Applied Thermal Engineering 25 (2005) 485–494

www.elsevier.com/locate/apthermeng

Influence of the cooling circulation water

on the efficiency of a thermonuclear plant
J. Gañán a, A. Rahman Al-Kassir a,*
, J.F. González a, A. Macı́as b, M.A. Diaz b

a
Department of Energy and Chemical Engineering, University of Extremadura, Avda. de Elvas, s/n, Badajoz 06071, Spain
b
Department of Electronics and Electromechanical Engineering, University of Extremadura,
Avda. de Elvas, s/n, Badajoz 06071, Spain

Received 12 May 2004; accepted 1 July 2004

Available online 19 August 2004

Abstract

In the present study, the feasibility of intercalating two cooling towers in the present circulation water
system used at Almaraz Nuclear Power Plant, located at Campo Arañuelo district (SW Spain), has been
technically evaluated in order to increase the efficiency of the thermodynamic cycle used at present. Thus,
the working cycle has been analyzed, the power produced by the turbines being calculated as a function of
the cooling circulation water temperature. Next, two natural convection counterflow cooling towers have
been calculated in order to be installed in parallel with the present cooling system (Lake Arrocampo). The
power obtained in the turbines provided with the new system has been estimated. Finally, a system com-
bining both the cooling towers and the Lake Arrocampo has been proposed, the increment in power using
one system or the other according to the weather conditions being calculated.
Ó 2004 Elsevier Ltd. All rights reserved.

Keywords: Efficiency; Condenser vacuum; Power; Cooling system

*
Corresponding author. Tel.: +34 666866409/34 924289600; fax: +34 924289601.
E-mail address: aawf@unex.es (A. Rahman Al-Kassir).

1359-4311/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved.
doi:10.1016/j.applthermaleng.2004.07.001
486 J. Gañán et al. / Applied Thermal Engineering 25 (2005) 485–494

Nomenclature

A area of the cooling tower (m2)

a fill compactness (m
2 m
3)
Cpw specific heat of water at constant pressure (kJ kg
1)
G mass flow rate of dry air (kg h
1)
ha air enthalpy at cooling tower entrance (kJ kg
1)
houtiso turbine outlet vapour isoentropic enthalpy (kJ kg
1)
hout0 turbine outlet saturated liquid enthalpy (kJ kg
1)
hout00 turbine outlet saturated vapour enthalpy (kJ kg
1)
hw enthalpy of the saturated air at temperature tw (kJ kg
1)
K global mass transfer coefficient (kg m
2 s
1)
L mass flow rate of water (kg h
1)
Sin turbine inlet superheated vapour entropy (kJ kg
1 K
1)
Sout turbine outlet entropy (kJ kg
1 K
1)
S out0 turbine outlet saturated liquid entropy (kJ kg
1 K
1)
S out00 turbine outlet saturated vapour entropy (kJ kg
1 K
1)
Tcw circulation water temperatures (°C)
tw1 water inlet temperature (°C)
tw2 water outlet temperature (°C)
v free volume of the cooling tower (m
3)
x dryness fraction
g efficiency

1. Introduction

The Spanish electric system is subjected to a constant increase of the electric energy require-
ment. Thus, in the last 12 months the net energy demand has grown up to 206,582 GW h, which
corresponds to a cumulative increase of 5.7% with respect to the same period of the year 2002.
Thus, the Spanish thermoelectric plants require modifications in order to obtain higher efficiencies
of their themodynamic cycles.
Almaraz Nuclear Plant (ANP) belongs to the PWR-type and is located at Campo Arañuelo
district (SW Spain) [1,2]. It consists of two 980 MWe units and an artificial dam (Lake
Arrocampo) used as circulation water cooling system. Since this is an open system consisting
of thermal screens, it is strongly influenced by the weather conditions existing in the environ-
ment. This may lead to a power limitation during the summer due to vacuum losses in the
condenser.
In the present study a technical evaluation of the feasibility of introducing cooling towers in the
present circulation water system of ANP has been carried out in order to increase the efficiency of
the thermodynamic cycle during the most unfavourable periods. The power produced by the tur-
bine has been calculated as a function of the temperature of water entering the condenser. Once
 J. Gañán et al. / Applied Thermal Engineering 25 (2005) 485–494 487

