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Technical note

The inﬂuence of condenser cooling seawater fouling on the thermal performance of a nuclear power plant Said M.A. Ibrahim a, Sami I. Attia b,⇑ a b

Department of Mechanical Power Engineering, Faculty of Engineering, AL-Azhar University, Nasr City, Cairo 11371, Egypt Nuclear Power Plants Authority, 4 El-Nasr Avenue, P.O. Box 8191, Nasr City, Cairo 11371, Egypt

a r t i c l e

i n f o

Article history: Received 24 June 2014 Received in revised form 30 August 2014 Accepted 21 October 2014

Keywords: PWR secondary cycle Condenser cooling seawater Fouling factor Thermodynamic Heat transfer

a b s t r a c t This study performs a thermodynamic analysis and energy balance to study the effect of fouling change on the thermal performance of the condenser and the thermal efﬁciency of a proposed nuclear power plant. The study is carried out on a pressurized water reactor nuclear power plant. The results of the study show that the increasing of fouling factor decreases the power output and the thermal efﬁciency of the nuclear power plant. The main results of this study is that the impact of an increase in the condenser cooling seawater fouling factor in the range 0.00015–0.00035 m2 K/W is led to a decrease in the plant output power and thermal efﬁciency of 1.36% and 0.448%, respectively. The present paper researches into a real practical factor that has signiﬁcant negative effect on the thermal efﬁciency of the nuclear power plants, which is fouling of condenser cooling seawater. This is abundantly important since one of the top goals of new power stations are to increase their thermal efﬁciency, and to prevent or minimize the reasons that lead to loss of output power. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction The condenser in a steam electric power generation station is one of the most inﬂuential items of equipment in the system as related to performance. The concept of fouling has been incorporated to understand the thermal losses inside the condenser. The fouling of the condenser cooling water has an impact on the thermal performance of the condenser which ﬁnally affects nuclear power plant’s efﬁciency and its output power. Fouling represents an important problem for condensers and heat exchangers. All industrial circuits cooled with natural fresh and marine water are affected by the phenomenon of biological fouling consisting in bioﬁlm growth and settlements of several kinds of living organisms. Biofouling is detrimental to open cooling systems as it causes undesirable effects, such as efﬁciency loss inside the heat exchanger, clogging of the seawater circuit pipes, and reduction in plant reliability over a period of time. Most of the power generation plants efﬁciently operate by using the basic tools of physical screening, physical cleaning and chemical dosing. A traditional chemical way to control microbial growth and biofouling in power plants remains the use of chlorine, in spite of the fact that chlorination was subjected to the environmental

⇑ Corresponding author. http://dx.doi.org/10.1016/j.anucene.2014.10.018 0306-4549/Ó 2014 Elsevier Ltd. All rights reserved.

authorities’ attention for more than 20 years, because of its halomethanes and other organohalogens by-products items. Fig. 1 illustrates how the temperature distribution is affected by the presence of the individual fouling layers. The importance of fouling phenomena stems from the fact that the fouling deposits increase the thermal resistance to heat ﬂow. According to the basic theory, the heat transfer rate in the exchanger depends on the sum of thermal resistances between the two ﬂuids. Fouling on one or both ﬂuid sides adds the thermal resistance to the overall thermal resistance and, in turn, reduces the heat transfer rate. Simultaneously, hydraulic resistance increases because of a decrease in the free ﬂow area. Consequently, the pressure drops and the pumping power increase. Increase in condenser cooling seawater fouling factor and temperature may have impact on the capacity utilization of thermal power plants in two concerns: (1) reduced efﬁciency: increased environmental temperature and fouling factor reduces thermal efﬁciency of a thermal power plant, (2) reduced load: for high environmental temperatures and fouling factor, thermal power plant’s operation will be limited by a maximum possible condenser pressure. The operation of plants with river or sea cooling water will in addition be limited by a regulated maximum allowable temperature for the return water or by reduced access to water. In the literature, there are few articles published to identify these climate and environmental change impacts; few have tried

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Nomenclature A c d h f K LMTD _ m P Q_ R r T TTD U V _ W w

tube area [m2] speciﬁc heat [kJ/kg K] diameter [m] enthalpy [kJ/kg] fouling factor [m2 K/W] thermal conductivity [W/m K] log mean temperature difference [°C] mass ﬂow rate [kg/s] pressure [bar] net rate of heat transferred [kW] thermal resistance[m2 K/W] radius [m] temperature [°C] terminal temperature difference[°C] overall heat transfer coefﬁcient [W/m2 K] velocity [m/s] net rate of work [kW] pure water

