Annals of Nuclear Energy 76 (2015) 421–430

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Annals of Nuclear Energy

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Technical note

The influence of condenser cooling seawater fouling on the thermalperformance of a nuclear power plant

http://dx.doi.org/10.1016/j.anucene.2014.10.0180306-4549/� 2014 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.

Said M.A. Ibrahim a, Sami I. Attia b,⇑a Department of Mechanical Power Engineering, Faculty of Engineering, AL-Azhar University, Nasr City, Cairo 11371, Egyptb 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 a b s t r a c t

Article history:Received 24 June 2014Received in revised form 30 August 2014Accepted 21 October 2014Available online 6 November 2014

Keywords:PWR secondary cycleCondenser cooling seawaterFouling factorThermodynamicHeat transfer

This study performs a thermodynamic analysis and energy balance to study the effect of fouling changeon the thermal performance of the condenser and the thermal efficiency of a proposed nuclear powerplant. The study is carried out on a pressurized water reactor nuclear power plant. The results of thestudy show that the increasing of fouling factor decreases the power output and the thermal efficiencyof the nuclear power plant. The main results of this study is that the impact of an increase in thecondenser cooling seawater fouling factor in the range 0.00015–0.00035 m2 K/W is led to a decrease inthe plant output power and thermal efficiency of 1.36% and 0.448%, respectively. The present paperresearches into a real practical factor that has significant negative effect on the thermal efficiency ofthe nuclear power plants, which is fouling of condenser cooling seawater. This is abundantly importantsince one of the top goals of new power stations are to increase their thermal efficiency, and to prevent orminimize the reasons that lead to loss of output power.

� 2014 Elsevier Ltd. All rights reserved.

1. Introduction

The condenser in a steam electric power generation station isone of the most influential items of equipment in the system asrelated to performance. The concept of fouling has been incorpo-rated to understand the thermal losses inside the condenser. Thefouling of the condenser cooling water has an impact on thethermal performance of the condenser which finally affects nuclearpower plant’s efficiency and its output power.

Fouling represents an important problem for condensers andheat exchangers. All industrial circuits cooled with natural freshand marine water are affected by the phenomenon of biologicalfouling consisting in biofilm growth and settlements of severalkinds of living organisms. Biofouling is detrimental to open coolingsystems as it causes undesirable effects, such as efficiency lossinside the heat exchanger, clogging of the seawater circuit pipes,and reduction in plant reliability over a period of time. Most ofthe power generation plants efficiently operate by using the basictools of physical screening, physical cleaning and chemical dosing.A traditional chemical way to control microbial growth andbiofouling in power plants remains the use of chlorine, in spite ofthe fact that chlorination was subjected to the environmental

authorities’ attention for more than 20 years, because of its halo-methanes and other organohalogens by-products items.

Fig. 1 illustrates how the temperature distribution is affected bythe presence of the individual fouling layers.

The importance of fouling phenomena stems from the fact thatthe fouling deposits increase the thermal resistance to heat flow.According to the basic theory, the heat transfer rate in the exchan-ger depends on the sum of thermal resistances between the twofluids. Fouling on one or both fluid sides adds the thermalresistance to the overall thermal resistance and, in turn, reducesthe heat transfer rate. Simultaneously, hydraulic resistanceincreases 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 tem-perature may have impact on the capacity utilization of thermalpower plants in two concerns: (1) reduced efficiency: increasedenvironmental temperature and fouling factor reduces thermalefficiency of a thermal power plant, (2) reduced load: for highenvironmental temperatures and fouling factor, thermal powerplant’s operation will be limited by a maximum possible condenserpressure. The operation of plants with river or sea cooling waterwill in addition be limited by a regulated maximum allowabletemperature for the return water or by reduced access to water.

