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Payback period estimation and parameter optimization of subcritical organic Rankine cycle system for waste heat recovery Xiao-Qiong Wang, Xiao-Ping Li, You-Rong Li*, Chun-Mei Wu Key Laboratory of Low-grade Energy Utilization Technologies and Systems of Ministry of Education, College of Power Engineering, Chongqing University, Chongqing 400044, China

a r t i c l e i n f o

a b s t r a c t

Article history: Received 18 January 2015 Received in revised form 27 April 2015 Accepted 12 May 2015 Available online xxx

This paper presents a theoretical model on the payback period of a subcritical ORC (organic Rankine cycle) system for recovering low-grade waste heat of ﬂue gas. Based on the minimum payback period principle, a detailed internal parameter optimization is carried out. Furthermore, the inﬂuences of external parameters on the payback period are analyzed and a new criterion of screening working ﬂuids is proposed. Results show that the payback period of the ORC system decreases before increasing with the increase of evaporation temperature, condensation temperature, and the pinch point temperature differences in the evaporator and condenser. The minimum payback period of the ORC system decreases monotonously with the increase of the inlet temperature, mass ﬂow rate of the ﬂue gas, and the electricity price. When the minimum payback period and the net power output are used as indicators of selecting working ﬂuids of the ORC system, this work identiﬁes a speciﬁc working ﬂuid for a given inlet ﬂue gas temperature. We demonstrate this process by showing that R236a, R245fa, and R113 should be selected as the working ﬂuids when the inlet temperatures of the ﬂue gas are around 150 C, 200 C and 250 C, respectively. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Organic Rankine cycle Payback period Waste heat recovery Parameter optimization Working ﬂuids

1. Introduction During the past century, there has been a dramatic increase of energy consumption, due in part to the rapid growth of the world population and the increase of development of industrial activity. The issue of meeting the global energy demand in the face of natural resources shortage provides a strong incentive to recover the low-grade waste heat. It has been found that more than 50% total heat generated in the industry is the low-grade waste heat, where temperatures are in the range of 100e220 C [1,2]. The ORC (organic Rankine cycle) is a promising technology that can effectively convert the low-grade waste heat into electricity [3e5]. The ORC technology has attracted increasing attention because of its simple construction, ﬂexibility, low operation cost and high recovery efﬁciency. Studies of parameter optimization, working ﬂuid selection, performance evaluation, and many other variables of the ORC system have been performed by numerous investigators [6e8]. Among current evaluation systems, there are three main

* Corresponding author. Tel.: þ86 23 65112284. E-mail address: [email protected] (Y.-R. Li).

categories: basic energy analysis, exergy analysis and thermoeconomic assessment. Rashidi et al. [9] performed a parametric optimization of a regenerative ORC using thermal efﬁciency, exergy efﬁciency and speciﬁc work as objective functions. It was found that the maximum values of the objective functions for R717 as the working ﬂuid are greater than those for water. Heberle et al. [10] added a heat production term to the ORC and modeled their system as series and parallel circuits. In the series circuits model, based on the second law analysis, it was concluded that the working ﬂuid with high critical temperature, such as isopentane, is suitable for the ORC. Fluids with low critical temperature, such as isobutane and R227ea, should be favored in the parallel circuits and power generation. With the net power output as an objective function, He et al. [11] proposed a theoretical formula on the optimal evaporation temperature in subcritical ORC system. It was found that there is a 25% difference in the maximum net power outputs of twentytwo working ﬂuids at the same conditions. When the critical temperature of the working ﬂuid approaches the inlet temperature of the low-grade waste heat source, the net power output exhibits the largest value. Dai et al. [12] compared and analyzed the ORC system performance with ten pure working ﬂuids under the same waste heat condition with the exergy efﬁciency as an objective

http://dx.doi.org/10.1016/j.energy.2015.05.095 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

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Nomenclature A C CBM CEPCI COM Cp h K M m NE P pe PP Q T W

heat transfer area, m2 cost, $ bare module cost, $ chemical engineering's plant cost index cost of operation and maintenance, $ purchased cost, $ speciﬁc enthalpy, kJ/kg heat transfer coefﬁcient, W/(m2$K) molecular weight, kg/kmol mass ﬂow rate, kg/s net earning per year, $/year pressure, Pa price of electricity, $/(kW$h) payback period, year heat ﬂow rate, W temperature, C power output or input, kW

Subscripts a air c condenser cri critical e evaporator eg electrical generator ex exergy f cooling fan fm ﬂuid machinery g ﬂue gas he heat exchanger i inlet is isentropic o outlet opt optimal p pump pp pinch point t turbine th thermal wf working ﬂuid

