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Applied Thermal Engineering 113 (2017) 1056–1070

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Applied Thermal Engineering

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Research Paper

Economical evaluation and optimization of organic Rankine cycle withmixture working fluids using R245fa as flame retardant

http://dx.doi.org/10.1016/j.applthermaleng.2016.11.0591359-4311/� 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.E-mail address: [email protected] (Y.-L. He).

Huan Xi a, Ming-Jia Li a, Ya-Ling He a,⇑, Yu-Wen Zhang a,b

aKey Laboratory of Thermo-Fluid Science and Engineering of Ministry of Education, School of Energy and Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, ChinabDepartment of Mechanical and Aerospace Engineering, University of Missouri, Columbia, MO 65211, USA

h i g h l i g h t s

� Parametric optimization of ORC using mixture working fluids was carried out.� R245fa was introduced as the flame retardant in the mixture working fluids.� Fraction of R245fa was employed as one of optimized variables.� Correlations between fraction of R245fa and heat source temperature were obtained.

a r t i c l e i n f o

Article history:Received 17 May 2016Revised 7 November 2016Accepted 7 November 2016Available online 9 November 2016

Keywords:Waste heat recovery (WHR)Organic Rankine cycle (ORC)Mixture working fluidsFlame retardantPerformance optimization

a b s t r a c t

A detailed economic model of organic Rankine cycle (ORC) system using mixtures as working fluid hasbeen built. By using R245fa as the flame retardant, R245fa/Isopentane, R245fa/Pentane, R245fa/Cisbutene and R245fa/Butene were considered as the potential working fluids. The heat source temper-atures investigated were 373.15–453.15 K. The optimization of 4 mixture and 5 pure working fluids werecarried out with the objective function of minimizing the Electricity Production Cost (EPC). GeneticAlgorithm (GA) was employed as the optimized method. Different from the most of the optimizationresearches about ORC with mixture working fluid, the mixture composition was set as one of the vari-ables in the present work. The results show that the mixture working fluid is more economic-efficientthan pure working fluid. The lower EPC value obtained by mixture working fluid was mainly due tothe decrease of capital cost, which is essentially caused by the decrease of capital cost of the evaporator.R245fa/Isopentane and R245fa/Pentane were recommended as the optimal working fluids for their min-imum EPC values. In addition, the correlations between the optimized mixture composition and heatsource temperature were obtained.

� 2016 Elsevier Ltd. All rights reserved.

1. Introduction

Environmental issues like air pollution and global warmingcaused by the overuse of fossil fuel have become increasingly sev-ere [1,2]. On the other hand, massive of low-temperature wasteheat generated during different industry processes released tothe environment caused a serious problem of energy waste. Forthese reasons, new environmentally-friendly technologies needto be developed to improve the overall energy utilization efficiencyand recover heat from low-temperature heat sources. OrganicRankine cycles (ORCs) as one of the candidates for waste heatrecovery has attracted increasing attention.

Organic Ranking cycle (ORC) is preferred as an efficientapproach due to their flexibility, good thermodynamic perfor-mance, and simpler configuration. In the design of the ORC system,one important factor is the working fluid selection. Pure workingfluids were generally utilized in ORC systems, for example, refrig-erants such as R11, R141b, R113, R123, R245fa, R245ca [3], or someflammable hydrocarbons like n-pentane [4], Isobutane [5]. How-ever, the most important limitation of pure working fluid is theconstant temperature during the phase change process in theevaporator and condenser, which is not suitable for sensible heatsources. By contrast, by using mixture working fluid, the systemperformance can be improved by reducing the mismatch of tem-perature profiles between the heat transfer fluid and working fluid.Therefore, there is a significantly arising interest in mixture work-ing fluids research. Zhao and Bao [6] discussed the influence ofcomposition shift on ORC using R601/R600a as working fluid; the

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Nomenclature

A heat transfer area (m2)B correction factor of Table 5C cost ($)cp specific heat capacity (kJ/(kg�K))CEPCI chemical engineering plant cost indexCRF capital recovery cost ($/(kW�h))de equivalent diameter (mm)D tube diameter (mm)EPC electricity production cost ($/(kW�h))F correction factor of Table 5GWP global warming potentialh specific enthalpy (kJ/kg)H total wind pressure of the fan (Pa)i interest ratek heat transfer coefficient (W/(m2�K))K correction factor of Table 5L length (m)LTpl plant life time (year)m massmf mass fractionp pressure (kPa)Pr Prandtl numberT temperature (K)ODP zone depletion potentialQ heat transfer flow rate (kW)q heat flux (W/m2)_m mass flow rate (kg/s)VV volume low rate (m3/s)c latent heat of vaporization (kJ/kg)y mole fractionRe Reynolds numberW power (kW)M molecular weight (kg/mole)v specific volume (m3/kg)

x the mole fraction of R245fax (with subscripts l and L) dryness4T pinch temperature (K)

Greek symbolsg efficiency (%)l dynamic viscosity (Pa�s)q density (kg/m3)

