Cooling Water System Design

Chemical Engineering Science 56 (2001) 3641–3658www.elsevier.nl/locate/ces

Cooling water system designJin-Kuk Kim, Robin Smith ∗

Department of Process Integration, UMIST, P.O. Box 88, Manchester M60 1QD, UK

Received 27 April 2000; received in revised form 10 January 2001; accepted 1 March 2001

Abstract

Research on cooling systems to date has focussed on the individual components of cooling systems, not the system as a whole.Cooling water systems should be designed and operated with consideration of all the cooling system components because of theinteractions between cooling water networks and the cooling tower performance. In re-circulating cooling water systems, coolingwater from the cooling tower is supplied to a network of coolers that usually has a parallel con1guration. However, re-use of coolingwater between di3erent cooling duties enables cooling water networks to be designed with series arrangements. This allows bettercooling tower performance and increased cooling tower capacity, both in the context of new design and retro1t. A methodologyhas been developed for the design of cooling networks to satisfy any supply conditions for the cooling tower. A model of coolingtower performance allows interactions between the performance of the cooling tower and the design of cooling water networks tobe explored systematically. In debottlenecking situations, better design of the cooling network using the new method, includingincreasing cooling tower blowdown, taking hot blowdown and strategic use of air coolers, can all be used to avoid investment innew cooling tower capacity and to improve the performance of the cooling tower in a systematic way. ? 2001 Elsevier ScienceLtd. All rights reserved.

Keywords: Cooling water systems; Cooling towers; Cooling water networks; Heat exchanger networks; Debottlenecking

1. Introduction

Air coolers, once-through cooling water systems andre-circulating cooling water systems, are all used for therejection of waste heat to the environment. Of these meth-ods, re-circulating cooling water systems are by far themost common because re-circulating cooling systems canconserve freshwater and reduce thermal pollution of re-ceiving waters, relative to once-through systems.Much attention has been paid to issues on cooling sys-

tems relating to cooling water treatment problems (Gale& Beecher, 1987; Barzuza, 1995; Gibson, 1999; NACE,1990), the reduction of freshwater consumption (Lefevre,1984), energy conservation (Burger, 1993; Pannkoke,1996; Willa, 1997) and other operating problems in cool-ing towers.However, little attention has been placed to the in-

teractions between cooling towers and heat exchangernetworks, even though changes to operating conditions

∗ Corresponding author. Tel.: +1-44(0)161-200-4382;fax: +1-44(0)161-236-7439.E-mail address: [email protected] (R. Smith).

of cooling water systems frequently happen in industrialsites. Design and operating problems of cooling towershave been the focus of attention to manufactures and pro-cess engineers. Research on cooling systems to date hasfocussed on the individual components of cooling sys-tems, not the system as a whole. Because of the inter-actions between cooling water networks and the coolingtower performance, cooling water systems should be de-signed and operated with consideration of all the coolingsystem components.Consider some of the possible changes to an existing

cooling water system. A new heat exchanger might be in-troduced into the heat exchanger network, or the heat dutyof coolers changed, or process changes might change theoperating conditions. These process changes inFuence theconditions of the cooling water return and consequentlya3ect the cooling tower performance. In such situations,it is often not clear how cooling water systems will bea3ected by new conditions and how the cooling waternetwork design a3ects the cooling system. A combinedwater and energy analysis should be used to investigatethe interactions for the overall system because the coolingwater system has energy as well as water implications.

0009-2509/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved.PII: S 0009-2509(01)00091-4

3642 J.-K. Kim, R. Smith / Chemical Engineering Science 56 (2001) 3641–3658

During the last two decades, design tools for heat ex-changer networks have been developed and successfullyapplied to a wide range of processes. The most commonlyused tool has been pinch analysis. This is based on target-ing before design and exploits conceptual understanding(Linnho3 & Smith, 1994). Various systematic methodsbased on pinch analysis have had a key role in savingenergy in process design.In parallel with studies for heat exchange networks,

increasing environmental concerns have resulted in a fo-cus on wastewater minimisation problems. Wang andSmith (1994a) introduced a design method for targetingmaximum water re-use based on the graphical representa-tion of water systems. This design methodology was ex-tended to design with Fowrate constraints and the designof distributed eIuent treatment systems (Wang & Smith,1994b, 1995). Kuo and Smith (1997, 1998a,b) improvedthis design methodology for total water system designby attempting to take account of the interactions betweenwater minimisation, regeneration systems and eIuenttreatment systems. Whilst these conceptually-based ap-proaches provide physical insights and design features forwater systems, energy implications in water-using sys-tems were not included.This paper will present a systematic method for the

design of cooling water systems that accounts for theinteractions and process constraints. The cooling towerand the cooling water network will be 1rst examinedseparately to discuss the nature of cooling water systemdesign. A model of cooling water systems will be devel-oped to examine the performance of the cooling tower tore-circulation Fowrate and return temperature and to pre-dict the eJciency of cooling. A methodology for coolingwater network design will then be developed, assuming1xed inlet and outlet conditions for the cooling water.Finally, the design of the overall cooling water systemwill be developed by investigating the interactions be-tween cooling water network design and cooling towerperformance. Debottlenecking procedures for the designof cooling water systems will also be developed.

2. Cooling water system model

The cooling water system consists of the cooling tower,re-circulation system and heat exchanger network. Thecooling water used in the heat exchanger network returnsto the cooling tower where the hot return cooling wateris cooled (Fig. 1). Blowdown is necessary to avoid thebuild-up of undesirable materials in the re-circulating wa-ter as a result of evaporation. The Fowrate loss caused byevaporation and blowdown is compensated by make-up.To investigate interactions within cooling water sys-

tems, a cooling water system model including the coolingtower and other system components is needed. A modelof the cooling tower is basic to this. In this study, the

Fig. 1. Cooling water systems.