Greek symbols g efﬁciency [%] l viscosity, [kg/m s] q density, [kg/m3] Subscripts add added c condenser CP condensate pump cw cooling water cwi cooling water inlet

to quantify them. Qureshi and Zubair (2005), studied the effect of fouling on the thermal performance of heat exchangers at different air inlet wet bulb temperatures. Lankinen et al. (2003), deﬁned the heat transfer efﬁciency as well as the external and internal pressure drops and the effect of fouling on the thermal hydraulic characteristics of the heat exchanger. Lei et al. (2012), discussed a simpliﬁed theoretical model to study fouling growth, the characteristic of fouling deposit, effects of working time, and cooling water velocity. Walker et al. (2012), presented a methodology to quantify the economic impact of condenser fouling on the performance of thermoelectric power plants. Webb and Ralph (2011), determined the performance and economic beneﬁts of using enhanced condenser tubes in an existing nuclear plant. Prieto et al. (2001), gave the data that allow carrying out heat balances as well as other important data needed to estimate fouling evolution for seawater refrigerated condenser in a 550 MW power plant.

CL cwo fw FWP HL HPT LPT i in mix o out p RCW Rej T w

cold leg cooling water outlet feed water feed water pump hot leg high pressure turbine low pressure turbine inlet inlet mixture outlet outlet pump reactor cooling water rejection turbine wall

Superscript . per unit time Abbreviations FW feed water HP high pressure LP low pressure NPP nuclear power plant PWR pressurized water reactor RC reactor coolant SG steam generator

Pugh1 et al. (2003), studied the fouling during the use of seawater as coolant. Ganan et al. (2005), showed that the performance of the pressurized water reactor (PWR) type Almaraz nuclear-power plant is strongly affected by the weather conditions having experienced a power limitation due to vacuum losses in condenser during summer. Durmayaz and Sogut (2006), presented a theoretical model to study the inﬂuence of the cooling water temperature on the thermal efﬁciency of a conceptual pressurized-water reactor nuclear power plant. Sanathara et al. (2013), gave a parametric analysis of surface condenser for 120 MW thermal power plant, focused on the inﬂuence of the cooling water temperature and ﬂow rate on the condenser performance, and thus on the speciﬁc heat rate of the plant and its thermal efﬁciency. The present study presents an analysis of the effect of the environmental conditions on the thermal performance of a proposed pressurized water reactor nuclear power plant (PWR NPP). The nuclear power plant performance depends on the thermal analysis of the condenser through heat transfer analysis taking into account the key parameters such as fouling factor and temperature of cooling seawater that affect the condenser performance, overall heat transfer coefﬁcient, and the thermal performance of the plant. This parametric study illustrates the impact of the fouling factor of condenser cooling seawater within a range of 0.00015–0.00035 m2 K/W, and temperature within a range of 15–30 °C. 2. Methodology

Fig. 1. Temperature distribution across fouled heat exchanger surfaces.

The present parametric study presents an energy balance and heat transfer analysis of the plant. Therefore, the study is

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423

Fig. 2. Diagram of PWR nuclear power plant.

performed to assess the impact of the change in fouling factor and cooling seawater temperature on the thermal efﬁciency of the proposed PWR NPP. The objective is to establish a theoretical methodology to evaluate the impact of fouling factor of seawater on the steam surface condenser overall heat transfer coefﬁcient of the PWR NPP within speciﬁc designed range of seawater temperature and fouling. Fig. 2 depicts a diagram of a proposed PWR NPP, to address the thermodynamic and heat balance analysis of the plant. A typical PWR NPP consists of a primary cycle which includes: nuclear reactor, steam generator, pressurizer, and reactor coolant pump, and the secondary cycle consisting of high pressure steam turbine (HPST), three low pressure steam turbines (LPST), moisture separator and reheater (MS/R), deaerator feed water heater, two highpressure feed water heaters (HPFWH), and three low pressure feed water heaters (LPFWH), condenser, and necessary pumps (feed water pump and condensate pump). The mathematical model representing the secondary thermodynamic cycle of the plant and its components used the engineering equation solver computer program (EES). The algorithm procedures are performed as follows: (i) Thermodynamic properties; pressure, P, temperature, T, entropy, S, enthalpy, h, moisture content, X, at all inlet and exit of all parts and components of the plant. (ii) Heat balance for each feed water heater and the steam generator. (iii) Output useful work of the turbines and pumps. (iv) Calculation of the amount of heat added to generate steam, as well as the amount of heat rejected from condenser and calculate the efﬁciency of the station. (v) Hence temperature entropy, T–S diagram of the plant and its components is obtained. (vi) Determination of cooling water inlet temperature, Tin and exit temperature, Tout and the temperature difference. (vii) Assigning the range of change of the fouling factor, f as 0.00015–0.00035 m2 K/W, and cooling seawater temperature, Tcwi as 15–30 °C. (viii) Computing the impact of the changes of cooling seawater temperature Tcwi and fouling factor, f on the thermal efﬁciency gth and output work Wnet of the plant. (ix) Drawing the relation between Tcwi and f verses the condenser overall heat transfer coefﬁcient, gth, and Wnet of the plant.

