Parametric investigation of working fluids for organic Rankine cycle applications

Applied Thermal Engineering 90 (2015) 64e74

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Research paper

Parametric investigation of working fluids for organic Rankine cycle applications J. Steven Brown*, Riccardo Brignoli, Timothy Quine Department of Mechanical Engineering, Catholic University of America, Washington, DC 20064, USA

h i g h l i g h t s
“Ideal” working fluids are investigated for organic Rankine cycles (ORC).
The thermodynamic space of “ideal” working fluids is parametrically investigated.
Five low- and high-temperature ORC applications are investigated.
1620 “ideal” and several “real” working fluids per application are investigated.

a r t i c l e i n f o

a b s t r a c t

Article history: Received 27 March 2015 Accepted 21 June 2015 Available online 9 July 2015

This paper investigates working fluids for organic Rankine cycle (ORC) applications with a goal of identifying “ideal” working fluids for five renewable/alternative energy sources. It employs a methodology for screening and comparing with good engineering accuracy the thermodynamic performance potential of ORC operating with working fluids that are not well characterized experimentally or by highaccuracy equations of state. A wide range of “theoretical” working fluids are investigated with the goals to identify potential alternative working fluids and to guide future research and development efforts of working fluids. The “theoretical” working fluids investigated are described in terms of critical state properties, acentric factor, and ideal gas specific heat capacity at constant pressure and are obtained by parametrically varying each of these parameters. The performances of these “theoretical” working fluids are compared to the performances of several “real” working fluids. The study suggests a working fluid's critical temperature and its critical ideal gas molar heat capacity have the largest impact on the cycle efficiency and volumetric work output, with “ideal” working fluids for high efficiency possessing critical temperatures on the order of 100%e150% of the source temperature and possessing intermediate values of critical ideal gas molar heat capacity. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Equation of state Organic Rankine cycle Parametric study Peng-Robinson Working fluids

1. Introduction Organic Rankine cycles (ORC) produce electricity from lowtemperature, non-traditional energy sources such as geothermal, biomass, waste heat recovery, and solar, with each representing 73%, 14%, 13%, and 0.5%, respectively, of current ORC applications [1]. Ref. [1] estimates the total worldwide installed electricity capacity of ORC in 2011 was 1.3 GW and [2] estimates the total

* 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 addresses: [email protected] (J.S. Brown), [email protected] (R. Brignoli), [email protected] (T. Quine). http://dx.doi.org/10.1016/j.applthermaleng.2015.06.079 1359-4311/© 2015 Elsevier Ltd. All rights reserved.

worldwide installed electricity capacity for all energy sources in 2011 was 5331 GW. Thus, ORC represents a very small fraction of the total, namely, only 0.024%. Therefore, wider application of ORC could improve energy sustainability by increasing the mix of renewables and alternative energy sources in the production of electricity. One obstacledamong othersdinhibiting wider spread use of ORC is that each application is essentially unique with different capacity, energy source and its temperature, low-temperature sink and its temperature, system components, and working fluid, to name a few. The latter is the focus of the current paper. While there is no claim here to review the literature, the interested reader is referred to a few recent papers [3e17] which focus primarily on working fluids for ORC applications. Bao and Zhao [3] reviewed a large number of literature sources and identified 77 commonly

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Nomenclature cop h ,

m P R ,

Q T T* s s* v V ,

W x Z

ideal gas specific heat at constant pressure [kJ/kg$K, kJ/ kmol$K] specific enthalpy [kJ/kg] mass flow rate [kg/s] pressure (kPa) universal ideal gas constant [kJ/kmol$K] heat transfer rate [kW] temperature [ C, K] non-dimensional temperature, T* ¼ Tr ¼ T/Tc entropy [kJ/kg K] non-dimensional entropy ¼ ðs  sf;Tr ¼0:7 Þ=sfg;Tr ¼0:7 specific volume [m3/kg] volumetric work output [kJ/m3] power [kW] quality compressibility factor

