Cooling water system design

Cooling water system design

Chemical Engineering Science 56 (2001) 3641–3658 www.elsevier.nl/locate/ces Cooling water system design Jin-Kuk Kim, Robin Smith ∗ Department of Pro...

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Chemical Engineering Science 56 (2001) 3641–3658

www.elsevier.nl/locate/ces

Cooling water system design Jin-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 the interactions between cooling water networks and the cooling tower performance. In re-circulating cooling water systems, cooling water from the cooling tower is supplied to a network of coolers that usually has a parallel con1guration. However, re-use of cooling water between di3erent cooling duties enables cooling water networks to be designed with series arrangements. This allows better cooling tower performance and increased cooling tower capacity, both in the context of new design and retro1t. A methodology has been developed for the design of cooling networks to satisfy any supply conditions for the cooling tower. A model of cooling tower performance allows interactions between the performance of the cooling tower and the design of cooling water networks to be explored systematically. In debottlenecking situations, better design of the cooling network using the new method, including increasing cooling tower blowdown, taking hot blowdown and strategic use of air coolers, can all be used to avoid investment in new cooling tower capacity and to improve the performance of the cooling tower in a systematic way. ? 2001 Elsevier Science Ltd. 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 and re-circulating cooling water systems, are all used for the rejection of waste heat to the environment. Of these methods, re-circulating cooling water systems are by far the most common because re-circulating cooling systems can conserve freshwater and reduce thermal pollution of receiving waters, relative to once-through systems. Much attention has been paid to issues on cooling systems 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 cooling towers. However, little attention has been placed to the interactions between cooling towers and heat exchanger networks, 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 industrial sites. Design and operating problems of cooling towers have been the focus of attention to manufactures and process engineers. Research on cooling systems to date has focussed on the individual components of cooling systems, not the system as a whole. Because of the interactions between cooling water networks and the cooling tower performance, cooling water systems should be designed and operated with consideration of all the cooling system components. Consider some of the possible changes to an existing cooling water system. A new heat exchanger might be introduced into the heat exchanger network, or the heat duty of coolers changed, or process changes might change the operating conditions. These process changes inFuence the conditions of the cooling water return and consequently a3ect the cooling tower performance. In such situations, it is often not clear how cooling water systems will be a3ected by new conditions and how the cooling water network design a3ects the cooling system. A combined water and energy analysis should be used to investigate the interactions for the overall system because the cooling water system has energy as well as water implications.

0009-2509/01/$ - see front matter ? 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 0 0 9 - 2 5 0 9 ( 0 1 ) 0 0 0 9 1 - 4

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During the last two decades, design tools for heat exchanger networks have been developed and successfully applied to a wide range of processes. The most commonly used tool has been pinch analysis. This is based on targeting before design and exploits conceptual understanding (Linnho3 & Smith, 1994). Various systematic methods based on pinch analysis have had a key role in saving energy in process design. In parallel with studies for heat exchange networks, increasing environmental concerns have resulted in a focus on wastewater minimisation problems. Wang and Smith (1994a) introduced a design method for targeting maximum water re-use based on the graphical representation of water systems. This design methodology was extended to design with Fowrate constraints and the design of distributed eIuent treatment systems (Wang & Smith, 1994b, 1995). Kuo and Smith (1997, 1998a,b) improved this design methodology for total water system design by attempting to take account of the interactions between water minimisation, regeneration systems and eIuent treatment systems. Whilst these conceptually-based approaches provide physical insights and design features for water systems, energy implications in water-using systems were not included. This paper will present a systematic method for the design of cooling water systems that accounts for the interactions and process constraints. The cooling tower and the cooling water network will be 1rst examined separately to discuss the nature of cooling water system design. A model of cooling water systems will be developed to examine the performance of the cooling tower to re-circulation Fowrate and return temperature and to predict the eJciency of cooling. A methodology for cooling water network design will then be developed, assuming 1xed inlet and outlet conditions for the cooling water. Finally, the design of the overall cooling water system will be developed by investigating the interactions between cooling water network design and cooling tower performance. Debottlenecking procedures for the design of 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. The cooling water used in the heat exchanger network returns to the cooling tower where the hot return cooling water is cooled (Fig. 1). Blowdown is necessary to avoid the build-up of undesirable materials in the re-circulating water as a result of evaporation. The Fowrate loss caused by evaporation and blowdown is compensated by make-up. To investigate interactions within cooling water systems, a cooling water system model including the cooling tower and other system components is needed. A model of the cooling tower is basic to this. In this study, the

Fig. 1. Cooling water systems. Table 1 Veri1cation of cooling tower model Case

1

2

3

4

Water Fowrate (kg=s) Air Fowrate (kg=s) CW inlet temperature (◦ C) CW outlet temperature (◦ C)

0.2 0.67 36.7 19.8

0.3 0.656 32 20.4

0.398 0.664 29.3 20.7

0.495 0.658 27.9 20.8

Model result CW outlet temp. (◦ C) Error (%)

19.83 0.15

−0:34

20.55

20.82 0.1

20.33

−0:73

cooling tower is assumed to be in counter-current contact with air drafted by a mechanical fan. The model needs to predict the conditions of the exit water and the air from the tower for given design and operating conditions. Details of the cooling tower model used in this work are presented in the appendix. Although the model has not been presented previously, it incorporates many principles from previous models and represents a compromise between simpli1ed models, which will not allow the system interactions to be examined reliably, and the very detailed simulation models, which are too detailed for system design. To verify the accuracy of the proposed model, experimental performance data was compared with simulation results from the model. Few experimental data are available to test the model. However, the experimental data of Bernier (1994) give cooling water outlet conditions under various inlet air and water conditions. Table 1 presents a comparison of this experimental data with predictions of the model. It can be seen that the proposed model is accurate 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 when water inlet conditions are changed. When cooling water inlet conditions are high temperature and low Fowrate, the cooling tower removes more heat from water and obtains a lower cooling water outlet temperature. Fig. 3 shows cooling tower performance in terms of e3ectiveness. The cooling tower e3ectiveness (e) is de1ned as the ratio