the referred cycle was analyzed, two natural convection counterflow cooling towers were calcu-
lated in order to be used in the present cooling system of the condenser (Lake Arrocampo).
Finally, a mixed dam-cooling towers system is proposed as an alternative to the cooling system
used at present. The power provided when using the new cooling system was estimated.

2. Experimental process

2.1. Analysis of the present thermodynamic cycle of ANP

In order to determine the efficiency of the working cycle, the values of the condenser pressure at
different circulation water temperatures ranging from 20 up to 32 °C have been considered [3].
Circulation water temperatures at the entrance of the condenser as well as the condenser pressures
are summarized in Table 1. These data will be used to calculate the circulation water temperature
at the condenser outlet. At 100% of operative power, the inlet conditions of the vapour to the low
pressure turbine remain constant, whereas the outlet conditions of the vapour will vary depending
on the condenser pressure.
The calculation of the thermodynamic conditions of the vapour leaving the low pressure tur-
bine was carried out according to the condenser pressures. The irreversibilities of the system,
i.e., non-isoentropic working fluid expansion, pressure loss, etc. were considered [4,5]. In order
to calculate the referred properties, the efficiency of the low pressure turbine was first calculated
considering the inlet and outlet vapour conditions shown in Table 2.
According to the MollierÕs diagram, the value of the entropy at the outlet (Sout) is given by
S out ¼ S out0 þ xðS out00
S out0 Þ ð1Þ

Table 1
Condenser pressure as a function of the circulation water temperature
Tcw (°C) 20 21 22 23 24 25 26 27 28 29 30 31 32
p (mmHg) 42.1 44.1 45.9 47.8 49.4 51.7 55 58 60.8 63.4 66.6 69.8 73
p (bar) 0.056 0.058 0.061 0.063 0.065 0.069 0.073 0.077 0.081 0.084 0.089 0.093 0.097

Table 2
Inlet and outlet vapour conditions
Calculated parameters Inlet conditions Outlet conditions
Temperature (°C) 261.2 38.7
Enthalpy (kJ kg
1) 2961.1 2320.7
Flow rate (kg s
1) 981.9 767.1
Pressure (bar) 11.96 0.07
Steam dryness fraction, x (%) 1.00 0.89
488 J. Gañán et al. / Applied Thermal Engineering 25 (2005) 485–494

After substitution a value of Sout = 7.47 kJ kg
1 K
1 has been obtained. Analogously, the entropy
of the superheated vapour at the turbine inlet (Sin) resulted 6.88 kJ kg
1 K
1. By application of
Eq. (1) to the isoentropic process, the steam dryness fraction for this case is estimated to be
xiso = 0.81.
A value of houtiso = 2135.1 kJ kg
1 was obtained by applying the following equation:
houtiso ¼ hout0 þ xðhout00
hout0 Þ ð2Þ
This parameter is used to calculate the efficiency (g), since
ðhin
hout Þ
g¼ ¼ 0:77 ð3Þ
ðhin
houtiso Þ
The efficiency and the values of condenser pressure at different circulation water temperatures is
used to calculate hout00 for each condenser pressure. The values obtained are shown in Table 3.
By means of the energy balance in the condenser [6] the outlet temperature of the cooling cir-
culation water was calculated as a function of the pressure inside the condenser. This calculation
was performed taking into account the outlet enthalpy of the low pressure turbine, the enthalpy at
the inlet of the condensation pump, the inlet temperature of the cooling circulation water, con-
denser exhausts and drainages as well as the corresponding mass flow rates. Other factors such
as the heat transfer between the condenser and the environment and the effects of the vapour
potential and kinetic energy were neglected.
Table 3 also shows the outlet temperatures of the cooling circulation water obtained for the dif-
ferent cases. Such temperatures will be used as inlet data for the calculation of the cooling tower.

