optimized heat exchangers. The streams and techno-economic data for the example are given in Table 1.

The starting point is the optimization of the heat-exchanger areas with respect to economics of all possiblematches between hot and cold streams, as described above.

Let Nh denote the number of hot streams (2) and Nc thenumber of cold streams (3). The theoretical maximumnumber of matches will then be Nh . Nc; = 6; assumingthat all hot streams can exchange heat with all cold streams.The heat exchangers are arranged in descending order ofNPV of savings. The reason for that will be explained later.For each heat exchange, only four key � gures are stored.These are: hot stream number and cold stream number in agiven match, NPV of savings and the amount of heat that isexchanged. The stored data can be regarded as a number ofboxes each one containing the information that is suf� cientfor describing one possible heat exchanger (see Figure 2).The optimization of heat exchanger areas (see Figure 2) hasbeen carried out with a discrete area step of 0.01 m2.

These data are representing what in the following will bereferred to as level 1. All heat-exchanger possibilities onlevel 1 have one thing in common; they are ‘virgin’ heat

exchangers, meaning that none of the streams involved hasexchanged heat before. The fact that the heat exchanged in amatch not necessarily corresponds to an EMAT = 10°C canbe explained either by the discrete area optimization or thatthe economics cease to improve by further increase in heat-exchanger area.

One heat exchanger on level 1 is now selected. Selectionof this heat exchanger means that the exchange of heatactually takes place, and the temperatures of the two streamsinvolved are modi� ed accordingly. The selected exchangeron level 1 now constitutes the seed of a HEN to bedeveloped further.

Then the next heat exchanger is selected. Some of theheat exchangers on level 1 might still be candidates forselection, but the � gures for the heat exchangers on level 1involving one of the two streams that took part in the � rstselected heat exchanger are no longer valid, because thetemperatures of these two streams have changed. Thismeans that areas of all matches of streams involving oneof the two streams in the selected heat exchanger on level 1have to be re-optimized. The maximum number of heatexchangers to re-optimize is Nh + Nc - 2:

A new group of possible heat exchangers, called level 2,is now formed by the heat exchangers from level 1 that arestill candidates, and the re-optimized heat exchangers (seeFigure 3). Again the heat exchangers are arranged indescending order of NPV of savings. Note that the heat

Table 1. Stream and techno-economic data for the example for illustrationof the method COMBINET.

Stream name Tstart°C Tend

°C _mm . Cp kW/°C

H1 70 10 4H2 75 35 12C1 5 70 5C2 35 65 7C3 30 85 6

Cost of hot utility 18 DKK/GJCost of cold utility 17 DKK/GJ

Cost of heat exchanger Area < 20 m2

FCT 50400 DKKCostArea 6793.6 DKK/m2

Area exponent (exp) 1 –

Cost of heat exchanger Area > 20 m2

FCT 120000 DKKCostArea 3312 DKK/m2

Area exponent (exp) 1 –

Time horizon 10 YearsYearly interest rate 6 %Yearly operating time 2000 HoursU (heat transfer coeff.) 1 kW m- 2 °C- 1

EMAT 10 °C

Figure 2. Level 1 for 5-stream problem.


METHOD FOR AUTOMATIC GENERATION OF HEAT EXCHANGER NETWORKS 665

exchangers available are on level 2, and their sizes dependon which heat exchanger was selected on level 1. Just as onlevel 1, level 2 continues by selecting heat exchangers indescending order of NPV of savings, i.e. the � rst heatexchanger on level 2 is selected.

Each time this procedure is repeated, a new level in thecombinatorial tree is generated with steadily decreasingnumbers of possible heat exchangers on each level. Whenno possible heat exchangers are left (after selection of a heatexchanger), the � nal level is reached, and a network hasbeen completed. The total NPV of savings for this networkis stored for later comparisons with other networks, and thekey data for the heat exchangers in the network are stored inorder to generate detailed information of this network incase it turns out to be the optimal solution. The � rst networkderived is the GREEDY network since, on each level, themost economical heat exchanger is selected (see Figure 3).

Deriving the next network is now rather simple. The lastheat exchanger added in the network is removed andsubstituted with the next ranking heat exchanger on thelast level, if any. This substitution may now lead to one morelevel (see Figure 4).