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of inlet cooling water is important in order to keep the driving force high. Other system components should be added to the cooling tower model to complete the cooling water system model. As the blowdown and make-up both have an effect on the heat and mass balances of the cooling water system, these need to be included (Fig. 1). In this study, it will be assumed that make-up water is added after cold blowdown has been taken. In practice it is often added to the cooling tower basin before cold blowdown. However, the e3ect of the location of the make-up on the heat balance for cooling water systems is not signi1cant. The cooling system model is Cooling tower model (see the appendix):

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

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)

F0 T0 = (F1 − B)T1 + MTM :

(6)

A key factor in the design and operation of cooling towers is the cycles of concentration. The cycles of concentration (CC) is de1ned as the ratio of the concentration of a soluble component in the blowdown stream to that in the make-up stream. The blowdown and make-up are calculated from the evaporation loss and cycles of concentration. The overall heat load of the cooling water network is also needed to determine the desired heat removal of the cooling tower. Cycles of concentration: FM CB = : (7) CC = CM FB Fig. 3. Cooling tower performance: cooling tower e3ectiveness.

of actual heat removal to the maximum attainable heat removal. The high e3ectiveness of tower represents better cooling performance and high heat removal. QACT : (1) e= QMAX Fig. 3 shows that when the inlet cooling water has conditions of high temperature and low Fowrate, the effectiveness of the cooling tower is high, in other words, the cooling tower removes more heat from the water. Bedekar, Nithiarasu, and Seetharamu (1998) presented experimental results demonstrating that the performance of cooling towers increases with a decrease in the L=G ratio. This agrees with the results from the cooling tower model. Maintaining high temperature and low Fowrate

Calculation of blowdown=makeup: E ; B= CC − 1 CC : M =E CC − 1

(8) (9)

Evaporation loss (see the appendix): E = G dW:

(10)

Heat load of HEN: QHEN = F2 Cp (T2 − T0 ):

(11)

The cooling system model, which will be used for the design 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 performance and predict the e3ectiveness of cooling towers.

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J.-K. Kim, R. Smith / Chemical Engineering Science 56 (2001) 3641–3658 Table 2 Hot process stream data of cooling water networks: Example 1 Heat exchanger Thot; in (◦ C) Thot; out (◦ C) CP (kW= ◦ C) Q (kW) 1 2 3 4

50 50 85 85

30 40 40 65

20 100 40 10

400 1000 1800 200

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, decreasing the Fowrate of the cooling tower supply has a more signi1cant bene1t on the e3ectiveness (hence increase in heat removal) than decreasing the inlet temperature. Other design guidelines can readily be derived from the model. 3. Design of cooling water networks The current practice for cooling water network design most often uses parallel con1gurations. In a parallel con1guration, the fresh cooling water is supplied directly to individual heat exchangers. After the cooling water has been used in each heat exchanger, the hot cooling water returns to the cooling tower (Fig. 4a). The minimum cooling water demand is determined by minimising the Fowrate to the individual heat exchangers (Fig. 4b). Under a parallel arrangement, return cooling water Fowrate becomes maximised but the return temperature is minimised. These conditions will lead to a poor cooling tower performance. No systematic methods have been suggested to deal with the design of cooling water networks. The traditional parallel design method is not Fexible when dealing with various process restrictions. A new cooling water network design methodology will now be developed. All cooling duties do not require cooling water at the cooling water supply temperature. This allows us, if appropriate, to change the cooling water network from a parallel to a series design (Fig. 5). A series arrangement, in which cooling water is re-used in the network, will return the cooling water with a higher temperature and lower Fowrate. From the predictions of the cooling tower model, the heat removal of cooling towers can be expected to increase under these conditions. In other words, if the design con1guration is converted from

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

parallel to series arrangements, the cooling tower can service a higher heat load for the coolers. 3.1. New design methodology for cooling water networks A simple problem (Example 1) will be used to develop the design methodology for cooling water networks. The cooling water system in Example 1 has four heat exchangers using cooling water as cooling medium for hot process streams. The temperature, Fowrate and cooling duty of hot process streams are given in Table 2. The data for hot process streams are represented as CP values, which is the product of heat capacity and Fowrate. It is assumed that the heat capacity of cooling water is constant throughout the temperature range. The cooling water network with a parallel con1guration for Example 1 has inlet and outlet CP’s of 106:4 kW= ◦ C, inlet temperature 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 analysis (Wang & Smith, 1994a) and developed for cooling water network design. In cooling water network analysis, it is assumed that any cooling-water-using operation can be represented as a counter-current heat exchange operation with a minimum temperature di3erence (Fig. 6a). The concept of the limiting water pro1le (Wang & Smith, 1994a) is taken from water pinch analysis and shown in Fig. 6b as a “limiting cooling water pro1le”. This is de1ned here to be the maximum inlet and outlet temperatures for the cooling water stream (Fig. 6b). These allowable temperatures are limited by the “minimum temperature di3erence” (STmin ). In new design this could be the practical minimum temperature di3erence for a given type of heat exchanger. In retro1t the

J.-K. Kim, R. Smith / Chemical Engineering Science 56 (2001) 3641–3658 Table 3 Limiting cooling water data: Example 1a Heat exchanger TCW; in (◦ C) TCW; out (◦ C) CP (kW= ◦ C) Q (kW) 1 2 3 4

