Simultaneous working fluids design and cycle optimization for Organic Rankine cycle using group contribution model

Applied Energy 202 (2017) 618–627

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Simultaneous working fluids design and cycle optimization for Organic Rankine cycle using group contribution model Wen Su, Li Zhao ⇑, Shuai Deng Key Laboratory of Efficient Utilization of Low and Medium Grade Energy (Tianjin University), MOE, Tianjin 300072, China

h i g h l i g h t s
A working fluid design and cycle optimization model is developed.
Optimal fluids are identified by considering cycle, environment and safety properties.
Novel working fluids for the application of ORC are found.

a r t i c l e

i n f o

Article history: Received 7 February 2017 Received in revised form 16 March 2017 Accepted 22 March 2017

Keywords: Working fluids design Cycle optimization Organic Rankine cycle Group contribution method

a b s t r a c t The performance of Organic Rankine Cycle (ORC) is significantly influenced by the used working fluid and the operating condition. Consequently, this paper presents a systematic model for the efficient design of working fluids and the optimization of cycle parameters at the molecular scale, so that optimal working fluids can be identified by simultaneously considering cycle parameters, environmental and safety properties. In the proposed model, working fluids are generated via the combination of groups. The required properties, which consist of thermodynamic, environmental and safety properties, are estimated by the published group contribution methods. Based on these estimated properties, cycle optimizations are performed to obtain the optimal performance of working fluids using an ORC model. Thereafter, optimal working fluids are identified, according to the cycle parameters, environmental and safety properties. Furthermore, working fluids design and cycle optimization for an example are conducted to demonstrate the proposed model. The optimal candidates, namely R254eb, R254cb, are found for the considered example through proposed methodology. The novel working fluids, which are firstly reported in ORC applications, are worth being studied in-depth through time-consuming and expensive experiments. Ó 2017 Elsevier Ltd. All rights reserved.

1. Introduction 1.1. Background and motivation With the increasing concerns over environmental problems and high energy prices, the waste or renewable heat sources, such as solar energy, biomass and geothermal energy have attracted widespread attention. So far, the typical technologies of development and utilization of low grade heat consist of power cycle represented by Organic Rankin Cycle (ORC) and vapor compression reverse cycle represented by refrigeration/heating cycle [1,2]. In terms of power generation, the success of ORC is largely attributed to the characteristics of simple structure, high reliability, and easy maintenance [3]. In order to achieve better energy efficiency,

⇑ Corresponding author. E-mail address: [email protected] (L. Zhao). http://dx.doi.org/10.1016/j.apenergy.2017.03.133 0306-2619/Ó 2017 Elsevier Ltd. All rights reserved.

organic compounds are widely applied as working fluids. The operating performance of an ORC mainly depends on the properties of working fluids as well as the design and operating characteristics of the cycle [4]. A suitable fluid for an ORC must demonstrate favorable thermodynamic and environmental properties, such as low specific volume, low toxicity, zero ozone depletion potential (ODP) and low global warming potential (GWP), as well as favorable process attributes such as high thermal and exergetic efficiency [5]. Thus, one of the significant challenges for the application of ORC is to select working fluids based on the operating conditions.

1.2. Traditional methodologies for the selection of working fluids Numerous works have addressed the selection of working fluids for various working conditions and heat source types of ORC, based on the power output, the cycle efficiency, etc. For example, Saleh

W. Su et al. / Applied Energy 202 (2017) 618–627

619

Nomenclature Symbols C CAMD EOS GCM GWP h H LC50 m M ODP ORC P Q q R RE T TEWI

heat capacity, kJ/kg K computer aided molecular design equation of state group contribution method global warming potential enthalpy, kJ/kg Enthalpy of saturated fluid, kJ/kg toxicity, mmol/L mass flow rate, kg/s molecular weight, g/mol ozone depletion potential organic Rankine Cycle pressure, Pa or bar total heat, kJ heat per unit mass, kJ/kg ideal gas constant radiative efficiency temperature, K total equivalent warming impact

W

work, kW

Greeks

x q g D

Subscripts 1,. . .,7 thermodynamic state points (Fig. 2) b boiling temperature c critical properties con condensation cool cooling source evap evaporation f working fluids h heat source max maximum net net output opt optimum p pressure or pump r reduced property t turbine th thermal cycle v vaporization vp vapor Superscripts 0 ideal gas g real gas l liquid working fluid