In the literature, there are few articles published to identifythese climate and environmental change impacts; few have tried

Nomenclature

A tube area [m2]c specific heat [kJ/kg K]d diameter [m]h enthalpy [kJ/kg]f fouling factor [m2 K/W]K thermal conductivity [W/m K]LMTD log mean temperature difference [�C]_m mass flow rate [kg/s]

P pressure [bar]_Q net rate of heat transferred [kW]

R thermal resistance[m2 K/W]r radius [m]T temperature [�C]TTD terminal temperature difference[�C]U overall heat transfer coefficient [W/m2 K]V velocity [m/s]_W net rate of work [kW]

w pure water

Greek symbolsg efficiency [%]l viscosity, [kg/m s]q density, [kg/m3]

Subscriptsadd addedc condenserCP condensate pumpcw cooling watercwi cooling water inlet

CL cold legcwo cooling water outletfw feed waterFWP feed water pumpHL hot legHPT high pressure turbineLPT low pressure turbinei inletin inletmix mixtureo outletout outletp pumpRCW reactor cooling waterRej rejectionT turbinew wall

Superscript. per unit time

AbbreviationsFW feed waterHP high pressureLP low pressureNPP nuclear power plantPWR pressurized water reactorRC reactor coolantSG steam generator

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

to quantify them. Qureshi and Zubair (2005), studied the effect offouling on the thermal performance of heat exchangers at differentair inlet wet bulb temperatures. Lankinen et al. (2003), defined theheat transfer efficiency as well as the external and internalpressure drops and the effect of fouling on the thermal hydrauliccharacteristics of the heat exchanger. Lei et al. (2012), discusseda simplified theoretical model to study fouling growth, the charac-teristic of fouling deposit, effects of working time, and coolingwater velocity. Walker et al. (2012), presented a methodology toquantify the economic impact of condenser fouling on the perfor-mance of thermoelectric power plants. Webb and Ralph (2011),determined the performance and economic benefits of usingenhanced condenser tubes in an existing nuclear plant. Prietoet al. (2001), gave the data that allow carrying out heat balancesas well as other important data needed to estimate fouling evolu-tion for seawater refrigerated condenser in a 550 MW power plant.

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

Pugh1 et al. (2003), studied the fouling during the use of seawateras coolant.

Ganan et al. (2005), showed that the performance of the pres-surized water reactor (PWR) type Almaraz nuclear-power plant isstrongly affected by the weather conditions having experienced apower limitation due to vacuum losses in condenser during sum-mer. Durmayaz and Sogut (2006), presented a theoretical modelto study the influence of the cooling water temperature on thethermal efficiency of a conceptual pressurized-water reactornuclear power plant. Sanathara et al. (2013), gave a parametricanalysis of surface condenser for 120 MW thermal power plant,focused on the influence of the cooling water temperature and flowrate on the condenser performance, and thus on the specific heatrate of the plant and its thermal efficiency.

The present study presents an analysis of the effect of theenvironmental conditions on the thermal performance of a pro-posed pressurized water reactor nuclear power plant (PWRNPP). The nuclear power plant performance depends on thethermal analysis of the condenser through heat transfer analysistaking into account the key parameters such as fouling factorand temperature of cooling seawater that affect the condenserperformance, overall heat transfer coefficient, and the thermalperformance of the plant. This parametric study illustrates theimpact of the fouling factor of condenser cooling seawater withina range of 0.00015–0.00035 m2 K/W, and temperature within arange of 15–30 �C.

2. Methodology

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

Fig. 2. Diagram of PWR nuclear power plant.

S.M.A. Ibrahim, S.I. Attia / Annals of Nuclear Energy 76 (2015) 421–430 423

performed to assess the impact of the change in fouling factor andcooling seawater temperature on the thermal efficiency of theproposed PWR NPP. The objective is to establish a theoreticalmethodology to evaluate the impact of fouling factor of seawateron the steam surface condenser overall heat transfer coefficientof the PWR NPP within specific designed range of seawater tem-perature and fouling.

Fig. 2 depicts a diagram of a proposed PWR NPP, to address thethermodynamic and heat balance analysis of the plant. A typicalPWR NPP consists of a primary cycle which includes: nuclearreactor, 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 separa-tor and reheater (MS/R), deaerator feed water heater, two high-pressure feed water heaters (HPFWH), and three low pressure feedwater heaters (LPFWH), condenser, and necessary pumps (feedwater pump and condensate pump).

