Second-law-based screening of working fluids for medium-low temperature organic Rankine cycles (ORCs): Effects of physical and chemical properties

Second-law-based screening of working fluids for medium-low temperature organic Rankine cycles (ORCs): Effects of physical and chemical properties

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Energy Procedia 158 Energy Procedia 00(2019) (2017)1406–1411 000–000 www.elsevier.com/locate/procedia

10th International Conference on Applied Energy (ICAE2018), 22-25 August 2018, Hong Kong, 10th International Conference on Applied Energy China(ICAE2018), 22-25 August 2018, Hong Kong, China

Second-law-based screening of working fluids for medium-low The 15th International Symposium on Districtfluids Heatingfor and medium-low Cooling Second-law-based screening of working temperature organic Rankine cycles (ORCs): Effects of physical and temperature organic Rankine cycles (ORCs): Effects of physical and chemical properties Assessing the feasibility of using the heat demand-outdoor chemical properties temperature functionWeiwu for aMa long-term district heat demand forecast a , Tao Liua, Min Lia* a,b,c

I. Andrić

a Weiwu Maaa, Tao Liua, Min a b Li * c c South University, 932 Lushan South Road, Changsha, 410083, China , O. Le Corre *,Central A. Pina , P. Ferrão , J. Fournier ., B. Lacarrière a

a Central South University, 932 Lushan South Road, Changsha, 410083, China IN+ Center for Innovation, Technology and Policy Research - Instituto Superior Técnico, Av. Rovisco Pais 1, 1049-001 Lisbon, Portugal b Veolia Recherche & Innovation, 291 Avenue Dreyfous Daniel, 78520 Limay, France Abstract c Département Systèmes Énergétiques et Environnement - IMT Atlantique, 4 rue Alfred Kastler, 44300 Nantes, France Abstract a

The diversity of both organic fluids and performance criteria makes the selection and evaluation of working fluids The diversity of bothcycles organic fluidsfull andofperformance criteria makes thechallenge, selection this and paper evaluation of working fluids for organic Rankine (ORCs) challenge. To overcome this first reports on secondfor organic Rankine (ORCs) full challenge. To overcome challenge, paper firstwhich reports reveal on secondlaw-based analyticalcycles expressions for ofthermal efficiency and athisturbine sizethis parameter, key Abstract law-based analytical expressions thermaltemperatures efficiency and and thermodynamic a turbine sizeproperties parameter, which fluids. reveal This key dimensionless parameters relating tofor operating of organic dimensionless parameters relating to than operating temperatures and thermodynamic properties of organic fluids. This paper systematically screens more 70 working fluids involving a wide range of physical and chemical District heating networks are commonly addressed in the literature as one of the most effective solutions for decreasing the paper systematically more thansector. 70 working fluidsrequire involving a with wide critical range ofarephysical and chemical properties. study screens shows that specific turbine sizesystems generally increases temperature, reduced ideal greenhouse This gas emissions from the building These high investments which returned through the heat properties. This study shows that specific turbine size generally increases with critical temperature, reduced ideal gas heat capacity, and the atom number of working fluids. Different-family fluids may lead to ten-fold relative sales. Due to the changed climate conditions and building renovation policies, heat demand in the future could decrease, gas heat capacity, andturbine the atom number of working fluids. fluids lead efficiency to ten-foldofrelative differences in specific size even though they have the Different-family same atom numbers. Themay thermal ORCs prolonging the investment return period. differences in specific turbine size even though they have the same atom numbers. The thermal efficiency of appears to be independent of critical temperature, or at most, a weak function of critical temperature for low boiling The main scope of this paper is to assess the feasibility of using the heat demand – outdoor temperature function for heat ORCs demand appears be independent of critical temperature, or(Portugal), at most, awas weak function ofindependent critical temperature low weakly boiling point wettoThe fluids and other halocarbons. This is a result of Jacob number of or dependent forecast. district of Alvalade, located in Lisbon used asbeing a case study. The district is for consisted of 665 point fluids andinother Thissuch is result of Jacob number being independent of orhigh) dependent weakly on thewet critical of organic fluids alkanes, alkenes, and scenarios benzenes. buildings that temperature vary both halocarbons. construction period anda as typology. Three weather (low, medium, and three district on the critical temperature of organic(shallow, fluids such as alkanes, alkenes, and benzenes. renovation scenarios were developed intermediate, deep). To estimate the error, obtained heat demand values were

