Optimizations of the waste heat recovery system for a large marine diesel engine based on transcritical Rankine cycle

Energy 113 (2016) 1109e1124

Contents lists available at ScienceDirect

Energy journal homepage: www.elsevier.com/locate/energy

Optimizations of the waste heat recovery system for a large marine diesel engine based on transcritical Rankine cycle Min-Hsiung Yang* Department of Naval Architecture and Ocean Engineering, National Kaohsiung Marine University, Taiwan, ROC

a r t i c l e i n f o

a b s t r a c t

Article history: Received 21 March 2016 Received in revised form 6 July 2016 Accepted 28 July 2016

The aim of this study is to investigate the economic performance of the waste heat recovery (WHR) system for a marine diesel engine. Four waste heat sources, which are exhaust gas, cylinder cooling water, scavenge air cooling water and lubricating oil of a marine diesel engine, are first applied to drive the transcritical Rankine cycle (TRC). R1234yf, R1234ze, R134a, R152a, R236fa and R290 are employed in the system as working fluids. The effects of expander inlet pressure and temperature on net power output, thermal efficiency, total cost, mass flow rate, and available efficiency of the WHR system are analyzed. The levelized energy cost is used to evaluate the economic optimizations and their corresponding optimal parameters in the WHR system. The results show that the optimal levelized energy cost of R236fa is the most excellent and is lower than that of R1234ze, R134a, R152a, R1234yf or R290 by 5.07%, 6.25%, 7.42%, 9.77% or 12.11%, respectively. The payback period, fuel oil saving, and CO2 emission reduction are applied to assess the suitability of these working fluids. Furthermore, the economic optimization correlations in terms of dimensionless optimal pressures and temperature difference ratios are proposed for the system design of the optimal operating conditions. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Diesel engine Waste heat recovery (WHR) Levelized energy cost Transcritical Rankine cycle (TRC) Optimization Economic

1. Introduction To prevent the marine environment polluted by ships from operational or accidental causes, International Convention for the Prevention of Pollution from Ships (MARPOL) developed by the International Maritime Organization (IMO) has been implemented since 1973. The MARPOL Convention addresses the rules about air pollution and emissions from ships with Annex VI [1]. Not only sulphur oxide (SOx) but also nitrogen oxide (NOx) emissions from marine engines have been limited in revised Annex VI. Furthermore, amendments entered into force in 2013 and mandatory measures were set to reduce emissions of greenhouse gases from international shipping. The energy efficiency design index (EEDI), which represents the CO2 emission per transport work for marine transportation, has been made mandatory for new ships. Moreover, the ship energy efficiency management plan (SEEMP), which is the policies concerning the methods of energy saving and CO2 reduction in shipping, has been made a requirement for all ships with a

* Postal address: No.142, Haizhuan Rd., Nanzi Dist., Kaohsiung City 81157, Taiwan, ROC. E-mail address: [email protected]. http://dx.doi.org/10.1016/j.energy.2016.07.152 0360-5442/© 2016 Elsevier Ltd. All rights reserved.

gross tonnage of 400 tons or above [2]. The results of previous investigations [3e10] revealed that the waste heat recovery (WHR) from marine diesel engine is one of the effective methods to raise the energy efficiency and to reduce the CO2 emission for merchant ships. Lower evaporation-temperature working fluids, which are organic fluids, are employed in the power cycle for waste heat recovering, to absorb the waste heat efficiently. The organic Rankine cycle (ORC) system has a great potential in applications of WHR system for the internal combustion engine. Yang and Yeh [3e5] investigated the performance of an ORC system for recovering waste heat from the cooling water and exhaust gas of a large marine engine to enhance the utilization of the waste heat. Employing exhaust gas of an internal combustion engine as the heat sources for an ORC system, the thermal efficiency can be increased and the specific fuel consumption can be reduced significantly [6,7]. Applying the exhaust gas and the cylinder cooling water of a diesel engine, Song et al. [8] and Yu et al. [9] investigated the performance of an ORC in the WHR system. In addition, the performances of an ORC system for recovering waste heat from exhaust gas of a diesel engine were evaluated [10e17]. Soffiato et al. [18] analyzed the effects of ORC and TRC systems

1110

M.-H. Yang / Energy 113 (2016) 1109e1124

which were applied to recover waste heat of cylinder cooling water, lubricating oil and scavenge air cooling water from the engines. Combining two power cycles into the WHR system and utilizing multi-heat sources, many researchers present some other ways to enhance the recovery of waste heat from the internal combustion engine. Choi and Kim [19] investigated thermodynamic performance of the exhaust gas heat from a propulsion engine for the container ship using RC and ORC systems. He et al. [20] proposed a WHR system, which was constituted by an ORC for applying waste heat of lubricant cooling and exhaust gas, and the Kalina cycle for recovering the waste heat of cooling water. Later, another dual-loop ORC was proposed by Shu et al. [21] to recover the waste heat of the exhaust gas and the cylinder cooling water of a four stroke engine using R124, R134a, R245fa, R600, R600a and R1234yf as the working fluids. To reduce the fuel consumption of a light-duty diesel engine, the dual-loop ORC also was employed to recover waste heat from the exhaust heat with a high temperature loop, and from the waste heat of the intake air and the cylinder cooling water with a low temperature loop [22e25]. In addition, a cascade ORC system was analyzed to recover waste heat sources from a diesel engine [26e28]. A review of the literature shows that most studies are mainly focused on the performance evaluation of ORC for the waste heat recovery form internal combustion engines [3e24,28], as shown in Table 1. Nevertheless, the ORC has a minimal temperature difference between heat source and working fluid in the evaporator [29,30]. On the contrary, the transcritical Rankine cycle (TRC) possesses a variable temperature profile to obtain an improved heat transfer in the vapor generator as the working fluid is heated by multi-heat-sources, and is seldom utilized [18,25e27,30,31] for waste heat recovery from internal combustion engines. From the inspection of above works, most of them investigated the effects of the waste heat recovered from exhaust gas [4,6,7,10e17,19,20,28] or cylinder cooling water [3] or both of them [5,8,9,21e25]. Only several studies [18,26,27,30] are conducted utilizing three waste heat sources of the internal combustion engine simultaneously.

Seldom investigations for WHR of the engines by TRC were reported [7,30]. In summary, this is the first paper in the open literature to study the economic performance of the WHR system employing four different waste heat sources of a large marine diesel engine for a merchant ship. The aim of this study is thus to investigate the economic performance of TRC using exhaust gas, cylinder cooling water, scavenge air cooling water and lubricating oil to conform the requirements of international convention, MARPOL. The economic parameter, levelized energy cost (LEC), is employed to evaluate the optimizations of the TRC system.

2. System analysis 2.1. System description To enhance the effect of waste heat recovery, four waste heat sources, which are exhaust gas, cylinder cooling water, scavenge air cooling water and lubricating oil of a large marine diesel engine, are employed to drive the TRC. Fig. 1 shows the schematic diagram of the multi-heat-sources TRC system for WHR from a diesel engine. The multi-heat-sources TRC system consists of a working fluid pump, an expander, a condenser, three heaters, and a vapor generator, as shown in Fig. 1. Two water pumps and one oil pump are installed to circulate the cylinder cooling water, scavenge air cooling water and lubricating oil in the system. It should be noted that in traditional cooling system of the marine diesel engine, the heat resources of scavenge air and lubricating oil are discharged directly without reusing. Only a part of heat from cylinder cooling is utilized to generate fresh water, and a part of waste heat from exhaust gas is applied to generate steam for heavy diesel oil heating. Beside this, the other remnants of waste heat resources are mostly discharged overboard. In the multi-heat-sources TRC system, the working fluid is pumped to state 1, and then passes through a three-way-valve. One part of working fluid flows into the Heater A and absorbs the heat

Table 1 Review of the works for recovering waste heat from the internal combustion engine [3e30]. Refs.