Greek symbols hIHX internal heat exchanger effectiveness [%] hp pump isentropic efficiency [%] ht turbine isentropic efficiency [%] h cycle thermal efficiency [%] P integral of cop over the temperature range 0.7  Tr  1.0, R 1:0T ¼ 0:7Tcc cop $dT, see Eq. (5) r density [kg/m3] u acentric factor

boil c Carnot cond est f fg g IHX þIHX max p r ref sat source t

65

boiler critical Carnot condenser estimated saturated liquid difference between saturated vapor and saturated liquid saturated vapor without internal heat exchanger with internal heat exchanger maximum pump reduced reference saturation source turbine

Acronyms EoS equation of state GWP global warming potential HCFC hydrochlorofluorocarbon HFC hydrofluorocarbon IHX internal heat exchanger NBP normal boiling point ODP ozone depletion potential ORC organic Rankine cycle P-R Peng-Robinson WHR waste heat recovery

Subscripts 0,…,10 thermodynamic state points (Fig. 1)

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 Equations of State (EoS) are available. Brown et al. [4] proposed a methodology for estimating thermodynamic parameters and performance of working fluids for ORC using the Peng-Robinson (P-R) EoS and demonstrated this approach to be simple and sufficiently accurate e for engineering calculations e for evaluating ORC performance for both well-described working fluids and for not-so-well-described working fluids (little or no experimental data and/or highaccuracy EoS are available). Brignoli and Brown [5] extended the methodology of [4] and developed a simulation model capable of modeling well-described and not-so-well-described working fluids in ORC applications. Lai et al. [6] investigated 13 potential working fluids described with BACKONE and PC-SAFT EoS for hightemperature ORC applications. Saleh et al. [7] investigated 31 potential working fluids described with BACKONE EoS for lowtemperature ORC applications. Maizza and Maizza [8] considered 24 working fluids, including eight zeotropic blends and one azeotropic blend, for waste heat recovery ORC applications. Chen et al. [9] compared the performance potential of carbon dioxide in a transcritical power cycle with a subcritical ORC operating with R123 for waste heat recovery applications. Drescher and Brüggemann [10] identified the family of alkylbenzenes as yielding the highest thermal efficiencies for biomass-powered ORC operating at 573 K. Lakew and Bolland [11] investigated six working fluids for

low-temperature ORC applications and identified R227ea as yielding the highest power output among the six. Several papers [12e17] employ molecular design and optimization methodologies to choose/design an optimal working fluid and thermodynamic cycle for low-temperature ORC applications. In particular, Papadopoulos et al. [12,13] systematically designed and selected working fluids by applying computer aided molecular design for singlecomponent working fluids and binary blends, respectively. They used multi-objective optimization methods to identify optimal working fluids subject particularly to criteria based on flammability, toxicity, ozone depletion potential (ODP), and global warming potential (GWP). Lampe et al. [14,15] simultaneously optimized the working fluid and thermodynamic cycle using the PC-SAFT equation of state. They mapped PC-SAFT parameters to real working fluids and interrogated a database of 200 working fluids. PalmaFlores et al. [16] coupled optimization techniques and computer aided molecular design to create a new family of organic working fluids and Molina-Thierry [17] simultaneously optimized blends of working fluids and the thermodynamic cycle for low-temperature ORC applications. The current paper extends the methodology of [4,18] and uses the simulation model of [5] to investigate a large number of theoretical working fluids which are described in terms of critical state properties, acentric factor, and ideal gas specific heat at constant pressure for five different ORC applications. To extend the methodology of Brown et al. [4] a new empirical correlation that allows for calculating the critical density as a function of the critical ideal gas specific heat is developed. For each application, we investigate

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the upper performance limits of the ORC in terms of efficiency and volumetric work output, with the goals to identify potential alternative working fluids and to guide future research and development efforts of working fluids. The performances of these theoretical fluids are compared with those of real fluids for which the high-accuracy fundamental Helmholtz EoS are available. As stated in Ref. [4], 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.