20 30 30 55 a ST

min

40 40 75 75

20 100 40 10

400 1000 1800 200

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

temperature di3erence could be chosen to comply with the performance limitations of an existing heat exchanger under revised operating conditions of reduced temperature di3erences and increased Fowrate. Also, the limiting cooling water pro1le might be determined by other process constraints, such as corrosion, fouling, cooling water treatment, etc. Any cooling water line at or below this pro1le is considered to be a feasible design. The limiting pro1le is used to de1ne a boundary between feasible and infeasible regions. The limiting cooling water pro1le allows the individual streams of the cooling water network to be represented on a common basis, as water and energy characteristics are represented simultaneously. It should be emphasised that the 1nal design will not necessarily feature the minimum temperature di3erence incorporated in the limiting data. It simply represents a boundary between feasible and infeasible conditions. Most coolers in the 1nal network design will feature temperature driving forces greater than those used for the speci1cation of limiting conditions. This study focuses primarily on retro1t design and hence restricts consideration to deal only with hot streams to be cooled by cooling water. Better design for cooling water networks will be exploited under a 1xed heat exchanger network con1guration. For grassroot design, the design of cooling water networks and heat exchanger networks should be addressed simultaneously. In this paper, the topology of the heat exchanger network is assumed to be 1xed. The duties on the hot and cold streams in the heat exchanger network are thus assumed to be not related to the cooling system. In other words, the streams cooled by cooling water do not a3ect other streams in the heat exchanger network. As the inlet temperature of cooling water to coolers is increased, the driving force for the heat exchangers is decreased and might require additional heat exchanger area. However, at the same time the Fowrate is increased. So the reduction of driving force from decreasing temperature di3erence is compensated by increased cooling water Fowrate. The limiting cooling water data for Example 1 have been extracted from the hot process stream data and given in Table 3. A “cooling water composite curve” can be constructed by combining all individual pro1les into a single curve within temperature intervals (Fig. 7a). The design of the cooling water network will be based on the

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cooling water composite curve, which represents overall limiting conditions of the whole network. The cooling water supply line is a straight line matched against the cooling water composite curve to represent the overall cooling water Fowrate and conditions. Maximising the outlet temperature of the cooling water supply line minimises the Fowrate of cooling water by maximising cooling water re-use (Fig. 7b). Each point where the supply line touches the composite curve creates a pinch in the design. It is important to note that the interpretation of the pinch does not imply a zero driving force of heat transfer, but minimum driving force. Only those parts of the design in which the supply line touches the composite curve will feature minimum driving forces, all other parts will feature temperature di3erences above minimum. The water main method of Kuo and Smith (1998a) for the design of water re-use networks can be extended to the design of cooling water networks. The original method identi1ed water re-use opportunities for problems in which re-use was constrained by concentration limits. Fig. 8a illustrates the approach as it applies to cooling water networks. The design problem is decomposed into distinct regions by cutting o3 the concave regions (pockets) of the composite curve. This creates two design regions in this problem with a pinch point that de1nes a maximum re-use supply line (Fig. 8a). The cooling water Fowrate requirements in each design region are determined by a line drawn across each pocket. The cooling water “mains” are set up at di3erent temperatures: cooling water supply temperature, pinch temperature and exit temperature (Fig. 8b). It should be noted that the mains at pinch temperature will not necessarily be a feature of the 1nal design. It is used in the design procedure to connect the two parts of the design (below and above the pinch) and is eliminated at a later stage. In other problems there might, in principle, be more than two concave regions (pockets) as discussed by Kuo and Smith (1998a). If this is 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 generate a grid diagram with cooling water mains and plot the cooling-water-using operations as shown in Fig. 8b. The second stage is to connect the operations with cooling water mains. The third stage is to merge operations that cross mains. The 1nal stage is to remove intermediate (pinch) cooling water mains. Following the method allows the design of the cooling water network to achieve the target predicted by the supply line. Details of the procedure are given by Kuo and Smith (1998a) and are readily adapted from the concentration constraints in the original paper to the temperature constraints that are a feature of the cooling water network design problem. Following the method often allows more than one network design to achieve the target. Certain design features are essential to achieve the target but others are optional.

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

Fig. 8. Cooling water main method for cooling water network design. Table 4 Comparison of exit conditions of cooling water networks

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

One design of cooling water network to achieve the target minimum Fowrate for Example 1 is shown in Fig. 9. In contrast with a parallel con1guration, it is necessary for cooling water to be re-used in the design to achieve the target. As a result of cooling water re-use, the exit temperature of the cooling water is higher and total Fowrate lower than a parallel design (Table 4). If features of the design in Fig. 9 are unacceptable for practical reasons such as control problems or pipework complexity, then the design can always be evolved. But this is likely to re-

Method

Flowrate (kg=s)

CP (kW= ◦ C)

TCW; out (◦ C)

Parallel Max. re-use %

25.402 21.495

106.36 90.0 −15.4

51.97 57.78 +11.2

sult in penalties being incurred and the design not achieving the target. 3.2. Design of cooling water networks without a pinch The procedure used so far for the design of cooling water networks is an adaptation of the procedure of Kuo and Smith (1998a). However, there are di3erences between the design of water systems as described by Kuo and Smith and the design of cooling water networks that need now to be taken into account. The purpose of water supply line targeting is di3erent in water system design

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Fig. 10. Temperature constraints for return cooling water. Fig. 11. Pinch migration.

and cooling water network design. Water systems focus on the minimisation of contaminated water to the environment, which forces the design of water networks to the minimum consumption of water. For cooling water networks, the system has a number of components and there are interactions between di3erent parts of the system. Minimum overall Fowrate of cooling water is not necessarily the optimum. The cooling water supply line should be based on consideration of the overall system. The interactions between the design of the cooling tower and the design of the cooling network will be examined in the next section. Also, the cooling water system cannot operate beyond a speci1c return cooling water temperature because the hot return cooling water temperature might cause fouling problems, corrosion or problems with the cooling tower packing. It is common practice to introduce temperature constraints for return cooling water to the tower. If the cooling water supply line does not correspond with minimum Fowrate (either because of system interactions or temperature constraints), then a pinch point is not created with the limiting cooling water composite curve (Fig. 10). The setting could be between minimum Fowrate (maximum re-use) and no re-use (parallel arrangement) as shown in Fig. 10. The water main method is based on the concept of the pinch point and cannot be applied to problems without a pinch. The new design methodology should provide for cooling water networks without a pinch. The limiting pro1le represents the boundary between feasible and infeasible operation. In other words, any composite curve below the original one is feasible. Thus, the cooling water composite curve can be modi1ed in the feasible region without creating feasibility problems (Fig. 11). If the cooling water composite curve could be modi1ed to make a pinch point with the desired cooling water supply line in the feasible region, the cooling water network problem would be changed into a problem with a pinch. Pinch migration is introduced here to convert problems without a pinch into those with a pinch with the 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 cooling water composite curve moves along the heat load axis. The second is temperature shift in which the cool-

Fig. 12. Cooling water composite curve modi1cation.

