- Email: [email protected]

Contents lists available at ScienceDirect

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

Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid Van Long Le a, *, Abdelhamid Kheiri a, Michel Feidt a, Sandrine Pelloux-Prayer b a b

University of Lorraine, Laboratory of Energetics & Theoretical & Applied Mechanics, 2, avenue For^ et de Haye, 54518 Vandœuvre-l es-Nancy, France EDF-R&D, Eco-Efﬁciency and Industrial Processes Department, Sites des Renardi eres, 77818 Moret-sur-Loing Cedex, France

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 July 2014 Received in revised form 17 October 2014 Accepted 19 October 2014 Available online xxx

This paper carried out the thermodynamic and economic optimizations of a subcritical ORC (Organic Rankine Cycle) using a pure or a zeotropic mixture working ﬂuid. Two pure organic compounds, i.e. npentane and R245fa, and their mixtures with various concentrations were used as ORC working ﬂuid for this study. Two optimizations, i.e. exergy efﬁciency maximization and LCOE (Levelized Cost of Electricity) minimization, were performed to ﬁnd out the optimum operating conditions of the system and to determine the best working ﬂuid from the studied media. Hot water at temperature of 150 C and pressure of 5 bars was used to simulate the heat source medium. Whereas, cooling water at temperature of 20 C was considered to be the heat sink medium. The mass ﬂow rate of heat source is ﬁxed at 50 kg/s for the optimizations. According to the results, the n-pentane-based ORC showed the highest maximized exergy efﬁciency (53.2%) and the lowest minimized LCOE (0.0863 $/kWh). Regarding ORCs using zeotropic working ﬂuids, 0.05 and 0.1 R245fa mass fraction mixtures present the comparable economic features and thermodynamic performances to the system using n-pentane at minimum LCOE. The ORC using R245fa represents the least proﬁtable system. © 2014 Elsevier Ltd. All rights reserved.

Keywords: Organic Rankine cycle (ORC) Waste heat recovery Working ﬂuid mixtures Exergy analysis Thermoeconomic optimization

1. Introduction In many industrial processes, a large amount of energy inputs is often lost as waste heat which is generated as a byproduct and released into the atmosphere. Some investigations [1e4] have estimated that 20e50% of industrial energy input is lost as waste heat. As the industrial sector is pursuing its efforts to improve the energy efﬁciency, capturing and converting industrial heat loss into electricity provides an attractive opportunity for an emission-free and less-costly energy resource. In practice, the most frequently used system for power generation from heat is steam power cycle (classical Rankine cycle). However, this kind of thermodynamic cycle becomes less proﬁtable at low temperature (below 340 C [5]) since low pressure steam requires more voluminous equipments. Furthermore, the shortage of steam superheating may cause partial steam condensation which erodes turbine blades during expansion process.

* Corresponding author. Tel.: þ33 383 595 592; fax: þ33 383 595 551. E-mail address: [email protected] (V.L. Le).

As reported by BCS Inc. [5], approximately 60% of industrial heat loss has its temperature lower than 230 C and nearly 90% lower than 316 C. Unfortunately, this abundant heat source cannot be proﬁtably converted into electricity by classical Rankine cycle because of the reasons described above. Since several decades, the ORC (Organic Rankine Cycle) technology has often been used for power production from low-grade heat source. The ORC operates in a similar way to the steam Rankine cycle, but uses an organic compound instead of water as working ﬂuid. As many organic compounds have a lower boiling point temperature and a higher vapor pressure than water, this enables low-temperature waste heat recovery by the ORC. Indeed, the major advantage of ORC in comparison to steam Rankine cycle for low-temperature and smallscale power production is related to the expansion machine. As explained in the work of Badr et al. [6] the steam enthalpy drops across the turbine are relative high due to its low molecular mass (i.e. 18 g/mol) for low power systems with moderate temperature differences across the expander. Indeed, if the whole steam energy is extracted in a single-stage impulse turbine, the turbine blades must have a velocity of about 500 m/s (for maximum turbine efﬁciency) which is more than twice the practical limit, dictated by the

http://dx.doi.org/10.1016/j.energy.2014.10.051 0360-5442/© 2014 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

2

V.L. Le et al. / Energy xxx (2014) 1e17

allowable stresses for most common turbine-wheel materials and constructional techniques. So the blades of single-stage impulse turbine must operate with a lower velocity, resulting in poorer efﬁciencies. The use of multi-stage turbines may resolve this problem, but would lead to higher cost and complicated small turbines. Using organic ﬂuids with higher molecular weights than water can result in greater turbine efﬁciency and thus less costly single stage expanders. Furthermore, the low speciﬁc enthalpy drop of organic vapor requires a higher mass ﬂow rate through the turbine for the same power output. This allows the blades to be larger and satisﬁes the full-admission condition of the turbine, even for small power outputs [6]. The use of a high molecular weight working medium with a sufﬁciently low saturation pressure in the condenser also leads to less disc friction losses. Regarding vapor partial condensation during expansion process, it is interesting to note that many common organic ﬂuids exhibit a vapor saturation curve on the Tes diagram with an approximately zero (isentropic ﬂuid) or positive (dry ﬂuid) slope ds/dT. As a consequence, isentropic expansion of saturated organic vapor results in saturated or superheated vapor, so that erosion of blades is avoided. In addition, the ORC technology also offers other advantages such as simple startup procedures, automatic and continuous operation, simple maintenance procedure, no operator attendance required, long life plant (>20 years) and no need to demineralize water. Therefore, the ORC technology arouses much interest for small to medium size power plant at low temperature. The main drawback of the ORC technology relates to organic working ﬂuids, i.e. their high cost, toxicity, ﬂammability, environmental concerns (ODP e Ozone Depletion Potential, GWP e Global Warming Potential), stability and compatibility. Furthermore, the thermal efﬁciency of the ORC is often lower than that of the steam Rankine cycle. Therefore, many studies have been carried out to ﬁnd out suitable operating ﬂuids for the ORC applications. Many cycle conﬁgurations such as subcritical, supercritical [7e12], dual pressure [13,14] and trilateral ﬂash cycle [15e17] have been also investigated to improve the performance and the proﬁtability of the plant. In practice, the subcritical ORC in which the saturated or slightly superheated vapor is expanded across a turbine is often used for waste heat recovery due to its simplicity. The single chemical compounds (pure ﬂuids) are often used as operating medium of subcritical ORC. However, this kind of ORC working ﬂuid has the disadvantage that the evaporation and condensation processes occur isothermally. This results in larger irreversibilities in the heat transfer processes due to bad temperature proﬁle matches between ORC working ﬂuid and external ﬂuids (heat source and sink media). Using a zeotropic mixture as ORC working medium can partially solve this problem. For the ORC optimization, the exergy efﬁciency should be used instead of thermal efﬁciency to be the objective function, because the thermal efﬁciency cannot reﬂect the ability to convert energy from low-grade waste heat into usable work [18]. In practice, many indicators have been used as objective function for ORC optimization. Wang et al. [19] optimized the exergy efﬁciency for different cogeneration power plants in cement industry. In the work of Dai et al. [18], the exergy efﬁciency was maximized for the performance evaluation of the ORC using different working ﬂuids. Roy et al. [20] carried out parametric optimization of a waste heat recovery system based on organic Rankine cycle using three indicators: net power output, ﬁrst- and second-law efﬁciencies. In the study of Shengjun et al. [8] ﬁve indicators, i.e. thermal efﬁciency, exergy efﬁciency, recovery efﬁciency, heat exchanger per unit power output and the Levelized Energy Cost, were used for the parametric optimization of subcritical ORC and transcritical power cycle system. In the part A of Astolﬁ et al. [21] the plant efﬁciency (or equivalently the net power output or second-law efﬁciency) of

binary geothermal power plants was optimized for a given geothermal source. In the part B of Astolﬁ et al. [22], the speciﬁc plant investment cost of binary ORC power plants represents the objective function to be minimized. Toffolo et al. [23] realized a thermodynamic optimization using net power output as objective function together with an economic evaluation validated on real cost data. The aim of this work is to present thermodynamic and economic optimizations of subcritical ORCs using pure and zeotropic working ﬂuids for industrial waste heat recovery at low temperature (150 C). The comparison of ORCs using different working ﬂuids under their optimization conditions was also discussed in this paper. 2. Working ﬂuids Many organic chemical compounds have been studied and used as ORC working ﬂuid for electricity generation at low temperature over the last decades. However, due to environmental concerns, i.e. the ozone layer depletion and the climate change, many synthetic chemicals were and will be phased out in the future. Recently, to control emissions from ﬂuorinated greenhouse gases (F-gases), including Hydroﬂuorocarbons (HFCs), the European Union has adopted two legislative acts, i.e. the ‘MAC Directive’ on air conditioning systems used in small motor vehicles, and the ‘F-gas Regulation’ which covers all other key applications in which F-gases are used [24]. While the ‘MAC Directive’ [25] prohibits the use of Fgases with a GWP being higher than 150 in all new cars and vans produced from 2017, the ‘F-gas Regulation’ [26] follows two tracks of action: Improving the prevention of leaks from equipment containing F-gases. Avoiding the use of F-gases where environmentally superior alternatives are cost-effective. As a consequence, many efforts have been made to ﬁnd alternatives to replace these ﬂuids while improving cycle performance. One of the most attractive ways to solve this problem is to use zeotropic mixtures instead of single (pure) chemical compounds as ORC working ﬂuid. The working ﬂuid mixture is characterized by a temperature glide during phase change at constant pressure. The term “temperature glide” describes the temperature difference between the saturated vapor temperature and the saturated liquid temperature of the mixture. This is considered as an advantage in comparison to the pure ﬂuid because it provides better temperature matches between the working ﬂuid and the heat source and the heat sink media. This thus reduces the irreversibilities associated with heat transfer processes and increases the cycle efﬁciency. Moreover, as the working ﬂuid mixtures are manufactured by mixing together different chemical components, these components may be selected in order to tailor the favorable characteristics (e.g. the GWP, the ﬂammability, the toxicity) and thermo-physical properties (e.g. critical temperature and pressure, temperature glide) to ﬁt a particular Rankine cycle system design and application. In this study, two pure organic compounds, i.e. R245fa and npentane, and their mixtures with various concentrations as described in Ref. [27] were used as ORC working ﬂuid. The thermodynamic and transport properties for studied working ﬂuids were generated using NIST Standard Reference Database, REFPROP version 9.1 [28]. The thermo-physical properties and environmental data of R245fa and n-pentane are shown in Tables 1 and 2, while the characteristics of their mixtures are presented in Table 3. Fig. 1 shows the Tes diagrams of R245fa, n-pentane and their

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

V.L. Le et al. / Energy xxx (2014) 1e17 Table 1 Thermo-physical data of pure working ﬂuids. Fluid

Molecular MM Tb Tcrit formula (kg/kmol) ( C) ( C)

R245fa C3H3F5 Pentane C5H12 a

134.05 72.15

3

Table 3 Characteristics of working ﬂuid mixtures [27].