The energy balance equations for the various processes involving steady ﬂow equipment such as nuclear reactor, turbines, pumps, steam generators, heaters, coolers, reheaters and condensers in a PWR NPP are given below. 2.1. Heat balance equations (i) The total turbine work, WT, kJ/kg is:

W T ¼ W HPT þ W LPT

ð1Þ

_ st ðhin hout Þ W HPT ¼ m

ð2Þ

_ st ðhin hout Þ W LPT ¼ m

ð3Þ

_ st is steam mass ﬂow rate inlet to each turbine, kg/s, where m hin is enthalpy of steam inlet to each Turbine, kJ/kg, hout is enthalpy of steam outlet from each turbine, kJ/kg, WHPT is high pressure turbine work, kJ/kg, and WLPT is low pressure turbine work, kJ/kg. (ii) The pumping work, WP, kJ/kg is:

W p ¼ W cp þ W fwp

ð4Þ

_ fw ðhin hout Þ W fwp ¼ m

ð5Þ

_ fw ðhin hout Þ W cp ¼ m

ð6Þ

_ fwh is feed water mass ﬂow rate inlet to each steam where m generator, kg/s, hin is enthalpy of feed water inlet to each pump, kJ/kg, hout is enthalpy of feed water outlet from each pump, kJ/kg, Wfwp is Feed water pump work, kJ/kg, and Wcp is condensate pump work, kJ/kg. (iii) Heat added to steam generator, Qadd, kJ/kg is:

Q add ¼ mst ðhout hin Þ

ð7Þ

_ st is steam mass ﬂow rate exit from steam generator, where m kg/s, hin is enthalpy of feed water inlet to steam generator, and kJ/kg, hout is enthalpy of steam outlet from steam generator, kJ/kg. (iv) Heat rejected from condenser, QRej, kJ/kg is:

_ mix hin m _ mix hout Þ Q Rej ¼ ðm

ð8Þ

_ mix is mixture mass ﬂow rate through condenser, kg/ where m s, hin is enthalpy of mixture inlet to condenser, kJ/kg, and hout is enthalpy of feed water outlet from condenser, kJ/kg.

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(v) Net work done, Wnet, kJ/kg is:

W net ¼ W T W p

ð9Þ

(vi) The cycle efﬁciency, gth,% is:

gth ¼

W net Q add

ð10Þ

2.2. Heat balance of feed water heaters (i) Closed feed water heaters,

_ st ðh1 h2 Þ ¼ m _ fw ðhout hin Þ m

ð11Þ

_ st is steam mass ﬂow rate extracted from turbine to where m feed water heater, kg/s, mfwh is feed water mass ﬂow rate inlet to feed water heater, kg/s, h1 is enthalpy of steam inlet to feed water heater, kJ/kg, h2 is enthalpy of steam outlet from feed water heater, kJ/kg, hin is enthalpy of mixture inlet to feed water heater, kJ/kg, and hout is enthalpy of feed water outlet from feed water heater, kJ/kg. (ii) Deaerator,

_ st þ m _ fw Þ hout ¼ ðm _ st h1 Þ þ ðm _ fw hinÞ ðm

ð12Þ

_ st is steam mass ﬂow rate extracted from turbine to deaerwhere m _ fwh is feed water mass ﬂow rate inlet to deaerator, kg/s, ator, kg/s, m hin is enthalpy of mixture inlet to deaerator, kJ/kg, and hout is enthalpy of feed water outlet from deaerator, kJ/kg. 2.3. Heat balance of steam generator

_ RCW C RCW ðT HL T CL Þ ¼ ðm _ st hout Þ ðm _ fw hin Þ m

ð13Þ

_ RCW is reactor coolant water mass ﬂow rate of primary where m _ fwh is feed water mass ﬂow rate inlet to steam circuit, kg/s, m _ st is steam mass ﬂow rate exit from steam generator, kg/s, m generator, kg/s, hin is enthalpy of feed water inlet to steam generator, kJ/kg, hout is enthalpy of steam outlet from steam generator, kJ/kg, THL is temperature of reactor coolant water at hot leg, °C, TCL is temperature of reactor coolant water at cold leg, °C, and CRCW is speciﬁc heat of reactor coolant water of primary circuit, kJ/kg K. 2.4. Heat balance of moisture separator and reheater

_ st hin ¼ ðm _ st hs Þ þ ðm _ fw þ m _ st Þ hout m

ð14Þ

_ st is steam mass ﬂow rate inlet to moisture separator and where m _ st is water mass ﬂow rate exit from moisture separeheater, kg/s, m rator and reheater to feed water, kg/s, hin is enthalpy of feed water inlet to moisture separator and reheater, kJ/kg, hout is enthalpy of steam outlet from moisture separator and reheater, kJ/kg, and hs is enthalpy of steam outlet from moisture separator and reheater, kJ/kg. 2.5. Heat balance of cooling water system (condenser) The condenser is a large shell and tube type heat exchanger. The steam in the condenser goes under a phase change from vapor to liquid water. External cooling water is pumped through thousands of tubes in the condenser to transport the heat of the condensation of the steam away from the plant. Upon leaving the condenser, the condensate is at a low temperature and pressure. The phase change in turn depends on the transfer of heat to the external cooling water. The rejection of heat to the surrounding by the cooling water is essential to maintain the low pressure in the condenser. The heat is absorbed by the cooling water passing through the condenser tubes.

