Developing a performance evaluation model of Organic Rankine Cycle for working fluids based on the group contribution method

Energy Conversion and Management 132 (2017) 307–315

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Energy Conversion and Management journal homepage: www.elsevier.com/locate/enconman

Developing a performance evaluation model of Organic Rankine Cycle for working fluids based on the group contribution method Wen Su, Li Zhao ⇑, Shuai Deng Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin University), MOE, Tianjin 300072, China

a r t i c l e

i n f o

Article history: Received 25 September 2016 Received in revised form 4 November 2016 Accepted 17 November 2016

Keywords: Organic Rankine Cycle Group contribution method Simulation model Working fluids

a b s t r a c t An Organic Rankine Cycle (ORC) model is presented in this paper to easily, quickly, and inexpensively evaluate the performance potentials of various working fluids. When given molecular structure of working fluid, the normal boiling temperature, critical properties, liquid density and ideal gas heat capacity can be obtained via the existing group contribution methods (GCMs). Other properties required in the ORC model are calculated out by the thermodynamic relationships with the estimated properties of GCMs. Based on the calculated properties, four basic processes of the ORC including compression, evaporation, expansion and condensation are modeled. Meanwhile, the cycle parameters of 21 potential working fluids for typical ORC operating conditions are obtained from the molecular structures by the developed model. Compared with the REFPROP, the model shows sufficient accuracy for engineering purposes. The relative errors of thermodynamic properties and cycle parameters are less than 10% for most of working fluids. It is concluded that the proposed model can estimate the ORC characteristics of any pure working fluid only based on its molecular structure. Thus, a large amount of working fluids formed by the combination of groups can be directly screened by this model, and the optimal working fluids can be identified for a quick assessment in engineering field. Ó 2016 Elsevier Ltd. All rights reserved.

1. Introduction With the gradual depletion of conventional energy sources, more and more efforts will be paid to use renewable energy sources like solar energy, wind energy, biomass and geothermal heat as well as waste heat for the production of electricity in order to meet the increasing global energy demands. Due to the fact that the source temperatures for the non-conventional energy sources are much lower than the temperatures of conventional energy sources, the organic compounds are more appropriate than water for cycles based on renewable energy sources. One of the technologies that can effectively utilize these organic compounds is called organic Rankine Cycle (ORC). In recent years, as a promising process for conversion of renewable energy sources to electricity, ORC has received extensive researches and applications on account of the characteristics of simple structure, high reliability, and easy maintenance [1]. For example, Chagnon-Lessard et al. [2] numerically simulated the subcritical and transcritical ORC for geothermal power plants, considered 36 working fluids and optimized the operation conditions with the maximized specific power output.

⇑ Corresponding author. E-mail address: [email protected] (L. Zhao). http://dx.doi.org/10.1016/j.enconman.2016.11.040 0196-8904/Ó 2016 Elsevier Ltd. All rights reserved.

Yag˘lı et al. [3] designed a subcritical and supercritical ORC to recover exhaust gas waste heat of biogas fuelled combined heat and power engine. Through the parametric optimization and exergetic analysis, the authors concluded that the supercritical ORC shows better performance than the subcritical ORC. A number of authors have developed simulation and optimization tools for the analysis of ORC applications [4]. For instance, Saleh et al. [5] compared the thermodynamic performances of 31 pure working fluids for ORCs of different types using BACKONE equation of state (EOS). The results showed that the highest values of efficiency are obtained for the high boiling substances with overhanging saturated vapor line in subcritical processes. Barbieri et al. [6] developed a model for the simulation of ORC based on group contribution methods (GCMs). In their model, the ideal gas heat capacity is obtained from the GCMs and other properties of working fluids are calculated from tables generated from experimental pressure-temperature-specific volume data contained in the literature. The ORC processes of six commonly working fluids were simulated by this model. Oyewunmi et al. [7] employed the SAFT-VR Mie EOS to calculate the thermodynamic properties of pure organic fluids and developed a model to assess large-glide fluorocarbon working fluid mixtures. Furthermore, Brown et al. [8,9] proposed a simple methodology of applying the Peng-Robinson (P-R) EOS to evaluate the performance potentials of many

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Nomenclature Symbols AAD C CAMD E EOS GCM GWP h H ODP ORC P Q R s T w

average absolute deviation heat capacity, kJ/kg K computer aided molecular design relative error equation of state group contribution methods global warming potential enthalpy, kJ/kg enthalpy of saturated fluid, kJ/kg ozone depletion potential Organic Rankine Cycle pressure, Pa or bar heat, kJ ideal gas constant entropy, kJ/kg K temperature, K work, kW