The mathematical model representing the secondary thermo-dynamic cycle of the plant and its components used the engineer-ing 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 andexit of all parts and components of the plant.

(ii) Heat balance for each feed water heater and the steamgenerator.

(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 andcalculate the efficiency of the station.

(v) Hence temperature entropy, T–S diagram of the plant and itscomponents is obtained.

(vi) Determination of cooling water inlet temperature, Tin andexit temperature, Tout and the temperature difference.

(vii) Assigning the range of change of the fouling factor, f as0.00015–0.00035 m2 K/W, and cooling seawater tempera-ture, Tcwi as 15–30 �C.

(viii) Computing the impact of the changes of cooling seawatertemperature Tcwi and fouling factor, f on the thermal effi-ciency gth and output work Wnet of the plant.

(ix) Drawing the relation between Tcwi and f verses the con-denser overall heat transfer coefficient, gth, and Wnet of theplant.

The energy balance equations for the various processesinvolving steady flow equipment such as nuclear reactor, turbines,pumps, steam generators, heaters, coolers, reheaters and condens-ers in a PWR NPP are given below.

2.1. Heat balance equations

(i) The total turbine work, WT, kJ/kg is:

WT ¼WHPT þWLPT ð1Þ

WHPT ¼ _mstðhin � houtÞ ð2Þ

WLPT ¼ _mstðhin � houtÞ ð3Þ

where _mst is steam mass flow rate inlet to each turbine, kg/s,hin is enthalpy of steam inlet to each Turbine, kJ/kg, hout

is enthalpy of steam outlet from each turbine, kJ/kg, WHPT ishigh pressure turbine work, kJ/kg, and WLPT is low pressureturbine work, kJ/kg.

(ii) The pumping work, WP, kJ/kg is:

Wp ¼Wcp þW fwp ð4Þ

W fwp ¼ _mfwðhin � houtÞ ð5Þ

Wcp ¼ _mfwðhin � houtÞ ð6Þ

where _mfwh is feed water mass flow rate inlet to each steamgenerator, kg/s, hin is enthalpy of feed water inlet to eachpump, kJ/kg, hout is enthalpy of feed water outlet from eachpump, 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 mstðhout � hinÞ ð7Þ

where _mst is steam mass flow rate exit from steam generator,kg/s, hin is enthalpy of feed water inlet to steam generator,and kJ/kg, hout is enthalpy of steam outlet from steamgenerator, kJ/kg.

(iv) Heat rejected from condenser, QRej, kJ/kg is:

Q Rej ¼ ð _mmix � hin � _mmix � houtÞ ð8Þ

where _mmix is mixture mass flow rate through condenser, kg/s, hin is enthalpy of mixture inlet to condenser, kJ/kg, and hout

is enthalpy of feed water outlet from condenser, kJ/kg.

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

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

Wnet ¼WT �Wp ð9Þ

The cycle efficiency, gth,% is:

(vi)

gth ¼Wnet

Q addð10Þ

2.2. Heat balance of feed water heaters

(i) Closed feed water heaters,

_mst � ðh1 � h2Þ ¼ _mfw � ðhout � hinÞ ð11Þ

where _mst is steam mass flow rate extracted from turbine tofeed water heater, kg/s, mfwh is feed water mass flow rateinlet to feed water heater, kg/s, h1 is enthalpy of steam inletto feed water heater, kJ/kg, h2 is enthalpy of steam outletfrom feed water heater, kJ/kg, hin is enthalpy of mixture inletto feed water heater, kJ/kg, and hout is enthalpy of feed wateroutlet from feed water heater, kJ/kg.

(ii) Deaerator,

ð _mst þ _mfwÞ � hout ¼ ð _msth1Þ þ ð _mfw � hinÞ ð12Þ

where _mst is steam mass flow rate extracted from turbine to deaer-ator, kg/s, _mfwh is feed water mass flow rate inlet to deaerator, kg/s,hin is enthalpy of mixture inlet to deaerator, kJ/kg, and hout isenthalpy of feed water outlet from deaerator, kJ/kg.

