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Progress in Nuclear Energy journal homepage: www.elsevier.com/locate/pnucene

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

Dept. of Mech. Power Engineering, AL-Azhar University, 11371, Nasr City, Cairo, Egypt Nuclear Power Plants Authority, 4 El-Nasr Avenue, 11371, Nasr City, Cairo, 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 2014 Received in revised form 10 September 2014 Accepted 9 November 2014 Available online 5 December 2014

This paper studies the impact of the salinity and temperature on the thermal performance of a proposed pressurized water reactor nuclear power plant. Applying the thermodynamic and heat transfer analyses based on the thermodynamic and heat transfer laws to gain some new aspects into the plant performance. The main results of this study are that many thermo-physical properties of seawater are affected by changes in salinity of the coolant extracted from environment. Also, the impact of increase in salinity leads to a decrease in the power output and the thermal efﬁciency of the nuclear power plant. 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. So, the paper offers an additional design dimension to be considered when designing new power stations. © 2014 Elsevier Ltd. All rights reserved.

Keywords: PWR secondary cycle Condenser Seawater Thermophysical properties Thermodynamic Heat transfer

1. Introduction Thermal power plants are built for prescribed speciﬁc design conditions based on the targeted power demand, metallurgical limits of structural elements, statistical values of environmental conditions, etc. At design stage, a cooling medium salinity and temperature is chosen for each site considering long term average climate conditions. However, the working conditions deviate from the nominal operating conditions in practice. For this reason, the efﬁciency of electricity production is affected by the deviation of the instantaneous operating salinity and temperature of seawater cooling water of a nuclear power plant from the design values of the cooling medium extracted from environment which transfers waste heat to the atmosphere via the condenser. The cooling process in nuclear power plants requires large quantities of cooling water. The huge amounts of water withdrawal and consumption mean that the electricity has to face the impacts of climate change, i.e. in the form of increasing sea salinity, temperatures or water scarcity. For instance, if seas exhibit too high

* Corresponding author. E-mail address: [email protected] (S.I. Attia). http://dx.doi.org/10.1016/j.pnucene.2014.11.004 0149-1970/© 2014 Elsevier Ltd. All rights reserved.

water salinity and temperatures the continued use of water for cooling purposes may be at risk because the cooling effect decreases and also water quality regulations could be violated. In this context, it is to distinguish between water withdrawal and water consumption. Water withdrawal represents the amount of water taken from a source, i.e. a lake or a river, and discharged back to the water body after use, while water consumption represents the amount of water withdrawal that is not returned to the source. Basically, there are two types of cooling water system designs: once-through (open loop) and recirculation (closed loop) water systems. In the former one, water is withdrawn from a local body of water, pumped through a heat exchanger to cool down and condense the steam inside the power plant. Thereby the water and the steam ﬂow in two separated water circuit. After cooling the steam, the cooling water temperature increased and back to its source. The high amounts of water withdrawal and consumption causes to that the electricity has to face the impacts of climate change. The main use of water in a thermoelectric power plant is for the cooling system that condenses steam and carries away the waste heat as part of a Rankine steam cycle. The total water requirements of such a plant depend on a number of factors, including the generation technology, generating capacity, the surrounding environmental and climatic conditions, and the plant's cooling system, which is

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the most important factor governing efﬁcient water. The function of cooling circulating systems is to condense the steam exhaust from thermal power plants steam. The majority of water on earth is seawater. Seawater is a solution of salts of nearly constant composition, dissolved in variable amounts of water. For scientiﬁc investigations and process design of many natural and technical processes, which have to do with seawater, it is of great importance to have a good base of thermodynamic data. Salinity is an important factor that affected on the plant performance; it is deﬁned as the total amount of dissolved material in grams in one kilogram of seawater. Salinity is usually expressed by symbol S. Thus, salinity is a dimensionless quantity, the average salinity of seawater is S ¼ 35 g/kg, which means that seawater is 3.5% salt and 96.5% H2O by weight. An increase in salinity and temperature of cooling water may have impact on the capacity utilization of thermal power plants in two concerns: (1) reduced efﬁciency: increased environmental salinity and temperature reduces thermal efﬁciency of a thermal power plant, (2) reduced load: for high environmental salinity and temperatures of thermal power plant's operation will be limited by a maximum possible condenser pressure. The operation of plants with river or sea cooling will in addition be limited by a regulated maximum allowable temperature for the return water or by reduced access to water. Heat losses from the thermal power plant cycle are due mainly to heat rejection through the condenser. Operating the condenser at optimum circulation water ﬂow rate is essentially important to ensure maximum efﬁciency and minimum operating cost of the plant. Anozie and Odejobi (2011) study the optimum condenser cooling water ﬂow rate in a thermal power plant. In this study, computer program codes were developed in Microsoft Excel macros for simulation of a thermal plant at various circulation water ﬂow rate, to determine the optimum condenser cooling water ﬂow rate for the process. The study revealed that operating the condenser at reduced cooling water ﬂow rate of 32,000 m3/h instead of the base case scenario of 32,660 m3/h, reduced the total heat transfer area requirement from 13,256 m2 to 8113 m2, with the condenser making the highest contribution to heat transfer area reduction. ndez Torres and Ruiz Bevia (2012) reported conventional Ferna seaside nuclear or coal-ﬁred power stations draw water directly from the sea, chlorinate it and send it into a “once-through” cooling circuit that discharges it directly back into the sea. This practice leads to a constant input of thermal and chemical pollution (residual chlorine and chlorination by-products) into ecosystems in the immediate vicinity of the power plant. To reduce chlorine usage and achieve a cleaner process, a new design for the cooling system of power plants is proposed. This can be accomplished by means of a cooling-stripping tower that operates in a closed circuit. With that purpose in mind, the design of such a cooling system conﬁguration was undertaken. Results show that the warm stream leaving the condensers at 38 C cools down to 27.1 C after exiting the coolingstripping tower. This decrease in the seawater coolant temperature before it is rejected to the sea therefore prevents thermal pollution. Furthermore, the small amount of seawater returned to the sea at 27.1 C contains no chlorination by-products. In addition, a dramatic reduction in the seawater intake by the cooling system is obtained, and represents only 5.2% of that needed by conventional systems. This, in turn, implies a reduction in the chlorine dosage and the ﬁlter sizes required for the seawater input stream. It is recommended that all power plants consider implementing the proposed design in order to prevent seawater pollution and damage to coastal ecosystems.

