Organic Rankine cycle model for well-described and not-so-well-described working fluids

Energy 86 (2015) 93e104

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Organic Rankine cycle model for well-described and not-so-well-described working fluids Riccardo Brignoli, J. Steven Brown* Department of Mechanical Engineering, Catholic University of America, Washington, DC 20064, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 October 2014 Received in revised form 3 March 2015 Accepted 25 March 2015 Available online 21 May 2015

This paper presents an ORC (organic Rankine cycle) model consisting of turbine, condenser, pump, and boiler, with an optional IHX (internal heat exchanger). The model includes well-described (considerable experimental data) working fluids using the high accuracy EoS (equations of state) contained in REFPROP. Moreover, and more importantly, the model allows one to quickly and easily create from a few to many thousands of P-R (Peng-Robinson) EoS for not-so-well-described (little or no experimental data) working fluids. The latter is realized by parametrically varying critical temperature (Tc), critical pressure (Pc), acentric factor (u), and ideal gas specific heat (cop;c ). Simulation results for a low-temperature ORC application show that efficiency (h) increases with increasing heat source temperature (Tmax), and does so more strongly when an IHX is included; whereas, volumetric work output (V) decreases with increasing Tmax. The results further show that both h and V strongly decrease with increasing heat sink temperature (Tcond). Parametrically varying Tc, Pc, u, and cop;c showed that: (1) Increasing Tc generally leads to higher h and lower V. (2) Increasing Pc monotonically increases V. (3) Variations in u do not significantly impact h or V. (4) h and V both generally decrease with increasing values of cop;c . © 2015 Elsevier Ltd. All rights reserved.

Keywords: Equation of state Organic Rankine cycle Peng-Robinson Simulation model Working fluids

1. Introduction There is growing interest in ORC (organic Rankine cycles) for the production of electrical energy from renewable energy sources (e.g., solar, geothermal, biomass) or from “waste heat” from industrial processes, fuel cells, and the like. For our purposes, what distinguishes renewable energy/waste heat sources from conventional energy sources (e.g., hydrocarbon fuels) are the much lower source temperatures for the non-conventional energy sources. This fact implies the high-side temperatures (saturation temperatures of the working fluid in the boiler for subcritical cycles) will be lower for Rankine cycles based on non-conventional energy sources than for ones based on conventional energy sources making working fluids derived from organic compounds more appropriate (“ideal”) than water for cycles based on non-conventional energy sources. This is the reason such cycles are often dubbed organic Rankine cycles.

* Corresponding author. Department of Mechanical Engineering, Catholic University of America, 620 Michigan Ave, NE, Washington, DC 20064, USA. Tel.: þ1 202 319 5170; fax: þ1 202 319 5173. E-mail address: [email protected] (J.S. Brown). http://dx.doi.org/10.1016/j.energy.2015.03.119 0360-5442/© 2015 Elsevier Ltd. All rights reserved.

In recent years, research and development and the resulting literature regarding ORC machines, applications, energy sources, and working fluids has been rapidly increasing. Here, only a few recent papers regarding primarily low-temperature energy sources will be discussed. Peris et al. [1] bench tested an ORC machine designed for low grade heat sources and showed that the cycle thermal efficiency increased as a function of increasing source temperature. Carcasci et al. [2] simulated an ORC for the recovery of waste heat from gas turbine engines. They considered four commonly existing working fluids and determined the choice of the “best” working fluid depended on the source temperature. Prando et al. [3] experimentally and numerically studied an ORC biomass application for district heating CHP (combined heat and power) in Northeast Italy and showed this to be a technically and economically viable approach for increasing the use of renewable energy resources in the production of electric energy in these types of applications. Tchanche et al. [4] discussed six different ORC architectures (basic, superheated, transcritical/supercritical, with IHX (internal heat exchanger), with reheating, and with integrated feedliquid heaters), five different heat resources (biomass, ocean, waste heat, geothermal, and solar), the types of applications for ORC machines, and characteristics of ORC machines, including listing some

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Nomenclature cop h hfg m_ M P Q_ s T v V _ W x X, Y, Z

ideal gas specific heat at constant pressure [kJ/kg K, kJ/ kmol K] enthalpy [kJ/kg] latent heat of vaporization [kJ/kg] mass flow rate [kg/s] molecular mass [kg/kmol] pressure (kPa) heat transfer rate [kW] entropy (kJ/kg K) temperature ( C, K) specific volume [m3/kg] volumetric work output [kJ/m3] power [kW] quality generic working fluids

Greek symbols internal heat exchanger effectiveness [%] pump isentropic efficiency [%] turbine isentropic efficiency [%] cycle thermal efficiency [%] integral of z over the temperature range 0.6 < Tr < 0.9, Z 0:9Tc ¼ z,dT, see Eq. (12)

hIHX hp ht h P r u z

0:6Tc

density [kg/m3] acentric factor any thermodynamic property

manufacturers, the sizes as measured by output power, and the types of working fluids. They concluded that the selection of an ORC machine is primarily based on application, source temperature, and required output power. A number of authors have developed simulation and optimization tools for the analysis of ORC applications. A few of these include Cataldo et al. [5] who studied 41 commonly existing working fluids contained in REFPROP [6] possessing critical temperatures between 100  C and 300  C for a low-temperature waste heat recovery ORC application. They used a genetic algorithm to select the optimal working fluids for two heat source inlet temperatures of 100  C and 150  C, identifying benzene and Novec649 as the “optimal” working fluids for a source temperature of 100  C. Victor et al. [7] developed an optimization model to investigate 35 commonly existing single-component working fluids and several binary blends for a low-temperature ORC application where the heat source temperature varied from 100  C to 250  C. Their results showed that single-component working fluids yielded higher efficiencies than binary blends. They concluded that their model is a useful tool for selecting the working fluid and the application temperatures. Barbieri et al. [8] developed an ORC simulation model where the thermodynamic properties of the working fluid are calculated from tables generated from experimental pressuretemperature-specific volume data contained in the literature and from ideal gas specific heat values calculated from group contribution methods. They applied their model to six commonly existing working fluids. In addition to the already mentioned papers, a number of others have focused primarily on a discussion of working fluids appropriate for ORC. While the current paper does not intend to discuss these papers and working fluids in detail, the interested reader is