Subscriptsbm subscripts of correction factor in Table 5bo boiling sectionC condensercri criticalcap capital costco condoning sectionE evaporatorF fang gasH pinch point of the evaporatori&m insurance and maintenance costL pinch point of the condenserm correction factor of Table 5net net powerph phase change sectionExp expenderwall wallWF working fluid1–9, 2a, 5a, 1⁄, 7⁄ state points in the cycle

superscriptelec electricity

H. Xi et al. / Applied Thermal Engineering 113 (2017) 1056–1070 1057

fraction ratio was fixed at 31.56%/68.44% (mass fraction), and theheat source temperature was 90 �C. The results showed that thecomposition shift led to a lower output work of expander, thehigher power consumption of the pump, lower net output work,and thermal efficiency. They also evaluated the output work, ther-mal efficiency and exergy efficiency of the ideal ORC systems fordifferent zeotropic mixtures consisting of 5 components (i.e.,R227ea, R245fa, R245ca, R236fa, and R236ea). The fractions of eachmixture were evenly distributed between 0 and 1 with a step-length of 0.2. The influence of the heat source temperature onthe optimal mass fraction of the different zeotropic mixture wasemphasized [7]. Heberle et al. [8] presented a detailed simulationof ORC system. The second law efficiency was calculated for isobu-tane/isopentane and R227ea/R245fa depending on 5 different frac-tion ratios. Le et al. [9] carried out the thermodynamic andeconomic optimization of a subcritical ORC using n-pentane/R245fa as working fluid under 5 different fraction ratios. The heatsource temperature used in the calculated process was 423.15 K.N-pentane was recommended for the highest maximized exergyefficiency and the lowest minimized LCOE (Levelized Cost of Elec-tricity). Garg et al. [10] investigated the system performance usingisopentane/R245fa as the working fluid with a fixed mole fractionof 0.7/0.3. The heat source temperatures were in the range of 385–425 K. The results showed that the mixture and the pure workingfluid showed a comparable irreversibility at their optimum expan-sion ratios. Genetic algorithm was widely adopted for ORC opti-mization. Dai et al. [11] operated optimization calculating forORC using GA, the exergy efficiency was employed as the objective

function, the working fluid selection was also performed based onthe calculation results. Wang et al. [12] operated a multi-objectiveoptimization of the ORC with R134a as working fluid. Exergy effi-ciency and overall capital cost were employed as the objectivefunctions. The effects of different optimized parameters on theexergy efficiency and capital cost were both examined accordingto the optimization results. The authors have also adopted GA asthe optimization method for different ORC system comparison[13] and working fluid selection [14].

From the above literature review, it can be observed that formixture working fluid, most works were carried out with fixedmixture composition. Few studies have reported about adoptingthe mixture composition as one of the optimized variables. In addi-tion, the formulations of mixture fraction to heat source tempera-ture were rarely mentioned. In view of this, in this paper, a numberof mixtures consisting of inert (nonflammable) working fluids andflammable working fluids (hydrocarbons) were explored. The inertworking fluid we selected was R245fa with high global warmingpotential (GWP) which was commonly adopted by the previousresearches [15,16]; the flammable working fluids we selected werepentane [17], isopentane [18], butane [19] and cisbutene [20]according to previous researches, with low GWP. R245fa was moti-vated by the possibility of suppressing the flammability of the lat-ter working fluids by blending with these working fluids,meanwhile, the mixture working fluid decreases the GWP relativeto R245fa used alone, which enhanced the working fluids’ environ-mental performance. Properties of working fluids’ components arelisted in Table 1. Based on the economic model, the economic

1058 H. Xi et al. / Applied Thermal Engineering 113 (2017) 1056–1070

performance of mixture and pure working fluids were both opti-mized and compared, and the formulations of mixture compositionto heat source temperature were fitted on the basis of the opti-mized results. Optimal working fluids for different heat sourcetemperatures were recommended based on the calculated results.

2. Modeling and calculation method

2.1. Thermodynamic model

ORC system consists of at least five principal components: evap-orator, expander, condenser, pump and working fluid. The workingfluid is saturated liquid when passing out the condenser, then bepumped to the evaporator to gain energy from heating source fluid.Generated high pressure working fluid vapor could be saturated orsuperheated expands in the expander.

The system layout and cycle T-s chart of ORC system are shownin Fig. 1. During the calculating process, several assumptions areintroduced in this study: (1) the heat transfer and flow processesare in steady-state; (2) pipe pressure drop and heat losses fromthe components are all neglected; and (3) the parameters of work-ing conditions are assumed as listed in Table 2, which is suppliedby the waste heat recovery-related company based on the actualindustry process in Xi’an, China.

It is necessary to note that during the calculating process, thecondensing temperature was assumed as 308.15 K except in thefollowing circumstance: the condensing pressure decreases belowatmosphere pressure under 308.15 K. In that case, the condensingtemperature should be raised to set condensing pressure equal tothe atmosphere pressure in order to avoid air getting into the cycle.It should be noted that steam turbines expand always work wellbelow atmospheric pressure (as low as 35 mbar), however, thereneeds extra equipment to extract non-condensable fluid. We donot advocate to transplant the vacuum keeping system into ORCsystem. As a kind of green energy technology, ORC should be posi-tioned as high applicability and simplification technology, anyextra equipment which makes the system complex, bulky and withhigher initial cost should not be recommended.

For the ORC systems, the power of expander and pump can beexpressed as:

WExp ¼ ðh1 � h2aÞ _mWF ¼ gExpðh1 � h2Þ _mWF ð1Þ

WP ¼ ðh5a � h4Þ _mWF ¼ ðh5 � h4Þ _mWF=gP ð2Þwhere gExp and gP are the isentropic efficiency of expander andpump, which are both assumed as 0.8. _mWF is the mass flow rateof the working fluid. hi is the specific enthalpy of the working fluidat the state point i (as shown in Fig. 1).

The pump motor efficiency (with the unit of 100%) is calculatedfrom [21]:

gmotor ¼ 75þ 11:5logWP � 1:5ðlogWPÞ2h i

=100 ð3Þ

Table 1Properties of the working fluids’ components.