Greek symbols h efﬁciency

function. The results showed that the ORC with R236EA as the working ﬂuid has the highest exergy efﬁciency, and adding an internal heat exchanger into the ORC system does not improve the performance under the given waste heat condition. Additional thermoeconomic criteria have also been applied in the performance evaluation of the ORC system. Guo et al. [13], Hettiarachchi et al. [14] and Li et al. [15e17] carried out the performance analysis and parametric optimization on subcritical ORC systems for the recovery of the low-grade waste heat. They used several different screening criteria, including the net power output per unit mass ﬂow rate of hot source, the ratio of the net power output to heat transfer area, and the electricity production cost. Their analysis indicated that a set of the optimum evaporation temperature and pinch point temperature differences of heat exchangers would maximize the net power output. However, the optimum parameter values depend on the used screening criteria. Zhang et al. [18] used up to ﬁve indicators to select the optimum working ﬂuid and optimize the operation parameters. They are thermal efﬁciency, exergy efﬁciency, recovery efﬁciency, heat exchanger area per unit power output, and the levelized energy cost. The results showed that the optimal working ﬂuid and the optimal values of the operation parameters are not all the same for different indicators. Furthermore, Shu et al. [19] established a multi-approach evaluation system to provide comprehensive evaluations on the ORC systems used in the low-grade waste heat recovery. The evaluation system covers three aspects: basic evaluations of energy distribution and system efﬁciency, evaluations of exergy distribution and exergy efﬁciency, and economic evaluations. Two typical ORC systems were used to illustrate the evaluation system for recovering low-grade waste heat. It was shown that this system provides a general method of ORC performance evaluation. The payback period of the ORC system is another important economical criterion in the commercial production of electricity [20]. It is the most direct indicator to reveal the exact period before the ORC system can make a net proﬁt. Furthermore, the way to shorten the payback period is also effective to improve performance of the ORC system. It is signiﬁcant to make estimation for the payback period of the ORC system and to optimize the

operating parameters based on the criterion of the minimum payback period. However, there are only a few investigations on the payback period of the ORC system. Therefore, a theoretical model on the payback period of the ORC system for recovering low-grade waste heat of ﬂue gas from industrial boiler is presented in this work. With the objective of minimizing the payback period, a detailed optimization of internal parameters is performed, including the evaporation temperature, condensation temperature, and pinch point temperature differences in the evaporator and condenser. The inﬂuence of external parameters on the payback period is also analyzed and a new criterion of screening working ﬂuids is proposed. 2. Theoretical model In general, a subcritical ORC system consists of an evaporator, a turbine, a condenser, a pump, a cooling fan and a generator. The schematic diagram of the system is shown in Fig. 1(a). The working ﬂuid is pumped to the evaporator and absorbs heat from the ﬂue gas, and then vaporizes into the saturation state vapor. Afterwards, the high pressure saturated vapor ﬂows into the turbine, where the vapor expands and drives the generator to produce electricity. Simultaneously, its enthalpy and pressure decrease. Then, the lowpressure vapor enters into the condenser and is condensed by the cooling air. The T-s diagram of the described processes is shown in Fig. 1(b). The inlet temperature of the ﬂue gas varies from 150 C to 250 C. The environment provides the cooling air temperature of T0 ¼ 20 C [21,22]. The selection of the working ﬂuids is based on the critical parameter and thermodynamic performance of the ﬂuids, as well as the operating conditions [23]. Here, the main selection criterion is the critical temperature of the working ﬂuid. After detailed screening, eleven working ﬂuids are selected for the subcritical ORC system. Their critical parameters are presented in Table 1. The thermodynamic properties of the working ﬂuids are calculated by the software Refprop 8.0 [24]. For simplicity, some assumptions are introduced into the theoretical model: (1) Heat losses and pressure drops in the heat exchangers and pipelines are ignored [21,25]; (2) The working ﬂuid at

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2.1. Evaporator In the evaporator, the working ﬂuid is preheated to its saturation temperature and then vaporized, as shown in Fig. 1. At the boiling section, the heat balance equation is expressed as

Qbo ¼ mwf ðh4 h3 Þ ¼ mg hg;i hg;pp

(1)

The temperature Tg,pp of the ﬂue gas between the preheating section and the boiling section can be determined by the evaporation temperature and pinch point temperature difference

Tg;pp ¼ Te þ DTe

(2)

According to the evaporation temperature Te, the enthalpy of the working ﬂuid can be determined. Therefore, the mass ﬂow rate of the working ﬂuid can be calculated as

mwf ¼

mg cp;g Tg;i Tg;pp

(3)

h4 h3

The heat ﬂow rate in the preheating section of the evaporator is expressed as

Qph ¼ mwf ðh3 h2 Þ ¼ mg hg;pp hg;o

(4)