Power cycle

Heat transfer calculation Economic evaluation Waste heat sources Exhaust gas Cylinder cooling water Scavenge air cooling water Lubricating oil

Yang and Yeh [3] ORC Yang and Yeh [4] ORC Yang and Yeh [5] ORC Vaja and Gambarotta [6] ORC Shu et al. [7] ORC Song et al. [8] ORC Yu et al. [9] ORC Srinivasan et al. [10] ORC Yue et al. [11] ORC Yang et al. [12] ORC Larsen et al. [13] ORC Yang et al. [14] ORC Tian et al. [15] ORC Kolsch et al. [16] ORC Katsanos et al. [17] ORC Soffiato et al. [18] ORC,TRC Choi and Kim [19] RC þ ORC He et al. [20] ORC þ Kalina Shu et al. [21] Dual-ORC Zhang et al. [22] Dual-ORC Song et al. [23,24] Dual-ORC Shu et al. [25] Dual-TRC Shu et al. [26] Dual-TRC Yu et al. [27] Dual-TRC Di et al. [28] ORC Yang [30] TRC

C C C e e e e e C C C C C C C e e e e e e e e C e C

C C C e e e e e e e e e C e e e e e e e e e e C e C

e C C C C C C C C C C C C C C e C C C C C C C C C C

C e C e e C C e e e e e e e e C e e C C C C C C e C

e e e e e e e e e e e e e e e C e e e e e e C C C C

e e e e e e e e e e e e e e e C e e e e e e e e e e

M.-H. Yang / Energy 113 (2016) 1109e1124

1111

Fig. 1. Schematic diagram of the WHR system for a marine diesel engine.

Table 2 The properties of working fluids. Item

R134a

R152a

R236fa

R290

R1234yf

R1234ze

Molar mass (kg/kmol) Tcri ( C) Pcri (MPa) ODP GWP (100 years)

102.03 101.06 4.059 0 1430

66.05 113.26 4.517 0 124

152.04 124.92 3.2 0 9400

44.1 96.74 4.251 0 3.3

114.04 94.7 3.382 0 4

114.04 109.36 3.635 0 6

160 140

T ( oC )

energy from lubricating oil, and the rest of working fluid passes through the Heater B and is heated by scavenge air cooling water, initially. After exiting from Heater A, the working fluid then enters Heater B where the two parts of working fluid mix and is heated together by the scavenging air cooling water. Subsequently, the temperature of working fluid increases in Heater C due to obtaining heat energy from higher-temperature cylinder cooling water. Eventually, the temperature of working fluid continue to rise and becomes higher than critical temperature by recovering waste heat from exhaust gas in the vapor generator. The working fluid then passes through the expander to produce useful work and is condensed in the condenser. By the boosting of the pump, working fluid completes the power cycle. While leaving Heater A, Heater B, and Heater C, cooling water of lubricating oil, scavenge air, and cylinder need to pass finally through the central cooling system to attain the proper temperature for maintaining normal operation of the diesel engine. To convert these waste heat sources to useful power effectively, the working fluids need to possess suitable critical temperature and favorable temperature profiles. Furthermore, zero ozonedepletion-potential (ODP) is also an essential criterion in selecting the working fluid for environmental protection. Therefore, refrigerants of R1234yf, R1234ze, R134a, R152a, R236fa and R290 are employed as the working fluids of the TRC in the WHR system. The properties of working fluids are shown in Table 2. In addition, Fig. 2 demonstrates the relationships between temperature and entropy of these working fluids.

R236fa

R1234yf

120

R134a

100

R1234ze

R152a R290

80 60 40 20

1.2

1.6

2

s ( kJ/kg-K)

2.4

Fig. 2. The temperature-entropy diagram of the working fluids.

2.2. Thermodynamic analysis The TRC system is shown schematically on a temperatureentropy diagram in Fig. 3(a). Although the entropy scales of exhaust gas, cylinder cooling water, scavenge air cooling water, lubricating oil and cooling water are different to that of the working fluid, the temperature profiles of four waste heat sources and cooling water are also plotted to assist better understanding of the temperature variations of the fluids in the heat exchangers of the TRC system. In order to recover the maximum of waste heat energy, the temperature difference between inlet and outlet of heat exchanger need to be enlarged as much as possible. It also results in a lower outlet temperature of waste heat source, and decreases the performance of heat transfer in heaters and vapor generator. Therefore, it is essential to consider both the performances of thermodynamics and heat transfer properly in this study. To reveal

1112

M.-H. Yang / Energy 113 (2016) 1109e1124

The thermodynamic equations, listed in Table 3(a), can be used to evaluate the heat transfer rate in the heaters, vapor generator and condenser. In addition, Table 3(b) gives the related equations for calculating the heat duty or the power of each component in the WHR system. Consequently, the net power output and thermal efficiency of the WHR system are calculated by

Vapor generator

s t ga aus Exh

Heater C

o

Temperature ( C)

Heater B Heater A der lin ng Cy ling ati c i o br air co r Lu l ge r ate oi ven wate w a Sc ling o h3 co inc Pin

P 2 1 inch h c P

1 7

Pin

4 ch

5

4

(2)

hth ¼ Wnet =Qtot

(3)

In order to indentify the proportion of all the waste heat sources applied to the WHR system, the parameter, available efficiency, ε, is employed and defined as

6

3


Wnet ¼ Wexp  Wpum;r þ Wpum;cyl þ Wpum;sca þ Wpum;lub

2 Pinch 5

ε ¼ Qtot =Qmax

Cooling water

(4)

where Qmax is the summation of the maximal heat capacities of all the waste heat sources which are obtained from their mass flow rates and temperature differences between inlet and minimal outlet temperatures, as shown in Table 4.

Entropy (kJ/kg-K)

(a)

2.3. Heat-transfer analysis

(b) Fig. 3. The (a) temperature-entropy, and (b) pressure-enthalpy diagrams of the WHR system.

The shell-and-tube heat exchanger is designed for the heaters, vapor generator and condenser in the WHR system. The vapor generator is assumed as the flooded type in this study. Considering the temperature-dependent thermodynamic and transport properties in supercritical and superheating state, an improved solution of LMTD method is used in this study. By discretizing the heat exchangers, the accuracy of heat transfer calculation can be enhanced. Thus, in this study the heaters, vapor generator and condenser are divided into N equal sections, and the properties variation in each step become small enough. Then, in each section, an average value of the properties can be obtained [3e5,27,30]. Consequently, the heat-transfer rate between the working fluid and exhaust gas of each section in vapor generator can be written as

Qexh;j ¼ Uexh;j Aexh;j F DTmean;exh;j ¼ mr ði5  i4 Þ=N the limitations of the minimal temperature difference between these waste heat sources and working fluid in the heaters and vapor generator, Pinch 1 to Pinch 4 are marked, respectively in Fig. 3(a). In addition, Pinch 5 is also used to represent the limitation of the minimal temperature difference between working fluid and cooling water in the condenser. Similarly, the WHR system is illustrated in a pressure-enthalpy diagram to depict the amount of heat energy transmission in heaters, vapor generator and condenser, as shown in Fig 3(b). The total heat energy which is recovered from exhaust gas, cylinder cooling water, scavenge air cooling water and lubricating oil in heaters and vapor generator can be expressed as

Qtot ¼ Qexh þ Qcyl þ Qsca þ Qlub

(1)

Table 3a The thermodynamic equations of waste heat sources and heat sink. Heat sources or heat sink Waste heat sources Exhaust gas Cylinder cooling water Scavenge air cooling water Lubricating oil Heat sink Cooling water

Thermodynamic equations Qexh ¼ mexh(iexh,i  iexh,o) Qcyl ¼ mcylcp,w(Tcyl,i  Tcyl,o) Qsca ¼ mscacp,w(Tsca,i  Tsca,o) Qlub ¼ mlubcp,lub(Tlub,i  Tlub,o) Qcw ¼ mcwcp,w(Tcw,i  Tcw,o)

(5)

where F is a correction factor, and DTmean represents the logarithmic mean temperature difference between the working fluid and exhaust gas in the vapor generator and can be expressed as [32].