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

ing water composite curve moves along the temperature axis. Of the two approaches, temperature shift is adopted because 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 temperature shift. Let us introduce a target temperature of 55◦ C for the cooling water for Example 1. A new pinch is created between the modi1ed composite curve and the new supply line, which is calculated from a simple heat balance (Fig. 13). The new calculated pinch of 38:5◦ C is migrated from the original pinch of 40◦ C. It is necessary for individual duties to apply a temperature shift for modi1cation of the composite curve. Cooling water streams 1, 2 and 3 take part in creating the original pinch, which means stream 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

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

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

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

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

of the limiting water pro1les according to the value of the temperature shift (1:5◦ C for this example). Modi1ed pro1les might cross the supply line and thus another step is needed. The second stage is to increase the Fowrate of the limiting water pro1le when the shifted-pro1le is restricted by temperature limitations. The limiting cooling water pro1le is modi1ed to satisfy temperature limitations by 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 shifting temperatures. However, for stream 1, it is necessary to increase Fowrate because the 20◦ C cooling water supply temperature restricts the temperature shift of the limiting data. The heat balance equations determine the increased Fowrate (Eq. (12)) and the new limiting exit temperature (Eq. (13)): CP new = CP old

old Tpold − Tcw; in new ; Tpnew − Tcw; in

(12)

new old Tcw; out = CP

old old Tcw; out − Tcw; in new + Tcw; in : CP new

(13)

After modi1cation of the conditions for each individual heat exchanger, the modi1ed cooling water pro1les are shown in Fig. 16 and the new limiting cooling water data are given as shown in Table 5. For stream 1, the CP is increased from 20 to 21:6 kW= ◦ C as a result of the second stage modi1cation. The new composite curve, which is constructed by combining all modi1ed limiting pro1les, is shown as Fig. 17. The modi1ed cooling water composite now creates a pinch point with the desired cooling water supply line. The cooling water network design can now be carried out using the cooling water mains method. The

Table 5 Temperature-shifted limiting cooling water dataa Heat exchanger TCW; in (◦ C) TCW; out (◦ C) CP (kW= ◦ C) Q (kW) 1a 2a 3a 4

20 28.5 28.5 55 a Modi1ed

38.5 38.5 73.5 75

21.6 100 40 10

400 1000 1800 200

data.

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

resulting design is shown in Fig. 18. The cooling tower return temperature and Fowrate agree with the target. The pinch migration and temperature shift method enables design with any target temperature. The cooling water network will have di3erent con1gurations with different target temperatures. This can be seen by comparing the maximum re-use design (Fig. 9) with the design with a temperature constraint (Fig. 18).

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

4. Debottlenecking of cooling water systems When cooling water networks need to increase the heat load of individual coolers or a new heat exchanger is introduced into an existing system, cooling water systems can become bottlenecked. As the increase of cooling load inFuences the cooling tower performance, and there are interactions between cooling water networks and the cooling tower, the best solution is often obtained by modifying the cooling water network.

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

Table 6 Limiting cooling water data of base casea Heat exchanger TCW; in (◦ C) TCW; out (◦ C) CP (kW= ◦ C) Q (kW) 1 2 3

4.1. General considerations for debottlenecking From the previous results of the cooling tower modelling and the cooling water network design, a general guideline for the design of cooling water systems can be suggested. The heat removal of the cooling tower can be increased by changing inlet cooling water conditions from high Fowrate and low temperature to low Fowrate and high temperature. This will, in general, require changing the cooling water network design from parallel to series or mixed parallel=series arrangements with re-use of cooling water, decreasing the Fowrate of cooling water and increasing the return temperature. By changing from parallel arrangements to cooling water re-use designs, the heat removal of the cooling tower can be increased without any energy penalty and without investment in a new cooling tower. A debottlenecking procedure for cooling water systems will now be developed using Example 2. The base case for Example 2 is shown in Fig. 19 and has three existing heat exchangers. The limiting cooling water data are given in Table 6. In this example, a new heat exchanger (Table 7) is introduced into the base case, which makes the cooling water system bottlenecked. New outlet conditions of the cooling water are given in Table 8 when the parallel arrangement is retained with the new heat exchanger. The Fowrate, temperature and the heat load of the cooling tower are increased and therefore the 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 needs to be installed to cool the cooling water to the maximum

28.8 33 36 a ST

min

37 37 52.7

200 635.5 488.9

1640.2 2542.1 8166.6

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

Table 7 Limiting cooling water data for new heat exchanger New heat exchanger

TCW; in (◦ C)

TCW; out (◦ C)

CP (kW= ◦ C)

Q (kW)

4

35

48

250

3250

Table 8 Cooling water outlet conditions of parallel design Case

Base

New

%

Outlet temperature (◦ C) Outlet CP (kW= ◦ C) Heat load (MW)

43.3 851.6 12.3

44.1 1020.9 15.6

1.8 19.9 26.3

permissible inlet temperature (28:8◦ C). Second, the heat load of the network (15:6 MW) is bigger than the heat removal of the tower (14:6 MW), which also means that another 1 MW of heat load needs to be dissipated by additional cooling. When the traditional parallel arrangements with new operating conditions are applied, the water Fowrate and the heat load of cooling tower are consequently increased. If there are no other design options than parallel arrangements, an additional cooling tower (or air cooling exchanger) is needed to satisfy the new bottlenecked conditions.