Therefore, the outlet temperature of the ﬂue gas can be determined by

Tg;o ¼ Tg;pp

mwf ðh3 h2 Þ mg cp;g

(5)

Based on the heat transfer equation of heat exchanger, the heat transfer areas in the preheating section and boiling section can be respectively calculated as

Fig. 1. Schematic diagrams (a) and T-s diagram (b) of a subcritical ORC system.

the turbine inlet and condenser outlet is considered as the saturated vapor and liquid, respectively; (3) Every component in the ORC system operates under steady state; (4) The pinch point temperature differences of the evaporator and condenser are not less than 5 C; (5) Isentropic efﬁciencies of the expander, pump and fan are 80%, 85% and 85% [26], respectively. Taking the above assumptions into account, the theoretical model on the payback period of the ORC system can be established based on the thermo-economics theory as follows:

Table 1 The critical parameters of the working ﬂuids. Working ﬂuid

M (kg/kmol)

Tcri ( C)

Pcri (MPa)

rcri (kg/m3)

Fluid type

R236fa isobutane R114 R245fa R123 R11 R113 n-hexane methanol heptane cyclohexane

152.04 58.12 170.92 134.05 152.93 137.37 187.38 86.18 32.04 100.20 84.16

124.92 134.66 145.68 154.01 183.68 197.96 214.06 234.67 239.45 266.98 280.49

3.20 3.63 3.26 3.65 3.66 4.41 3.39 3.03 8.10 2.74 4.08

551.04 224.59 720.36 489.31 524.99 554.00 560.00 183.50 275.56 232.00 273.00

isentropic isentropic isentropic isentropic isentropic isentropic isentropic dry wet dry isentropic

Aph ¼

Qph ; Kph DTm;ph

(6a)

Abo ¼

Qbo Kbo DTm;bo

(6b)

where, K is the total heat transfer coefﬁcient of the evaporator, and DTm is the logarithmic mean heat transfer temperature difference.

DTm;ph ¼

DTm;bo ¼

Tg;o T2 DTe ln

Tg;o T2 DTe

;

Tg;i T4 DTe ln

Tg;i T2 DTe

(7a)

(7b)

In general, the convective heat transfer of the working ﬂuid side in the evaporator is much greater than that of the ﬂue gas side. Therefore, the total heat transfer coefﬁcient in the evaporator depends mainly on the convective heat transfer coefﬁcient of the ﬂue gas side [27]. 2.2. Turbine The isentropic efﬁciency of the turbine is deﬁned by

his;t ¼

h4 h5 h4 h5;s

(8)

where, h5,s is the enthalpy of the working ﬂuid at the outlet of the turbine under the isentropic compression condition.

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On the basis of the enthalpy drop, the power output of the turbine can be calculated as

Wt ¼ mwf ðh4 h5 Þ

(9)

2.3. Condenser

Qpc ¼ mwf ðh5 h6 Þ ¼ ma ha;o ha;pp Qco ¼ mwf ðh6 h1 Þ ¼ ma ha;pp ha;i

(10) (11)

The cooling air temperature Ta,pp at the pinch point can be determined by

Ta;pp ¼ Tc DTc

mwf ðh6 h1 Þ cp;a Ta;pp Ta;i

(13)

mwf ðh5 h6 Þ ma cp;a

(14)

The heat transfer areas can be determined by the heat transfer equation

Apc ¼

Qpc ; Kpc DTm;pc

(15a)

Aco ¼

Qco Kco DTm;co

(15b)

where, the logarithmic mean heat transfer temperature difference DTm can be expressed as

DTm;pc ¼

DTm;co ¼

T5 Ta;o DTc ln

T5 Ta;o DTc

T1 Ta;i DTc ln

T1 Ta;i DTc

;

(16a)

(16b)

2.4. Pump The working condition of pump can be determined by the evaporation temperature Te and condensation temperature Tc. The isentropic efﬁciency is deﬁned by

his;p ¼

h2;s h1 h2 h1

(17)

where, h2,s is the enthalpy of the working ﬂuid at the outlet of the pump under the isentropic compression condition. On the basis of the enthalpy raise, the power input is

Wp ¼ mwf ðh2 h1 Þ

(18)

ma Dp rhf

(19)

where, Dp is the pressure loss of the cooling air in the condenser and the pipeline. Therefore, the net power output of the ORC system is determined by the power output of turbine and the power inputs of the pump and cooling fan,

Wnet ¼ Wt Wp Wf

(20)

On the basis of classical thermodynamics, the thermal efﬁciency and the exergy efﬁciency can be determined [28] by

(12)

The mass ﬂow rate and the outlet temperature of the cooling air can be respectively calculated by

Ta;o ¼ Ta;pp

The cooling air is driven by a fan and ﬂows through the condenser where it is heated by the working ﬂuid. The power input can be calculated as