Greeks

x q g

acentric factor saturated liquid density, kg/m3 efficiency, %

thousands of working fluids in ORC. For not-so-well-described (little or no experimental data is available) working fluids, GCMs were used to estimate the critical properties, ideal gas heat capacity, and acentric factor. The effects of thermodynamic properties on the ORC operation were also investigated by the proposed model. It should be noted that the above-mentioned models are usually for the common or widely-used working fluids. For the novel fluids, EOSs combined with the GCMs are generally employed to calculate the required properties. However, the involved iterative calculation is against the rapid performance analysis of working fluids’ application in ORC. So far, no simulation models especially for potential assessment of application of novel working fluids in ORC can be found. Besides the above mentioned papers, a number of others have focused on the selection of working fluids [10,11]. A comprehensive review of ORC working fluids was presented by Bao and Zhao [12]. The authors identified 77 commonly existing singlecomponent working fluids and 44 zeotropic blends appearing in the various papers they reviewed. The identified working fluids are well-characterized by considerable experimental data. Their thermodynamic properties can be obtained from the two widely used libraries, namely REFPROP [13] and CoolProp [14]. Each library contains high accuracy EOSs for commonly used working fluids. However, the selected working fluids from the commonly used substances can’t be assured to be the optimal working fluids for different applications of ORC. Therefore, a systematic approach called computer aided molecular design (CAMD) has been developed to generate a vast number of conventional or novel working fluids which may exhibit favorable characteristics in the cycle. For example, Samudra and Sahinidis [15] proposed an optimization-based framework for CAMD. Potential working fluids are formed by the combination of groups and GCMs are applied to predict the properties of formed working fluids. Papadopoulos et al. [16,17] employed GCMs to estimate the thermodynamic properties of the generated working fluids and considered the ORC process-related properties as performance criteria at the CAMD stage. Unlike Papadopoulos et al. who employed simulated annealing as the optimization algorithm, Palma-Flores et al.

f D

calculated properties difference

Subscripts 1, . . .7 thermodynamic state points (Fig. 1) b boiling temperature c critical properties con condensation evap evaporation net net output p pressure or pump r reduced property REF REFPROP t turbine th thermal cycle v vaporization vp vapor Superscripts 0 ideal gas g real gas l liquid working fluid

[18,19] adopted a mixed integer non-linear programming. Furthermore, more functional groups were considered by Palma-Flores et al. For more details about CAMD, the interested reader is referred to a recent review of CAMD to design working fluids for ORC by Linke et al. [20]. However, to the best of authors’ knowledge, in the process of CAMD, the above literatures always consider the thermodynamic properties as an objective function to screen the candidates. Thus, the working fluids determined by CAMD may not be the fluids, which have the best performances in the cycle. Although the EOSs can be used to assess the cycle performances of these fluids, more efficient tools are required to connect performance assessments between the cycle and the working fluids, considering the extensive computational effort of EOSs iterations. From the above literature research, it can be found that a simulation model is required to establish the connection between the ORC performances and the working fluids, so that the model can quickly evaluate the performance of novel working fluids. Therefore, in this study, a group contribution model for the subcritical ORC is developed. All the properties required in the simulation model are obtained from the molecular structure of working fluids. GCMs are employed to establish the structure-property relationships. Consequently, the novel working fluids generated from the CAMD can be evaluated by the developed model in this work. The advantage of the model is that it allows one to investigate a potential working fluid without performing any property software or without needing to perform any detailed EOS modeling. It can be used to quickly, easily and inexpensively investigate, screen, and compare large numbers of working fluids with reasonable engineering accuracy for different ORC applications.

2. Group contribution methods for thermodynamic properties In order to evaluate the thermodynamic processes and thermal efficiency of the ORC from the structure of working fluid, thermodynamic properties of working fluid must be determined accurately from the molecular structure. In this contribution, GCMs

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are applied to establish the relationship between the properties and the structure. Since some involved properties in the ORC model, such as the vapor pressure, the latent heat can be calculated from the physical constants, five necessary properties including the boiling temperature, the critical temperature, the critical pressure, the liquid density and the heat capacity are estimated by the GCMs in the following subsections.

for refrigerant systems has the deviation 0.2071%. For other classes of working fluids, such as HFOs and PFOs, the group contribution method GCVOL, which was developed by Ihmels and Gmehling [25], is employed to get the saturated liquid density at the condensation temperature.