Subscripts 0, …,10 thermodynamic state points (Fig. 1) boil boiler c critical cond condenser est estimated f saturated liquid g saturated vapor IHX without internal heat exchanger þIHX with internal heat exchanger max maximum net net out outlet p pump r reduced ref reference sat saturation t turbine vap vapor Acronyms EoS equation of state E% percent error, see Eq. (11) FEQ fundamental Helmholtz equation IHX internal heat exchanger NBP normal boiling point ORC organic Rankine cycle P-R Peng-Robinson RMSE% root mean square percent error, see Eq. (10)

referred to a recent comprehensive review of ORC working fluids by Bao and Zhao [9]. In this paper, the authors reviewed a large number of literature sources and identified 77 commonly existing single-component working fluids and 44 zeotropic blends appearing in the various papers they reviewed. The identified working fluids are all well-described ones, that is, they are ones that are well-characterized by considerable experimental data and/ or they are ones for which high accuracy EoS (equations of state) are available. While there are several tools discussed and used in the literature for calculating the thermophysical properties necessary to investigate ORC performance, two widely used libraries are REFPROP [6] and CoolProp [10]. Each library contains well-characterized, high accuracy EoS for over 100 working fluids. REFPROP [6] is a nonopen source program that has been available to the public for some 25 years and is widely used in the refrigeration industry. CoolProp [10] is an open source program with similar capabilities and has been available to the public for the last few years. Both these librarieseand other similar oneseare useful for evaluating well-described working fluids; however, they are unable to evaluate not-so-well-described working fluids (ones where little or no experimental data and/or EoS are available) without a user expending considerable additional effort (time, money, experimentation, and programming). For not-so-well-described working fluids, Brown et al. [11] presented a simple, inexpensive, fast, and sufficiently accurate methodology for engineering purposes for calculating thermodynamic properties and investigating the performance potentials of not-so-well-described working fluids for ORC applications. The methodology of Brown et al. [11] is based on constructing simple cubic EoS [e.g., P-R (Peng-Robinson)] from estimated thermodynamic parameters critical temperature (Tc),

R. Brignoli, J.S. Brown / Energy 86 (2015) 93e104

critical pressure (Pc), acentric factor (u), and ideal gas specific heat at constant pressure (cop ), where the thermodynamic parameters are estimated using group contribution methods based on knowing only a molecule's structure and its NBP (normal boiling point) temperature. (Note: the NBP temperature also can be estimated from group contribution methods if it is not experimentally known.) The current paper presents an ORC simulation model consisting of a turbine, a condenser, a pump, and a boiler, with an optional IHX. Note: If an IHX is included, the model provides results both with and without the IHX to show the effects of it on the system performance. The model is capable of simulating both subcritical and supercritical cycles. While the modelelike others in the literatureecan simulate ORC employing well-described working fluids through the use of high accuracy EoS contained in REFPROP [6] or CoolProp [10], its novelty and usefulness is that it also can simulate not-so-well-described working fluids using P-R EoS developed using the methodology of Brown et al. [11]. Moreover, it can do this not only for one or a few not-so-well-described working fluids, but it can do this in a matter of a few seconds for many thousands of not-so-well-described working fluids that may or may not exist in reality by creating them parametrically through varying critical state properties, acentric factor, and ideal gas specific heat at constant pressure. Thus, one of the major benefits of the simulation model is that it can be used to quickly, easily, and inexpensively investigate, screen, and compare with reasonable engineering accuracy large numbers of potential working fluidsdboth well-described ones and, more importantly, not-so-well-described onesdfor ORC applications. As stated in Brown et al. [11], if the goal of identifying additional, appropriate working fluids for various ORC applications could be realized, it would help to increase the use of ORC, increase the mix of renewables in electricity production, lead to increased energy sustainability, and lower the negative environmental impacts of working fluids used in energy systems. The simulation model presented in this paper is a tool that could be used to realize this goal.

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2. Organic Rankine cycle Fig. 1 shows a schematic of the simulated ORC. The simulation is thermodynamically based only and does not include heat transfer and pressure drop effects in the heat exchangers and in the pipes/ lines. Thus, the model does not include transport properties such as thermal conductivity and viscosity. The ORC is an ideal Rankine cycle consisting of a boiler, a turbine, a condenser, a pump, and an optional IHX. Table 1 shows the two independent, intensive properties used to determine thermodynamic state points around the cycle. The turbine and pump are characterized by isentropic efficiencies and the IHX is characterized either by its effectiveness or the low-pressure side superheat. The inlet state of the condenser (state point 8) is the outlet state from the low-pressure side of the IHX and the outlet state of the condenser (state point 0) is a saturated liquid state at the specified condensing temperature. (Note: the condensing pressure is the vapor pressure of the working fluid corresponding to the condensing temperature.) The inlet state of the boiler (state point 10) is the outlet state from the high-pressure side of the IHX and the outlet state of the boiler is determined by the scheme outlined in Table 2. The mass flow rate of the working fluid is determined by the net power output from the cycle and the resulting thermodynamic state points of the working fluid at the inlets and outlets to the pump and the turbine. When the optional IHX is included, the model performs simulations for cycles both with and without the presence of the IHX. In the case where the IHX low-pressure side superheat is specified rather than the effectiveness, the program performs a check to ensure the specified superheat is not greater than (T7 e T9) and further ensures that T10 < T3, otherwise the program provides a warning indicating the IHX input is unacceptable. When the optional IHX is not included or its presence is not allowed because T7 < T2, then state 8 is identical to state 7 and state 10 is identical to state 2. Finally, Eqs. (1)e(9) provide relationships for determining cycle parameters and performance measures. The net cycle efficiency is given by:

h¼

_ net W Q_

(1)

boil

_ net is the net cycle power output defined in Eq. (2) and where W Q_ boil is the heat rate input to the cycle defined in Eq. (3).