DTmean;exh;j


 Texh;i;j  Tr;o;j  Texh;o;j  Tr;i;j .
i ¼ h
Texh;o;j  Tr;i;j ln Texh;i;j  Tr;o;j

(6)

The Uexh,jAexh,j of each section in the vapor generator is defined by Ref. [32].

Uexh;j Aexh;j ¼ 1





hr;j Ar;j þ



1

2pkt Lt lnðDo =Di Þ



 .
þ 1 hexh;j Aexh;j

(7)

where hr,j and hexh,j are the heat-transfer coefficients of the working fluid and exhaust gas and can be calculated from the equations of Table 5 in the j-section of vapor generator, respectively. Similarly, the Ar,j and Aexh,j are the surface area of the working fluid side and exhaust gas side in that section of vapor generator. Furthermore, to calculate the heat-transfer coefficients for exhaust gas and working fluid in the vapor generator, several empirical correlations listed in Table 5 [32e35] are used. Substituting the heat-transfer coefficients calculated from the correlations in Table 5 into Eq. (7), the overall heat-transfer coefficient, Uexh,j, of the j-section of vapor generator

M.-H. Yang / Energy 113 (2016) 1109e1124

1113

Table 3b The thermodynamic equations of capacity calculation for each component.

WHR system

Waste heat sources circulating pump

Component

The thermodynamic equations

Heater A Heater B Heater C Vapor generator Expander Condenser Pump Cylinder cooling water pump Scavenge air cooling water pump Lubricating oil pump

Qlub ¼ (1  x)mr(i2  i1) Qsca ¼ mr(i3  i2) þ xmr(i2  i1) Qcyl ¼ mr(i4  i3) Qexh ¼ mr(i5  i4) Wexp ¼ mr(i5  i6)/hexp Qcon ¼ mr(i6  i7) Wpum,r ¼ mrv7(p1  p7)/hpum Wpum,cyl ¼ mcyl(Dpcyl)/(rwhpum) Wpum,sca ¼ msca(Dpsca)/(rwhpum) Wpum,lub ¼ mlub(Dplub)/(rwhpum)

Table 4 The waste heat source conditions of the marine diesel engine [38]. Waste heat source

Mass flow rate (kg/s)

Inlet temperature ( C)

Minimal outlet temperature ( C)

Exhaust gas Cylinder cooling water Scavenge air cooling water Lubricating oil

148.51 158 162.5 277.78

290 90 76 60.2

138 73 36 45

Table 5 The equations of heat-transfer coefficient for heat exchangers in the TRC system [32e35]. Equation of heat-transfer coefficient and conditions  Nu ¼ 0:022Re0:84 Pr 0:36

0:25

Pr Prwall

Re > 2  105 2 6 Nu ¼ 4

3 7 5

ðfb =8ÞRe
r Prr  12:7ðfb =8Þ

0:5

2 Prr3 1



þ1:07

cPav cPb



 kb kwall

mb mwall

Fluid or wall

Phase

Heat exchanger

Working fluid

Liquid

Heaters A-C

Supercritical

Vapor generator

Vapor

Condenser

Condensation

Condenser

Exhaust gas

gas

Vapor generator

Cylinder cooling water Scavenge air cooling water Lubricating oil Cooling water

Liquid

Heaters A-C



0.5  Pr < 2000 3  103 < Re < 5  106 Nu ¼ 0.0131Re0.883Pr0.36 4.5  105 < Re < 7  106 11=4 0 0

grf ðrf rg ÞD3o ifg A f kr ðTsat Twall Þ

Nu ¼ 0:729@ m

 Nu ¼ 0:71Re0:5 Pr 0:36

Pr Prwall

0:25

1000 < Re < 2  105 Nu ¼ 0:023Re0:8 Pr 0:3 Re > 104 0.7  Pr < 160

Condenser

Prwall is evaluated using the properties at the wall temperature of the tubes. rf and rg are the liquid and vapor densities of the working fluid, respectively; Tsat represents the condensation temperature in the condenser, and i'fg is the modified latent heat of the working fluid.

can be evaluated. Then, the heat-transfer area of the j-section, Aexh,j can be obtained from Eq. (5). Therefore, the total heat-transfer area of the vapor generator for recovering waste heat energy from exhaust gas, Aexh, can be calculated by

parameters to show the temperature differences between these waste heat sources and working fluid in vapor generator and heaters. Therefore, these temperature differences in the heaters and vapor generator are averaged and expressed as

0 Aexh ¼

N X

Aexh;j

(8)

j¼1

Likewise, employing the correlations of heat-transfer coefficients in Table 5 and Eqs. (5)e(8), the heat-transfer area of Heaters A-C, Acyl, Asca and Alub, for recovering waste heat energy from cylinder cooling water, scavenge air cooling water and lubricating oil can also be evaluated. The empirical correlations used to obtain the heat-transfer coefficients for cooling water and working fluid in the condenser are also presented in Table 5. In addition, △Texh,j, △Tcyl,j, △Tsca,j, and △Tlub,j, which are the important

BPN B j¼1 DTexh;j

DTvap ¼ B B @

N

PN  Qexh þ

j¼1

DTcyl;j

N

PN  Qcyl þ

j¼1

DTsca;j

N

1 PN C, C j¼1 DTlub;j  Qlub C  Qsca þ C Qtot N A (9)

1114

M.-H. Yang / Energy 113 (2016) 1109e1124

Similarly, the whole heat transfer area of the condenser, Acon, which contains the superheating and condensing regions can be evaluated from correlations in Table 5 and Eqs. (5)e(7). 2.4. Economic analysis In this study, the system cost evaluation equations widely employed in economic analysis are applied to evaluate the equipments cost of the TRC system for preliminary design [36]. The bare module cost for shell-and-tube heat exchangers, working fluid pump and heat sources circulating pumps are given by

CBM;X

  ¼ Cp;X B1;X þ B2;X FM;X FP;X

(10)

where material factor, FM, and the constants, B1 and B2, are given in Table 6. The bare module cost for expander is expressed as

  CBM;exp ¼ Cp;exp FBM FP;exp

(11)

In Eqs. (10) and (11), the purchased cost of equipment, CP,X, at ambient operating pressure and using carbon steel construction can be shown as

log Cp;X ¼ K1;X þ K2;X log Y þ K3;X ðlog YÞ2

(12)

where Y stands for the capacities of expander and pumps or the areas of heaters, vapor generator and condenser, respectively, in the TRC system, as shown in Table 6. Furthermore, K1, K2, and K3 are the coefficients of equipments cost, as shown in Table 6 [36]. Furthermore, the pressure factors, FP, for heat exchanger, pump, and expander in Eqs. (10) and (11) also can be obtained from

log FP;X ¼ C1;X þ C2;X logð10P  1Þ þ C3;X ðlogð10P  1ÞÞ2

(13)

where the C1, C2, and C3 are coefficients of pressure factor and can be found in Table 6. Since the unit in the parentheses of the second and third terms in the right hand side of Eq. (13) is bar (gage pressure), a pressure unit transformation from MPa to bar is thus needed to fit the equation request. Subsequently, the total purchased cost of equipments in the year 2014 can be calculated by Ref. [3e5].

CRF ¼

ið1 þ iÞLT

(15)

ð1 þ iÞLT  1

where i is the interest rate, and LT is the lifetime of the WHR system. Finally, the economic parameter, levelized energy cost, LEC can be evaluated from Eq. (16) [37].