Copyright 2018 Elsevier All rights reserved. compared©with results fromLtd. a dynamic heat demand model, previously developed and validated by the authors. © 2019 The Authors. Published by Elsevier Ltd. th International Conference on Applied Copyright © showed 2018 Elsevier Ltd. Allresponsibility rights reserved. Selection and peer-review under of the scientific committee The results that when only weather change is license considered, the marginofof the error10could be acceptable for some applications This is an open access article under the CC BY-NC-ND (http://creativecommons.org/licenses/by-nc-nd/4.0/) th International Conference on Applied Selection and peer-review under responsibility of the scientific committee of the 10 Energy (ICAE2018). (the error in annual demand was lower than 20% for all weather scenarios considered). However, after introducing Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Appliedrenovation Energy. Energy (ICAE2018). scenarios, the error value increased up to 59.5% (depending on the weather and renovation scenarios combination considered). Keywords: Oragnic Rankine Cycle; Second-law-based analysis;within Working The value of slope coefficient increased on average thefluids range of 3.8% up to 8% per decade, that corresponds to the Keywords: Rankine Cycle; Second-law-based analysis;during Working decrease Oragnic in the number of heating hours of 22-139h thefluids heating season (depending on the combination of weather and renovation scenarios considered). On the other hand, function intercept increased for 7.8-12.7% per decade (depending on the coupled scenarios). The values suggested could be used to modify the function parameters for the scenarios considered, and improve the accuracy of heat demand estimations. © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. * Corresponding author. Tel.: +86 18573119955.

address:author. [email protected] * E-mail Corresponding Tel.: +86 18573119955. Keywords: Heat demand; Forecast; Climate change E-mail address: [email protected] 1876-6102 Copyright © 2018 Elsevier Ltd. All rights reserved. Selection peer-review under responsibility the scientific 1876-6102and Copyright © 2018 Elsevier Ltd. All of rights reserved. committee of the 10th International Conference on Applied Energy (ICAE2018). Selection and peer-review under responsibility of the scientific committee of the 10th International Conference on Applied Energy (ICAE2018). 1876-6102 © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the Scientific Committee of The 15th International Symposium on District Heating and Cooling. 1876-6102 © 2019 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of ICAE2018 – The 10th International Conference on Applied Energy. 10.1016/j.egypro.2019.01.342

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1. Introduction The urgent need to exploit low-grade heat sources has renewed a surge of interest in the thermodynamic analysis of organic Rankine cycles (ORCs) [1]. Of greater concern are the effects of working fluids on the performance of ORCs, including net power output, thermal efficiency, exergetic efficiency, minimum superheat degree, turbine expansion ratio, and component sizes [2]. Among these criteria, thermal efficiency has been the center of attention, and relationships between thermal efficiency and various thermodynamic properties have been widely examined [3, 4]. On the other hand, the number of published studies that discussed thermodynamic indexes associated with the turbine size [5] is small, pointing to the need for further investigation into the impact of physical and chemical features of working fluids on the design of turbine. Furthermore, whereas the effect of critical temperature on thermal efficiency has been widely investigated, it remains an ongoing debate because scholars have voiced opposition to the relation between thermal efficiency and critical temperature. It has been argued that thermal efficiency generally increases with the critical temperature of the used fluid [6, 7]. On the other hand, several lines of evidence appear to suggest that thermal efficiency may be independent of critical temperature. For example, Liu et al. illustrated that thermal efficiency is a weak function of critical temperature [8]. Anchored on the second law of thermodynamics, Li and Zhao developed theoretical expressions for thermal efficiency, which are entirely independent of critical temperature [9]. It seems, therefore, that further investigations are necessary to clarify the effect of critical temperature on the thermal efficiency of ORCs. Finally, and perhaps most importantly, considerable research has devoted to explaining the effects of working-fluids only from the viewpoint of thermodynamics, rather less attention has been paid to exploring potential associations between the thermodynamic performance of ORCs and chemical features of the working fluids. The primary aim of this paper is to fill the knowledge gaps identified above. For this purpose, this paper firstly develops a theoretical model for determining thermal efficiency of ORCs, an analytical expression that includes only the evaporating and the condensing temperatures, as well as several key working-fluid properties. Secondly, this paper critically analyzes by screening 74 fluids the influences of thermodynamic and chemical characteristics of working fluids on the thermodynamic performance of ORCs, including thermal efficiency, minimum superheat (MS), and turbine volume per unit work (i.e, specific turbine volume, STV). The findings of this study provide new insight into these relationships and contribute to guidelines for synthesizing new organic fluids for medium-low temperature ORCs. 2. Theoretical analysis 2.1. Analytical equation for thermal efficiency As illustrated in Fig. 1, Rankine cycles consists of the following four processes: isentropic compression in a pump (1 – 2), constant pressure heat addition in an evaporator (2 – 5), isentropic expansion in a turbine (5 – 6s), and constant pressure heat rejection in a condenser (6s – 1). The irreversibilities in actual pumps and turbines can be characterized by isentropic efficiencies. Conventionally, the thermal efficiency of an ORC is calculated by: (1)  t  h5  h6 s h5  h1  where hi denotes the enthalpy of the ith state point, and ηt is the isentropic efficiency of the turbine. The problem with Eq. (1) is the calculation of enthalpies that requires high accuracy equations of state or property diagrams. To overcome this problem, Li and Zhao developed a set of theoretical expressions for the thermal efficiency of medium-low temperature ORCs [9]: 2 2 3  cT3 c p ,1T1  T6 s  T1   T3  c pT3  T5  T3             r  T3  T1   T1  r  T3  T1    1  C r  tC 1    1 cT3 c pT3 T5  T3 2     C r r T3  T1  

