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Thermodynamic analysis of organic Rankine cycle using zeotropic mixtures Li Zhao ⇑, Junjiang Bao Key Laboratory of Efﬁcient Utilization of Low and Medium Grade Energy, MOE, Tianjin University, No. 92 Weijin Road, 300072 Tianjin, PR China

h i g h l i g h t s A thermodynamic model mainly includes Jacob number is proposed. Ten zeotropic mixture pairs are the working ﬂuid candidates. Heat source inlet temperature has a signiﬁcant inﬂuence on the best composition of zeotropic mixtures. The extent of performance improvement has a positive correlation with temperature glide.

a r t i c l e

i n f o

Article history: Received 23 September 2013 Received in revised form 25 March 2014 Accepted 27 March 2014 Available online 21 April 2014 Keywords: Organic Rankine cycle Zeotropic mixture Jacob number Varying temperature heat source

a b s t r a c t In recent years, more and more attention has been paid to organic Rankine cycle (ORC), which is simply structured, highly reliable and easily maintainable. In order to improve the efﬁciency of ORC systems, zeotropic mixtures whose phase change process is variable temperature, are used as working ﬂuids to match the temperature proﬁles of the heat source and heat sink. In this paper, a thermodynamic model which mainly includes Jacob number and the ratio of evaporation temperature and condensation temperature is proposed to forecast the thermal efﬁciency, output work and exergy efﬁciency of ORC system with zeotropic mixture. Furthermore, the proposed model programmed by Mablab 2010a is veriﬁed by the theoretical data. Then, for different heat source inlet temperature, using different zeotropic mixture pairs, output work that is objective function is maximized by optimizing the evaporation temperature. The results show that if the other working conditions are ﬁxed, the heat source inlet temperature has a signiﬁcant inﬂuence on the best composition of zeotropic mixtures at the optimal evaporation temperature. With the increase of heat source inlet temperature, there exists a heat source inlet temperature that pure working ﬂuid has better system performance than zeotropic mixture. The extent of ORC system performance improvement has a positive correlation with zeotropic mixture’s temperature glide. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Various thermodynamic cycles, including the organic Rankine cycle (ORC), Kalina cycle ,trilateral ﬂash cycle and supercritical Rankine cycle, have been studied for power generation [1]. Compared to other cycles, whose system structure is complex, twophase expansion is difﬁcult or operating pressure is high, organic Rankine cycle is simply structured, highly reliable and easily maintainable [2]. Various types of heat source, including waste heat [3], solar energy [4–6], geothermal energy [7], biomass energy [8] and ocean energy [9], etc., can be utilized by the ORC systems. Meanwhile, it can be coupled with other energy equipment, such as thermoelectric generators [10], fuel cell [11], ICE (internal ⇑ Corresponding author. Tel.: +86 22 27404188. E-mail address: [email protected] (L. Zhao). http://dx.doi.org/10.1016/j.apenergy.2014.03.067 0306-2619/Ó 2014 Elsevier Ltd. All rights reserved.

combustion engine) [12], seawater desalination system [13], Brayton cycle [14] and GT–MHR (gas turbine–modular helium reactor) [15]. As the critical component in an ORC system, an expander determines whether the whole system is relatively efﬁcient and costeffective [2]. Expanders, can be categorized into many types, such as axial turbine [16], rotary expanders [17], scroll expanders [18] and reciprocal piston expanders [19]. The dynamic modeling [20,21] and control [19] are also very signiﬁcant for ORC systems. The design methods are the guarantees of the efﬁcient and costeffective ORC systems [22–24]. The temperature of some heat sources (such as waste heat or geothermal heat) is varying during the process; therefore the system efﬁciency of ORC systems with pure working ﬂuids is quite poor. That is the result of constant-temperature evaporation and condensing for pure working ﬂuids, which leads to bad

L. Zhao, J. Bao / Applied Energy 130 (2014) 748–756

749

Nomenclatures Abbreviation ORC organic Rankine cycle GT–MHR gas turbine–modular helium reactor CHP combined heat and power CCHP combined cooling, heat and power TG temperature glide or thermoelectric generators REC ratio of evaporation temperature and condensation temperature Symbols Cp E h Ja m p Q r

speciﬁc heat at constant Pressure (kJ/kg K) exergy ﬂux (kW) speciﬁc enthalpy (kJ/kg) Jacob number mass ﬂow rate (kg/s) pressure (kPa) heat ﬂux (kW) latent heat (kJ/kg)