LEC ¼

CRF  Ctot þ COM Wna

(16)

where Wna is the annual net power output of the WHR system, and COM is the operations and maintenance cost [37]. In this study, a differential method is applied to obtain the minimal levelized energy cost, LECmin of the TRC system for the economic optimization. The optimal operating parameters, the optimal expander inlet pressure, P 5,o, and temperature T5,o can be calculated by

vðLECÞ ¼0 vP5

(17)

vðLECÞ ¼0 vT5

(18)

Then the corresponding LECmin of the TRC can be obtained. Since the thermodynamic performances of the TRC system is obviously affected by the pressures and temperatures of expander inlet and condensation for the working fluid, it is important to depict the relations between these four operating conditions and economic performance. Due to the condensation occurs at saturation, the condensed pressure is the function of the condensed temperature. In this study, two dimensionless parameters, which are pressures ratio, g and temperature difference ratio, q, are introduced to analyze the economic performance and are expressed as

g¼

P5 P7

(19)

q¼

T5  T7 T5 þ 273:16

(20)

  Ctot ¼ CBM;vap þ CBM;exp þ CBM;con þ CBM;pum 2001 ,CEPCI2014 =CEPCI2001

where CEPCI is the chemical engineering plant cost index considering the effect of time on purchased equipment cost. The total investment cost of the WHR system in this study is mainly determined by the cost of the major components, including heaters, vapor generator, expander, condenser and pumps. Note that the cost of the working fluid is not considered in this study [3e5,30]. Moreover, the capital recovery cost, CRF is estimated based on the following relation [37].

(14)

3. Numerical procedure In this study, the primary data of WARTSILA RTeflex96C marine diesel engine with 12 cylinders at 85% load are used, as shown in Table 7 [38]. The mass flow rate, inlet temperatures and minimal outlet temperatures of the exhaust gas, cylinder cooling water,

Table 6 Equipment cost parameters [36]. X

Y

K1,X

K2,X

K3,X

B1,X

B2,X

FM,X

C1,X

C2,X

C3,X

Vapor generator Heaters A-C Condenser Pump Expander

Aexh, (m2) Acyl, Asca, Alub (m2) Acon (m2) Wpum (kW) Wtur (kW)

4.3247

0.3030

0.1634

1.63

1.66

1.4

0.0388

0.11272

0.08183

3.3892 2.7051

0.0536 1.4398

0.1538 0.1776

1.89 0

1.35 1

1.6 3.4

0.3935 0

0.3957 0

0.00226 0

M.-H. Yang / Energy 113 (2016) 1109e1124

scavenge air cooling water and lubricating oil from the marine diesel engine are listed in Table 4. Note that although the exhaust gas has higher temperature at exhaust valve in the diesel engine, as it passes through the economizer, a part of heat energy is absorbed and the inlet temperature of exhaust gas at vapor generator reduces and is assumed as 290  C, as shown in Table 4. Moreover, the known data and related parameters of the WHR system are given in Table 8 for thermodynamic as well as economic analysis. Hence, the mass flow rates of working fluid and cooling water are varied to evaluate net power output and total cost of the TRC system with various operating pressures and temperatures. The minimal LEC for each working fluid and their corresponding optimal operating temperatures and pressures of the WHR system can be obtained. Finally, the mass flow rate of working fluids and outlet temperatures of the waste heat sources are also evaluated to depict the thermal and recovery efficiencies of the entire power system.

1115

Table 8 Parameters used in the TRC system. Parameter

Value

Expander inlet temperature, T2 ( C) Expander inlet pressure, P2 (MPa) Condensation temperature, T4 ( C) Cooling water inlet temperature, Tcw,i ( C) Pinch 1 to Pinch 3 for Heaters A, B and C ( C) Pinch 4 for vapor generator ( C) Pinch 5 for condenser ( C) The efficiencies of pumps and expander, hpum, htu The effectiveness of condenser and vapor generator Correction factor, F

140e220 3.4e8 30e45 25 6 6 5 0.75 0.95 0.9

3.1. Verification In this study, the thermal efficiency of the proposed TRC system with R1234ze under various expander inlet pressures are compared with previously published results [39], as shown in Fig. 4. In the TRC system, the expander inlet temperature, T5, and condensation temperature, T7, are assumed as 139  C and 20  C, respectively. Moreover, the isentropic efficiencies of the pump and expander are both assumed as 0.8. Note that in the TRC system, the inlet temperatures of heat source and heat sink fluids are 150  C and 5  C, respectively. The mass flow rate of heat source of the TRC system is 0.1 kg/s. As a whole, the numerical results obtained in this study are consistent with those reported in the literature [39]. 3.2. Calculation procedure In this study, the calculation program is written in FORTRAN and the numerical simulation procedure of the WHR system is demonstrated in Fig. 5. The limitations of pinch points in the heaters, vapor generator and condenser are assumed properly to indentify the available heat transfer rates form waste heat sources to working fluids, or from working fluids to cooling water. Since the thermodynamic and transport properties of the working fluids, heat sources and heat sink play the important role in the simulation work, the essential subroutine, the NIST database (REFPROP 9.0) developed by National Institute of Standards and Technology [40], is linked by main program for thermodynamic analysis as well as heat transfer calculation. Note that the heat exchangers are discretized into 100 sections to calculate the heat transfer rate more accurately with varied properties due to temperature change. The performance and total cost of the WHR system can be obtained to evaluate the economic optimization. Furthermore, the payback period, CO2 emission reduction, and fuel oil consumption saving can be calculated. In this study, the increments of pressures and temperatures are 0.002 MPa and 0.01  C, respectively. The relative errors for thermodynamic analysis and iterative convergence criteria of heat-transfer area of heat exchangers are 0.01% and 0.1%,

Fig. 4. Flow diagram of simulation process.

Parameters of waste heat sources input Limitation of pinch points NIST database Thermodynamic analysis

Heat transfer calculation

Capacities of Expander and pumps

Capacities of heat exchangers

Performance analysis

System cost evaluation

Economic optimization Table 7 Primary data of WARTSILA RT-flex96C marine diesel engine with 12 cylinders at 85% load [38]. Power (kW) Bore  stroke (mm) Speed (rpm) Exhaust gas temperature ( C) Fuel consumption rate (kg/kW-h)

68,640 960  2500 102 308 0.167

Payback period, CO2 reduction and oil saving Optimal correlations Fig. 5. Comparison of thermal efficiencies obtained from this study and those of previous work [39].

1116

M.-H. Yang / Energy 113 (2016) 1109e1124

respectively. A relative error of 0.1% is specified as the stopping criterion in obtaining the economic optimization. 4. Results and discussion 4.1. Parametric analysis Fig. 6(a)-(f) demonstrates the effects of expander inlet pressure, P5, on net power output, Wnet, thermal efficiency, hth, total costs of

the equipment, Ctot, levelized energy cost, LEC, mass flow rate, mr, and available efficiency, ε, of the WHR system for R134a, R152a, R236fa, R290, R1234yf and R1234ze at T5 ¼ 170  C and T7 ¼ 30  C. As P5 increases, the values of Wnet and hth both rise apparently, as shown in Fig. 6(a)e(b). This is because the higher the expander inlet pressure of working fluid is, the more the power output of expander will be. At a lower P5, R236fa performs the largest power output and R152a presents the highest thermal efficiency compared with other working fluids. However, both the increasing

(b)

(a)

(c)

(d)

(e)

(f)

40

Fig. 6. The effects of P5 on (a) Wnet, (b) hth, (c) Ctot, (d) LEC, (e) mr and (f) ε for the TRC at T5 ¼ 170  C.