Working fluid Tcria(K) Pcri

b (kPa)

R245fa (C3H3F5) 427.16 3651.0Cisbutene (C4H8) 418.09 4009.8Butene (C4H8) 419.29 4005.1Isopentane (C5H12) 460.35 3378.0Pentane (C5H12) 469.7 3370.0

a Pc: critical pressure.b Tc: critical temperature.c ODP: ozone depletion potential.d GWP: global warming potential.

where the motor power input is:

WelecP ¼ WP=gmotor ð4ÞThe net output power is defined as:

Wnet ¼ WExp �WelecP �WF ð5Þ

where WF is power consumption of the fan for waste gas and cool-ing air side, which can be calculated as [18]:

WF ¼ 2:778� 10�7H � VV;g � FL

g1 � g2 � g3ð6Þ

where H is the total wind pressure of the fan, VV,g is the gas flow ratewith a unit of m3/h. g1, g2, g3 are fan efficiency, transmission effi-ciency, and electric efficiency, they are assumed as 0.7, 1.0, 0.9,respectively. FL is the altitude correction coefficient which can becalculated as [22]:

FL ¼ 0:98604þ 0:01435� 10�2HL þ 2:495� 10�9H2L ð7Þ

where HL in the above formula is altitude with the unit of meter.To calculate the net output power, the mass flow rate of work-

ing fluids and cooling air are indispensable. The mass flow rate isusually calculated according to the pinch points temperature andpinch point location. In this work, the pinch point temperature ofthe evaporator (DTH) and condenser (DTL) are both fixed at 8.0 K.For the mixture working fluids, the temperature glide during theevaporating and condensing processes perhaps make the pinchpoint location varying under different working conditions and dif-ferent mixture compositions. To confirm the pinch point locationand calculate mass flow rate, the following method should beadopted (take evaporator as example): In the evaporator, the pos-sible location of pinch point should be at point (see Fig. 1): 7(1),7⁄(1⁄), 8(6), 9(5a), then pinch point temperature should be calcu-lated according to one of the following 4 equations:

DTH1 ¼ Tg;7 � T1 ð8Þ

DTH2 ¼ Tg;7� � T1� ð9Þ

DTH3 ¼ Tg;8 � T6 ð10Þ

DTH3 ¼ Tg;9 � T5a ð11ÞStep 1: point 7(1) is first assumed as the pinch point, then DTH1

is assigned the value of 8.0 K.Step 2: based on the above assumption, DTH2, DTH3, DTH4 arecalculated according to the energy balance between (1–1⁄ and(7–7⁄), (7⁄–8) and (1⁄–6), (8–9) and (6–5a).Step 3: compare the four temperature differences above, ifDTH2, DTH3, DTH4 are less than 8.0 K, the mass flow rate shouldbe calculated as:

_mWF ¼ cp;g _mgðT7 � T7� Þ=ðh1 � h1� Þ ð12Þ

Flammability ODPc GWPd

Nonflammable 0 1030Flammable n.a n.aFlammable n.a n.aFlammable 0 �20Flammable 0 �20

Fig. 1. System layout and cycle T-s chart of ORC system.

Table 2Assumed working conditions.

Waste gas mass flow rate (kg�s�1) 15.0Environment temperature (K) 293.15Environment pressure (kPa) 101.3Condensing temperature (K) 308.15Expander isentropic efficiency 0.8Pump isentropic efficiency 0.8Pinch temperature difference in the evaporator (K) 8.0Pinch temperature difference in the condenser (K) 8.0


where cp;g is the specific heat capacity of the waste gas.Otherwise, if there exists a DTH less than DTH1, the assumption

in Step 1 is disproved, then DTH2 should be is assigned the value of8.0 K and the Step 2–3 need to be repeated to calculate the temper-ature difference until one the assumption is proved right and thelocation of pinch point is determined.

2.2. Economic model

Electricity production cost (EPC) is the ratio of the total systemcost to the net power output, which can be calculated by:

EPC ¼ ðCRF � Ccap þ Cm&iÞ=ðh �WnetÞ ð13Þwhere Ccap signifies the capital cost, comprising the investments forthe evaporator, expander, condenser, pump, fans and working fluid.

Ccap ¼ ðCbm;E þ Cbm;Exp þ Cbm;P þ Cbm;CÞ CEPCI2014CEPCI1996þ Cbm;F

� CEPCI2014CEPCI2011

þ CWF ð14Þ

wherein CEPCI1996 = 382, CEPCI2011 = 582, CEPCI2014 = 586.77 (CEPCImeans Chemical Engineering Plant Cost Index) [23].

CRF is the capital recovery cost, which is estimated based on thefollowing equation.

CRF ¼ ið1þ iÞLTpl ð1þ iÞLTpl � 1h i.

ð15Þ

where i is the interest rate, assumed to be moderate at 5%, LTpl is theplant life time, assumed at 15 years. h is system working hours perannual operation period (h/year), in this work, it was assumed as7500 h. Cm&i means the insurance and management cost of the sys-tem, which can be calculated as [24,25]:

Cm&i ¼ 1:65%Ccap ð16Þ

As the key factor of the cost estimation model, componentinvestment cost provided by a current price quote from a suitablevendor (a seller of equipment), and adjusted using appropriate fac-tors. Each component investment in Eq. (14) could be predicted bythe following correlations and the corresponding coefficients K, B,C and F are listed in Table 3 [26,27].