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J.-K. Kim, R. Smith / Chemical Engineering Science 56 (2001) 3641–3658 Table 9 E3ects of cooling water inlet conditions Case

Heat removal of cooling water system (MW)

Parallel (A) Maximum re-use (B) Target

14.61 15.69 15.60

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

Fig. 22. Cooling water supply line targeting.

Fig. 21. Feasible cooling water supply line.

4.2. Debottlenecking design procedures of cooling water systems A design procedure for debottlenecking cooling water systems will now be developed. The cooling water composite curve can 1rst be constructed from the limiting cooling water data. The cooling water network performance can be changed within a feasible region that is bounded by the maximum re-use supply line and the parallel design supply line (Fig. 21a). In Fig. 21b, the feasible cooling water supply line (line AB) represents the attainable outlet conditions from the cooling tower model by changing design con1gurations. As the inlet conditions to the cooling tower a3ect the cooling tower performance, it is necessary to know how the inlet conditions 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 network (Fig. 21a). But the heat removal of the cooling water system is changed as inlet conditions to the cooling tower are changed (Table 9). The heat removal of cooling water systems increases as the design con1guration changes from parallel to maximum re-use (A to B in Fig. 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 network should be 28:8◦ C.

(2) Heat removal from the cooling water system should be equal to the heat load of the cooling water network. In this example, it is not necessary to achieve a temperature lower than 28:8◦ C. From Table 9 it can be seen that the target conditions lie somewhere along the feasible cooling water supply line. The next stage is to 1nd the target supply conditions for the cooling tower. The feasible cooling water supply line can move from BN to BM in Fig. 22. The target conditions, which satisfy the desired temperature to cooling water network (28:8◦ C), are found by changing the cooling water supply conditions from BN to BM . The heat removal of the cooling system is the same as the heat load of the cooling water network at the target conditions (B∗ ), where the inlet temperature to the cooling water network is satis1ed. Target conditions are given by the intersection between the feasible cooling water supply line and the isothermal line of the cooling system outlet temperature. The target conditions for debottlenecking have then been found using the cooling system model. The target conditions are CP of 725 kW= ◦ C and a temperature of 50:3◦ C. At target conditions, the cooling demand of networks are satis1ed without additional cooling capacity. Below the target temperature, the current cooling systems cannot operate for cooling demand. The next stage is to design the cooling water network with target conditions. As the new cooling water supply line has no pinch with the limiting composite curve (Fig. 23), the temperature shift and pinch migration method is applied to this case as explained in the previous section. The new pinch point

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Table 10 CP vs. cooling water network design Heat exchanger

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

CP (kW= ◦ C)

%

Parallel (no re-use)

Target (re-use)

1 2 3 4 Total

200 310 341.64 169.27 1020.9

200 310 488.9 236.1 1235

Common linea

1020.9

725

· ·

43.1 39.48 20.97

−28:98

a Common line means the cooling water pipe line between the cooling tower and the cooling water network.

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 water pro1le is modi1ed (Fig. 24). The 1nal design for the debottlenecked cooling water system is shown in Fig. 25. The re-use design looks super1cially to be more complex than the corresponding parallel design. The design can be evolved for design simplicity. Some modi1cations will bring a penalty in performance, others will not bring a penalty. We can also make an illustrative economic comparison between the design in Fig. 25 and the corresponding parallel design. If a parallel design is adopted for the cooling water system, the additional cooling cost (including both the capital and operating costs) would be 34:6 k$=yr (Kim, Savalescu, & Smith, 2000). The design

in Fig. 25 requires three new pipes between coolers. Assuming a 50 m piping distance and a velocity of 1:5 m=s, the piping cost would be 14:6 k$=yr, a 58% reduction compared with the parallel design. The piping cost was calculated from the correlation suggested by Alva-Algaez (1999). Capital cost was annualised over 3 years with an interest rate of 15%. If the existing pipes between HE 1 or 2 and the cooling tower can be re-used, the new design needs one pipe line with an annualised capital cost of 3:6 k$=y. The suggested method for cooling water network design is based on a conceptual design methodology and therefore, other design con1guration can be evolved. The design complexity can be reduced for design simplicity but this would likely result in a penalty for the cooling system performance. The design of cooling water systems involves trade-o3s including cooling tower costs, pressure drops, piping costs, design complexity, etc. An optimisation method is required to make the trade-o3s in a structured way and this will be the objective of future work. The proposed debottlenecking procedure enables the cooling tower to manage the increased heat load by changing the network design from parallel to series arrangements. The design method targets the cooling tower conditions and then designs the cooling water network for the new target conditions. The design procedure for debottlenecking cooling water systems can be summarised as follows: (1) De1ne the feasible cooling water supply line from composite curve and parallel supply line. (2) Target cooling tower supply conditions from cooling systems model and the feasible cooling water supply line. (3) Design the cooling water network for target conditions with pinch migration and temperature shifting. The Fowrate to individual heat exchangers is likely to be changed. The design of individual heat exchangers thus needs to be checked to ensure that the design is feasible. Also, the procedure changes the conditions of the return cooling water and the recirculating cooling water