temperature matching in the evaporator and condenser and large irreversibility. In order to improve the efﬁciency of such cycles, zeotropic mixtures, whose phase change process is variable temperature, are using as working ﬂuids to match the temperature proﬁles of the heat source and heat sink, thus a better system performance could be obtained [2]. Li et al. [25] investigated the inﬂuence of evaporating temperature and internal heat exchanger. Three pure ﬂuids (R123, R141b and R245ca) and one mixture (R141b/RC318) were used as working ﬂuids. They concluded that the ORC system efﬁciency of the mixture R141b/RC318 would be better than that of R141b after adding an internal heat exchanger. Wang and Zhao [26] compared three different compositions (0.9/0.1, 0.65/0.35 and 0.45/0.55) of R245fa/R152a to pure R245fa at a low temperature solar ORC. For zeotropic mixtures, a signiﬁcant increase of thermal efﬁciencies can be obtained when the outlet of evaporator is superheated with IHE. In an experimental study of by Wang et al. [4], the system efﬁciency of zeotropic mixtures are comparatively higher than that of R245fa in the experimental condition. In the experimental superheating period, the average power output of M3 (R245fa/ R152a, 0.7/0.3) is higher than that of M1 (R245fa) and M2 (R245fa/R152a, 0.9/0.1) by 29.10% and 28.03%, respectively. Investigating second law efﬁciency of subcritical cycles, Heberle et al. [27] presented simulations for ORC with isobutane/isopentane and R227ea/R245fa mixtures as working ﬂuids. The composition of mixture, heat source temperature and temperature difference of cooling water are the concerned parameters. The second law efﬁciency increases in the range of 4.3% and15% for mixtures compared to that of pure ﬂuids for a heat source temperature below 120 °C. Garg et al. [28,29] respectively used isopentane/R-245fa, CO2/isopentane and CO2/propane as working ﬂuids, and evaluated the system performance. A technique of identifying the required source temperature for a given output of the plant and the maximum operating temperature of the working ﬂuid is developed by the authors. For the heat source temperature of 150 °C and 250 °C, when using mixtures as the working ﬂuids of ORC systems, Chys et al. [30] found a potential increment of 16% and 6% in system efﬁciency respectively. The power generation at optimal condition can be increased by 20% for the low temperature heat source comparing with the pure working ﬂuids. With mixtures of SF6– CO2 as working ﬂuids at a geothermal power plants, Yin et al. [31] investigated both supercritical and transcritical cycles. For working ﬂuids with SF6, the highest Brayton and Rankine cycle

s T W

g

speciﬁc entropy (kJ/kg K) temperature (K) power (kW) efﬁciency

Subscript 0 1, 2, 3 et exer therm c e ﬂuid h p t net

ambient condition al. the state points of the ORC system exergy thermal cooling or condenser evaporation or evaporator working ﬂuid heat source pump turbine the net power

efﬁciencies are yielded at the composition of 15 and 20 mol%, respectively. From the above survey of literatures, the researches about zeotropic mixture ORC are increasing, but it is still limited and mainly concerned with speciﬁc cases (only one or two heat source temperature and few working ﬂuids), and meanwhile, the model to forecast the performance of ideal ORC systems using zeotropic mixtures does not exist. In this paper, a thermodynamic model is proposed to evaluate the output work, thermal efﬁciency and exergy efﬁciency of ideal ORC systems for different zeotropic mixtures. Meanwhile, the inﬂuence of the heat source temperature on the optimal mass fraction of different zeotropic mixture is emphasized. The effect of temperature glide on the performance of zeotropic ORC systems is also discussed. 2. Thermodynamic analysis of the ORC system with zeotropic mixture 2.1. System presentation The ORC system conﬁguration is shown in Fig. 1(a), including an evaporator, an expander, a condenser and a feed pump. There is usually a storage tank for the collection of working ﬂuids and the maintain of working ﬂuid state at the feed pump inlet. Pumping from the storage tank by the feed pump, working ﬂuid is heated and vaporized in the evaporator by the heat source. The high pressure and temperature vapor enters the turbine, where thermal energy is converted into mechanical energy. Meanwhile, the generator is driven and electricity is generated. After that, the exhaust vapor leaves from the expander and passes the condenser, where it is condensed into saturated or subcooled liquid. The liquid ﬂuid passes through the tank and is pumped into the evaporator, which is the initiate of next cycle. The thermodynamic processes are illustrated on the T–s diagram in Fig.1(b) and (c) for ORC systems with pure ﬂuid and zeotropic mixture. In general, ORC systems have four basic operational processes: liquid ﬂuid’s pressurization process 1–2, liquid ﬂuid’s isobaric vaporization process 2–4, gaseous ﬂuid’s expansion process 4–5 and gaseous ﬂuid’s isobaric liquefaction process 5–1. For the ideal case, the processes 1–2 and 4–5 are the isentropic processes 1–2s and 4–5s, respectively. The difference between pure ﬂuids and zeotropic mixtures is that non-isothermal phase change for zeotropic mixture which will lead to better temperature matching for the varying