Table 1Veri1cation of cooling tower model

Case 1 2 3 4

Water Fowrate (kg=s) 0.2 0.3 0.398 0.495Air Fowrate (kg=s) 0.67 0.656 0.664 0.658CW inlet temperature (◦C) 36.7 32 29.3 27.9CW outlet temperature (◦C) 19.8 20.4 20.7 20.8

Model result CW outlettemp. (◦C) 19.83 20.33 20.55 20.82

Error (%) 0.15 −0:34 −0:73 0.1

cooling tower is assumed to be in counter-current contactwith air drafted by a mechanical fan. The model needs topredict the conditions of the exit water and the air fromthe tower for given design and operating conditions. De-tails of the cooling tower model used in this work arepresented in the appendix. Although the model has notbeen presented previously, it incorporates many princi-ples from previous models and represents a compromisebetween simpli1ed models, which will not allow the sys-tem interactions to be examined reliably, and the verydetailed simulation models, which are too detailed forsystem design.To verify the accuracy of the proposed model, experi-

mental performance data was compared with simulationresults from the model. Few experimental data are avail-able to test the model. However, the experimental data ofBernier (1994) give cooling water outlet conditions undervarious inlet air and water conditions. Table 1 presentsa comparison of this experimental data with predictionsof the model. It can be seen that the proposed model isaccurate on the basis of the limited data available.Fig. 2 shows predictions of the model to demonstrate

how the cooling water outlet temperature is a3ected whenwater inlet conditions are changed. When cooling waterinlet conditions are high temperature and low Fowrate, thecooling tower removes more heat from water and obtainsa lower cooling water outlet temperature. Fig. 3 showscooling tower performance in terms of e3ectiveness. Thecooling tower e3ectiveness (e) is de1ned as the ratio

J.-K. Kim, R. Smith / Chemical Engineering Science 56 (2001) 3641–3658 3643

Fig. 2. Cooling tower performance: cooling water outlet temperature.

Fig. 3. Cooling tower performance: cooling tower e3ectiveness.

of actual heat removal to the maximum attainable heatremoval. The high e3ectiveness of tower represents bettercooling performance and high heat removal.

e=QACT

QMAX: (1)

Fig. 3 shows that when the inlet cooling water hasconditions of high temperature and low Fowrate, the ef-fectiveness of the cooling tower is high, in other words,the cooling tower removes more heat from the water. Be-dekar, Nithiarasu, and Seetharamu (1998) presented ex-perimental results demonstrating that the performance ofcooling towers increases with a decrease in the L=G ra-tio. This agrees with the results from the cooling towermodel. Maintaining high temperature and low Fowrate

of inlet cooling water is important in order to keep thedriving force high.Other system components should be added to the cool-

ing tower model to complete the cooling water systemmodel. As the blowdown and make-up both have an ef-fect on the heat and mass balances of the cooling watersystem, these need to be included (Fig. 1). In this study,it will be assumed that make-up water is added after coldblowdown has been taken. In practice it is often addedto the cooling tower basin before cold blowdown. How-ever, the e3ect of the location of the make-up on the heatbalance for cooling water systems is not signi1cant. Thecooling system model isCooling tower model (see the appendix):

T1 = f(F2; T2; G; TWBT); (2)

F1 = f(F2; T2; G; TWBT); (3)

E = f(F2; T2; G; TWBT): (4)

Make-up=blowdown:

F0 = F1 − B+M; (5)

F0T0 = (F1 − B)T1 +MTM : (6)

A key factor in the design and operation of coolingtowers is the cycles of concentration. The cycles of con-centration (CC) is de1ned as the ratio of the concentra-tion of a soluble component in the blowdown stream tothat in the make-up stream. The blowdown and make-upare calculated from the evaporation loss and cycles ofconcentration. The overall heat load of the cooling wa-ter network is also needed to determine the desired heatremoval of the cooling tower.Cycles of concentration:

CC =CB

CM=

FM

FB: (7)

Calculation of blowdown=makeup:

B=E

CC− 1; (8)

M = ECC

CC− 1: (9)

Evaporation loss (see the appendix):

E =G dW: (10)

Heat load of HEN:

QHEN = F2Cp(T2 − T0): (11)

The cooling system model, which will be used for thedesign of cooling water systems involves Eqs. (2)–(11).The model that has been developed is relatively simple,but is accurate enough to evaluate the cooling tower per-formance and predict the e3ectiveness of cooling towers.


Fig. 4. Parallel con1guration of cooling water networks.

Fig. 5. New design option for cooling water networks.

From the results of the cooling tower modelling, decreas-ing the Fowrate of the cooling tower supply has a moresigni1cant bene1t on the e3ectiveness (hence increasein heat removal) than decreasing the inlet temperature.Other design guidelines can readily be derived from themodel.

3. Design of cooling water networks

The current practice for cooling water network designmost often uses parallel con1gurations. In a parallel con-1guration, the fresh cooling water is supplied directly toindividual heat exchangers. After the cooling water hasbeen used in each heat exchanger, the hot cooling wa-ter returns to the cooling tower (Fig. 4a). The minimumcooling water demand is determined by minimising theFowrate to the individual heat exchangers (Fig. 4b). Un-der a parallel arrangement, return cooling water Fowratebecomes maximised but the return temperature is min-imised. These conditions will lead to a poor cooling towerperformance.No systematic methods have been suggested to deal

with the design of cooling water networks. The traditionalparallel design method is not Fexible when dealing withvarious process restrictions. A new cooling water networkdesign methodology will now be developed.All cooling duties do not require cooling water at the

cooling water supply temperature. This allows us, if ap-propriate, to change the cooling water network from aparallel to a series design (Fig. 5). A series arrange-ment, in which cooling water is re-used in the network,will return the cooling water with a higher temperatureand lower Fowrate. From the predictions of the cool-ing tower model, the heat removal of cooling towerscan be expected to increase under these conditions. Inother words, if the design con1guration is converted from

Table 2Hot process stream data of cooling water networks: Example 1

Heat exchanger Thot; in (◦C) Thot;out (◦C) CP (kW=◦C) Q (kW)

1 50 30 20 4002 50 40 100 10003 85 40 40 18004 85 65 10 200

Fig. 6. Representation of heat exchangers using cooling water.

parallel to series arrangements, the cooling tower can ser-vice a higher heat load for the coolers.