Wf ¼

The condenser is also divided into two sections, precooling and condensing. The heat balance equations in each section of the condenser can be written as

ma ¼

2.5. Air cooling fan

hth ¼

hex ¼

Wnet mg cp;g Tg;i Tg;o

(21)

Wnet T

(22)

g;i mg cp;g Tg;i Tg;o T0 ln Tg;o

To estimate the payback period, the total cost of the ORC system must be determined, which is dominated by the cost of the major components, including the evaporator, turbine, condenser, pump, air cooling fan and generator. The presented theoretical model employs the general correlations [29e33], which are described below. The costs of heat exchangers (evaporator and condenser), ﬂuid machinery (pump and turbine), cooling fan and generator can be calculated by, respectively

lgCp;he ¼ K1;he þ K2;he lgAhe þ K3;he ðlgAhe Þ2

(23)

lgCp;fm ¼ K1;fm þ K2;fm lgWfm þ K3;fm ðlgWfm Þ2

(24)

lgCp;f ¼ K1;f þ K2;f lgQv þ K3;f ðlgQv Þ2

(25)

Cp;eg ¼ 1850000ðWnet =11800Þ0:94

(26)

where Qv is the cooling air ﬂow rate and Wnet is the power output of the generator. In these equations, Cp is a basic cost of the equipment under the assumption of ambient operating pressure and carbon steel construction in the year of 2009. The basic cost should be corrected for the material of construction and the operating pressure as follows

CBM ¼ Cp FBM

(27)

FBM ¼ B1 þ B2 FM Fp

(28)

where CBM is the corrected cost. FM is the correction factor of material. Fp is the correction factor of operating pressure

log Fp ¼ C1 þ C2 log P þ C3 ðlog P Þ2

(29)

In Eqs. 23e29, K1, K2, K3, B1, B2, C1, C2, and C3 are coefﬁcients for cost evaluation of the equipment, which are shown in Table 2.

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X.-Q. Wang et al. / Energy xxx (2015) 1e12

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The total investment cost consists of six parts,

CBM ¼ CBM;e þ CBM;c þ CBM;t þ CBM;p þ CBM;f þ CBM;eg

(30)

According to the CEPCI (Chemical Engineering Plant Cost Index) values, the cost of the equipment is further converted from the 2009 costs to the 2012 costs.

CBM;2012 ¼ CBM;2009 $CEPCI2012 =CEPCI2009

(31)

where, CEPCI2009 is set as 521.9, CEPCI2012 is set as 584.6 [35]. On the other hand, the annual NE (net earning) of the ORC system is determined by the net power output and the price of electricity

NE ¼ pe Wt Wp Wf top

(32)

where, pe is the price of electricity, top is the operation time as 8000 h/year. Based on the total investment cost and the annual net earning, the static PP (payback period) of the ORC system can be estimated as [20].

PP ¼

CBM NE

(33)

The ﬂow chart of the calculation procedure is shown in Fig. 2. In this model, the input parameters are the working ﬂuid and external parameters, including electricity price, the temperature and mass ﬂow rate of the ﬂue gas, etc. The internal parameters, including the evaporation temperature, condensation temperature and the pinch point temperature differences in the evaporator and condenser, are the variables to be optimized based on the minimum payback period. 3. Results and discussion In order to validate the calculation procedure on the presented model, we carried out performance calculation of the ORC system using the same operating conditions as those reported by Zhang et al. [18], Wang et al. [29] and Xu et al. [36]. The maximum deviations of the thermal efﬁciency, exergy efﬁciency, and net power output of the ORC system were found to be about 0.95%, 0.39% and 1.3%, respectively, as shown in Table 3. Therefore, the calculation procedure is sufﬁciently credible to study the payback period of the ORC system. 3.1. Variation of payback period For a ﬁxed electricity price, a constant ﬂue gas temperature and a given ﬂue gas ﬂow rate, the payback period of the ORC system depends mainly on the evaporation temperature, the condensation temperature, and the pinch point temperature differences in the

Fig. 2. Flow chart of the calculation procedure.

evaporator and condenser. Taking isobutane and heptane as the working ﬂuids, Fig. 3 shows the variation of the payback period with the evaporation temperature Te and the condensation temperature Tc when mg ¼ 10 kg/s and pe ¼ 0.1 $/(kW h). The payback period of the ORC system initially decreases before increasing with the increase of the evaporation and condensation temperatures. In the ORC system, the enthalpy drop of the working ﬂuid in the turbine is mainly determined by the evaporation temperature. With the increase of the evaporation temperature, the enthalpy drop of the working ﬂuid in the turbine increases. However, the amount of heat transferred in the evaporator decreases, which reduces the mass ﬂow rate of the working ﬂuid. Therefore, the maximum power output of the turbine exists during the increase of the evaporation temperature. Furthermore, the decrease of the mass ﬂow rate of the working ﬂuid yields a decrease of the heat transfer area of the evaporator and the condenser, which leads to a reduction of the cost of the equipment. These comprehensive effects contribute to the variation of the payback period with the