(2)

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Fig.1 A Rankine cycle using a dry fluid (ds/dT > 0)

 T6s  T7



6s

7

3

where r is the heat of evaporation of the working fluid at the evaporating temperature T3, c, cp and cp,1 are the average heat capacity during the preheating process, the superheating process and the desuperheating process, respectively. and ηC denotes the Carnot efficiency, ηC = (T3 – T1)/T3. There is still a problem with Eq. (2), the determination of T6s still depends on equations of state. Thus, it is desirable to develop an analytical equation for η that is only a function of the evaporating and condensing temperatures, as well as several key thermal properties. To eliminate T6s, we need to calculate the temperature difference between T6s and T7. According to the Maxwell relation and Clapeyron equation, we have

 T   cp    r      1   dTb  c p  a  T b  c p  b

(3)

If the first and the second items of the integrand are replaced by the mid-point value of each a-b line, the first two terms tend to cancel each other out; and T6s – T7 is approximately equal to (4) T6 s  T7  1  rm m c p ,m T3  T1 





where rm, βm, cp,m are the averages of these saturate-vapor parameters from T1 to T3. Using Eq. (4) and T1 = T7, the Eq. (2) can be written as

 1   Ja  c p ,1 T3  T1  r T3 T1 2  2  Ja s  C     t C 1  2 1  Ja  Ja s  

(5)

Where Ja = c(T3–T1)/r, Jas = cp (T5–T3)/r, τ = 1–rmβm/cp,m, λ = (T5–T3)/ (T3–T1). 2.2. Specific turbine displacement Specific turbine volume, STV, can be defined as the volume of a working fluid at the turbine outlet per unit turbine power output: (6) STV= v6 s wout where v is specific volume, and wout denotes the cycle work output. STV characterizes the turbine volume used in an ORC. The purpose of the following second-law analysis is to build a relationship between STV and thermal properties of the working fluid. According to Li and Zhao [9]:

  T   tC r  C 3 wout 2  

2  T6s  T1 c pT1  T6s  T1  c p ,1T3 2    c 1  C   2c p       T3  T1 T3  T3  T1  T1    

(7)

3. Results and Discussion 3.1. Model validation The new analytical equation for η developed in Section 2 is a function of the operating temperatures (T1, T3, and T5) and several thermal properties of the working fluid. The accuracy of the equation is validated by comparing it with the conventional equation, Eq. (1). The comparisons are shown in Fig. 2 for several fluids. Fig. 2 illustrates that Eq. (5) agree well with Eq. (1) for the selected fluids. The figure show that the discrepancies increase with the evaporating temperature. Because the increasement of desuperheat degrees causes errors in the calculations of mean

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Fig. 2 Comparison of thermal efficiencies calculated by Eq. (1) and (5) for ORCs (η vs. T3)