acentric factor Saturated liquid density, kg/m3 efficiency, % difference

et al. [6] compared the thermodynamic performances of 31 pure working fluids for different types of ORC using BACKONE equation of state (EOS). The results showed that the highest values of efficiency are obtained for the high boiling substances. Galashov et al. [7] analyzed the properties of ozone-friendly low-boiling working fluids for ORC based on the database ‘‘REFPROP”. Studies indicated that pentane, butane and R245fa have the best thermodynamic and environmental properties among the considered substances. A comprehensive review of ORC working fluids was presented by Bao and Zhao [5]. They identified 77 commonly existing single-component working fluids and 44 zeotropic blends appearing in the various papers they reviewed. Furthermore, Jacopo et al. [8] proposed a general framework to select working fluids and cycle configurations for a given heat source. Four different ORC configurations and 27 working fluids were optimized by considering the cycle efficiency and heat source recovery factor. Hærvig et al. [9] developed guidelines on how to choose the optimal working fluids based on the hot source temperature. 26 commonly used working fluids were investigated by optimizing net power output at hot source temperatures in the range 50–280 °C. However, the optimal working fluids identified by the above methods are all from a prepostulated dataset of several available candidates. As a result, the search is limited to a compiled list of candidates containing conventional molecules. Such a small set is extremely limiting in view of the vast number of molecules that could be considered as candidates of ORC working fluids. Thus, a systematic approach called computer aided molecular design (CAMD) has been utilized to select the working fluids in recent years. 1.3. Pros and cons of existing CAMDs Instead of testing existing molecules from an available dataset of already known candidates, CAMD tools utilize a database

containing a few molecular groups that are used to generate and search a vast number of conventional or novel molecular structures to identify those molecules that offer the best performance with respect to the properties of interest. CAMD methods have been widely used for the design of polymers [10], solvents [11] and refrigerants [12,13], resulting in significant reduction of the associated costs as well as considerable improvement of process performance. However, the first application of CAMD in the screening of working fluids for ORC was conducted by Papadopoulos et al. [14–16] in 2010. They employed the group contribution methods (GCMs) to estimate the physical properties, considered the ORC process-related properties as performance criteria at the CAMD stage and then introduced optimal working fluids candidates into ORC process simulations to select few that exhibit favorable process performance using EOSs. The resulting candidate molecules were finally qualitatively evaluated based on their ODP and GWP. In addition, an optimization-based CAMD approach was also proposed by Palma-Flores et al. [17]. Unlike Papadopoulos et al. who employed simulated annealing as the optimization algorithm, Palma-Flores et al. adopted a mixed integer non-linear programming. Furthermore, more functional groups were considered by Palma-Flores et al. Another optimization-based method for the design of optimum ORC working fluids, namely the continuous molecular targeting method, was developed by Lampe et al. [18–20]. Working fluids were designed based on the perturbed chain statistical associating fluid theory (PC-SAFT) EOS, which considers molecules as chains of spherical segments that interact through van der Waals interactions, hydrogen bonds, and polar interactions. Instead of the optimum molecular structures, the resulting working fluids were represented by the optimum values of the segment number, diameter and the van der Waals attraction between segments. A recent review of CAMD to design working fluids for ORC was presented by Patrick et al. [21]. The merits

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and shortcomings of the existing CAMD models were summarized and discussed. However, to the best of authors’ knowledge, in the above literatures, the physical parameters are always considered as an objective function to screen the candidates at the CAMD stage and then the cycle performances of these candidates are evaluated, based on the calculated thermodynamic properties from the EOSs. Extensive computational effort is required for the working fluids design, due to the iterative processes of EOSs. Furthermore, the existing design models of working fluids can’t assure the finding of the best working fluids for a given heat source, because these models don’t integrate the screening of working fluids with the optimization of ORC working conditions. 1.4. Focus of the study The above literature review shows that existing researches have the following limitations in the screening of working fluids for ORC.
Traditional selection methods can only identify the optimal working fluids from a pre-postulated dataset of conventional molecules.
For the existing CAMDs, potential candidates are determined with the goal of physical properties. The identified working fluids can’t be assured to have optimal cycle performance.
Extensive computational effort of existing CAMDs is required for the analysis of cycle performance, due to the iterative processes of EOSs. The focus of this study is to solve the listed limitations of existing researches and implement the selection of working fluids and the optimization of cycle parameters at the molecular scale. A systematic model is developed to design working fluids and optimize the key process parameters for the subcritical ORC, based on the GCMs. New working fluids are generated by the combination of groups and cycle optimizations are performed with the objective of maximal output work. Optimal fluids are determined by simultaneously considering the cycle parameters, the environmental and safety properties of the candidates. This paper is structured as follows: in Section 2, the systematic model is developed to design working fluids and optimize the cycle processes. A design and optimization example is introduced in Section 3. In Section 4, the obtained results for this example are presented and discussed. Conclusions are drawn in Section 5. 2. Working fluids design and cycle optimization 2.1. Calculation of physical properties Since ORC generally consists of a linked sequence of state points with physical properties variables, the physical properties of working fluids are essential to the cycle analysis. In this contribution, GCMs are applied to estimate the basic properties, such as the boiling temperature, the critical parameters and the ideal gas heat capacity. Furthermore, the environmental and safety properties of working fluids are also determined by the GCMs. Other properties such as the vapor pressure and the latent heat are derived from the basic properties, according to the established relationships. Due to the fact that these involved properties have been presented to develop a performance evaluation model of ORC in the published paper by the authors [22], the properties required for the design of working fluids and the optimization of cycle processes are briefly described as follows:

