Energy & Fuels 2005, 19, 1723-1728
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Recirculating Cooling-Water Network with an Intermediate Cooling-Water Main Xiao Feng,* Renjie Shen, and Bin Wang Department of Chemical Engineering, State Key Laboratory of Multi-Phase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an 710049, People’s Republic of China Received November 10, 2004. Revised Manuscript Received March 25, 2005
Recirculating cooling-water systems are, by far, the most common method used for the rejection of waste heat to the environment. To reduce the recirculating cooling-water flow rate to improve the performance of the cooling tower, and, at the same time, to make the recirculating coolingwater network simpler and more flexible, so that it is easier to operate and control, a new recirculating cooling-water network configuration with an intermediate cooling-water main is proposed in this paper. In the network, an intermediate cooling-water main is positioned between the cooling-water supply main and the cooling-water return main, with the temperature usually at the pinch. The intermediate main receives used recirculating cooling water from some coolers at temperatures less than or equal to its temperature and provides cooling water to some other coolers, which can use cooling water at temperatures higher than or equal to its temperature. In this way, the recirculating cooling water into or out of each cooler will be coming from or going into one of the three mains. Compared to the traditional parallel network, the new configuration can obviously reduce the recirculating cooling-water flow rate and increase the return temperature to the cooling tower, so that the effectiveness of the cooling tower is increased. In addition, compared to the series arrangements that have been proposed recently, the new configuration has a simpler network, which will be easier to operate and control. A methodology has been developed for the design of cooling networks with an intermediate cooling-water main.
1. Introduction Recirculating cooling-water systems are, by far, the most common method used for the rejection of waste heat to the environment. The cooling-water system consists of the cooling tower, the recirculation system, and the cooler network (Figure 1). The recirculating cooling water absorbs waste heat from the cooler network and then returns to the cooling tower with an increased temperature through the cooling water return main (Pout). The temperature of the recirculating cooling water decreases in the cooling tower, as the result of evaporation. Blowdown is necessary, to avoid the buildup of undesirable materials in the recirculating cooling water. The flow-rate loss caused by evaporation and blowdown is compensated by makeup new water, and then the recirculating cooling water will be returned to the heat-exchanger network, to be recycled. The design and operating problems of cooling towers in recirculating cooling-water systems have been the focus of attention of manufacturers and process engineers with a concern for energy conservation. Much attention has been given to the issue about how to enhance the effectiveness of the cooling tower.1-7 The (1) Kim, J.; Smith, R. Cooling Water System Design. Chem. Eng. Sci. 2001, 56, 3641-3658. (2) Burger, R. Cooling Towers: The Often Over-looked Profit Center. Chem. Eng. (N.Y., NY, U.S.) 1993, 100, 100-104. (3) Bernier, M. A. Cooling Tower Performance: Theory and Experiments. ASHRAE Trans. 1994, 100, 114-121. (4) Pannkoke, T. Cooling Tower Basics. Heat./Piping/Air Cond. 1996, 68, 137-155.
effectiveness of the cooling tower (e) is defined as1
e)
QAct QMax
(1)
where QAct is the actual heat removal in the cooling tower (given in kilowatts) and QMax is the maximum attainable heat removal in the cooling tower (given in kilowatts). Figure 2 shows the influence of the recirculating cooling-water inlet temperature and flow rate on the effectiveness of the cooling tower.1 When the inlet cooling water has conditions of high temperature and low flow rate, the effectiveness of the cooling tower is high; in other words, the cooling tower removes more heat from the water. The current practice for cooling-water network design most often uses a parallel design (Figure 3a). In a parallel configuration, 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. Under a parallel arrangement, the flow rate of the returning cooling water becomes maximized, but the return tem(5) Willa, J. L. Improving Cooling Towers. Chem. Eng. (N.Y., NY, U.S.) 1997, 104, 92-96. (6) Kim, J.; Savalescu, L.; Smith, R. Design of Cooling Systems for Effluent Temperature Reduction. Chem. Eng. Sci. 2000, 56, 18111830. (7) Gale, T. E.; Beecher, J. A Better Cooling Water System. Hydrocarbon Process. 1987, 60, 27-29.
10.1021/ef049711z CCC: $30.25 © 2005 American Chemical Society Published on Web 04/15/2005
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Figure 1. Schematic diagram of the cooling-water systems. (CT ) cooling tower; HE n ) heat exchanger n.)
Figure 2. Influence of the recirculating cooling-water factors (water inlet temperature and flow rate) on the effectiveness of the cooling tower.