Table 3
Enthalpies at outlet of the low pressure turbine as a function of the condenser temperature and the cooling circulation
water outlet temperature
Outlet enthalpies Outlet enthalpies Condenser Circulation water Circulation water Mass flow
LP turbine condenser pressure inlet temperature outlet temperature rate
(kJ kg
1) (kJ kg
1) (bar) (°C) (°C) (kg s
1)
2299.6 144.42 0.054 19.5 30.3 37462
2301.8 146.56 0.056 20 30.8 37462
2306.1 149.94 0.058 21 31.9 37425
2309.7 152.98 0.061 22 32.9 37425
2313.5 156.16 0.063 23 33.9 37425
2316.5 158.68 0.065 24 34.9 37387
2320.6 162.23 0.068 25 35.9 37387
2326.2 166.96 0.073 26 36.9 37387
2331.1 171.18 0.077 27 37.9 37387
2335.5 174.94 0.081 28 38.9 37350
2339.3 178.25 0.084 29 39.9 37350
2344.3 182.53 0.089 30 40.9 37350
2348.4 186.05 0.093 31 41.9 37350
2352.5 189.62 0.097 32 42.9 37313
2355.1 191.79 0.099 32.4 43.3 37313
 J. Gañán et al. / Applied Thermal Engineering 25 (2005) 485–494 489

According to the characteristics of the condenser and turbines it has been estimated that a con-
densation pressure below 37 mmHg does not improve the efficiency of the cycle. This pressure cor-
responds to an inlet temperature of the cooling circulation water of 17.5 °C. The outlet enthalpy
of the vapour from the low pressure turbine corresponding to this pressure is equal to 2288.17
kJ kg
1. A cooling circulation water outlet temperature of 28.4 °C was calculated at the lowest
pressure for which the condenser remains operative, according to the design technical conditions.

2.2. Calculation of the cooling towers

A maximum flow rate of cooling circulation water of 135,000 m3 h
1 was provided by the con-
denser of each unit of the plant operating at 100% power. The difference between the inlet hot
temperature of the water entering the tower with respect to that of the cooled water leaving the
pool of the tower at 100% operating conditions is 10.9 °C.
Prior to the cooling tower design, a study of the weather conditions (i.e., wet bulb temperature,
wind speed, relative humidity) of the area was carried out. The values of such parameters were
obtained from the National Institute of Meteorology [7] and the National Institute of Statistics
[8], with wind velocity of 1–3 Beauford Scale [9]. Fig. 1 summarizes the most noticeable data used
in the present study.
The water temperature corresponding to Lake Arrocampo (final heat sink of ANP) was meas-
ured along 2001. Fig. 2 summarizes the average values obtained. From Figs. 1 and 2 a tower pro-
viding the referred cooling range in the ‘‘most unfavourable possible conditions’’ (i.e., considering
the maximum wet bulb temperature registered in this area) will be designed. Obviously, these con-
ditions would be rarely reached, and along the rest of the year the tower will be ‘‘overdimen-
sioned’’. In order to avoid this, the so-called design wet bulb temperature will be used, i.e., a
temperature value that is not exceeded in more than 5% of the total number of working hours

Abs. min. T ºC
Abs. max. T ºC
70 90
Average T ºC
Relative hum. (%) 80
60
70
50
Relative humidity (%)

60
Temp (ºC)

40 50

30 40

30
20
20
10
10

0 0
jan feb mar apr may jun jul aug sep oct nov dec
Months

Fig. 1. Meteorological parameters in Campo Arañuelo district during 2001.