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L. Zhao, J. Bao / Applied Energy 130 (2014) 748–756

ﬂuids. Due to the impossibility of wet expansion in the expander, dry working ﬂuids are better choices and considered. In this paper, ﬁve pure working ﬂuids including R227ea, R236fa, R236ea, R245ca and R245fa, are the basic components and ten zeotropic mixture pairs are the working ﬂuid candidates. The ﬂuid properties of pure ﬂuids are shown in Table 1. About the thermal stability, from the literature [32], the three of the ﬁve working ﬂuids including R227ea, R236fa and R245fa were reported that excellent thermal stability up to the following temperatures at which no decomposition was observable in 50–100 h: 425 °C for R227ea, 400 °C for R236fa and 300 °C for R245fa. Due to the similar atoms and structure, the other two ﬂuids (R236ea and R245ca) could be thought as thermal stability in the investigative temperature range. The properties of the mixtures are obtained by REFPROP 9.0 [33]. 2.3. Thermodynamic model Based on the mass and energy balance, the basic equations describing the ORC systems for each individual component are listed as follows: For evaporator:

_ heatsource C p eva ðT h Qe ¼ m _ fluid ðh4 h2 Þ ¼m

in

Th

out Þ

ð1Þ

For expander:

_ fluid ðh4 h5 Þ Wt ¼ m _ fluid ðh4 h5s Þ ¼ gt m

ð2Þ

For condenser:

_ fluid ðh5 h1 Þ Qc ¼ m

ð3Þ

For pump:

_ fluid ðh2 h1 Þ Wp ¼ m ¼

ð4Þ

_ fluid ðh2s h1 Þ m

gp

With respect to the thermodynamic models to predict the thermal efﬁciency and net work for organic Rankine cycle using pure ﬂuids, there been several related researches on it. Liu et al. [34] presented a thermodynamic model to calculate the thermal efﬁciency and total heat-recovery efﬁciency. Their results showed that thermal efﬁciency is a weak function of the critical temperature, although the thermal efﬁciency is lower when the critical temperature of working ﬂuids is low. Through the thermodynamic derivation, Mikielewicz and Mikielewicz [35] proposed a performance index to predict the thermal efﬁciency, which deﬁned a Jacob number. In fact, this Jacob number was not the ratio of vaporization latent heat and sensible heat, but very chose to it. Moreover, Kuo et al. [36] proposed a ﬁgure of merit deﬁned as:

Figure of meritðFOMÞ ¼ Ja0:1

T cond T ev ap

0:8 ð5Þ

Fig. 1. The basic ORC system.

temperature heat source and less thermodynamic irreversibility therefore a higher system performance.

which including the Jacob number, evaporation and condensing temperature. Different from [35], this Jacob number was deﬁned as Ja = CpDT/Hv, where CpDT was the vaporization sensible heat and Hv is vaporization latent heat. From their results, a larger ratio of

2.2. The working ﬂuid candidates

Table 1 Fluid properties of pure ﬂuids.

Because the system efﬁciency, system component sizes, expander design, the system stability, safety and environmental concerns are all affected by the selection of working ﬂuid, working ﬂuid selection is a very important procedure in the design process of an ORC system. Based on the slope of saturation vapor curve, the working ﬂuids could be categorized into dry, wet and isentropic

Working ﬂuid

Alternative name

Pcr (MPa)

Tcr (°C)

1,1,1,2,3,3,3-Heptaﬂuoropropane 1,1,1,3,3,3-Hexaﬂuoropropane 1,1,1,2,3,3-Hexaﬂuoropropane 1,1,1,3,3-Pentaﬂuoropropane 1,1,2,2,3-Pentaﬂuoropropane