In literature, there are few works published to identify these climate and environmental change impacts, few have tried to quantify them. Sharqawy et al. (2010) reviewed and examined correlations and data for the thermo-physical properties of seawater including density, speciﬁc heat capacity, thermal conductivity, dynamic viscosity, vapor pressure, boiling point elevation, latent heat of vaporization, speciﬁc enthalpy, and entropy. Wiesenburg and Little (1989) studied the effect of changing the salt content on many properties of seawater, such as density, thermal expansion, temperature of maximum density, viscosity, speed of sound, vapor pressure, etc. Knowledge of the way these parameters change, as well as processes that cause the changes, is essential to the design of systems that will effectively operate in the ocean. Feistel (2008) determined the speciﬁc Gibbs energy of seawater from experimental data of heat capacities, freezing points, vapor pressures, and mixing heats at atmospheric pressure in the temperature range of 6 to 80 C and 0e120 g/kg in absolute ndez Torres and Ruiz Bevia (2012) studied the Chlosalinity. Ferna rine use reduction in nuclear or conventional power plants: a combined cooling-and-stripping tower for coastal power plants. Safarov et al. (2009) measured a (p, r, T) data of seawater are measured and a new equation of state will be developed. A new installation using the well known vibration-tube densimeter method was constructed. Calibration procedures were carried out using double-distilled water and well deﬁned aqueous NaCl solutions. Millero et al. (2008) determined a Reference Composition consisting of the major components of Atlantic surface seawater using these earlier analytical measurements. Komiya et al. (2008) carried out in-situ analyses of major, trace, and rare-earth elements of carbonate minerals in rocks with primary sedimentary structures in shallow and deep sea-deposits, in order to eliminate secondary carbonate and contamination of detrital materials, and to estimate the redox condition of seawater through time. Millero (2000) calculated the density based on the salinity determined from conductivity need to be adjusted for the offsets due to changes in the composition of seawater. And describes how this correction should be made using existing information. Anozie and Odejobi (2011) study the optimum condenser cooling water ﬂow rate in a thermal power plant. In this study, computer program codes were developed in Microsoft Excel macros for simulation of a thermal plant at various circulation water ﬂow rate, to determine the optimum condenser cooling water ﬂow rate for the process. Barigozzi et al. (2011) study how the performance of the waste-to-energy cogeneration plant can be improved by optimizing the condensation system, with particular focus on the combination of wet and dry cooling systems. Poornima et al. (2006) show Impact on phytoplankton and primary productivity: Use of coastal waters as condenser coolant in electric power plants. Conradie et al. (1998) analyse the Performance optimization of drycooling systems for power plants through SQP methods. In this study the application of modern optimization techniques to obtain cost optimal design and performance of dry-cooling systems for power plant applications. Hajmohammadi et al. (2013) examine New Methods to Cope with Temperature Elevations in Heated Segments of Flat Plates Cooled by Boundary Layer Flow. Ganan et al. (2005) studied the performance of the pressurized water reactor (PWR)-type Almaraz nuclear-power plant and showed that it 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) presented a parametric analysis of surface condenser for 120 MW thermal power plant, to focus on the inﬂuence of the cooling water temperature and ﬂow