ql ¼ Mw

, X

Nk ðAk þ Bk T þ C k T 2 Þ

ð4Þ

k

2.1. Boiling temperature For boiling temperature Tb, a recently published neural network by the authors is employed [21]. The input parameters of the network consist of molecular groups and a topological index EATII. This ANN model is highly accurate in predicting Tb of working fluids and the average absolute deviation is 1.87%. According to the established network, Tb can be calculated by the following equation. " , !!# 8 16 X X Nk EATII T b ¼ 199:425 W i 2 1 þ exp 4 W ik  W ie þ bi Ck 98:584 i¼1 k¼1

þ 479:835 ð1Þ where Wi is the weight of neuron i in the hidden layer; Wik is the input weight between group k and neuron i; Wie is the EATII input weight of neuron i; bi is the constant of the neuron i in the hidden layer; Ck is a constant for group k; Nk is the number of group k in the fluid.

where MW denotes the molecular weight, Ak, Bk, Ck are k-th group coefficients of the polynomial function. 2.4. Heat capacity Heat capacity is a measure of the amount of energy required by a unit kilogram of a substance to raise its temperature by a unit degree. According to the state of matter, heat capacity can be categorized into ideal gas heat capacity C 0p , liquid heat capacity C lp and real gas heat capacity C pg . Ideal gas heat capacity is the foundation of thermodynamic properties calculation [26,27], while liquid and real gas heat capacities are required to calculate the enthalpy difference of thermodynamic processes. Therefore, the Joback method [28], which is a polynomial method, is used to determine the ideal gas heat capacity C 0p for the prediction of liquid and real gas heat capacities. The ideal gas heat capacity can be obtained by

C 0p ¼

" # " # X X N k c0pAk  37:93 þ Nk c0pBk þ 0:21 T k

Critical properties are the basis for the estimation of a large variety of thermodynamic properties using the corresponding states principle. In this study, a method developed by MarreroMorejón and Pardillo-Fontdevila [22] is used to calculate the critical temperature Tc and critical pressure Pc. The approach is called group-interaction contribution, which considers the contribution of interactions between bonding groups in the molecule instead of the contribution of simple groups. The properties are determined by summing the number frequency of each groupinteraction occurring in the molecule times its contribution, and the specific expressions for Tc, Pc are as follows:

2

( ) ( )2 31 X X 4 T c ¼ T b 0:5851  0:9286 Nk ðtck Þ  Nk ðt ck Þ 5 "

k

" # X 0 N k cpCk  0:000391 T 2 þ

2.2. Critical properties

k

ð2Þ

k

#2 X Pc ¼ 0:1285  0:0059N atoms  Nk ðpck Þ

ð3Þ

k

where Nk means the number of group k in the molecule; tck, pck are the group contribution values for the Tc, Pc respectively; Natoms represents the total number of atoms in the molecule. For the calculation of Tc, boiling temperature Tb predicted by Eq. (1) is used. 2.3. Liquid density In the process of liquid compression, liquid density is required to calculate the compression work. In order to get the liquid density of working fluids at any temperature and pressure, two kinds of artificial neural network-group contribution methods proposed by Moosavi et al. [23,24] are employed for hydrocarbons and refrigerant systems (HCFCs, HFCs, HFEs, PFAs and PFAAs) respectively. The input parameters of the networks include the temperature, the pressure, the molar mass and the number of groups. Compared with the experimental data, the average absolute deviation of the network for hydrocarbons is 0.3177%, and the network

k

" # X 7 0 þ N k cpDk  2:06  10 T 3

ð5Þ

k

where Nk is the number of group k, C 0pAk , C 0pBk , C 0pCk , C 0pDk are the contributions of the k-th atomic or molecular group. For the liquid heat capacity, it’s derived from the ideal gas heat capacity using the modified Rowlinson–Bondi equation, which is reported by Poling et al. [29]. The thermodynamic equation is given by

C lp  C 0p 0:49 ¼ 1:586 þ 1  T=T c R " # 6:3ð1  T=T c Þ1=3 0:4355 þ x 4:2775 þ þ 1  T=T c T=T c

ð6Þ

where R is the ideal gas constant, which is equal to 8.314 J mol1 K1. x is the acentric factor. As for the real gas heat capacity, it is related to the value of the ideal gas state at the same temperature by

C pg ¼ C 0p þ DC rp

ð7Þ

where DC rp is a residual heat capacity. It can be calculated by the Lee-Kesler method [30].