DHvapa ds/dT Pcrit Dcrit (bar) (kg/m3) (kJ/kg)

15.1 154.0 36.5 36.1 196.6 33.7

516.1 232.0

193.3 370.1

Dry ﬂuid Dry ﬂuid

Heat of vaporization at 20 C.

Mass fraction DTglidea ( C) Pcrit Representative (%) chemical (bar) components (A þ B) A B Min Max Pentane þ R245fa a b

mixtures with various concentrations. All these ﬂuids present a positive slope (ds/dT) of vapor saturation curve on the Tes diagram. Mixtures bubble point temperature at the atmospheric pressure is in the range of 10e29 C (cf. Table 3).

30e95 70e5 4.8

8.2

Tbb ( C)

GWP (100 yr.) Min

Max

34e37 10e29 75.25 728.5

Temperature glide at the atmospheric pressure. Bubble point temperature.

basic equations of energy analysis for ORC system are described as follow: Pumping process Pump isentropic efﬁciency

3. Thermodynamic modeling In a basic ORC (Fig. 2), the working ﬂuid is ﬁrst compressed to high pressure (evaporating pressure) from the saturated liquid at low pressure (condensing pressure). It is then heated, vaporized or even superheated by absorbing the energy from the heat source (e.g. hot water) in the evaporator (high-pressure heat exchanger). In next step, the working medium releases its energy to drive the turbine blades during the expansion process. The turbine is coupled with an electrical generator to transform the mechanical energy into electricity which can be used for the internal demand or injected into the national power grid. Finally, the working ﬂuid is cooled down and condensed by the cooling water in the condenser (low-pressure heat exchanger) before being pumped again to the evaporator. Several assumptions for ORC modeling in this paper are described below.

p

his ¼

his p;out hp;in hp;out hp;in

(1)

Pump power input

_ p ¼ m_ W wf hp;out hp;in

(2)

The pump motor efﬁciency is calculated from Ref. [29]

h i2 _ p 1:5 log _ hmotor ¼ 75 þ 11:5 log10 W 10 W p

(3)

Motor power input Each process of the cycle is considered as a steady-state and adiabatic process, Heat and friction losses in the connecting pipes and the heat exchangers are neglected, Potential and kinetic energy of the media are neglected, Heat transfer is calculated for the fully developed ﬂow, Shell and tube heat exchanger is considered with standard type E shells (Courtesy of the Tubular Exchanger Manufacturers Association), single-cut segmental bafﬂes and un-ﬁnned tubes. The given parameters for the ORC modeling are described in Table 4. The pinch point positions of heat transfer processes at high and low pressure in the ORC for pure working ﬂuids are often at the beginning of phase change processes of the working ﬂuid as shown in Fig. 3. In the case of zeotropic mixture ﬂuid, due to the ﬂuid temperature glides during evaporating and condensing processes, pinch points may be either located at the beginning or at the end or both of phase change processes of the working ﬂuid as shown in Fig. 4.

_p h _ elec ¼ W W motor p

(4)

High-pressure heat transfer process

evap ¼ m_ h ðhhsi hhso Þ h Q_ h ¼ m_ wf hevap wf ;out wf ;in

(5)

Expansion process Turbine isentropic efﬁciency

htis ¼

ht;in ht;out ht;in his t;out

(6)

3.1. Energy analysis model Energy analysis is based on the ﬁrst law of thermodynamics which is basically a statement of the conservation of energy. The

Table 2 Safety and environmental data of pure working ﬂuids. Fluid

TAuto NFPA classiﬁcation ODP GWP Atmospheric Price ($/kg) ( C) (100 life (yr.) Health Flammability Reactivity yr.)

R245fa 412 2 Pentane 260 2

0 4

1 0

0 0

1030 7.7 <25 N.A

37 2

Fig. 1. Tes diagrams of n-pentane, R245fa and their mixtures.

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

4

V.L. Le et al. / Energy xxx (2014) 1e17

Fig. 3. Pinch points positions in heat transfer processes for ORC using pure working ﬂuid. Fig. 2. Scheme of waste heat to power plant driven by an ORC.

3.2. Exergy analysis model

Turbine power output

_ t ¼ m_ W wf ht;in ht;out

(7)

Generator power output

_ elec ¼ h W _t W gen t

(8)

Condensation process

cond _ Q_ c ¼ m_ wf hcond wf;in hwf ;out ¼ mc ðhcso hcsi Þ

(9)

ORC system Net mechanical power output

_ tW _p _ net ¼ W W

(10)

Net electrical power output

_ elec W _ elec _ elec ¼ W W net t p

(11)

The loss of useful (noble) energy of the system or device cannot be justiﬁed by the ﬁrst law of thermodynamics, because it does not distinguish the quality and quantity of energy. Over last decades, the exergy analysis (availability analysis), based on the second law of thermodynamics, has been found to be a useful method in the design, evaluation, optimization and improvement of energy systems. Thanks to exergy analysis method, the location, cause and true magnitude of energy resource waste and loss can be determined [30]. In the exergy analysis method, the temperature (T0) and pressure (p0) of the environment (dead state) are often taken as standard-state values (i.e. 25 C and 1 atm, respectively) for computational ease. However, these properties may be speciﬁed differently depending on the application [30]. In the current work, the heat sink inlet temperature (20 C) and the atmospheric pressure (1 atm) are respectively selected as the dead state temperature and pressure. 3.2.1. Exergy balance The equations for ORC exergy analysis are presented below. Pumping process _ p , for pumping The supplied exergy (pump power input), W process is calculated by equation (2) Useful exergy (Exergy received by the ﬂuid)

First-law efﬁciency (thermal efﬁciency)

. _ net Q_ hI ¼ W h

(12)

Table 4 Given parameters for ORC modeling. Isentropic efﬁciency of pump and turbine, his (%) Electrical generator efﬁciency, hgen (%) Heat source and sink media Heat source inlet temperature, Thsi ( C) Heat sink inlet temperature, Tcsi ( C) Heat source inlet pressure, Phsi (bar) Heat sink inlet pressure, Pcsi (bar) Heat source mass ﬂow rate, m_ h (kg/s)

80 95 Water 150 20 5 2 50

Fig. 4. Pinch points positions in heat transfer processes for ORC using the zeotropic working ﬂuid.

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

V.L. Le et al. / Energy xxx (2014) 1e17

_ p ¼ m_ Ex wf hp;out hp;in T0 sp;out sp;in

(13)

3.2.2. Exergy efﬁciency The exergy efﬁciency of a system or device can be calculated by the following equation [31,32]

(14)

hEx ¼

Destroyed exergy in the pump

I_p ¼ T0 m_ wf sp;out sp;in

5

_ Ex useful _ Ex

(26)

available

High-pressure heat transfer process Exergy supplied by the heat source (exergy change in the heat source)

_ ¼ m_ ½h h Ex h h hsi hso T0 ðshsi shso Þ

(15)

Exergy received by the working ﬂuid

h i evap evap evap evap _ evap ¼ m_ Ex wf hwf ;out hwf ;in T0 swf ;out swf ;in wf

(16)

As mentioned in the work of Hasan et al. [33], available exergy, _ Ex available , of the ORC system in equation (26) could be the heat source inlet exergy or the exergy change in the heat source. In this paper, available exergy of the ORC is considered to be the exergy change in the heat source as given in equation (15), and useful _ exergy, Ex useful , is considered to be the net mechanical power output of the system as given in equation (10). Thus, the exergy efﬁciency of ORC system is calculated as follow:

hEx ¼

_p _ tW W _ Ex

(27)

h

Destroyed exergy in the heat exchanger

h i þ m_ h ðshso shsi Þ sevap I_evap ¼ T0 m_ wf sevap wf;out wf;in

(17)

hWHR ¼

Expansion process Available exergy

_ t ¼ m_ W wf ht;in ht;out

(18)

_ _ Ex hsi ¼ mh ½hhsi h0 T0 ðshsi s0 Þ

(19)

In this study, the sum of total ﬂow rate of the irreversibility, I_tot , _ c , in and ﬂow rate of the exergy received by the cooling water, Ex condensation process is considered to be the total exergy loss of the _ tot . ORC, Ex loss

_ c _ tot ¼ I_tot þ Ex Ex loss

Destroyed exergy in the turbine

I_t ¼ T0 m_ wf st;out st;in

(20)

Condensation process Exergy supplied to the cooling water

h i cond cond cond cond _ _ Ex cond ¼ mwf hwf ;in hwf ;out T0 swf ;in swf;out

_ c ¼ m_ c ½hcso h T ðscso s Þ Ex 0 csi csi

(21)

(23)

ORC system The total ﬂow rate of the irreversibility in the ORC system is the sum of destroyed exergy ﬂow rate in the components.