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Fig. 3 Effects of the critical temperature on η and STV

thermal properties increasing. The maximum relative error is only 2.96% in Fig. 2. The ranges of the evaporating temperature involved in figure are large enough for common medium-low temperature applications. Therefore, it can be concluded that these analytical equations are accurate enough for engineering applications. 3.2. Effects of critical temperature Critical temperature, together with critical pressure, are extremely important thermodynamic properties and play a fundamental role in determining the thermodynamic performances of ORCs [10, 11]. Therefore, this work screened 74 fluids for clarifying the correlations between Tc and thermodynamic indexes, including η, STV, c/r. Fig. 3 shows the relationships between critical temperature Tc and η and STV. Under the condition of given T1 and T3, there is a positive correlation between Tc and STV among the screened working fluids: STV increases with Tc. On the other hand, Fig. 3 reveals that thermal efficiency widely spreads along a horizontal line for a given set of T1 and T3, especially for the substances with high Tc. This trend suggests that the thermal efficiency of ORCs tends to be independent of Tc over a wide range of critical temperature. While a weak positive correlation between Tc and η may exist for working fluids having low Tc, especially the wet fluids, the superheat at the turbine inlet assumed in the analysis of wet fluids has a strong influence on η; thus, the minimum superheat, instead of Tc, is probably the leading factor for the variations in the thermal efficiency of ORCs using wet fluids (hollow squares in Fig. 3). The relationships between Tc and η (or Tc and STV) should be regarded as overall large-range trends for substances involving a wide spectrum of critical temperatures. Since the spread of η and STV along the trend lines seems to be highly “random”, the overall trends may be invalid within narrow ranges of Tc. Admittedly, the relationship between η and Tc remains a contentious issue in the literature. Some researchers claimed that the thermal efficiency generally increases with the critical temperature [6, 7], whereas some researchers have described that the thermal efficiency is a weak function of the critical temperature [8]. Our theoretical and computational results presented here tend to confirm that η is independent of Tc. First, Fig. 3 clearly validates the independence between η and Tc applicable to a great number of fluids. Second, the theoretical expression for η, derived from the second law of thermodynamics, indicates that thermal efficiency is essentially independent of critical temperature. 3.3. Effects of Ja number The theoretical formula reveals that the thermal efficiency depends closely on Ja number or c/r under the condition of given T1 and T3. This correlation is confirmed by Fig. 4, which shows that η decreases with c/r for given condensing and evaporating temperatures. By contrast, observing Fig. 4, it is uncertain whether c/r has a definite effect on STV. The distribution of STV in Fig. 4 seems to be rather random. Because of the positive correlation Tc ~ STV revealed in Fig. 3, the relation between c/r and Tc is also unclear and similar to that between c/r and Tc. Fig. 5 shows such associations between c/r and the critical parameters (Tc and Pc). Overall, it is difficult to

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Fig. 4 Relationships between c/r and η and STV

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Fig. 5 Relationships between c/r and critical temperature and pressure

draw a generally valid relationship between c/r and STV (or Tc) only from the perspective of thermodynamics. 3.4. Effects of chemical features

In fact, the seeming “random” relationship between c/r and Tc and STV, as shown in Figs. 5 and 4, is a result of the chemical features of working fluids. To confirm this conclusion, different symbols are used in Fig. 5 to label different families of working fluids. If the families of working fluids are considered, two entirely different trends emerge from Fig. 5. First, c/r tends to be independent of Tc and vary within very narrow ranges (i.e., nearly a constant) for some families of organic substances such as alkanes, alkenes, and benzenes. There are only two exceptions to this general trend among the screened alkanes and alkenes, i.e., propane and propylene, respectively. These two fluids are wet fluids, differing from their corresponding homologues. The second general pattern is that c/r may increase with decreasing Tc for wet fluids and other halocarbons (dry fluids). Since c/r is the key fluid property correlating to thermal efficiency (Fig. 4), the second varying trend explains why the thermal efficiency of wet fluids and some low boiling-point fluids depends weakly on the critical temperature (Fig. 3). Figs. 6 and 7 show how STV and minimum superheat (MS) vary with the reduced ideal gas heat capacity and the atom number of fluid molecules, respectively. These two figures reveal similar varying trends. For wet fluids, minimum superheat is required so that the expanded vapor at the turbine outlet is just saturated. The MS depends on the evaporating and the condensing temperatures, as well as the thermodynamic characteristic of the working fluid. (Fig. 6) and n (Fig. 7), Under the condition of given T1 and T3, while MS generally decreases with appears to be a more appropriate property for predicting MS required by a wet fluid. In Fig. 7, minimum superheat may differ considerably for the working fluids of the same atom number. The great difference is probably due to the is very good, despite chemical features of the substances. By contrast, the goodness-of-fit between MS and