DC rp ¼ ðDC rp Þ

ð0Þ

þ xðDC rp Þ

ð1Þ

ð8Þ

where (DC rp )(0) is the simple fluid contribution and (DC rp )(1) is the deviation function. These variables are functions of the reduced temperature Tr and pressure Pr. For the involved x in the calculation of C lp and C pg , an empirical correlation based on the Antoine vapor pressure equation is used to estimate the acentric factor x and the expression is given as follows [31]

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x¼

0:3ð0:2803 þ 0:4789T br Þ log Pc 1 ð1  T br Þð0:9803  0:5211T br Þ

ð9Þ

T br ¼ T b =T c

ð10Þ

where Pv pr and T r are the reduced vapor pressure and reduced temperature respectively. The equation parameters A, B, C and D can be determined through the following theoretical correlations.

A ¼ 35Q 3. Organic Rankine cycle model According to the characteristics of heat sources, various ORC configurations, such as the regenerative ORC [32] and the autocascade Rankine cycle [33], have been proposed in the literatures. However, no matter what the type of ORC is, the cycle consists of heat transfer and energy conversion. Thus, in this study, a classical ORC, which involves four basic thermodynamic processes, namely, compression, evaporation, expansion and condensation, is modeled. For the convenience of modeling, the T-s diagram of the classical ORC is presented in Fig. 1. Based on the thermodynamic properties calculated from the GCMs, the simulations for four processes are presented respectively in the following subsections. 3.1. Compression The saturated liquid working fluid at the outlet of condenser is compressed to high pressure in the feed pump. For the unit mass flow of working fluid, the specific power consumed by the pump is defined as the difference between the enthalpies at the outlet and inlet of the pump. Due to the fact that the liquid’s pressurization is a non-isentropic process, the isentropic efficiency of pump is assumed to be 0.65 in the calculation of the specific pumping work [9]. When given the inlet and outlet pressure of pump, the pumping work can be determined by

wp ¼ h2  h1 ¼

P2  P1

ð11Þ

q1 gp

3:758Kwb þ lnðPc =101:325Þ Kwb  ln T br 36 Tb wb ¼ 35 þ þ 42 ln T br  T 6br T br ¼ T br Tc

ac ¼

B þ C ln T r þ DT 6r Tr

ð12Þ

When the pressure drop of evaporator is ignored, the evaporation process is a constant-pressure transfer of heat. The working fluid is heated from sub-cooled liquid at the pump outlet to two phase region to super-heated vapor at the turbine inlet by the heat source in the evaporator. Thus, the specific heat transfer rate from the evaporator into the working fluid consists of three parts and the absorbed heat is given by

Q ev ap ¼ h5  h2 ¼ Q 23 þ Q 34 þ Q 45

ð14Þ

where Q 23 denotes the heat absorbed in the sub-cooled liquid state (2–3); Q 34 is the heat needed to vaporize the working fluid from the saturated liquid to saturated vapor (3–4); Q 45 : the amount of heat needed to be super-heated (4–5). In this work, the specific evaporation heats of three parts are obtained by the following equations respectively.

Z

T3

C lp dT

ð15Þ

Q 34 ¼ DHv ðT 3 Þ Z T5 C pg dT Q 45 ¼

ð16Þ

Q 23 ¼

ð17Þ

T4

where heat capacity C lp and C pg are calculated from C 0p ; DHv represents the enthalpy of vaporization of organic compounds, which equals the latent heat of evaporation. For the enthalpy of evaporation involved in the simulation of evaporative process, a widely used correlation between DHV and the reduced temperature Tr is employed to get DHV at any temperature[29].



DH v ¼ DH v b

T

ð13Þ

3.2. Evaporation

T2

where q1 is the saturated liquid density, and it’s estimated by the GCMs, gp is the isentropic efficiency of pump. Under the condition that the pressure drops in the heat exchangers and pipes are neglected, the pressures P1, P2 are equal to the vapor pressures at the condensation and evaporation temperatures respectively. In order to obtain the consumed power of pump, a vapor pressure equation developed by the Riedel [29] is applied to estimate the vapor pressure of working fluid by means of

ln Pv pr ¼ A 

B ¼ 36Q

C ¼ 42Q þ ac D ¼ Q Q ¼ Kð3:758  ac Þ K ¼ 0:0838

1  Tr 1  T br

0:38 ð18Þ

where DHVb denotes the enthalpy of evaporation at the normal boiling temperature. It’s determined by the Riedel method [29].

4

3

5

DHv b ¼ 1:093RT c T br

ln P c  1:013 0:93  T br

ð19Þ

3.3. Expansion

2

7

6s

6 The turbine converts the kinetic energy of working fluid into electrical power in the expansion process. The specific power generated by the turbine is given by

1

wt ¼ h5  h6 ¼ ðh5  h6s Þgt

s Fig. 1. T-s diagram of the classical ORC.