2.3. Heat balance of steam generator

_mRCW � CRCW � ðTHL � TCLÞ ¼ ð _mst � houtÞ � ð _mfw � hinÞ ð13Þ

where _mRCW is reactor coolant water mass flow rate of primarycircuit, kg/s, _mfwh is feed water mass flow rate inlet to steamgenerator, kg/s, _mst is steam mass flow rate exit from steamgenerator, kg/s, hin is enthalpy of feed water inlet to steam gen-erator, kJ/kg, hout is enthalpy of steam outlet from steam gener-ator, kJ/kg, THL is temperature of reactor coolant water at hotleg, �C, TCL is temperature of reactor coolant water at cold leg,�C, and CRCW is specific heat of reactor coolant water of primarycircuit, kJ/kg K.

2.4. Heat balance of moisture separator and reheater

_mst � hin ¼ ð _mst � hsÞ þ ð _mfw þ _mstÞ � hout ð14Þwhere _mst is steam mass flow rate inlet to moisture separator andreheater, kg/s, _mst is water mass flow rate exit from moisture sepa-rator and reheater to feed water, kg/s, hin is enthalpy of feed waterinlet to moisture separator and reheater, kJ/kg, hout is enthalpy ofsteam 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. Thesteam in the condenser goes under a phase change from vapor toliquid water. External cooling water is pumped through thousandsof tubes in the condenser to transport the heat of the condensationof the steam away from the plant. Upon leaving the condenser, thecondensate is at a low temperature and pressure. The phase changein turn depends on the transfer of heat to the external coolingwater. The rejection of heat to the surrounding by the coolingwater is essential to maintain the low pressure in the condenser.The heat is absorbed by the cooling water passing through the con-denser tubes.

The thermal performance of a condenser and the condenseroverall heat transfer coefficient decreases with increase in foulingfactor and temperature of the coolant extracted from environment,where the increase of fouling factor and temperature decrease thecondenser overall heat transfer coefficient and increase the pres-sure and temperature of the exhaust steam of the turbine andhence decrease the power output and the thermal efficiency ofthe nuclear power plant. The rise in cooling water temperature,mass flow rate and overall heat transfer coefficient are related tothe rejected heat as:

QRej ¼ ð _mmix � hinÞ � ð _mfw � houtÞ ð15Þ

QRej ¼ _mCW � C � DT ð16Þ

DT ¼ ðTcwo � TcwiÞ ð17Þ

QRej ¼ U � A � DT lm ð18Þ

DTLMTD ¼Tcwe � Tcwið Þ

ln ðTc�TcwiÞðTc�TcweÞ

� �0@

1A ð19Þ

where _mCW is cooling water mass flow rate of condenser, kg/s, _mfwh

is feed water mass flow rate of outlet from condenser, kg/s, _mmix ismixture mass flow rate of inlet to condenser, kg/s, hin is enthalpy ofmixture inlet to condenser, kJ/kg, hout is enthalpy of feed water out-let 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 istemperature difference between the cooling water exit and inlettemperature, �C, U is overall heat transfer coefficient, W/m2 K, C isspecific heat, kJ/kg K, A is heat transfer area, m2 and DTLMTD is logmean 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 factoris, Holman (2010):

Ui;f ¼1

Ai � ðRi þ Rw þ Ro þ Rf Þð Þ ð20Þ

where Ai is inside tube area, m2, Ri is thermal resistance ofinner seawater, m2 K/W, Ro is thermal resistance of outercondensation film, m2 K/W, Rw is thermal resistance of tubewall, 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 asrelated to temperature and fouling factor is, Holman (2010):

Ui;c ¼1

ðAi � ðRi þ Rw þ RoÞÞð21Þ

where Ai is inside tube area, m2, Ri is thermal resistance ofinner seawater, m2 K/W, Ro is thermal resistance of outercondensation film, m2 K/W, and Rw is thermal resistance oftube 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):

Uo;f ¼1

ðAo � ðRi þ Rw þ Ro þ RfÞÞð22Þ

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

S.M.A. Ibrahim, S.I. Attia / Annals of Nuclear Energy 76 (2015) 421–430 425

condensation film, m2 K/W, Rw is thermal resistance of tubewall, 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 isgiven as a function of both temperature and fouling factor as,Holman (2010):

Uo;c ¼1

ðAo � ðRi þ Rw þ RoÞÞð23Þ

where Ao is outside tube area, m2, Ri is thermal resistance ofinner seawater, m2 K/W, Ro is thermal resistance of outercondensation film, m2 K/W, and Rw is thermal resistance oftube wall, m2 K/W.