3.1. New design methodology for cooling waternetworks

A simple problem (Example 1) will be used to developthe design methodology for cooling water networks. Thecooling water system in Example 1 has four heat ex-changers using cooling water as cooling medium for hotprocess streams. The temperature, Fowrate and coolingduty of hot process streams are given in Table 2. Thedata for hot process streams are represented as CP val-ues, which is the product of heat capacity and Fowrate.It is assumed that the heat capacity of cooling water isconstant throughout the temperature range. The coolingwater network with a parallel con1guration for Example1 has inlet and outlet CP’s of 106:4 kW=◦C, inlet tem-perature of 20◦C and outlet temperature of 51:97◦C.To develop a systematic method for the design of such

systems, some clues can be taken from water pinch anal-ysis (Wang & Smith, 1994a) and developed for coolingwater network design. In cooling water network analysis,it is assumed that any cooling-water-using operation canbe represented as a counter-current heat exchange oper-ation with a minimum temperature di3erence (Fig. 6a).The concept of the limiting water pro1le (Wang & Smith,1994a) is taken from water pinch analysis and shownin Fig. 6b as a “limiting cooling water pro1le”. This isde1ned here to be the maximum inlet and outlettemperatures for the cooling water stream (Fig. 6b).These allowable temperatures are limited by the “min-imum temperature di3erence” (STmin). In new designthis could be the practical minimum temperature di3er-ence for a given type of heat exchanger. In retro1t the


Table 3Limiting cooling water data: Example 1a

Heat exchanger TCW; in (◦C) TCW;out (◦C) CP (kW=◦C) Q (kW)

1 20 40 20 4002 30 40 100 10003 30 75 40 18004 55 75 10 200

aSTmin = 10◦C, cooling water inlet temperature = 20◦C.

temperature di3erence could be chosen to comply withthe performance limitations of an existing heat exchangerunder revised operating conditions of reduced tempera-ture di3erences and increased Fowrate. Also, the limit-ing cooling water pro1le might be determined by otherprocess constraints, such as corrosion, fouling, coolingwater treatment, etc. Any cooling water line at or belowthis pro1le is considered to be a feasible design. Thelimiting pro1le is used to de1ne a boundary betweenfeasible and infeasible regions. The limiting cooling wa-ter pro1le allows the individual streams of the coolingwater network to be represented on a common basis, aswater and energy characteristics are represented simul-taneously. It should be emphasised that the 1nal designwill not necessarily feature the minimum temperaturedi3erence incorporated in the limiting data. It simplyrepresents a boundary between feasible and infeasibleconditions. Most coolers in the 1nal network design willfeature temperature driving forces greater than thoseused for the speci1cation of limiting conditions.This study focuses primarily on retro1t design and

hence restricts consideration to deal only with hot streamsto be cooled by cooling water. Better design for coolingwater networks will be exploited under a 1xed heat ex-changer network con1guration. For grassroot design, thedesign of cooling water networks and heat exchanger net-works should be addressed simultaneously. In this paper,the topology of the heat exchanger network is assumedto be 1xed. The duties on the hot and cold streams in theheat exchanger network are thus assumed to be not re-lated to the cooling system. In other words, the streamscooled by cooling water do not a3ect other streams in theheat exchanger network.As the inlet temperature of cooling water to coolers

is increased, the driving force for the heat exchangers isdecreased and might require additional heat exchangerarea. However, at the same time the Fowrate is increased.So the reduction of driving force from decreasing tem-perature di3erence is compensated by increased coolingwater Fowrate.The limiting cooling water data for Example 1 have

been extracted from the hot process stream data and givenin Table 3. A “cooling water composite curve” can beconstructed by combining all individual pro1les into asingle curve within temperature intervals (Fig. 7a). Thedesign of the cooling water network will be based on the

cooling water composite curve, which represents overalllimiting conditions of the whole network. The coolingwater supply line is a straight line matched against thecooling water composite curve to represent the overallcooling water Fowrate and conditions. Maximising theoutlet temperature of the cooling water supply line min-imises the Fowrate of cooling water by maximising cool-ing water re-use (Fig. 7b). Each point where the supplyline touches the composite curve creates a pinch in thedesign. It is important to note that the interpretation of thepinch does not imply a zero driving force of heat trans-fer, but minimum driving force. Only those parts of thedesign in which the supply line touches the compositecurve will feature minimum driving forces, all other partswill feature temperature di3erences above minimum.The water main method of Kuo and Smith (1998a)

for the design of water re-use networks can be extendedto the design of cooling water networks. The originalmethod identi1ed water re-use opportunities for problemsin which re-use was constrained by concentration limits.Fig. 8a illustrates the approach as it applies to coolingwater networks. The design problem is decomposed intodistinct regions by cutting o3 the concave regions (pock-ets) of the composite curve. This creates two design re-gions in this problem with a pinch point that de1nes amaximum re-use supply line (Fig. 8a). The cooling wa-ter Fowrate requirements in each design region are deter-mined by a line drawn across each pocket. The coolingwater “mains” are set up at di3erent temperatures: cool-ing water supply temperature, pinch temperature and exittemperature (Fig. 8b). It should be noted that the mains atpinch temperature will not necessarily be a feature of the1nal design. It is used in the design procedure to connectthe two parts of the design (below and above the pinch)and is eliminated at a later stage. In other problems theremight, in principle, be more than two concave regions(pockets) as discussed by Kuo and Smith (1998a). If thisis the case, each additional pocket requires an additional“main”. However, the design principles are unchanged.The method is in four steps. The 1rst step is to gener-

ate a grid diagram with cooling water mains and plot thecooling-water-using operations as shown in Fig. 8b. Thesecond stage is to connect the operations with coolingwater mains. The third stage is to merge operations thatcross mains. The 1nal stage is to remove intermediate(pinch) cooling water mains. Following the method al-lows the design of the cooling water network to achievethe target predicted by the supply line. Details of theprocedure are given by Kuo and Smith (1998a) andare readily adapted from the concentration constraintsin the original paper to the temperature constraintsthat are a feature of the cooling water network designproblem.Following the method often allows more than one net-

work design to achieve the target. Certain design featuresare essential to achieve the target but others are optional.


Fig. 7. Cooling water composite curve and targeting for maximum re-use.

Fig. 8. Cooling water main method for cooling water network design.

Fig. 9. Cooling water network design with maximum re-use.

One design of cooling water network to achieve the targetminimum Fowrate for Example 1 is shown in Fig. 9. Incontrast with a parallel con1guration, it is necessary forcooling water to be re-used in the design to achieve thetarget. As a result of cooling water re-use, the exit tem-perature of the cooling water is higher and total Fowratelower than a parallel design (Table 4). If features of thedesign in Fig. 9 are unacceptable for practical reasonssuch as control problems or pipework complexity, thenthe design can always be evolved. But this is likely to re-

Table 4Comparison of exit conditions of cooling water networks

Method Flowrate (kg=s) CP (kW=◦C) TCW;out (◦C)

Parallel 25.402 106.36 51.97Max. re-use 21.495 90.0 57.78% −15.4 +11.2

sult in penalties being incurred and the design not achiev-ing the target.