Feng et al.
cooling tower can service a higher heat load for the coolers, which can satisfy the needs of extended production. Kim and Smith extended the water pinch technology to the recirculating cooling-water system and presented the series design methodology for a cooler network.1 Using this method, the network can reach the design targetsthat is, the returning cooling water reaches the highest temperature and lowest flow rate, and the highest effectiveness of the cooling tower is obtained. They then extended the series design to a cooling-water system retrofit,8 by especially considering how to reduce the pressure decrease and increase the efficient use of cooling towers of an existing cooling-water system. However, the cooler network in the series arrangement, with the coolers connected directly to each other, is complex and not flexible. If fluctuations of heat load or temperature occur in some coolers, other coolers will be influenced. To make the network simple and to increase the flexibility of the network, in this paper, a new recirculating cooling water network configuration with an intermediate cooling water main is proposed, which has a simpler network and is easier to operate and control. The design methodology has also been developed using mathematical programming. Note that Kim and Smith8 introduced a similar concept about an intermediate water main, as a design strategy, and it was removed during the last step of the design strategy; therefore, their use of the water main is totally different. Note that the work in this paper only focuses on the recirculating cooling-water network, and the other parts of the cooling-water system (e.g., the cooling tower) are the same as those in the model developed by Kim and Smith,1,8 so the results presented in this paper are applicable. The optimization design in this paper does not involve those components. 2. Design of Recirculating Cooling-Water Networks with an Intermediate Cooling Water Main
Figure 3. Diagram of the design option for cooling-water networks: (a) parallel design and (b) series design.
perature is minimized. These conditions will lead to poor performance of the cooling tower. At the same time, it will use more water and dictates higher operating costs. To solve the previously mentioned problem, Kim and Smith introduced a series design for cooling-water networks.1 In a series arrangement, the cooling water is reused in the network before it returns to the cooling tower (see Figure 3b). In comparison with the parallel design, a series configuration will return the cooling water with a higher temperature and at a lower flow rate, because the cooling water can be reused several times. From Figure 2, we can know that the cooling towers with a series design will lead to high effectiveness and, therefore, have a good effect on energy savings. From the predictions of the cooling tower model, the heat removal of cooling towers can be expected to increase under these conditions. On the other hand, the cooling system will have higher potential, because of a smaller flow rate. Especially, the
Water networks with internal water mains are simple and easy to operate and control,8 so the configuration can be extended to the recirculating cooling-water networks. Figure 4 shows that, in this new configuration, there is an intermediate cooling-water main (Pm) with a temperature Tm between the cooling-water supply main (Pin) and the cooling-water return main (Pout). The temperature in the intermediate cooling-water main is greater than that of the cooling-water supply main and lower than that of the cooling-water return main. The intermediate main then receives used recirculating cooling water from some coolers at temperatures less than or equal to its temperature and provides cooling water to some other coolers, which can use the cooling water at temperatures higher than or equal to its temperature. In this way, the recirculating cooling water into or out of each cooler will be coming from or going into one of the three mains. Thus, by controlling the (8) Kim, J.; Smith, R. Automated Retrofit Design of Cooling-Water Systems. AIChE J. 2003, 49 (7), 1712-1730. (9) Feng, X.; Seider, W. D. New Structure and Design Methodology for Water Networks. Ind. Eng. Chem. Res. 2001, 40 (26), 6140-6146.
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The heat balance at the inlet mixing point for each heat exchanger is in in m in in Lm,i Tin + Lout,i Tin + Lout,i Tm ) (Lm,i + Lout,i + m )Tiin Lout,i
(i ) 1, ..., N) (3)
where Tin is the water temperature of the cooling water supply main, Tm the water temperature of the intermediate cooling water main, Tin i the inlet temperature of m the heat-capacity flow rate heat exchanger i, and Lout,i of heat exchanger i from the intermediate cooling-water main to the cooling-water return main. The restraints of outflow for each heat exchanger are in in Lout,i )0 Lm,i
Figure 4. Schematic diagram of the recirculating water system with an intermediate water main.
(i ) 1, ..., N)
(4)
The heat load for each heat exchanger is
temperature of the intermediate cooling-water main, if fluctuations of heat load or temperature occur in some coolers, other coolers will not be influenced. Compared with the traditional parallel network, the new configuration can obviously reduce the recirculating coolingwater flow rate and increase the return temperature to the cooling tower, so that the effectiveness of the cooling tower is increased. On the other hand, compared with the series arrangements, the new configuration has a simpler network and is easier to operate and control. To design a cooler network with a minimum recirculating water flow rate, the most important thing is to determine the optimum temperature of the intermediate cooling-water main. There are more coolers that can supply water to the intermediate cooling-water main when its temperature is higher, but less coolers can use water from the main. In contrast, the intermediate cooling-water main can receive less used water but can supply water to more coolers when its temperature is lower. An optimum temperature in the intermediate cooling-water main must exist.