The thermal performance of a condenser and the condenser overall heat transfer coefﬁcient decreases with increase in fouling factor and temperature of the coolant extracted from environment, where the increase of fouling factor and temperature decrease the condenser overall heat transfer coefﬁcient and increase the pressure and temperature of the exhaust steam of the turbine and hence decrease the power output and the thermal efﬁciency of the nuclear power plant. The rise in cooling water temperature, mass ﬂow rate and overall heat transfer coefﬁcient are related to the rejected heat as:

_ mix hin Þ ðm _ fw hout Þ Q Rej ¼ ðm

ð15Þ

_ CW C DT Q Rej ¼ m

ð16Þ

DT ¼ ðT cwo T cwi Þ

ð17Þ

Q Rej ¼ U A DT lm 0 1 ð T T Þ cwe cwi A DT LMTD ¼ @ ðT c T cwi Þ ln ðT c T cwe Þ

ð18Þ ð19Þ

_ CW is cooling water mass ﬂow rate of condenser, kg/s, m _ fwh where m _ mix is is feed water mass ﬂow rate of outlet from condenser, kg/s, m mixture mass ﬂow rate of inlet to condenser, kg/s, hin is enthalpy of mixture inlet to condenser, kJ/kg, hout is enthalpy of feed water outlet from condenser, kJ/kg, Tc is condenser saturation temperature, °C, Tcwo is temperature of cooling water outlet from condenser, °C, Tcwi is temperature of cooling water inlet to condenser, °C, DT is temperature difference between the cooling water exit and inlet temperature, °C, U is overall heat transfer coefﬁcient, W/m2 K, C is speciﬁc heat, kJ/kg K, A is heat transfer area, m2 and DT LMTD is log mean temperature difference, °C. 2.6. Important factors affected by fouling are as follows (i) Inside overall heat transfer coefﬁcient with fouling: The inside overall heat transfer coefﬁcient of seawater, Ui,f, changes as a function of both temperature and fouling factor is, Holman (2010):

U i;f ¼

1 ðAi ðRi þ Rw þ Ro þ Rf ÞÞ

ð20Þ

where Ai is inside tube area, m2, Ri is thermal resistance of inner seawater, m2 K/W, Ro is thermal resistance of outer condensation ﬁlm, m2 K/W, Rw is thermal resistance of tube wall, m2 K/W, and Rf is fouling factor thermal resistance, m2 K/W. (ii) Inside overall heat transfer coefﬁcient without fouling: The inside overall heat transfer coefﬁcient of seawater, Ui,c as related to temperature and fouling factor is, Holman (2010):

U i;c ¼

1 ðAi ðRi þ Rw þ Ro ÞÞ

ð21Þ

where Ai is inside tube area, m2, Ri is thermal resistance of inner seawater, m2 K/W, Ro is thermal resistance of outer condensation ﬁlm, m2 K/W, and Rw is thermal resistance of tube wall, m2 K/W. (iii) Outside overall heat transfer coefﬁcient with fouling: The outside overall heat transfer coefﬁcient of seawater, Uo,f as a function of temperature and fouling factor is, Holman (2010):

U o;f ¼

1 ðAo ðRi þ Rw þ Ro þ Rf ÞÞ

ð22Þ 2

where Ao is outside tube area, m , Ri is thermal resistance of inner seawater, m2 K/W, Ro is thermal resistance of outer

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condensation ﬁlm, m2 K/W, Rw is thermal resistance of tube wall, m2 K/W, and Rf is fouling factor thermal resistance, m2 K/W. (iv) Outside overall heat transfer coefﬁcient without fouling: The inside overall heat transfer coefﬁcient of seawater, Uo,c is given as a function of both temperature and fouling factor as, Holman (2010):

U o;c ¼

1 ðAo ðRi þ Rw þ Ro ÞÞ

ð23Þ

The inside overall heat transfer coefﬁcient of seawater, Ut changes with temperature and fouling factor as, Holman (2010):