I_component

(30)

4. Economic model and optimizations

Shell-and-tube heat exchanger is commonly chosen for the heat exchangers in this work. Fig. 5 shows the generic geometry of shell and tube heat exchanger. While several heat exchanger parameters are given in Table 5, several other parameters can be modiﬁed later to satisfy the pressure constraints. Some guidelines can be considered for heat exchanger design as follow [34]

(22)

Destroyed exergy in the condenser

h i I_cond ¼ T0 m_ wf swf;out swf;in þ m_ c ðscso scsi Þ

(29)

4.1. Heat exchanger surface area calculation

Exergy received by the cooling water

Tube pitch, PT, is usually chosen so that the pitch ratio PT/do is either 1.25, 1.33 or 1.5 It is desirable to maintain the liquid velocity in the tubes in the range of 0.91e2.44 m/s (3e8 ft/s) The spacing between adjacent bafﬂes, B, should be between 0.2 and 1.0 shell diameter Ds The equations for heat transfer surface area calculation of shelland-tube heat exchanger are described as follow. Heat transfer rate, Q_

(24)

Q_ ¼ UAFðDTlm Þ

(25)

where U is the overall heat transfer coefﬁcient; A is the heat transfer surface area; F is the LMTD (logarithmic mean temperature difference) correction factor; DTlm is the logarithmic mean temperature difference.

Exergy balance of ORC system

_p¼W _ t þ Ex _ c þ I_tot _ þW Ex h

(28)

The ﬂow rate of heat source inlet exergy is computed by

Useful exergy

X

_p _ tW W _ Ex hsi

_ t ¼ m_ Ex wf ht;in ht;out T0 st;in st;out

I_tot ¼

The ratio of the useful exergy (net mechanical power output) of _ the ORC to the heat source inlet exergy, Ex hsi , is considered to be the exergy recovery ratio, hWHR, and calculated as follow

(31)

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

6

V.L. Le et al. / Energy xxx (2014) 1e17

Fig. 5. Shell and tube heat exchanger geometry.

The reference heat transfer area, A, is computed from

A ¼ Ao ¼ pdo LNt

(32)

where Nt is the number of tube of the heat exchanger; do is the outer diameter of tube; L is the tube length. The overall heat transfer coefﬁcient, U, is calculated by equation (33) [35]

U¼

Rf;i do do lnðdo =di Þ do 1 þ Rf ;o þ þ þ 2k ao ai di di

1 (33)

where ai and ao are heat transfer coefﬁcient inside and outside tubes, respectively; k is the ﬂuid thermal conductivity; do and di are outer and inner diameters of tubes; Rf,i and Rf,o are fouling factors inside and outside tubes, respectively. The total fouling resistance in the heat exchanger is calculated from the fouling resistance inside and outside tubes

4.1.1. Heat transfer and pressure drop in shell-side The shell-side heat transfer coefﬁcient is calculated by the BelleDelaware method as described in Ref. [37]. The shell-side heat transfer coefﬁcient, as, is given as [38]

as ¼ aid Jc Jl Jb Js Jr

where aid is the heat transfer coefﬁcient for pure cross-ﬂow in an ideal tube bank; Jc is correction factor for bafﬂe window ﬂow; Jl is the correction factor for bafﬂe leakage effects; Jb is the correction factor for bundle bypass effects; Jr is the laminar ﬂow correction factor; Js is the correction factor for unequal bafﬂe spacing. The combined effect of all these correction factors for a reasonable well-designed shell-and-tube heat exchanger is approximately 0.6 [37]. This value is used in the present paper for shell-side heat transfer calculation. The heat transfer coefﬁcient for pure cross-ﬂow in an ideal tube bank is calculated with Ref. [37]:

aid ¼ ji Cps Rf;i do Rf ¼ þ Rf;o di

DTlm

_ 2=3 0:14 ks ms ms As Cps ms mw s

(37)

(34)

The data of fouling resistances are given in Table 5. The logarithmic mean temperature difference, DTlm, is calculated as follow:

(36)

The subscript “s” and the superscript “w” stand for the shell side and the wall, respectively. The Colburn j-factor for an ideal tube bank is calculated in equation (38)

Th;out Tc;in Th;in Tc;out ¼ ln Th;out Tc;in = Th;in Tc;out

ji ¼ a1 (35)

The LMTD (logarithmic mean temperature difference) correction factor F in equation (31) is computed as described in Ref. [36].

a

ðRes Þa2

(38)

where PT is the tube pitch.

a¼ Table 5 Shell and tube heat exchanger data.

1:33 PT =do

a3 1 þ 0:14ðRes Þa4

(39)

Tube diameter (BWG 20) Inner tube diameter, di (mm) Outer tube diameter, do (mm)

12.7 10.92

The constants a1, a2, a3 and a4 are found as described in Ref. [37]. The shell-side pressure drop is calculated by the following equation

Pressure drop allowance (bar) Shell side Tube side

0.5 0.2

Dps ¼

2

Fouling factor (m C/W) [35] Hot water Cold water Refrigerant (liquid) Refrigerant (vapor) Total fouling resistance with two-phase ﬂow in the tube and liquid in the shell [62]

1.761 104 1.761 104 1.761 104 3.522 104 0.67 103

fG2s ðNb þ 1ÞDs 0:14 2rDe ms mw s

(40)

where Nb is the number of bafﬂe, Nb ¼ L/B 1; Gs is the shell-side _ s ; As is the bundle cross ﬂow area, mass velocity, Gs ¼ m=A As ¼ (DsCB)/PT. The shell-side equivalent diameter is calculated for square tube pitch

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

V.L. Le et al. / Energy xxx (2014) 1e17

De ¼

. 4 PT2 pd2o 4

f ¼ 64=Re

(49)

(41)

pdo

4.1.2.2. Heat transfer and pressure drop for two-phase ﬂuid

The friction factor for the shell is calculated from

f ¼ exp½0:576 0:19 lnðRes Þ

(42)

where

400 < Res 106

4.1.2. Heat transfer and pressure drop in tube side 4.1.2.1. Heat transfer and pressure drop for single-phase ﬂuid. The Gnielinski correlation [39] is used to predict the heat transfer coefﬁcient for single-phase ﬂuid in smooth tube

Nu ¼

7

ðf =8ÞðRe 1000ÞPr 1 þ 12:7ðf =8Þ0:5 Pr 2=3 1

(43)

Two-phase heat transfer coefﬁcient calculation The two-phase zone is in present work divided into 50 segments (Discretization Method) subjected to an identical heat transfer rate DQ_ for heat transfer calculation. The results of heat transfer calculation with 50-segments discretization were compared to the results obtained by the calculation with more segment numbers (100, 200, and 350) discretization. The comparison showed that the differences were lower than 1%. The correlations estimating the heat transfer coefﬁcients for ﬂow boiling and condensation are described below. - Flow boiling The correlation of GungoreWinterton (1987) [41] is used to predict the heat transfer coefﬁcient for ﬂow boiling process in horizontal tube. The two-phase heat transfer coefﬁcient, aTP, is computed from

aTP ¼ Eal k a ¼ Nu D

(44)

where a is the heat transfer coefﬁcient; Nu is the Nusselt number; k is the ﬂuid thermal conductivity; D is the tube diameter. The correlation is valid for

0:5 Pr 2000

The enhancement factor, E, is calculated by equation (51)

x 0:75 r 0:41 l E ¼ 1 þ 3000Bo0:86 þ 1:12 1x rv

The friction factor in equation (43) is obtained from the correlation of Petukhov [40] for the smooth tube

f ¼ ½0:790 lnðReÞ 1:642

(45)

(51)

Single-phase liquid heat transfer coefﬁcient, al, is calculated from the DittuseBoelter [42] correlation:

D 0:8 ðPrÞ0:4 kl al ¼ 0:023 Gð1 xÞ ml D

3 103 < Re < 5 106

(50)

(52)

where G is the mass velocity; x is the vapor quality. The boiling number, Bo, in equation (51) is calculated by following equation

Bo ¼ qG DHvap

(53)

With

104 < Re < 5 106 The frictional pressure drop, DPfrict, for tube-side ﬂuid is calculated as follow

DPfrict ¼ f

LrV 2 2D

Fr ¼ Npt

(46)

Npt

where is the number of tube passes; V is the ﬂuid velocity. In addition, the change of direction in the passes introduces an additional pressure drop, DPr, due to sudden expansions and contractions that the tube ﬂuid experiences during a return. This is calculated by equation (47)

DPr ¼

rV 4Npt

2

(47)

2

Therefore, the total pressure drop for tube-side ﬂuid becomes

DPtube ¼

f

LNpt D

If the tube is horizontal and the Froude number calculated by equation (54) is less than 0.05 then E should be multiplied by E2 calculated with equation (55)

! þ 4Npt

rV 2 2

(48)

where the friction factor f is calculated by equation (45) for fully developed turbulent ﬂow. For fully developed laminar ﬂow the friction factor is calculated by equation (49)

G2 ðrl Þ2 gD

E2 ¼ Fr ð0:12FrÞ

(54)

(55)

The contribution of nucleate boiling in GungoreWinterton correlation is corrected for mixture utilizing Thome [43] nucleate pool boiling equation as presented in Ref. [44]

FC ¼

1

aI Bo q DTglide 1 exp 1þ rl DHvap bl q

(56)

where aI is the ideal heat transfer coefﬁcient calculated with the GungoreWinterton correlation without mixture effects but with the mixture physical properties; DTglide is the temperature glide; Bo is a scaling factor assumed to be 1.0 (i.e. the theory assumes all heat transfer at a bubble interface is latent heat); q is the local heat ﬂux attributable to nucleate boiling; bl is the liquid phase mass transfer coefﬁcient that can be assumed to have a constant value of 0.0003 m/s.

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

8

V.L. Le et al. / Energy xxx (2014) 1e17

The GungoreWinterton correlation is now modiﬁed as the enhancement factor, E, includes the mixture correction factor applied to the boiling number (which models the nucleate boiling contribution to the ﬂow boiling process)

h x i0:75 r 0:41 l E ¼ 1 þ 3000ðBoFC Þ0:86 þ 1:12 1x rv The

rest

of

correlation

remains

the

same

as

(57) before.