R-227ea R-236fa R-236ea R-245fa R-245ca

28.7 31.9 34.1 36.1 38.9

101 124 139 153 174

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L. Zhao, J. Bao / Applied Energy 130 (2014) 748–756

vaporization latent heat and sensible heat would result in a smaller ﬁgure of merit, therefore a larger thermal efﬁciency, which illuminated the results of literature [8]. From the study of Stijepovic et al. [37], a smaller the ratio of vaporization latent heat and sensible heat would lead to a larger exergy efﬁciency. However, they all focused on pure working ﬂuids. Next, a thermodynamic model which mainly includes Jacob number and the ratio of evaporation temperature and condensation temperature is derived to forecast the thermal efﬁciency, output work and exergy efﬁciency of ideal ORC systems with zeotropic mixture. In order to simplify the analysis, the assumption that the expansion processes in the expander and the pressurization process in the pump are isentropic has been made in this study. It is worth noting that the assumptions of the isentropic expansion processes in the expander and the isentropic pressurization process in the pump would not affect the comparison between our model and the theoretical model for an ideal ORC system. So the Eq. (6) holds with s5s = s5. According to the state points in Fig. 1(c), the entropy change from the state point 1 to 5 (i.e. 5s) can be approximately simpliﬁed as: 3 s5 s1 s4 s3 þ s3 s1 h4Th þ C p13 ln TT 31 e

p13 ln T 3 ¼ Tre þ C T1

ð6Þ

where T e is evaporation temperature for zeotropic mixture which can be expressed as:

h4 h3 T e ¼ s4 s3

ð7Þ

The working ﬂuid’s total absorbed heat in the evaporator can be obtained as:

_ fluid ½C p13 ðT 3 T 1 Þ þ r Qe ¼ m

ð8Þ

The working ﬂuid’s rejected heat the in condenser can be determined as the area between the curve 5-6-1 and x-axis. In fact, compared to the area between the curve 5-6-1 and x-axis, the area of triangle 5-6-1 is so small that it can be neglected. Therefore, the area of trapezoid formed by curve 5-1 and x-axis is thought as the working ﬂuid’s rejected heat the in the condenser, which could be expressed as:

_ fluid ½T 1 ðs5 s1 Þ þ 12 ðT 5 T 1 Þðs5 s1 Þ Qc m _ fluid ðT 1 þ T 5 Þðs5 s1 Þ m _ fluid T c ðs5 s1 Þ ¼ 1m

ð9Þ

2

where T c is condensation temperature for zeotropic mixture which can be expressed as:

h6 h1 T c ¼ s6 s1

ð10Þ

The working ﬂuid mass ﬂow rate is obtained based on energy conservation in evaporator:

_ fluid ¼ m

Pm _ heatsource ðT h C

in

T sat l DT PP Þ

r

W net Q e Q c Q ¼ ¼1 c Qe Qe Qe

ð12Þ

The output work can be deﬁned as:

W net ¼ W t W p ¼ Q e Q c

gexer ¼

W net DE e

ð14Þ

where DEe is the exergy at the side of the heat source in evaporation which could be expressed as:

_ heatsource ½hh DEe ¼ m

in

h0 T 0 ðsh

in

s0 Þ

ð15Þ

Substituting Eqs. (7) and (8) into (11), the thermal efﬁciency can be expressed as:

gtherm ¼ 1

Ja ln REC ðREC 1Þ1 þ 1=REC 1 þ Ja

ð16Þ

where Ja is the Jacob number, deﬁning as the ratio of sensible heat and the latent heat of evaporation, i.e.

p13 ðT 3 T 1 Þ=r Ja ¼ C

ð17Þ

REC is the ratio of evaporation and condensation temperature and can be obtained as:

T e REC ¼ Tc

ð18Þ

Due to the small different between temperature glides in the evaporator and condenser, with the approximation of arithmetic average evaporation temperature equals to the thermodynamic average evaporation temperature, the radio of T3 and T1 can be simpliﬁed as follows: T 4 þT 3 3 T e 12 TGe T e T 4 T T3 2 2 ¼ T þT ¼ REC T T 6 1 6 1 T1 T c 12 TGc T c 2 2

ð19Þ

Substituting Eqs. (7)–(9) into (12), the output work of an ideal ORC is obtained as:

Pm _ heatsource T h in T sat l DT PP Þ½Jað1 lnREC ðREC 1Þ1 W net ¼ C þ 1 1=REC ð20Þ Substituting Eqs. 7, 8, 9, and (14) into (13), the exergy efﬁciency can be simpliﬁed as:

gexer ¼

P ðT h in T sat l DT PP Þ½Jað1 ln REC ðREC 1Þ1 Þ þ 1 1=REC C hh in h0 T 0 ðsh in s0 Þ

ð21Þ

The detail explanations of Eqs. (16), (20), and (21) could be found in Appendix A. Based on the above equations, a program is carried out by MATLAB 2010a with a function calling REFPROP 9.0. Table 2 presents all the input system parameters. To simplify the calculation, it has been made the following assumptions in this paper: the heat and pressure losses in all heat exchangers are neglected; the irreversibilities in the pipes are small and negligible; the organic working