_ tW _p _ net ¼ W W

(2)

_ 5  h10 Þ Q_ boil ¼ mðh

(3)

_ t is the turbine power output given by Eq. (4), W _ p is the where W pump power input given by Eq. (5), m_ is the mass flow rate of the working fluid, and h is the specific enthalpy at the various state points defined in Fig. 1.

_ t ¼ mðh _ 5  h7 Þ W

(4)

_ p ¼ mðh _ 2  h0 Þ W

(5)

The heat rejection from the cycle is Q_ cond is given by:

_ 8  h0 Þ Q_ cond ¼ mðh

(6)

The turbine efficiency ht is given by Eq. (7), the pump efficiency hp is given by Eq. (8), and the IHX effectiveness hIHX is given by Eq. Fig. 1. Schematic of the simulated ORC defined by 11 state points.

(9).

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R. Brignoli, J.S. Brown / Energy 86 (2015) 93e104 Table 1 Determination of thermodynamic state points around the cycle shown in Fig. 1.

Thermodynamic state point 0 1 2 3

4

5

6 7 8 9 10

Subcritical cycle

Case defined in Table 2

Two independent, intensive properties T ¼ Tcond and x ¼ 0 P ¼ Pboil and s ¼ so P ¼ Pboil and h determined from hp P ¼ Pboil ¼ Psat (Tmax) and x ¼ 0 P ¼ Pboil ¼ Pmax and x ¼ 0 P ¼ Pboil ¼ Pmax and T ¼ Tmax P ¼ Pboil ¼ Psat (Tmax) and x ¼ 1 P ¼ Pboil ¼ Pmax and x ¼ 1 P ¼ Pboil ¼ Pmax and T ¼ Tmax P ¼ Pboil ¼ Psat (Tmax) and x ¼ 1 P ¼ Pboil ¼ Pmax and T ¼ Tmax P ¼ Pboil ¼ Pmax and T ¼ Tmax P ¼ Pcond and s ¼ s5 P ¼ Pcond and h determined from ht P ¼ Pcond and T determined from hIHX P ¼ Pcond and x ¼ 1 P ¼ Pboil and h determined from IHX heat balance

all all all a b c a b c a b c All All All All All

h ¼ specific enthalpy, P ¼ pressure, T ¼ temperature, v ¼ specific volume, x ¼ quality, and h ¼ efficiency, with subscripts boil ¼ boiler, cond ¼ condenser, IHX ¼ internal heat exchanger, max ¼ maximum, p ¼ pump, and t ¼ turbine.

ht ¼

h7  h5 h6  h5

(7)

hp ¼

h1  h0 h2  h0

(8)

hIHX ¼

T7  T8 T7  T2

(9)

containing working fluids, Brown et al. [11] showed that the method of Ambrose [13] is the best one for Tc and that the method of Wilson [17] is the best one for Pc. 3.2. Acentric factor Brown et al. [11] considered three methods for predicting acentric factor; however, because all three methods yielded similar accuracies they recommended using the method of Reid et al. [18]. 3.3. Ideal gas specific heat

3. Equations of state An EoS is needed to calculate the thermodynamic properties for the 11 state points (Table 1) around the cycle. If the simulated ORC includes a well-described working fluid, then the simulation model simply uses the default, high-accuracy EoS contained in REFPROP [6] to calculate thermodynamic properties. If on the other hand, the simulated ORC includes a not-so-well-described working fluid (one not contained in the database of REFPROP [6] and one for which little or no data exist and/or EoS are available), then the simulation model can build a P-R EoS following the methodology described in Brown et al. [11] and Brown [12]. To accomplish the later, one simply needs to know the working fluid's molecular structure and its NBP temperature to employ group contribution methods to estimate Tc, Pc, u, and cop from which a P-R EoS can be constructed. This P-R EoS then can be used to calculate thermodynamic properties at the 11 state points. In the following subsections, the methodology for estimating Tc, Pc, u, and cop presented in Brown et al. [11] is briefly summarized.

Brown et al. [11] recommended the method of Joback [19] to estimate cop , except for siloxanes for which they recommended the method of Harrison and Seaton [20]. 3.4. Property estimations In this subsection, the estimation results from Brown et al. [11] for a group of 31 working fluids (see Table 3, which is taken from Saleh et al. [21]) are summarized for the thermodynamic parameters Tc, Pc, and cop which are necessary to construct a P-R EoS and for the thermodynamic properties Pvap, hfg, rf, and rg which are necessary to make cycle calculations. Fig. 2 shows the root mean square percent error [RMSE%, see Eq. (10)] of Tc and Pc for the 31 fluids and Fig. 3 shows the percent error [E%, see Eq. (11)] of cop for the same fluids. Figs. 2 and 3 are modified from Brown et al. [11]. Note:

vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi u n h . i2 . uX zest  zref zref n RMSE% ¼ 100,t

(10)