Only in the case that this occurs, the subsequent networkcan have a NPV of savings that exceeds the prior network.This new network is then generated. The procedure isrepeated and the NPV of savings of the newest networkis compared with the best previous one. If the new networkis better, it replaces the previously best network. Each time anetwork has been generated and compared, the heat exchan-ger added last, is replaced with the next ranking possibleheat exchanger on that level. This is continued until allpossible heat exchangers have been investigated on a givenlevel ‘X’. In this case the procedure ‘jumps’ one level back(to the level ‘X-1’), and proceeds by replacing thepreviously selected heat exchanger on this level by thenext ranking heat exchanger. By repeating this processover and over again, different networks are generated andcompared. Thus the combinatorial tree will be investigated.

When all possibilities have been investigated the best solu-tion is stored.

Only the four key data, mentioned earlier, for each heatexchanger are stored. As the order in which these are addedto the network is given implicitly by the placement of data inthe array containing these key � gures, this is suf� cient todescribe the optimal network.

At an arbitrary time in the combinatorial procedure, onlya small part of the combinatorial tree has to be stored. Thereason for this is: all heat-exchanger possibilities on a givenlevel ‘X’ are exhausted before this level is updated (dueto the selection of a different heat exchanger in the level‘X-1’), and consequently these data can be erased as soon asthat particular heat-exchanger investigation is completed.This means that on each level only the space for storing keydata for the maximum number of possible matches isrequired.

Excluding Equivalent Variants of Networks

Each network can be regarded as a possible path from theroot (level 1) in the combinatorial tree to the � nal level. Thenumber of levels depends on the path. It is obvious thatdifferent paths can actually describe the same networkphysically, because in that sense, the order in which anidentical set of heat exchangers is added to a network is ofno importance. Note that identical heat exchangers not onlyrefer to identical stream numbers in matches, but also to heatload and temperatures.

To save computing time, it would be desirable to elim-inate the calculation of physically identical networks. Such afeature is not easily incorporated in the procedure described

Figure 4. Second completed network generated.

Figure 3. LEVEL 1 and LEVEL 2 when heat exchanger ‘1’ is selected onLEVEL 1 and LEVEL 2 (First completed network (the ‘GREEDY’network)).



above. A feature to save a modest amount of computing timeis implemented in the PC-program COMBINET. Thisfeature discovers if a still incomplete network, that ispresently being developed, has already been the subject toan investigation. A more detailed explanation of how thisfeature is implemented will not be given here.

Reducing the Combinatorial Search Domain

As indicated above, the computational work growsrapidly when the number of streams increases and oftenbecomes the limiting factor. A procedure for eliminatingcalculations of identical networks, making the combinationalgorithm more effective cannot solve this problem.

By specifying a maximum number of possible heatexchangers on each level (Nmax) to be considered in thecombinatorial procedure and in addition specifying a maxi-mum allowable number of levels (Nlevmax) in the procedure,the maximum number of networks to be investigated isde� ned as: (Nmax)

Nlevmax and may be limited as desired.As mentioned above, the possible heat exchangers on

each level are ranked in descending order of NPV of savings.The consequence of introducing the above limits is that onlythe economically most important heat exchangers areincluded in the combinatorial procedure. The remainder ofthe network is completed, by simply including the matchesin the order in which they have been ranked when themaximum number of levels has been reached. The conse-quences of this have not been rigorously studied, but itseems reasonable to give highest priority to important heatexchangers rather than using the computer resources tocombine small and relatively unimportant heat exchangers.

In the computer program, Nlevmax and Nmax can bespeci� ed by the user, according to computer resource andcomputing time available. This way of limiting the compu-tational work has one disadvantage. When dealing with verylarge problems, where the potential number of heat exchan-gers in a network greatly exceeds Nlevmax, only a part of thenetwork is considered in the optimization. This will favourthe generation of networks consisting of some very econom-ical (‘greedy’) heat exchangers (the ones considered in theoptimization). The presence of these very economical heatexchangers may prevent further heat recovery. The penaltyfor this is not considered, but most likely the result is a non-optimal network.