3.2. Design of cooling water networks without a pinch

The procedure used so far for the design of coolingwater networks is an adaptation of the procedure of Kuoand Smith (1998a). However, there are di3erences be-tween the design of water systems as described by Kuoand Smith and the design of cooling water networks thatneed now to be taken into account. The purpose of watersupply line targeting is di3erent in water system design


Fig. 10. Temperature constraints for return cooling water.

and cooling water network design. Water systems focuson the minimisation of contaminated water to the envi-ronment, which forces the design of water networks tothe minimum consumption of water. For cooling waternetworks, the system has a number of components andthere are interactions between di3erent parts of the sys-tem. Minimum overall Fowrate of cooling water is notnecessarily the optimum. The cooling water supply lineshould be based on consideration of the overall system.The interactions between the design of the cooling towerand the design of the cooling network will be examinedin the next section.Also, the cooling water system cannot operate beyond

a speci1c return cooling water temperature because thehot return cooling water temperature might cause foulingproblems, corrosion or problems with the cooling towerpacking. It is common practice to introduce temperatureconstraints for return cooling water to the tower.If the cooling water supply line does not correspond

with minimum Fowrate (either because of system inter-actions or temperature constraints), then a pinch pointis not created with the limiting cooling water compositecurve (Fig. 10). The setting could be between minimumFowrate (maximum re-use) and no re-use (parallel ar-rangement) as shown in Fig. 10. The water main methodis based on the concept of the pinch point and cannotbe applied to problems without a pinch. The new designmethodology should provide for cooling water networkswithout a pinch.The limiting pro1le represents the boundary between

feasible and infeasible operation. In other words, anycomposite curve below the original one is feasible. Thus,the cooling water composite curve can be modi1ed inthe feasible region without creating feasibility problems(Fig. 11). If the cooling water composite curve could bemodi1ed to make a pinch point with the desired coolingwater supply line in the feasible region, the cooling waternetwork problem would be changed into a problem witha pinch. Pinch migration is introduced here to convertproblems without a pinch into those with a pinch withthe desired supply line (Fig. 11).Two approaches to pinch migration could be adopted

(Fig. 12). The 1rst is to shift heat load in which the cool-ing water composite curve moves along the heat loadaxis. The second is temperature shift in which the cool-

Fig. 11. Pinch migration.

Fig. 12. Cooling water composite curve modi1cation.

Fig. 13. Find a new pinch point: Example 1.

ing water composite curve moves along the temperatureaxis. Of the two approaches, temperature shift is adoptedbecause heat load shift will result in an energy penalty.The next problem is how to 1nd the new pinch and

how to modify the composite curve with a temperatureshift. Let us introduce a target temperature of 55◦C forthe cooling water for Example 1. A new pinch is createdbetween the modi1ed composite curve and the new sup-ply line, which is calculated from a simple heat balance(Fig. 13). The new calculated pinch of 38:5◦C is migratedfrom the original pinch of 40◦C. It is necessary for indi-vidual duties to apply a temperature shift for modi1cationof the composite curve. Cooling water streams 1, 2 and3 take part in creating the original pinch, which meansstream 1, 2 and 3 are the candidates for temperature shift.The limiting cooling water modi1cations are in two

stages. The 1rst stage (Fig. 14) is to shift the temperature


Fig. 14. Limiting cooling water pro1le modi1cation: First stage.

Fig. 15. Limiting cooling water pro1le modi1cation: Second stage.

of the limiting water pro1les according to the value ofthe temperature shift (1:5◦C for this example). Modi1edpro1les might cross the supply line and thus another stepis needed. The second stage is to increase the Fowrateof the limiting water pro1le when the shifted-pro1le isrestricted by temperature limitations. The limiting coolingwater pro1le is modi1ed to satisfy temperature limitationsby increasing the cooling water Fowrate CP (Fig. 15).For Example 1, streams 2 and 3 can be modi1ed to

obtain new limiting cooling water data simply by shiftingtemperatures. However, for stream 1, it is necessary toincrease Fowrate because the 20◦C cooling water supplytemperature restricts the temperature shift of the limitingdata. The heat balance equations determine the increasedFowrate (Eq. (12)) and the new limiting exit temperature(Eq. (13)):

CPnew = CPold Toldp − T old

cw; in

T newp − T new

cw; in; (12)

T newcw;out = CPold T

oldcw;out − T old

cw; in

CPnew + T newcw; in: (13)

After modi1cation of the conditions for each individualheat exchanger, the modi1ed cooling water pro1les areshown in Fig. 16 and the new limiting cooling water dataare given as shown in Table 5. For stream 1, the CP isincreased from 20 to 21:6 kW=◦C as a result of the secondstage modi1cation. The new composite curve, which isconstructed by combining all modi1ed limiting pro1les, isshown as Fig. 17. The modi1ed cooling water compositenow creates a pinch point with the desired cooling watersupply line. The cooling water network design can nowbe carried out using the cooling water mains method. The

Fig. 16. Pinch migration and temperature shift: Example 1.

Table 5Temperature-shifted limiting cooling water dataa


1a 20 38.5 21.6 4002a 28.5 38.5 100 10003a 28.5 73.5 40 18004 55 75 10 200

aModi1ed data.

Fig. 17. New temperature-shifted cooling water composite curve.

resulting design is shown in Fig. 18. The cooling towerreturn temperature and Fowrate agree with the target.The pinch migration and temperature shift method en-

ables design with any target temperature. The coolingwater network will have di3erent con1gurations with dif-ferent target temperatures. This can be seen by compar-ing the maximum re-use design (Fig. 9) with the designwith a temperature constraint (Fig. 18).


Fig. 18. Cooling water network design without a pinch.

4. Debottlenecking of cooling water systems

When cooling water networks need to increase the heatload of individual coolers or a new heat exchanger isintroduced into an existing system, cooling water sys-tems can become bottlenecked. As the increase of coolingload inFuences the cooling tower performance, and thereare interactions between cooling water networks and thecooling tower, the best solution is often obtained by mod-ifying the cooling water network.