M.-H. Yang / Energy 113 (2016) 1109e1124

rates of Wnet and hth become smaller at a higher P5 for each working fluid, because the power consumption of working fluid pumps, Wpum,r, also increases obviously. Note that the investigation range of P5 for R152a is narrower than the other working fluid distinctly due to its higher critical pressure, as shown in Table 2. Note that the values of Ctot increase evidently with P5 due to the significant effect of pressure factor on component cost evaluation in Eq. (15) for each working fluid, as revealed in Fig. 6(c). In Fig. 6(d) the values of levelized energy cost (LEC) decrease first, and then increase sharply with P5, and a concave upward profile of LEC can be observed for these working fluids in the TRC system. Obviously, the smallest LEC with corresponding optimal P5 can be found for each working fluid. It should be noted that the effects of wider range of P5 are investigated, but only the results in proper range are illustrated for the optimal economic performance. The minimal LEC, LECmin, represents an optimal performance corresponding to the optimal P5, P5,o, in economic evaluation of the WHR system. Furthermore, among these working fluids, R236fa not only possesses the smallest LECmin ¼ 0.0257 $/kWh but also has the lowest corresponding optimal expander inlet temperature, at P5,o ¼ 4.06 MPa in the TRC system. In the inspections of Fig. 6(e)-(f), mass flow rate, mr, and available efficiencies, ε, of working fluids in the TRC system increase slightly with P5. At fixed expander inlet temperature, an increase in P5 raises both the mass flow rate of working fluids and the available efficiencies of the TRC system. It can also be learned that the TRC operated with R290 requires the smallest mass flow rate because R290 has the largest specific entropy variation among these working fluids during heating processes. Furthermore, R236fa possesses the smallest available efficiencies in the TRC system. Since, in super-critical state, the thermodynamic properties of working fluid can be determined by pressure and temperature, the expander inlet temperature also affects the performance of TRC distinctly. Therefore, the effects of the expander inlet temperature, T5, on Wnet, hth, Ctot, LEC, mr and ε for the TRC are investigated and shown in Fig. 7(a)e(f), at T7 ¼ 30  C. Note that in this section, the expander inlet pressures, P5, are adopted appropriately due to the large difference in the critical pressures of these working fluids. Thus, P5's are set to 4 MPa for R236fa and R1234yf in the TRC system. Similarly, P5's are assumed as 5 MPa for R134a, R152a and R1234ze. In addition, for R290, P5 is 6 MPa. The results reveal that with an increase in T5, the values of Wnet decrease obviously for all the working fluids, as demonstrated in Fig. 7(a). This is because the amount of total heat energy recovered from these waste heat sources, Qtot, reduces with expander inlet temperature. It is obvious that R1234yf has the smallest Wnet among these working fluids. On the other hand, slight rise of thermal efficiencies on increasing T5 can be observed in Fig. 7(b) for these working fluids. The rates of incensement for R236fa and R1234yf become smaller at larger T5, and slight decline can be found at higher T5. In addition, R152a performs the highest thermal efficiency at higher T5. From Fig. 7(c), the values of Ctot reduce sharply with increasing T5, initially. This is because the reduction of mass flow rate of working fluid results in a decrease in capacities of the components and leads to a decline in total cost of the WHR system. The decreasing rates of Ctot become smaller with increasing T5, and after attaining the minimal values, Ctot tends to rise at higher T2. This is resulted from the significant increase of heat transfer area in the vapor generators and the evident decline of temperature differences between these waste heat sources and working fluid in heating process. It is worth noting that R1234yf also behaves the smallest Ctot among these working fluids. Consequently, the curves of LEC for these working fluids are downward sloping initially, then achieve their minimums, and finally increase with T5, as depicted in Fig 7(d). In addition, R236fa has the lowest LEC for which LECmin ¼ 0.0253 $/kWh with corresponding T5,o ¼ 168.21  C. Furthermore, the optimal expander inlet

1117

temperature, T5,o, for R1234yf is 148.22  C and is the lowest among these working fluids. It may be attributed to the lowest critical temperature of R1234yf, as shown in Table 2. The mass flow rate of working fluid also reduces with T5, as demonstrated in Fig 7(e). The available efficiencies of these waste heat sources also decline with T5, as shown in Fig 7(f). It should be noted that R236fa requires the largest mass flow rate but performs the smallest utilizing proportion of waste heat sources among these working fluids in the TRC system. This also means that the ability of aborts heat energy from waste heat sources for R236fa is the weakest among these working fluids in the TRC system operated at fixed high and low temperatures. It should be noted that compared with an ORC system, the TRC system possesses a variable temperature profile to obtain an improved heat transfer in heating process. In addition, using the zeotropic mixture as the working fluid in the TRC not only increases the thermal efficiency of the whole power system, but also improves the exergy efficiencies of the heating and condensation processes [41]. This is because in the condensation process, the working fluid is condensed isobarically but not isothermally. Consequently, this temperature glide of condensation also reduces irrversibilities of the heat transfer process. Therefore, employing proper zeotropic mixtures as the working fluids will be an important way to improve the economic performance of a TRC in WHR. 4.2. Economic optimization In this section, an important parameter of LEC is selected to evaluate the economic performance among these working fluids. To investigate the optimal economic conditions of the TRC system for recovering waste heat from large merchant diesel engine, the contours of LEC for various expander inlet temperatures, T5, and pressures, P5, are mapped for R134a, R152a, R236fa, R290, R1234yf and R1234ze, respectively in Fig. 8(a)e(f) at T7 ¼ 30  C. The results depict that the minimal levelized energy cost, LECmin, can be obtained for each working fluid. Moreover, the corresponding optimal expander inlet temperature, T5,o, and optimal expander inlet pressure, P5,o, can also be determined of the WHR system. It is worthwhile to note that the LECmin of R236fa is the lowest among these working fluids at T5,o ¼ 170.22  C and P5,o ¼ 4.08 MPa. From the inspection of optimal expander inlet pressures and temperatures of these working fluids, R290 has the highest P5,o whereas R236fa possesses the lowest one. From Table 2, it is obvious that the optimal expander inlet pressures are affected by the critical pressures significantly. Meanwhile, R152a and R1234yf exhibit the highest and lowest T5,o, respectively among these working fluids. To further analyze the optimal economic performance, the LECmin's and their corresponding optimal operating parameters of the TRC system, such as mr,o, Wnet,o, Ctot, hth,o, and ε,o are listed in Table 9. It can be conducted that the LECmin of the proposed system utilized R236fa is the smallest and is lower than that of R1234ze, R134a, R152a, R1234yf or R290 by 5.07%, 6.25%, 7.42%, 9.77% or 12.11%, respectively. Furthermore, in the comparison of optimal available efficiencies, R1234yf has the largest ε,o among these working fluids. It may be mainly affected by the lowest critical temperature of R1234yf, as shown in Table 2. It should be noted that the both Wnet,o and hth,o of the system with R152a are the largest among these working fluids. Nevertheless, R152a also has the largest Ctot, which is leaded by the highest T5,o. It also declines the economic performance of R152a in the WHR system. In addition, although R290 requires the smallest optimal mass flow rate, mr,o, it behaves the worst economic performance due to its highest P5,o. Overall, from Table 9, it also indicates that the sequences of the LECmin are obviously different from those of Wnet,o and hth,o in the WHR system. In WHR system, the working fluid needs to absorb the heat

1118

M.-H. Yang / Energy 113 (2016) 1109e1124

(a)

(b)

(c)

(d)

(e)

(f)

Fig. 7. The effects of T5 on (a) Wnet, (b) hth, (c) Ctot, (d) LEC, (e) mr and (f) ε for the TRC.

energy as much as possible in the heaters and vapor generator. Therefore, in the TRC system, the higher the expander inlet temperature is, the more the power output will be. However, a higher temperature of working fluid will decline the temperature difference between waste heat source and working fluid in the heat exchanger. It leads to the decrease of heat-transfer performance and the increase of heat-exchange area in heaters and vapor generator. The net power output of TRC system, which is great affected by temperature difference between waste heat sources and

working fluid in the heat exchangers, will influence the economic performance significantly. Consequently, to depict net power output and economic performance of the TRC system, the contours of LEC with various averaged temperature differences in heaters and Wnet for these working fluids are demonstrated in Fig. 9 at T7 ¼ 30  C. As expected, the values of LECmin and their corresponding △Tvap,o and Wnet,o for these working fluids can be obtained. It is worth noting that the △Tvap,o of R236fa is the highest, followed by R1234yf, R1234ze, R290, R134a and R152a. It also

M.-H. Yang / Energy 113 (2016) 1109e1124

Fig. 8. Contours of LEC for (a) R134a, (b) R152a, (c) R236fa, (d) R290, (e) R1234yf and (f) R1234ze.