1 ðAi ðRi þ Rw þ Ro þ Rf;i þ Rf;o ÞÞ

ð24Þ

where Ao is outside tube area, m2, Ri is thermal resistance of inner seawater, m2 K/W, Ro is thermal resistance of outer condensation ﬁlm, m2 K/W, Rw is thermal resistance of tube wall, m2 K/W, Rf,i is inside tube fouling factor thermal resistance, m2 K/W, and Rf,o is outside tube fouling factor thermal resistance, m2 K/W. - Thermal resistance of inner seawater, Ri, m2 K/W is, Holman (2010):

Ri ¼

1 h i Ai

ð25Þ

where Ao is outside tube area, m2, and hi is heat transfer coefﬁcient for ﬂow inside circular tubes, W/m2 K. - Thermal resistance of outer water, Ro, m2 K/W is, Holman (2010):

1 ho Ao

Ro ¼

ð26Þ

where Ao is outside tube area, m2, and ho is ﬁlm condensation heat transfer coefﬁcient in bundles of horizontal tubes, W/m2 K. - Thermal Resistance of Tube Wall, Rw, m2 K/W is, Holman (2010):

ln

Rw ¼

ro ri

f A

ð28Þ

where A is tube surface area, m2, and f is fouling factor, m2 K/W. - Heat transfer coefﬁcient for ﬂow inside circular tubes, hi, W/m2 K is, Holman (2010):

hi ¼

Nu k d

ð29Þ

0:4 Nu is Nusselt number ¼ 0:023 R0:8 e Pr ;

Re The Reynolds number ¼

qVd l

ð30Þ ð31Þ

,

Pr Prandtl Number ¼

g ql ðql qv Þ hfg k ll ðT st T w Þ Nh do

!0:25

ð33Þ

where qL is liquid density, kg/m3, qV is steam or vapor density, kg/ m3, lL is liquid dynamic viscosity, N/m2 s, Tst is steam or vapor saturation temperature, °C, Nh is number of horizontal tubes, hfg is latent heat for condensation, kJ/kg, k is thermal conductivity, W/ m K, g is acceleration of gravity, m/s2, and Tw is condenser tube surface wall temperature, °C. Modeling assumptions for the secondary cycle are: (i) The thermodynamic conditions of steam at the exit of the SG are ﬁxed. (ii) Thermal power of the PWR changes slowly to provide constant thermodynamic properties of steam at exit of the SG since the variation in cooling water temperature occurs seasonally and very slowly. (iii) The condenser vacuum varies with the temperature of cooling water extracted from environment at ﬁxed mass ﬂow rate into the condenser. (iv) Constant cooling water temperature difference. (v) Constant mass ﬂow rate of steam entering the condenser, and mass ﬂow rate of cooling water. (vi) Fixed total surface area of the tube and materials property. (vii) There is no pressure drop across the plant. (viii) Constant condenser heat transfer area and heat load. (ix) The potential and kinetic energies of the ﬂow and heat losses from all equipment and pipes are negligible. 2.7. The relations between the output power, thermal efﬁciency and seawater fouling The relations between the output power and thermal efﬁciency of the plant, and the condenser cooling seawater fouling are not obtained directly but through a sequence of substitutions in the above given equations as follows:

ð27Þ

2p k

where k is thermal conductivity of tube, W/m K, ro is outer radius, m, and ri is inner radius, m. - Thermal resistance of seawater fouling factor, Rf, m2 K/W is, Holman (2010):

Rf ¼

3

ho ¼ 0:725

where Ao is outside tube area, m2, Ri is thermal resistance of inner seawater, m2 K/W, Ro is thermal resistance of outer condensation ﬁlm, m2 K/W, and Rw is thermal resistance of tube wall, m2 K/W. (v) Inside and outside overall heat transfer coefﬁcient, Ui,f with fouling:

U i;t ¼

where q is inside seawater density, kg/m3, v is ﬂow velocity, m/s, d is tube diameter, m, l is inside seawater dynamic viscosity, N/m2 s, k is inside thermal conductivity W/m K, and Cp is inside seawater speciﬁc heat capacity, kJ/kg K. - Film condensation in bundles of horizontal tubes, ho, W/m2 K is, Holman (2010):

lC p k

;

ð32Þ

- Equations 25–28 relate the effect of condenser cooling seawater fouling and the thermal resistance. An increase in the fouling factor increases the thermal resistance. - Equations 20–24 are the relations between the thermal resistance and the overall heat transfer coefﬁcient of the condenser. According to these relations an increase in the thermal resistance will decrease the overall heat transfer coefﬁcient of the condenser. Overall this means that an increase in, f, results in the end in a decrease in the overall heat transfer coefﬁcient. - The effect on the heat rejection from the exhaust steam to the condenser cooling seawater is given by equations 15–19, which relate the overall heat transfer coefﬁcients and condensate temperature. According to these equations, a decrease in the heat rejection results in a decrease in the overall heat transfer coefﬁcients and this leads to an increase in the exhaust steam temperature. - The increase in the exhaust steam temperature increases the exhaust steam pressure accordingly. The turbine output depends on the exit steam temperature and pressure. These effects are given by equations 1–10, which indicate that the increase in the temperature and pressure of the exhaust steam will decrease the output power and in turn the thermal efﬁciency of the nuclear power plant.