4.1. General considerations for debottlenecking

From the previous results of the cooling tower mod-elling and the cooling water network design, a generalguideline for the design of cooling water systems can besuggested. The heat removal of the cooling tower canbe increased by changing inlet cooling water conditionsfrom high Fowrate and low temperature to low Fowrateand high temperature. This will, in general, require chang-ing the cooling water network design from parallel to se-ries or mixed parallel=series arrangements with re-use ofcooling water, decreasing the Fowrate of cooling waterand increasing the return temperature. By changing fromparallel arrangements to cooling water re-use designs, theheat removal of the cooling tower can be increased with-out any energy penalty and without investment in a newcooling tower.A debottlenecking procedure for cooling water systems

will now be developed using Example 2. The base case forExample 2 is shown in Fig. 19 and has three existing heatexchangers. The limiting cooling water data are given inTable 6. In this example, a new heat exchanger (Table 7)is introduced into the base case, which makes the coolingwater system bottlenecked.New outlet conditions of the cooling water are given in

Table 8 when the parallel arrangement is retained with thenew heat exchanger. The Fowrate, temperature and theheat load of the cooling tower are increased and thereforethe cooling tower performance would be inFuenced. Fig.20 shows the performance of the parallel arrangement.First, the cooling water inlet temperature (Tin = 30:4◦C)to the network is hotter than the desired inlet temperature(28:8◦C). This means additional cooling equipment needsto be installed to cool the cooling water to the maximum

Fig. 19. Base case of cooling water systems: Example 2.

Table 6Limiting cooling water data of base casea


1 28.8 37 200 1640.22 33 37 635.5 2542.13 36 52.7 488.9 8166.6

aSTmin = 10◦C, cooling water inlet temperature = 28:8◦C.

Table 7Limiting cooling water data for new heat exchanger

New heat TCW; in (◦C) TCW;out (◦C) CP (kW=◦C) Q (kW)exchanger

4 35 48 250 3250

Table 8Cooling water outlet conditions of parallel design

Case Base New %

Outlet temperature (◦C) 43.3 44.1 1.8Outlet CP (kW=◦C) 851.6 1020.9 19.9Heat load (MW) 12.3 15.6 26.3

permissible inlet temperature (28:8◦C). Second, the heatload of the network (15:6 MW) is bigger than the heatremoval of the tower (14:6 MW), which also means thatanother 1 MW of heat load needs to be dissipated byadditional cooling.When the traditional parallel arrangements with new

operating conditions are applied, the water Fowrate andthe heat load of cooling tower are consequently increased.If there are no other design options than parallel ar-rangements, an additional cooling tower (or air coolingexchanger) is needed to satisfy the new bottleneckedconditions.


Fig. 20. Changes of cooling water systems with parallel arrangements.

Fig. 21. Feasible cooling water supply line.

4.2. Debottlenecking design procedures of coolingwater systems

A design procedure for debottlenecking cooling wa-ter systems will now be developed. The cooling watercomposite curve can 1rst be constructed from the limit-ing cooling water data. The cooling water network per-formance can be changed within a feasible region thatis bounded by the maximum re-use supply line and theparallel design supply line (Fig. 21a). In Fig. 21b, thefeasible cooling water supply line (line AB) representsthe attainable outlet conditions from the cooling towermodel by changing design con1gurations. As the inletconditions to the cooling tower a3ect the cooling towerperformance, it is necessary to know how the inlet con-ditions a3ect the cooling water system.The cooling water supply line has the same heat load

(15:6 MW) from the viewpoint of the cooling water net-work (Fig. 21a). But the heat removal of the coolingwater system is changed as inlet conditions to the cool-ing tower are changed (Table 9). The heat removal ofcooling water systems increases as the design con1gura-tion changes from parallel to maximum re-use (A to B inFig. 24b).For our example, the following conditions should be

satis1ed for the new cooling water network design.

(1) The inlet temperature to the cooling water networkshould be 28:8◦C.

Table 9E3ects of cooling water inlet conditions

Case Heat removal ofcooling water system (MW)

Parallel (A) 14.61Maximum re-use (B) 15.69Target 15.60

Fig. 22. Cooling water supply line targeting.

(2) Heat removal from the cooling water system shouldbe equal to the heat load of the cooling water net-work.

In this example, it is not necessary to achieve a tem-perature lower than 28:8◦C. From Table 9 it can be seenthat the target conditions lie somewhere along the feasi-ble cooling water supply line.The next stage is to 1nd the target supply conditions

for the cooling tower. The feasible cooling water supplyline can move from BN to BM in Fig. 22. The target con-ditions, which satisfy the desired temperature to coolingwater network (28:8◦C), are found by changing the cool-ing water supply conditions from BN to BM . The heat re-moval of the cooling system is the same as the heat loadof the cooling water network at the target conditions (B∗),where the inlet temperature to the cooling water networkis satis1ed. Target conditions are given by the intersec-tion between the feasible cooling water supply line andthe isothermal line of the cooling system outlet tempera-ture.The target conditions for debottlenecking have then

been found using the cooling system model. The targetconditions are CP of 725 kW=◦C and a temperature of50:3◦C. At target conditions, the cooling demand of net-works are satis1ed without additional cooling capacity.Below the target temperature, the current cooling systemscannot operate for cooling demand. The next stage is todesign the cooling water network with target conditions.As the new cooling water supply line has no pinch withthe limiting composite curve (Fig. 23), the temperatureshift and pinch migration method is applied to this caseas explained in the previous section. The new pinch point


Fig. 23. Target conditions of cooling water supply line and new pinchpoint.

Fig. 24. Pinch migration and temperature shift: Example 2.