For expander,

Cbm;Exp ¼ CExpFbm;Exp ð17Þ

logCExp ¼ K1;Exp þ K2;Exp logWExp þ K3;Exp logWExp� �2 ð18Þ

for the pump,

Cbm;P ¼ CPFbm;P ð19Þ

logCP ¼ K1;P þ K2;P logWP þ K3;PðlogWPÞ2 ð20Þ

Fbm;P ¼ B1;P þ B2;PFm;PFp;P ð21Þ

log FP;P ¼ C1;P þ C2;P logprp þ C3;PðlogprpÞ2 ð22Þ

prp ¼ pE � pC ð23Þfor heat exchangers (take evaporator as an example),

Cbm;E ¼ CEFbm;E ð24Þ

logCE ¼ K1;E þ K2;E logAE þ K3;EðlogAEÞ2 ð25Þ

Fbm;E ¼ B1;E þ B1;EFm;EFp;E ð26Þ

log Fp;E ¼ C1 þ C2 logðpE � p0Þ þ C3ðlogðpE � p0ÞÞ2 ð27Þfor the fan of waste gas and cooling air,

Cbm;F ¼ CFFbm;FFp;F ð28Þ

logCF ¼ K1;F þ K2;F log qV þ K3;Fðlog qV Þ2 ð29Þ

log Fp;F ¼ C1 þ C2 logpF þ C3ðlogpFÞ2 ð30Þwhere qV is the gas flow rate with a unit of m3/h.

For the working fluid,

CWF ¼ cWFmWF ð31Þwhere cWF is the unit price of working fluid with a unit of $/kg, mWF

is the total working fluid charge the unit of kg, which will be intro-

0 20 40 60 80 1000.43

0.44

0.45

0.46

0.47

0.48

Opt

imal

valu

e of

obj

ectiv

e fu

nctio

n(E

PC)/

$·kW

h

Evolution time

-1

Fig. 2. Variation of the optimal objective function value with the evolution times.

Table 3Coefficients in equations evaluating the investment of system components [26,27].

Component K1 K2 K3 B1 B2 C1 C2 C3 Fm Fbm

Evaporator 3.853 0.424 0 1.53 1.27 0 0 0 2.8 /Condenser 3.853 0.424 0 1.53 1.27 0 0 0 2.8 /Expander 3.514 0.598 0 / / / / / / 3.5Pump 3.579 0.321 0.003 1.8 1.51 0.168 0.348 0.484 1.8 /Fan (with electric device) 3.1761 �0.1373 0.34314 0 0.20899 �0.0328 / / / 1.12

Table 4Configurations of genetic algorithms.

Population size 100Chromosome vector [T1, P1, x]Crossover probability 0.4Mutation probability 0.9Elite count 20Stop generation 100


duced in part 2.4. Eqs. (17)–(30) are referred from Refs. [26,27],while Eq. (31) is referred from Ref.[28].

The cost estimation model used in this manuscript are widelyadopted. The purchased cost is the key factor of the cost estimationmode, which is provided by a current price quote from a suitablevendor (a seller of equipment), and adjusted using appropriatescaling factors (such as K), and for inflation (such as CEPCI2014),to provide the estimated capital cost.

2.3. Calculation of the heat exchangers area

To calculate the heat transfer area of evaporator and condenser,the heat transfer coefficient should be determined [29]. In theevaporator and condenser, the convective heat transfer coefficientof the organic working fluid side is generally more than 2000 W/(m2�K) [30,17] which is much great than that of the gas side. Thus,the overall heat transfer coefficient in the evaporator and con-denser are mainly dependent on the convective heat transfer coef-ficient of gas side; in some related works, it was even assumed tobe the constants to simplify the calculation [31,32]. Therefore, inthis work the total heat transfer coefficient is estimated byemploying the Kern formula [33]:

kph ¼ kbo ¼ kco ¼ 0:36kde

Re0:55g Pr1=3l

lwall

� �0:14

ð32Þ

where kph, kbo and kco are the heat transfer coefficient during thephase change, boiling and condensing processes. l is the dynamicviscosity of the gas side. de is the equivalent diameter of the tube.k is heat conductivity coefficient, Re and Pr are the Reynolds numberand Prandtl number, respectively.

The logarithmic mean temperature difference (LMTD) methodis widely used in heat exchanger design and calculation. Based onthe above analysis, the overall heat transfer coefficient in the heatexchangers are mainly dependent on the convective heat transfercoefficient of the gas side. It is necessary to point out that thephysical properties of waste gas were assumed as the fixed val-ues in some related work [34]; even so, the physical propertiesof the gas are temperature-dependent, especially in the relativelyhigh-temperature ranges [35]. Thus, the assumption of constantproperties may lead to inaccurate results. An alternative solutionis discretizing the heat exchangers so that the properties varia-tion in each step is small and could be treated as an average con-stant value. The heat transfer for each step i as well as thecorresponding properties of the waste gas and cooling air, andthe fractional UAi values are calculated from the following equa-tions (assumed as counter-flow configuration, take evaporator asan example):

Q i ¼ _mgðhg;iþ1 � hg;iÞ ð33Þ

Q i ¼ _mWFðhWF;iþ1 � hWF;iÞ ð34Þ

Q i ¼ kAiðTg;iþ1 � TWF;iþ1Þ � ðTg;i � TWF;iÞ

ln Tg;iþ1�TWF;iþ1Tg;i�TWF;i

h i ð35Þ

For evaporator, it can be divided into three regions: a super-heated region, a two-phase region, and a supercooled region. Forthe condenser, the last two regions are applicable. Each region isthen subdivided into 20 steps.

For the calculating method of waste gas physical properties inthis work, we adopt the formulas presented in Ref. [36], and forthe cooling air, the physical properties calculating formulas werefitted based on the data from Refprop 9.0.