1. The boiling temperature Tb: A highly accurate model developed from the artificial neural network is employed [23]. 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=ð1 þ expð4 W ik  W ie þ bi ÞÞ 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. 2. The critical properties: Critical temperature Tc and critical pressure Pc are estimated through the method of Marrero-Morejón and Pardillo-Fontdevila [24]. This approach is called groupinteraction contribution, which considers the contribution of interactions between bonding groups in the molecule instead of the contribution of simple groups. The specific expressions for Tc, Pc are as follows:

2

( ) ( )2 31 X X T c ¼ T b 40:5851  0:9286 Nk ðt ck Þ  Nk ðtck Þ 5 k

" P c ¼ 0:1285  0:0059Natoms 

ð2Þ

k

X Nk ðpck Þ

#2 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. 3. The acentric factor: This can be calculated out after the boiling temperature and the critical properties are determined using the above relationships, as follows [25]

x¼

ð0:30:2803 þ 0:4789T br Þ log Pc 1 ð1  T br Þð0:9803  0:5211T br Þ

T br ¼ T b =T c

ð4Þ ð5Þ

4. The vapor pressure: It’s usually determined by the evaporation or condensation temperature of working fluids. In this study, the following equation developed by the Riedel [26] is applied to estimate the vapor pressure of working fluids.

ln Pv pr ¼ A 

B þ C ln T r þ DT 6r Tr

ð6Þ

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

ð7Þ

B ¼ 36Q

ð8Þ

C ¼ 42Q þ ac

ð9Þ

D ¼ Q

ð10Þ

The used parameter Q can be obtained by

Q ¼ Kð3:758  ac Þ

ð11Þ

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where K = 0.0838. The parameter ac is calculated out using the following equation.

ac ¼

3:758Kwb þ lnðP c =101:325Þ Kwb  ln T br

ð12Þ

The involved parameter wb in Eq. (12) is expressed by

wb ¼ 35 þ

36 þ 42 ln T br  T 6br T br

ð13Þ

5. The liquid density q: Two kinds of artificial neural networkgroup contribution methods proposed by Moosavi et al. [27,28] are employed to get the liquid density of working fluids at any temperature and pressure for hydrocarbons and refrigerant systems (HCFCs, HFCs, HFEs, PFAs and PFAAs) respectively. As for the other classes of working fluids, such as HFOs and PFOs, the group contribution method GCVOL, which was developed by Ihmels and Gmehling [29], is employed to get the saturated liquid density.

X

ql ¼ Mw =

  Nk Ak þ Bk T þ C k T 2

ð14Þ

k

where MW denotes the molecular weight, Ak, Bk, Ck are k-th group coefficients of the polynomial function. 6. The heat capacity: In order to get the liquid heat capacity C lp and real gas heat capacity C pg for the calculation of involved heat in the cycle analysis, the ideal gas heat capacity C 0p is obtained by the Joback method [30].

"

C 0p

# " # X X 0 0 ¼ Nk cpAk  37:93 þ Nk cpBk þ 0:21 T k

k

" # # X X 7 2 0 0 þ Nk cpCk  0:000391 T þ Nk cpDk  2:06  10 T 3 "

k

k

ð15Þ C 0pAk ,

C 0pBk ,

C 0pCk ,

C 0pDk

where are the contributions of the k-th atomic or molecular group. For the liquid heat capacity, it’s derived from the heat capacity of ideal gas using the modified Rowlinson–Bondi equation, which is reported by Poling et al. [26]. 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

ð16Þ

ð17Þ

DC rp

where is a residual heat capacity. It can be calculated by the Lee-Kesler method [31].

DC rp ¼ ðDC rp Þ

ð0Þ

þ xðDC rp Þ

ð1Þ

ð18Þ

where (DC rp )(0) is the simple fluid contribution and (DC rp )(1) is the deviation function. 7. The enthalpy of evaporationDHV : A widely-used correlation between DHV and the reduced temperature Tr is employed to get DHV at any temperature [26].



DH v ¼ DH v b

1  Tr 1  T br

DHv b ¼ 1:093RT c T br

ln Pc  1:013 0:93  T br

ð20Þ

8. Environmental properties: Due to the destruction of the ozone molecules in the stratosphere, working fluids with zero ODP are required. Therefore, the compounds with chlorine, bromine or iodine groups, which have non-zero ODP, are directly excluded in the selection of working fluids [32]. As for another environmental problem-global warming, two indexes, namely GWP and total equivalent warming impact (TEWI) can be employed to quantify the global warming impact of working fluids [33]. GWP is the index that determines the direct potential contribution of a chemical substance to global warming. In addition to the direct impact of working fluids, any thermodynamic system, which requires energy input, indirectly affects the environment, due to the CO2 emissions in the energy production processes. In order to account for the gobal warming impact from both direct and indirect emissions, another index TEWI is used. In this study, direct impact is considered for simplicity. GWP is employed to evaluate the potential contribution of working fluids to global warming. The calculation of GWP is an extremely complicated process which involves interactions between surface and atmosphere, such as atmospheric radiative transfer and atmospheric chemical reactions. GWP of a substance is related to its atmospheric abundance and is a variable in itself. However, radiative efficiency (RE) is an intermediate parameter for GWP calculation and it is a constant value used to describe inherent property of a substance. In general, GWP is proportional to the RE. Thus, in this study, An organic group contribution approach developed by Zhang et al. [34] is utilized to estimate RE of organic working fluids, so that the GWP of generated working fluids can be compared on the basis of the calculated RE. The specific expression for RE is defined

RE ¼

X Nk rk

ð21Þ

k

where rk is the contribution of group k. Furthermore, when the working fluid belongs to the perfluorinated compound, the following equation is applied to the estimation of RE.