Table 2 The coefﬁcients for cost evaluation [34]. Coefﬁcients

Turbine

Pump

Cooling fan

Evaporator

Condenser

Generator

K1 K2 K3 C1 C2 C3 B1 B2 Fm FBM

2.2476 1.4965 0.1618 / / / / / / 3.5

3.3892 0.0536 0.1538 0.3935 0.3957 0.00226 1.89 1.35 1.5 /

3.1761 0.1373 0.3414 / / / / / / 5

4.3247 0.3030 0.1634 0.03881 0.11272 0.08183 1.63 1.66 1 /

4.0336 0.2341 0.0497 / / / 1.96 1.21 1 /

/ / / / / / / / / 1.5

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Table 3 Comparison between the present results and those from Refs. [18,29,36]. Working ﬂuids

R236fa R123 R245fa

Heat source

175 C 90 C 90 C 80 C 146.85 C 90 C

This work

Results from references

hth, %

hex, %

Wnet, kW

hth, %

hex, %

Wnet, kW

11.2 9.6 10.6 5.5 10.3 10.4

44.9 49.7 53.9 33.7 43.2 51.7

94.8 9.3 8.5 7.4 78.7 8.8

11.2 [36] 9.6 [18] 10.5 [18] / 10.3 [29] 10.4 [18]

45.0 49.8 54.1 / / 51.9

95.0 [36] / / 7.5 [29] 78.5 [29] /

[36] [18] [18]

[18]

evaporation temperature. In addition, with the increase of condensation temperature, both the enthalpy drop of the working ﬂuid in the turbine and the heat transfer area of the condenser decrease. Therefore, there is an optimum condensation temperature to minimize the payback period. Fig. 4 shows the variation of the payback period with the pinch point temperature differences in the evaporator and the condenser

at mg ¼ 10 kg/s and pe ¼ 0.1 $/(kW h). The payback period of the ORC system is indicated to decrease before increasing with the increase of the pinch point temperature differences. A minimum value of the payback period is reached at a speciﬁc combination of the pinch point temperature differences. With the increase of the pinch point temperature difference in the evaporator, the mean

Fig. 3. Variation of payback period with evaporation temperature and condensation temperature.

Fig. 4. Variation of payback period with pinch point temperature differences in the evaporator and condenser for isobutane (a) and for heptane (b).

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X.-Q. Wang et al. / Energy xxx (2015) 1e12

heat transfer temperature difference increases signiﬁcantly, which results in a reduction of the heat transfer area. Therefore, the increase of the pinch point temperature difference in the evaporator has a marked impact on the decrease of the system investment cost, which affects the payback period. However, the increase of the pinch point temperature difference in the evaporator contributes to a reduction of the heat transfer quantity. Thus, the mass ﬂow rate of the working ﬂuid decreases, which leads a decrease of the net power output. When the reduction of the system investment cost is more than that of the net power output, the payback period of system tends to decrease. On the contrary, when the pinch point temperature difference in the evaporator is large enough, the decrease of the system investment cost becomes the smaller one, which leads to the increase of the payback period. With the increase of the pinch point temperature difference of the condenser, the heat transfer area of the condenser decreases. Therefore, the investment cost reduces. Meanwhile, the temperature rise of the cooling air decreases, and then the mass ﬂow rate of cooling air increases, which results in the increase of the power input of the cooling fan. As a result, the payback period ﬁst decreases before increasing with the increase of the pinch point temperature difference of the condenser. 3.2. The optimization of the internal parameters From the above analysis, it was found that there is a set of the optimal values of the evaporation temperature, condensation temperature and the pinch point temperature differences in the evaporator and condenser corresponding to the minimum payback period of the ORC system. Fig. 5 shows the variation of the optimal values with the inlet temperature of the ﬂue gas for the ORC system with isobutane, R245fa, R11 and heptane as the working ﬂuids,