- Condensation Shah (2009) [45] correlation is in the present work used to predict the heat transfer coefﬁcient for the condensation process in plain tubes. According to this empirical correlation, there are two heat transfer regimes during the condensation in plain tube. The equations of two-phase heat transfer coefﬁcient, aTP, for each regime are presented below: In regime I (turbulent regime)

aTP ¼ aI

(58)

In regime II (mixed regime)

aTP ¼ aI þ aNu

(59)

where aI and aNu are calculated by the following correlations

ð0:0058þ0:557pr Þ 3:8 ml aI ¼ aLS 1 þ 0:95 14mv Z

aNu ¼

ð1=3Þ 1:32ReLS

" #1=3 rl ðrl rv Þgðkl Þ3 ðml Þ2

aLS

(60)

(61)

xG ½gDrv ðrl rv Þ0:5

(66)

amono is the condensing heat transfer coefﬁcient calculated with mixture properties using the Shah (2009) correlation for pure ﬂuids. aVS is the superﬁcial heat transfer coefﬁcient of the vapor phase, i.e. assuming vapor phase to be ﬂowing alone in the tube, calculated by the following equation. aVS ¼ 0:023

VVS rv D 0:8 ðPrv Þ0:4 kv mv D

(67)

GxD 0:8 ðPrv Þ0:4 kv mv D

(68)

Or

aVS ¼ 0:023

Two-phase pressure drop calculation The two-phase pressure drop (DP) of ﬂuid ﬂows inside the tubes is the sum of three contributions: the static pressure drop DPstat, the momentum pressure drop DPmom and the frictional pressure drop DPfrict The static pressure drop is given by

(69)

For a horizontal tube, there is no change in static head, i.e. H ¼ 0 so DPstat ¼ 0. The two-phase momentum pressure drop reﬂects the change in ﬂow kinetic energy and is calculated using a void fraction obtained from drift ﬂux model, as described by Didi et al. (2002) [47]

("

DPmom ¼ G

ð1 xÞ2 x2 þ rl ð1 3 Þ rv 3

"

#

out

ð1 xÞ2 x2 þ rl ð1 3 Þ rv 3

# ) in

(70)

(62)

The boundary between regimes I and II is given by the following relation. Regime I occurs when Jv 0.98(Z þ 0.263)0.62, where Jv is the dimensionless vapor velocity deﬁned by equation (63)

Jv ¼

DTglide DHvap

DPstat ¼ rtp gH sin q

The heat transfer coefﬁcient assuming liquid phase ﬂowing alone in the tube, aLS, is calculated by DittuseBoelter [42] correlation

k ¼ 0:023ðReLS Þ0:8 ðPrl Þ0:4 l D

YV ¼ xCpv

The void fraction, 3 , is obtained from the Steiner version of drift ﬂux model of Rouhani and Axelsson [48] for horizontal tubes

3

x ¼ rv

(63)

(

x 1x þ ½1 þ 0:12ð1 xÞ rv rl )1 1:18ð1 xÞ½gsðrl rv Þ0:25 þ Gr0:5 l

(71)

Z is Shah's correlating parameter calculated by equation (64)

Z ¼ ð1=x 1Þ0:8 ðpr Þ0:4

(64)

The Bell and Ghaly (1973) [46] method is used to correct the predictions of Shah (2009) [45] for mixture condensation in plain tubes. According to this method, the condensation heat transfer coefﬁcient, amix, of zeotropic mixtures in the plain tubes is calculated by equation (65)

1 amix where

1

Y ¼ þ V amono aVS

(65)

The two-phase frictional pressure gradient is calculated by the correlation of Müller-Steinhagen and Heck [49]

dp dz

¼ cð1 xÞ1=3 þ bx3

(72)

frict

where the factor c is

c ¼ a þ 2ðb aÞx

(73)

where a and b are the frictional pressure gradients when all the ﬂow is assumed liquid and vapor, respectively, a and b are obtained from

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

V.L. Le et al. / Energy xxx (2014) 1e17 Table 6 Components of total capital investment. P P CTBM ¼ CBM þ Cspare þ Cwf Csite ¼ 0.05CTBM Cserv ¼ 0.05CTBM Calloc

Total bare module cost, CTBM Cost of site preparation, Csite Cost of service facilities, Cserv Allocated costs for utility plants and related facilities Total direct permanent investment, CDPI Cost of contingencies and contractor's fee, Ccont Total depreciable capital, CTDC Cost of land, Cland Cost of royalties, Croyal Cost of plant startup, Cstartup Total permanent investment, CTPI Working capital, CWC Total capital investment, CTCI

a¼

dp dz

b¼

lo

CDPI ¼ CTBM þ Csite þ Cserv þ Calloc Ccont ¼ 0.18CDPI CTDC ¼ CDPI þ Ccont Cland ¼ 0 Croyal ¼ 0 Cstartup ¼ 0.1CTDC CTPI ¼ CTDC þ Cland þ Croyal þ Cstartup CWC ¼ 0 CTCI ¼ CWC þ CTPI

2G2 ¼ fl di rl

dp 2G2 ¼ fv dz vo di rv

0:079 Re0:25

ZZ

log10 Cp0 ¼ K1 þ K2 log10 ðAÞ þ K3 ½log10 ðAÞ2

(79)

(74)

(75)

0:95 0 _ gen Cp;gen ¼ 60 W

(80)

Bare module factors, FBM, for pumps and heat exchangers are calculated by the following equation

FBM ¼ B1 þ B2 FM FP

(81)

(76)

The two-phase frictional pressure gradient in equation (72) is then integrated to determine the pressure drop from inlet to outlet. Thus [49]

DPfrict ¼

where CBM is bare module equipment cost: sum of direct and indirect costs for each unit as described in Ref. [29]; Cp0 is purchased equipment cost in base conditions: equipment made of the most common material, usually carbon steel, and operating at ambient pressure; FBM is bare module factor. It is necessary to note that all the data for purchased cost of equipment described in Turton et al. [29] were obtained with an average value of the CEPCI (Chemical Engineering Plant Cost Index) of 397. The updated value of 584.6 of CEPCI for the year of 2012 is used in present economic evaluation. The purchased equipment cost for base conditions, Cp0 , is calculated by equation (79)

where A is the capacity or size parameter for the equipment; K1, K2 and K3 are the constants given in Table 7. 0 The purchased equipment cost of the electrical generator, Cp;gen , is calculated with equation (80) as presented in Ref. [51]

The friction factors, fl and fv, are obtained from the corresponding Reynolds number by:

f ¼

9

dP dZ

0

dZ ¼ frict

3 ð1 xÞ4=3 ½a þ 2ðb aÞx 4

1 9 ðb aÞð1 xÞ7=3 þ bx4 4 14

xout

where B1 and B2 are the constants given in Table 7; FM is equipment material factor for pump and heat exchangers found in Table 7; FP is operating pressure factor. Bare module factor for the other equipments can be found in Table 8. The pressure factor, Fp, for the equipment is computed by the following general form

log10 Fp ¼ C1 þ C2 log10 P þ C3 ðlog10 PÞ2

(82)

xin

(77) For the practical design, the allowance pressure drop of the ﬂuids in the shell side and tube side of shell and tube heat exchanger are set to be 0.5 and 0.2 bar, respectively. 4.2. Economic model 4.2.1. Total capital investment The capital cost of a power plant must take into consideration many costs other than the purchased cost of equipment. Table 6 presents a summary of the costs that must be in the present evaluation considered for the total capital cost adapted from Seider et al. [50]. The bare module cost, CBM, for each piece of equipment is calculated by equation (78) as described in Turton et al. [29].

CBM ¼ Cp0 FBM

(78)

The pressure in equation (82) is the relative one which unit is bar gauge (1 bar ¼ 0.0 barg). The pressure factors are always greater than unity. The constants C1, C2 and C3 are given in Table 7. The cost of working ﬂuid, Cwf, is a signiﬁcant addition to the capital cost. The amount of working ﬂuid was in Ref. [52] estimated as the liquid amount to ﬁll the total process (equipments and piping). In the work of Toffolo et al. [23], on the basis of available data from a real isobutane power plant, about 370 kg of isobutane are needed for each kg/s of working ﬂuid. For R134a, these authors assumed that 760 kg of R134a are needed for each kg/s of working ﬂuid. In this work, where the target is to perform economic optimizations, the working ﬂuid amount is assumed to be, for all cases, the liquid amount to ﬁll two times the volumes of heat exchanger sections that working ﬂuid passes through. In addition to bare module costs for each process unit in the ﬂow-sheet, it is often recommended to provide funds for spares, Cspare, especially for liquid pumps, to permit uninterrupted operation when a process unit becomes inoperable. Pumps are relatively

Table 7 Constants for the calculation of bare module cost of equipments [29]. Equipments

K1

K2

K3

C1

C2

C3

B1

B2

Fm

Pump HEX Turbine Pump motor

3.3892 4.3247 2.2476 1.956

0.0536 0.303 1.4965 1.7142

0.1538 0.1634 0.1618 0.2282

0.3935 0.03881 e e

0.3957 0.11272 e e

0.00226 0.08183 e e

1.89 1.63 e e

1.35 1.66 e e

1.6 1.0 e e

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

10

V.L. Le et al. / Energy xxx (2014) 1e17

selling costs and costs for research and development [29]. These costs are considered to be zero for the waste heat to power project in the present economic evaluation.