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So there is no direct mathematical relation between output power and thermal efﬁciency and condenser cooling seawater fouling. The relation is indirect through the interconnected given equations as discussed above. The computer program conducts the chain of calculations to give in the end the required effect of the studies parameter, fouling, on the power output and thermal efﬁciency of the PWR NPP.

3. Results and discussions Thermodynamic analysis of the proposed PWR NPP is conducted to investigate the key parameters such as heat added to steam generator, heat rejection, net turbine work, and overall plant thermal efﬁciency. Fig. 3 illustrates the calculation of the thermodynamic and heat balance analysis of the proposed PWR NPP. This

Fig. 3. Illustration of the EES model equivalent to the proposed PWR NPP thermodynamic and heat balance analysis.

Table 1 Thermodynamic data for the studied PWR NPP. Station No.

Temperature, T [°C]

Pressure, P [bar]

Enthalpy, h [kg/kJ]

Entropy, s [kJ/kg K]

Quality, X

_ [kg/s] Mass ﬂow rate, m

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36

289.5 289.5 289.5 252.8 216.2 179.6 179.6 179.6 289.5 289.5 199.5 106.4 69.78 33.16 33.16 33.27 65.75 102.4 139 179.6 181 212.2 248.8 252.8 216.2 216.2 179.6 143 106.4 106.4 69.75 69.75 33.16 252.8 20 30

73.8 73.8 73.8 41.68 21.55 9.932 9.932 9.932 73.8 9.932 3.93 1.267 0.3088 0.05079 0.05079 9.932 9.932 9.932 9.932 9.932 73.8 73.8 73.8 41.68 21.55 21.55 9.932 3.93 1.267 1.267 0.3088 0.3088 0.05079 41.68 3 2

2763 2763 2763 2678 2583 2478 761.5 2777 1286 3028 2859 2689 2510 2314 138.9 140.2 276 429.7 585.3 761.5 771.1 909.6 1080 1099 1099 926.1 926.1 602.1 602.1 446 446 292 292 1286 84.12 125.8

5.779 5.779 5.779 5.82 5.868 5.926 2.136 6.588 3.154 7.085 7.177 7.288 7.419 7.579 0.4799 0.481 0.9022 1.333 1.728 2.136 2.141 2.436 2.774 2.819 2.836 2.483 2.499 1.77 1.79 1.378 1.401 0.9519 0.9796 3.174 0.2961 0.4365

0.9975 0.9975 0.9975 0.9283 0.8841 0.8513 0 1 0 Superheated Superheated Superheated 0.9503 0.8978 0 Sub. liquid Sub. liquid Sub. liquid Sub. liquid 0 Sub. liquid Sub. liquid Sub. liquid 0 0.09234 0 0.08166 0 0.0697 0 0.06599 0 0.06319 0.11 Sub. liquid Sub. liquid

1608 171.1 1437 153 100.7 1355 176 1008 171.1 1008 69.45 64.21 52.42 821.6 1008 1008 1008 1008 1008 1184 1608 1608 1608 153 153 253.7 133.7 69.45 69.45 133.7 133.7 186.1 186.1 171.1 41,197 41,197

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ﬁgure represents the basis of the parametric study and analysis of the present work. Table 1 summarizes the calculation of the thermodynamic properties at design conditions satisfying the heat balance for the proposed PWR NPP. Fig. 3 and Table 1 are the basis of the parametric study and analysis of the present work. Many factors are affected by changes in the condenser cooling seawater temperature fouling factor, and such important factors are discussed in the following paragraphs: Fig. 4 indicates the variations of the inside overall heat transfer coefﬁcient, Ui,f with condenser cooling seawater temperature fouling factor, f at different values of condenser cooling seawater temperature, Tcwi. Ui,f decreases with increasing f and Tcwi. When f increases by 0.00002 and (0.00015–0.00035) m2 K/W, respectively, Ui,f decreases approximately by 25 and 211.6 W/m2 K, respectively at ﬁxed Tcwi. Fig. 5 gives the relation between the outside overall heat transfer coefﬁcient of seawater, Uo,f and the condenser cooling seawater temperature fouling factor, f at different values of condenser cooling seawater temperature, Tcwi. Uo,f decreases with increasing f and Tcwi. For an increase in f of 0.00002 and (0.00015–0.00035) m2 K/W, respectively, Uo,f decreases approximately by 24 and 198 W/m2 K respectively for the same Tcwi.