490 J. Gañán et al. / Applied Thermal Engineering 25 (2005) 485–494

35

30

25

Temp (ºC) 20

15 Abs. min. T ºC
Abs. Max. T ºC
10 Average T ºC

0
jan feb mar apr may jun jul aug sep oct nov dec
Months

Fig. 2. Average temperatures of the Lake Arrocampo during 2001.

during the summer, from June until September, in the Northern Hemisphere. The calculation is
performed from the year average parameter values obtained from the local weather data.
A design dry temperature of 34 °C was considered. Taking into account that the average rela-
tive humidity of this period is 42% (i.e. wet bulb temperature will be equal to 24 °C), it is reason-
able to suppose that the dry bulb temperature of 34 °C is exceeded at the hours of maximum
exposure to the sunlight (11:00–18:00) for less than 15–20 days. These days would correspond
to the months of July and/or August. According to this hypothesis, the temperature of 34 °C
would be exceeded approximately during 140–150 hours along the considered period. Such num-
ber of hours does not reach more than 5% of the total operating hours.
A condenser flow rate of 135,000 m3 h
1 and a cooling range of 11 °C were considered as the
initial calculation conditions. Taking into account these data and the meteorological parameters,
a cooling tower was geometrically dimensioned in order to provide the mentioned cooling range
for the given conditions. For the calculation of the base diameter and height of the tower, the
recomendations of the Cooling Technology Institute [10,11] were followed. This kind of towers
must be loaded with ratios ranging from 1.4 to 2.7 ‘ s
1 m
2. The area of the tower is calculated
as follows:
A ¼ 37; 500 ‘ s
1 =2:7 ‘ s
1 m
2 ¼ 13; 888 m2 ð4Þ
its diameter in the exchange section resulting to be 133 m. This diameter would be comprised be-
tween 88% and 92% of the base diameter. Thus, the base diameter will be of 141 m, with a height
of 170 m.
The geometric characteristics of the tower to be built have been contrasted with those provided
by the manufacturer [12] for the same operating conditions. The values obtained are shown below:

Base diameter = 141 m

Tower height = 170 m
Water distribution height = 14.5 m
 J. Gañán et al. / Applied Thermal Engineering 25 (2005) 485–494 491

Diameter at the water distribution height = 126.31 m

Height at the air entrance section = 8.5 m
Type of fill: closed laminar, cool film-type
Fill dimensions: diameter = 125 m, height = 5 m
Estimated design point (cooling factor): L/G = 1.37

The towers were designed and calculated together with their fills, so that two objectives are
reached. Firstly, a water–air mass flow rate ratio (L/G) comprised between 1 and 1.5 and secondly
an air speed lower than 3.5 m s
1 for the air passing through the water drops eliminators.
The thermodynamic characteristic of the tower (Kav/L) for the L/G range was determined by
the MerkelÕs integral [13] as shown below:
Z tw1
Kav dtw
¼ C pw ð5Þ
L tw2 hw
ha

3. Results and discussion

The tower characteristic curve is plotted in Fig. 3. In this figure the approximation and the ther-
modynamic characteristic of the tower Kav/L as a function of the water–air mass flow rate pro-
portion (L/G) are shown. The referred approximation corresponds to the difference between the
cooled water outlet temperature and that of the ambient air wet bulb.
From the characteristic curve, plotted as Kav/L versus L/G, the cooled water outlet temperature
is determined as a function of the given weather conditions along the year. Thus, a possible
decrease in the circulation water inlet temperature may be evaluated.
Fig. 4 includes the average temperatures of the lake water along the year, together with those
obtained by the cooling towers operating at their design point (i.e., L/G = 1.37). It indicates the
temperatures below 17.5 °C, i.e., those temperatures that do not imply an increase in the thermo-
dynamic efficiency of the cycle.

Fig. 3. Characteristic curve of the cooling towers.