Fig. 25. Final design of debottlenecked cooling water systems.

is calculated (Fig. 23) and then the limiting cooling waterpro1le is modi1ed (Fig. 24). The 1nal design for the de-bottlenecked cooling water system is shown in Fig. 25.The re-use design looks super1cially to be more com-

plex than the corresponding parallel design. The designcan be evolved for design simplicity. Some modi1cationswill bring a penalty in performance, others will not bringa penalty. We can also make an illustrative economiccomparison between the design in Fig. 25 and the corre-sponding parallel design. If a parallel design is adoptedfor the cooling water system, the additional cooling cost(including both the capital and operating costs) would be34:6 k$=yr (Kim, Savalescu, & Smith, 2000). The design

Table 10CP vs. cooling water network design

Heat exchanger CP (kW=◦C) %

Parallel (no re-use) Target (re-use)

1 200 200 ·2 310 310 ·3 341.64 488.9 43.14 169.27 236.1 39.48Total 1020.9 1235 20.97

Common linea 1020.9 725 −28:98

aCommon line means the cooling water pipe line between thecooling tower and the cooling water network.

in Fig. 25 requires three new pipes between coolers. As-suming a 50 m piping distance and a velocity of 1:5 m=s,the piping cost would be 14:6 k$=yr, a 58% reductioncompared with the parallel design. The piping cost wascalculated from the correlation suggested by Alva-Algaez(1999). Capital cost was annualised over 3 years with aninterest rate of 15%. If the existing pipes between HE 1or 2 and the cooling tower can be re-used, the new de-sign needs one pipe line with an annualised capital costof 3:6 k$=y. The suggested method for cooling water net-work design is based on a conceptual design methodologyand therefore, other design con1guration can be evolved.The design complexity can be reduced for design sim-plicity but this would likely result in a penalty for thecooling system performance. The design of cooling watersystems involves trade-o3s including cooling tower costs,pressure drops, piping costs, design complexity, etc. Anoptimisation method is required to make the trade-o3s ina structured way and this will be the objective of futurework.The proposed debottlenecking procedure enables the

cooling tower to manage the increased heat load bychanging the network design from parallel to seriesarrangements. The design method targets the coolingtower conditions and then designs the cooling waternetwork for the new target conditions. The design pro-cedure for debottlenecking cooling water systems can besummarised as follows:

(1) De1ne the feasible cooling water supply line fromcomposite curve and parallel supply line.

(2) Target cooling tower supply conditions from coolingsystems model and the feasible cooling water supplyline.

(3) Design the cooling water network for target condi-tions with pinch migration and temperature shifting.

The Fowrate to individual heat exchangers is likelyto be changed. The design of individual heat exchangersthus needs to be checked to ensure that the design is fea-sible. Also, the procedure changes the conditions of thereturn cooling water and the recirculating cooling water


Fig. 26. E3ects of limitation on return cooling water supply conditions.

Fig. 27. Cooling water system design with hot blowdown extraction.

Fowrate. As a result, the pressure drop in the equipmentand piping will also change. Thus, the performance ofthe cooling water pumps needs to be checked becausethe pumping head, eJciency and required power dependon the Fowrate carried by the pump. When the design(Fig. 25) is compared with parallel arrangements, the CPvalue of individual heat exchangers in the parallel designis the same or less than that for the re-use design. How-ever, the CP value of the common line for the paralleldesign is greater than that of the re-use design (Table 10).So, it is not straightforward to predict which design ismore favourable in terms of cooling water pumping.

5. Heat load distribution for debottlenecking

The proposed debottlenecking procedure for cool-ing water systems maintains high temperature and lowFowrate of return cooling water to increase the heatremoval capacity of the cooling tower. However, theincrease in temperature is not favourable from the view-point of water treatment. Higher temperatures increasethe corrosion potential in cooling systems. The corrosion

rate increases with increase in temperature and corrosionrate doubles for every 10◦C rise in temperature (NACE,1990). Also fouling is related to temperature. For ex-ample, calcium carbonate, which is the most commonscaling problem in cooling water systems, has inversesolubility characteristics with temperature.Temperature limits for the return cooling water are re-

quired when cooling water treatment is important. Also,if plastic packing is used in the cooling tower it shouldbe able to take the required increase in temperature with-out deforming or this will cause a deterioration of cool-ing tower performance. In the next section, the e3ectsof temperature limitations for cooling water systems willbe investigated in conjunction with other design optionsnecessary to satisfy the design constraints.

5.1. Heat load distribution of cooling systems

Let us recall Example 2. The 1nal design of the debot-tlenecked cooling water systems is shown in Fig. 25 witha return cooling water temperature of 50:3◦C, which isincreased by 6:7◦C for debottlenecking. The return tem-perature limit will now be assumed to be 47◦C for thisexample. The previous target temperature (50:3◦C) isnow higher than the acceptable temperature limit (47◦C),which means that the required heat removal for the cool-ing systems is not obtained by changing the networkdesign. The Fowrate of the cooling water supply linecannot decrease beyond the 47◦C temperature limitation(Fig. 26a). So the maximum heat removal for the cool-ing water system occurs when the target temperature hasreached the temperature limit.The cooling system model under best conditions (BC)

in Fig. 26b gives 29:3◦C for the cooling water inlet tem-perature, which is higher than desired inlet temperature(28:8◦C). Furthermore, the heat removal for the bestconditions (15:2 MW) does not satisfy the heat load forthe network (15:6 MW). Other design options should be


Table 11Heat load distribution between cooling tower and hot blowdown

Hot blowdown Cooling tower Heat removal of TCW; in: Cooling systemCooling system Model (◦C)

Flowrate Heat load Flowrate Heat load (kW)(t=h) (kW) (t=h) (kW)

0 0 736.9 15179 15179 29.315 819.9 721.9 14570.2 15390.1 29.04...

......

......

...22.4 1224.5 714.5 14374.2 15598.7 28.8

Table 12Heat load distribution between cooling tower and air heat exchanger

Air heat exchanger Cooling tower Heat removal of TCW; in: Cooling systemCooling system model (◦C)

ST Heat Load TCT; in Heat load (kW)(◦C) (kW) (◦C) (kW)

0 0 47 15179 15179 29.32 1714.1 45 13671.9 15386 29.05...

......

......

...3.9 3342.5 43.1 12257.3 15598.8 28.8

Fig. 28. Cooling water system design with air heat exchanger.

incorporated along with best cooling water supply con-dition. The cooling water system with a return tempera-ture limitation needs another modi1cation to supplementcooling.The cooling tower performance and heat removal are

inFuenced by water supply conditions. Changing coolingwater supply conditions may be a way to reduce the heatload of the cooling tower. From the cooling tower model,the heat load capacity of the cooling tower is increasedwhen the Fowrate or temperature of the cooling water isdecreased. Other design options for heat load distributionare possible.

5.2. Hot blowdown extraction

If the cold blowdown is changed to hot blowdown,the heat load of the cooling tower is reduced because

the Fowrate to the cooling tower is decreased. Hot blow-down is extracted from the return hot cooling water asshown in Fig. 27. Because the temperature of the hot re-turn does not change as a result of the hot blowdown,but the Fowrate is decreased, the amount of hot blow-down that needs to be extracted can be found from thecooling system model. Table 11 shows an iterative pro-cedure to 1nd the target Fowrate of hot blowdown. Atthe target conditions, the cooling water system achievescooling requirements of both temperature and heat load.In Fig. 27, the return Fowrate of cooling water changesfrom 736.9 to 714:5 t=h as a result of hot blowdown ex-traction. In this case, the required hot blowdown exceedsthe original cold blowdown Fowrate, which results inan increase of make-up water and decrease of cycles ofconcentration.