(v) Inside and outside overall heat transfer coefficient, Ui,f withfouling:

The inside overall heat transfer coefficient of seawater, Ut

changes with temperature and fouling factor as, Holman (2010):

Ui;t ¼1

ðAi � ðRi þ Rw þ Ro þ Rf;i þ Rf ;oÞÞð24Þ

where Ao is outside tube area, m2, Ri is thermal resistance of innerseawater, m2 K/W, Ro is thermal resistance of outer condensationfilm, m2 K/W, Rw is thermal resistance of tube wall, m2 K/W, Rf,i isinside tube fouling factor thermal resistance, m2 K/W, and Rf,o isoutside tube fouling factor thermal resistance, m2 K/W.

- Thermal resistance of inner seawater, Ri, m2 K/W is, Holman(2010):

Ri ¼1

hiAið25Þ

where Ao is outside tube area, m2, and hi is heat transfer coefficientfor flow inside circular tubes, W/m2 K.

- Thermal resistance of outer water, Ro, m2 K/W is, Holman(2010):

Ro ¼1

hoAoð26Þ

where Ao is outside tube area, m2, and ho is film condensation heattransfer coefficient in bundles of horizontal tubes, W/m2 K.

- Thermal Resistance of Tube Wall, Rw, m2 K/W is, Holman(2010):

Rw ¼ln ro

ri

� �2pk

ð27Þ

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 ¼fA

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 ¼Nu � k

dð29Þ

Nu is Nusselt number ¼ 0:023 � R0:8e � P0:4

r ; ð30Þ

Re The Reynolds number ¼ qVdl

ð31Þ

,

Pr Prandtl Number ¼ lCp

k; ð32Þ

where q is inside seawater density, kg/m3, v is flow velocity, m/s, dis tube diameter, m, l is inside seawater dynamic viscosity, N/m2 s,k is inside thermal conductivity W/m K, and Cp is inside seawaterspecific heat capacity, kJ/kg K.

- Film condensation in bundles of horizontal tubes, ho, W/m2 K is,Holman (2010):

ho ¼ 0:725g � ql � ðql � qvÞ � hfg � k3

ll � ðTst � TwÞ � 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 sat-uration temperature, �C, Nh is number of horizontal tubes, hfg islatent heat for condensation, kJ/kg, k is thermal conductivity, W/m K, g is acceleration of gravity, m/s2, and Tw is condenser tube sur-face wall temperature, �C.

Modeling assumptions for the secondary cycle are:

(i) The thermodynamic conditions of steam at the exit of the SGare fixed.

(ii) Thermal power of the PWR changes slowly to provide con-stant thermodynamic properties of steam at exit of the SGsince the variation in cooling water temperature occurs sea-sonally and very slowly.

(iii) The condenser vacuum varies with the temperature of cool-ing water extracted from environment at fixed mass flowrate 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 lossesfrom all equipment and pipes are negligible.

2.7. The relations between the output power, thermal efficiency andseawater fouling

The relations between the output power and thermal efficiencyof the plant, and the condenser cooling seawater fouling are notobtained directly but through a sequence of substitutions in theabove given equations as follows:

- Equations 25–28 relate the effect of condenser cooling seawaterfouling and the thermal resistance. An increase in the foulingfactor increases the thermal resistance.

- Equations 20–24 are the relations between the thermal resis-tance and the overall heat transfer coefficient of the condenser.According to these relations an increase in the thermal resis-tance will decrease the overall heat transfer coefficient of thecondenser. Overall this means that an increase in, f, results inthe end in a decrease in the overall heat transfer coefficient.