ð20Þ

In the ideal case, the expansion of working fluid is an isentropic process 5–6s, which means there is no difference of entropy between the state points 5 and 6s. For the real process, the isentropic efficiency gt is usually used to present the irreversibility of expansion. In this work, gt is assumed to be 0.85 [9]. Meanwhile,

W. Su et al. / Energy Conversion and Management 132 (2017) 307–315

in order to obtain the enthalpy at the state point 6s, the corresponding temperature is determined from the equality of entropy between the state points 5 and 6s. Therefore, the entropy difference Ds between the different state points must be calculated in the simulation of expansion process. According to the general thermodynamic relationship, the entropy difference of the real gas can be obtained by

Ds ¼ s6s  s5 ¼

sd6s

þ Ds  0

ð21Þ

sd5

where Ds means the entropy difference of the ideal gas. It can be derived from the ideal gas equation of state. The differential equation for the ideal gas entropy difference is expressed by 0

0

ds ¼

C 0p R dT  dp P T

ð22Þ

Thus, the entropy difference of the ideal gas can be obtained by integrating the differential equation.

Z

Ds0 ¼ s06s  s05 ¼

6s

0

Z

ds ¼ 5

T 6s

T5

  P 6s dT  R ln T P5

C 0p

ð23Þ

For the departure functions of the entropy sd5 , sd6s , the general definition is

sd ¼ sðT; PÞ  s0 ðT; PÞ

ð24Þ

In this study, the Lee-Kesler method is used to calculate the departure function of entropy [30].

sd ¼ ðsd Þ

ð0Þ

þ xðsd Þ

ð1Þ

ð0Þ

ð25Þ ð1Þ

where ðsd Þ represents the simple fluid contribution and ðsd Þ the deviation function.

is

3.4. Condensation To complete the thermodynamic cycle, the exhaust vapor from the turbine must be condensed into saturated liquid by the heat sink. Just like the calculation of absorbed heat in the evaporator, the specific condensation heat rate can be expressed as

Q con ¼ h6  h1 ¼ Q 67 þ Q 71

ð26Þ

where Q 67 is the released heat from exhaust to saturated vapor; Q 71 denotes the heat removed from saturated vapor to saturated liquid. These two parts of heat can be calculated by

Z Q 67 ¼

T7

T6

C pg dT

Q 71 ¼ DHv ðT 1 Þ

ð27Þ ð28Þ

where the temperature at the point 6 is determined from the calculated temperature at the point 6s. The enthalpy of evaporation at the condensation temperature is obtained by Eq. (18). After analyzing the four thermodynamic processes of ORC, the cycle efficiency is given by

w gth ¼ net  100% Q ev ap

ð29Þ

where wnet is the net cycle power output defined in the following equation.

wnet ¼ wt  wp

ð30Þ

From the above modeling of the classical ORC, it can be found that the input parameters of the model include the molecular structure of working fluid, the condensation temperature, the evaporation temperature and the superheating temperature. A computer program in Matlab 2015b is developed to simulate the basic processes and get the cycle performance. Since there involves

311

no iterative calculations in the developed model, optimal working fluids can be screened rapidly from thousands of potential working fluids. Furthermore, the established models for heat transfer and energy conversion can also be applied to simulate the cycle processes for other ORC configurations. 4. Estimation of ORC performance The purpose of this section is to demonstrate the accuracy of the ORC model. Given the molecular structures of various working fluids, the ORC performances at typical conditions are predicted by GCMs. The calculated results are compared with the simulations of the same cycles using REFPROP [13]. The errors of the developed model for thermodynamic properties and cycle parameters are presented and discussed. 4.1. ORC working fluids and operating conditions Table 1 demonstrates the 21 working fluids used in this work. Besides the molecular structure and molar mass, the environmental properties including the atmospheric lifetime, ozone depletion potential (ODP) and global warming potential (GWP) are also presented in Table 1. It can be seen that most of the selected working fluids have zero ODP. They are all environmental-friendly working fluids and may have the potential to be used at different ORC applications. In order to obtain the accuracy of the proposed model, the minimum evaporative temperature is set to be 0.8Tc and the maximum evaporation temperature is kept 10 K below the critical point, as also suggested by Delgado-Torres [34]. For the evaporative temperature, each temperature interval is set to be 5 K. For the condensation temperature, it is kept constant at 0.7Tc. In case the liquid drops are formed at the outlet of the turbine, the superheat temperature at the inlet of the turbine is fixed at 5 K. Based on the calculated results from the proposed model and the REFPROP [13] in the typical temperatures of ORC, the following relative error is used to denote the accuracy of the model for a working fluid.

