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 CCHHEEMMIICCAALL  EENNGGIINNEEEERRIINNGG  TTRRAANNSSAACCTTIIOONNSS  
 

VOL. 39, 2014 

A publication of 

 
The Italian Association 

of Chemical Engineering 

www.aidic.it/cet 
Guest Editors: Petar Sabev Varbanov, Jiří Jaromír Klemeš, Peng Yen Liew, Jun Yow Yong  

Copyright © 2014, AIDIC Servizi S.r.l., 

ISBN 978-88-95608-30-3; ISSN 2283-9216 DOI: 10.3303/CET1439009 

 

Please cite this article as: Sun J., Feng X., Wang Y., 2014, Optimisation of cooling-water systems considering temperature-

rise and pressure-drop, Chemical Engineering Transactions, 39, 49-54  DOI:10.3303/CET1439009 

49 

Optimisation of Cooling-Water Systems Considering 

Temperature-Rise and Pressure-Drop 

Jin Sun, Xiao Feng*, Yufei Wang 

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing, China, 102249 

xfeng@cup.edu.cn 

Cooling-water systems (CWS) are widely used in process industries as a cold utility. In re-circulating CWS, 

cooling water from the cooling tower (CT) is transported only by pumps on the main supply pipeline and 

supplied to a coolers network that usually has a parallel configuration. However, series-parallel 

configuration of coolers can obviously reduce the cooling water flow-rate and increase its return 

temperature as well as the effectiveness of the CT, but the pressure drop along pipelines will increase 

accordingly. To save energy and cost, a mathematical model is established to optimise the cooling water 

system. A two-step solution strategy is proposed to obtain the optimal cooling-water network (CWN) with 

minimal total cost. Firstly the optimal heat exchanger network (HEN) is obtained, and then the optimal 

pump network with auxiliary pumps is synthesized. The proposed optimisation model can identify the 

optimal distribution of cooling water within the network and the optimal installation location and capacity of 

pumps required for CWS. An example has been provided to demonstrate the effectiveness of the method. 

1. Introduction 

CWS is one of the most popular methods to discharge waste heat of processes to the environment. 

Typical re-circulating CWS are composed of three major components: a heat exchanger network (HEN), a 

cooling tower and a pump network. The most influential factor to the temperature and flow-rate of cooling 

water is the HEN. The most popular design of a HEN in CWS is in parallel configuration where cooling 

water transported to each cooler with the same temperature. However, the optimal structure may not 

require the same supply temperature of the cooling water because not all hot streams have the same inlet 

and target temperatures. For hot streams with higher target temperature, there exists possibility to reuse 

cold utility between coolers. Compared with parallel configuration, this serial configuration can not only 

save cooling water, but also improve the efficiency of the cooling tower and achieve better effect of energy 

saving. 

Over the last decade, a large number of studies about CWS have been reported in the literature, ranging 

from insight-based Pinch analysis to mathematical-based optimisation methods. Kim and Smith (2001) 

proposed a cooling water design approach based on Pinch analysis to target minimum cooling water 

consumption of CWN. Due to low heat transfer temperature difference, the heat transfer area of CWN is 

large which incurs excessive investment cost. Based on mathematical optimisation technique, Feng et al. 

(2005) proposed the internal water main structure with simple configuration which can be designed and 

controlled easily. Picón-Núñez et al. (2007) studied the effect of the configuration of CWN on the total heat 

exchanger area. Ponce-Ortega et al. (2007) proposed a new superstructure and a mathematical 

programming model for the optimal synthesis of CWN and minimized the utility and capital costs 

simultaneously. Serna-González and Ponce-Ortega (2011) presented a total cost targeting method for 

heat exchanger network synthesis. Nemet et al. (2013) presented an optimisation methodology for a Heat 

Exchanger Network design over its entire lifespan. Besides, Sun et al (2014) proposed the auxiliary pump 

network to minimize the total cost of the cooling water pump network. In this paper, a thermodynamic 

model and a hydraulic model are established respectively to optimise the total cost of CWN, and a two-

step sequential approach is proposed for the optimisation of CWS. 

mailto:xfeng@cup.edu.cn
http://www.sciencedirect.com/science/article/pii/S1359431107002062


 
50 

 
2. Superstructure and Model of the HEN in CWS 

2.1 The Superstructure of CWS 
Figure 1(a) depicts the traditional parallel configuration of the HEN in CWS. In the configuration, hot 

process stream i exchange heat with cooling water on parallel branch pipe i. Hot process stream i 

corresponds to cooler E-i. The inlet and target temperatures of hot process stream i are 
H,in

i
T and

H,out

i
T , 

respectively.  