5.3. Introduction of air heat exchangers

If the temperature of the hot return cooling water canbe decreased, the heat duty of the cooling tower wouldalso be decreased. To decrease the cooling water returntemperature, air heat exchangers can be installed betweenthe cooling tower and the cooling water network as shownin Fig. 28. The Fowrate of the return hot cooling waterdoes not change as a result of the air heat exchanger butthe temperature is decreased. The heat load removed bythe air heat exchanger can be targeted using the coolingtower system model as shown in Table 12. In Fig. 28,the return temperature of the cooling water changes from47◦C to 43:1◦C by the air heat exchanger. As the air


Table 13Results of heat load distribution

Case Heat removal of cooling system Heat Load of HEN (MW)

Cooling tower Hot blowdown Air heat exchanger

Hot blowdown 14374:2 kW 1224:5 kW 15.6(92.15%) (7.85%)

Air heat exchanger 12257:4 kW 3342:5 kW 15.6(78.58%) (21.42%)

heat exchanger inFuences only the temperature of the hotreturn cooling water, there is no change in the cycles ofconcentration.Hot blowdown is a more e3ective method than the air

heat exchanger from the viewpoint of energy distribution.The capacity of the cooling tower is used more e3ec-tively in the hot blowdown case (Table 13) because theinlet conditions of the cooling tower favour high temper-ature and low Fowrate. However, hot blowdown incurspenalties from an increase in make-up water and thermaldischarge to the liquid eIuent.

5.4. Other debottlenecking design options

As explained previously, the driving force for cool-ing is increased when the ratio of water Fowrate to airFowrate is decreased. So an increase in the air Fowrateis an alternative way to increase the driving force forcooling, and consequently the heat removal of the cool-ing tower. From the cooling tower system model, the in-creased target air Fowrate is 846 t=h (15.54% increaserelative to the base case) and the cooling tower removes15:6 MW, the heat load of the cooling water network asshown in Fig. 29.The use of cold seawater is yet another way to decrease

the return temperature of the hot cooling water. Whencold seawater is available to use as a cooling medium, theair heat exchanger may be replaced with a cooler usingcold seawater.For this study, the system interactions have focused on

bottlenecked cooling systems to suggest design optionsfor heat load distribution. However, we should not for-get that the cooling tower itself leaves room to improvethe cooling tower performance. For example, the pack-ing can be changed to one with a higher eJciency, toprovide greater surface area between the air and water.Also, improving the water distribution system across thecooling tower packing to provide a more uniform distri-bution pattern can improve the performance. Finally, theperformance of the air fan can be improved to increasethe induced=forced air Fowrate. Thus, greater cooling canbe obtained by upgrading the water and air distributionsystems.

Fig. 29. Cooling water system design with increase of air Fowrate.

6. Conclusions

Amathematical model of cooling systems has been de-veloped to predict the tower performance and to providedesign guidelines for cooling water system design.A new methodology for the design of cooling water

networks has been developed to satisfy any supply con-ditions for the cooling tower. Design can be carried outwith any target temperature by introducing the conceptsof pinch migration and temperature shift. From the inter-actions between the cooling tower performance and thedesign of the coolers, the proposed debottlenecking pro-cedures allow increased capacity without investment innew cooling tower equipment when the cooling towercapacity is limiting.The heat load distribution of cooling systems has

also been considered when a cooling water system isbottlenecked beyond cooling tower capacity or when atemperature constraint limits the return temperature. Anumber of design options for debottlenecking coolingsystems have been discussed to improve cooling towerperformance and to distribute heat load between thecooling tower and other design options.

Notation

A interfacial area, m2=m3

B Fowrate of blowdown, t=hC concentrationCC cycles of concentrationCP heat capacity multiplied by Fowrate, kW=◦C


CPA heat capacity of air, kJ=kg◦CCPL heat capacity of water, kJ=kg◦CCS humid heat capacity of air, kJ=kg◦CDH di3erential increment of enthalpyDL di3erential increment of water Fowrate,

kg=s m2

DT di3erential increment of temperature, ◦CST Tb− Ta, ◦CSTshift amount of temperature shift, ◦CSTmin minimum temperature approach, ◦CDW di3erential I increment of air humidityDZ di3erential increment of cooling tower

height, mE evaporation loss, t=he cooling tower e3ectivenessF FowrateF0 outlet water Fowrate of cooling tower after

makeup, t=hF1 outlet water Fowrate of cooling tower, t=hF2 inlet water Fowrate of cooling tower, t=hF3 cooling water Fowrate Fowing into the cool-

ing water network, t=hFa return Fowrate of cooling water after heat

load distribution, t=hFb return Fowrate of cooling water before heat

load distribution, t=hFH Fowrate of hot blowdown extraction, t=hG dry air Fowrate, kg=s m2

H enthalpy, kJ=kgHG heat transfer coeJcient of air, kW=m2◦CHL heat transfer coeJcient of water, kW=m2◦CKG mass transfer coeJcient of air, m=sM Fowrate of make-up, t=hMW molecular weight of water, kg=kg molMAir molecular weight of air, kg=kg molQ heat loadP total pressure, barPS vapour pressure, barT temperature, ◦CT ∗ migrated pinch temperature, ◦CTa return temperature of cooling water after

heat load distribution, ◦CTb return temperature of cooling water before

heat load distribution, ◦CT1 outlet water temperature of cooling tower,

◦CT2 inlet water temperature of cooling tower, ◦CT3 cooling water temperature Fowing into the

cooling water network, ◦CW air Humidity, kg water=kg airZ height of cooling tower height, mA0; B0; C0 constant value of vapour pressure equationA1; b1; c1 constant value of heat transfer coeJcient

equation in hGA2; b2; c2 constant value of heat transfer coeJcient

equation in hL

A3; b3; c3 constant value of mass transfer coeJcientequation in kG

Greek letters

� conversion criterion for modelling 0 latent heat of vaporisation, kJ=kg

Subscripts

ACT actual valueB blowdownCAL calculated valueCT cooling towerCW cooling waterDBT dry bulb temperatureG airHot hot process stream in heat exchangeri interfacein inlet conditionsL waterM make-upMax maximumMin minimumout outlet conditionsP pinch pointWBT wet bulb temperature0 reference temperature1 bottom of cooling tower2 top of cooling tower

Superscripts

AHE air heat exchangerCWN cooling water networksHB hot blowdownNew migrated pinch pointOld original pinch pointR heat removal

Acknowledgements

The authors would like to express their appreciationto Roy Holliday of Betz Dearborn, Tony Attenburgh ofBechtel Water and Alan Moore of AspenTech for advicegiven during the research project.