S.M.A. Ibrahim, S.I. Attia / Progress in Nuclear Energy 79 (2015) 115e126

rate on the condenser performance, and thus on the speciﬁc heat rate of the plant and its thermal efﬁciency. This 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 performance analysis of the condenser through heat transfer analysis taking into account the key parameters such as the cooling seawater salinity and temperature that affect the condenser performance, overall heat transfer coefﬁcient and thermal performance of the plant. This parametric study shows the impact of salinity within a range of 0e100 g/kg, and the temperature within a range of 15e30 C, on the seawater thermo-physical properties such as density, speciﬁc heat, viscosity and thermal conductivity that reﬂect effect in the condenser and plant performance. The analysis shows the signiﬁcant impact on the condenser performance and the condenser overall heat transfer coefﬁcient. An increase of seawater salinity leads to a reduction in the condenser performance and this reduction increases temperature and pressure of the steam exhausted from the turbine and hence a slightly reduction in the nuclear power plant output power and its thermal efﬁciency. Pressurized water reactors are the mostly used in the nuclear power plants worldwide (62% according to number and 68% according to output power). There are 273 PWRs operating around the world out of a total of 437 reactors, with a total net installed capacity of more than 251,400 MW. 2. Methodology The present research develops a mathematical model which involves studying, analyzing, and evaluation of the thermal performance and thermodynamic of the secondary cycle of nuclear power plant. The objective is to establish a theoretical methodology to evaluate the impact of thermo-physical properties of seawater on the overall heat transfer coefﬁcient, of the steam surface condenser of a PWR NPP, within speciﬁc designed range of seawater salinity and temperature. A model of condenser heat balance is developed to determine the functional relationship between the seawater cooling water salinity and temperature and the condenser pressure. Employing this condenser heat balance, a cycle analysis is carried out to determine the design heat balance conditions and thermal efﬁciency for prescribed range of cooling water salinity and temperatures.

117

Fig. 1 illustrates a diagram of a proposed PWR nuclear power plant, to address its thermodynamic and heat balance analysis of a PWR NPP. 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 high pressure feed water heaters (HPFWH), and three low-pressure feed water heaters (LPFWH), condenser, and necessary pumps (feed water pump and condensate pump). A computer program was developed based on the mathematical model representing the secondary circuit of the plant and its components was performed using the engineering equation solver computer program (EES) (www.fchart.com). Engineering Equation Solver (EES) is a general purpose equation solver, an intelligent computer-aided instruction software package (F-Chart Software), modeling and analysis tool which has started life speciﬁcally for the purpose of engineering education. It is quite capable (it is also used in industry) and is more than adequate for engineering education purposes. It has thermodynamic and heat transfer data base and properties of solid and ﬂuid and also math functions and draw graphs (www.fchart.com). EES automatically identiﬁes and groups equations that must be solved simultaneously. This feature simpliﬁes the process for the user and ensures that the solver will always operate at optimum efﬁciency. Second, EES provides many built-in mathematical and thermophysical property functions useful for engineering calculations (www.fchart.com). The development of a mathematical model is depending upon studying, analysis, and evaluation of the thermal performance and thermodynamic of the secondary cycle of nuclear power plant with respect to how the impacts, climatic conditions of environment affect the marginal of condenser cooling water and the extent of its impacts on the efﬁciency and performance of the nuclear plant, so the thermal and thermodynamics properties, parameters, variables as well as mathematical relationships will be formulated to determine the thermal efﬁciency through the application of the energy and mass conservation laws that governing the mass and heat balance. The mathematical model calculate the actual work done of turbines, pumps, and the amount of heat added required to generate steam and the amount of heat rejected from the condenser, and consequently the plant efﬁciency via selecting the temperature of cooling water inlet and outlet of the condenser and

Fig. 1. Diagram of PWR nuclear power plant.

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the temperature difference. The tables and ﬁgures hereafter are reﬂected the obtained results that included the parameters and variables such as (efﬁciency e temperatures e the availability e ﬂow rates of cooling water e etc.), in addition to conducting parametric study of the main factors that affect the thermal performance of the plant. The algorithm procedures are performed as follows: ▪ Calculate 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. ▪ Perform heat balance for each feed water heater and the steam generator. ▪ Compute the output useful work of the turbines and pumps. ▪ Calculation of the amount of heat added to generate steam, as well as the amount of heat rejected from condenser and hence calculate the efﬁciency of the station. ▪ Draw Tes diagram of the plant and its components, as well as numerical tabulation of results. ▪ Determination of the cooling seawater inlet temperature, Tin and exit temperature, Tout and the temperature difference. ▪ Assign the range of change of cooling seawater salinity Sp as 0e100 g/kg, and temperature Tcwi, as 15e30 C. ▪ Compute impact of the changes of cooling water temperature, Tcwi, and salinity, Sp, on the thermo-physical properties of the seawater, the thermal efﬁciency hth and output work Wnet of the plant. ▪ Draw the relation of Tcwi and S with the thermo-physical properties of the Seawater, overall heat transfer coefﬁcient, the hth and Wnet of the plant. ▪ Conclude the main results of the effect of increase of cooling seawater salinity Sp, and temperature Tcwi from graphs. Modeling assumptions for the secondary cycle are: ▪ The thermodynamic conditions of steam at exit of the steam generator are ﬁxed. ▪ 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. ▪ The condenser vacuum varies with the temperature of cooling water extracted from environment at ﬁxed mass ﬂow rate into the condenser. ▪ Constant condenser cooling water temperature difference. ▪ Constant mass ﬂow rates of condensate and cooling water. ▪ There is no pressure drop across the plant. ▪ Constant condenser heat transfer area and heat load. ▪ The potential and kinetic energies of the ﬂow and heat losses from all of these equipment and pipes are negligible.