Table 8 Bare module factors for turbine, pump motor and electrical generator. Equipment

FBM

Reference

Turbine (stainless steel) Pump motor (explosion proof) Electrical generator Working ﬂuid

6.1 1.5 1.5 1.25

[29] [29] [23] [23]

4.2.3. Approximate proﬁtability measures Annual sales revenue Annual operating hours

inexpensive but require frequent maintenance to prevent leaks [50]. Allocated costs, Calloc, in Table 6 are included to provide or upgrade off-side utility plants (i.e. cooling water). The capital investment cost for wet cooling tower plant is estimated as a function of volumetric ﬂow rate of cooling water of about 50 $/gpm (13.2 $/L/ min) as mentioned in Ref. [53]. The cost of land, Cland, is assumed to be zero because the process will be built attached to existing equipment [52]. The cost of royalties, Croyal, is also assumed to be zero in the present work. Working capital funds, CWC, are needed to cover operating costs for the early operation of the plant including the cost of the inventory and funds to cover accounts receivable [50]. The working capital is considered to be zero in this study. 4.2.2. Total production cost The total production cost, CTPC, is the sum of the costs of manufacture, CCOM, and general expenses, CGE.

CTPC ¼ CCOM þ CGE

(83)

The total annual cost of manufacture, CCOM, is the sum of direct manufacturing costs, CDMC, and ﬁxed costs, CFix, that components are presented in Table 9.

CCOM ¼ CDMC þ CFix

(84)

As deﬁned in Refs. [50], the depreciation is simply a measure of the decrease in value of a component over time. Some companies use depreciation cost, CD, as a means to set aside a fund to replace a plant when it is no longer operable. In this paper the depreciation cost for waste heat to power plant is set to be zero. In the present economic evaluation, costs of operators and managers are taken to be zero because the operators and managers that are already hired for the process from which heat source originates can handle ORC unit. In addition, operating overhead is taken to be zero because those costs would be incorporated into plant operations and not the operation of this speciﬁc process [52]. General expenses, CGE, i.e. costs associated with management level and administrative activities not directly related to the manufacturing process, include administration costs, distribution, Table 9 Direct manufacturing cost and ﬁxed cost. Components

Formula

Direct costs Utilities

Direct manufacturing costs Cooling water

CDMC 14.8$/1000m3

Wages and beneﬁts Salaries and beneﬁts Materials and services Maintenance overhead

CWB ¼ 0.035CTDC CSB ¼ 0.25CWB CMS ¼ CWB CMO ¼ 0.05CWB

Fixed costs

Fixed manufacturing costs

CFix

Property taxes and insurance

Cost of property taxes and liability insurance

CPI ¼ 0.02CTDC

(85)

Annual electricity generation

_ elec Mel ¼ Hannual W net

(86)

Annual sales revenue

Sannual ¼ Mel Cel

(87)

Assuming that all power generated by ORC system is used internally, the annual sales revenue corresponds to the reduction of company's energy bills. Therefore, the electricity price, Cel, in equation (87) may be considered as the electricity price for industrial consumers. This price is respectively 0.0682 $/kWh [54] and ~0.11 $/kWh by the year 2012 in USA and in France. Therefore, an electricity price of 0.1 $/kWh is used in the present work. The corporate tax rate, tcorp, of 33.33% (France) [55] is considered in the present work. Simple Return On Investment (ROI) The return on investment is calculated by the following equation [50]

ROI ¼

1 tcorp ðSannual CTPC Þ net earnings ¼ total capital investment CTCI (88)

Simple Payback Period (PBP) Payback period is the time required, after start-up, for the annual earnings to equal the original investment. Because it is simple and even more understandable than ROI, PBP is widely used in early evaluations to compare alternatives [50].

PBP ¼

CTDC CTDC ¼ cash flow ð1 tÞðSannual CTPC Þ þ CD

(89)

Levelized Cost Of Electricity e LCOE The Levelized Cost of Electricity of the project is calculated by equation (90) as described in Ref. [56]

LCOE ¼

Costs

Maintenance

Hannual ¼ 0:9 365 24

P CTCI þ nt¼1 CTPC t ð1þiÞ Pn Mel

(90)

t¼1 ð1þiÞt

where LCOE is Levelized Costs of Electricity in $/kWh; Mel is electricity output in year t in kWh; i is annual interest rate (discount rate) and set to 7% [23]; n is economical lifetime of plant and set to be 20 years; t is the year of operation (1,2,…,n) 4.3. Optimizations and constraints Two optimizations are performed in this paper, i.e. the exergy efﬁciency maximization and the LCOE minimization. The

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

V.L. Le et al. / Energy xxx (2014) 1e17

11

optimizations were performed by one of built-in multi-dimensional optimization methods, i.e. conjugate direction method, Variable Metric Method, Nelder-Mead Simplex Method, DIRECT Optimization Algorithm and Genetic Method, integrated in EES software [57]. The boundaries of independent variable range are chosen considering the following constraints. The evaporating temperature must be lower than the critical temperature of working ﬂuid and higher than the condensing temperature. The temperature of working ﬂuid exiting high-pressure heat exchanger (working ﬂuid highest temperature) must be lower than or equal to the difference between heat source inlet temperature and pinch value of high-pressure heat transfer process. The highest temperature of working ﬂuid must be lower than its applicable maximum temperature (e.g. lower than the applicable maximum temperature of working ﬂuid in REFPROP). The temperature of working ﬂuid exiting low-pressure heat exchanger (i.e. the condensing temperature or the bubble point temperature at low pressure for the mixtures in the current paper) must be higher than or equal to the sum of heat sink inlet temperature and pinch value of low-pressure heat transfer process. The saturation pressure at condensing temperature should be similar to or greater than the atmospheric pressure (1 atm) to prevent air penetration [58]. The vapor quality of working ﬂuid exiting the turbine must be greater than 0.95 to avoid droplet erosion of turbine blades. 5. Results and discussions 5.1. Exergy efﬁciency maximization The exergy efﬁciency, hEx, maximization is led with the Conjugate Directions Method in EES software [57]. This method is sometimes called the Direct Search method or Powell's method. The basic idea of this method is to use a series of one-dimensional searches to locate the optimum. In its simplest form, EES will hold all but one of the optimization variables constant, and then vary the single remaining variable in order to locate the value at which the objective function is maximized (or minimized) along the onedimensional path. This process is repeated for each independent variable as many times as necessary to achieve the stopping criteria (relative convergence tolerance is set to be 109). The optimization results obtained by this method were also validated by the DIRECT Optimization Algorithm and Genetic Method. These methods are the two other methods integrated in EES and designed to locate a global optimum when local optima exist in the search region. The same results were obtained by three methods but it is very much faster with the Conjugate Directions Method. In the case of exergy efﬁciency maximization, three optimization variables were considered, i.e. evaporating and condensing temperatures (bubble point temperature at high and low pressure for zeotropic mixtures, respectively), and superheating degree of the working ﬂuid entering the turbine. Regarding the pinch values of heat transfer processes at high and low pressures, they are in the current paper set to be 5 C for ORC exergy efﬁciency optimization. Performing the exergy efﬁciency maximization with three variables above, and considering the constraints as previously described, the results show that at maximum exergy efﬁciency, the evaporating temperature is between the boundaries (lower and upper limits) of its variable range at maximum exergy efﬁciency. The condensing temperature and the superheating degree are found to be at the lower limits of their variable ranges for the

Fig. 6. Exergy efﬁciency variation by considering evaporating and condensing temperature (for ORC using R245fa).

maximum exergy efﬁciency. As shown in Fig. 6, the maximum ORC exergy efﬁciency is, in the case with R245fa, reached with an evaporating temperature of 119.8 C (this value situates between the lower and upper limits) and with the lowest possible value (lower limit of variable range) of condensing temperature. Fig. 7 presents the exergy efﬁciency variation (for ORC using R245fa) as a function of the evaporating temperature and the superheating degree of the working ﬂuid entering the turbine. The maximum exergy efﬁciency is obtained with an evaporating temperature of 119.8 C and the lowest superheating degree (i.e. without superheating). Indeed, when carrying out the exergy efﬁciency optimization for the ORC using different working ﬂuids in this work, the maximum exergy efﬁciency is always obtained with the lowest (lower limit of optimization variable range) condensing temperature (i.e. 30 C in the present case), without superheating the ﬂuid entering the turbine, and with evaporating temperature as presented in Table 10. Comparing the results of the exergy efﬁciency maximization carried out for the ORC using pure compounds (i.e. R245fa and npentane) and their mixtures, the exergy efﬁciencies are the highest for the cycle using two pure working ﬂuids (Fig. 8), the lowest

Fig. 7. Exergy efﬁciency variation by considering evaporating temperature and superheating degree of the working ﬂuid entering the turbine (for ORC using R245fa).