is the maximum inlet temperature of where Tin,max i heat exchanger i,
3. Mathematical Model of Optimum Design
where max(Tout,max ) is the maximum of all of the heat i exchangers’ maximum outlet temperatures. The heat-capacity flow rate restrictions are
The model is mainly for heat-transfer processes in the recirculating cooling-water system. The mathematical model developed here uses several assumptions: (i) heat loss in the cooler network is ignored, and (ii) water loss in the cooler network is ignored. The cooler network can be regarded as a network that is influenced by only one factor: temperature. For the network shown in Figure 4, the objective of the model is to obtain the minimum heat-capacity flow rate. That is to say, the objective is to determine the minimum recirculating cooling-water flow rate at the maximum return temperature: N
min(
∑ i)1
N
in Lm,i
+
∑ i)1
in Lout,i )
(for i ) 1, ..., N)
(2)
in where Lm,i is the heat-capacity flow rate of heat exchanger i from the cooling-water supply main to the in intermediate cooling-water main, Lout,i the heat-capacity flow rate of heat exchanger i from the cooling-water supply main to the cooling-water return main directly, and N the number of heat exchangers.
in m in + Lout,i + Lout,i )(Tout - Tin (Lm,i i i ) ) Wi (i ) 1, ..., N) (5)
where Tout is the outlet temperature of heat exchanger i i and Wi is the heat load of heat exchanger i. The temperature restrictions are as follows: in,max 0 < Tin i e Ti
(i ) 1, ..., N)
e Tout,max 0 < Tout i i
(i ) 1, ..., N)
(6)
(7)
is the maximum outlet temperature of where Tout,max i heat exchanger i, and out e Tout,max 0 < Tm,i i
(i ) 1, ..., N)
) Tin < Tm < max(Tout,max i
(i ) 1, ..., N)
(8) (9)
N
in in m (Lm,i + Lout,i + Lout,i ) e Lmax ∑ i i)1
(i ) 1, ..., N) (10)
where Lmax is the maximum heat-capacity flow rate of i heat exchanger i. in Lm,i g0
(i ) 1, ..., N)
(11)
in g0 Lout,i
(i ) 1, ..., N)
(12)
m g0 Lout,i
(i ) 1, ..., N)
(13)
The heat-capacity flow rate balance of the intermediate cooling-water main is N
∑ i)1
N
in Lm,i -
m Lout,i ) Lm ∑ out i)1
(14)
where Lm out is the heat-capacity flow rate discharged from the intermediate cooling-water main directly into
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Table 1. Hot Process Stream Data of Cooling-Water Networks of Example 1a heat exchanger
Tin (°C)
Tout (°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
a
From Kim and Smith.1
Table 2. Limiting Cooling-Water Data of Example 11 heat exchanger Tin,max (°C) Tout,max (°C) CP (kW/°C) Q (kW) 1 2 3 4
20 30 30 55
40 40 75 75
20 100 40 10
400 1000 1800 200
Figure 5. Cooling water pinch of example 1.1
the cooling-water return main without passing through any heat exchanger. The heat balance in the intermediate cooling-water main is N
∑ i)1
N
in out (Lm,i × Tm,i ))
m Lout,i × Tm ∑ i)1
(15)
The heat exchanger, whose maximum inlet temperature is less than that of the intermediate cooling-water main, must use water from the cooling-water supply main. On the other hand, the heat exchanger, whose maximum inlet temperature is greater than that of the intermediate cooling-water main, can be decided by actual operation to use water from either the cooling-water supply main or the intermediate cooling-water main. In the mathematical model, the optimum intermediate temperature will be decided as a result of solving the model, which has no direct relationship with the pinch of the system or with whether the cooling-water system has a pinch. The model is a mixed-integer nonlinear programming (MINLP) model, and we use the commercial software LINGO to solve it. The optimum intermediate temperature, minimum recirculating flow rate, and cooling-water network are obtained after the model is solved. Note that, because, in the intermediate cooling-water main, water at different temperatures is mixed, the minimum recirculating water flow rate is normally slightly greater than that in the network with an optimal series design. 4. Case Study Example 1 is used to show the design methodology for cooling-water networks with an intermediate coolingwater main. The cooling-water system in the example has four heat exchangers that use recirculating cooling water with an inlet temperature of 20 °C. The temperature, flow rate, and cooling duty of hot process streams are given in Table 1. The limiting cooling-water data for the example are given in Table 2 if the minimum temperature difference is limited to 10 °C. A pinch chart (Figure 5) can be constructed using pinch technology. Figure 5 shows that the pinch is 40 °C and the target recirculating flow rate is 90 kW/°C. Kim and Smith designed cooler networks with pinch technology, as shown in Figure 6.1
Figure 6. Schematic diagram of the recirculating coolingwater system design with the series design of example 1.