WLPT ¼ m_ st ð hin hout Þ

(3)

Where m_ st ¼ steam mass ﬂow rate inlet to each turbine, kg/s, hin ¼ enthalpy of steam inlet to each turbine, kJ/kg, hout ¼ enthalpy of steam outlet from each turbine, kJ/kg, WHPT ¼ high pressure turbine work, kJ/kg, and WLPT ¼ low pressure turbine work, kJ/kg. ▪ The pumping work, WP, kJ/kg is:

Wp ¼ Wcp þ Wfwp Wfwp ¼ m_ fw Wcp ¼ m_ fw

hin hout hin hout

(4)

hin ¼ enthalpy of steam inlet to each pump, kJ/kg, hout ¼ enthalpy of steam outlet from each pump, kJ/kg, Wfwp ¼ feed water pump work, kJ/kg, and Wcp ¼ condensate pump work, kJ/kg. ▪ Heat added to steam generator, Qadd, kJ/kg is:

Qadd ¼ m_ st ðhout hin Þ

hin ¼ enthalpy of feed water inlet to steam generator, kJ/kg, and hout ¼ enthalpy of steam outlet from steam generator, kJ/kg. ▪ Heat rejected from condenser, QRej, kJ/kg is:

QRej ¼ ðm_ mix *hin m_ mix *hout Þ

hin ¼ enthalpy of mixture inlet to condenser, kJ/kg, and hout ¼ enthalpy of feed water outlet from condenser, kJ/kg. ▪ Net work done, Wnet, kJ/kg is:

Wnet ¼ WT Wp

(2)

(9)

▪ The cycle efﬁciency, hth, % is:

2.2. Heat balance of cooling water system (condenser)

WHPT ¼ m_ st ð hin hout Þ

(8)

Where m_ mix ¼ mixture mass ﬂow rate through condenser, kg/s,

2.1. Thermodynamic equations

(1)

(7)

Where m_ st ¼ steam mass ﬂow rate exit from steam generator, kg/s,

hth ¼

WT ¼ WHPT þ WLPT

(6)

Where m_ fwh ¼ steam mass ﬂow rate inlet to each pump, kg/s,

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:

▪ The total turbine work, WT, kJ/kg is:

(5)

Wnet Qadd

(10)

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

S.M.A. Ibrahim, S.I. Attia / Progress in Nuclear Energy 79 (2015) 115e126

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 rise in cooling water temperature and mass ﬂow rate is related to the rejected heat as:

QRej ¼ ðm_ mix *hin Þ

m_ fw *hout

(11)

QRej ¼ m_ CW *C*DT

(12)

DTcw ¼ ðTcwo eTcwi Þ

(13)

QRej ¼ U*A*DTlm

(14)

ðTcwe Tcwi Þ Þ DTlm ¼ ð ðT Tcwi Þ lnððTccTcwe ÞÞ

(15)

Where m_ CW ¼ cooling water mass ﬂow rate of condenser, kg/s, m_ fw ¼ feed water mass ﬂow rate of outlet from condenser, kg/s, m_ mix ¼ mixture mass ﬂow rate of inlet to condenser, kg/s, hi ¼ enthalpy of mixture inlet to condenser, kJ/kg, hout ¼ enthalpy of feed water outlet from condenser, kJ/kg, Tc ¼ condenser saturation temperature, C, Tcwo ¼ temperature of cooling water outlet from condenser, C, Tcwi ¼ temperature of cooling water inlet to condenser, C, DTcw ¼ temperature difference between the cooling water exit and inlet temperature, C, U ¼ overall heat transfer coefﬁcient, W/m2 K, C ¼ Speciﬁc heat, kJ/kg K, A ¼ heat transfer area, m2, and DTlm ¼ log mean temperature difference, C. Many properties of seawater are affected by changes in salinity. Properties examined include density, speciﬁc heat capacity, thermal conductivity, dynamic viscosity. The results are presented in terms of regression equations as functions of salinity and temperature. The available correlations for each property are summarized with their range of validity and accuracy. Density, rsw , kg/m3 is: The density of seawater,rsw , as a function of temperature, pressure, and salinity is a fundamental oceanographic property. The thermo-physical seawater density correlation property is given as (Sharqawy et al., 2010):

rsw

¼ a1 þ a2 t þ a3 t 2 þ a4 t 3 þ a5 t 4 þ b1 Sp þ b2 S t þ b3 Sp t 2 þ b4 Sp t 3 þ b5 Sp t 4

Cpsw ¼ A þ BT þ CT 2 þ DT 3

Where a1 ¼ 9.999 102, a2 ¼ 2.034 102, a3 ¼ 6.162 103, a4 ¼2.261 105, a5 ¼ 4.657 108, b1 ¼ 8.020 102, b2 ¼ 2.001, b3 ¼1.677 102, b4 ¼ 3.060 105, b5 ¼ 1.613 105, and the validity is: rsw in kg/m3; 10 t 180 C; 0 Sp 0.16 kg/kg. Speciﬁc heat, Cpsw, J/kg K is: The speciﬁc heat of seawater, Cpsw, is the amount of heat required to increase the temperature of one kilogram of seawater one degree Celsius at constant pressure. Speciﬁc heat of seawater changes as a function of both temperature and salinity. The thermophysical seawater speciﬁc heat correlation property is (Sharqawy et al., 2010):

(17)