One way to handle this problem is to develop an estimat-ing function, for the remaining heat-recovery potential andan estimating function of the cost for this. Victorov3 used anestimating function for heat-recovery potential. In COMBI-NET the problem is handled differently, namely by applyingthe formerly described method called GREEDY to derive anetwork consisting of the remaining streams and part ofstreams. The GREEDY method is conceptually simple andfast. Another way to reduce the tendency of getting toogreedy networks when dealing with very large problems isto select a rather high value of Nmax and a rather low valueof Nlevmax. This allows less greedy heat exchangers to beincluded in the start of the combining procedure.

Inclusion of Utilities in Optimization

Utilities are included in the optimization procedure. Thisfeature can be made optional. When dealing with large

problems, one theory may be to concentrate forces on thecombinatorial procedure of exchanging heat betweenprocess streams rather than on the calculation of utilityexchangers.

COMBINET and the Method of Victorov3

In the following, the characteristic features of the twomethods are listed.

COMBINET

· heat-exchanger areas are individually optimized withrespect to economics. This ensures that the heat exchan-ger area does not exceed what can be paid off;

· When limiting the combinatorial search domain, themost economical heat exchangers are to be combined.Maximum number of levels (Nlevmax) and maximumnumber of heat exchangers on each level (Nmax) are thelimiting conditions. This feature ensures that the proce-dure is always capable of � nding a solution in theamount of time available, no matter how large theproblem is.

· no use of cost estimating functions;· no pinch rules for controlling the HENS;· well-suited for optimization of other parameters like:

recovered heat, heat-exchanger area or number of units.

Method of Victorov3

· heat-exchanger areas are calculated in accordance withheat load and EMAT;

· When limiting combinatorial calculations, a speci� edmaximum number of branches on each level will beinvestigated further. The branches to be investigatedfurther are the one with most energy recovery potential,i.e. energy recovered at the branch plus an estimate forthe remaining potential.

· no limit in number of levels is reported;· use of estimating functions;· no heat exchange across pinch-points is allowed.

RESULTS

Case Presented by Victorov3

This case study addresses an aromatics plant8, consistingof four hot and � ve cold process streams. The processstreams are given in Table 2. Some of the main resultsfrom two networks derived by COMBINET (the bestnetwork and the network ranking as number 20 have beenselected) and the network generated by Victorov3 arepresented in Table 3. The three HENs derived with thetwo methods are shown in Figures 5, 6 and 7.

Case Studies Presented by Zheljew et al.4

The methods used for optimization of HENS, producingthe results that were reported4, are not known to the authorsof the present paper and, therefore, can not be discussed.However, the results are presented together with results fromthe method COMBINET for comparison of economicaloptimization performance.



The stream data for the eight cases are given in Table 4and Table 6 together with techno-economic data inTable 5. The most important results are reported in Table 7and Table 8.

DISCUSSION

The con� guration of the HEN derived by Victorov3 forthe 9-stream aromatics-plant problem (see Figure 7) is verysimilar to the ‘best’ HEN found by COMBINET (see Figure5). In fact, the difference between the two con� gurationsonly appears in the order in which the stream match H3-C3is applied. The heat loads in several of the same streammatches, however, are different. The network of Victorov3

recovers 68200kW. The network of COMBINET (#1)recovers 268kW less heat, but this network has lower totalannual cost (see Table 3). The reason for the lower total costof the COMBINET #1 network is mainly that in the network

Figure 6. Network #20 generated by COMBINET.

Figure 7. Network reported by Victorov3.

Figure 5. Network #1 generated by COMBINET.

Table 2. Stream data for Aromatics Plant.

StreamTstart°C

Tend°C

_mm.Cp

kW °C- 1

H1 327 40 100H2 220 160 160H3 220 60 60H4 160 45 400C1 100 300 100C2 35 164 70C3 85 138 350C4 60 170 60C5 140 300 200Hot utility 350 350 –Cold utility 25 30 –

Additional data for this comparison:Overall heat-transfer coef� cient: 0.5 kWm- 2 °C- 1

Economical data:Hot utility 70 £ kW- 1.yearCold utility 7 £ kW- 1.yearHeat-exchanger cost: 700.area0.83 £Annuity: 29.83 %/year

Pinch target:Qh, minimum: 17280 kWQc, minimum: 25000 kWQ, recovery: 68900 kWPinch temperature: 155 °CHRAT: 10 °C

Table 3. Main results from case of Aromatics Plant.