2.4. Working fluid charge estimation

In the economic model described in Section 2.2, as seen in Eq.(14), the working fluid cost should be calculated. As we know,the working fluid cost is equal to the product of the unit price ($/kg) and working fluid charge (kg). The unit price of the working flu-ids was obtained from the related manufacturers. To estimate theworking fluid charge, the method presented in Ref. [37] wereadopted. Take evaporator as an example, the mass flow rate ofvaporized working fluid at the position with a distance of l fromthe inlet should be calculated as:

q00WF ¼ qpDl=c ð36Þ

where q is the heat flux (W/m2), and c is the latent heat (J/kg), D istube diameter.

The total mass flow rate (for each tube) can be calculated as:

qWF ¼ qpDL=xLc ð37Þ

(a) Initial population (b) Evolving for 25 times

(c) Evolving for 75 times (d) Evolving for 100 times

Fig. 3. Population distributions under different evolution times.

Table 5Calculating results of program stability evaluation.

Calculation times Value of objective function (EPC/$�kW�h�1) x of R245fa T1 (K) p1 (kPa)

1 0.4283 0.8552 373.88 1142.122 0.4291 0.8556 369.94 1144.943 0.4296 0.8532 368.03 1126.484 0.4290 0.8541 370.68 1141.965 0.4291 0.8535 370.00 1129.95Relative error 0.295% 0.285% 1.56% 1.61%


where xL is the dryness at the evaporator outlet, L is tube length.Thus, the dryness at the position with a distance of l from the

evaporator inlet can be expressed as:

xl ¼ q00WF

�qWF ¼ xLl=L ð38Þ

It can be seen from Eq. (37) that xl is changed linearly with l.Thus, the working fluid charge (kg) is:

1.151.201.251.30

0.840.880.920.96

0.6750.7000.7250.750

0.5550.5700.5850.600

0.470.480.490.50

0.4080.4140.4200.426

0.3500.3550.3600.365

0.290.300.310.32

0.1 0.3 0.5 0.7 0.90.2 0.4 0.6 0.80.2700.2750.2800.285

453.15 K

443.15 K

433.15 K

423.15 K

413.15 K

403.15 K

393.15 K

383.15 K

T g/K

EPC

/$·k

W-1

xR245fa

373.15 K

Fig. 4. Variation of the EPC with the mole fractions of R245fa for R245fa/Butene mixture under different heat source temperatures.


mE ¼Z L

0

AE

v dl ¼Z x0

0AE

lnv 0 � ln v 00 þ v 0 � v 0xLð ÞxLðv � v 000Þ

� �LxL

� �dx

¼ AELElnv 0 � ln v 00xL þ v 0 � v 0xLð Þ

xLðv � v 000Þ ð39Þ

373.15 393.15 413.15 433.15 453.150.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Cap

ital c

ost/

106 $

R245fa/Pentane R245fa Pentane

EPC

/ $·k

WWh-1

Tg/K

(a) R245fa/Pentane

373.15 393.15 413.15 433.15 453.150.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

2.0

2.5

3.0

3.5

4.0

4.5

5.0

ButeneR245faR245fa/Butene

Cap

ital c

ost/

106 $

EPC

/ $·k

W-11

Tg /K

-1

(c) R245fa/Butene

Fig. 5. Variations of the EPC and total cost with heat source

The same procedure can be easily adopted to condenser:

mC ¼ ACLClnv 0 � ln v 00xL þ v 0 � v 0xLð Þ

xLðv � v 000Þ ð40Þ

373.15 393.15 413.15 433.15 453.150.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Isopentane

Cap

ital c

ost/

106 $

R245fa/Isopentane R245fa

EPC

/ $·k

Wh-1

Tg/K

(b) R245fa/Isopentane

373.15 393.15 413.15 433.15 453.150.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

2.0

2.5

3.0

3.5

4.0

4.5

Cap

ital c

ost/

106 $

R245fa/Cisbutene R245fa Cisbutene

EPC

/ $·k

W

Tg /K

(d) R245fa/Cisbutene

temperatures for the mixture and pure working fluids.


where mE and mC are the working fluid charge in evaporator andcondenser, respectively. AE and AC are total heat exchanger area ofevaporator and condenser, respectively. v’ and v’’ are the specificvolume of vapor and liquid working fluid, respectively.

The working fluids charged in pump and expander possess avery low proportion. However, to make the calculation resultsmore accurate, the ratio of this part of working fluids was set as17.5%. We obtained this value from the experimental measure-ment in Ref. [38]. Based on the preceding description and analysis,the total working fluid charge is estimated by:

mWF ¼ ðmC þmEÞ=ð1� 17:5%Þ ð41Þ

3. Description and evaluation of the optimization method

3.1. Description of the Genetic algorithm method

Genetic algorithm (GA) is widely used as an optimizer for dis-continuous, non-differentiable, or highly nonlinear problems.Inspired by Darwinian survival of the fittest principle, GA is a kindof bionics process. There are three basic and indispensable opera-tors: selection operator, crossover operator, and mutationoperator.