RE ¼ 0:06133 þ 0:07057nc

where R is the ideal gas constant, which is equal to 8.314 J mol1 K1. 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

where DHVb denotes the enthalpy of evaporation at the normal boiling temperature. It’s determined by the Riedel method [26].

1 6 nc 6 6

ð22Þ

where nc stands for the number of carbon atom. 9. Safety properties: The flammability is an index used to assess the flammability characteristics of the organic working fluids. It can be calculated out through a group contribution method proposed by Shigeo et al. [35]. For the toxicity. It represents the degree to which a substance can damage an organism. It can be obtained through the following group contribution method developed by Chao et al. [36].

X logðLC 50 Þ ¼  Nk ak

ð23Þ

k

where LC50 means the toxicity, ak denotes the toxicity contribution of group k. Although this method is based on the acute toxicity of chemical substances to the fathead minnow and does not directly determine the toxic effects of a substance to humans, it is useful for comparing the toxicity of the generated working fluids. 2.2. Thermodynamic cycle model

0:38

ð19Þ

Many different ORC configurations, such as the regenerative ORC [37] and the auto-cascade Rankine cycle [38], have been pro-

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Heat source Qevap

2

5 Evaporator

Pump wt

Turbine

1

wp

6

Condenser

Qcon Heat sink Fig. 1. Schematic of a classical ORC.

posed, based on the characteristics of heat source. However, all these configurations are generated from the modification of classic ORC. Thus, in this work, a classic ORC shown in Fig.1 is considered. The ORC configuration includes an evaporator, a turbine, a condenser and a feed pump. There is usually a storage tank for the collection of working fluid and the maintenance of working fluid liquid state at the feed pump inlet. The corresponding thermodynamic processes of the classical ORC are illustrated on the T-s diagram in Fig. 2 for pure fluids. In general, ORC systems have four basic thermodynamic processes. Before modeling the cycle processes, the following assumptions are made to simplify the calculation of thermodynamic cycle in this paper.
The steady state of ORC has been reached.
Heat losses in the components, pressure drops in the evaporator, pipes and condenser are ignored.
Although each working fluid would require a specific turbine, pump and heat exchangers design [39], average values of the main parameters affecting these components performance are used in the model, due to the difficulty of predicting in advance the specific type and features of these components.
In order to avoid the wet expansion in the turbine, the working fluid is superheated in the evaporator. At the outlet of the condenser, the working fluid is saturated liquid. According to the above assumptions, the equations describing these processes are presented as follows. (1) Compression process 1-2: The saturated liquid working fluid at the outlet of condenser is compressed to high pressure in the feed pump. The consumed work can be calculated by the equation

W p ¼ mf ðh2  h1 Þ ¼ mf

P2  P1

q1 gp

ð24Þ

Fig. 2. T-s diagram of the classical ORC.

Where mf denotes the mass flow rate of working fluid, q1 is the saturated liquid density, gp represents the isentropic efficiency of pump. (2) Isobaric evaporation process 2–5: The heat transfer rate from the heat source into the working fluid consists of three parts and it can be determined by

Q ev ap ¼ mf ðh5  h2 Þ ¼ mf ðq23 þ q34 þ q45 Þ Z q23 ¼

T3

T2

C lp dT

q34 ¼ DHv ðT 3 Þ

ð25Þ ð26Þ ð27Þ

W. Su et al. / Applied Energy 202 (2017) 618–627

Z q45 ¼

T5

T4

C pg dT

ð28Þ

where q23 denotes the heat absorbed in the sub-cooled liquid state (2–3); q34 is the heat needed to vaporize the working fluid from the saturated liquid to saturated vapor (3–4); q45 is the amount of heat needed to be super-heated (4–5). Based on the energy conservation in evaporator, the working fluid mass flow rate can be obtained for a given heat source

mf ¼

C p mh ðT hin  T 3  DT e Þ q34 þ q45

ð29Þ

where Cp is the heat capacity of heat source, mh represents the mass flow rate of heat source, Th-in is the inlet temperature of heat source. DTe is the pinch point temperature difference. (3) Expansion process 5–6: The turbine converts the kinetic energy of working fluid into electrical power in the expansion process. The power generated by the turbine is given by

W t ¼ mf ðh5  h6 Þ ¼ mf ðh5  h6s Þgt

623

2. Optimization target: The desired targets should be defined in a very clear manner. In general, for a given heat source, the net power output can be employed as an objective function. Many published literatures have conducted the selection of working fluids in terms of the maximal net power [9,41]. Therefore, in this work, the output work is maximized for each combinational working fluid. The physical properties are firstly calculated from GCMs. Then, under a given heat source, cycle parameters such as the evaporation temperature and the superheating temperature can be optimized to get the maximal output work, based on the thermodynamic model of ORC. 3. Assessment of the combinational working fluids: In this final stage, the group combinations from the first step are assessed, according to the cycle parameters, the environmental and safety properties. Optimal working fluids are identified.