1

3.1. Critical state properties Brown et al. [11] employed five common group contribution methods of Ambrose [13], Joback [14], Lydersen [15], Marrero [16], and Wilson [17] to estimate Tc and Pc. All five methods can be used for non-silicon containing working fluids; whereas, only the methods of Ambrose [13], Lydersen [15], and Wilson [17] can be used for silicon containing working fluids. Brown et al. [11] showed that the methods of Ambrose [13] and Marrero [16] are the best ones for non-silicon containing working fluids. For silicon

Table 2 Determination of the high-pressure (boiler) state points based on cycle operating conditions of Tmax (maximum temperature) and Pmax (maximum pressure). Case

Operating condition

a b c

Tmax < Tc Tmax > Tc

Cycle type Pmax is not used Pmax < Pc Pmax > Pc

Subcritical Subcritical Supercritical

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Table 3 Group of 31 working fluids contained in Brown et al. [11]dwhich were taken from Saleh et al. [21]dlisted in ascending order of NBP temperature. Common name

Chemical formula

IUPAC name

CAS number

NBP [K]

R41 R32 R125 R1270 R143a R290 R218 RE125 RC270 R134a RE170 R152a R13I1 R227ea R600a RC318 R236fa R600 RE134 RE245mc R236ea neopentane R245fa R245ca R601a R338mccq RE245 perfluoropentane RE347mcc R601 hexane

CH3F CH2F2 CF3eCHF2 CH3eCH]CH2 CF3eCH3 CH3eCH2eCH3 CF3-CF2-CF3 CF3eOeCHF2 (CH2)3 CF3eCH2F CH3eOeCH3 CHF2eCH3 CF3I CF3-CHF-CF3 (CH3)2CHeCH3 (CF2)4 CF3-CH2-CF3 CH3-(CH2)2eCH3 CHF2eOeCHF2 CF3eCF2eOeCH3 CF3eCHFeCHF2 (CH3)4C CF3eCH2eCHF2 CHF2eCF2eCH2F (CH3)2CHeCH2eCH3 CF3eCF2eCF2eCH2F CHF2-O-CH2-CF3 CF3-(CF2)3-CF3 CF3eCF2eCF2eOeCH3 CH3-(CH2)3eCH3 CH3-(CH)4eCH3

fluoromethane difluoromethane 1,1,1,2,2-pentafluoroethane 1- propene 1,1,1-trifluoroethane propane octafluoropropane (difluoromethoxy) (trifluoro) methane cyclopropane 1,1,1,2-tetrafluoroethane methoxymethane 1,1-difluoroethane trifluoroiodomethane 1,1,1,2,3,3,3-heptafluoropropane isobutane octafluorocyclobutane 1,1,1,3,3,3-hexafluoropropane butane (difluoromethoxy) (difluoro) methane 1,1,1,2,2-pentafluoro-2-methoxyethane 1,1,1,2,3,3-hexafluoropropane neopentane 1,1,1,3,3-pentafluoropropane 1,1,2,2,3-pentafluoropropane isopentane 1,1,1,2,2,3,3,4-octafluorobutane 2-(difluoromethoxy)-1,1,1-trifluoroethane dodecafluoropentane 1,1,1,2,2,3,3-heptafluoro-3-methoxypropane pentane hexane

593-53-3 75-10-5 354-33-6 115-07-1 420-46-2 74-98-6 76-19-7 3822-68-2 75-19-4 811-97-2 115-10-6 75-37-6 2314-97-8 431-89-0 75-28-5 115-25-3 690-39-1 106-97-8 1691-17-4 22410-44-2 431-63-0 463-82-1 460-73-1 679-86-7 78-78-4 662-35-1 1885-48-9 678-26-2 375-03-1 78-78-4 110-54-3

195.00 221.40 225.06 225.53 225.91 231.04 236.36 238.06 241.67 247.08 248.37 249.13 250.60 256.81 261.40 267.30 271.71 272.66 277.85 278.76 279.34 282.65 288.29 298.28 300.98 301.00 302.39 302.90 307.35 309.21 341.86

where z is any thermodynamic property and the subscripts “est” and “ref” indicate “estimated” and “reference”, respectively, and n represents the number of fluids. Further note:

.   Pref E% ¼ 100$DP=P ¼ 100$ Pest  Pref

(11)

where:

0:9T Z c

P¼

z$dT

(12)

0:6Tc

4. Simulation model This section outlines a simulation model written in Microsoft® Visual Basic 2010 implementing the ORC of Section 2 and the EoS scheme as outlined in Section 3. Fig. 6 shows the main screen for inputting cycle parameters (the left-hand side.) The parameters describing the working fluid in terms of molecular mass (M), NBP temperature, Tc, Pc, u, and cop are shown on the right-hand side. Note: while Fig. 6 shows only one working fluid, multiple fluids can be described simultaneously (1) by loading fluids from REFPROP [6] or CoolProp [10], (2) by loading previously stored user-created working fluids, or (3) by creating new working fluids. Fig. 7 shows the screen where the thermodynamic parameters of newly

Generically P is the integration of any thermodynamic property z over the temperature range 0.6  Tr  0.9, where Tr ¼ T/Tc, which represents a typical application temperature range for ORC systems. Fig. 4 shows E% for Pvap and hfg for the 31 fluids and Fig. 5 shows E% for rf, and rg for the same fluids. These figures are modified from Brown et al. [11]. For Pvap, hfg, rf, and rg, 85.7%, 100%, 74.3%, and 82.9% fall within ±10% of the reference values when the critical state properties are estimated using the method of Marrero [16] and 72.2%, 100%, 58.3%, and 80.6% when the critical state properties are estimated using the method of Ambrose [13]. However, as stated in Brown et al. [11], accurate estimates of rf are not critical in cycle performance estimates. The results summarized in this section demonstrate that the methodology presented in Brown et al. [11] and herein is able to predict with good engineering approximation the thermodynamic properties needed to make cycle calculations. Thus, the methodology will prove particularly useful for evaluating the cycle performance potentials of not-so-well-described working fluids.