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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 equipment and piping will also change. Thus, the performance of the cooling water pumps needs to be checked because the pumping head, eJciency and required power depend on the Fowrate carried by the pump. When the design (Fig. 25) is compared with parallel arrangements, the CP value of individual heat exchangers in the parallel design is the same or less than that for the re-use design. However, the CP value of the common line for the parallel design is greater than that of the re-use design (Table 10). So, it is not straightforward to predict which design is more favourable in terms of cooling water pumping. 5. Heat load distribution for debottlenecking The proposed debottlenecking procedure for cooling water systems maintains high temperature and low Fowrate of return cooling water to increase the heat removal capacity of the cooling tower. However, the increase in temperature is not favourable from the viewpoint of water treatment. Higher temperatures increase the corrosion potential in cooling systems. The corrosion

rate increases with increase in temperature and corrosion rate doubles for every 10◦ C rise in temperature (NACE, 1990). Also fouling is related to temperature. For example, calcium carbonate, which is the most common scaling problem in cooling water systems, has inverse solubility characteristics with temperature. Temperature limits for the return cooling water are required when cooling water treatment is important. Also, if plastic packing is used in the cooling tower it should be able to take the required increase in temperature without deforming or this will cause a deterioration of cooling tower performance. In the next section, the e3ects of temperature limitations for cooling water systems will be investigated in conjunction with other design options necessary to satisfy the design constraints. 5.1. Heat load distribution of cooling systems Let us recall Example 2. The 1nal design of the debottlenecked cooling water systems is shown in Fig. 25 with a return cooling water temperature of 50:3◦ C, which is increased by 6:7◦ C for debottlenecking. The return temperature limit will now be assumed to be 47◦ C for this example. The previous target temperature (50:3◦ C) is now higher than the acceptable temperature limit (47◦ C), which means that the required heat removal for the cooling systems is not obtained by changing the network design. The Fowrate of the cooling water supply line cannot decrease beyond the 47◦ C temperature limitation (Fig. 26a). So the maximum heat removal for the cooling water system occurs when the target temperature has reached the temperature limit. The cooling system model under best conditions (BC ) in Fig. 26b gives 29:3◦ C for the cooling water inlet temperature, which is higher than desired inlet temperature (28:8◦ C). Furthermore, the heat removal for the best conditions (15:2 MW) does not satisfy the heat load for the network (15:6 MW). Other design options should be

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Table 11 Heat load distribution between cooling tower and hot blowdown Hot blowdown

Cooling tower

Flowrate (t=h)

Heat load (kW)

Flowrate (t=h)

Heat load (kW)

0 15 .. . 22.4

0 819.9 .. . 1224.5

736.9 721.9 .. . 714.5

15179 14570.2 .. . 14374.2

Heat removal of Cooling system (kW)

TCW; in : Cooling system Model (◦ C)

15179 15390.1 .. . 15598.7

29.3 29.04 .. . 28.8

Heat removal of Cooling system (kW)

TCW; in : Cooling system model (◦ C)

15179 15386 .. . 15598.8

29.3 29.05 .. . 28.8

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

Cooling tower

ST (◦ C)

Heat Load (kW)

TCT; in (◦ C)

Heat load (kW)

0 2 .. . 3.9

0 1714.1 .. . 3342.5

47 45 .. . 43.1

15179 13671.9 .. . 12257.3

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

incorporated along with best cooling water supply condition. The cooling water system with a return temperature limitation needs another modi1cation to supplement cooling. The cooling tower performance and heat removal are inFuenced by water supply conditions. Changing cooling water supply conditions may be a way to reduce the heat load of the cooling tower. From the cooling tower model, the heat load capacity of the cooling tower is increased when the Fowrate or temperature of the cooling water is decreased. Other design options for heat load distribution are 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 blowdown is extracted from the return hot cooling water as shown in Fig. 27. Because the temperature of the hot return does not change as a result of the hot blowdown, but the Fowrate is decreased, the amount of hot blowdown that needs to be extracted can be found from the cooling system model. Table 11 shows an iterative procedure to 1nd the target Fowrate of hot blowdown. At the target conditions, the cooling water system achieves cooling requirements of both temperature and heat load. In Fig. 27, the return Fowrate of cooling water changes from 736.9 to 714:5 t=h as a result of hot blowdown extraction. In this case, the required hot blowdown exceeds the original cold blowdown Fowrate, which results in an increase of make-up water and decrease of cycles of concentration. 5.3. Introduction of air heat exchangers If the temperature of the hot return cooling water can be decreased, the heat duty of the cooling tower would also be decreased. To decrease the cooling water return temperature, air heat exchangers can be installed between the cooling tower and the cooling water network as shown in Fig. 28. The Fowrate of the return hot cooling water does not change as a result of the air heat exchanger but the temperature is decreased. The heat load removed by the air heat exchanger can be targeted using the cooling tower system model as shown in Table 12. In Fig. 28, the return temperature of the cooling water changes from 47◦ C to 43:1◦ C by the air heat exchanger. As the air

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Table 13 Results of heat load distribution Case

Heat removal of cooling system Cooling tower

Hot blowdown

Hot blowdown

14374:2 kW (92.15%)

1224:5 kW (7.85%)

Air heat exchanger

12257:4 kW (78.58%)

heat exchanger inFuences only the temperature of the hot return cooling water, there is no change in the cycles of concentration. 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 e3ectively in the hot blowdown case (Table 13) because the inlet conditions of the cooling tower favour high temperature and low Fowrate. However, hot blowdown incurs penalties from an increase in make-up water and thermal discharge to the liquid eIuent.

Heat Load of HEN (MW) Air heat exchanger 15.6 3342:5 kW (21.42%)

15.6

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

5.4. Other debottlenecking design options

6. Conclusions

As explained previously, the driving force for cooling is increased when the ratio of water Fowrate to air Fowrate is decreased. So an increase in the air Fowrate is an alternative way to increase the driving force for cooling, and consequently the heat removal of the cooling tower. From the cooling tower system model, the increased target air Fowrate is 846 t=h (15.54% increase relative to the base case) and the cooling tower removes 15:6 MW, the heat load of the cooling water network as shown in Fig. 29. The use of cold seawater is yet another way to decrease the return temperature of the hot cooling water. When cold seawater is available to use as a cooling medium, the air heat exchanger may be replaced with a cooler using cold seawater. For this study, the system interactions have focused on bottlenecked cooling systems to suggest design options for heat load distribution. However, we should not forget that the cooling tower itself leaves room to improve the cooling tower performance. For example, the packing can be changed to one with a higher eJciency, to provide greater surface area between the air and water. Also, improving the water distribution system across the cooling tower packing to provide a more uniform distribution pattern can improve the performance. Finally, the performance of the air fan can be improved to increase the induced=forced air Fowrate. Thus, greater cooling can be obtained by upgrading the water and air distribution systems.

