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

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 xxx (2014) 1e17 Contents lists available at ScienceDirect Energy journal homepage: www.elsevier.com/locate/energy Thermodynamic and economic...

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Energy xxx (2014) 1e17

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

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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.

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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.

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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)

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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]



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

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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.

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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

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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



dp dz



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

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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

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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).

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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).

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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

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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)

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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

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