Fig. 6 represents the variations of condenser temperature, Tc with fouling factor, f at different values of condenser cooling seawater, Tcwi. It is seen that Tc is affected by both f and Tcwi; hence Tc increases with increasing f and Tcwi. When f increases by 0.00002 and (0.00015–0.00035) m2 K/W, respectively, Tc increases approximately by 0.3 and 3 °C, respectively, at constant values of Tcwi. Fig. 7 depicts the variations of condenser pressure, Pc with fouling factor, f at different values of condenser cooling seawater temperature, Tcwi. Pc increases with increasing f and Tcwi. For an increase in f by about 0.00002 and (0.00015–0.00035) m2 K/W, respectively, Pc increases approximately by 0.00112 and 0.01184 bar, respectively, at unchanged values of Tcwi. Fig. 8 presents the variations of output power, Wnet with the fouling factor, f at different values of condenser cooling seawater temperature, Tcwi. It is shown that Wnet decreases with increasing f and Tcwi. An increase in f of 0.00002 and (0.00015– 0.00035) m2 K/W, respectively, results a decrease in Wnet approximately by 1349.32 and 13319.93 kW, respectively at constant Tcwi. Fig. 9 illustrates the overall thermal efﬁciency, gth versus fouling factor, f at different values of condenser cooling seawater temperature, Tcwi. The results show that gth of the plant decreases with increasing both f and Tcwi. When f increases by 0.00002, and (0.00015–0.00035) m2 K/W, respectively, gth decreases approximately by 0.046 and 0.448%, respectively for the same Tcwi.

1200 o

T cwi = 30 [ C]

1150

o

T cwi = 27 [ C]

Ui,f (W/m2 K)

1100

o

1050

T cwi = 24 [ C]

1000

o

T cwi = 21 [ C]

950

o

T cwi = 18 [ C]

900 o

T cwi = 15 [ C]

850 0.00013

0.00017

0.00021

0.00025

0.00029

0.00033

0.00037

2

f (m K/W) Fig. 4. Inside overall heat transfer coefﬁcient, Ui,f with fouling factor, f at different values of condenser cooling seawater temperature, Tcwi.

1150 o

Tcwi = 30 [ C]

1100

o

Tcwi = 27 [ C]

Uo,f (W/m2 K)

1050

o

1000

Tcwi = 24 [ C]

950

o

Tcwi = 21 [ C]

900

o

Tcwi = 18 [ C]

850 o

Tcwi = 15 [ C]

800 0.00013

0.00017

0.00021

0.00025

0.00029

0.00033

0.00037

2

f (m K/W) Fig. 5. Outside overall heat transfer coefﬁcient, Uo,f with fouling factor, f at different values of condenser cooling seawater temperature, Tcwi.

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S.M.A. Ibrahim, S.I. Attia / Annals of Nuclear Energy 76 (2015) 421–430

52.5 o

Tcwi = 30 [ C]

48.5

o

T c (°C)

Tcwi = 27 [ C]

44.5

o

Tcwi = 24 [ C]

40.5

o

Tcwi = 21 [ C] o

Tcwi = 18 [ C]

36.5

o

Tcwi = 15 [ C]

32.5 0.00013

0.00017

0.00021

0.00025

0.00029

0.00033

0.00037

2

f (m K/W) Fig. 6. Condenser temperature, Tc with fouling factor, f at different values of condenser cooling seawater temperature, Tcwi.

0.13 o

Tcwi = 30 [ C]

0.12

o

0.11

Tcwi = 27 [ C]

0.1

o

P c (bar)

Tcwi = 24 [ C]

0.09 o

0.08

Tcwi = 21 [ C]

0.07

Tcwi = 18 [ C]

o

0.06 0.05 0.00013

o

Tcwi = 15 [ C]

0.00017

0.00021

0.00025

0.00029

0.00033

0.00037

2

f (m K/W) Fig. 7. Condenser pressure, Pc with fouling factor, f at different values of condenser cooling seawater temperature, Tcwi.

1.010 x106 o

Tcwi = 15 [ C]

1000000 990000

o

Tcwi = 18 [ C]

W net (kW)

980000 o

970000

Tcwi = 21 [ C]

960000

Tcwi = 24 [ C]

o

950000

o

Tcwi = 27 [ C]

940000

o

Tcwi = 30 [ C]

930000 920000 0.00013

0.00017

0.00021

0.00025

0.00029

0.00033

0.00037

2

f (m K/W) Fig. 8. Output power Wnet with fouling factor f at different values of condenser cooling seawater temperature Tcwi.

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S.M.A. Ibrahim, S.I. Attia / Annals of Nuclear Energy 76 (2015) 421–430

37 o

Tcwi = 15 [ C]

36.5 o

Tcwi = 18 [ C]

36

η th (%)

o

Tcwi = 21 [ C]

35.5 o

Tcwi = 24 [ C]

35

o

Tcwi = 27 [ C]

34.5

o

Tcwi = 30 [ C]

34 0.00013

0.00017

0.00021

0.00025

0.00029

0.00033

0.00037

2

f (m K/W) Fig. 9. Overall thermal efﬁciency, gth with fouling factor, f at different values of condenser cooling seawater temperature, Tcwi.