ð11Þ

where DT PP is the pinch point temperature difference and T sat l is the temperature of the saturation liquid when the evaporation begins. The thermal efﬁciency can be expressed as:

gtherm ¼

The exergy efﬁciency can be expressed as:

ð13Þ

Table 2 Input system parameters. Initial system parameter

Value

Heat source air inlet temperature (K) Heat source air inlet mass ﬂow (kg/s) Heat source air pressure (bar) Heat sink water inlet temperature (K) Pinch point in the evaporator (K) Pinch point in the condenser (K) Isentropic pump efﬁciency Isentropic turbine efﬁciency

423.15 25 1 293.15 30 5 65% 70%

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L. Zhao, J. Bao / Applied Energy 130 (2014) 748–756

Table 3 The calculated results of comparison between this work and Chys et al. work [30]. Medium

Pgen (kW)

R245fa-R365mfc R245fa-isopentane Isobutane-isopentane R245fa-pentane

gcycle (%)

Ppump (kW)

[30]

This work

[30]

This work

[30]

This work

5.0 6.3 6.6 5.4

4.99 6.24 6.61 5.31

109.5 110.8 112.8 112.7

109.9 111.6 112.5 111.4

10.82 10.82 10.99 11.12

10.88 10.82 10.99 11.12

Table 4 The calculated results of comparison between this work and Ref. [27] with isobutane/ isopentane (0.5:0.5, by mass).

353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15

0.210

Exergy efﬁciency (%) [27]

This work

29.2 31.4 33.2 35 36.7 38.3 40.1 41.6 43.1 45.1 47.8

29.4 31.5 33.5 34.9 36.6 38.1 40.2 41.8 43.0 45.3 47.7

Output Work [MW]

Geothermal water inlet temperature (K)

0.205 0.200 0.195 0.190 0.185 330

R236fa/R236ea

335

340

345

350

355

360

365

Evaporation Temperature [K]

(a) ﬂuid is heated into saturated vapor in the evaporator and cooled to saturated liquid in the condenser.

Mass flow rate [Kg/s]

Using the same input conditions as those in Chys et al. [30] that is a theoretical research, a thermodynamic calculation is carried out to validate the programme. The heat source with inlet temperature of 423.15 K, outlet temperature of 408.15 K and mass ﬂow of 15 kg/s is water at 5 bar, while the heat sink with inlet temperature of 298.15 K and outlet temperature of 308.15 K is water at 4 bar. The efﬁciencies of pump, turbine and generator are respectively 80% ,60% and 97%. The pinch points in the evaporator and condenser are severally 20 K and 10 K. The results of comparison are listed in Table 3. From that, it shows excellent agreement between the calculated results this paper and Ref. [30]. In an another theoretical research [27], the heat source is the geothermal water of inlet temperature between 353.15 K and 453.15 K, the exergy efﬁciency is calculated and the other details

0.028 11

0.026 0.024

10

0.022

9

0.020 8 0.018 7 330

0.016 335

340

345

350

355

360

Specific Output Work [Kj/Kg]

2.4. Validation

12

365

Evaporation Temperature [K]

(b) Fig. 2. Effect of evaporation temperature on (a) output work, and (b) mass ﬂow rate and speciﬁc output work.

Table 5 Results for zeotropic mixtures with mass fraction ratio 1:1 using different methods.

a b c d e

Fluids

Ja

gtherma (%)

Wneta (MW)

gexera (%)

gthermb (%)

Wnetb (MW)

gexerb (%)

TGe (K)

RDc (%)

RDd (%)

RDe (%)

R227ea/R236fa R227ea/R236ea R236ea/R236fa R245fa/R227ea R245fa/R236fa R245ca/R227ea R245fa/R236ea R236fa/R245ca R245ca/R236ea R245fa/R245ca