Where A ¼ 5:328 9:76 102 Sp þ 4:04 104 S2p , B ¼ 6:913 103 þ 7:351 104 Sp 3:15 106 S2p , C ¼ 9:6 106 1:927 106 Sp þ 8:23 109 S2p , D ¼ 2:5 109 þ 1:666 109 Sp 7:125 1012 S2p , and the validity is: Cpsw in (J/kg K); 0 < T < 180 C; 0 < Sp < 160 g/kg Thermal conductivity, ksw, W/m K is: The thermal conductivity, ksw, is an important property of seawater and one of the most difﬁcult liquid properties to measure. Consequently data on seawater thermal conductivity is very limited. For aqueous solutions containing an electrolyte, such as seawater, the thermal conductivity usually decreases with an increase in the concentration of the dissolved salts. The thermophysical seawater thermal conductivity correlation property is (Sharqawy et al., 2010):

log10 ðksw Þ ¼ log10 ð240þ0:0002 SP Þþ0:434 2:3 343:5 þ 0:037Sp t þ 273:15 0:333 1 647þ0:03 Sp t þ 273:15

(18)

Where the validity is: ksw in W/m K; 20 < t < 180 C; 10 < Sp < 160 g/kg Dynamic Viscosity, msw, kg/m s is: Dynamic viscosity of seawater, msw, is deﬁned as the internal ﬂuid friction or the forces of drag which its molecular and ionic constituents exert on one another. It changes as a function of both temperature and salinity. The thermo-physical seawater dynamic viscosity correlation property is (Sharqawy et al., 2010):

msw ¼ mw 1 þ AS þ BS2

(19)

Where A ¼ 1.541 þ 1.998 102 t 9.52 105 t2, B ¼ 7.974e7.561 102 t þ 4.724 104 t2, mw ¼ 4.2844 105 þ (0.157 (t þ 64.993)2 91.296)1, and the validity is: msw and mw in kg/m s; 0 < t < 180 C; 0 < S < 150 g/kg 2.3. Salinity effects on the thermal performance of the proposed nuclear power plant - Heat Transfer Coefﬁcient for Flow Inside Circular Tubes, hi, W/ m2 K is (Holman, 2010):

hi ¼ (16)

119

Nu *ksw d

Where

(20)

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

Re The Reynolds number ¼

Pr Prandtl Number ¼

rsw V d ; msw

msw Cpsw ; ksw

rsw ¼ seawater density, kg/m3, v ¼ ﬂow velocity, m/s, d ¼ tube diameter, m, msw ¼ seawater dynamic viscosity, N/m2 s,

(21) (22)

(23)

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ksw ¼ seawater thermal conductivity, W/m K, and Cpsw ¼ seawater speciﬁc heat capacity, J/kg K. - Film Condensation Heat Transfer Coefﬁcient in Bundles of Horizontal Tubes, ho, W/m2 K is (Holman, 2010):

ho ¼ 0:725

g* r * ðr r Þ* h * k3 0:25 v l l fg ml * ðTst Tw Þ* Nh * do

(24)

rV ¼ steam or vapor density, kg/m3, mL ¼ liquid dynamic viscosity, N/m2 s,

Tst ¼ steam or vapor saturation temperature, C. Nh ¼ number of horizontal tubes, hfg ¼ latent heat for condensation, kJ/kg, k ¼ thermal conductivity, kW/m K, g ¼ acceleration of gravity, m/s2, and Tw ¼ condenser tube surface wall temperature, C is given by Holland et al. (1970).

Tw ¼

1þ

di Þ* Ti o do hi di ðh d Þ o o

(25)

- Inside Overall Heat Transfer Coefﬁcient, Ui, W/m2 K is (Holman, 2010):

Ui ¼

1 ðAi * ðRi þ Rw þ Ro ÞÞ

(26)

Where Ao ¼ outside tube area, m2, Ri ¼ thermal resistance of inner seawater, m2 K/W, Ro ¼ thermal resistance of outer condensation ﬁlm, m2 K/W, and Rw ¼ thermal resistance of tube wall, m2 K/W. - Outside Overall Heat Transfer Coefﬁcient, Uo, W/m2 K is (Holman, 2010):

Uo ¼

1 ðAo * ðRi þ Rw þ Ro ÞÞ

(27)

Where Ao ¼ outside tube area, m2, Ri ¼ thermal resistance of inner seawater, m2 K/W, Ro ¼ thermal resistance of outer condensation ﬁlm, m2 K/W, Rw ¼ thermal resistance of tube wall, m2 K/W, and - Thermal Resistance of Inner Tubes Seawater, Ri, m2 K/W is (Holman, 2010):

Ri ¼

1 hi Ai

(28)

hi ¼ Heat transfer coefﬁcient for ﬂow inside circular tubes, W/ m2 K. - Thermal Resistance of Outer Condensate Steam, Ro, m2 K/W is (Holman, 2010):

1 ho Ao

Rw ¼

ro ri

2pk

(30)