- The effect on the heat rejection from the exhaust steam to the con-denser cooling seawater is given by equations 15–19, which relatethe overall heat transfer coefficients and condensate temperature.According to these equations, a decrease in the heat rejectionresults in a decrease in the overall heat transfer coefficients andthis leads to an increase in the exhaust steam temperature.

- The increase in the exhaust steam temperature increases theexhaust steam pressure accordingly. The turbine outputdepends on the exit steam temperature and pressure. Theseeffects are given by equations 1–10, which indicate that theincrease in the temperature and pressure of the exhaust steamwill decrease the output power and in turn the thermal effi-ciency of the nuclear power plant.

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

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

Fig. 3. Illustration of the EES model equivalent to the propos

Table 1Thermodynamic data for the studied PWR NPP.

Station No. Temperature, T [�C] Pressure, Enthalpy,P [bar] h [kg/kJ]

1 289.5 73.8 27632 289.5 73.8 27633 289.5 73.8 27634 252.8 41.68 26785 216.2 21.55 25836 179.6 9.932 24787 179.6 9.932 761.58 179.6 9.932 27779 289.5 73.8 128610 289.5 9.932 302811 199.5 3.93 285912 106.4 1.267 268913 69.78 0.3088 251014 33.16 0.05079 231415 33.16 0.05079 138.916 33.27 9.932 140.217 65.75 9.932 27618 102.4 9.932 429.719 139 9.932 585.320 179.6 9.932 761.521 181 73.8 771.122 212.2 73.8 909.623 248.8 73.8 108024 252.8 41.68 109925 216.2 21.55 109926 216.2 21.55 926.127 179.6 9.932 926.128 143 3.93 602.129 106.4 1.267 602.130 106.4 1.267 44631 69.75 0.3088 44632 69.75 0.3088 29233 33.16 0.05079 29234 252.8 41.68 128635 20 3 84.1236 30 2 125.8

3. Results and discussions

Thermodynamic analysis of the proposed PWR NPP is con-ducted to investigate the key parameters such as heat added tosteam generator, heat rejection, net turbine work, and overall plantthermal efficiency. Fig. 3 illustrates the calculation of the thermo-dynamic and heat balance analysis of the proposed PWR NPP. This

ed PWR NPP thermodynamic and heat balance analysis.

Entropy, Quality, Mass flow rate, _m [kg/s]s [kJ/kg K] X

5.779 0.9975 16085.779 0.9975 171.15.779 0.9975 14375.82 0.9283 1535.868 0.8841 100.75.926 0.8513 13552.136 0 1766.588 1 10083.154 0 171.17.085 Superheated 10087.177 Superheated 69.457.288 Superheated 64.217.419 0.9503 52.427.579 0.8978 821.60.4799 0 10080.481 Sub. liquid 10080.9022 Sub. liquid 10081.333 Sub. liquid 10081.728 Sub. liquid 10082.136 0 11842.141 Sub. liquid 16082.436 Sub. liquid 16082.774 Sub. liquid 16082.819 0 1532.836 0.09234 1532.483 0 253.72.499 0.08166 133.71.77 0 69.451.79 0.0697 69.451.378 0 133.71.401 0.06599 133.70.9519 0 186.10.9796 0.06319 186.13.174 0.11 171.10.2961 Sub. liquid 41,1970.4365 Sub. liquid 41,197

S.M.A. Ibrahim, S.I. Attia / Annals of Nuclear Energy 76 (2015) 421–430 427

figure represents the basis of the parametric study and analysis ofthe present work.

Table 1 summarizes the calculation of the thermodynamicproperties at design conditions satisfying the heat balance for theproposed PWR NPP. Fig. 3 and Table 1 are the basis of the paramet-ric study and analysis of the present work.

Many factors are affected by changes in the condenser coolingseawater temperature fouling factor, and such important factorsare discussed in the following paragraphs:

Fig. 4 indicates the variations of the inside overall heat transfercoefficient, Ui,f with condenser cooling seawater temperaturefouling factor, f at different values of condenser cooling seawatertemperature, Tcwi. Ui,f decreases with increasing f and Tcwi. Whenf increases by 0.00002 and (0.00015–0.00035) m2 K/W, respec-tively, 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 heattransfer coefficient of seawater, Uo,f and the condenser coolingseawater temperature fouling factor, f at different values ofcondenser cooling seawater temperature, Tcwi. Uo,f decreaseswith increasing f and Tcwi. For an increase in f of 0.00002and (0.00015–0.00035) m2 K/W, respectively, Uo,f decreasesapproximately by 24 and 198 W/m2 K respectively for the sameTcwi.