Appendix : The mathematical modelling of coolingtowers

A one-dimensional steady-state model will be devel-oped to illustrate the working principles of cooling towersand predict cooling tower eJciency. The model needs tobe reasonably accurate but also simple.


Fig. 30. Cooling tower.

The cooling mechanism in a cooling tower is a com-bination of heat and mass transfer. Latent heat is carriedacross the interface between water and air by di3usionof water vapour. Sensible heat is also transferred by tem-perature di3erence between the water and air. The waterto be cooled enters the top of the tower and the coolingair is either induced or forced through the tower from thebottom to the top for a counter-current tower (Fig. 30).The mathematical model developed here employs severalassumptions:

1. adiabatic operation in the cooling tower,2. dry air and water Fowrate are constant,3. no drift and leakage loss,4. the location of the air fan has no e3ect,5. interfacial areas are equal for heat and mass transfer,6. no inFuence of temperature on the transfer coeJcients,7. thermodynamic properties are constant across the cross

section of the tower.

Fig. 31 represents a section of the tower with di3eren-tial height dZ and shows the Fow of water and air that areseparated by the interface. The phenomena of mass andheat transfer are modelled as transfer coeJcients multi-plied by driving force based on interface temperature. To1nd interface temperature, heat balances are set up foroverall control volume (I), water (II) and air side (III) inthe manner of Olander (1960).

Fig. 31. Control volume of cooling tower model.

Control volume (I):

enthalpy in =GH + CPL(L+ dL)(TL + dTL − T0);

enthalpy out = LCPL(TL − T0) +G(H + dH);

where

dH = CSdTG + {CPA(TG − T0) + 0} dW;

LCPL dTL =GCS dTG +G{CPA(TG − T0)

−CPL(TL − T0) + 0} dW: (A.1)

Control volume (II):

enthalpy in = CPL(L+ dL)(TL + dTL − T0)

−GdWCPL(Ti − T0);

enthalpy out = LCPL(TL − T0);heat transfer = hLa(Ti − TL) dZ;

where

dWdTL ≈ 0

LCPL dTL = {GCPL dW − hLa dz}(Ti − TL): (A.2)

Control volume (III):

enthalpy in =GH;

enthalpy out =G(H + dH)

−G dW{CPA(TG − T0) + 0};heat transfer = hGa(Ti − TG) dZ;

GCS dTG = hGa(Ti − TG) dz: (A.3)

From these three equations, the equation for interfacetemperature is obtained in Eq. (A.4). However, the inter-face temperature cannot be determined without the dif-ferential value of humidity and air temperature.

Ti − TL =GCS(dTG=dz) +G{CPA(TG − T0)− CPL(TL − T0) + 0}(dW=dz)

GCPL(dW=dz)− hLa: (A.4)


Fig. 32. Flowchart of cooling tower modelling.

Air humidity, which represents mass transfer of watervapour from the interface to the air, is represented by thefollowing equation:

dWdz

=kGaG

(Wi −W ): (A.5)

Air and water temperatures are also represented in thesame way as the air humidity equation. The equation forwater temperature (Eq. (A.6)) represents heat transferfrom water to the interface and that of the air temperature(Eq. (A.7)) represents heat transfer from the interface toair.

dTL

dz=

hLaLCPL

(TL − Ti); (A.6)

dTG

dz=

hGaGCS

(Ti − TG): (A.7)

These di3erential equations (Eqs. (A.6) and (A.7))need the value of interface temperature. But the di3eren-tial increments of humidity and air temperature are alsoneeded to calculate the interface temperature in Eq. (A.4).This means an iterative method is necessary to obtain thevalue of the interface temperature in the model.Additional information is needed for mathematical

modelling. The absolute humidity at the interface (Eq.(A.8)) is calculated using a vapour pressure equation(Eq. (A.9)).

Wi =MWpS

MAir(P − pS); (A.8)

pS = exp{A0 − B0

C0 + T

}: (A.9)

Lyderson (1983) presented coeJcients for Eq. (A.9):

A0 = 23:7093; B0 = 4111; C0 = 237:7for 0◦C¡T ¡ 57◦C;

A0 = 23:1863; B0 = 3809:4; C0 = 226:7for 57◦C¡T ¡ 135◦C:

Coulson and Richardson (1996) discussed the resultsof several workers on experimental measurements of heatand mass transfer coeJcients in water-cooling towers.For the air–water system, heat and mass transfer coef-1cients are represented as a function of air and waterFowrate as follows.

hLa= a1Gb1Lc1; (A.10)

hGa= a2Gb2Lc2; (A.11)

kGa= a3Gb3Lc3: (A.12)

TheFowchartfor theproposedmodelisshowninFig. 32.This 1nds the conditions of the exit water and air whenthe inlet air and water conditions are given. First, the exitwater temperature (TL1) is assumed and then numericallyintegrated from the bottom to top of the tower (Z0−Zmax).The Runge–Kutta method has been used for solving or-dinary di3erential equations. The role of the inside loopis to 1nd the interface temperature at every di3erentialincrement. The calculated inlet temperature (TL2;CAL) iscompared with the real inlet temperature (TL2). The valueof the exit water temperature (TL1) is updated if the con-dition is not satis1ed. The whole procedure is repeateduntil the convergence criterion (�) is satis1ed.Consider now the calculation of the evaporation loss.

To calculate the evaporation we need to know the condi-tions of the exit air or water as Olander (1961) explainedthat at least 1ve variables of the nine external variables indesign equations of direct contact air–water cooler wereneeded to make the problem determinate. But these val-ues are not known for given inlet air and water condi-tions. As the increased air humidity is due to evaporated


water vapour, the evaporation loss is calculated from thevalue of the air humidity and air Fowrate.

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