COMBINET #1 COMBINET #20 Victorov3

Area: heat exchanger 8705 8187 9323hot utility 462 471 459cold utility 1374 1398 1362

Total area: m2 10541 10056 11144No of heat exch 16 15 16Heat recovery kW 67932 67305 68200Total cost k£ year- 1 2133 2151 2143



of Victorov3 the heat exchange between H1 and C1 has alower EMAT than the trade-off approach temperature (TAT).The COMBINET network shows that the value of TAT forthis heat exchange is 11.75°C. By using EMAT = 10°C asrestriction instead of TAT, an additional area of 1960 m2–1638m2= 322 m2 is required. The additional cost for thislarger heat exchanger is 52335 £=year and the value ofmarginally recovered heat is 100 . 1:75 . (70 + 7) = 13475£=year. Most of this marginally recovered heat is recovered

Table 7. Results (from cases in Table 4).

No ofexch

No ofutility

ex ACC AUC ATC

Author H C EU y- 1 EU y- 1 EU y- 1

7 SP1Pont and Donald 5 0 2 8357 21815 30172Walde 6 0 2 8530 21815 30345Wagen and Zeis 5 0 3 8378 21820 30198Zheljew 5 0 2 8305 21837 30142COMBINET #1 5 0 3 8453 21368 29821COMBINET #20 7 0 3 9301 21371 30672

7 SP2Pho and Lapidus 6 1 0 4821 24097 28918Walde 6 1 0 4464 24097 28561Wagen and Zeis 6 2 0 6041 25013 31054Zheljew 5 2 0 4539 24077 28616COMBINET #1 6 2 0 4446 24536 28982COMBINET #20 6 1 0 4958 24519 29477

8 SP1Grossmann 7 4 1 11224 30004 41228Nishida 10 2 1 9729 30635 40364Zheljew 6 4 1 8706 29766 38472Strehlow 8 2 1 9988 28503 38491Walde 6 4 1 8541 29958 38499COMBINET #1 6 4 1 8498 28473 36971COMBINET #20 9 1 1 8741 28457 37198

10 SP1Nishida 8 0 2 9464 34520 43984Walde 7 0 3 9437 34520 43957Wagen and Zeis 9 0 2 9819 34571 44390Zheljew 7 0 3 9615 34520 44135Linnh and Flower 8 0 2 9350 34507 43857COMBINET #1 9 0 2 9410 34281 43691COMBINET #20 9 0 2 9648 34281 43929

20 SP1Zheljew 14 0 4 5598 19695 25293Wagen and Zeis 14 0 6 4913 19151 24064Strehlow 14 0 6 6123 19672 25795Walde 13 0 6 3970 21694 25664COMBINET #1 12 0 7 5669 18290 23959COMBINET #20 13 0 6 5777 18294 24071

Table 4. Stream data for � ve cases.

Tstart,h

KTend,h

K_mm . Cp

kW K- 1Tstart,c

KTend,c

K_mm . Cp

kW- 1 K- 1

Case 7 SP1544 422 12.554 311 494 8.4397500 339 14.770 450 483 10.465472 339 17.723 366 478 13.899

355 450 17.280

Case 7 SP2583 478 12.533 311 494 8.4397551 339 6.9628 366 477 8.4397517 366 8.3184 422 478 21.775

339 411 13.841

8 SP1516 433 11.816 366 489 8.862505 389 9.2309 339 477 12.238461 339 15.033 358 439 18.515427 366 10.602 333 422 9.0991

Case 10 SP1433 366 11.816 333 433 7.6221522 411 10.550 389 495 6.0819500 339 14.770 311 494 8.4397544 422 12.554 355 450 17.280472 339 17.723 366 477 13.899

Case 20 SP1561 505 14.981 464 489 11.773544 522 12.591 422 461 12.591533 500 12.976 433 455 18.441511 461 8.9672 411 444 13.736486 444 16.188 400 439 7.0894477 422 10.212 380 411 16.879458 433 13.451 389 402 5.8551422 394 6.5513 350 377 12.111389 350 10.929 333 366 7.5957350 333 9.9694 300 333 7.3426

Table 6. Stream data for three cases.