In this work, fractions of working fluid, expander inlet pressureand temperature (i.e. T1 and P1), are selected as variables. Thethree-dimensional array [T1, P1, x] is chromosome. When generat-

50

100

150

200

250

373.15 393.15 413.15 433.15 453.150.04

0.06

0.08

0.10

0.12

0.14


Wne

t /kW

η th

Tg/K

(a) R245fa/Pentane

50100150200250300

0.04

0.06

0.08

0.10

0.12

0.14

R245fa/Butene R245fa Butene

Wne

t /kW

η th

Tg/K

(c) R245fa/Butene

373.15 393.15 413.15 433.15 453.15

Fig. 6. Variations of the net power and thermal efficiency with the he

ing the initial populations [T1n, p1n, x]n, the constraint conditionsare:

x 2 [0.05, 0.95];T1 2 [333.15 K, Tmax], while Tmax = min{(Tcrit-10), (Tgas-8)};p1 2 [200 kPa, psat,T].

x is a randomly generated number between 0.05 and 0.95. Thelower bound of T1 is 333.15 K, which is lower than all the optimalworking conditions. The upper bound is given as the pinch pointtemperature and the critical temperature of the working fluid.The constraint (Tgas-8) is set according to the pinch point temper-ature, while the constraint (Tcrit-10) follows the rule that the high-est temperature of the cycle should be 10 K lower than criticaltemperature [20]. To enable the state of [T1, p1, x] to be overheatedor saturated, the lower bound of p1 is 200 kPa, which is low enoughfor all the working fluids and systems under the given conditions.The upper bound is generated by employing the saturation pres-sure psat,T associating with the generated T1 and x.

When the EPC is chosen as the fitness function, the fitness func-tion can be expressed as:

EPC ¼ f ðT1; P1; xÞ ð42ÞThe selection operator is used for selecting the excellent parents

(with the better value of fitness function) among existing chromo-somes to create the next generation. In this work, the selection

50

100

150

200

250

0.04

0.06

0.08

0.10

0.12

0.14

R245fa/Isopentane R245fa Isopentane

Wne

t /kW

η th

Tg/K

(b) R245fa/Isopentane

50

100

150

200

250

300

0.04

0.06

0.08

0.10

0.12

0.14

R245fa/Cisbutene R245faCisbutene

Wne

t /kW

η th

Tg/K

(d) R245fa/Cisbutene

373.15 393.15 413.15 433.15 453.15

373.15 393.15 413.15 433.15 453.15

at source temperatures for the mixture and pure working fluids.


operator we adopt is ‘‘deterministic sampling” method [39]. Thecrossover operator is responsible for generating new chromosomesby combining the selected two chromosomes. The simple arith-metic crossover is employed in this work. The fundamental ofarithmetic crossover is presented as follows [40]:

c1 ¼ af1 þ ð1� aÞf 2c2 ¼ af2 þ ð1� aÞf 1

�ð43Þ

where c1 and c2 are offsprings, f1 and f2 are parents, a is a randomnumber between 0 and 1. To avoid converging on local solutions,the mutation operator is used. The ‘‘elite-preservation strategy” is

373.15 393.15 413.15 433.15 453.1525

30

35

40

45

P eva /

%

Tg/K


(a) evaporator

373.15 393.15 413.15 433.15 453.151.0

1.5

2.0

2.5

3.0

P pum

p / %

Tg/K


(c) pump

373.15 393.15 413.15 433.15 453.150

5

10

15

P fan /

%

Tg/K


(e) fans

Fig. 7. Percentage of each component in the total capital cost using R245fa

employed to protect the elites from crossover and mutation thusaccelerating convergence [41]. Configurations of the GA in this workare listed in Table 4.

Based on the above description, Genetic algorithm program waswritten by the authors with FORTRAN language. Subroutines con-tained in REFPROP 9.0 were called during the simulation processto calculate the thermodynamics properties of working fluids.

3.2. Evaluation of Genetic algorithm program

Along with the evolving process, the individuals with worse fit-ness are weeded out, while the individuals with better fitness are

373.15 393.15 413.15 433.15 453.1540

45

50

55

60

65

70

P con /

%

Tg/K


(b) condenser

373.15 393.15 413.15 433.15 453.154

8

12

16

P exp /

%

Tg/K


(d) expander

373.15 393.15 413.15 433.15 453.150.0

0.2

0.4

0.6

0.8

P WF /

%

Tg/K


(f) working fluid

, Pentane and their mixture under different heat source temperatures.


assigned with high probabilities to survive to the next generation;the individuals should finally converge in a small area. The optimalindividual with the minimum value of EPC could be singled outfrom the final population. The working condition of heat sourcetemperature 413.15 K using working fluid R245fa/Isopentane isperformed as an example to evaluate the feasibility and stabilityof the optimization method. Fig. 2 shows the variation of the opti-mal objective function value with the evolution times. It can beseen that as the evolution times increased, the optimal value ofobjective function updated by the smaller value until the iteration

373.15 393.15 413.15 433.15 453.1515

20

25

30

35

40

45

P eva /

%

Tg/K


(a) evaporator

373.15 393.15 413.15 433.15 453.151.0

1.5

2.0

2.5

3.0

3.5

4.0

P pum

p / %

Tg/K


(c) pump

373.15 393.15 413.15 433.15 453.150

5

10

15

20

P fan /

%

Tg/K


(e) fans

Fig. 8. Percentage of each component in the total capital cost using R245fa,

is stopped (with the stop generation of about 100). Fig. 3 shows thepopulation distribution under different evolution times. As shownin Fig. 3(a), the randomly generated individuals in the initial pop-ulation are distributed dispersedly. Along with the evolution timeincreased, the degree of convergence of the individuals alsoincreased. When the value of evolution time reaches 100, as canbe seen in Fig 3(d), the individuals converge in a small area aroundthe optimal individual. To evaluate the stability of the in-houseGenetic algorithm program, calculations are performed 5 timesrepeatedly under the same parameter settings and the results are

373.15 393.15 413.15 433.15 453.1545

50

55

60

65

70

P con /

%

Tg/K


(b) condenser

373.15 393.15 413.15 433.15 453.154

6

8

10

12

14

16

P exp /

%

Tg/K

R245fa/Isopentane R245fa Pentane

(d) expander

373.15 393.15 413.15 433.15 453.150.0

0.2

0.4

0.6

0.8

P WF /

%

Tg/K


(f) working fluid

Isopentane and their mixture under different heat source temperatures.


listed in Table 5. It shows that for the 5 times calculations, opti-mized value of objective function and parameters relative errorswere below 2%, which is enough to meet the requirement of theindustrial demand.