ð30Þ

where gt represents the isentropic efficiency of turbine, it is usually used to present the irreversibility of expansion. Based on the zero entropy difference between the state points 5 and 6 s, the isentropic temperature of the turbine outlet can be determined, so that the difference of enthalpy between the inlet and outlet of turbine can be calculated. (4) Condensation process 6–1: To complete the thermodynamic cycle, the exhaust vapor from the turbine must be condensed into saturated liquid by the heat sink. Just like the evaporation process, the condensation heat rate can be expressed as

Q con ¼ mf ðh6  h1 Þ ¼ mf ðq67 þ q71 Þ Z q67 ¼

T7

T6

C pg dT

q71 ¼ DHv ðT 1 Þ

ð31Þ ð32Þ ð33Þ

where the released heat from exhaust to saturated vapor is denoted by q67, q71 represents the heat removed from saturated vapor to saturated liquid. After modeling the four thermodynamic processes of ORC, the net output power for a specific heat source is given by

W net ¼ W t  W p

ð34Þ

Thus, the cycle efficiency is defined as

gth ¼

W net  100% Q ev ap

ð35Þ

As for the accuracy of the ORC simulation model, the paper published by the authors indicates that the relative errors of the model for cycle parameters are generally less than 10%, compared with the commercial software-REFPROP [22]. 2.3. Design and optimization strategy The proposed working fluid design and cycle optimization strategy primarily consists of the following steps: 1. Identifying feasible working fluid structure: This step is to find all possible feasible combinations from the chosen set of groups. When combining the molecular groups, chemical structure constraints must be satisfied [40].

Fig. 3. Flow diagram of working fluids design and cycle optimization model.

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W. Su et al. / Applied Energy 202 (2017) 618–627

Based on the above three steps, the flow diagram of working fluids design and cycle optimization is presented in Fig.3. A computer program in Matlab 2015b is developed to design working fluids and optimize the cycle parameters. 3. Design and optimization example In order to test the above working fluids design and cycle optimization model, five groups CH3, CH2, CH, C and F are selected as building blocks of the possible working fluids candidates. For sake of illustration, the generated molecules with a maximum of three alkyl groups are considered in this work. Furthermore, for this example, alkanes are eliminated because of the high flammability. Table 1 lists the 42 compounds obtained after solving the combinational problem, according to the order of the increasing number of atom C, F. Some of them, such as compounds 6, 10, 35, 41 are already known as R152a (CH3CHF2), R134a (CH2FCF3), R245fa (CHF2CH2CF3) or R227ea (CF3CHFCF3), respectively. They have been recommended as potential working fluids in the application of ORC. Furthermore, besides zero ODP, reasonably short atmospheric lifetime, as well as low GWP, compounds 6 and 35 have also shown interesting thermodynamic properties as reported [42,43]. After the selection and combination of groups, cycle optimization is conducted. In this example, the heat source is modeled as

a 10 kg/s stream of exhaust gas, which is available at 453.15 K, as listed in Table 2. Furthermore, the required parameters of ORC are also given in Table 2. For the considered example of this study, only the evaporation temperature is optimized to get the maximal output work for every generated working fluid, based on the thermodynamic model of ORC. In the subcritical configuration of ORC, the maximum evaporation temperature is kept 10 K below the critical point, as also suggested by Delgado-Torres [44]. After that, considering the cycle parameters, environmental and safety properties simultaneously, the optimal working fluids can be identified. 4. Results and discussion 4.1. Physical constants Based on the developed model, the properties required for the cycle optimization are calculated from the physical constants. Thus, the physical constants including Tb, Tc, Pc, x, are estimated from the molecular structures firstly. The corresponding values for the combinational compounds are presented in Table 1. It can be seen that with the increasing number of alkyl and F groups, the values of Tb, Tc, x increase, while the critical pressure Pc decreases. Furthermore, considering the given parameters of subcritical ORC, when the maximum evaporation temperature (Tc-10) is lower than the condensation temperature, the corresponding working fluids should be excluded. For the generated

Table 1 Sample list of the resulting compounds and their physical constants. ID

Working fluids

M (g/mol)

Tb (K)

Tc (K)

Pc (MPa)

x

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42

CH3F CH2F2 CHF3 CF4 CH3CH2F CH3CHF2 CH3CF3 CH2FCH2F CH2FCHF2 CH2FCF3 CHF2CHF2 CHF2CF3 CF3CF3 CH3CH2CH2F CH3CH2CHF2 CH3CH2CF3 CH3CHFCH3 CH3CHFCH2F CH3CHFCHF2 CH3CHFCF3 CH3CF2CH3 CH3CF2CH2F CH3CF2CHF2 CH3CF2CF3 CH2FCH2CH2F CH2FCH2CHF2 CH2FCH2CF3 CH2FCHFCH2F CH2FCHFCHF2 CH2FCHFCF3 CH2FCF2CH2F CH2FCF2CHF2 CH2FCF2CF3 CHF2CH2CHF2 CHF2CH2CF3 CHF2CHFCHF2 CHF2CHFCF3 CHF2CF2CHF2 CHF2CF2CF3 CF3CH2CF3 CF3CHFCF3 CF3CF2CF3