Fs,i

1

i

I

.

.

.

Fi,ec,i
in

T
c,i

out
T Fs,i

1,1

i,1

I,1

.

.

.

c,

i,1

in
T

1,N

i,N

I,N

.

.

.

1,2

i,2

I,2

.

.

.

Fi,ecu
in

T

(a) Parallel configuration (b) Series-parallel configuration

c,out

i,N
T

Fs,1

Fs,I

F1,e

FI,e

F1,eFs,1

Fs,I FI,e

c,

1,1

in
T

c,

I,1

in
T

c,out

1,N
T

c,out

I,N
T

. . .

. . .

. . .

cu

in
T

 

Figure 1: Two different configurations of HEN for CWS 

Figure 1(b) shows the superstructure for the series-parallel configuration of the HEN in CWS. For the 

purpose of simplicity and operability, the serial number of coolers in each parallel branch pipe is no more 

than N and each hot stream corresponds to only one cooler. There are I parallel branch lines and N 

coolers installed serially on the branch pipe i. The models of the series-parallel configuration of the HEN in 

this article are the same as that of Ponce-Ortega et al. (2007). Eqs. (1) - (2) show the Energy balances for 

each parallel pipe in this configuration. 
H,in H,out

i i i i
( )                 i

H H
F CP T T q I      

(1) 

c,out c,in

s,i Cu i,N i,1 , ,

1

( )        i
N

i n i n

n

F Cp T T q y I


     
 

(2) 

where 
H

F and 
s,i

F are flow-rates of hot stream and cold utility on parallel branch i; 
i

H
CP and 

Cu
Cp  the 

specific heat capacity of hot stream and cold utility;
H,in

i
T and 

H,out

i
T  the inlet and target temperature of hot 

stream and cold utility; 
i

q  the heat load of hot stream ;
,i n

q the heat exchanged on the n th cooler of 

parallel line i, and 
,i n

y  is a binary variable. 

The binary variable 
,i n

y  is introduced to indicate the existence of the n-th cooler on parallel branch pipe i. 

The capital letter I represents the number of hot process streams and its set. The constraint condition of 

the binary variable 
,i n

y  is shown as follows: 

,

1

       i
N

i n

n

y N I


    (3) 

,

1 1

      
I N

i n

i n

y I
 


 

(4) 

where  N and I are the total number of parallel branch lines and hot process streams. 

The cooling water inlet temperature of the first cooler in each parallel branch equals the outlet temperature 

of the cooling tower. The constraint conditions of the temperatures are as follows: 
c,in in

i,1 Cu
              iT T I  

 
(5) 

, ,

, , 1
          i , n 1,2,...N-1;

c out c in

i n i n
T T I


   

 
(6) 

c,out max

i,N C
               iT T I    (7) 



 
51 

in max

s,i Cu Cu , , s,i Cu C

1

+           i
N

i n i n

n

F Cp T q y F Cp T I


  
 

 (8) 

where 
c,in

i,1
T is inlet temperature of the first cooler in parallel line i, 

max

C
T  is the maximum temperature of 

cold utility and 
,

,

c out

i n
T  is the outlet temperature of cold utility for the n th cooler in parallel  line i. 

The minimum mass flow-rate of cooling water can be deduced from Eq.(8) and is expressed as the 

following Equation: 

, ,
min 1

s,i max

Cu

                          i
( )

N

i n i n

n

in

C Cu

q y

F I
Cp T T

  



 

(9) 

where
min

s,i
F is the minimum mass flow-rate of cooling water in parallel pipe i.  