2. Organic Rankine cycle The ORC was described in Ref. [5] and will be repeated here for convenience. Fig. 1 shows a schematic of the simulated ORC coupled with the external source and sink. The ORC is an ideal Rankine cycle consisting of a boiler, a turbine, a condenser, a pump, and an optional internal heat exchanger (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. Heat transfer and pressure drop effects in the heat exchangers and in the pipes/lines are not included. 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 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. 2.1. Applications defined by energy source and sink As stated in the introduction, the energy sources supplying nearly all of the worldwide installed ORC capacity are geothermal, biomass, waste heat recovery, and solar. Table 3 provides typical source and condensing (sink) temperatures for each of these applications as gleaned from several literature sources [1,19e24]. Based on these data, Table 4 defines five ORC applications in terms of source and condensing temperatures for (1) geothermal, (2) lowtemperature solar, (3) low-temperature waste heat recovery (WHR), (4) high-temperature WHR, and (5) high-temperature solar/biomass. 2.2. “Types” of ORC While [7] found it useful to classify seven “types” of ORC, they are in effect of a single type differing only in the relative positions of their thermodynamic state points on a T-s state diagram as determined by the working fluid, source and sink temperatures, pump efficiency (hp), turbine efficiency (ht), and IHX effectiveness (hIHX). Regarding the working fluiddthe primary focus of the current paperdthe shape of its saturation dome on a T-s state diagram is determined primarily by its critical temperature (Tc) and its ideal gas molar heat capacity at constant pressure at the critical temperature ðcop;c Þ. Fig. 2 (taken from Ref. [4]) shows examples for R32 (cop;c ¼ 47.2 kJ/kmol$K), MM (cop;c ¼ 334.2 kJ/kmol$K), and MD3M (cop;c ¼ 822.3 kJ/kmol$K). Note: MM is hexamethyldisiloxane and MD3M is dodecamethylpentadiloxane. The figure shows that as cop;c increases the saturated vapor line changes from having a negative slope to having one of an increasingly positive slope, which leads to a slanting of the saturation domes of MM and MD3M [Note: the axes have been made non-dimensional for ease of viewing (see the Nomenclature Section for definitions.)]. While we do not intend or see the need to illustrate the seven “types” of cycles of [7], Figs. 3e6 do illustrate four “types” of cycles since the others can be easily visualized from these. Fig. 3 shows a subcritical cycle where the slope of the saturated vapor line is negative and Tmax > Tc. Note Tmax is the maximum cycle temperature and is assumed to be equal to the source temperature. For this case Pmax is assumed to be equal to 0.9Pc. In addition, the cycle consists of an IHX. Other subcritical cycles where the slopes of the saturated vapor line are negative could include ones where state point 7 (turbine outlet) is a two-phase mixture. For cycles where Tsat < Tmax < Tc (where Tsat is the saturation temperature in the boiler) the outlet from the turbine or IHX is assumed to be a saturated vapor under isentropic expansion conditions. This then determines the inlet to the turbine which in turn establishes Pmax. Figs. 4 and 5 are subcritical cycles where the slopes of the saturated vapor lines are positive. Fig. 4 is for Tmax < Tc (Pmax is equal to the saturation pressure corresponding to the saturation temperature Tmax in this case) and Fig. 5 is for Tmax > Tc (Pmax is assumed to be equal to 0.9Pc in this case.). In either case, an IHX could be included. Finally, Fig. 6 illustrates a supercritical cycle where the slope of the saturated vapor line is positive. Other supercritical cycles could include ones where the slope of the saturated vapor line is negative and ones where state point 7 (turbine outlet) is a two-phase mixture. Note: for all cycles, the state points are shown on Fig. 1. 3. Equations of state

Fig. 1. Schematic of the simulated ORC defined by 11 state points, coupled with the external source and sink. Figure taken from Ref. [4].

An EoS is needed to calculate the thermodynamic properties for the state points (Fig. 1 and Table 1) around the cycle. For well-

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Table 1 Determination of thermodynamic states points around the cycle shown in Fig. 1. Table taken from Ref. [5]. Thermodynamic state point

Subcritical cycle

Case defined in Table 2

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

0 1 2 3 4 5 6 7 8 9 10

all all all a b a b a b all all all all all

h ¼ specific enthalpy, P ¼ pressure, s ¼ entropy, 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.