34.04 52.03 70.02 88.01 48.07 66.06 84.05 66.06 84.05 102.04 102.04 120.03 138.02 62.1 80.09 98.08 62.1 80.09 98.08 116.07 80.09 98.08 116.07 134.06 80.09 98.08 116.07 98.08 116.07 134.06 116.07 134.06 152.05 116.07 134.06 134.06 152.05 152.05 170.04 152.05 170.04 188.03

189.45 213.08 198.01 167.33 241.98 244.72 229.22 268.52 265.40 240.53 257.28 225.64 197.35 279.86 294.38 289.11 263.00 295.17 317.61 285.26 274.70 291.08 285.08 260.40 309.99 317.86 300.56 318.40 320.25 292.83 302.05 293.89 268.82 319.77 292.51 315.97 282.13 283.21 254.90 267.39 253.67 233.51

306.51 338.30 310.75 259.21 385.60 382.94 354.54 415.37 406.97 364.91 392.22 341.47 296.36 434.39 452.91 440.03 410.35 451.39 482.90 430.56 424.21 440.94 430.79 390.49 468.10 476.12 445.79 477.82 477.99 434.09 449.38 436.21 396.14 475.24 430.56 469.09 416.05 419.39 374.78 389.97 371.65 340.96

5.61 5.81 4.88 3.75 5.07 4.55 3.67 5.05 4.52 3.82 4.23 3.56 3.17 4.45 4.01 3.42 4.24 4.22 3.96 3.35 3.60 3.74 3.50 3.11 4.43 4.00 3.40 4.20 3.94 3.34 3.89 3.63 3.22 3.62 3.11 3.70 3.15 3.40 3.03 2.70 2.72 2.71

0.20 0.27 0.26 0.21 0.22 0.24 0.21 0.32 0.32 0.30 0.32 0.28 0.27 0.27 0.26 0.25 0.23 0.30 0.30 0.27 0.21 0.30 0.28 0.27 0.37 0.37 0.35 0.38 0.38 0.34 0.39 0.37 0.35 0.36 0.35 0.38 0.34 0.35 0.34 0.33 0.31 0.33

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Value

Exhaust gas inlet temperature (K) Exhaust gas inlet mass flow (kg/s) Superheating temperature (K) Condensation temperature (K) Heat sink water inlet temperature (K) Pinch point in the evaporator (K) Pinch point in the condenser (K) Isentropic pump efficiency Isentropic turbine efficiency

453.15 10 5 303.15 288.15 15 10 65% 85%

Mass flow rate (kg/s)

Steady system parameter

Table 3 Results of cycle optimization.

52

(a)

9

48

8

44

7

40

6 360

Working fluids

Tc (K)

Teavp,opt (K)

Wnet,max (kW)

gth (%)

41 39 40 24 42 33 37 38 20 35 30 23 32 16 27 31 34 12 29 21 15 17 36 19 18 10 26 11 7 25 22 28 9 6 8 14 5 2

CF3CHFCF3 CHF2CF2CF3 CF3CH2CF3 CH3CF2CF3 CF3CF2CF3 CH2FCF2CF3 CHF2CHFCF3 CHF2CF2CHF2 CH3CHFCF3 CHF2CH2CF3 CH2FCHFCF3 CH3CF2CHF2 CH2FCF2CHF2 CH3CH2CF3 CH2FCH2CF3 CH2FCF2CH2F CHF2CH2CHF2 CHF2CF3 CH2FCHFCHF2 CH3CF2CH3 CH3CH2CHF2 CH3CHFCH3 CHF2CHFCHF2 CH3CHFCHF2 CH3CHFCH2F CH2FCF3 CH2FCH2CHF2 CHF2CHF2 CH3CF3 CH2FCH2CH2F CH3CF2CH2F CH2FCHFCH2F CH2FCHF2 CH3CHF2 CH2FCH2F CH3CH2CH2F CH3CH2F CH2F2

371.65 374.78 389.97 390.49 340.96 396.14 416.05 419.39 430.56 430.56 434.09 430.79 436.21 440.03 445.79 449.38 475.24 341.47 477.99 424.21 452.91 410.35 469.09 482.90 451.39 364.91 476.12 392.22 354.54 468.10 440.94 477.82 406.97 382.94 415.37 434.39 385.60 338.30

361.65 364.78 379.97 380.49 330.96 386.14 381.92 380.62 379.48 378.56 377.97 378.38 377.59 377.76 376.44 376.45 374.82 331.10 374.71 373.62 375.89 376.13 370.48 374.81 375.85 354.13 374.46 369.88 344.64 374.54 367.41 368.85 369.31 359.31 367.86 358.89 356.06 328.27