1.22 0.97 0.86 0.83 0.75 0.71 0.71 0.67 0.65 0.61

13.35 13.51 13.99 13.59 14.21 13.45 14.38 14.14 14.36 14.69

0.229 0.211 0.199 0.207 0.194 0.208 0.188 0.194 0.188 0.182

40.44 37.21 35.11 36.59 34.20 36.68 33.23 34.27 33.13 32.11

13.30 13.79 14.04 14.10 14.32 14.42 14.43 14.54 14.61 14.75

0.228 0.215 0.200 0.215 0.195 0.223 0.189 0.200 0.191 0.183

40.30 37.97 35.22 37.94 34.48 39.31 33.35 35.23 33.70 32.24

0.95 2.51 0.34 5.63 1.56 10.99 0.46 4.73 2.54 0.84

0.37 2.07 0.36 3.75 0.77 7.21 0.35 2.83 1.74 0.41

0.35 2.07 0.33 3.68 0.81 7.19 0.37 2.79 1.71 0.40

0.35 2.04 0.31 3.69 0.82 7.17 0.36 2.80 1.72 0.40

The The The The The

theoretical data. results obtained by our model. relative deviation of gtherm calculated by different methods. relative deviation of Wnet calculated by different methods. relative deviation of gexer calculated by different methods.

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L. Zhao, J. Bao / Applied Energy 130 (2014) 748–756

can be found in Ref. [27]. The results of comparison are listed in Table 4. It also shows reasonable accuracy.

obtained by our model is increasing, however, the real value of thermal efﬁciency of theoretical data is not always increasing. For example, the results of r245fa/r227ea and r245ca/r227ea

3. Results and discussion 3.2. The determination of the optimal evaporation temperature 3.1. Comparison between our model and theoretical data At the heat source air inlet temperature of 423.15 K, evaporation temperature of 363.15 K and condensation temperature of 298.15 K, the thermal efﬁciency, net work and exergy efﬁciency for zeotropic mixtures with mass fraction ratio 1:1 (i.e., 50%/50%, by mass fraction) calculated by different methods are presented in Table 5. Our model are Eqs. 16, 19, and 20, while the theoretical data is based on the mass and energy balance, for example, Eqs. (1)–(4) and Eqs. (12)–(14). The RD (relative deviation) is given by:

RD ¼

xn xt 100% xn

ð22Þ

where xn is the theoretical data while xt is the value obtained by our model. The maximum RD of all the zeotropic mixtures is 7.21% for R245ca/R227ea with a temperature glide larger than 10 K in the evaporator. Besides this, other mixtures have a rather high accuracy less than 4%. It is applicable to determine the thermal efﬁciency, net work and exergy efﬁciency. Refs. [36,38] mentioned that the thermal efﬁciency has a negative correlation with Jacob number for the ﬁxed evaporation temperature and condensation temperature. However, this conclusion is not suitable for zeotropic mixture. It can been seen from Table 4 that with the decrease of the Jacob number, the thermal efﬁciency

In this part, output work is used as objective function, which is usually the optimizing index in the waste recovery or geothermal plant. The input system parameters are listed in Table 3, of which, the heat source inlet temperature is ﬁxed as 423.15 K. The working ﬂuid studied is R236fa/R236ea (0.5/0.5, by mass fraction) and the evaporation temperature is varying from 333.15 K to 363.15 K. As shown in Fig. 2(a), with the increase of evaporation temperature, the output work increases ﬁrstly, and then decrease, i.e., there is a maximum output work corresponding to an optimal evaporation temperature. For R236fa/R236ea, this value is 350 K. This law also exists in the ORCs with pure working ﬂuids [39]. The direct reason is, as presented in Fig. 2(b), when evaporation temperature increases, the mass ﬂow rate will decrease while speciﬁc net work will increase, and this combined effect results in the maximum of output work. 3.3. Effect of the heat source inlet temperature on optimal output work In this section, with the method of evaporation temperature optimization previously, the inﬂuence of the heat source inlet temperature on the optimal output work for different zeotropic mixtures are shown in Figs. 3 and 4. It can be seen from Fig. 3(a) that at the heat source inlet temperature of 398.15 K, using R245ca/R236ea as working ﬂuid, the optimal output work ﬁrstly increase and then decrease with the increase of R245ca mass frac-

0.324 0.098

Output Work [MW]

Output Work [kW]

0.320 0.096 0.094 0.092 0.090

0.316 0.312 0.308 0.304 0.300

Output Work of R245ca/R236ea

Output Work of R245ca/R236ea

0.088 0.0

0.2

0.4

0.6

0.8

0.0

1.0

0.2

0.4

0.6

0.8

Mass fraction of R245ca

Mass fraction of R245ca

(a) 398.15K

(c) 453.15K

1.0

0.246 0.360 0.355

Output Work [MW]

Output Work [MW]

0.243 0.240 0.237 0.234 0.231 0.228

Output Work of R245ca/R236ea

0.0

0.2

0.4

0.6

0.350 0.345 0.340 0.335 0.330 Output Work of R245ca/R236ea

0.325

0.8

1.0

0.0

0.2

0.4

0.6

0.8

Mass fraction of R245ca

Mass fraction of R245ca

(b) 438.15K

(d) 458.15K

1.0

Fig. 3. The output work of R245ca/R236ea at different mass fractions for the different heat source inlet temperature (a) 398.15 K, (b) 438.15 K, (c) 453.15 K, and (d) 458.15 K.