4. Results and discussions

4.1. Comparison between the calculating methods

In the most of the related work, the mixture compositions wereusually discretely assumed as fixed values. Take R245fa/Butene as

373.15 393.15 413.15 433.15 453.1525

30

35

40

P eva /

%

Tg/K


(a) evaporator

373.15 393.15 413.15 433.15 453.151.0

1.5

2.0

2.5

3.0

3.5

4.0

P pum

p / %

Tg/K


(c) pump

373.15 393.15 413.15 433.15 453.150

5

10

15

20

P fan /

%

Tg/K


(e) fans

Fig. 9. Percentage of each component in the total capital cost using R245fa

an example, under the given heat source temperatures, the optimalEPC values under different mixture compositions (mole fractions ofR245fa, varied from 0.1 to 0.9) were calculated. The calculatedresults are presented in Fig. 4. It can be seen from Fig. 4 that the‘‘optimal mixture composition (corresponding with lowest EPCvalue for given heat source temperature)” under different heatsource temperatures are distributed between 0.25 and 0.55,roughly showing an increasing trend along with the increase ofheat source temperatures. Above method was commonly used toobtain the ‘‘optimal mixture composition” for mixture workingfluid, however, several shortcomings exist about this method:

373.15 393.15 413.15 433.15 453.1545

50

55

60

65

P con /

%

Tg/K


(b) condenser

373.15 393.15 413.15 433.15 453.154

6

8

10

12

14

P exp /

%

Tg/K


(d) expander

373.15 393.15 413.15 433.15 453.150.0

0.2

0.4

0.6

0.8

P WF /

%

Tg/K


(f) working fluid

, Butene and their mixture under different heat source temperatures.

373.15 393.15 413.15 433.15 453.1525

30

35

40

P eva /

%

Tg/K


373.15 393.15 413.15 433.15 453.1545

50

55

60

65

P con /

%

Tg/K


(a) evaporator (b) condenser

373.15 393.15 413.15 433.15 453.15

1.5

2.0

2.5

3.0

3.5

4.0

P pum

p / %

Tg/K

R245fa/Cisbutene R245faCisbutene

373.15 393.15 413.15 433.15 453.154

6

8

10

12

14

P exp /

%

Tg/K


(c) pump (d) expander

373.15 393.15 413.15 433.15 453.150

5

10

15

20

P fan /

%

Tg/K


373.15 393.15 413.15 433.15 453.150.0

0.2

0.4

0.6

0.8

P WF /

%

Tg/K


(e) fans (f) working fluid

Fig. 10. Percentage of each component in the total capital cost using R245fa, Cisbutene and their mixture under different heat source temperatures.


firstly, the confirmed ‘‘optimal mixture composition” is essentiallyis an interval with accuracy of 0.1, not a unique value; secondly,the trends of objective function value (i.e. EPC value in the presentwork) and mixture composition are usually complex, singularityappears sometime [42], thus ulteriorly reducing the reliability ofthe calculated result. For these reasons described above, in thiswork, coupled with inlet temperature and pressure of expander,the mixture composition (i.e. mole fraction of R245fa) was set asone of the variables to be optimized. GA was recommended as aneffective method to optimize the system performance and obtainthe ‘‘optimal mixture composition”. When to obtain the optimalmixture compositions under certain heat source temperatures,

the calculating times were decreased 9 times. The reliability ofthe optimal program has been validated in Section 3.2. Based onthis, compared with the above-motioned method showed inFig. 4, the accuracy of the calculated optimal mixture compositionwas improved at the same time.

4.2. Comparison between mixtures and their components

Fig. 5 shows the variations of the EPC and total cost with heatsource temperatures for the mixture and pure working fluids. Itcan be seen that for all working fluids, the EPC value decreasedwith the increase of heat source temperature. For the capital cost,

373.15 393.15 413.15 433.15 453.150.0

0.2

0.4

0.6

0.8

1.0

R245fa/ Pentane

x R24

5fa

Tg /K

R245fa/ Isopentane

R245fa/ ButeneR245fa/ Cisutene

Fig. 11. Variations of the optimized mole fractions with heat source temperatures.


it showed a reverse tendency. As can be seen from Fig. 5 that themixture working fluid showed a better economic performance(lower EPC and capital cost) compared to the pure working fluid.Lower capital cost obtained by the system using mixture workingfluid means that under same heat source condition, using mixtureworking fluid leads to a smaller physical scale of ORC plant com-pared with the pure working fluid. From Fig. 5 it also can be seenthat, for the pure and mixture working fluids, the operating condi-tion for a lower EPC value always corresponds to a relative lowercapital cost value. Fig. 6 shows the variations of the net powerand thermal efficiency with the heat source temperature for themixture and pure working fluids. It can be seen from Fig. 6 thatwhen operated under the optimized working conditions, the netpower of the mixture working fluid does not have a clear advan-tage compared with the pure working fluid, which illustrates thatthe decreased EPC value of mixture working fluid is mainly due tothe decrease of the capital cost.