Where k ¼ thermal conductivity of tube, W/m K,

2.4. The relations between the output power, thermal efﬁciency and seawater salinity The relations between the output power and thermal efﬁciency and the condenser cooling seawater salinity are deduced through a sequence of substitutions in equations (1)e(30), as follows: - The relations between condenser cooling seawater salinity and heat transfer coefﬁcient ﬂow inside tubes hi are given by equations (20)e(23). - The relations between heat transfer coefﬁcient ﬂow inside tubes, hi and thermal resistance of the condenser is represented by equations (28)e(30). - Equations 26 and 27 relate the thermal resistance and the inside and outside overall heat transfer coefﬁcients, Ui and Uo. It is clear that an increase in the thermal resistance will reduce the values of the inside and outside overall heat transfer coefﬁcients of the condenser. - The effect on the heat rejection from the exhaust steam to the condenser cooling seawater is given by equations (11)e(15), which show the relations between 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 also the exhaust pressure. The turbine output depends on the exit steam temperature and pressure. These effects are given by equations (1)e(10), which depict that increasing exhaust steam temperature and pressure will result in decreasing the output power and accordingly the thermal efﬁciency of the plant. So there is no direct mathematical relation between output power and thermal efﬁciency and condenser cooling seawater salinity. 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 salinity on the power output and thermal efﬁciency of the PWR NPP. 3. Results and discussions

Where Ai ¼ inside tube surface area, m2, and

Ro ¼

ln

ro ¼ outer radius of condenser tubes, m, and ri ¼ inner radius of condenser tubes, m.

Where rL ¼ liquid density, kg/m3,

Tc þ ðhhi

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

(29)

Where Ao ¼ outside tube surface area, m2, and ho ¼ ﬁlm condensation heat transfer coefﬁcient in bundles of horizontal tubes, W/m2 K.

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 thermal efﬁciency. Fig. 2 represents the calculated thermodynamic and heat balance analysis of the proposed PWR NPP by using EES software program. Fig. 3 shows the thermodynamic and heat balance analysis of the proposed PWR NPP; on the temperature entropy (Tes) diagram of steam Rankine cycle as obtained from the heat balance of the plant on EES software program. Table 1 summarizes the calculations of the thermodynamic properties at design conditions satisfying the heat balance for the

S.M.A. Ibrahim, S.I. Attia / Progress in Nuclear Energy 79 (2015) 115e126

121

Fig. 2. Illustration of the EES model equivalent to the proposed PWR NPP thermodynamic and heat balance analysis.

proposed PWR NPP. Fig. 2 and Table 1 are the basis of the parametric study and analysis of the present work. The following ﬁgures show the effect of the condenser cooling seawater salinity on some thermo-physical properties and important factors that affect the thermal performance of the studied nuclear power plant: Fig. 4 represents the variation of the density of seawater,rsw , with condenser cooling seawater salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi. The density of seawater changes with both salinity and temperature, where rsw ; increases with increasing Sp and decreases with increasing Tcwi. For an increase in, Sp of 10 g/kg, and (0e100) g/kg, respectively, increase rsw approximately by 7.8 and 77.6 kg/m3, respectively at ﬁxed values of Tcwi. Fig. 5 illustrates the variation of speciﬁc heat of seawater, Cpsw, with condenser cooling seawater salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi. Cpsw decreases with increasing Sp and Tcwi. The addition of sea salt dampened this decrease, and for a salinity of 20% the effect of temperature was reversed and the heat capacity increased with temperature

increase. The results indicate that when, Sp increases to 10 g/kg, Cpsw decreases approximately by 58 J/kg K, until a value of S of 20 g/ kg, then Cpsw increases at constant values of Tcwi. Fig. 6 gives the variation of the thermal conductivity of condenser cooling seawater, ksw, with salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi. ksw decreases with an increase in Sp and increases almost linearly with increasing Tcwi. An increase in Sp of 10 g/kg, and (0e100) g/kg, respectively, decreases ksw by approximately 0.5 103 and 5.5 103 W/m K, respectively at constant values of Tcwi. Fig. 7 illustrates the variation of viscosity of seawater, msw with condenser cooling seawater salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi. msw increases with increasing Sp and with decreasing Tcwi. The viscosity of seawater is greater than the viscosity of pure water at all temperatures. For an increase in Sp by 10 g/kg, and (0e100) g/kg, respectively, msw increases by about 0.22 104 and 0.286 103 kg/m s, respectively, at any ﬁxed Tcwi. Fig. 8 indicates the variation of inside condenser tube heat transfer coefﬁcient, hi with condenser cooling seawater salinity, Sp,

Fig. 3. Tes diagram of proposed PWR nuclear power plant thermodynamic and heat balance analysis.

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Table 1 Thermodynamic data for the proposed PWR NPP. Station no.

Temperature T [ C]

Pressure p [bar]

Enthalpy h [kg/kJ]

Entropy s [kJ/kg K]

Quality X

Mass ﬂow rate m_ [kg/s]

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 41197 41197

at different values of condenser cooling seawater temperature, Tcwi. It is shown that hi decreases with increasing Sp and increases with increasing Tcwi. When Sp increases by 10 g/kg, and (0e100) g/kg, hi decreases approximately by 56 and 622 W/m2 K, respectively at ﬁxed Tcwi. Fig. 9 shows the relation between the inside overall heat transfer coefﬁcient, Ui and condenser cooling seawater salinity, Sp, at different values condenser cooling seawater temperature, Tcwi. It seen that Ui decreases with increasing Sp and increases with increasing Tcwi. The results indicate that for seawater salinity, Sp, increase of 10 g/kg, and (0e100) g/kg, Ui decreases by about 2 and 18 W/m2 K, respectively, at constant Tcwi.