2.2 The objective function  
The objective function is the total annual cost, namely the annualized capital cost for the heat exchangers 

and the utility cost, as shown in Eqs. (10)-(11). Eq. (12) is the investment cost of a heat exchanger.  

1

1

min  =
I

i

i

F f


  (10) 

cu

1 , , s,i

n=1

min  [ ]                  i
N

Ex

i f i n i n Y
f A C y C H F I     

 
(11) 

Ex
C a bA


 

 

(12) 

where  
1f

A is heat exchanger area;
cu

C  the unit cost for the cold utility;
Y

H  the equipment operating time 

per year;
s,i

F  the cold utility of flow-rate and a , b ,   are heat exchanger cost parameters.  

3. Pump network model 

3.1 The minimum pressure head of parallel branch pipes 

The method proposed by Sun et al (2014) to calculate the minimum pressure head of a cooler can be 

referred to calculate the minimum pressure head of each parallel pipe. The minimum pressure head of 

parallel pipe n can be calculated by Eq. (13). 

min

n

A D

D A

P
H z z

g



    (13) 

where 
A D

P


 is the pressure drop between node A and node D, respectively; 
A

z and
D

z  the height of 

section A and D, respectively;   the water density and g is the gravity factor. 

The total pressure drop from node A (the inlet section) to node D (the outlet section) consists the pressure 

drops of the header feed pipe and of parallel branch pipes, which can be formulated as Eq. (14). In this 

article, the detail pressure drop of CWN follows Sun et al (2014) method. 

A D A B B C C D
P P P P

   
      (14) 

3.2 The optimisation of cooling water auxiliary pump network 

The Sun et al’s method (2014) to optimise the auxiliary pump network is adopted in this paper. The 

objective function is the total cost of the main and auxiliary pump networks which includes the operation 

cost and the capital cost of pumps and motors, and can be formulated as Eq. (15).  

2 2
min ( )

i j i jmain auxi f P P M M
F OC OC A CC CC CC CC        (15) 

where 
main

OC and
auxi

OC are the operation cost of main pump network and auxiliary pump network, 

respectively; 
2f

A is  the annualized factor of pumps and motors;
iP

CC ,
jP

CC are the capital cost of main 

pumps and auxiliary pumps; 
iM

CC and 
jM

CC are the capital cost of main motors and auxiliary motors, 

respectively. 



 
52 

 
4. Case study 

The example, taken from Ponce-Ortega et al. (2007), is used as the case study. The hot stream data is 

shown in Table 1. The specified data are follows: 
min

T  is taken as 10 ºC, the inlet temperature for the 

cold utility is 20 ºC and the maximum allowable temperature of cooling water is 55 ºC. The cost function 
for the capital cost of the heat exchangers is based on $1,000+700 A (area in m

2
). The annual operating 

time of equipment is assumed to be 2.88×10
7 

s/y and the annualisation factor (
1f

A ) for capital cost of heat 

exchangers to be 0.2983. The Cpc for the cold utility is taken as 4.18 kJ/(kg ºC), the film heat transfer 
coefficient for the side of the cold utility as 2.5 kW/(m

2 
℃), and the unit cost of cooling water as $ 5×10

-6
/kg. 

All these data are from Ponce-Ortega et al. (2007). 

Table 1: Hot process stream data 

Stream 
in

H,i
T  (ºC) 

out

H,i
T (ºC) H

i
FCP (kW/ºC) h(W/m

2
 ºC) 

1 50 30 20 854 

2 50 40 100 743 

3 85 40 40 520 

4 85 65 10 1,352 

 
Based on the above model, the optimal HEN is shown in Figure 2, which is the same as that in Ponce-

Ortega et al. (2007). In this series-parallel configuration, coolers E1, E2 and E3 are installed in series, with 

a parallel branch pipe containing cooler E4.  Figure 2 shows the flow-rate distribution and heat exchange 

area in detail. The total cost of the optimal series-parallel structure of HEN and the parallel configuration of 

HEN are 64,978 $/y and 80,639 $/y. The annual saving of the total cost can achieved at 19.4%. 