Tstart,h

KTend,h

K_mm . Cp

kW K- 1Tstart,c

KTend,c

K_mm . Cp

kW K- 1

Case 6 SP4633 423 200 283 403 300553 373 250 373 543 200463 393 300 413 593 250

Case 6 SP5643 573 300 333 433 200543 473 250 389 495 250473 303 220 311 494 300

Case 16 SP1648 498 100 283 403 350573 453 125 283 383 50533 433 180 398 498 400473 333 200 453 493 500453 333 250 513 633 500433 313 150 553 593 45423 303 125483 443 375463 423 300443 403 350

Table 5. Techno-economic data for the cases in Table 4 and Table 6.

Units Cases Table 4 Cases Table 6

Hot utility K 509 873Cold utility K 311–355 293–313Cost of hot utility EU/GJ 1.2349 20.7Cost of cold utility EU/GJ 0.59239 7.5Area cost: heater EU/m2 1456.3 300

cooler EU/m2 1456.3 900heat exch. EU/m2 1456.3 900

Area exponent – 0.6 0.6Time horizon Years 10 5Yearly operating time Hours 8500 7000U: heater J m- 2 K- 1 1137 50

cooler J m- 2 K- 1 852 150heat exchanger* J m- 2 K- 1 852 150

EMAT K 11.1 11.1

* For the case 6 SP5 (Uheat exchangers= 200) EU: Economic unit.



in the network of COMBINET #1 in the subsequent heatexchange with stream C2. This example illustrates veryclearly that in some cases, when optimizing heat recovery(and minimizing number of units), the result may be heatexchangers with severe penalties in the form of area cost.The COMBINET network was derived with a speci� edEMAT = 10°C according to the problem formulation byVictorov3. It should be mentioned that by specifying alower EMAT, networks achieving slightly lower totalannual cost can be derived by COMBINET.

The application of the COMBINET method to theselected eight cases4 has, in general, resulted in networkswith very favourable economics (see Table 7 and Table 8).In � ve of the eight cases, COMBINET generated networkswith the lowest total annual costs and in one case the secondlowest total annual costs. The number of units in networksderived by COMBINET was about the same as in networksgenerated by the other methods.

Some comments are appropriate. It should be pointed outthat one disadvantage of many of the cases from theclassical literature, and hence, of the cases chosen forcomparison purposes in the present study, is that they arenon-pinch cases. Another, and more important disadvantageis the very low pay-back times encountered in several of thecases.

As mentioned above, the eight cases were unusual in thesense that all networks derived by COMBINET had pay-back times lower than 0.3 year. In fact, several of thenetworks had pay-back times of 0.01 year or less. Thisfact favours the pinch-point method for generation ofnetworks (even though many of these cases can be categor-ized as non-pinch problems), as the annual capital costs for a

network only amount to about one % of the annual costs ofsavings. Consequently, an actual trade-off between capitalcosts and savings do not come into play in such cases. Forsome of the results4, network con� gurations were reported.In some cases inconsistencies occurred.

Considering that the COMBINET method is not limitedto the generation of pinch networks, but rather seeks thegeneration of economically attractive networks, it is ratherreassuring that this method is also capable of derivingcompetitive networks in such cases Pay-back times thatare that short are believed to be quite rare in practicalsituations. The present method is constructed for the appli-cation to practical and common problems. The authorsexperience is that in such cases, there is a balanced trade-off between capital costs and savings. It is believed that it isin these situations that the present method would have itsgreatest advantages.

FLAT ECONOMIC OPTIMUM IN CONFIGURATION

For each case that has been optimized with COMBINET,the 20 most economical networks were stored. All of thecases studied have shown that the 20 networks stored foreach case had almost equally good economics, but withdifferent matches of streams exchanging heat. That is:con� gurationally there is a � at economic optimum.Although COMBINET is based on simple rules and astraight-forward procedure the method is still capable ofidentifying several solutions having almost the same valuein objective function. The usual existence of a � at optimumin total annual cost as function of minimum approachtemperature has been noted by other investigators9–10.However, in the present case the � at economic optimumconcerns the con� gurations and not necessarily the mini-mum approach temperature.