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

12

V.L. Le et al. / Energy xxx (2014) 1e17

Table 10 Operating conditions of ORCs at maximum exergy efﬁciency. R245fa mass fraction

Tevapa ( C)

Pevap (bar)

Pcond (bar)

Thso ( C)

Tcso ( C)

m_ wf (kg/s)

m_ c (kg/s)

DTglideb

0 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1

125.5 126.2 126.1 125.2 123.8 122.4 121.1 119.9 118.9 119.8

10.11 11.46 12.62 14.51 16.00 17.17 18.07 18.78 19.33 19.20

0.82 1.05 1.25 1.56 1.79 1.93 2.01 2.06 2.08 1.78

111.9 113.2 113.1 111.2 108.2 104.8 101.0 96.8 92.4 94.9

26.0 33.6 38.7 44.6 46.6 45.8 43.1 38.7 32.7 25.6

15.87 15.62 16.01 17.82 20.54 24.05 28.5 34.13 41.02 48.08

275.1 119.6 87.28 70.29 70.1 77.84 94.19 126.2 199.9 430.7

0 6.3 10.6 15.6 17.4 17.0 14.8 11.1 6.1 0

a b

( C)

Bubble point temperature at high pressure in the case of mixtures. Temperature glide at the condensing pressure.

exergy efﬁciency is found for the ORC using 0.3 R245fa mass fraction mixture. It is interesting to note that the maximum exergy efﬁciency of the ORC using mixtures ﬂuids varies in a counter direction to the mixture temperature glide at the low pressure (condensing pressure). The highest (resp. lowest) maximized exergy efﬁciency is found with the ORC using the working ﬂuid mixture featuring the smallest (resp. largest) temperature glide. As shown in Fig. 8, although the maximum exergy efﬁciency of the ORC using n-pentane is slightly higher than the exergy efﬁciency of the cycle using R245fa, the exergy recovery ratio, hWHR, is higher for the ORC using R245fa. The highest value of the exergy recovery ratio is obtained for the cycle using the 0.7 R245fa mass fraction mixture. Regarding the ratio of the total irreversibility rate, I_tot , to the net _ net , some studied zeotropic mixtures mechanical power output, W present a slightly lower value of this ratio compared to the pure working media (cf. Fig. 9). This means that the total irreversibility generated by entropy generation in the cycle using these ﬂuid mixtures is lower than that the one created in a cycle using pure media for the same power output. However, if the exergy ﬂow rate _ c , is taken into account as exergy received by the cooling water, Ex loss, then the ratio of the sum of the total irreversibility rate and the exergy ﬂow rate absorbed by the cooling water to the net power output is always higher for the ORC using mixtures ﬂuids. This is coherent with the fact that the exergy efﬁciency of the cycle using pure media is always higher. When the exergy amount associated with the heat sink medium can be recovered, e.g. for domestic water heating, the ORC using a ﬂuid mixture is more advantageous than the cycle using a pure working ﬂuid. As found in Table 10, the

Fig. 8. Maximized exergy efﬁciencies and exergy recovery ratios under exergy efﬁciency optimization.

outlet temperature of the cooling water is much higher for system using zeotropic mixtures when considering the same condensing temperature and pinch value of low-pressure heat transfer process. With regard to the repartition of the irreversibility in the ORC components at maximum exergy efﬁciency, the exergy destruction in the high-pressure heat exchanger is always higher than the one in other components. As shown in Fig. 10, the exergy destruction in the evaporator contributes nearly to half of the total irreversibility in the case of ORC using n-pentane and 0.5 R245fa mass fraction mixture. The irreversibility in the condenser and the turbine is similar. The smallest irreversibility rate is found in the pump. The other results of the exergy efﬁciency optimization are shown in Table 11. Although ORCs using pure working ﬂuids present the most desirable thermodynamic performance, some zeotropic mixture-based ORCs are more proﬁtable. Indeed, the LCOE and payback period of the ORC at maximum exergy efﬁciency are the lowest for the power plant using 0.05 R245fa mass fraction mixture. The least proﬁtable cycle at maximum exergy efﬁciency is the R245fa-based ORC with the longest payback period, and the largest LCOE. Although the ratio of the total capital investment to the net power output is the smallest for the system using npentane, the LCOE and the payback period of this pure compoundbased ORC are slightly greater than these of the cycle using 0.05 and 0.1 R245fa mass fraction mixture. The proﬁtability of waste heat to power project will be discussed with more details in the LCOE minimization section. As the electricity is produced from industrial waste heat recovery, a part of the greenhouse gas emitted by the energy fossil combustion for power generation may be reduced. Fig. 11 presents the CO2 emissions issued from electricity generation with different fossil fuels divided by electricity output generated by the fossil fuels. In the case of “Mix” (cf. Fig. 11), the speciﬁc CO2 emissions calculated are the emissions due to fossils fuels consumption for electricity generation divided by the overall output of electricity generation from fossil fuels, nuclear, hydro (excluding pumped storage), geothermal, solar, wind, tide, wave, ocean and biofuels [59]. By recovering waste heat using an ORC, the CO2 emissions due to electricity generation can be substantially reduced as shown in Table 11. 5.2. LCOE minimization The feasibility of transforming waste heat into power can be conﬁrmed after economic investigation. In the previous section, the proﬁtability of ORCs using pure and zeotropic working ﬂuids was

Fig. 9. Ratios of total irreversibility rate and total exergy loss to the net power output at maximum exergy efﬁciency.

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

V.L. Le et al. / Energy xxx (2014) 1e17

13

Fig. 10. Repartition of the exergy destruction in the ORC components at maximum exergy efﬁciency.

Table 11 Thermodynamic performance and economic characteristics of the ORCs at maximum exergy efﬁciency. R245fa mass fraction

_ net (kW) W

hI (%)

hEx (%)

LCOE ($/kWh)

_ net ($/kW) CTCI =W

PBP (yr.)

ROI (e)

CO2 emit a (ton/year)

0 (Pentane) 0.05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 1 (R245fa)

1184 1083 1045 1054 1119 1215 1335 1474 1619 1602

14.6 13.8 13.3 12.7 12.6 12.6 12.8 13.0 13.2 13.7

53.2 50.1 48.3 46.6 46.4 47.2 48.5 50.2 51.8 53.0

0.1055 0.1015 0.1033 0.1076 0.1084 0.1087 0.1091 0.1110 0.1123 0.1237

3707 3820 3951 4157 4195 4202 4204 4243 4211 4339

16.37 14.92 15.48 16.88 17.15 17.26 17.43 17.14 18.78 25.32

0.0556 0.0610 0.0587 0.0539 0.0530 0.0527 0.0522 0.0501 0.0484 0.0359

5055 4619 4464 4488 4766 5173 5679 6272 6890 6828

a

Calculated from CO2 emissions per kWh for the case “Mix” as shown in Fig. 11.

assessed by the mean of the exergy efﬁciency optimization. The current section shows the results of the LCOE minimization in considering four optimization variables, i.e. evaporating and condensing temperatures and two pinch values of heat transfer processes. The working ﬂuid exiting the evaporator is assumed to be the saturated vapor. The LCOE optimization is performed by the Conjugate Direction Method, and equally validated by the DIRECT Optimization Algorithm and Genetic Method. Likewise, the previously mentioned constraints were considered for the LCOE minimization. As shown in Fig. 12, the minimum LCOE of the ORC using npentane is reached with an evaporating temperature of 107 C and a condensing temperature of 38.1 C. The LCOE variation for npentane-based ORC by considering the evaporating temperature and the pinch value of high-pressure heat transfer process is shown in Fig. 13. Fig. 14 presents the evolution of LCOE as a function of the condensing temperature and pinch value for low-pressure heat transfer process. The other operating parameters of the system at minimum LCOE are presented in Table 12. Indeed, the lowest and

the highest LCOEs are found with respectively n-pentane- and R245fa-based systems. As for ORCs using zeotropic working ﬂuids, the minimized LCOE is the smallest for the system using 0.05 and 0.1 R245fa mass fraction mixtures. Therefore, the comparison of the thermodynamic performances and economic characteristics at minimum LCOE between ORCs using pure and zeotropic working ﬂuids are carried out for these four operating media. As shown in Table 13, the lowest LCOE of 0.0863 $/kWh is found with the ORC using n-pentane. This value is just slightly higher than the LCOE for geothermal power plant operating with isobutane and R134a with geothermal ﬂuid inlet temperature of 150 C in the work of Toffolo et al. [23]. The largest LCOE of 0.1082 $/kWh is obtained for the R245fa-based ORC. The ORCs using two working ﬂuid mixtures, i.e. 0.05 and 0.1 R245fa mass fraction mixtures, exhibit the comparable economic characteristics in comparison to

Fig. 11. World CO2 emissions per kWh from electricity generation (average 2008e2010) [50].

Fig. 12. LCOE variation as a function of the evaporating and condensing temperature (for the ORC using n-pentane).

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

14

V.L. Le et al. / Energy xxx (2014) 1e17 Table 13 Economic characteristics of the ORC using the pure working ﬂuids and the working ﬂuid mixtures at minimum LCOE. Cost

Pentane

R245fa

Mixture (0.05)

Mixture (0.1)

CTCI (M$) CTPC (k$) _ net ($/kW) CTCI =W Sannual (M$) ROI PBP (yr.) LCOE ($/kWh)

5.165 556.7 3184 1.211 0.0844 10.78 0.0863

6.101 647.1 4012 1.130 0.0528 17.22 0.1082

5.360 581.1 3207 1.247 0.0828 10.98 0.0872

5.361 575.2 3228 1.238 0.0825 11.02 0.0873

Table 14 Components of total capital investment of the ORCs at minimum LCOE. Cost

Fig. 13. LCOE variation by considering the evaporating temperature and pinch value of high-pressure heat transfer process (for the ORC using n-pentane).

p CBM (k$) evap (k$) CBM t CBM (M$) cond (k$) CBM motor (k$) CBM gen CBM (k$) wf (k$) CBM spares (k$) CBM

Csite (k$) Cserv (k$) Calloc (k$) Ccont (k$) Cstarup (k$)

Fig. 14. LCOE variation as a function of condensing temperature and pinch value of low-pressure heat transfer process (for the ORC using n-pentane).

the n-pentane-based ORC. Indeed, although the sale revenues in the case of the ORC using zeotropic mixture ﬂuids are slightly higher than these in the case of n-pentane-based ORC, the total production costs and total capital investments for the zeotropic mixtures-based ORCs are higher. The speciﬁc total capital investment of the system at minimum LCOE is the smallest for the plant using n-pentane (3184 $/kW) followed by 0.05 and 0.1 R245fa mass fraction mixtures (3207 $/kW and 3228 $/kW, respectively) and R245fa pure (4012 $/kW). These speciﬁc total capital investments are consistent with those

Pentane

R245fa

Mixture (0.05)

Mixture (0.1)

37.2

70.3

40.1

28.7

417.6

378.4

447.7

293.5

2.197

2.160

2.229

1.510

576.4

431.0

602.5

408.2

41.1

73.9

44.6

32.0

98.1

94.7

101.1

100.6

26.2

766.5

48.2

71.3

78.3

144.2

84.7

60.7

173.6 173.6 159.9 716.3 469.5

206.0 206.0 169.3 846.0 554.6

179.9 179.9 172.4 743.4 487.3

180.4 180.4 161.2 743.4 487.3

calculated in Refs. [60], where the speciﬁc investment cost varies between 2764 $/kW and 5512 $/kW (with a $/V exchange rate of 1.2939 $/V by the year 2011) depending on the working ﬂuid. These ﬁndings are also consistent with the results presented by Lecompte et al. [61]. The components of total capital investment for the plants using the different working ﬂuids are presented in Table 14. The highest equipment bare module cost is found for the turbine. Indeed, the bare module cost of this equipment contributes to approximately 40% of the total capital investment of the project. This percentage cost is generally consistent with that calculated in Ref. [23] where the cost of the expander/generator accounts for 44.8% and 40.4% of the total cost of equipment for MW-size geothermal power plants using isobutane and R134a, respectively. This ﬁnding is also

Table 15 Direct manufacturing costs and ﬁxed costs of the ORCs under LCOE optimization. Cost

Pentane

R245fa

Mixture (0.05)

Mixture (0.1)

Utilities (k$) CWB (k$) CSB (k$) CMS (k$) CMO (k$) CPI (k$)

94.8 164.3 41.1 164.3 8.2 93.9

89.7 194.1 48.5 194.1 9.7 110.9

91.4 170.6 42.6 170.6 8.5 97.5

85.5 170.6 42.6 170.6 8.5 97.5

Table 16 System thermodynamic performance and CO2 emission reduced by using waste heat to power system under LCOE optimization.