1119

1120

M.-H. Yang / Energy 113 (2016) 1109e1124

240

Table 9 The optimal parameters for economic performance evaluation of the TRC at T7 ¼ 30  C. R134a

R152a

R236fa

R290

R1234yf

R1234ze

LECmin ($/kWh) P5,o (MPa) T5,o ( C) mr,o (kg s1) Wnet,o (kW) Ctot,o (106 $) εo (%) hth,o (%)

0.0272 6.25 180.34 80.26 3307.58 6.809 61.96 14.66

0.0275 5.44 194.82 49.64 3390.33 7.045 59.32 15.92

0.0256 4.08 170.22 95.85 3305.12 6.392 54.3 14.58

0.0287 6.7 179.63 40.73 3231.23 7.01 61.69 14.4

0.0281 5.77 169.1 96.57 3159.85 6.703 64.03 13.41

0.0269 5.32 176.77 84.3 3293.88 6.701 62.09 14.59

R134a

R1234yf

R290

R236fa 160

T ( oC )

Item

R152a

R1234ze 200

120 80 40

4.3. Comparisons of economic considerations and environment protection Payback period and fuel oil saving are another important

1

1.5

2

s ( kJ/kg-K )

2.5

(a)

101

R1234yf R236fa

R1234ze R134a

P (Mpa)

means that in economic optimization, the TRC operated with R236fa performs better heat-transfer potential than any other working fluids. Furthermore, the sequences of the △Tvap,o are obviously distinct to those of Wnet,o or LECmin among these working fluids. Fig. 10(a)-(b) shows the temperature-entropy and pressureenthalpy diagrams of these working fluids in the WHR system for the economic optimization at T7 ¼ 30  C. In Fig. 10(a), the curves on the diagram indicate the geometrical variations of temperature and entropy in the heating and cooling processes as the WHR system operates with each working fluid. In heating process, the curve inflection of each working fluid can be observed. Meanwhile, it can be found that the optimized curve of R290 behaves the largest variation in entropy for heating process, followed by R152a, R134a, R1234ze, R1234yf and R236fa. It also notes that TRC system operated with R236fa in economic optimization needs the largest mass flow rate, mr,o. Fig. 10(b) demonstrates not only optimal inlet pressure but also optimal outlet pressure of the expander for these working fluids. In TRC system, reducing P7 or increasing P5 will enhance the thermodynamic performance. However, increasing P5 will raise the manufacturing cost of components, whereas reducing P7 will decrease the equipment cost caused by pressure factor of the TRC system, as mentioned in Eqs. (11)e(13). Therefore, the expander outlet pressure plays a more important role for economic consideration. In Fig. 10(b), R236fa has not only the lowest P5,o but also the smallest P7 among these working fluids.

100

R290 R152a 200

400

i (kJ/kg)

600

800

(b) Fig. 10. Optimal (a) temperature-entropy and (b) pressure-enthalpy diagrams of the working fluids investigated in this study.

indexes of economic considerations for investment of WHR system in a large marine diesel engine. Furthermore the effect of CO2 emission reduction for waste heat recovering power system is also a significant indicator of environmental protection. In this study, the payback period, fuel oil saving, and CO2 emission reduction of the TRC system for recovering waste heat from a large marine diesel engine are investigated and compared to assess the suitability of these working fluids. In addition, several parameters [36e38,42] are employed and listed in Table 10. Subsequently, the payback period of the WHR system and the corresponding P5,o and T5,o can be obtained for each working fluid at T7 ¼ 30  C, as shown in Fig. 11(a). As expected, the payback period of R236fa is 3.02 years and is the shortest among these working fluids. Furthermore, the sequences of payback period for these working fluids are the same with that of LECmin in the TRC. The fuel consumption rate of the marine diesel engine is assumed as 0.167 kg/kWh, as shown in

Table 10 Parameters used in the evaluation for economic considerations and environmental protection.

Fig. 9. Contours of LEC with various △Tvap and Wnet.

Parameter

Value

Annual operation hours [36] Lifetime [36] Interest rate [36] Operations and maintenance cost rate, COM [37] Heavy oil price for diesel generator in 2015 [42] Specific CO2 emission [37]

7200 h/year 20 year 5% (Ctot)  1.5% 291.3 $/ton 0.52 kg_CO2/kWh

M.-H. Yang / Energy 113 (2016) 1109e1124

Table 7. Fig. 11(b) shows the heavy diesel oil saving of the WHR system for each working fluid due to the large amount of net power generated without extra fuel consumption in the TRC system. In heavy-diesel-oil-saving comparison, R152a is superior to R134a, R236fa, R1234ze, R290, and R1234yf by 2.5%, 2.58%, 2.93%, 4.92%, and 7.29%, respectively. Moreover, note that the emission of CO2 is proportional to the fuel consumption which is also proportional to the net power output of an internal combustion engine. Therefore, the net power output obtained by WHR system without consuming fuel can be applied to evaluate the CO2 emission reduction of the TRC system. Fig. 11(c) demonstrates the CO2 emission reduction per year of these working fluids for the TRC. The results reveal that CO2 emission reduction of R152a is 7.81  106 kg/year and is larger than that of R134a, R236fa, R1234ze, R290 or R1234yf by 1.91  106 kg/ year, 1.96  106 kg/year, 2.22  106 kg/year, 3.67  106 kg/year or 5.31  106 kg/year, respectively. 4.4. Optimal economic correlations The condensation temperature, T7, which is the expander outlet temperature and relates to the corresponding expander outlet pressure, P7, of working fluid, is an important parameter to evaluate thermodynamic and economic performances for TRC power plant. Fig. 12(a)-(b) reveal the variations of the optimal expander inlet pressure and temperature for 30  C  T7  45  C. As expected, both the corresponding optimal expander inlet pressure, P5,o, and temperature, T5,o, can be obtained in economic optimization. In

1121

Fig. 12(a), as T7 increases, the values of P5,o decline first for all the working fluids. Note that the decline of P5,o for R152a is not so obvious compared with other working fluids. Then the curves of P5,o rise with T7, and concave curves can be observed for R134a, R152a and R1234yf. On the other hand, the values of P5,o almost remain as constants for R236a, R290, R1234ze on increasing T7 in the TRC system. In Fig. 12(b), firstly the optimal expander inlet temperatures, T5,o, decrease with T7 for all the working fluids, then reach their lowest values. Finally, the values of T5,o for these working fluids tend to increase at higher T7. Subsequently, it can be understood that T7 greatly affects T5,o in the TRC system for recovering waste heat from a large marine diesel engine. Furthermore, from T7 ¼ 30  C to 41  C, R1234yf performs lowest T5,o, and the values of T5,o of R1234ze is the smallest among these working fluids. To combine the effects of parameters, P7, T7 and their corresponding P5,o, T5,o, on economic performance analysis of TRC system, dimensionless parameters, optimal pressures ratio, go and optimal temperature difference ratio, qo are conducted from Fig. 13(a)-(b) and Eqs. (19) and (20). Therefore, go stands for the relationships between expander inlet and outlet pressures of the working fluids, which concern to thermodynamic performance and components cost of the power system. Moreover, qo identifies the connections between high and low temperatures of the TRC system, which relates to heat transfer, power output and thermal efficiency of the power system. Fig. 13(a) illustrates the variations of LECmin for the economic optimization of each working fluid with

R134a R152a R236fa R290 R1234yf R1234ze 2.6

3

2.8

Payback period (year)

3.2

(a)

R134a

R134a

R152a

R152a

R236fa

R236fa

R290

R290

R1234yf

R1234yf

R1234ze

R1234ze

3.5

3.75

4

4.25

Heavy diesel oil saving (106kg/year)

(b)

4.5

60

65

70

75

CO2 emission reducing (106kg/year)

(c)

Fig. 11. (a) Payback period, (b) heavy diesel oil saving and (c) CO2 emission reduction of the optimization.