Fig. 6 Relationships between the reduced ideal gas heat capacity and STV and MS

Fig. 7 Relationships between the atom number and STV and MS

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being a macroscopic thermodynamic parameter. The general trends of STV shown in Figs. 6 and 7 are quite revealing. First, the computational results reveal that STV generally increases with the atom number for the same family of working fluids. For example, the solid line shown in Fig. 7 highlights the increasing trend of alkanes (red solid circles), especially STV increase from 1.02 m3/MJ for propane (3-alkane) to 6527.7 m3/MJ for dodecane (12-alkane). For benzene homologues (red hollow circles), STV increases from 27.2 m3/MJ for Benzene to 252.7 m3/MJ for o-xylene (i.e., 1,2-dimethylbenzene). Second, Fig. 7 shows that organic fluids having the same n but belonging to different families may result in STV having different order-of-magnitude. A good example of this is the difference in STV between n-alkane and benzenes of the same number of atoms: benzenes lead to STV almost ten times greater than alkanes. 4. Conclusion The purpose of this paper is to cast a new light on how physical and chemical features of working fluids influence thermodynamic performances of ORCs. For this purpose, this paper develops an analytical expression for thermal efficiency and specific turbine size for ORCs, which provides a fast and accurate approach to computer simulations of ORCs without recourse to thermodynamic diagrams or equations of states. More than 70 working fluids were screened and compared in terms of various thermodynamic parameters. The results reported here suggest that the influence of working fluids cannot be explained only from the viewpoint of thermodynamics, and the chemical properties of fluids must be considered, for example, 1) c/r appears to be independent of Tc for dry alkanes, alkenes, and benzenes; on the other hand, c/r may increase with decreasing Tc for low boiling-point wet fluids and halocarbons; 2) For organic fluids being the same family, STV generally increases, and MS decreases with the atom number of working fluids; 3) Organic fluids belonging to different families can result in relative differences in STV as large as ten times. Acknowledgements The authors would like to acknowledge the National Natural Science Foundation of China (No. 51778626). References [1] Yang MH, Yeh RH. Thermodynamic and economic performances optimization of an organic Rankine cycle system utilizing exhaust gas of a large marine diesel engine. Applied Energy 2015; 149: 1e12. [2] Bao J, Zhao L. A review of working fluid and expander selections for organic Rankine cycle. Renewable and Sustainable Energy Reviews 2013; 24: 325-342. [3] Sarkar J. Property-based selection criteria of low GWP working fluids for organic Rankine cycle. Journal of the Brazilian Society of Mechanical Sciences and Engineering 2017; 39(4): 1419-1428. [4] Toffolo A, Lazzaretto A, Manente G, Paci M. A multi-criteria approach for the optimal selection of working fluid and design parameters in Organic Rankine Cycle systems. Applied Energy 2014; 121: 219-232. [5] Yamamoto T, Furuhata T, Arai N. Design and testing of the organic Rankine cycle. Energy 2001; 26(3): 239-251. [6] Xu J, Yu C. Critical temperature criterion for selection of working fluids for subcritical pressure Organic Rankine cycles. Energy 2014; 74: 719-733. [7] Lai N A, Wendland M, Fischer J. Working fluids for high-temperature organic Rankine cycles. Energy 2011; 36(1): 199-211. [8] Wang EH, Zhang HG, Fan BY, Ouyang MG, Zhao Y, Mu QH. Study of working fluid selection of organic Rankine cycle (ORC) for engine waste heat recovery. Energy 2011; 36(5): 3406-3418. [9] Li M, Zhao B. Analytical thermal efficiency of medium-low temperature organic Rankine cycles derived from entropy-generation analysis. Energy 2016; 106: 121-130. [10] Sprouse C, Depcik C. Review of organic Rankine cycles for internal combustion engine exhaust waste heat recovery. Applied thermal engineering 2013; 51(1): 711-722. [11] Bertinat M P. Fluids for high temperature heat pumps. International journal of refrigeration 1986; 9(1): 43-50.