Fig. 2. RMSE% for critical state property estimates of the group of fluids in Table 3 using the group contribution methods of Ambrose [13] and Marrero [16]. Figure modified from Brown et al. [11].

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Fig. 3. E%, relative to reference values from REFPROP [6], for cop estimates of the group of fluids listed in Table 3 using the group contribution methods of Joback [19], where the critical state properties are based on the methods of Ambrose [13] and Marrero [16]. Figure modified from Brown et al. [11].

Fig. 4. E%, relative to reference values from REFPROP [6], for Pvap and hfg estimates of the group of fluids listed in Table 3, except RE125, RE134, and RE245, using the group contribution methods of Ambrose [13] and Marrero [16] coupled with the P-R EoS. Figure modified from Brown et al. [11].

created working fluids are specified, which can then be stored for later use. A powerful option for creating many working fluids simultaneously by parametrically varying Tc, Pc, u, and cop;c also exists as shown in Fig. 8. Note: the example shown in Fig. 8 creates 8736 working fluids in a couple of seconds. Further note that, for this option, cop;c is used [see Eq. (14)] to determine the coefficients cop;0 ; cop;1 ; cop;2 ; and cop;3 needed to determine cop [Eq. (13)] as a

temperature (Tr) and further assuming all fluids have a reduced ideal gas specific heat at constant pressure ðcop;r ¼ cop =cop;c Þ value of one at Tr ¼ 1. With these assumptions and using R290 (propane) as the reference fluid, then cop;r is given by:

function of T.

Once the cycle and working fluid(s) have been described, the model simulates the cycle for all of the listed working fluids. Fig. 9 shows the resulting output screen. The upper portion shows cycle parameters and performance measures, where for each fluid the performance is provided for simulations both with and without an IHX to demonstrate the effects an IHX has on the

cop ¼ cop;0 þ cop;1 T þ cop;2 T 2 þ cop;3 T 3

(13)

The coefficients cop;0 ; cop;1 ; cop;2 ; and cop;3 are determined from cop;c by assuming all fluids have similar slopes with reduced

cop;r ¼ 0:267 þ 0:7083 Tr

(14)

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99

Fig. 5. E%, relative to reference values from REFPROP [6], for rf and rg estimates of the group of fluids listed in Table 3, except RE125, RE134, and RE245, using the group contribution methods of Ambrose [13] and Marrero [16] coupled with the P-R EoS. Figure modified from Brown et al. [11].

Fig. 6. Main input screen describing ORC and working fluid.

performance; the lower left-hand side shows a schematic of the ORC; the lower middle shows, for each selected fluid in the upper part, T, P, h, s, v, and x for the 11 state points described in Fig. 1; and, the lower right-hand side shows the resulting cycle on a T-s state diagram. The output results can be written to a Microsoft® Excel file. 5. Simulation results 5.1. Validation of model through simulations of working fluids In a previous paper, Brown et al. [11] simulated 31 working fluids of Saleh et al. [21] listed in Table 3 in an ORC application defined by a Tmax/Tcond combination of 100  C/30  C, with hp ¼ 0.65, ht ¼ 0.85, and W_ net ¼ 1 MW. The simulations included both subcritical and supercritical cycles, both with and without the

presence of an IHX. If an IHX was present, its outlet temperature on the low-pressure side was 10  C higher than the condensing temperature. Brown et al. [11] provide more details of the simulations and the operating conditions. These same working fluids, representing a large variety and complexity, were investigated once again for the same ORC application and operating conditions using the simulation model described herein and the results were validated with those of Brown et al. [11], which already has been validated with those Saleh et al. [21]. Note: group contributions of Ambrose [13] and Marrero [16] (see Section 3) were used to estimate Tc, Pc, u, and cop needed to build P-R EoS. Fig. 10 duplicated from Brown et al. [11] with updated results from the simulations of the present paper shows RMSE% of four output parameters for the 31 fluids for the application and operating conditions described above.

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Fig. 7. Screen for creating working fluids.

Fig. 8. Screen for creating working fluids parametrically.

The present results are identical (within limits of rounding er_ rors) of those of Brown et al. [11]. In summary, the RMSE% for m, vt,out,h-IHX, and hþIHX relative to reference values from REFPROP [6] for all fluids except RE125, RE134, RE245, and R338mccq are: (i) 2.87, 2.46, 1.45, 1.12, respectively, for the results of Saleh et al. [21], (ii) 5.42, 6.68, 5.11, and 4.07, respectively, for the P-R EoS based on estimates of critical state properties using the method of Ambrose [13], and (iii) 6.56, 4.57, 3.37, and 3.22, respectively, for the P-R EoS based on estimates of critical state properties using the method of _ vt,out,h-IHX, and hþIHX relative to Marrero [16]. The RMSE% for m, reference values from Saleh et al. [21] for RE125, RE134, RE245, and R338mccq are: (i) 4.31, 1.78, 2.69, and 3.65, respectively, for the P-R EoS based on estimates of critical state properties using the method of Ambrose [13], and (ii), 13.24, 7.30, 8.52, and 8.96, respectively, for the P-R EoS based on estimates of critical state properties using the method of Marrero [16]. The exercise of repeating a large part of the simulations of Brown et al. [11] confirms and validates the simulation model described herein. In the next subsection, the model will be used to conduct a parametric study of “ideal” working fluids for ORC applications.