80

1122

M.-H. Yang / Energy 113 (2016) 1109e1124

R134a R152 R236fa R290 R1234yf R1234ze

P5,o (MPa)

7

6

5

4

3

30

33

36

39

T7 (oC)

42

45

(a) 200 R134a R152 R236fa R290 R1234yf R1234ze

T5,o (oC)

180

160

140

120

100

30

33

36

39

T7 (oC)

42

45

(b) Fig. 12. The variations of (a) P5,o and (b) T5,o with various T7.

various corresponding go and qo for 30  C  T7  45  C. It is obvious that the concave curves of LECmin can be observed for each working fluid of the TRC system. Note that go and qo influence the LECmin significantly for 30  C  T7  45  C. This means that go and qo are important parameters in determining LECmin of the TRC system for economic optimization analysis. In addition, three sets of 2D projections are displayed in Fig. 13(b) to reveal the relations between one of them to the others, respectively. The optimal pressures ratio, go, and optimal temperature difference ratio, qo, can be observed clearly with their lowest value of LECmin for these working fluids. The results indicate that R236fa has the lowest LECmin at go ¼ 8.48 and qo ¼ 0.233. Furthermore, the values of go also increase as qo rise. It implies that higher temperature difference ratio of TRC needs higher pressures ratio, however, an excessively high qo leads to a larger corresponding go but lower optimal economic performance. In addition, the optimal temperature difference ratio, qo, for the TRC system with the lowest LECmin from large to small are R152a, R290, R134a, R236fa, R1234yf, and R1234ze. On the other hand, the optimal pressures ratio, go, with the lowest LECmin from large to small are R236fa, R152a, R134a, R1234ze, R290, and R1234yf. To further analyze the relationships among go, qo and LECmin, Correlations are developed to the optimized conditions for each working fluid and can be expressed as

Fig. 13. The variations of LECmin and the corresponding go and qo for the optimized in (a) 3D diagram and (b) 2D projections.


 LECmin ¼ 102 a þ bgo þ cgo 2 þ dqo þ eqo 2

(21)

Note that the related parameters are limited properly in Table 11 and the relevant coefficients, a, b, c, d and e, are listed in Table 12 for these working fluids. 5. Conclusions The economic performances of the WHR system for a large marine diesel engine are evaluated and compared with six zeroODP working fluids. Four waste heat sources of a large marine diesel engine, which are exhaust gas, cylinder cooling water, scavenge air cooling water and lubricating oil, are applied to the TCR system. The effects of expander inlet pressures and temperatures on net power output, thermal efficiency, total cost of equipment, levelized energy cost, mass flow rate, and available efficiency of the WHR system are analyzed for R134a, R152a, R236fa, R290,

M.-H. Yang / Energy 113 (2016) 1109e1124

1123

Table 11 The limitations of parameters for correlations. Parameter

R134a

R152a

R236fa

R290

R1234yf

R1234ze

P5 (MPa) P7 (MPa)

4.1e7.6 0.77e1.16 4.7e8.08 0.224e0.331

4e6.6 0.69e1.04 5.24e8.26 0.241e0.334

3.3e5.1 0.32e0.51 6.32e11.83 0.207e0.295

4.4e8 1.08e1.53 3.88e6.21 0.231e0.331

3.9e6 0.78e1.15 3.92e7.38 0.201e0.315

3.8e6.5 0.58e0.88 4.24e9.19 0.185e0.326

go qo

Table 12 The optimal parameters for economic performance evaluation of the TRC. Item

R134a

R152a

R236fa

R290

R1234yf

R1234ze

a b c d e

0.6954 0.9859 0.0474 0.3244 0.3509

1.2346 0.8868 0.0391 0.4231 0.5227

3.5894 1.1384 0.0588 0.835 1.5309

5.5897 2.0449 0.1843 0.1379 0.1558

1.9077 1.7133 0.1214 0.3977 0.5641

0.9134 1.1705 0.0598 0.3837 0.4739

R1234yf and R1234ze. The results support the conclusions as follows: 1. The economic optimizations and their corresponding optimal parameters of R134a, R152a, R236fa, R290, R1234yf and R1234ze in TRC system are presented theoretically. The optimal levelized energy cost of R236fa is the most excellent and is lower than that of R1234ze, R134a, R152a, R1234yf or R290 by 5.07%, 6.25%, 7.42%, 9.77% or 12.11%, at T7 ¼ 30  C. 2. In the optimizations of economic analyses, both net power output and thermal efficiency of R152a are the largest among these working fluids. R1234yf possesses the largest available efficiency due to having the lowest critical temperature. 3. The optimal temperature-entropy and pressure-enthalpy diagrams of the TRC system for these working fluids are obtained to analyze the economic optimization. 4. The payback period of R236fa is the shortest among these working fluids. In comparison of heavy-diesel-oil-saving, R152a is superior to R134a, R236fa, R1234ze, R290 and R1234yf by 2.5%, 2.58%, 2.93%, 4.92%, and 7.29%. The CO2 emission reduction of R152a is 7.81  106 kg/year and is larger than that of R134a, R236fa, R1234ze, R290 or R1234yf by 1.91  106 kg/year, 1.96  106 kg/year, 2.22  106 kg/year, 3.67  106 kg/year or 5.31  106 kg/year. 5. The economic optimization correlations of the TRC system using dimensionless optimal pressures ratio and optimal temperature difference ratio are proposed for 30  C  T7  45  C. Acknowledgements The financial support for this research from the Engineering Division of the Ministry of Science and Technology, Republic of China, through contract MOST 104-2221-E-022-013, is greatly appreciated.

cp CEPCI CBM D Dh FP FM g h i k K1, K2, K3 Lt M m N Nu P Pr Q Re s T Texh,i Texh,o DTmean Tr,i Tr,o DTvap U v W X x Y

specific heat, kJ kg1 K1 chemical engineering plant cost index bare module cost, $ diameter, m hydraulic diameter, m pressure factor material factor acceleration due to gravity, m s2 heat-transfer coefficient, kW m2 K1 enthalpy, kJ kg1 thermal conductivity, kW m1 K1 coefficients of equipment cost, $ thickness of tube wall, m molecular weight of working fluid, g mole1 mass flow rate, kg s1 section number of the heat exchangers Nusselt number pressure, MPa Prandtl number heat transfer rate, kW Reynolds number entropy, kJ kg1 K1 temperature,  C exhaust gas inlet temperature,  C exhaust gas outlet temperature,  C logarithmic mean temperature difference,  C working fluid inlet temperature,  C working fluid outlet temperature,  C averaged temperature difference in the heaters and vapor generator,  C overall heat-transfer coefficient of the heat exchanger, kW m2 K1 specific volume, m3 kg1 power of the expander or pump, kW equipment type mass flow rate factor the capacity or size parameter of equipment, kW or m2

Greek symbols △ related error, difference g pressures ratio ε available efficiency h efficiency m dynamic viscosity, Paes r density, kg m3

Nomenclature Acon heat-transfer area of condenser, m2 Acyl heat-transfer area of Heater C, m2 Aexh heat-transfer area of Vapor generator, m2 Alub heat-transfer area of Heater A, m2 Asca heat-transfer area of Heater B, m2 B1, B2 bare module factor of equipment C cost, $ C1, C2, C3 pressure factor of equipment CP purchased equipment cost, $

Subscripts con condensation, condenser cw cooling water cyl cylinder cooling water exh exhaust gas exp expander f liquid g vapor i inside, inlet j section

1124

lub max net o pum r sca t th vap wall

M.-H. Yang / Energy 113 (2016) 1109e1124

lubricating oil maximal net outside, optimization pump working fluid scavenge air cooling water tube thermal vapor generator tube wall of heat exchangers