A mathematical model of cooling systems has been developed to predict the tower performance and to provide design guidelines for cooling water system design. A new methodology for the design of cooling water networks has been developed to satisfy any supply conditions for the cooling tower. Design can be carried out with any target temperature by introducing the concepts of pinch migration and temperature shift. From the interactions between the cooling tower performance and the design of the coolers, the proposed debottlenecking procedures allow increased capacity without investment in new cooling tower equipment when the cooling tower capacity is limiting. The heat load distribution of cooling systems has also been considered when a cooling water system is bottlenecked beyond cooling tower capacity or when a temperature constraint limits the return temperature. A number of design options for debottlenecking cooling systems have been discussed to improve cooling tower performance and to distribute heat load between the cooling tower and other design options. Notation A B C CC CP

interfacial area, m2 =m3 Fowrate of blowdown, t=h concentration cycles of concentration heat capacity multiplied by Fowrate, kW= ◦ C

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

CPA CPL CS DH DL DT ST STshift STmin DW DZ E e F F0 F1 F2 F3 Fa Fb FH G H HG HL KG M MW MAir Q P PS T T∗ Ta Tb T1 T2 T3 W Z A0; B0; C0 A1 ; b 1 ; c 1 A2 ; b 2 ; c 2

heat capacity of air, kJ=kg◦ C heat capacity of water, kJ=kg◦ C humid heat capacity of air, kJ=kg◦ C di3erential increment of enthalpy di3erential increment of water Fowrate, kg=s m2 di3erential increment of temperature, ◦ C Tb − Ta, ◦ C amount of temperature shift, ◦ C minimum temperature approach, ◦ C di3erential I increment of air humidity di3erential increment of cooling tower height, m evaporation loss, t=h cooling tower e3ectiveness Fowrate outlet water Fowrate of cooling tower after makeup, t=h outlet water Fowrate of cooling tower, t=h inlet water Fowrate of cooling tower, t=h cooling water Fowrate Fowing into the cooling water network, t=h return Fowrate of cooling water after heat load distribution, t=h return Fowrate of cooling water before heat load distribution, t=h Fowrate of hot blowdown extraction, t=h dry air Fowrate, kg=s m2 enthalpy, kJ=kg heat transfer coeJcient of air, kW=m2◦ C heat transfer coeJcient of water, kW=m2◦ C mass transfer coeJcient of air, m=s Fowrate of make-up, t=h molecular weight of water, kg=kg mol molecular weight of air, kg=kg mol heat load total pressure, bar vapour pressure, bar temperature, ◦ C migrated pinch temperature, ◦ C return temperature of cooling water after heat load distribution, ◦ C return temperature of cooling water before heat load distribution, ◦ C outlet water temperature of cooling tower, ◦ C inlet water temperature of cooling tower, ◦ C cooling water temperature Fowing into the cooling water network, ◦ C air Humidity, kg water=kg air height of cooling tower height, m constant value of vapour pressure equation constant value of heat transfer coeJcient equation in hG constant value of heat transfer coeJcient equation in hL

A3; b3 ; c3

3655

constant value of mass transfer coeJcient equation in kG

Greek letters  0

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

Subscripts ACT B CAL CT CW DBT G Hot i in L M Max Min out P WBT 0 1 2

actual value blowdown calculated value cooling tower cooling water dry bulb temperature air hot process stream in heat exchanger interface inlet conditions water make-up maximum minimum outlet conditions pinch point wet bulb temperature reference temperature bottom of cooling tower top of cooling tower

Superscripts AHE CWN HB New Old R

air heat exchanger cooling water networks hot blowdown migrated pinch point original pinch point heat removal

Acknowledgements The authors would like to express their appreciation to Roy Holliday of Betz Dearborn, Tony Attenburgh of Bechtel Water and Alan Moore of AspenTech for advice given during the research project. Appendix : The mathematical modelling of cooling towers A one-dimensional steady-state model will be developed to illustrate the working principles of cooling towers and predict cooling tower eJciency. The model needs to be reasonably accurate but also simple.

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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 = CS dTG + {CPA (TG − T0 ) +

LCPL dTL = GCS dTG + G {CPA (TG − T0 )

Fig. 30. Cooling tower.

−CPL (TL − T0 ) +

The cooling mechanism in a cooling tower is a combination of heat and mass transfer. Latent heat is carried across the interface between water and air by di3usion of water vapour. Sensible heat is also transferred by temperature di3erence between the water and air. The water to be cooled enters the top of the tower and the cooling air is either induced or forced through the tower from the bottom to the top for a counter-current tower (Fig. 30). The mathematical model developed here employs several assumptions: 1. 2. 3. 4. 5. 6. 7.

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

Fig. 31 represents a section of the tower with di3erential height dZ and shows the Fow of water and air that are separated by the interface. The phenomena of mass and heat transfer are modelled as transfer coeJcients multiplied by driving force based on interface temperature. To 1nd interface temperature, heat balances are set up for overall control volume (I), water (II) and air side (III) in the manner of Olander (1960).

Ti − TL =

0 } dW;

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 = hL a(Ti − TL ) dZ; where dW dTL ≈ 0 LCPL dTL = {GCPL dW − hL a d z }(Ti − TL ):

(A.2)

Control volume (III): enthalpy in = GH; enthalpy out = G(H + dH ) −G dW {CPA (TG − T0 ) +

0 };

heat transfer = hG a(Ti − TG ) dZ; GCS dTG = hG a(Ti − TG ) d z:

(A.3)

From these three equations, the equation for interface temperature is obtained in Eq. (A.4). However, the interface temperature cannot be determined without the differential value of humidity and air temperature.