5.2. Parametric investigation of working fluids In this section simulation results are presented for a typical ORC defined by Tcond ¼ 30  C, Tmax ¼ 120  C, Pmax ¼ 4000 kPa, _ net ¼ 1 MW, ht ¼ 80%, hp ¼ 90%, and hIHX ¼ 70%. Given the W relatively low value of the maximum high-side temperature, R290 (propane) is selected as the baseline working fluid given that its Tc,R290 ¼ 369.89 K and Pc,R290 ¼ 4251.2 kPa [6]. Table 4 shows that the much simpler and easy to implement P-R EoS provides similar (for engineering purposes) results for cycle efficiency both without and with an IHX and for volumetric work output as does the much more complex and difficult to implement FEQ EoS of REFPROP [6]. This example demonstrates the utility and power of the methodology described in Section 3, particularly for not-so-well-described working fluids. Several questions could now be asked. Among these are more conventional ones such as: (1) How are the ORC cycle performances impacted by changes in the heat source and heat sink temperatures? (2) Imagine one has potential working fluids X, Y, and Z. Are any of the working fluids X, Y, or Z appropriate for this ORC application? Or more unconventional and interesting questions that are

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Fig. 9. Screen showing simulation results.

particularly well-suited for the methodology and simulation model presented herein such as: (3) Is there a more “ideal” working fluid than R290, or for that matter working fluids X, Y, and Z, for this ORC application? (4) If so, what should the thermodynamic parameters Tc, Pc, u, and cop;c be for this “ideal” working fluid? While the approach illustrated in Section 5.1 is appropriate for answering the first two questions, it is less useful in addressing the latter two questions. Rather, to answer these questions, parametric variations in the thermodynamic parameters Tc, Pc, u, and cop;c could potentially identify combinations of the parameters which might yield more “ideal” working fluids. While a “real” molecule based on any particular combination of these thermodynamic parameters may or may not actually exist, a parametric approach such as the one

described here can guide and inform searches for “actual” working fluids. As an example of how the model could be used to answer the first two questions, consider R290 as the baseline working fluid described by the thermodynamic parameters Tc,R290 ¼ 369.89 K, Pc,R290 ¼ 4251.2 kPa, uR290 ¼ 0.1521, and cop;c;R290 ¼ 86.65 (kJ/ kmol K) [6] operating in the ORC described at the beginning of this subsection. Fig. 11 shows how h and V vary as a function of heat source temperature (Tmax) and Fig. 12 shows how h and V vary as a function of heat sink temperature (Tcond). Note: in both figures the ordinates have been non-dimensionalized relative to the h or V value for operating conditions of Tmax ¼ 120  C and Tcond ¼ 30  C. Fig. 11 shows that as Tmax increases from 100  C to 150  C h-IHX/hIHX,R290 increases from 94.5% to 101.8%, hþIHX//hþIHX,R290 increases from 85.1% to 112.4%, and V/VR290 decreases from 102.8% to 98.2%. Fig. 12 shows that as Tcond increases from 21  C to 39  C h-IHX/hIHX,R290 decreases from 113.8% to 87.2%, hþIHX/hþIHX,R290 decreases from 112.4% to 87.6%, and V/VR290 decreases from 119.5% to 81.8%. The results show that h increases with increasing Tmax, and does so more strongly when an IHX is included; whereas, V decreases with increasing Tmax. The results further show that both h and V strongly decrease with increasing Tcond. As a second example, consider how the model could be used to answer the latter two questions. Once again consider R290 as the baseline working fluid operating in the same ORC as described above. Figs. 13e16 show normalized (using R290) values for cycle

Table 4 ORC simulation results for R290 (propane) based on a P-R EoS and on the default, high-accuracy fundamental Helmholtz (FEQ) EoS in REFPROP [6]. Note: for the P-R EoS the method of Marrero [16] was used for estimating the critical state properties. Fig. 10. RMSE% for ORC of Brown et al. [11] and Saleh et al. [21] obtained from simulations using the model presented herein. The RMSE% for the three groupings to the left of the dividing line are relative to reference values from REFPROP [6] and the two groupings to the right are for RE125, RE134, RE245, and R338mccq relative to reference values from Saleh et al. [21]. The abscissa labels indicate the method by which the critical state properties are determined.

h-IHX (%) hþIHX (%)

V (kJ/m3)

P-R EoS

FEQ EoS

% Difference

10.83 11.89 942.1

10.93 12.08 946.0

0.91 1.57 0.41

The subscripts eIHX and þIHX imply without and with IHX, respectively.

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Fig. 11. Normalized cycle efficiency and volumetric work output as Tmax is varied while holding Pmax, W_ net , ht, hp, hIHX, and Tcond fixed. Note: solid symbols refer to efficiency and the open symbol refers to volumetric work output.

Fig. 12. Normalized cycle efficiency and volumetric work output as Tcond is varied while holding Pmax, W_ net , ht, hp, hIHX, and Tmax fixed. Note: solid symbols refer to efficiency and the open symbol refers to volumetric work output.