537.08 513.94 472.49 462.54 452.01 423.03 374.94 361.64 324.99 322.66 317.16 312.37 307.24 288.73 278.05 269.55 250.05 249.69 245.98 245.86 242.71 242.67 241.63 237.55 236.59 232.06 228.59 223.93 217.51 213.15 212.15 197.71 185.24 160.69 156.96 147.91 128.55 35.76

20.71 20.32 21.52 21.45 16.53 21.03 22.21 21.75 20.70 20.42 20.25 19.90 19.79 19.07 18.50 18.17 17.50 0.10 17.30 15.51 16.73 14.75 16.20 16.93 16.33 0.10 16.22 11.94 0.09 15.17 13.58 13.62 11.07 8.26 0.10 9.18 6.84 0.02

molecules, four working fluids including compounds 1,3,4,13 are firstly abandoned.

380

36 400

390

Evaporation temperature (K)

(b) 370

Output work (kW)

ID

370

Specific output work (kJ/kg)

10

Table 2 Specifications of the ORC condition.

360

350

340 360

370

380

390

400

Evaporation temperature (K) Fig. 4. Effect of evaporation temperature on (a) mass flow rate and specific output work, (b) output work.

Table 4 Performance comparison of working fluids. ID

Working fluids

mf (kg/s)

Pevap (MPa)

Pcon (MPa)

RE

Log (LC50)

41 39 40 24 42 33 37 38 20 35 30 23 32 16 27

CF3CHFCF3 CHF2CF2CF3 CF3CH2CF3 CH3CF2CF3 CF3CF2CF3 CH2FCF2CF3 CHF2CHFCF3 CHF2CF2CHF2 CH3CHFCF3 CHF2CH2CF3 CH2FCHFCF3 CH3CF2CHF2 CH2FCF2CHF2 CH3CH2CF3 CH2FCH2CF3

19.17 17.86 12.49 11.49 31.00 10.81 8.14 7.85 5.98 6.45 6.33 5.97 6.09 4.93 5.11

2.22 2.47 2.22 2.58 2.17 2.65 1.65 1.62 1.33 1.15 1.15 1.34 1.17 1.13 0.91

0.56 0.56 0.35 0.44 1.11 0.35 0.22 0.21 0.19 0.15 0.15 0.19 0.14 0.17 0.11

0.26 0.24 0.28 0.16 0.27 0.29 0.24 0.22 0.16 0.26 0.29 0.14 0.27 0.18 0.31

3.28 3.28 2.84 2.82 3.41 2.84 3.14 3.14 2.69 2.70 2.70 2.69 2.70 2.24 2.26

4.2. Cycle optimization of working fluids Results of the maximization of net output work are shown in Table 3. For the working fluids with relatively low critical temperature, such as compounds 2,7,10, the optimum evaporation temperature coincides with the maximum allowed evaporation temperature (Tc-10). However, under the given cycle parameters in Table 2, most of the combinational molecules have lower values of optimum evaporation temperature than the maximum allowed temperatures. In general, increasing the evaporation temperature on the one hand increases the specific output work, but on the other hand decreases mass flow rate of working fluid, as shown

for the compound 37 in Fig. 4(a). The combined effect causes a parabolic trend of the output work with the increase of the evaporation temperature, as indicated in Fig. 4(b). It can be seen that with the increase of evaporation temperature, the output work increases firstly, and then decreases, i.e., there is a maximum output work corresponding to an optimal evaporation temperature. For the compound 37, the optimal evaporation temperature is 381.92 K. This law is also validated by the Ref. [45]. Working fluids in Table 3 are ordered according to the decreasing values of maximal output work. The highest value (537.08 kW)

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Table 5 Available information for the optimum working fluids. ID