Table 2 Determination of the high-pressure (boiler) state points based on cycle operating conditions of Tmax (maximum temperature) and Pmax (maximum pressure). Table taken from Ref. [5]. Case

Operating condition

a b

Tmax < Tc Tmax > Tc

Cycle type Pmax ¼ Psat Pmax ¼ 0.9Pc

Subcritical Subcritical

described working fluids, libraries such as REFPROP [25] or CoolProp [26] can be used for these calculations. However, for not-sowell-described working fluids, it is convenient to be able to create EoS quickly, easily, and with reasonable engineering accuracy in order to be able to make cycle calculations and evaluate the performance potentials of these fluids prior to investing time and money in experimentation, modeling, and development efforts. One of the goals of this paper is exactly this: to be able to evaluate a large number of theoretical (ones that may or may not exist in reality) working fluids for several ORC applications with an aim to identify “ideal” ones for each application. In previous papers [4,5], it has been shown that for not-so-welldescribed working fluids simple cubic EoS [e.g. P-R] can be easily and quickly developed to provide quite good accuracies for cycle

calculations. The methodology of [4,5,18] involves using a known normal boiling point (NBP) temperature to easily and quickly estimate critical temperature (Tc), critical pressure (Pc), critical density (rc), ideal gas specific heat at constant pressure ðcop Þ, and acentric factor (u) using group contribution methods. If the NBP temperature is not known, one also can use a group contribution method to first estimate it prior to estimating Tc, Pc, rc, cop , and u. The latter case introduces additional uncertainty since the NBP temperature tends to be a more difficult property to estimate than the others. As stated previously, to develop a P-R EoS one needs to know Tc, Pc, rc, cop , and u. However [27], shows that the P-R EoS can be implemented with only three of these parameters: Tc, cop , and u by recognizing that Tc, Pc, and rc are related through the critical compressibility factor Zc:

Zc ¼

Pc rc RTc

(1)

where R is the ideal gas constant. Note: for the P-R EoS, Zc is a constant value of 0.307 [28]. Also Fig. 7 demonstrates through the use of eighty-eight working fluids contained in Ref. [25] that rc can be related to cop;c through a simple empirical correlation:

Table 3 Typical source and condensing temperatures for several ORC applications.

Source temperature (K)

Condensing temperature (K)

Geothermal

Biomass

Waste heat recovery

Solar

323e363 [19] 353e433 [20] 353e393 [21] 350e450 [22] 293 [19] Not given [20] Not given [21] Not given [22]

553 [19] 573 [23] 523e623 [1]

443e523 [19]

393e553 [19] 720 [24] 548 [1]

373 [19] 333 [23] 333e373 [1]

303e313 [19]

303e373 [19] 305 [24] Not given [1]

Table 4 Definition of five ORC applications (defined by the source and condensing temperatures).

Source temperature (K) Condensing temperature (K)

Geothermal

Low-temperature solar

Low-temperature waste heat recovery

High-temperature waste heat recovery

High-temperature solar/biomass

363 293

393 303

443 303

523 313

553 313

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Fig. 2. Effect of cop;c on the shape of the saturation dome. Figure taken from Ref. [4].

Fig. 5. Schematic of a subcritical ORC cycle where the slope of the saturated vapor line is positive, where Tmax > Tc, and without the presence of an IHX. Note: state points are defined on Fig. 1.

0:834  rc ¼ 224:77 cop;c

(2)

where rc is in units of mol/dm3 and cop;c is in units of kJ/kmol$K. Note: the eighty-eight working fluids are of widely different types, have a wide range of NBP temperatures, and possess different levels of molecular complexities. Furthermore, as discussed in Ref. [5], cop can be related to cop;c by assuming all fluids have similar slopes with reduced temperature (Tr) and recognizing that 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:

cop;r ¼ 0:2917 þ 0:7083Tr

(3)

Fig. 3. Schematic of a subcritical ORC cycle where the slope of the saturated vapor line is negative, where Tmax > Tc, and with the presence of an IHX. Note: state points are defined on Fig. 1.

To show that Eq. (3) is capable of well-predicting working fluids, Fig. 8 shows the percent error:

Fig. 4. Schematic of a subcritical ORC cycle where the slope of the saturated vapor line is positive, where Tmax < Tc, and without the presence of an IHX. Note: state points are defined on Fig. 1.

Fig. 6. Schematic of a supercritical ORC cycle where the slope of the saturated vapor line is positive and without the presence of an IHX. Note: state points are defined on Fig. 1.