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L. Zhao, J. Bao / Applied Energy 130 (2014) 748–756

0.28

0.24

0.18

0.22 398.15K 403.15K 408.15K 413.15K 418.15K 423.15K 428.15K 433.15K

0.20 0.18 0.16 0.14 0.12 0.10

Output Work [MW]

Output Work [MW]

R245fa 10/90 20/80 30/70 40/60 50/50 60/40 70/30 80/20 90/10 R236ea

0.20

0.26

0.08

0.16 0.14 0.12 0.10

0.0

0.2

0.4

0.6

0.8

1.0

Mass fraction of R245ca

0.08

395

Fig. 4. The output work of R245ca/R227ea at different mass fractions for the different heat source inlet temperature.

400

405

410

415

420

425

430

Mass fraction of R245fa Fig. 6. The output work of R245fa/R236ea for the heat source inlet temperature from 398.15 K to 428.15 K at different mass fraction.

14

R245ca/R227ea R245ca/R236ea R245fa/R236ea

0.40

10

R245ca 10/90 20/80 30/70 40/60 50/50 60/40 70/30 80/20 90/10 R236ea

0.35

8

Output Work [MW]

Temperature Glide [K]

12

6 4 2

0.30 0.25 0.20 0.15

0 0.10 0.0

0.2

0.4

0.6

0.8

1.0

Mass fraction of the higher boiling point component

0.05 390

Fig. 5. The temperature glides for different zeotropic mixtures at the heat source inlet temperature 428.15 K.

tion. When the mass fraction of R245ca is 0.6, there exists a maximum value for the optimal output work. When the heat source inlet temperature increase, the optimal output work at different R245ca mass fraction will all increase. However, the R245ca mass fraction corresponding to the maximum optimal output work will decrease from 0.6 (Fig. 3(a)) to 0.3 (Fig. 3(c)). Furthermore, when the heat source inlet temperature reaches 458.15 K, the output work of pure R245ca is larger than R245ca/R236ea. As presented in Fig. 4, when using other zeotropic mixtures, the same tendency is found. This results declare that the superiority of ORCs with zeotropic mixtures has close connections with the heat source inlet temperature, which means that when the heat source inlet temperature is higher than some value, ORCs with zeotropic mixtures are not as good as those with pure working ﬂuids. At the same time, compared Fig. 3 with Fig. 4, it can be found that the heat source inlet temperature at which ORCs with zeotropic mixtures are not as good as those with pure working ﬂuids is not the same for different zeotropic mixtures. For example, when using R245ca/R236ea, ORCs with pure R245ca have better system performance than those with R245ca/R236ea at the heat source inlet temperature 458.15 K, while for R245ca/R227ea, this temperature is 428.15 K. The mixtures considered have ﬂuids which are quite similar in terms of thermodynamic properties. In order to remove the effect of similar working ﬂuids on the results, the research about hydrocarbons in Ref. [40] is also reviewed for comparison. In this

400

410

420

430

440

450

460

The heat source inlet temperature [K] Fig. 7. The output work of R245ca/R236ea for the heat source inlet temperature from 398.15 K to 458.15 K at different mass fraction.

paper, with the geothermal resource of 280 °F(410.93 K) and 360 °F(455.37 K), the optimal composition of Isopentane/isobutane changed from 42%/58% to 35%/65%. This result showed that the inﬂuence of heat source inlet temperature on the optimal composition of zeotropic mixture for ORC systems is independent of the working ﬂuid’s type. 3.4. Effect of the temperature glide for different zeotropic mixtures In this part, the effect of the temperature glide on the optimal output work is discussed. The temperature glides for different zeotropic mixtures at the heat source inlet temperature 428.15 K are plotted in Fig. 5. It can be seen from Fig. 5 that due to the largest difference of boiling point, R245ca/R227ea has the largest temperature glide, while R245fa/R236ea stays lowest. The optimal output work for different heat source inlet temperature with various zeotropic mixtures are presented in Figs. 6–8. Compared with these three ﬁgures, it can be found that larger temperature glide means greater improvement for the optimal output work at the different mass fractions. Ref. [38] found that the optimal output work is closely linked with the heat source inlet temperature and it is a weak function of working ﬂuids. From current results, it only holds true for the zeotropic mixture with small temperature glide.