Fig. 10 depicts the variation of the outside overall heat transfer coefﬁcient, Uo with condenser cooling seawater salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi. Uo decreases with increasing Sp and increases with increasing Tcwi. An increase in Sp of 10 g/kg, and (0e100) g/kg, respectively, decrease Uo by about 2 and 18 W/m2 K, respectively, for unchanged Tcwi. Fig. 11 gives the effect of condenser cooling seawater salinity, Sp _ net of the plant. It and temperature, Tcwi on the output power W _ net decreases slightly with increasing S and Tcwi. The shows that W results depict that when Sp increases by 10 g/kg, and (0e100) g/kg, _ net decreases approximately by 336 and respectively, W 460.665 kW, respectively at constant values of Tcwi.

Fig. 4. Seawater density variations, rsw , with condenser cooling seawater salinity, Sp and temperature, Tcwi.

Fig. 5. Seawater speciﬁc heat, cpsw, variations with condenser cooling seawater salinity, Sp and temperature, Tcwi.

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Fig. 6. Seawater thermal conductivity variations, Ksw with condenser cooling seawater salinity, Sp and temperature, Tcwi. Fig. 9. Variations of inside overall heat transfer coefﬁcient, Ui with condenser cooling seawater salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi.

Fig. 7. Seawater viscosity variations, msw, with condenser cooling seawater salinity, Sp and temperature, Tcwi.

The overall thermal efﬁciency of the plant, hth, decreases slightly with increasing condenser cooling seawater salinity, Sp, and with increasing condenser cooling seawater temperature, Tcwi, as given in Fig. 12, which presents the variation of hth, with, Sp at different values of Tcwi. For an increase in, Sp of 10 g/kg, and (0e100) g/kg, respectively, hth decreases by about 0.01 and 0.14%, respectively for constant Tcwi. The increase in salinity affects the thermo-physical properties of condenser cooling seawater which in turn affects the heat transfer coefﬁcient for ﬂow inside tubes of the condenser, hi and this gives the observed effects on the thermal resistance and in turn on the overall heat transfer coefﬁcients, Ui and Uo. The reduction in the condenser overall heat transfer coefﬁcient as the salinity increases,

Fig. 8. Variations of inside condenser tube heat transfer coefﬁcient, hi with condenser cooling seawater salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi.

Fig. 10. Variations of outside overall heat transfer coefﬁcient, Uo with condenser cooling seawater salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi.

will lower the output power and hence the overall thermal efﬁciency of the plant. The following results indicate the properties of seawater which _ net and thermal efﬁciency, have direct effect on the output power, W hth, of the PWR NPP. Figs. 13e16 depict the effect of density, rsw, thermal conductivity, ksw, viscosity, msw, and speciﬁc heat, Cpsw, of the condenser cooling seawater on the output power and thermal

Fig. 11. Variations of output power,W_ ne with condenser cooling seawater salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi.

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Fig. 12. Variations of overall thermal efﬁciency, hth with condenser cooling seawater salinity, Sp, at different values of condenser cooling seawater temperature, Tcwi.

Fig. 15. Variations of output power, W_ net and thermal efﬁciency, hth with thermo physical property, msw at different values of salinity, Sp.

Fig. 13. Variations of output power, W_ net and thermal efﬁciency, hth with thermo physical property, seawater density, rsw at different values of salinity, Sp.

efﬁciency of the PWR NPP. The results indicate that cooling water _ net , while r has the viscosity, msw has the most adverse effect on W sw least effect with increasing Sp. Thus an increase in msw by _ net by about 1551.67 kW, 0.001002e0.001259 kg/m s, decreases W _ net by about and increase in rsw by 998e1075 kg/m3, decreases W 209.61 kW. Also the viscosity of seawater, msw , has the largest effect on, hth while the density, rsw has the lowest effect with increasing Sp. Thus an increases in, msw by 0.001002e0.001259 kg/m s, decreases, hth by about 0.0519%, and an increase in, rsw 998e1075 kg/ m3, decreases, hth by approximately 0.007%, as S increases. Fig. 17 summarizes the effect of condenser cooling seawater _ net of salinity, Sp on the thermal efﬁciency, hth and output power, W the nuclear power plant.

Fig. 14. Variations of output power, W_ net and thermal efﬁciency, hth with thermo physical property, ksw at different values of salinity, Sp.

Fig. 16. Variations of output power, W_ net and thermal efﬁciency, hth with thermo physical property, Cpsw at different values of salinity, Sp.

4. Conclusions A condenser heat balance model is developed to determine the effect of cooling water salinity and temperature on the thermal performance of PWR NPP. Thus, a cycle analysis for the proposed PWR NPP is carried out to determine the heat balance conditions originating from salinity and temperature changes of the cooling medium. It can be concluded that many thermo-physical properties of seawater are affected by changes in salinity and temperature of the coolant extracted from environment, including the condenser overall heat transfer coefﬁcient, where the increase of salinity leads to a reduction in the condenser overall heat transfer coefﬁcient and this results in an increase in the pressure and temperature of the exhaust steam of the turbine and this decreases the power output and the thermal efﬁciency of the nuclear power plant. Thus the output power and the thermal efﬁciency of the plant decrease with increasing cooling water salinity and temperature. Technological measures, whether chemical or otherwise should be devised to keep the salinity of the condenser cooling seawater within the limits that do not cause appreciable reduction in the output power and thermal efﬁciency of the nuclear power plant, or even to eliminate such effect completely if at all possible. This is important in the light of efforts and money spent to improve the thermal efﬁciency of new generations of the power plants. There is no doubt that the impact of environmental and climate changes on the characteristics of the condenser cooling seawater are an important design consideration when constructing nuclear power plants. Increasing cooling water salinity and temperatures decrease the power output, which means that the reduction must be compensated for in order to meet this reduction in output in