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implement a P-R EoS, which will yield results with good engineering accuracies using the methodology proposed in Ref. [4]. Each “theoretical” working fluid used hereafter will have Tc, u, and cop;c assigned as independent parameters, and Pc, rc, and cop calculated by Eqs. (1)e(3), respectively.

4. Theoretical working fluids for ORC applications

Fig. 7. Dependence of rc on cop;c for eighty-eight working fluids taken from Ref. [25] consisting of widely different types, a wide range of NBP temperatures, and different levels of molecular complexities. The solid line is the best-fit line [Eq. (2)].

 . E% ¼ 100$DP=P ¼ 100$ðPest  Pref Þ Pref

(4)

for cop given by Eq. (3) for twenty working fluids contained in Ref. [25] of different types, wide range of normal boiling point (NBP) temperatures, and molecular complexities, where: 1:0T Z c

cop $dT

P¼

(5)

0:7Tc

and where the subscripts “est” and “ref” indicate “estimated” [Eq. (3)] and “reference” [25], respectively. It should be pointed out that Eq. (3) provides good engineering accuracy and thus it will be used to build the theoretical fluids employed in the next paragraph. In summary, the above discussion demonstrates that by making use of Eqs. (1)e(3), one needs to know only Tc, cop , and u to

In this section, we investigate theoretical working fluids for each of the five ORC applications described in Section 2.1 and Table 4. We do so by making use of the model of [5] to parametrically vary Tc, cop;c , and u to create “theoretical” working fluids which then are simulated in the five ORC applications using a modified version of the simulation model of [5]. This systematic investigation of the thermodynamic space of working fluids is similar to what has been done for refrigeration applications [29,30] and is intended to exhaustively represent the investigated thermodynamic space. Guided by previous work [e.g., [27,29,30]], herein we chose to investigate a thermodynamic space of 1620 working fluids for each ORC application by varying Tc, cop;c , and u as specified in Table 5. A large range of Tc/Tmax was chosen to ensure sufficient interrogation of the appropriate thermodynamic space for each ORC application. The chosen range for cop;c was guided by our previous work cited above in recognition that as cop;c increases the slope of the saturated vapor line increases on a T-s state diagram. Already at values of 500 kJ/kmol$K the fluid becomes molecularly too complex and the saturated vapor line becomes too skewed for the fluid to be useful in subcritical cycles. Regarding the lower bound, only molecularly simple fluids such as carbon dioxide and ammonia have cop;c less than 50 kJ/kmol$K. The range for u was chosen to capture the nonspherical behavior and polarity of most working fluids [31]. Note: we take Tmax to be Tsource in these parametric variations. Figs. 9e18 show results for the five ORC applications as inverse volumetric work output (volumetric work output implies size of equipment and thus capital costs) vs. efficiency (implies operating costs). Note while we chose to emphasize the costs as listed above, in reality both performance parameters affect both V and h. For example, achieving high h would reduce operating costs but would likely increase capital costs by for example requiring a more efficient turbine or more heat transfer surface area or both. On Figs. 9e18 the x's and the plus signs represent theoretical working fluids where Tc < Tsource and Tc > Tsource, respectively, and the solid gray circles represent real working fluids (the default, high-accuracy Fundamental Helmholtz EoS contained in REPROP [25] were used for the property calculations of the real working fluids), which are listed in Table 6 in order of ascending h in three groupings of V for each application. One of the first things to note when comparing a particular application without and with an IHX is that the use of an IHX provides less scatter in the data since the IHX helps to overcome the thermodynamic irreversibilities associated with the more complex molecules and thus improves h for “underperforming” working fluids. A second thing to note is that the “best” working fluids are the ones located in the lower right hand portion of the grouping of fluids, that is, near the “knee” of the curve. The reason for this is Table 5 Parametric variations in Tc, cop;c , and u.

Fig. 8. Percent error for cop given by Eq. (3) for twenty working fluids taken from Ref. [25] consisting of widely different types, a wide range of NBP temperatures, and different levels of molecular complexities.