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L. Zhao, J. Bao / Applied Energy 130 (2014) 748–756

The Eq. (17) could be turned into:

0.30

Output Work [MW]

0.27 0.24

R245ca 10/90 20/80 30/70 40/60 50/50 60/40 70/30 80/20 90/10 R227ea

0.21 0.18 0.15 0.12 0.09 395

400

405

410

415

420

425

430

p13 Ja C ¼ T3 T1 r Substituting Eq. (24) into (23), it could be expressed as: Ja

gtherm ¼ 1 T 3 T 1 ¼1

Mass fraction of R245ca

ð25Þ

T1

1þ

C p13 ðT 3 T 1 Þ r

Substituting Eqs. (17)–(19) into (25) and with the approximation of T c =T 1, the thermal efﬁciency can be expressed as:

gtherm ¼ 1 4. Conclusions

T c ln TT 31 þ TTec

C ðT T Þ 1 þ p13 r 3 1 T c JaT 1 ln TT 31 þ TTec T 1 T 3 T 1 C ðT T Þ 1 þ p13 r 3 1 T c Ja ln TT 31 þ TTec T 1 T 3 1

¼1

435

Fig. 8. The output work of R245ca/R227ea for the heat source inlet temperature from 398.15 K to 433.15 K at different mass fractions.

ð24Þ

Ja ln REC ðREC 1Þ1 þ 1=REC 1 þ Ja

ð26Þ

For output work:

In this paper, the thermodynamic analysis of organic Rankine cycle using zeotropic mixture is presented. The following conclusions can be drawn: (1) A thermodynamic model is proposed to forecast the thermal efﬁciency, output work and exergy efﬁciency of an ideal ORC system with zeotropic mixuture. There is not a rigorously negative correlation between the thermal efﬁciency and Jacob number. (2) When the other system parameters are ﬁxed, there exists an optimal evaporation temperature corresponding to a maximum output work. (3) At ﬁxed other working conditions, for the optimal evaporation temperature, the heat source inlet temperature has a signiﬁcant inﬂuence on the best composition of zeotropic mixtures. With the increase of heat source inlet temperature, there exists a heat source inlet temperature that pure working ﬂuid has better system performance than zeotropic mixture. (4) The extent of performance improvement with zeotropic mixtures as working ﬂuids has a positive correlation with its temperature glide.

W net ¼ W t W p ¼ Q e Q c _ fluid ½C p13 ðT 3 T 1 Þ þ r m _ fluid T c ðs5 s1 Þ ¼m p13 ln T 3 Þ _ fluid ½C p13 ðT 3 T 1 Þ þ r T c ðTr þ C ¼m T1 e h i m C P _ heatsource ðT h in T sat l DT PP Þ p13 ln T 3 ¼ C p13 ðT 3 T 1 Þ þ r T c Tre þ C r T1 h i _ heatsource ðT h in T sat l DT PP Þ 1 þ C p13 ðTr 3 T 1 Þ C p13 T c ln TT 31 TTec ¼ C P m r " # _ heatsource ðT h in T sat l DT PP Þ 1 þ Cp13 ðT 3 T 1 Þ Tc T Ja ln T 3 Tc ¼ C P m r

T1

3 1 T1

T1

Te

ð27Þ Substituting Eqs. ()()()(17)–(19) into (27), the output work of an ideal ORC is obtained as:

Pm _ heatsource ðT h W net ¼ C

in

T sat l DT PP Þ½Jað1 ln REC

ðREC 1Þ1 Þ þ 1 1=REC

ð28Þ

Substituting Eqs. (27) and (14) into (13), the exergy efﬁciency can be simpliﬁed as

gexer ¼

P ðT h in T sat l DT PP Þ½Jað1 lnREC ðREC 1Þ1 Þ þ 1 1=REC C hh in h0 T 0 ðsh in s0 Þ ð29Þ

Acknowledgement This study was supported by National Natural Science Foundation of China (No. 51276123). Appendix A. The demonstration of Eqs. (16), (20), and (21) is listed as follows:

gtherm ¼ WQnete ¼ Q eQQe c ¼ 1 QQ ce ¼1

¼1 ¼1

_ fluid T c ðs5 s1 Þ m _ fluid ½C p13 ðT 3 T 1 Þ þ r m T c Tre þ C p13 ln TT 31 C p13 ðT 3 T 1 Þ þ C p13 T c ln TT 31 þ TT ce r C ðT T Þ 1 þ p13 r 3 1

r

ð23Þ

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