efficiency without and with an IHX and volumetric work output as Tc, Pc, u, and cop;c , respectively, are parametrically varied while holding the other three parameters fixed. Fig. 13 shows that increasing Tc generally leads to higher h and lower V. This inverse relationship between h and V as a function of Tc has been noted by others (e.g., Brown [22] and McLinden et al. [23]). Also note that h is improved with the use of an IHX up to Tc/Tc,R290 ¼ 1, after which an IHX no longer provides a benefit relative to the baseline case. Fig. 14 shows that increasing Pc monotonically increases V. However, h increases with Pc for values of Pc/Pc,R290 < 0.8 after which it decreases for cycles without the presence of an IHX. The maximum h value shifts slightly to the right at a value of Pc/Pc,R290 ¼ 0.85 for cycles with the presence of an IHX. Also note that h is improved with the use of an IHX up to Pc/Pc,R290 ¼ 0.95, after which an IHX no longer provides a benefit relative to the baseline case. Fig. 15 shows that variations in u do not significantly impact h or V. Fig. 16 shows that h and V both generally decrease with increasing values of cop;c with h being significantly improved over the baseline case when using an IHX for cop;c /cop;c;R290 >1. As stated in Brown et al. [22], molecular complexity provides an indication of the value of the vapor molar heat capacity which is further indicative of the value of cop . Thus, the parametric study for low-temperature applications would suggest “ideal” working fluids based on a purely thermodynamic view should be small molecules that have large Tc to yield good h, large Pc to yield good V, and small

Fig. 13. Normalized cycle efficiency and volumetric work output as Tc is parametrically varied while holding Pc, u, andcop;c fixed. Note: solid symbols refer to efficiency and the open symbol refers to volumetric work output.

Fig. 14. Normalized cycle efficiency and volumetric work output as Pc is parametrically varied while holding Tc, u, and cop;c fixed. Note: solid symbols refer to efficiency and the open symbol refers to volumetric work output.

Fig. 15. Normalized cycle efficiency and volumetric work output as u is parametrically varied while holding Tc, Pc, and cop;c fixed. Note: solid symbols refer to efficiency and the open symbol refers to volumetric work output.

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be lower than the R290 value; and one would expect both h and V for R1270 to be similar to the R290 values. These expectations are in fact borne out as shown in Table 6. Thus, parametric studies such as illustrated here can be powerful tools in identifying potential working fluids for ORC applications. 6. Conclusion

Fig. 16. Normalized cycle efficiency and volumetric work output as cop;c is parametrically varied while holding Tc, Pc, and u fixed. Note: solid symbols refer to efficiency and the open symbol refers to volumetric work output.

Table 5 Normalized [relative to R290 (propane)] thermodynamic parameters for three working fluids. The R290 (propane) values are Tc,R290 ¼ 369.89 K, Pc,R290 ¼ 4251.2 kPa, uR290 ¼ 0.1521, and cop;c;R290 ¼ 86.65 (kJ/kmol K) [6].

R717 (ammonia) R600 (n-butane) R1270 (propylene)

Tc/Tc,R290

Pc/Pc,R290

u/uR290

cop;c =cop;c;R290

1.10 1.15 0.98

2.67 0.89 1.07

1.68 1.32 0.96

0.44 1.50 0.85

cop;c to yield good h and V. Such molecules, however, would likely require the use of an IHX to maximize h. However, “real” working fluids are chosen by manufacturers based on a design “optimization” subject to many constraints and criteria in addition to thermodynamic considerations, e.g., among these could be ready availability of the working fluid, its environmental impact, its cost, its compatibility with system materials and lubricants, its safety, its impact on heat transfer and pressure drop in the heat exchangers, its impact on the efficiency of the turbine/expander, the type of turbine/expander, etc. Moreover, the choice of fluid is impacted by the type of ORC application and the heat source and heat sink temperatures. For example, working fluids appropriate for lowtemperature heat sources may not be appropriate for much higher temperature heat sources. In fact, there are a number of working fluids that are commercially usedefrom ones with simpler molecular complexity such as R134a to ones with more molecular complexity such as siloxanes. Table 5 shows the normalized values for Tc/Tc,R290, Pc/Pc,R290, u/ uc,R290 andcop;c =cop;c;R290 for three working fluids: R717 (ammonia), R600 (n-butane), and R1270 (propylene). These three were chosen for illustration purposes. R717 is a simple molecule with large Tc, large Pc, and small cop;c . R600 is a hydrocarbon with one more carbon than R290 and R1270 is an unsaturated hydrocarbon with the same number of carbons as R290. Based on what the parametric study showed, one would expect both h and V for R717 to be greater than the R290 values; one would expect the h value for R600 to be greater than the R290 value while expecting the V value for R600 to Table 6 ORC simulation results for three working fluids relative to R290 (propane). The EoS are the default, high-accuracy FEQ in REFPROP [6].

R717 (ammonia) R600 (n-butane) R1270 (propylene)