For the Aromatics Plant the main characteristics of the 20economically most favourable networks stored by COMBI-NET are shown in the Figures 8 and 9.

The total annual costs of the 14 ‘best’ networks show adeviation of less than 0.17%, and for the 20 ‘best’ networksthe deviation is less than 0.81%. The numbers of units inthese networks vary between 15 and 18 (see Figure 8). Thetotal heat-exchanger areas deviate as much as 741 m2 (7.5%)and the costs of investment vary between 2.1529 million £and 2.3076 million £, corresponding to a deviation of 7.2%(see Figure 9). The con� guration of the heat-exchangernetwork derived by COMBINET ranking as number 20 isshown in Figure 8.

The variation of objective function in Figure 8 (totalannual cost) between the 20 networks derived by COMBI-NET is of no practical importance. However, other para-meters, which might be important, for instance number ofunits or cost of investment show relatively much largervariations. Therefore, the � rst network (#1) is not necessa-rily the most favourable network considering other objec-tives that often are dif� cult to include quantitatively in theobjective function.

Having preserved a number of different solutions, almostequal in objective function, to choose among, it is possibleto pay attention to other qualitative properties such as ease-of-operation, reliability, space limitations, number of units,unwanted matches etc.

Table 8. Results (from cases in Table 6).

No ofexch

No ofutility

exACCThous

AUCThous

ATCThous

Author H C EU y- 1 EU y- 1 EU y- 1

6 SP4Nishida 5 1 0 37.2 3659 3696Walde 5 1 0 43.0 3758 3801Strehlow 5 1 0 42.5 3654 3697Wagenk and Zeis 4 2 0 43.6 3651 3695Zheljew 6 1 0 48.7 3651 3700COMBINET #1 6 1 0 43.2 3651 3695COMBINET #20 7 2 0 50.6 3651 3702

6 SP5Wagenk and Zeis 4 2 0 44.9 28429 28474Rockstroh1 5 2 0 34.31 28429 28464Zheljew 4 2 0 44.9 28429 28474COMBINET #1 5 2 0 49.1 28429 28478COMBINET #20 5 2 0 54.3 28430 28484

16 SP1Strehlow 14 1 7 187.7 31525 31713Wagenk and Zeis 15 1 5 262.7 38839 39102heljew 21 2 4 263.3 36222 36485COMBINET #12 13 3 7 166.5 34069 34236COMBINET #202 13 4 6 158.3 34838 34996

1This number appears not to be consistent with the speci� cations of thecase. The authors of the present paper have calculated annual capital costfor this network to 50.47 EU.

2The EMAT has been speci� ed to 2 K instead of 11.1 K, as thecost of utility for the Strehlow solution corresponds to a minimumheating and cooling demand with a EMAT less than 2 K.



For the eight additional cases the relative deviation inobjective function were at a similar low level as in the caseof the Aromatics Plant.

CONCLUSION

In the present paper a method for automatic synthesis ofHENs, called COMBINET has been presented and theperformance of this method compared with other methodsthrough case studies. Applying COMBINET to cases fromliterature has, in general, resulted in economically verycompetitive networks compared to those generated by

other methods. In six (out of nine) cases COMBINETgenerated the most economical network.

The method is capable of handling and solving problemswith a large number of streams within a given amount oftime by limiting the combinatorial search domain, and iscapable of � nding close-to-optimal solutions in these cases.Problems consisting of 16 and 20 streams were successfullyoptimized. This method differs from most other methods forHENS by not using pinch rules. Since this method can becharacterized as an automatic and straightforward methodthat requires a minimum of expertise of the user it isbelieved to be a practical and effective tool for synthesisof high-performance heat-exchanger networks. Another

Figure 9. Total heat-exchanger area and cost of investment for the 20 economically most favourable networks derived by COMBINET for the AromaticsPlant.

Figure 8. The total annual cost and number of units for the 20 economically most favourable networks derived by COMBINET for the Aromatics Plant.



important aspect is that the method no matter the size of theproblem is capable of producing a solution within anacceptable amount of time.