Initial value

Final value

Step

Tc (K) cop;c (kJ/kmol$K)

0.7Tsource 60

1.55Tsource 510

0.05Tsource 50

u ()

0

0.8

0.1

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Fig. 9. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for geothermal ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 0%. Note hCarnot ¼ 19.3%.

Fig. 12. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for low-temperature solar ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 55%. Note hCarnot ¼ 22.9%.

that they are efficient (high h) and have small 1/V values, that is, they have high volumetric work output implying smaller equipment to deliver the same work output, thus leading to smaller capital costs. 4.1. Geothermal application

Fig. 10. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for geothermal ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 55%. Note hCarnot ¼ 19.3%.

Fig. 11. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for low-temperature solar ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 0%. Note hCarnot ¼ 22.9%.

The geothermal application is defined by Tcond ¼ 293 K, _ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 55% Tsource ¼ 363 K, W when the IHX is included. Figs. 9 and 10 show the simulation results for the cases without and with the IHX, respectively. The Carnot efficiency (hCarnot) is 19.3%. The results show there are several common, real working fluids that are appropriate for this low temperature application, including “natural” working fluids cyclopropane, butane, and pentane and common refrigerants R236fa, R245fa, and R123. While the listed hydrocarbons have no ODP and have 100-year GWPs less than about 10 [32], the common HCFC and HFC refrigerants have less attractive environmental characteristics, namely R123, R245fa, and R236fa have 100-year GWPs of 77, 1030, and 9810 [32], respectively, and R123 has an ODP of 0.02 [33]. A further advantage of the

Fig. 13. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for low-temperature waste heat recovery ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 0%. Note hCarnot ¼ 31.6%.

J.S. Brown et al. / Applied Thermal Engineering 90 (2015) 64e74

Fig. 14. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for low-temperature waste heat recovery ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 55%. Note hCarnot ¼ 31.6%.

hydrocarbons is they are generally lower in cost than the HCFC and HFC refrigerants. On the other hand, one of the big disadvantages of the hydrocarbons is they are flammable. 4.2. Low-temperature solar application The low-temperature solar application is defined by _ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and Tcond ¼ 303 K, Tsource ¼ 393 K, W hIHX ¼ 55% when the IHX is included. Figs. 11 and 12 and Table 6 show the simulation results for the cases without and with the IHX, respectively. The Carnot efficiency (hCarnot) is 22.9%. The results show appropriate common, real working fluids are the same as for the geothermal application. 4.3. Low-temperature waste heat recovery (WHR) application The low-temperature WHR application is defined by _ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and Tcond ¼ 303 K, Tsource ¼ 443 K, W hIHX ¼ 55% when the IHX is included.

Fig. 15. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for high-temperature waste heat recovery ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 0%. Note hCarnot ¼ 40.2%.

71

Fig. 16. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for high-temperature waste heat recovery ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 55%. Note hCarnot ¼ 40.2%.

Figs. 13 and 14 and Table 6 show the simulation results for the cases without and with the IHX, respectively. The Carnot efficiency (hCarnot) is 31.6%. The results show appropriate common, real working fluids are the same as for the other two low-temperature applications; however, the results also indicate there is some improvement possible over commonly used existing working fluids. 4.4. High-temperature waste heat recovery (WHR) application The high-temperature WHR application is defined by _ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and Tcond ¼ 313 K, Tsource ¼ 523 K, W hIHX ¼ 55% when the IHX is included. Figs. 15 and 16 and Table 6 show the simulation results for the cases without and with the IHX, respectively. The Carnot efficiency (hCarnot) is 40.2%. The results show there are several common, real working fluids that are appropriate for this high temperature application,

Fig. 17. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for high-temperature solar/biomass ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 0%. Note hCarnot ¼ 43.4%.

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The results show appropriate common, real working fluids are the same as for the high temperature WHR application. Regardless, the results indicate there is some improvement possible over commonly used existing working fluids. 4.6. “Selected” working fluids

Fig. 18. Performance of real working fluids (Table 6) and 1620 theoretical working fluids for high-temperature solar/biomass ORC defined by source and condensing temperatures in Table 4 with W_ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and hIHX ¼ 55%. Note hCarnot ¼ 43.4%.

including “natural” working fluids butane, pentane, hexane, and cyclopentane and common refrigerants R245fa and R123. If one allows for less volumetric work output, more complex molecules such as the siloxane MM, cyclohexane, and toluene become attractive as well. Regardless, the results indicate there is some improvement possible over commonly used existing working fluids.