E¼

N fmodel;i  fREF;i 1X 100  N i¼1 fREF;i

ð31Þ

where N is the number of the cycles calculated for different evaporating temperatures. f represents the calculated values. The subscripts ‘‘REF” and ‘‘model” mean that the results are obtained from the REFPROP [13] and the developed model respectively. For the 21 working fluids considered in this work, the average absolute deviation (AAD) of the ORC model is defined as

AAD ¼

NF 1 X jEj NF i¼1

ð32Þ

where NF is the number of considered working fluids. 4.2. Simulation results Since the estimation of all the necessary properties in the ORC model involves the physical constants of working fluids, namely Tb, Tc, Pc, x, accurate estimation of physical constants is a prerequisite for developing a precise model. In this work, the calculated physical constants are compared with the data of REFPROP [13]. The distribution of relative error for different working fluids is presented in Fig. 2. It can be seen that the network proposed by the authors is very accurate in predicting Tb of working fluids. Due to the fact that critical temperature Tc is correlated with Tb by the GCM, highly precise boiling temperature guarantees the estimation accuracy of critical temperature. The AADs for Tb, Tc are 1.81%, 1.79% respectively, as shown in Table 2. For critical pressure Pc,

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Table 1 21 potential working fluids considered in this work. Working fluids

CAS number

Molecular structure

Molar mass (g/mol)

Lifetime (Year)

ODP

GWP

R123 R125 R134a R143a R152a R218 R227ea R236ea R236fa R245ca R245fa R290 R600 R600a R601 R601a n-C6H14 C5F12 R1233zd R1234yf R1234ze

306-83-2 354-33-6 811-97-2 420-46-2 75-37-6 76-19-7 431-89-0 431-63-0 690-39-1 679-86-7 460-73-1 74-98-6 106-97-8 75-28-5 109-66-0 78-78-4 110-54-3 678-26-2 102687-65-0 754-12-1 29118-24-9

CHCl2ACF3 CF3ACHF2 CF3ACH2F CF3ACH3 CHF2ACH3 CF3ACF2ACF3 CF3ACHFACF3 CF3ACHFACHF2 CF3ACH2ACF3 CHF2ACF2ACH2F CF3ACH2ACHF2 CH3ACH2ACH3 CH3ACH2ACH2ACH3 CHA(CH3)3 CH3ACH2ACH2ACH2ACH3 2(CH3)ACHACH2ACH3 CH3A(CH2)4ACH3 CF3A(CF2)3ACF3 CF3ACH@CHCl CF3ACF@CH2 CF3ACH@CHF

152.93 120.02 102.03 84.04 66.05 188.02 170.03 152.04 152.04 134.05 134.05 44.096 58.12 58.12 72.149 72.149 86.175 288.03 130.5 114.04 114.04

1.3 28.2 13.4 47.1 1.5 2600 38.9 11 242 6.5 7.7 12 ± 3 12 ± 3 12 ± 3 12 ± 3 12 ± 3 – 4100 0.07 0.03 –

0.02 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 – 0 0 0 0

77 3170 1300 4800 138 8830 3350 1330 8060 716 858 3.3 4 3 4±2 4±2 – 8550 1 4 6

20

Tb

30

Tc 10

Pc

20

Pvp V

Cp0

w 10

E%

E%

0

0 -10

-10

-20

Fig. 2. Relative errors of the physical constants Tb, Tc, Pc, x.

Fig. 3. Relative errors of the thermodynamic properties Pvp, q, DHv , C 0p .

Table 2 AADs of the ORC model for properties and cycle parameters. Property

AAD %

Cycle parameter

AAD %

Tb Tc Pc

1.81 1.79 5.26 9.80 10.92 2.01 8.77 1.56

Qevap Qcon wp wt wnet

5.05 5.08 10.70 7.25 8.28 4.89

x

Pvp

q

DHV C 0p

gth

R123 R125 R134a R143a R152a R218 R227ea R236ea R236fa R245ca R245fa R290 R600 R600a R601 R601a n-C6H14 C5F12 R1233zd R1234yf R1234ze

R123 R125 R134a R143a R152a R218 R227ea R236ea R236fa R245ca R245fa R290 R600 R600a R601 R601a n-C6H14 C5F12 R1233zd R1234yf R1234ze