Working fluids

Compounds name

CAS number

ASHRAE number

Boiling temperature

20 23

CH3CHFCF3 CH3CF2CHF2

1,1,1,2-Tetrafluoropropane 1,1,2,2-Tetrafluoropropane

421-48-7 40723-63-5

R254eb R254cb

272.15 K 272.37 K

is obtained by the compound 41 (R227ea). The corresponding cycle efficiency is 20.71%. Although the efficiency of the compound 41 is not the highest, the cycle efficiency decreases with the decrease of the output work on the whole. Furthermore, considering the error of the thermodynamic cycle model presented in our previous work [22], the optimal working fluids are screened from the top 15 of working fluids in the rank of maximal output work. Other parameters, such as mass flow rate, vapor pressure, environmental and safety properties are compared for these working fluids. 4.3. Identification of optimum ORC working fluids Table 4 presents the considered properties for the top 15 of working fluids in the rank of output work. Due to the absence of element Cl and alkanes, the ODP and flammability of the candidates are not considered in the identification of optimum working fluids. From the Table 4, it can be observed that the top 6 of working fluids, namely the compounds 41, 39, 40, 24, 42 and 33, not only show a maximum operating pressure over 2 MPa, but also have a large mass flow rate over 10 kg/s. Therefore, the economic performance of ORC system with these working fluids can’t be assured. For the remaining candidates of working fluids, the radiative efficiency, which is related with the GWP, and the logarithm of toxicity Log(LC50) are considered. As listed in Table 4, the relatively low values of RE are obtained by the compounds 20, 23. For the traditional fluid compound 35 (R245fa), the cycle performance is equivalent to that of compounds 20, 23. However, the global warming contribution of R245fa is much higher. Furthermore, for the compounds 20, 23, the values of Log(LC50) are also lower than most of other candidates. Therefore, the optimum working fluids for the given parameters in Table 2 are the compounds 20, 23. According to the molecular structures, the available information for the optimal compounds can be found from the database including SciFinder [46] and Chemical Abstracts Service (CAS) [47], as presented in Table 5. Table 5 indicates that the two working fluids are structural isomers. So far, only the normal boiling temperatures have been determined experimentally. Compared with the experimental values, the results calculated from the GCMs are much higher. The relative errors are 4.82%, 4.67%, respectively. Furthermore, to the best of author’s knowledge, no published literatures have contributed to study the cycle performance of these two compounds. Therefore, experimental studies should be conducted for the properties and cycle performances of the screened compounds. 5. Conclusions In this study, a systematic model for molecular design and cycle optimization is developed to screen the working fluids and optimize the cycle parameters for organic Rankine cycle (ORC) using group contribution methods. The results of the considered example indicate that the proposed model can design working fluids and optimize cycle parameters simultaneously. Based on the cycle parameters, environmental and safety properties of combinational subtances, new working fluids, namely R254eb, R254cb, are found to be the best candidates for the example. Compared with the existing methods for selection of working fluids, the developed

model can screen the working fluids and optimize the cycle parameters at the molecular scale. Novel working fluids can be identified for the application of ORC. However, in conventional practice, novel working fluids can only be found through experimental work which is clearly irreplaceable but involves high costs. Therefore, The developed model of this study may assist experimental work through their predictive capabilities by guiding searches to options worth investing. In our future work, more groups will be considered. The algorithm of group combination with chemical structure constraints will be used to generate the numerous working fluids. Other properties, such as the freezing temperature, viscosity and conductivity will be also considered in the proposed model. Combinational working fluids from groups will be evaluated quantitatively by balancing these properties well. Furthermore, modification of the proposed model can also be employed to design working fluids for other thermodynamic cycles, such as the other types of ORC, heat pump and refrigeration. Acknowledgements This work is sponsored by the National Nature Science Foundation of China (51476110). References [1] Dong KK, Ji SL, Kim J, Mo SK, Min SK. Parametric study and performance evaluation of an organic Rankine cycle (ORC) system using low-grade heat at temperatures below 80 °C. Appl Energy 2017;189:55–65. [2] Miah JH, Griffiths A, Mcneill R, Poonaji I, Martin R, Leiser A, et al. Maximising the recovery of low grade heat: an integrated heat integration framework incorporating heat pump intervention for simple and complex factories. Appl Energy 2015;160:172–84. [3] Ziviani D, Beyene A, Venturini M. Advances and challenges in ORC systems modeling for low grade thermal energy recovery. Appl Energy 2014;121:79–95. [4] Collings P, Yu Z, Wang E. A dynamic organic Rankine cycle using a zeotropic mixture as the working fluid with composition tuning to match changing ambient conditions. Appl Energy 2016;171:581–91. [5] Bao J, Zhao L. A review of working fluid and expander selections for organic Rankine cycle. Renew Sustain Energy Rev 2013;24:325–42. [6] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32:1210–21. [7] Galashov N, Tsibulskiy S, Serova T. Analysis of the properties of working substances for the organic rankine cycle based database ‘‘REFPROP”. In: EPJ web of conferences; 2016. [8] Vivian J, Manente G, Lazzaretto A. A general framework to select working fluid and configuration of ORCs for low-to-medium temperature heat sources. Appl Energy 2015;156:727–46. [9] Hærvig J, Sørensen K, Condra TJ. Guidelines for optimal selection of working fluid for an organic Rankine cycle in relation to waste heat recovery. Energy 2016;96:592–602. [10] Mukherjee R, Gebreslassie B, Diwekar UM. Design of novel polymeric adsorbents for metal ion removal from water using computer-aided molecular design. Clean Technol Environ 2016:1–17. [11] Zhou T, Wang J, Mcbride K, Sundmacher K. Optimal design of solvents for extractive reaction processes. Aiche J 2016. [12] Khetib Y, Larkeche O, Meniai A-H, Radwan A. Group contribution concept for computer-aided design of working fluids for refrigeration machines. Chem Eng Technol 2013;36:1924–34. [13] Larkeche O, Meniai AH, Cachot T. Modelling the absorption refrigeration cycle using partially miscible working fluids by group contribution methods. Mol Phys 2012;110:1305–16. [14] Papadopoulos A, Stijepovic M, Linke P, Seferlis P, Voutetakis S. Multi-level design and selection of optimum working fluids and ORC systems for power and heat cogeneration from low enthalpy renewable sources. Comput Aided Chem Eng 2012;30:66–70.

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