After determining the optimal heat exchanger network, the minimum pressure head of all parallel branches 

can be calculated. Table 2 shows the main parameters of coolers and pipes with fittings, which are used to 

calculate the minimum pressure head of parallel lines. Four main pumps are installed in parallel in the 

main pump network, three of which are on duty and one on standby. All the factors are referred to Sun et 

al (2014).  

The Minimum pressure head of parallel branches are given in Table 3. Tables 3 and 4 compare the total 

cost of pump network before and after pump network optimisation, which are 1.22 ×10
5 

$/y and1.14×10
4 

$/y. The annual saving of the total cost can achieved at 6.1%.  

The optimal cooling water network after pump network optimisation is shown in Figure 3. The main pump 

pressure head is 11 m and an auxiliary pump with pressure head of 10 m is installed on parallel branch 

pipe B-1-C.  

Table 2: Data for the piping layout of pipeline network 

Pipe 

segment 

Pipe 

length 

(m) 

Inside 

diameter 

(m) 

Mass 

flowrate 

(kg/s) 

Coolers 

Ei 

Maximum 

installation 

height of 

coolers (m) 

Pipe fittings 

A-B 80 0.24 70.26 － － 

Gate valve (2
*
) 

Globe valve(1) 

Check valve (1) 

Orifice valve (1) 

Bend (3) 

B-1-C 300 0.18 39.5 

E1 

E2 

E4 

15 

Sudden contraction  (1) 
Sudden expansion (1) 
Bend (2) 

Gate valve (2) 

B-2-C 75 0.16 30.76 E3 8 

Sudden contraction (1) 
Sudden expansion (1) 
Bend (2) 

Gate valve (2) 

C-D 120 0.24 0.949 － － 
Bend (2) 

Gate valve (2) 

* Number in brackets indicates the number of pipe fittings. 



 
53 

CW

H1

H2

H3

H4

3

4

2

2

1

14

3

50℃

50℃

85℃

85℃ 65℃

40℃

40℃

30℃

A

  D

20℃

22.425℃28.489℃29.702℃

34.366℃

126.79 m
2

5.04 m
2

89.64 m
2

36.27 m
2

B

C

29.882 kg/s

39.339 kg/s

CT

20℃

 

Figure 2: Optimal heat exchanger network of CWS without auxiliary pump installation 

Table 3: Pump pressure heads and costs before optimisation 

Pipe section Pump Hi(m) min
n

H (m) OC×10
4
($/y)

 
CC×10

4
($/y)

 
TC×10

4
($/y)

 

A-B Pi 21 - 8.2 4.03 12.23 

B-1-C - - 21 0 0 0 

B-2-C - - 11 0 0 0 

Table 4: Pump pressure heads and costs after optimisation 

Pipe section Pump Hi(m) OC×10
4
($/y)

 
CC×10

4
($/y)

 
TC×10

4
($/y)

 

A-B Pi 11 4.6 2.43 7.03 
B-1-C P1 10 2.5 1.95 4.45 
B-2-C - - 0 0 0 

 

 

Figure 3: Optimal cooling water network with auxiliary pump installation (after pump network optimisation) 



 
54 

 
5. Conclusions 

The thermodynamic model is developed to obtain the HEN with minimum heat exchanger cost and utility 

cost and the hydraulic model is proposed to optimise the pump network. For the simplification of solving 

process, the two-step sequential approach adopted for the two models separately to obtain the optimal 

CWN, for the minimum pressure head of the network can be targeted when the configuration of the HEN in 

the CWN is determined. The result of the case study shows that this method is effective and can be useful 

for CWN design and retrofit. Simultaneously optimising the HEN and the pump network to obtain the 

optimal cooling water system will be our further work, for there are interactions between the HEN and the 

pump network. 

Acknowledgement 

Financial support from the National Basic Research Program of China (973 Program: 2012CB720500) and 

NSFC-ANR under Grant No. 21261130583 is gratefully acknowledged. 

References 

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