-30 -20

obvious deviation exists for some working fluids, the AAD is 5.26%. Since the acentric factor x is calculated as a function of the estimated values of Tb, Tc, Pc, a large deviation is observed. For most of working fluids, the absolute value of relative error for x is less than 10%. Table 2 indicates the AAD for x is 9.8%. Fig. 3 shows the relative error distribution of thermodynamic properties for different working fluids. All these properties are functions of temperature. In the ORC model, the properties are

employed to calculate the heat and work involved in the cycle. Fig. 3 indicates that for the considered working fluids, the ideal gas heat capacity has the least error and the AAD is 1.56%. Therefore, the liquid and real gas heat capacity can be accurately obtained from the theoretical correlations with the ideal gas heat capacity. As for the liquid density and the enthalpy of evaporation, the relative errors locate in the interval of 10% and 10% for most working fluids. As shown in Table 2, the AADs for density and enthalpy are 2.01%, 8.77% respectively. Large deviations exist for the vapor pressure and the AAD is 10.92%. It’s because that the vapor pressure is theoretically determined by the calculated values of Tb, Tc, and Pc. The errors for the physical constants lead to the large deviations of the vapor pressure. For the heat involved in the evaporation and condensation processes, the deviations for the considered working fluids are shown in Fig. 4. It can be observed that the absolute deviations are less than 10% for most working fluids. The AADs for evaporation and condensation heat are 5.05%, 5.08% respectively. The good prediction of heat results from the accurate estimations of heat capacity and enthalpy of evaporation.

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30

wp wt

20

wout

E%

10

0

-10

-30

R123 R125 R134a R143a R152a R218 R227ea R236ea R236fa R245ca R245fa R290 R600 R600a R601 R601a n-C6H14 C5F12 R1233zd R1234yf R1234ze

-20

Fig. 5. Relative errors of the work wp, wt, wnet.

10 5 0 -5

E%

-10 -15 -20 -25

R123 R125 R134a R143a R152a R218 R227ea R236ea R236fa R245ca R245fa R290 R600 R600a R601 R601a n-C6H14 C5F12 R1233zd R1234yf R1234ze

As for the work, Fig. 5 indicates that large deviations are obtained for pumping work. The AAD is 10.70%, Such large errors are caused by the vapor pressure, which has the AAD 10.92%. For the turbine and net power output, they have the same errors for most of working fluids, as shown in Fig. 5. The reason is that compared with the turbine work, the ratio of work consumed by pump is very small, thus the deviation of net work is mainly determined by the expansion work error. Fig. 5 also shows that the relative errors of turbine and net work are less than 10% for most of working fluids. The AADs are 7.25%, 8.28% for turbine and net work respectively. Fig. 6 presents the errors of cycle efficiency for various working fluids. Due to the small deviations of evaporation heat and net power output, the errors of cycle efficiency locate in the interval of -10% and 10% for most working fluids. As listed in Table 2, the AAD for cycle efficiency is 4.89%. The variety of relative errors for different working fluids originates from the used GCMs and the employed thermodynamic relationships. Since the contributions of groups in a particular property are often determined using regression techniques, based on the known experimental data and the group contribution values remain the same regardless of the molecular structure in which it is used, the used GCMs can’t assure an accurate prediction for every generated molecule. According to the obtained properties from the GCMs, the thermodynamic processes are analyzed by the existing semi-empirical relationships. The accuracies of these relationships are different for various kinds of working fluids. For instance, the Lee-Kesler method is more appropriate for slightly polar substances [30]. Furthermore, the errors of the input parameters generated from GCMs may also increase the deviations of these relationships. When given the evaporation, superheating and condensation temperatures, all the cycle parameters can be obtained by the proposed model for a specified working fluid. Thus, the cycle temperature plays an important role in the accuracy of the performance prediction. The reason is that the accuracy of the used correlations for the cycle processes is strongly dependent on the cycle temperature and some relationships, such as the vapor pressure, may have large errors at high reduced temperature. However, from the simulation results, it can be found that the relative errors of the model for properties and cycle parameters are generally less than 10% for most working fluids in the typical temperatures of ORC. Compared with the method of Barbieri et al. [6], the developed model can

Fig. 6. Relative errors of the cycle efficiency gth .

rapidly analyze the ORC performances of different working fluids only from the molecular structure and provide quite reasonable engineering estimates of ORC cycle parameters.

20

Qevap Qcon

15 10

E%

5 0 -5

-15

R123 R125 R134a R143a R152a R218 R227ea R236ea R236fa R245ca R245fa R290 R600 R600a R601 R601a n-C6H14 C5F12 R1233zd R1234yf R1234ze

-10

Fig. 4. Relative errors of the heat Qevap, Qcon.