Figure 7. Schematic diagram of the recirculating coolingwater system design with an intermediate cooling water main of example 1.
The optimum intermediate temperature (Tm) can be obtained as 40 °C in this example, using the mathematical model built in this paper, which is equal to the pinch temperature. The new structure of cooler networks is shown in Figure 7. The design achieves the target recirculating flow rate. Furthermore, the network is simple and fairly flexible, because the coolers are not connected directly. It is easier, in this configuration, to add or reduce some cooler(s) than in the series configuration. At the same time, there is no inference among the heat exchangers, as long as the temperature in the intermediate water main remains unchanged, because they are not connected directly. For example, the fourth cooler can work normally, no matter how the temperatures of other three coolers fluctuate. There is no similar advantage in the cooler networks designed with pinch technology (see Figure 6).
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Table 3. Limiting Cooling-Water Data of Example 2 heat exchanger Tin,max (°C) Tout,max (°C) CP (kW/°C) Q (kW) 1 2 3 4 5 6 7 8 9 10
20 50 30 25 50 25 35 45 55 30
50 70 55 70 65 40 60 55 75 50
20 35 45 15 30 50 60 40 100 70
600 700 1125 675 450 750 1500 400 2000 1400
Next, we present a more-complex network with 10 coolers. The limiting cooling-water data for example 2 are given in Table 3. The recirculating cooling water with inlet temperature of 20 °C. A pinch diagram of example 2 (Figure 8) shows that the pinch is 60 °C and the target recirculating water flow rate is 186.3 kW/°C. Cooler networks designed with the series design are shown in Figure 9. This figure shows that the recirculating water flow rate reaches the target and the network is very complicated with many interactions among the coolers. Using the mathematical model built in this paper, the optimum intermediate temperature (Tm) of example 2 can be obtained as 49 °C, which is less than the pinch temperature. The result shows that the intermediate temperature has no direct relationship with the pinch temperature of the system. The target
Figure 10. Schematic diagram of the recirculating coolingwater system design with an intermediate cooling-water main of example 2.
recirculating flow rate in the new structure of cooler networks is 195.6 kW/°C, which is slightly higher than that in Figure 9. Figure 10 shows the network arrangement, which is very simple and fairly flexible, because the coolers are not connected directly. 5. Conclusions
Figure 8. Cooling-water pinch of example 2.
A new recirculating cooling-water network configuration with an intermediate cooling-water main is proposed. The configuration has a simpler and flexible network. A corresponding mathematical model for optimum design has been developed in this paper. Using the design methodology developed in this paper, the recirculating cooling-water network has a higher temperature and lower flow rate in the returning cooling water; thus, the effectiveness of the cooling tower is higher. Operational expenses will be saved because of the reduced work that is necessary to circulate the cooling water. The cooling-water networks can satisfy extended production without buying new equipment, to a certain extent. The new networks, which incorporate a feature of avoiding direct connection of the coolers, are simpler and easier to design and control. Meanwhile, it is easier to add or reduce some coolers in the networks. Acknowledgment. Financial support provided by the National Natural Science Foundation of China (under Grant Nos. 20376066 and 20436040) and the National Key Basic Research Development Program of China (under Grant No. 2003CB214500) are gratefully acknowledged. Notation
Figure 9. Schematic diagram of the recirculating coolingwater system design with the series design of example 2.
Lmax ) maximal heat-capacity flow rate of heat exchanger i i in Lm,i ) heat-capacity flow rate of heat exchanger i from the cooling-water supply main to the intermediate cooling-water main
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Lm out ) heat-capacity flow rate discharged from the intermediate cooling-water main directly to the cooling-water return main without passing through any heat exchanger m Lout,i ) heat-capacity flow rate of heat exchanger i from the intermediate cooling-water main to the cooling-water return main in Lout,i ) heat-capacity flow rate of heat exchanger i from the cooling-water supply main to the cooling-water return main N ) number of heat exchangers Pin ) cooling-water supply main Pm ) intermediate cooling-water main Pout ) cooling-water return main
Feng et al. QAct ) actual heat removal at the cooling tower QMax ) maximum attainable heat removal at the cooling tower Tin ) water temperature in the cooling-water supply main Tin i ) inlet temperature of heat exchanger i Tin,max ) maximum inlet temperature of heat exchanger i i Tout ) outlet temperature of heat exchanger i i Tout,max ) maximal outlet temperature of heat exchanger i i Tm ) water temperature in the intermediate cooling-water main out Tm,i ) water temperature from heat exchanger i to the intermediate cooling-water main Wi ) heat load of heat exchanger i EF049711Z