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Fig. 17. The effect of condenser cooling seawater salinity, Sp on the thermal efﬁciency, hth and output power, W_ net of the nuclear power plant.

next years. Environmental considerations will also become even more important when building new power plants. The present results and conclusions address an important subject related to a factor that reduces the thermal efﬁciency of power plants. It is required to mitigate or prevent of the adverse effects of condensers cooling seawater salinity increase. This study offers an additional design dimension to be considered when designing new power stations. Nomenclature A BPE c d h k m_ P Q_ R T TTD U V w_ Sp w

Tube area [m2] Boiling point elevation [K] Speciﬁc Heat [kJ/kg K] Diameter [m] Enthalpy [kJ/kg] Thermal conductivity [W/m K] Mass ﬂow rate [kg/s] Pressure [bar] Net rate of heat transferred [kW] Thermal resistance [m2 K/W] Temperature [ C] Terminal temperature difference [ C] Overall heat transfer coefﬁcient [W/m2 K] Velocity [m/s] Net rate of work [kW] Salinity [g/kg] Pure water

Greek Symbols Efﬁciency [%] Viscosity [kg/m s] Density [kg/m3]

h m r

Subscripts add Added c Condenser CP Condensate pump cw Cooling water cwi Cooling water inlet CL Cold leg cwo Cooling water outlet fw Feed water FWP Feed water pump HL Hot leg HPT High pressure turbine LPT Low pressure turbine i Inlet in Inlet mix Mixture

o out p RCW Rej T w

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 IAPWS International Association for the Properties of Water and Steam References Anozie, A.N., Odejobi, O.J., 2011. The search for optimum condenser cooling water ﬂow rate in a thermal power plant. Appl. Therm. Eng. 31, 4083e4090. Barigozzi, G., Perdichizzi, A., Ravelli, S., 2011. Wet and dry cooling systems optimization applied to a modern waste-to-energy cogeneration heat and power plant. Appl. Energy 88, 1366e1376. € ger, D.G., 1998. analysis the performance optimization Conradie, A.E., Buys, J.D., Kro of dry-cooling systems for power plants through SQP methods. Appl. Therm. Eng. 18, 25e45. Durmayaz, Ahmet, Sogut, Oguz Salim, 2006. Inﬂuence of cooling water on the efﬁciency of a pressurized water reactor nuclear power plant. Int. J. Energy Res. 30, 799e810. Feistel, Rainer, 2008. A Gibbs Function for Seawater Thermodynamics for- 6 to 80 C and Salinity up to 120 g kg1. ndez Torres, María J., Ruiz Bevi Ferna a, Francisco, 2012. Chlorine use reduction in nuclear or conventional power plants: a combined cooling-and-stripping tower for coastal power plants. J. Clean. Prod. 26, 1e8. Ganan, J., Rahman Al-Kassir, A., Gonzalez, J.F., Macıas, A., Diaz, M.A., 2005. Inﬂuence of the Cooling Circulation Water on the Efﬁciency of a Thermonuclear Plant. Hajmohammadi, Mohammad R., Mohammad, Moulod, Joneydi Shariatzadeh, Omid, Nourazar, Seyed Salman, 2013. New methods to cope with temperature elevations in heated segments of ﬂat plates cooled by boundary layer ﬂow. Therm. Sci. 159. OnLine-First Issue 00. Holland, F.A., Moores, R.M., Watson, F.A., Wilkinson, J.K., 1970. Heat Transfer. Holman, J.P., 2010. Heat Transfer, tenth ed. http://www.fchart.com. Komiya, Tsuyoshi, Hirata, Takafumi, Kitajima, Kouki, Yamamoto, Shinji, Shibuya, Takazo, Sawaki, Yusuke, Ishikawa, Tomoko, Shu, Degan, Li, Yong, Han, Jian, 2008. Evolution of the composition of seawater through geologic time, and its inﬂuence on the evolution of life. Gondwana Res. 14, 159e174. Millero, Frank J., 2000. Effect of changes in the composition of seawater on the density-salinity relationship. Deep-Sea Res. I 47, 1583e1590. Millero, Frank J., Feistel, Rainer, Wright, Daniel G., McDougall, Trevor J., 2008. The composition of standard seawater and the deﬁnition of the referencecomposition salinity scale. Deep-Sea Res. I 55, 50e72.

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Sanathara, Milan V., Oza, Ritesh P., Gupta, Rakesh S., 2013. Parametric analysis of surface condenser for 120 MW thermal power plant. Int. J. Eng. Res. Technol. (IJERT) 2 (3). March e 2013. Sharqawy, Mostafa H., John, H., Lienhard, V., Zubair, Syed M., 2010. Thermophysical Properties of Seawater: a Review of Existing Correlations and Data. Wiesenburg, Denis A., Little, Brenda J., 1989. A Synopsis of the Chemical/physical Properties of Seawater.

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