0.00013 0.00017 0.00021 0.00025850

900

950

1000

1050

1100

1150

1200

Ui,f

(W

/m2 K

)

f (m2 K/W)

Fig. 4. Inside overall heat transfer coefficient, Ui,f with fouling factor, f a

0.00013 0.00017 0.00021 0.00025800

850

900

950

1000

1050

1100

1150

Uo,

f (W/m

2 K)

f (m2 K/W)

Fig. 5. Outside overall heat transfer coefficient, Uo,f with fouling factor, f

Fig. 6 represents the variations of condenser temperature, Tc

with fouling factor, f at different values of condenser coolingseawater, Tcwi. It is seen that Tc is affected by both f and Tcwi; henceTc increases with increasing f and Tcwi. When f increases by 0.00002and (0.00015–0.00035) m2 K/W, respectively, Tc increases approx-imately by 0.3 and 3 �C, respectively, at constant values of Tcwi.

Fig. 7 depicts the variations of condenser pressure, Pc with foul-ing factor, f at different values of condenser cooling seawater tem-perature, Tcwi. Pc increases with increasing f and Tcwi. For anincrease in f by about 0.00002 and (0.00015–0.00035) m2 K/W,respectively, Pc increases approximately by 0.00112 and0.01184 bar, respectively, at unchanged values of Tcwi.

Fig. 8 presents the variations of output power, Wnet with thefouling factor, f at different values of condenser cooling seawatertemperature, Tcwi. It is shown that Wnet decreases with increasingf and Tcwi. An increase in f of 0.00002 and (0.00015–0.00035) m2 K/W, respectively, results a decrease in Wnet approxi-mately by 1349.32 and 13319.93 kW, respectively at constant Tcwi.

Fig. 9 illustrates the overall thermal efficiency, gth versusfouling factor, f at different values of condenser cooling seawatertemperature, Tcwi. The results show that gth of the plant decreaseswith increasing both f and Tcwi. When f increases by 0.00002, and(0.00015–0.00035) m2 K/W, respectively, gth decreases approxi-mately by 0.046 and 0.448%, respectively for the same Tcwi.

0.00029 0.00033 0.00037

Tcwi = 15 [ oC]

Tcwi = 18 [oC]

Tcwi = 21 [ oC]

Tcwi = 24 [ oC]

Tcwi = 27 [ oC]

Tcwi = 30 [ oC]

t different values of condenser cooling seawater temperature, Tcwi.

0.00029 0.00033 0.00037

Tcwi = 15 [oC]

Tcwi = 18 [oC]

Tcwi = 21 [oC]

Tcwi = 24 [oC]

Tcwi = 27 [oC]

Tcwi = 30 [oC]

at different values of condenser cooling seawater temperature, Tcwi.

0.00013 0.00017 0.00021 0.00025 0.00029 0.00033 0.0003732.5

36.5

40.5

44.5

48.5

52.5

Tcwi = 15 [oC]

Tcwi = 18 [oC]

Tcwi = 21 [oC]

Tcwi = 24 [oC]

Tcwi = 27 [oC]

Tcwi = 30 [oC]

Tc

(°C

)

f (m2 K/W)

Fig. 6. Condenser temperature, Tc with fouling factor, f at different values of condenser cooling seawater temperature, Tcwi.

0.00013 0.00017 0.00021 0.00025 0.00029 0.00033 0.000370.05

0.06

0.07

0.08

0.09

0.1

0.11

0.12

0.13

Tcwi = 15 [oC]

Tcwi = 18 [oC]

Tcwi = 21 [oC]

Tcwi = 24 [oC]

Tcwi = 27 [oC]

Tcwi = 30 [oC]

P c(b

ar)

f (m2 K/W)

Fig. 7. Condenser pressure, Pc with fouling factor, f at different values of condenser cooling seawater temperature, Tcwi.