7

respectively, when mg ¼ 10 kg/s and pe ¼ 0.1 $/(kW h). Obviously, with the increase of the inlet temperature of the ﬂue gas, the optimal evaporation temperature Te,opt initially increases until approaching the critical temperature of the working ﬂuid, and then remains constant. This indicates that the optimal evaporation temperature depends mainly on the critical temperature of the working ﬂuid if the inlet temperature of the ﬂue gas is high enough. Correspondingly, the optimal pinch point temperature difference DTe,opt in the evaporator remains mostly constant before sharply increasing, as shown in Fig. 5(b). The optimal condensation temperature and pinch point temperature difference in the condenser increase with the increase of the inlet temperature of the ﬂue gas. Additionally, when the inlet temperature of the ﬂue gas is approximately 230 C, the optimal evaporation temperature Te,opt of the ORC system with R11 as the working ﬂuid is approximately equal to the critical temperature. Therefore, the working ﬂuid at the turbine outlet is in the liquidevapor coexistent region, which leads to a slight reduction of the optimal pinch point temperature difference DTc,opt in the condenser, as shown in Fig. 5(d). When R245fa and R11 are selected as the working ﬂuid of the ORC system, the optimal parameters (evaporation temperature Te,opt, pinch point temperature difference DTe,opt, and the corresponding temperature Tg,pp,opt of the ﬂue gas between the preheating section and boiling section of the evaporator) varying with the inlet temperature of the ﬂue gas are shown in Fig. 6. Note that there is an inﬂection point in the variation curves of both the optimal evaporation temperature and the optimal pinch point temperature difference with the inlet temperature of the ﬂue gas. As a result of the increase of the optimal evaporation temperature before the inﬂection point, the enthalpy drop of the working ﬂuid in the turbine increases, and the net power output of the ORC increases. However, the increase of the optimal evaporation

Fig. 5. Optimal values of the evaporation temperature (a), condensation temperature (c) and the pinch point temperature differences in the evaporator (b) and condenser (d) with the inlet temperature of the ﬂue gas.

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Fig. 6. Variations of the optimal evaporation temperature, optimal pinch point temperature difference and corresponding temperature of the ﬂue gas between the preheating section and boiling section of the evaporator with the inlet temperature of the ﬂue gas.

temperature is limited by the critical temperature of the working ﬂuid. At a high inlet temperature of the ﬂue gas, the increase of the system cost plays a greater role on the payback period than the increase of the net power output. As a consequence, there is an obvious increase of the optimal pinch point temperature difference in the evaporator while the optimal evaporation temperature is keeping constant after the inﬂection point. In addition, the corresponding temperature Tg,pp,opt of the ﬂue gas between the preheating and boiling sections of the evaporator increases linearly except at the inﬂection point. From Figs. 5 and 6(a) and Table 1, it is noted that the inlet temperature of the ﬂue gas corresponding to the inﬂection point is always about 20e30 C higher than the critical temperature of the working ﬂuid. The optimal values of the internal parameters are different when different evaluation indicators are used as the objective function. Fig. 7 shows a quantitative comparison of the optimal values of the internal parameters with different objective functions when Tg,i ¼ 200 C. The working ﬂuids are R245fa and R11. The evaluation indicators include the thermal efﬁciency, the exergy efﬁciency, the net power output, the LEC (levelized energy cost) [14], and the minimum payback period. The thermal efﬁciency and exergy efﬁciency can be improved by increasing the evaporation temperature and decreasing the pinch point temperature difference in the evaporator. However, when the net power output of the ORC is selected as the indicator, the higher evaporation temperature is not always the better. Furthermore, the optimal values with the minimum LEC are similar to those determined using the minimum payback period. When the economics of the ORC system is taken into account, the optimal pinch point temperature differences in the evaporator and condenser clearly increase, because they can decrease the heat transfer area and the system cost. 3.3. The effects of the external parameters The minimum payback period of the ORC system at the optimal internal parameters depends on the external parameters. Fig. 8 shows the variation of the minimum payback period with the inlet temperature of the ﬂue gas at the different mass ﬂow rates of the ﬂue gas when pe ¼ 0.1 $/(kW h). It is seen that the minimum payback period decreases dramatically with the increase of the inlet temperature of the ﬂue gas, especially when the inlet temperature is low. The higher the inlet temperature of the ﬂue gas, the larger heat transfer quantity in the evaporator, which results in an increase of the mass ﬂow rate of the working ﬂuid. On the other hand, the optimal evaporation temperature also increases with the increase of the inlet temperature of the ﬂue gas.

Fig. 7. Comparison of optimal values of internal parameters with different evaluation indicators.

Therefore, the enthalpy drop of the working ﬂuid in the turbine increases. Due to these two main effects, the power output of the ORC system increase signiﬁcantly, which leads to a rapid reduction of the minimum payback period. For example, for the ORC system with heptane as the working ﬂuid at mg ¼ 1 kg/s, the minimum payback period at Tg,i ¼ 250 C is 67.4% less than one at Tg,i ¼ 150 C. For the selected four working ﬂuids, heptane yields the longest payback period at Tg,i ¼ 150 C while it shows a better performance at Tg,i ¼ 250 C. Conversely, isobutene has a lower critical temperature than that of heptane. The minimum payback period of the ORC system with isobutane as the working ﬂuid is the shortest at Tg,i ¼ 150 C, but the longest at Tg,i ¼ 250 C. It is suggested that the working ﬂuid with high critical temperature is more applicable to the ORC system when the inlet temperature of the ﬂue gas is high. The inﬂuence of the mass ﬂow rate of the ﬂue gas on the minimum payback period at pe ¼ 0.1 $/(kW h) is presented in

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Fig. 8. Variation of the minimum payback period with the inlet temperature of the ﬂue gas.