The study has demonstrated a � at economical optimumwith respect to the con� gurations of the heat-exchangernetworks. However, major differences in con� gurations,which may be far more important, can occur betweensolutions having almost equally good economics. Therefore,the claim is that the focus should not be an optimization oftotal cost only, but also include other considerations. Theoptimization tool COMBINET can deliver a set of ‘close-to-optimal’ con� gurations. Therefore, it can be considered tobe a powerful tool in the process of � nding good economicalsolutions that at the same time satisfy secondary require-ments, which often are dif� cult to quantify and incorporatein an objective function.

NOMENCLATURE

ACC annual capital costAUC annual utility costATC annual total costCostArea speci� c cost of heat exchanger areaCostExchanger cost of heat exchangerCp speci� c heat capacityEMAT heat-exchanger minimum approach temperatureEU economic unitexp area exponent in cost function of heat exchangerFCT � xed charge term of heat exchangerHEN heat-exchanger networkHENS heat-exchanger network synthesisHRAT heat-recovery approach-temperature_mm mass � owNc number of cold streamsNh number of hot streamsNlevmax maximum number of levels in combining procedureNmax maximum number of heat exchangers to be combined on

each levelNPV net present valueTAT trade-off approach temperatureTDF temperature driving forceU overall heat-transfer coef� cientX integer referring to number of level

REFERENCES

1. Linnhoff, B. and Flower, J. R., 1978, Synthesis of heat exchangernetworks, AIChE J, 24(4): 633–642.

2. Gundersen, T. and Naess, L., 1987, The synthesis of cost optimal heatexchanger networks—An industrial review of the state of the art, CompChem Eng, 12(6): 503–530.

3. Victorov, V. K., 1995, New combinatorial method for synthesis ofHENs, Trans IChemE, Chem Eng Res Des, 73 (A8): 915–918.

4. Zheljew, T., Wagenknecht, M., Hartmann, K. and Kaushus, W., 1985,Vergleichende analyse von synthesemethoden zur strukturierung vonwarmeubertragungssystemen (WUS), Wissenschaftlische Zeitschrift THLeuna-Merseburg, 27(1): 70–89.

5. Mikkelsen, J. and Qvale, B., 1997, Economic optimization of heatexchanger network synthesis (HENS) using a combinatorial approach,Proc TAIES’97 (Beijing, China), pp 356–363.

6. Petersen, P. M., Nielsen, T. H. and Qvale, B., 1992, Heat recovery andeconomics by sequential implementation of components in heat exchan-ger networks, ASME-Proc ECOS’92, (Zaragoza, Spain).

7. Mikkelsen, J., 1993, Optimering af Varmegenvindingsanlæg, LfE, DTU,PE 93-3, MSc Thesis.

8. Linnhoff, B., Townsend, D. W., Boland, D., Hewitt, G. F., Thomas,B. E. A., Guy, A. R. and Marsland, R. H., 1982, User Guide on ProcessIntegration for the Ef� cient Use of Energy (IChem E, Rugby, UK).

9. Shenoy, U. V., Sinha, A. and Bandyopadhyay,S., 1998, Multiple utilitiestargeting for heat exchanger networks, Trans IchemE, Chem Eng ResDes, 76 (A2): 259–272.

10. Sama, D. A., 1995, Second law insight analysis compared with pinchanalysis as a design method, Second Law Analysis: Towards the 21stCentury.

ACKNOWLEDGEMENTS

This work represents an extension and application of concepts developedfor the MSc Thesis7 of one of the authors. The advice and inspiration of theinformal MSc advisory committee consisting of Peter Maagoe Petersen,Bent Lorentzen and Sten Stoltze is acknowledged.

ADDRESS

Correspondence concerning this paper should be addressed to Dr. J.Mikkelsen, Dk-TEKNIK ENERGY AND ENVIRONMENTAL, GladsaxeM� llevej 15, DK-2860 Soeborg, Denmark. E-mail: [email protected]

The manuscript was received 24 July 2000 and accepted for publicationafter revision 12 July 2001.



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A Combinatorial Method for the Automatic Generation of Multiple, Near-Optimal Heat Exchanger Networks