492 J. Gañán et al. / Applied Thermal Engineering 25 (2005) 485–494

35

30

25

Temp (ºC)
20

15

10
LAKE Arrocampo
5 Cooling tower

0
jan feb mar apr may jun jul aug sep oct nov dec
Months

Fig. 4. Condenser inlet temperatures.

Power increment (% )

3,93% 3,95%
3,76% 3,84%
3,44%

2,74%

May June July August September October

Fig. 5. Increase in the power with the cooling towers.

Fig. 5 summarizes the results of the calculation process in terms of power increase of the tur-
bines. Thus, the use of the cooling system used at present (Lake Arrocampo) with two natural
convection counterflow cooling towers leads to an improvement of the performance.
When the average temperatures of the lake are compared with those obtained by using the cool-
ing towers operating at their design point during the same period of time, an increase in the effi-
ciency is observed between May and October. During the coldest months, the temperature of the
water cooled by the towers would be too low for the condenser operation. Thus, the specific vol-
ume of the vapour would increase excessively. This would lead to a growth in its outlet rate from
the low pressure turbine. In such case, the efficiency of the thermodynamic cycle would not in-
crease. The installation of a circuit operating in parallel with the present one would consist of
a cooling tower for each turbine, together with the Lake Arrocampo. By means of a three-ways
 J. Gañán et al. / Applied Thermal Engineering 25 (2005) 485–494 493

Fig. 6. Modifications to the cooling system.

valves system and the appropriate connections (see Fig. 6), it would be possible to operate with
the cooling towers during the unfavourable months. This would lower the circulation water tem-
perature, thus increasing the condenser vacuum and consequently improving the efficiency of the
system. On the other hand, the installation of the cooling towers involves a high initial investment
(29.5 millions Euros each one), thus requiring a long repayment period (20 years). However, it
must be taken into account that when the plant is not operative, a loss of 3 millions Euros/day
is estimated.

4. Conclusions

The installation of the cooling towers operating in parallel with the present one would involve
two important advantages. Firstly, it would increase the power obtained during the unfavourable
494 J. Gañán et al. / Applied Thermal Engineering 25 (2005) 485–494

period. Secondly, an adequate vacuum along the year would be assured. This second advantage is
specially noticeable, as during the hottest months the condenser vacuum could reach excessively
low values for an adequate operating of the system.
On the other hand, the installation of the proposed system involves a high initial investment
(29.5 millions Euros each tower), thus requiring a repayment period of 20 years. The implemen-
tation of the new cooling system proposed would assure the proper operativity of the plant along
the year, avoiding the undesirable stops in summer months.

References

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[2] S.A. Tecnatom, PWR—Plant Technology, Condensation system and feeding water, Madrid, 1992.
[3] F.J. Rey, S. Monterto, Influence of the circulation water temperature on the efficiency of the ANP, BSc Thesis—
UEX, Spain, 2002.
[4] C. Mataix, Termal Turbomachines, Dossat, Madrid, 2000.
[5] T. Schwarz, Heat transfer and fouling behaviour of Siemens PER steam generators-long-term operating
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[6] L. Jiang, R. Lin, H. Jin, Z. Lin, Study on thermodynamic characteristic and optimization of steam cycle system in
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[7] INM, Weather conditions of Campo Arañuelo district 2001, National Institute of Meteorology, Spain, 2001.
[8] INE, Annuary 2001, National Institute of Statistics, Extremadura, Spain, 2001.
[9] F. Beaufort, The Beaufort Wind Scale, National Weather Service Chicago, 1838.
[10] CTI, Blue Book, Cooling Technology Institute, 1967.
[11] CTI, Bibliography of Technical Papers, ATC-105, Cooling Technology Institute, 2002.
[12] S.A. Ensidus, Cooling towers design, Madrid, 2001.
[13] F. Merkel, Verdunstungskuehlung, VDI Forchungsarbeiten, 275, Berlin, 1925.