Acronyms LEC levelized energy cost LMTD logarithmic mean temperature difference MARPOL International Convention for the Prevention of Pollution from Ships ODP ozone depletion potential ORC Organic Rankine cycle RC Rankine cycle SEEMP ship energy efficiency management plan TRC transcritical Rankine cycle WHR Waste heat recovery References [1] International Convention for the Prevention of Pollution from Ships, 2015 http://www.imo.org/. [2] EEDI. SEEMP. 2015. http://www.imo.org/MediaCentre/HotTopics. [3] Yang MH, Yeh RH. Analyzing the optimization of an organic Rankine cycle system for recovering waste heat from a large marine engine containing a cooling water system. Energy Convers Manag 2014-09;88:999e1010. [4] Yang MH, Yeh RH. Thermodynamic and economic performances optimization of an organic Rankine cycle system utilizing exhaust gas of a large marine diesel engine. Appl Energy 2015;149:1e12. [5] Yang MH, Yeh RH. Thermo-economic optimization of an organic Rankine cycle system for large marine diesel engine waste heat recovery. Energy 2015;88: 256e68. [6] Vaja I, Gambarotta A. Internal combustion engine (ICE) bottoming with organic Rankine cycles (ORCs). Energy 2010;35:1084e93. [7] Shu G, Li X, Tian H, Liang X, Wei H, Wang X. Alkanes as working fluids for high-temperature exhaust heat recovery of diesel engine using organic Rankine cycle. Appl Energy 2014;119:204e17. [8] Song J, Song Y, Gu C. Thermodynamic analysis and performance optimization of an organic Rankine cycle (ORC) waste heat recovery system for marine diesel engines. Energy 2015;82:976e85. [9] Yu G, Shu G, Tian H, Wei H, Liu L. Simulation and thermodynamic analysis of a bottoming organic Rankine cycle (ORC) of diesel engine (DE). Energy 2013;51: 281e90. [10] Srinivasan KK, Mago PJ, Krishnan SR. Analysis of exhaust waste heat recovery from a dual fuel low temperature combustion engine using an organic Rankine cycle. Energy 2010;35:2387e99. [11] Yue C, Han D, Pu W. Analysis of the integrated characteristics of the CPS (combined power system) of a bottoming organic Rankine cycle and a diesel engine. Energy 2014;72:739e51. [12] Yang F, Zhang H, Song S, Bei C, Wang H, Wang E. Thermoeconomic multiobjective optimization of an organic Rankine cycle for exhaust waste heat recovery of a diesel engine. Energy 2015;93:2208e28. [13] Larsen U, Pierobon L, Haglind F, Gabrielii C. Design and optimisation of organic Rankine cycles for waste heat recovery in marine applications using the principles of natural selection. Energy 2013;55:803e12. [14] Yang F, Zhang H, Bei C, Song S, Wang E. Parametric optimization and performance analysis of ORC (organic Rankine cycle) for diesel engine waste heat recovery with a fin-and-tube evaporator. Energy 2015;91:128e41. [15] Tian H, Shu G, Wei H, Liang X, Liu L. Fluids and parameters optimization for the organic Rankine cycles (ORCs) used in exhaust heat recovery of Internal Combustion Engine (ICE). Energy 2012;47:125e36. [16] Kolsch B, Radulovic J. Utilisation of diesel engine waste heat by organic Rankine cycle. Appl Therm Eng 2015;78:437e48. [17] Katsanos CO, Hountalas DT, Pariotis EG. Thermodynamic analysis of a Rankine cycle applied on a diesel truck engine using steam and organic medium.

Energy Convers Manag 2012;60:68e76. [18] Soffiato M, Frangopoulos CA, Manente G, Rech S, Lazzaretto A. Design optimization of ORC systems for waste heat recovery on board a LNG carrier. Energy Convers Manag 2015;92:523e34. [19] Choi BC, Kim YM. Thermodynamic analysis of a dual loop heat recovery system with trilateral cycle applied to exhaust gases of internal combustion engine for propulsion of the 6800 TEU container ship. Energy 2013;58: 404e16. [20] He M, Zhang X, Zeng K, Gao K. A combined thermodynamic cycle used for waste heat recovery of internal combustion engine. Energy 2011;36:6821e9. [21] Shu G, Liu L, Tian H, Wei H, Yu G. Parametric and working fluid analysis of a dual-loop organic Rankine cycle (DORC) used in engine waste heat recovery. Appl Energy 2014;113:1188e98. [22] Zhang HG, Wang EH, Fan BY. A performance analysis of a novel system of a dual-loop bottoming organic Rankine cycle (ORC) with a light-duty diesel engine. Appl Energy 2013;102:1504e13. [23] Song J, Gu C. Parametric analysis of a dual loop organic Rankine cycle (ORC) system for engine waste heat recovery. Energy Convers Manag 2015;105: 995e1005. [24] Song J, Gu C. Performance analysis of a dual-loop organic Rankine cycle (ORC) system with wet steam expansion for engine waste heat recovery. Appl Energy 2015;156:280e9. [25] Shu G, Liu L, Tian H, Wei H, Xu X. Performance comparison and working fluid analysis of subcritical and transcritical dual-loop organic Rankine cycle (DORC) used in engine waste heat recovery. Energy Convers Manag 2013;74: 35e43. [26] Shu G, Yu G, Tian H, Wei H, Liang X, Huang Z. Multi-approach evaluations of a cascade- organic Rankine cycle (C-ORC) system driven by diesel engine waste heat: part A e thermodynamic evaluations. Energy Convers Manag 2016;108: 579e95. [27] Yu G, Shu G, Tian H, Wei H, Liang X. Multi-approach evaluations of a cascadeorganic Rankine cycle (C-ORC) system driven by diesel engine waste heat: part B-techno-economic evaluations. Energy Convers Manag 2016;108: 596e608. [28] Di Battista D, Mauriello M, Cipollone R. Waste heat recovery of an ORC-based power unit in a turbocharged diesel engine propelling a light duty vehicle. Appl Energy 2015;152:109e20. [29] Velez F, Segovia J, Chejne F, Antolín G, Quijano A, Carmen Martín M. Low temperature heat source for power generation: exhaustive analysis of a carbon dioxide transcritical power cycle. Energy 2011;36:5497e507. [30] Yang MH. Thermal and economic analyses of a compact waste heat recovering system for the marine diesel engine using transcritical Rankine cycle. Energy Convers Manag 2015;106:1082e96. [31] Yang MH, Yeh RH. Economic performances optimization of the transcritical Rankine cycle systems in geothermal application. Energy Convers Manag 2015;95:20e31. [32] Kreith F, Bohn MS. Principles of heat transfer. fifth ed. New York: West Publishing Company; 1993. [33] Petukhov BS, Krasnoshchekov EA, Protopopov VS. An investigation of heat transfer to fluids flowing in pipes under supercritical conditions. In: International developments in heat transfer, papers presented at the 1961 international heat transfer conference, January 8e12, part III, paper 67, ASME. Boulder, CO, USA: University of Colorado; 1961. p. 569e78. [34] Cengel YA. Heat transfer, a practical approach. second ed. New York: McGraweHill; 2003. [35] Incropera FP, Dewitt DP. Fundamentals of heat and mass transfer. fifth ed. New York: John Wiley & Sons; 2002. [36] Turton R, Bailie RC, Whiting WB. Analysis, synthesis and design of chemical processes. fourth ed. New Jersey: Prentice Hall PTR; 2013. [37] Feng Y, Zhang Y, Li B, Yang J, Shi Y. Comparison between regenerative organic Rankine cycle (RORC) and basic organic Rankine cycle (BORC) based on thermoeconomic multi-objective optimization considering exergy efficiency and levelized energy cost (LEC). Energy Convers Manag 2015;96:58e71. €rtsila € Company. Engines & generating sets for the marine industry. 2015 [38] Wa [accessed 16.5.15], http://www.wartsila.com/products/marine-oil-gas/ engines-generating-sets/. [39] Le VL, Feidt M, Kheiri A, Pelloux-Prayer S. Performance optimization of lowtemperature power generation by supercritical ORCs (organic Rankine cycles) using low GWP (global warming potential) working fluids. Energy 2014;67:513e26. [40] NIST Standard Reference Database 23. NIST thermodynamic and transport properties of refrigerants and refrigerant mixtures REFROP, version 9.0. 2010. [41] Chen H, Goswami DY, Rahman MM, Stefanakos EK. A supercritical Rankine cycle using zeotropic mixture working fluids for the conversion of low-grade heat into power. Energy 2011;36:549e55. [42] National Institute of Statistics and Economic studies. International prices of heavy fuel oil. 2016 [accessed 21.5.16], http://www.insee.fr/en/bases-dedonnees/bsweb/.