5. Conclusion In this work, a model for predicting the ORC performances of various working fluids has been developed using group contribution methods (GCMs). Based on the thermodynamic properties calculated from the molecular structure by the GCMs, the model can be applied to any working fluid. In order to evaluate the performance of the ORC model, the properties and cycle parameters of 21 potential working fluids are calculated. Compared with the REFPROP, the results show that the proposed model is able to yield sufficient accuracy for ORC simulation. The relative errors of the model for properties and cycle parameters are generally less than 10% for most working fluids. Compared with the existing methods, the developed model can be applied to simulate the ORC processes only based on the given molecular structure. Thus, it can be easily, quickly, and inexpensively used to select thousands of potential working fluids. Rapid analysis and optimization of the performance of working fluid in ORC can be achieved.

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In our future work, modifications of the developed model will be carried out by developing accurate relationships for the properties above the critical temperature, so that the modified model can be applied to the supercritical ORC. Furthermore, the proposed model will be used to design and select the working fluids for a practical ORC system by the method of computer aided molecular design. Through the combination of groups, various working fluids will be formed. Their cycle performances will be obtained by the proposed model. Thus, the optimal working fluids can be identified, allowing for more focused attention to be placed on only a few promising working fluids which then can be studied indepth through time-consuming and expensive experiments. Acknowledgements This work is sponsored by the National Nature Science Foundation of China (51476110).

Table 4 Group parameters of R123 for the estimation of critical parameters. Group interactions

Numbers

tck

pck (Natoms = 8)

˜CHA and ACl ˜C— and AF ˜CHA and ˜C—

2 3 1

0.0142 0.0176 0.0025

0.0131 0.0161 0.0085

Table 5 Comparison between calculated and experimental values of physical constants. Physical constants

Calculated values

Experimental data

Tb (K) Tc (K) Pc (MPa) w

299.94 460.04 3.70 0.25

300.97 456.83 3.66 0.28

Table 6 Group parameters of R123 for the estimation of C 0p . Groups

Appendix A An example is given to demonstrate the detailed model calculation procedure. The used working fluid is R123, which has the molecular structure CHCl2ACF3. The molar mass of R123 is 152.93 g/mol. Firstly; the physical constants are obtained by the chosen group contribution methods. For the boiling temperature Tb, the working fluid is decomposed in groups as shown in Table 3. The required topological index EATII is obtained from the given calculation flowchart in Ref. [21]. Furthermore, for the weights and thresholds of the established network, readers are referred to the Ref. [21]. According to the values of the involved parameters, Tb can be estimated using Eq. (1). Table 4 presents the required parameters for the estimation of critical parameters. Substitute these values into Eqs. (2) and (3), Tc and Pc can be obtained, according to the estimated Tb. After that, the acentric factor x is determined using Eq. (9). The comparison between calculated and experimental values of physical constants is given in Table 5. It can be seen that the employed models for physical constants give good agreements with the experimental data. For the typical ORC, under the given evaporation (Tevap), superheating (Tsup) and condensation (Tcon) temperatures, the cycle parameters can be obtained from the calculated physical properties by the developed ORC model. However, before analyzing the cycle performance, thermodynamic properties such as vapor pressure, liquid density and heat capacity, are required to simulate the basic processes. Therefore, when the vapor pressures are determined by Eq. (12), the liquid density at the pump inlet can be obtained by the employed artificial neural network-group contribution method [23]. For the working fluid R123, the groups for the network consist of ACF3 and ACHCl2. Furthermore, ideal gas heat capacity C 0p is required in the calculation of sensible heat. According to the molecular structure of R123, the divided groups and group contributions for C 0p are presented in Table 6. Based on the calculated value of ideal gas heat capacity, the liquid heat capacity C lp and the real gas heat capacity C pg are obtained by Eqs. (6) and (7) respectively. After that, the cycle parameters can be determined by the proposed model.

Table 3 Input parameters of R123 for the estimation of Tb. Parameters

˜CHA

˜C—

AF

ACl

EATII

Values

1

1

3

2

23.3096

˜CHA ˜C— AF ACl

Numbers 1 1 3 2

c0pAk 23 66.2 26.5 33.3

c0pBk 2.04/10 4.27/10 9.13/100 9.63/100

c0pCk

c0pDk 4

2.65/10 6.41/104 1.91/104 1.87/104

1.2/107 3.01/107 1.03/107 9.96/108

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