Table 12 Operating conditions of the ORC for the LCOE minimization. R245fa mass fraction

Tevap ( C)

Pinchh ( C)

Tcond ( C)

Pinchc ( C)

Thso ( C)

Tcso ( C)

m_ wf (kg/s)

m_ c (kg/s)

R245fa mass fraction

_ net W (kW)

hI

hEx

hWHR

(%)

(%)

(%)

0 (Pentane) 0.05 0.1 1 (R245fa)

107.0 104.5 102.8 109.7

2.6 3.4 4.6 4.8

38.1 32.8 30.1 41.5

6.3 6.6 7.3 9.2

84.5 81.5 80.7 85.7

33.5 34.2 35.4 33.7

29.92 31.2 31.9 61.1

216.7 216.2 202.2 212.4

0 (Pentane) 0.05 0.1 1 (R245fa)

1624 1671 1660 1521

11.7 11.5 11.3 11.1

47.2 47.1 46.4 44.8

34.1 35.1 34.9 32.0

_ net I_tot =W

_ tot =W _ net Ex loss

CO2 emit (ton/year)

0.9489 0.9443 0.957 1.0533

1.118 1.125 1.157 1.234

6942 7144 7095 6476

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

V.L. Le et al. / Energy xxx (2014) 1e17

15

Fig. 15. Repartition of the exergy destruction in the ORC components at minimum LCOE.

consistent with the results presented by Lecompte et al. [61] who found that the relative cost of the expander represents a percentage of total investment cost between 22 and 34% depending on the working ﬂuid. In the work of Pierobon et al. [51], the cost of axial turbine contributes respectively to 78.6% and 72.5% of the total investment cost of the MW-size ORCs using acetone and cyclopentane for waste heat recovery. The total bare module cost of the heat exchangers including the evaporator and the condenser represents about 13e20% of the total capital investment. Consequently, the turbine is represented as a key component of the ORC system and its bare module cost strongly inﬂuences the economic feasibility of the waste heat to power project. In the case of R245fa-based ORC, the bare module cost of the working ﬂuid represents an equally important part (about ~12.6%) of the total capital investment. This is caused by the high cost of R245fa (37 $/kg). The direct manufacturing costs and the ﬁxed costs are presented in Table 15. Table 16 presents the thermodynamic performance of the ORCs studied at minimum LCOE. The highest ﬁrst-law and exergy efﬁciency are reached with the n-pentane-based ORC, while the plant using 0.05 R245fa mass fraction mixture presents the highest power output and exergy recovery ratio. The worst thermodynamic performance is found for the system using R245fa. As shown in Table 16, a signiﬁcant amount of emitted CO2 can be reduced by using the waste heat to power plant. Regarding the sharing of the exergy destruction in ORC components (Fig. 15) for LCOE minimization, the highest percentage of exergy destruction is always observed in the evaporator but its contribution to the total irreversibility ﬂow rate is smaller than that in the case of the exergy efﬁciency optimization. Whereas the contribution of the destroyed exergy ﬂow rate in the condenser to the total exergy destruction in the system has increased. The contribution of exergy destruction in the turbine to the total irreversibility for the system at minimum LCOE is smaller than that for the system at maximum exergy efﬁciency.

6. Conclusions The current study performs thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC using a pure or a zeotropic mixture working ﬂuid. Two pure organic compounds, i.e. n-pentane and R245fa, and their mixtures with various concentrations were used as ORC working ﬂuid. Two optimizations, i.e. the exergy efﬁciency maximization and the LCOE minimization, were carried out to bring out the optimum operating conditions of the system and to determine the best ORC working ﬂuid from the studied media. Some conclusions for this work can be drawn as follow: For exergy efﬁciency maximization In the case of the exergy efﬁciency maximization, the exergy efﬁciency (53.2%) was the highest for n-pentane-based power

plant, followed by R245fa-based power plant (53.0%). Concerning the maximized exergy efﬁciency of zeotropic ﬂuidbased ORCs, it varies in a counter direction to the temperature glide at condensing pressure of the working ﬂuid mixtures. The best (resp. worst) maximized exergy efﬁciency corresponds to the working ﬂuid mixture featuring the smallest (resp. highest) temperature glide. Under exergy efﬁciency maximization, pure ﬂuid-based ORCs present higher thermodynamic performances. However, some ORCs using zeotropic working ﬂuids present several advantages, namely higher exergy recovery ratio (ORC using 0.7 R245fa mass fraction mixtures), and lower LCOE and payback period. Although the R245fa-based ORC presents desirable thermodynamic performances, this pure working ﬂuid-based system is least proﬁtable at maximum exergy efﬁciency. For LCOE minimization As for the LCOE minimization, n-pentane-based ORC represents the most proﬁtable cycle: the lowest speciﬁc total capital investment (3184 $/kW), the shortest payback period (10.78 years) and the smallest minimized LCOE (0.0863 $/kWh). The ORC using n-pentane also presents the highest exergy efﬁciency and ﬁrst-law efﬁciency at minimum LCOE. The other pure working ﬂuid-based ORC, i.e. the ORC using R245fa, presents the worst economic characteristics and thermodynamic performance under LCOE minimization. Two zeotropic mixtures (of n-pentane and R245fa)-based ORCs present at minimum LCOE the comparable economic features and thermodynamic performances to the system using pure n-pentane. Furthermore, the ﬂammability of n-pentane could be diminished by mixing together with R245fa, a nonﬂammable compound. Regarding the components of the total capital investment at minimum LCOE, the turbine bare module cost is the most important. This contributes approximately to 40% of the total capital investment of the plant. Therefore, the turbine is considered to be key component of ORC. The turbine cost strongly inﬂuences the economic feasibility of waste heat to power plant driven by an ORC. In the case of ORC using R245fa, the cost of working ﬂuid represents an equally important part (~12.6%) of the total capital investment. Thus, the medium cost could be an important factor for the working ﬂuid selection. Acknowledgment The authors thank the French National Research Agency (ANR10-EESI-001) who has funded the work reported in this paper. Nomenclature A B C

heat transfer surface area (m2) bafﬂe spacing (m) clearance between the adjacent tubes, C ¼ PT do (m)

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

16 ·

Ex g G h I_ k L m_ MM P Pr Q_ Re s S_gen T U V _ W x

V.L. Le et al. / Energy xxx (2014) 1e17

exergy ﬂow rate (kW) gravitational acceleration (m/s2) mass velocity (kg m1 s2) speciﬁc enthalpy (kJ/kg) ﬂow rate of exergy destruction (or ﬂow rate of irreversibility) (kW) thermal conductivity (W m1 K1) length (m) mass ﬂow rate (kg/s) molecular mass (g/mol) pressure (bar) Prandtl number heat transfer ﬂow rate (kW) Reynolds number speciﬁc entropy (kJ kg1 K1) ﬂow rate of generated entropy (kW/K) temperature ( C) overall heat transfer coefﬁcient (W m2 K1) velocity (m/s) power output/input (kW) vapor quality

Greek letters h efﬁciency (%) a heat transfer coefﬁcient (W m2 K1) m dynamic viscosity (Pa s) r density (kg/m3) DHvap heat of vaporization (kJ kg1 K1) Subscripts/superscripts cond condenser/condensation evap evaporator/evaporation crit critical t turbine p pump b normal boiling point in/out inlet/outlet i/o inside/outside is isentropic hsi/hso heat source inlet/outlet csi/cso heat sink inlet/outlet tot total h/c heat source/sink or hot/cold wf working ﬂuid elec electrical gen generator I/II ﬁrst/second law of thermodynamics lm logarithmic mean v/l vapor/liquid References [1] Viswanathan VV, Davies RW, Holbery JD. Opportunity analysis for recovering energy from industrial waste heat and emissions. 2006. [2] Pellegrino JL, Margolis N, Justiniano M, Miller M, Thedki A. Energy use, loss and opportunities analysis: U.S. manufacturing & mining. 2004. p. 17. [3] Cook E. The ﬂow of energy in an industrial society. W.H. Freeman and Company; 1971. [4] Blaney BL. Industrial waste heat recovery and the potential for emissions reduction. Cincinnati, OH: U.S. Environmental Protection Agency, Industrial Environmental Research Laboratory; 1984. [5] BCS I. Waste heat recovery: technology and opportunities in U.S. industry. 2008. [6] Badr O, Probert SD, O'Callaghan PW. Selecting a working ﬂuid for a Rankinecycle engine. Appl Energy 1985;21(1):1e42.