Percentage of each system component (i.e. evaporator, con-denser, pump, expander, working fluid and fans) in the total capitalcost using different mixture and pure working fluids under differ-ent heat source temperature are showed in Figs. 7–10. It is inter-esting to note that in most situations, for the pure and mixtureworking fluids, the percentage of the evaporator and condenserin the total capital cost decreased with the increase of heat sourcetemperature. For other components including pump, expander,working fluid, and fans, they showed opposite trends. Also, it

-0.20 -0.16 -0.12 -0.08 -0.04 0.00

CisbuteneButeneIsopentanePentane

R

T g /K

393

383

373

423

413

403

453

443

433

Fig. 12. Variations of the characterization parameter R with hea

clearly showed that the mixture working fluid with a larger per-centage of the condenser, pump, and expander in the capital cost,but a lower percentage of the capital cost of the evaporator in themost situations. Combined with the conclusion from Fig. 5, it canbe inferred that for the mixture working fluid, the decrease ofthe EPC value is mainly due to the decrease of the capital cost,which is essentially caused by the decrease of the evaporator cap-ital cost.

4.3. Analysis of the mixture working fluids behavior

Fig. 11 shows the variations of the optimized mole fractionswith heat source temperatures. It can be observed that the distri-bution of the optimized mixture compositions shows almost thelinear behavior. In the process of actual application, the correla-tions should be useful to predict the mixture compositions withgood accuracy, using only a few key design parameters and with-out the need of knowledge of working fluid properties and theiruse in ORCs. This method adopted in the present work could beused for making the correlations when the waste heat source scaleand the working fluid are confirmed. In this work with the givenworking conditions, the correlation between optimized mole frac-tions of R245fa (xR245fa) and heat source temperature (Tg/K) for theselected 4 different mixtures are given by Eqs. (44)–(47):

R245fa/Pentane:

xR245fa ¼ ð1096:63� 0:9216TgÞ=1000 ðR ¼ 0:9209Þ ð44ÞR245fa/Isopentane:

xR245fa ¼ ð537:47þ 0:7844TgÞ=1000 ðR ¼ 0:8769Þ ð45ÞR245fa/Butene:

xR245fa ¼ ð�731:62þ 2:72TgÞ=1000 ðR ¼ 0:8947Þ ð46ÞR245fa/Cisbutene:

xR245fa ¼ ð�1611:67þ 5:27TgÞ=1000 ðR ¼ 0:9698Þ ð47ÞIt can be observed from the above formulas that as the critical

temperature of the flammable working fluid increased, the slopeof fitted straight line decreased. In the mixtures, act as the flameretardants, the mole fractions of R245fa increased as the increaseof heat source temperature, this rule is correct except for R245fa/Pentane. These formulas fitted from the optimized results usingEPC as objective function should provide a reference for mixturecomposition determination for the recommended 4 mixtures.

0.00 0.02 0.04 0.06 0.08 0.10 0.12 0.14

R245fa/CisbuteneR245fa/ButeneR245fa/IsopentaneR245fa/Pentane

.15 K

.15 K

.15 K

.15 K

.15 K

.15 K

.15 K

.15 K

.15 K

t source temperatures for pure and mixture working fluids.


4.4. Recommendation of working fluid for different heat sourcetemperatures

By taking R245fa as the reference working fluid, a characteriza-tion parameter R is defined as:

RWF ¼ ðEPCR245fa � EPCWFÞ=EPCR245fa ð48Þ

where the subscripts ‘‘WF” in Eq. (48) represents different workingfluids. RWF is inversely proportional to EPCWF, the lower value of EPCcorresponds to the superior economic performance, therefore, thehigher value of RWF, the better of the accordingly working fluid.

Fig. 12 shows the variations of the characterization parameter Rwith heat source temperatures for pure and mixture working flu-ids. Fig. 12 should be divided into two parts, the left part is for pureworking fluid and the right part is for mixture working fluid. Mostof the R values for pure working fluids (on the left part) are nega-tive. This illustrates that compared with the reference workingfluid R245fa, pure working fluid with negative R value is poorlyperformed. As it to the mixture working fluid on the right part,the R value of them are all positive. They show superior economicperformance compared with R245fa and other pure working fluids.It can be observed from Fig. 12 that under medium heat sourcetemperature (i.e. 383.15–403.15 K), R245fa/Pentane is recom-mended as the optimal mixture working fluid for its maximum Rvalue (represents minimum EPC value). While for relatively low(373.15 K) and high (413.15–453.15 K) heat source temperaturesin this work, working fluid R245fa/Isopentane is recommended.As it to pure working fluids, Isopentane and Pentane are consideredas the optimal working fluids when working under heat sourcetemperature of 373.15–423.15 K and 433.15–453.15 K, respec-tively. Compared with the recommended pure working above,their mixtures with R245fa showed not only superior economicperformances but also the lower flammability. Compared withthe widely used working fluids R245fa, the economic performanceand environment performance are both improved by using the rec-ommended mixture working fluid.

5. Conclusions

Optimized calculation for 5 pure working fluids and 4 mixtureworking fluids were performed by using GA as the optimizationmethod. By using EPC as the objective function, the mixture com-position was set as one of the variables during the calculating pro-cess. The main conclusions are as follows:

(1) The mixture working fluid showed a better economic perfor-mance (lower EPC and capital cost). The lower EPC valueobtained by mixture working fluid was mainly due to thedecrease of the capital cost, which is essentially caused bythe decrease of capital cost of the evaporator.

(2) The correlations between optimized mixture composition(i.e. the mole fraction of R245fa) and heat source tempera-ture (Tg) for the selected 4 mixture working fluids were fit-ted from the optimization results.

(3) R245fa/Pentane and R245fa/Isopentane are recommendedas the optimal mixtures working fluids for temperaturerange of (383.15–403.15 K) and (373.15, 413.15–453.15 K),respectively.

Acknowledgements

The authors gratefully acknowledge the support from theNational Key Basic Research Program of China (973 Program)

(2013CB228304) and the Key Project of National Natural ScienceFoundation of China (No. 51436007).

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