h-IHX/h-IHX,R290

hþIHX//hþIHX,R290

V/VR290

1.30 1.26 0.93

1.18 1.22 0.93

1.80 0.44 1.06

This paper presents an organic Rankine cycle (ORC) model consisting of a turbine, a condenser, a pump, and a boiler, with the possibility of including an optional IHX. The model allows for simulations of well-described (considerable experimental data are available) working fluids using the high accuracy equations of state (EoS) contained in REFPROP [6] and CoolProp [10]. Moreover, and more importantly, the model allows one to quickly and easily create Peng-Robinson (P-R) EoS for not-so-well-described (little or no experimental data are known) working fluids. It also allows one to quickly and easily create P-R EoS for a large number (many thousands) of theoretical working fluids by parametrically varying critical state properties, acentric factor, and ideal gas specific heat at constant pressure. In both cases, the P-R EoS can be coupled with the cycle model to allow for easy, fast, and inexpensive screening and comparison of the performance potentials of a large number of well-described and not-so-well-described working fluids in subcritical and supercritical ORC. The model was used to investigate the effects of the heat source temperature (Tmax) and heat sink temperature (Tcond) on cycle efficiency (h) and volumetric work output (V). The results show that h increases with increasing Tmax, and does so more strongly when an IHX is included; whereas, V decreases with increasing Tmax. The results further show that both h and V strongly decrease with increasing Tcond. The model was further used to parametrically vary critical temperature (Tc), critical pressure (Pc), acentric factor (u), and ideal gas specific heat at constant pressure (cop;c ) for a typical lowtemperature ORC application. By varying these fundamental thermodynamic parameters, the paper shows that: (1) Increasing Tc generally leads to higher h and lower V. (2) Increasing Pc monotonically increases V. However, h increases with Pc for values of Pc/ Pc,R290 < 0.8 after which it decreases for cycles without the presence of an IHX. The maximum h value shifts slightly to the right at a value of Pc/Pc,R290 ¼ 0.85 for cycles with the presence of an IHX. Also note that h is improved with the use of an IHX up to Pc/ Pc,R290 ¼ 0.95, after which an IHX no longer provides a benefit relative to the baseline case. (3) Variations in u do not significantly impact h or V. (4) h and V both generally decrease with increasing values ofcop;c with h being significantly improved over the baseline case when using an IHX for cop;c /cop;c;R290 >1. The methodology and simulation model presented in the paper can be powerful tools in identifying potential working fluids for ORC applications and guiding research and development efforts of alternative working fluids. As stated in Brown et al. [11], if the goal of identifying additional, appropriate working fluids for various ORC applications could be realized, it would help to increase the use of ORC, increase the mix of renewables in electricity production, lead to increased energy sustainability, and lower the negative environmental impacts of working fluids used in energy systems. Interested readers are welcome to contact either author to obtain an installation package of the simulation model. References [1] Peris B, Navarro-Esbri J, Moles F, Collado R, Mota-Babiloni A. Performance evaluation of an organic Rankine cycle (ORC) for power applications from low grade heat sources. Appl Therm Eng 2015;75:763e9.

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[2] Carcasci C, Ferraro R, Miliotti E. Thermodynamic analysis of an organic Rankine cycle for waste heat recovery from gas turbines. Energy 2014;65: 91e100. [3] Prando D, Renzi M, Gasparella A, Baratieri M. Monitoring of the energy performance of a distric heating CHP plant based on biomass boiler and ORC generator. Appl Therm Eng 2015. http://dx.doi.org/10.1016/ j.applthermaleng.2014.12.063. [4] Tchanche BF, Petrissans M, Papadakis G. Heat resource and organic Rankine cycle machines. Renew Sust Energ Rev 2014;39:1185e99. [5] Cataldo F, Mastrullo R, Mauro AW, Vanoli GP. Fluid selection of organic Rankine cycle for low-temperature waste heat recovery based on thermal optimization. Energy 2014;72:159e67. [6] Lemmon EW, Huber ML, McLinden MO. NIST standard reference database 23: NIST reference fluid thermodynamic and transport properties-REFPROP, version 9.1. Gaithersburg: National Institute of Standards and Technology; 2013. Standard reference data program. [7] Victor RA, Kim J-K, Smith R. Composition optimisation of working fluids for organic Rankine cycles and Kalina cycles. Energy 2013;55:114e26. [8] Barbieri ES, Morini M, Pinelli M. Development of a model for the simulation of organic Rankine cycles based on group contribution techniques. In: Proceedings of ASME Turbo Expo 2011, Vancouver, British Columbia, Canada; 2011. [9] Bao J, Zhao L. A review of working fluid and expander selection for organic Rankine cycle. Renew Sust Energ Rev 2013;24:325e42. [10] Bell IH, Wronski J, Quoilin S, Lemort V. Pure and pseudo-pure fluid thermophysical property evaluation and the open-source thermophysical property library CoolProp. Ind Eng Chem Res 2014;53:2498e508. [11] Brown JS, Brignoli R, Daubman S. Methodology for estimating thermodynamic parameters and performance of working fluids for organic Rankine cycles. Energy 2014;73:818e28.

[12] Brown JS. Predicting performance of refrigerants using the Peng-Robinson equation of state. Int J Refrig 2007;30(8):1319e28. [13] Reid RC, Prausnitz JM, Poling BE. The properties of gases and liquids. 4th ed. New York: McGraw-Hill; 1987. p. 154e6. [14] Poling BE, Prausnitz JM, O'Connell JP. The properties of gases and liquids. 5th ed. New York: McGraw-Hill; 2001. p. 2.3e4. [15] Lydersen AL. Estimation of critical properties of organic compounds. Univ Wis Coll Eng Eng Exp Stn Rpt 1955;3. [16] Poling BE, Prausnitz JM, O'Connell JP. The properties of gases and liquids. 5th ed. New York: McGraw-Hill; 2001. p. 2.1e2.19. [17] Poling BE, Prausnitz JM, O'Connell JP. The properties of gases and liquids. 5th ed. New York: McGraw-Hill; 2001. p. 2.9e2.12. [18] Reid RC, Prausnitz JM, Poling BE. The properties of gases and liquids. 4th ed. New York: McGraw-Hill; 1987. p. 23. [19] Poling BE, Prausnitz JM, O'Connell JP. The properties of gases and liquids. 5th ed. New York: McGraw-Hill; 2001. p. 3.6e7. [20] Harrison BK, Seaton WH. Solution to missing group problem for estimation of ideal gas heat capacities. Ind Eng Chem Res 1988;27:1536e40. [21] Saleh B, Koglbauer G, Wendland M, Fischer J. Working fluids for lowtemperature organic Rankine cycles. Energy 2007;32:1210e21. [22] Brown JS. Preliminary selection of R-114 replacement refrigerant using fundamental thermodynamic parameters (RP-1308). HVAC&R Res 2007;13: 697e709. [23] McLinden MO, Kazakov AF, Brown JS, Domanski PA. A thermodynamic analysis of refrigerants: possibilities and tradeoffs for low-GWP refrigerants. Int J Refrig 2014;38:80e92.