GCS (dTG =d z) + G {CPA (TG − T0 ) − CPL (TL − T0 ) + GCPL (dW=d z) − hL a

0 }(dW=d z)

:

(A.4)

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

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Fig. 32. Flowchart of cooling tower modelling.

Air humidity, which represents mass transfer of water vapour from the interface to the air, is represented by the following equation: kG a dW = (Wi − W ): (A.5) dz G Air and water temperatures are also represented in the same way as the air humidity equation. The equation for water temperature (Eq. (A.6)) represents heat transfer from water to the interface and that of the air temperature (Eq. (A.7)) represents heat transfer from the interface to air. hL a dTL = (TL − Ti ); (A.6) dz LCPL hG a dTG = (Ti − TG ): dz GCS

(A.7)

These di3erential equations (Eqs. (A.6) and (A.7)) need the value of interface temperature. But the di3erential increments of humidity and air temperature are also needed to calculate the interface temperature in Eq. (A.4). This means an iterative method is necessary to obtain the value 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)). MW pS ; (A.8) Wi = MAir (P − pS )   B0 : (A.9) pS = exp A0 − C0 + T Lyderson (1983) presented coeJcients for Eq. (A.9): A0 = 23:7093; B0 = 4111; C0 = 237:7 for 0◦ C ¡ T ¡ 57◦ C;

A0 = 23:1863; B0 = 3809:4; C0 = 226:7 for 57◦ C ¡ T ¡ 135◦ C: Coulson and Richardson (1996) discussed the results of several workers on experimental measurements of heat and mass transfer coeJcients in water-cooling towers. For the air–water system, heat and mass transfer coef1cients are represented as a function of air and water Fowrate as follows. hL a = a1 G b1 Lc1 ;

(A.10)

hG a = a2 G b2 Lc2 ;

(A.11)

kG a = a3 G b3 Lc3 :

(A.12)

TheFowchartfortheproposedmodelisshowninFig. 32. This 1nds the conditions of the exit water and air when the inlet air and water conditions are given. First, the exit water temperature (TL1 ) is assumed and then numerically integrated from the bottom to top of the tower (Z0 − Zmax ). The Runge–Kutta method has been used for solving ordinary di3erential equations. The role of the inside loop is to 1nd the interface temperature at every di3erential increment. The calculated inlet temperature (TL2; CAL ) is compared with the real inlet temperature (TL2 ). The value of the exit water temperature (TL1 ) is updated if the condition is not satis1ed. The whole procedure is repeated until the convergence criterion () is satis1ed. Consider now the calculation of the evaporation loss. To calculate the evaporation we need to know the conditions of the exit air or water as Olander (1961) explained that at least 1ve variables of the nine external variables in design equations of direct contact air–water cooler were needed to make the problem determinate. But these values are not known for given inlet air and water conditions. As the increased air humidity is due to evaporated

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water vapour, the evaporation loss is calculated from the value of the air humidity and air Fowrate. References Alva-Algaez, A. (1999). Integrated design of water systems. Ph.D. Thesis, UMIST, Manchester, UK. Barzuza, I. (1995). Minimising solids buildup. Chemical Engineering, 102, 114 –116. Bedekar, S. V., Nithiarasu, P., & Seetharamu, K. N. (1998). Experimental Investigation of the Performance of a counter-Fow, packed-bed mechanical cooling tower. Energy, 23, 943–947. Bernier, M. A. (1994). Cooling tower performance: Theory and experiments. ASHRAE Transactions Res., 100, 114–121. Burger, R. (1993). Cooling towers: The often over-looked. Chemical Engineering, 100, 100 –104. Coulson, J. M., & Richardson, J. F. (1996). Chemical engineering: Fluid =ow, heat transfer and mass transfer. (5th ed.). Oxford: Pergamon Press. Gale, T. E., & Beecher, J. (1987). A better cooling water system. Hydrocarbon Processing, 60, 27–29. Gibson, W. D. (1999). Recycling cooling and boiler water. Chemical Engineering, 106, 47–51. Kim, J., Savalescu, L., & Smith, R. (2000). Design of cooling systems for eIuent temperature reduction. Chemical Engineering Science, 56, 1811–1830. Kuo, W. J., & Smith, R. (1997). EIuent treatment system design. Chemical Engineering Science, 52, 4273–4290.

Kuo, W. J., & Smith, R. (1998a). Designing for the interactions between water-use and eIuent treatment. Transactions of the Institute of Chemical Engineers 76, Part A, 287–301. Kuo, W. J., & Smith, R. (1998b). Design of water-using systems involving regeneration. Transactions of the Institute of Chemical Engineers 76, Part B, 94 –114. Lefevre, M. R. (1984). Reducing water consumption in cooling towers. Chemical Engineering Progress, 80, 55 – 62. Linnho3, B., & Smith, R. (1994). Pinch analysis for network design. HDEH. Lyderson, A. L. (1983). Mass transfer in engineering practice. New York: Wiley. NACE (National Association of Corrosion Engineers) (1990). Cooling water treatment manual (3rd ed.). NACE, US. Olander, D. R. (1960). The internal consistency of simultaneous heat and mass transfer relationships. A.I.Ch.E. Journal, 6, 346–347. Olander, D. R. (1961). Design of direct contact cooler-condensers. I& EC, 53, 121–126. Pannkoke, T. (1996). Cooling tower basics. HPAC, 68, 137–155. Wang, Y. P., & Smith, R. (1994a). Wastewater minimisation. Chemical Engineering Science, 49, 981–1006. Wang, Y. P., & Smith, R. (1994b). Design of distributed eIuent treatment systems. Chemical Engineering Science, 49, 3127–3145. Wang, Y. P., & Smith, R. (1995). Wastewater minimisation with Fowrate constraints. Transactions of the Institute of Chemical Engineers 73, Part A, 889 –904. Willa, J. L. (1997). Improving cooling towers. Chemical Engineering, 104, 92–96.