[7] Song Y, Wang J, Dai Y, Zhou E. Thermodynamic analysis of a transcritical CO2 power cycle driven by solar energy with liquiﬁed natural gas as its heat sink. Appl Energy 2012;92:194e203. [8] Shengjun Z, Huaixin W, Tao G. Performance comparison and parametric optimization of subcritical organic Rankine cycle (ORC) and transcritical power cycle system for low-temperature geothermal power generation. Appl Energy 2011;88(8):2740e54. [9] Chen H, Yogi Goswami D, Rahman MM, Stefanakos EK. Energetic and exergetic analysis of CO2- and R32-based transcritical Rankine cycles for low-grade heat conversion. Appl Energy 2011;88(8):2802e8. [10] Baik Y-J, Kim M, Chang KC, Kim SJ. Power-based performance comparison between carbon dioxide and R125 transcritical cycles for a low-grade heat source. Appl Energy 2011;88(3):892e8. [11] Cayer E, Galanis N, Nesreddine H. Parametric study and optimization of a transcritical power cycle using a low temperature source. Appl Energy 2010;87(4):1349e57. [12] Cayer E, Galanis N, Desilets M, Nesreddine H, Roy P. Analysis of a carbon dioxide transcritical power cycle using a low temperature source. Appl Energy 2009;86(7e8):1055e63. [13] Ahmadi P, Dincer I. Thermodynamic analysis and thermoeconomic optimization of a dual pressure combined cycle power plant with a supplementary ﬁring unit. Energy Convers Manag 2011;52(5):2296e308. [14] Kim TS, Park HJ, Ro ST. Characteristics of transient operation of a dualpressure bottoming system for the combined cycle power plant. Energy 2001;26(10):905e18. [15] 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. [16] Zia J, Sevincer E, Chen H, Hardy A, Wickersham P, Kalra C, et al. High-potential working ﬂuids for next generation binary cycle geothermal power plants. General Electric Global Research; 2013. [17] Fischer J. Comparison of trilateral cycles and organic Rankine cycles. Energy 2011;36(10):6208e19. [18] Dai Y, Wang J, Gao L. Parametric optimization and comparative study of organic Rankine cycle (ORC) for low grade waste heat recovery. Energy Convers Manag 2009;50(3):576e82. [19] Wang J, Dai Y, Gao L. Exergy analyses and parametric optimizations for different cogeneration power plants in cement industry. Appl Energy 2009;86(6):941e8. [20] Roy JP, Mishra MK, Misra A. Parametric optimization and performance analysis of a waste heat recovery system using organic Rankine cycle. Energy 2010;35(12):5049e62. [21] Astolﬁ M, Romano MC, Bombarda P, Macchi E. Binary ORC (organic Rankine cycles) power plants for the exploitation of mediumelow temperature geothermal sources e part A: thermodynamic optimization. Energy 2014;66: 423e34. [22] Astolﬁ M, Romano MC, Bombarda P, Macchi E. Binary ORC (organic Rankine cycles) power plants for the exploitation of mediumelow temperature geothermal sources e part B: techno-economic optimization. Energy 2014;66: 435e46. [23] Toffolo A, Lazzaretto A, Manente G, Paci M. A multi-criteria approach for the optimal selection of working ﬂuid and design parameters in organic Rankine cycle systems. Appl Energy 2014;121:219e32. [24] Commission E. EU legislation to control F-gases. 2013. [25] Parliament E, Union CotE. Directive 2006/40/EC of the European Parliament and of the Council of 17 May 2006 relating to emissions from air-conditioning systems in motor vehicles and amending council directive 70/156/EEC. Ofﬁcial J Eur Union 2006;49(L 161):12e8. [26] Parliament E, Union CotE. Regulation (EU) No 517/2014 of the European Parliament and of the Council of 16 April 2014 on ﬂuorinated greenhouse gases and repealing regulation (EC) No 842/2006 Text with EEA relevance. Ofﬁcial J Eur Union 2014;57(L 150):195e230. [27] Mahmoud AM, Radcliff TD, Lee J, Luo D, Cogswell FJ. Non-azeotropic working ﬂuid mixtures for Rankine cycle systems. United Technologies Corporation; 2013. [28] Lemmon EW, Huber ML, McLinden MO. NIST standard reference database 23: reference ﬂuid thermodynamic and transport properties-REFPROP. Version 9.1 ed. Gaithersburg: National Institute of Standards and Technology; 2013. [29] Turton R, Bailie RC, Whiting WB, Shaeiwit JA. Analysis, synthesis, and design of chemical processes. Pearson Education Inc.; 2009. [30] Kreith F, Goswami DY. The CRC handbook of mechanical engineering. 2nd ed. CRC Press; 2005. nerge tique des syste mes et [31] Feidt M. Thermodynamique et optimisation e de s. Tech. & Doc./Lavoisier; 1996. proce [32] Micheal J, Moran HNS, Boettner Daisie D, Bailey Margaret B. Fundamentals of engineering thermodynamics. 7th ed. Don Fowley; 2011. [33] Hasan AA, Goswami DY, Vijayaraghavan S. First and second law analysis of a new power and refrigeration thermodynamic cycle using a solar heat source. Sol Energy 2002;73(5):385e93. [34] Serth RW. Process heat transfer principles and applications. 1st ed. Academic Press; 2007. [35] TEMA. Standards of the tubular exchanger manufacturers association. 9th ed. 2007. New York, USA. [36] Bowman RA, Mueller AC, Nagle WM. Mean temperature difference in design. Trans ASME 1940;62(4):283e94.

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

V.L. Le et al. / Energy xxx (2014) 1e17 [37] Kakaç S, Liu H, Pramuanjaroenkij A. Heat exchangers: selection, rating, and Thermal design. 2nd ed. CRC Press; 2002. [38] Bell KJ. Delaware method for shell-side design. In: Shah RK, Subbarao EC, Mashelkar RA, editors. Heat transfer equipment design. Hemisphere Publishing Corporation; 1988. p. 828. [39] Gnielinski V. New equations for heat and mass transfer in turbulent pipe and channel ﬂow. Int Chem Eng 1976;16:359e68. [40] Petukhov BS. Heat transfer and friction in turbulent pipe ﬂow with variable physical properties. Adv Heat Transfer 1970;6:503e64. [41] Gungor KE, Winterton RHS. Simpliﬁed general correlation for saturated ﬂow boiling and comparisons of correlations with data 1987;65(2). [42] Dittus FW, Boelter LMK. Heat transfer in automobile radiators of the tubular type. University of California Press; 1930. [43] Thome JR. Prediction of the mixture effect on boiling in vertical thermosyphon reboilers. Heat Transfer Eng 1989;10(2):29e38. [44] Kattan N, Favrat D, Thome JR. Re502 and two near-azeotropic alternatives. Part I: intube ﬂow boiling tests. ASHRAE winter meeting, Chicago, symposium CH-95-12 ASHRAE Trans 1995;101(1):1e36. Paper CH-95-12-3. [45] Shah MM. An improved and extended general correlation for heat transfer during condensation in plain tubes. HVAC&R Res 2009;15(5):889e913. [46] Bell KJ, Ghaly MA. An approximate generalized method for multicomponent partial condenser. In: American institute of chemical engineers symposium, vol. 69; 1973. p. 72e9. [47] Ould Didi MB, Kattan N, Thome JR. Prediction of two-phase pressure gradients of refrigerants in horizontal tubes. Int J Refrigeration 2002;25(7):935e47. [48] Rouhani SZ, Axelsson E. Calculation of void volume fraction in the subcooled and quality boiling regions. Int J Heat Mass Transfer 1970;13(2):383e93. [49] Müller-Steinhagen H, Heck K. A simple friction pressure drop correlation for two-phase ﬂow in pipes. Chem Eng Process Process Intensif 1986;20(6): 297e308.

17

[50] Seider WD, Seader JD, Lewin DR. Product and process design principles: synthesis, analysis, and evaluation. John Wiley; 2003. [51] Pierobon L, Nguyen T-V, Larsen U, Haglind F, Elmegaard B. Multi-objective optimization of organic Rankine cycles for waste heat recovery: application in an offshore platform. Energy 2013;58:538e49. [52] Herrmann Rodrigues L, Nie E, Raza A, Wright B. Low grade heat recovery. Senior design reports (CBE). University of Pennsylvania; 2010. [53] Bekdash F, Moe M. A tool for budgetary estimation of cooling towers unit costs based on ﬂow. In: Symposium on cooling water intake technologies to protect aquatic organisms. Virginia, USA: U.S. Environmental Protection Agency; 2003. [54] EIA US. Electric power monthly. 2014. [55] KPMG. Corporate tax rates table. 2014. [56] Kost C, Mayer JN, Thomsen J, Hartmann N, Senkpiel C, Philipps S, et al. Levelized cost of electricity renewable energy technologies. Fraunhofer Institute for Solar Energy System ISE; 2013. [57] Klein SA. EES: engineering equation solver. Academic professional V9.447-3D ed. Madison: F-Chart Software; 2013. [58] Souza GFMd. Thermal power plant performance analysis. Springer Science & Business Media; 2012. [59] IEA. CO2 emissions from fuel combustion highlights. 2012. [60] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine cycles. Appl Therm Eng 2011;31(14e15):2885e93. [61] Lecompte S, Huisseune H, van den Broek M, De Schampheleire S, De Paepe M. Part load based thermo-economic optimization of the organic Rankine cycle (ORC) applied to a combined heat and power (CHP) system. Appl Energy 2013;111:871e81. [62] Kakaç S. Boilers, evaporators, and condensers. John Wiley & Sons; 1991.

Please cite this article in press as: Le VL, et al., Thermodynamic and economic optimizations of a waste heat to power plant driven by a subcritical ORC (Organic Rankine Cycle) using pure or zeotropic working ﬂuid, Energy (2014), http://dx.doi.org/10.1016/j.energy.2014.10.051

Copyright © 2023 C.COEK.INFO. All rights reserved.