Fig. 9. With the increase of the mass ﬂow rate of the ﬂue gas, the heat transfer quantity in the evaporator increases, resulting in the increase of the power output of turbine. Accordingly, the heat transfer area of the heat exchangers increases. Thus, the investment cost also increases. Compared to the increase of power output, the increase of investment cost is smaller, especially when the mass ﬂow rate is low. Therefore, the minimum payback period decreases monotonously with the increase of the mass ﬂow rate of

the ﬂue gas. At low mass ﬂow rate, the minimum payback period signiﬁcantly decreases. At higher mass ﬂow rate, the decrease in the minimum payback period is less pronounced. For example, when Tg,i is 150 C(Fig. 9(a)),the minimum payback period of the ORC system with R245fa as the working ﬂuid at mg ¼ 1 kg/s is 202.0% larger than one at mg ¼ 10 kg/s, while the minimum payback period at mg ¼ 10 kg/s is only 27.0% larger than one at mg ¼ 20 kg/s.

Fig. 9. Variation of the minimum payback period with the mass ﬂow rate of the ﬂue gas at pe ¼ 0.1 $/(kW h).

Fig. 10. Variation of the minimum payback period with the electricity prize at mg ¼ 10 kg/s.

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Fig. 11. The variation of the minimum payback period with the critical temperature of working ﬂuids at pe ¼ 0.1 $/(kW h).

Fig. 10 shows the variation of the minimum payback period with the electricity price at mg ¼ 10 kg/s. Eqs. 32 and 33 show that there an inverse relationship between the payback period and the electricity price: the minimum payback period decreases with the

increase of the electricity price. As one of the external parameters, the electricity price has hardly any effect on the thermodynamic performance of the ORC system. Therefore, it has no relation on the screening of the working ﬂuids.

Fig. 12. The minimum payback period and corresponding net power output and thermal efﬁciency with different working ﬂuids at mg ¼ 10 kg/s and pe ¼ 0.1 $/(kW h).

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3.4. The effects of different working ﬂuids Recently, the inﬂuence of the critical temperature of the working ﬂuids on the ORC performance has been investigated. Rayegan and Tao [37] found that the higher critical temperature of organic working ﬂuids can allow the solar ORC systems to operate at higher evaporation temperatures and reach higher thermal efﬁciencies. He et al. [11] calculated the optimal evaporation temperature of a subcritical ORC system when the waste heat source temperature was 150 C. They found that a larger net power output is produced when the critical temperature of the working ﬂuid approaches the inlet temperature of waste heat source. Xu et al. [36] proposed a method to couple the waste heat source with the ORC in order to screen working ﬂuids. As far as the thermal efﬁciency is concerned, they recommended using working ﬂuids with critical temperatures in the range of [Tg,i(20e30), Tg,i þ 100]. The critical temperature of working ﬂuid also has an important inﬂuence on the payback period of ORC system. Fig. 11 shows the variation of the minimum payback period of the ORC system with different working ﬂuids when mg ¼ 10 kg/s and pe ¼ 0.1 $/(kW h). As previously mentioned, when the inlet temperature of the ﬂue gas is about (20e30) C higher than the critical temperature of the working ﬂuid, the optimal evaporation temperature is limited by the critical temperature. Therefore, when the critical temperature of the working ﬂuid is above Tg,i(20e30) C, the minimum payback period of the ORC system remains approximately constant and is determined by the inlet temperature of the ﬂue gas. When the critical temperature of the working ﬂuid is much lower than the inlet temperature of the ﬂue gas, the optimal pinch point temperature difference in the evaporator is so large that the decrease of the net power output has a greater impact on the minimum payback period than the decrease of the system investment cost. As a result, the minimum payback period decreases with the increase of the critical temperature of working ﬂuids. Therefore, with the objective function of the minimum payback period, using a working ﬂuid that has a critical temperature above Tg,i(20e30) C is recommended. The minimum payback period of the ORC system and the corresponding net power output and thermal efﬁciency with different working ﬂuids at mg ¼ 10 kg/s and pe ¼ 0.1 $/(kW h) is represented in Fig. 12. Note that the working ﬂuid with the shortest payback period does not always yield the largest net power output or the highest thermal efﬁciency. At Tg,i ¼ 150 C, R236fa yields the largest net power output among eleven kinds of working ﬂuids, while all of them provide almost the same payback period, as shown in Fig. 12(a). However, from Fig. 12(b) and (c), it can be seen that R245fa and R113 shows preferable performance in both the payback period and the net power output at Tg,i ¼ 200 C and 250 C, respectively. Therefore, R236fa, R245fa and R113 are recommended as the working ﬂuid of the ORC system when the inlet temperatures of the ﬂue gas are around 150 C, 200 C and 250 C, respectively. 4. Conclusion A theoretical model on the payback period of the ORC system is established, which provides a new evaluation method of the ORC system performance. Based on the minimum payback period, the internal parameters of the ORC system are optimized and the inﬂuence of external parameters on the payback period is analyzed. The main conclusions can be summarized as follows: (1) The payback period of the ORC system initially decreases before increasing with the increase of the evaporation