∆f= 0.00001 (m2 K/W)

∆ηth =0.023 (%) & ∆W= 674.79 (kW), 0.0689 (%)

∆f= 0.00002 (m2 K/W)

∆ηth=0.046 (%) & ∆W= 1349.32(kW), 0.138 (%)

∆f= 0.00003 (m2 K/W)

∆ηth =0.068 (%) & ∆W= 2023.56 (kW), 0.2066 (%)

∆f= 0.00004

(m2

K/W)

∆ηth =0.091(%) & ∆W= 2697.5 (kW), 0.2754 (%)

∆f= 0.00005

(m2

K/W)

∆ηth=0/114 (%) & ∆W= 3371.14(kW), 0.344 (%)

∆f= 0.0001 (m2 K/W)

∆ηth =0.227 (%) & ∆W= 6734.41(kW), 0.687(%)

∆f= 0.0002 (m2 K/W)

∆ηth =0.448 (%) & ∆W= 13319.93 (kW), 1.38 (%)

Fig. 10. The effect of cooling seawater fouling, f on the thermal efﬁciency and output power of the NPP.

∆T=1 (oC) & ∆f= 0.00001 (m2 K/W) ∆T= 2

(o C)

& ∆f= 0.00002

(m2

K/W)

∆ηth = 0.161(%) & ∆Wnet= 4814.9 (kW), 0.481 (%) ∆ηth= 0.322 (%) & ∆Wnet= 9631.57 (kW), 0.963 (%)

∆T= 3 (o C) & ∆f= 0.00003 (m2 K/W)

∆ηth= 0.484 (%) & ∆Wnet= 14449.79 (kW), 1.4445 (%)

∆T= 4 (o C) & ∆f= 0.00004 (m2 K/W)

∆ηth= 0.6468 (%) & ∆Wnet= 19269.33 (kW), 1.926(%)

K/W)

∆ηth= 0.808 (%) & ∆Wnet= 24089.97 (kW), 4.81 (%)

∆T= 10 (oC) & ∆f= 0.0001 (m2 K/W)

∆ηth= 1.616 (%) & ∆Wnet= 48111.8 (kW), 4.8094 (%)

∆T= 15 (oC) & ∆f= 0.0002 (m2 K/W)

∆ηth = 2.544 (%) & ∆Wnet= 75585.61 (kW), 7.556 (%)

∆T= 5

(oC)

& ∆f= 0.00005

(m2

Fig. 11. The impact of cooling seawater temperature, Tcwi and fouling factor, f on the thermal efﬁciency and output power of the NPP.

The increase in fouling of condenser cooling water causes an increase in the thermal resistance of the condenser and this in turn reduces the overall heat transfer coefﬁcients, Ui,f and Uo,f. The decrease in the overall heat transfer coefﬁcients will lead to an increase in the turbine exhaust steam temperature and hence the corresponding exhaust steam pressure. The increase in exhaust steam pressure, which is a power loss leads to the observed reduction in the output power and the thermal efﬁciency of the studied nuclear power plant. Fig. 10 summarizes the effect of cooling seawater fouling, f on the thermal efﬁciency and output power of the nuclear power plant. The large increase in fouling reduces signiﬁcantly both Wnet and gth of the plant. Fig. 11 summarizes the impact of changes in cooling seawater temperature, Tcwi and fouling factor, f on the thermal efﬁciency and output power of the nuclear power plant. The combined effect of increases in Tcwi and f can result in high decreases in both output power and thermal efﬁciency of the plant.

4. Conclusions Fouling of condenser tubes is one of the most important factors affecting their thermal performance, which reduces effectiveness and heat transfer capability. The present model predicts the decrease in heat transfer rate with the growth of fouling. It is concluded that the thermal efﬁciency of the nuclear power plant is reduced by up to 0.448% for an increase in the fouling factor of the condenser cooling seawater in the range 0.00015– 0.00035 m2 K/W. The power loss for the same range of the fouling factor is founded to be 13319.93 kW. These are quite signiﬁcant reductions in the thermal efﬁciency and power output of the plant in view of the extensive efforts and money spent to increase the thermal efﬁciency by even 1%. Therefore, the paper offers an additional design factor to be considered in the design of new power stations. Therefore, condenser cooling seawater fouling attack must be prevented either completely or partially in order to mitigate the

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undesired drawbacks on the output power and thermal efﬁciency of the nuclear power plant. Fouling may be avoided by chemical methods or otherwise. Production capacity reduction due to an increase in fouling would represent a drop of power production that might need to be replaced somewhere. The effect of climatic changes shows to be important in the design of more effective cooling techniques and to device methods to compensate for the loss in plant output and system capacity.

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