0.00013 0.00017 0.00021 0.00025 0.00029 0.00033 0.00037920000

930000

940000

950000

960000

970000

980000

990000

1000000

1.010 x106

Wne

t(kW

)

Tcwi = 15 [oC]

Tcwi = 18 [oC]

Tcwi = 21 [oC]

Tcwi = 24 [oC]

Tcwi = 27 [oC]

Tcwi = 30 [oC]

f (m2 K/W)

Fig. 8. Output power Wnet with fouling factor f at different values of condenser cooling seawater temperature Tcwi.

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

0.00013 0.00017 0.00021 0.00025 0.00029 0.00033 0.0003734

34.5

35

35.5

36

36.5

37

f (m2 K/W)

η th

( %)

Tcwi = 15 [oC]

Tcwi = 18 [oC]

Tcwi = 21 [oC]

Tcwi = 24 [oC]

Tcwi = 27 [oC]

Tcwi = 30 [oC]

Fig. 9. Overall thermal efficiency, gth with fouling factor, f at different values of condenser cooling seawater temperature, Tcwi.

∆f= 0.0002 (m2 K/W)

∆f= 0.00001 (m2 K/W)

∆f= 0.00003 (m2 K/W)

∆f= 0.00002 (m2 K/W)

∆f= 0.00004 (m2 K/W)

∆f= 0.00005 (m2 K/W)

∆f= 0.0001 (m2 K/W)

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

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

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

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

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

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

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

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= 3 (oC) & ∆f= 0.00003 (m2 K/W)

∆T= 2 (oC) & ∆f= 0.00002 (m2 K/W)

∆T= 4 (oC) & ∆f= 0.00004 (m2 K/W)

∆T= 5 (oC) & ∆f= 0.00005 (m2 K/W)

∆T= 10 (oC) & ∆f= 0.0001 (m2 K/W)

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

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

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

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

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

∆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 (%)

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

S.M.A. Ibrahim, S.I. Attia / Annals of Nuclear Energy 76 (2015) 421–430 429

The increase in fouling of condenser cooling water causes anincrease in the thermal resistance of the condenser and this in turnreduces the overall heat transfer coefficients, Ui,f and Uo,f. Thedecrease in the overall heat transfer coefficients will lead to anincrease in the turbine exhaust steam temperature and hence thecorresponding exhaust steam pressure. The increase in exhauststeam pressure, which is a power loss leads to the observed reduc-tion in the output power and the thermal efficiency of the studiednuclear power plant.

Fig. 10 summarizes the effect of cooling seawater fouling, f onthe thermal efficiency and output power of the nuclear powerplant. 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 efficiencyand output power of the nuclear power plant. The combined effectof increases in Tcwi and f can result in high decreases in both outputpower and thermal efficiency of the plant.

4. Conclusions

Fouling of condenser tubes is one of the most important factorsaffecting their thermal performance, which reduces effectivenessand heat transfer capability. The present model predicts thedecrease in heat transfer rate with the growth of fouling.

It is concluded that the thermal efficiency of the nuclear powerplant is reduced by up to 0.448% for an increase in the fouling fac-tor of the condenser cooling seawater in the range 0.00015–0.00035 m2 K/W. The power loss for the same range of the foulingfactor is founded to be 13319.93 kW. These are quite significantreductions in the thermal efficiency and power output of the plantin view of the extensive efforts and money spent to increase thethermal efficiency by even 1%. Therefore, the paper offers an addi-tional design factor to be considered in the design of new powerstations.

Therefore, condenser cooling seawater fouling attack must beprevented either completely or partially in order to mitigate the

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

undesired drawbacks on the output power and thermal efficiencyof the nuclear power plant. Fouling may be avoided by chemicalmethods or otherwise.

Production capacity reduction due to an increase in foulingwould represent a drop of power production that might need tobe replaced somewhere. The effect of climatic changes shows tobe important in the design of more effective cooling techniquesand to device methods to compensate for the loss in plant outputand system capacity.

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