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temperature, the condensation temperature, and the pinch point temperature differences in the evaporator and condenser. There is a group of optimal internal parameters that minimize the payback period. (2) When the critical temperature of working ﬂuids is above Tg,i(20e30) C, the optimal evaporation temperature, condensation temperature and pinch point temperature difference in the condenser increase monotonously with the increase of the inlet temperature of ﬂue gas, while the optimal pinch point temperature difference in the evaporator remains approximately constant. (3) When the inlet temperature, mass ﬂow rate of the ﬂue gas, and the electricity price increase, the minimum payback period of the ORC system decreases. (4) When the minimum payback period and the net power output are used as two indicators to select the optimum working ﬂuid, R236fa, R245fa and R113 are recommended as the working ﬂuid of the ORC system when the inlet temperatures of the ﬂue gas are around 150 C, 200 C and 250 C, respectively. Acknowledgment This work is supported by National Basic Research Program of China (973 Program, Grant No. 2011CB710701). We are grateful to Dr. Aaron H. Persad from University of Toronto for his helpful grammatical edits. References [1] Lecompte S, Huisseune H, Broek MVD, Schampheleire SD, Paepe MD. 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. [2] Wang ZQ, Zhou NJ, Guo J, Wang XY. Fluid selection and parametric optimization of organic Rankine cycle using low temperature waste heat. Energy 2012;40:107e15. [3] Schuster A, Karellas S, Kakaras E, Spliethoff H. Energetic and economic investigation of organic Rankine cycle applications. Appl Therm Eng 2009;29: 1809e17. [4] Larjola J. Electricity from industrial waste heat using high-speed organic Rankine cycle (ORC). Int J Prod Econ 1995;41:227e35. [5] Yamamoto T, Furuhata T, Arai N. Design and testing of the organic Rankine Cycle. Energy 2001;26:239e51. [6] Guo J, Xu M, Cheng L. Thermodynamic analysis of waste heat power generation system. Energy 2010;35:2824e35. [7] Wang D, Ling X, Peng H, Liu L, Tao L. Efﬁciency and optimal performance evaluation of organic Rankine cycle for low grade waste heat power generation. Energy 2013;50:343e52. [8] Quoilin S, Declaye S, Tchanche BF, Lemort V. Thermo-economic optimization of waste heat recovery organic Rankine Cycles. Appl Therm Eng 2011;31: 2885e93. [9] Rashidi MM, Galanis N, Nazari F, Basiri Parsa A, Shamekhi L. Parametric analysis and optimization of regenerative clausius and organic Rankine cycles with two feedwater heaters using artiﬁcial bees colony and artiﬁcial neural network. Energy 2011;36:5728e40. [10] Heberle F, Bruggemann D. Exergy based ﬂuid selection for a geothermal organic Rankine cycle for combined heat and power generation. Appl Therm Energy 2010;30:1326e32. [11] He C, Liu C, Gao H, Xie H, Li YR, Wu SY. The optimal evaporation temperature and working ﬂuids for subcritical organic Rankine cycle. Energy 2012;38:136e43. [12] 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;50:576e82. [13] Guo T, Wang HX, Zhang SJ. Fluids and parameters optimization for a novel cogeneration system driven by low-temperature geothermal sources. Energy 2011;36:2639e49. [14] Hettiarachchia HDM, Golubovica M, Woreka WM. Optimum design criteria for an organic Rankine cycle using low-temperature geothermal heat sources. Energy 2007;32:1698e706. [15] Li YR, Wang JN, Du MT, Wu SY, Liu C, Xu JL. Effect of pinch point temperature difference on cost-effective performance of organic Rankine cycle. Int J Energy Res 2013;37:1952e62. [16] Li YR, Du MT, Wu CM, Wu SY, Liu C, Xu JL. Economical evaluation and optimization of subcritical organic Rankine cycle based on temperature matching analysis. Energy 2014;68:238e47.

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