4.5. High-temperature solar/biomass application The high-temperature solar/biomass application is defined by _ net ¼ 1 MW, ht ¼ 85%, hp ¼ 90%, and Tcond ¼ 313 K, Tsource ¼ 553 K, W hIHX ¼ 55% when the IHX is included. Figs. 17 and 18 and Table 6 show the simulation results for the cases without and with the IHX, respectively. The Carnot efficiency (hCarnot) is 43.4%.

Table 7 shows descriptions of theoretical working fluids in terms of Tc, cop;c , and u located on the Pareto fronts (the locus of solutions that provide the largest h for a given V) of Figs. 10, 12, 14, 16 and 18 for the five ORC applications with an IHX. Generally speaking, Tc and cop;c have the largest effects on h and V. Table 7 shows “selected” fluids should have Tc from about 1.0 to 1.5 times of Tsource and 100 kJ/kmol$K < cop;c < 200 kJ/kmol$K. As noted by others [e.g., [29,30]], there is a fundamental trade-off between h and V since large values of Tc lead to large h and small V, and vice-versa for small values of Tc. There also is a similar relationship between h and V as a function of cop;c . Figs. 19e20 illustrate these two facts with the example of real working fluids for the high-temperature WHR application (similar figures could be generated for the other four applications). In summary, the discussion in this paragraph suggests “ideal” working fluids should have Tc values 10e50 % greater than Tsource and intermediate cop;c values to obtain a good balance between h and V. 5. Conclusion This paper investigates working fluids for five organic Rankine cycle applications, corresponding to five renewable heat source temperatures, by parametrically varying the thermodynamic parameters critical temperature, critical ideal gas molar heat capacity, and acentric factor with a goal of identifying “ideal” working fluids. It employees and extends the simple methodology described in Ref. [4] to evaluate the performance of an ORC employing “theoretical” fluids to investigate the upper performance limit of each ORC application in terms of efficiency and volumetric work output. The performances of these “theoretical” working fluids are compared with those of real working fluids for which highaccuracy fundamental Helmholtz EoS are available. To extend the

Table 6 Performance of real working fluids from Figs. 9e18 for the five ORC applications. Note the units of V are in kJ/m3, and in a given grouping the fluids are listed in order of ascending values of h.

Geothermal (Figs. 9e10)

Low-temperature solar (Figs. 11 e12)

Low-temperature waste heat recovery (Figs. 13e14)

High-temperature waste heat recovery (Figs. 15e16)

High-temperature solar/ biomass (Figs. 17e18)

1/V < 0.01 0.01 < 1/V < 0.03 0.03 < 1/V < 0.06 1/V < 0.01

IHX

þIHX

R170, R717, R1270, R227ea, R290, cyclopropane, R134a, R236fa, R245fa, R600, R601, R123 Hexane, cyclopentane Cyclohexane R170, R717, R227ea, R1270, R290, R134a, R236fa, cyclopropane, R245fa, R600, R601, R123, cyclopentane

R170, R717, R1270, R290, R134a, cyclopropane, R227ea, R236fa, R245fa, R600, R123, R601 Hexane, cyclopentane Cyclohexane R170, R717, R1270, R290, R227ea, R134a, R236fa, cyclopropane, R245fa, R600, R123, R601, cyclopentane Hexane, cyclohexane MM R170, R717, R227ea, R1270, R290, R134a, R236fa, cyclopropane, R245fa, R600, R123, R601, cyclopentane Hexane, cyclohexane MM, toluene R227ea, R1270, R290, R134a, R236fa, cyclopropane, R717, R600, R245fa, R123, R601, hexane, cyclopentane MM, cyclohexane, toluene

0.01 < 1/V < 0.03 0.03 < 1/V < 0.06 1/V < 0.01

Hexane, cyclohexane MM R170, R227ea, R1270, R290, R134a, R236fa, cyclopropane, R600, R245fa, R601, R123, cyclopentane

0.01 < 1/V < 0.03 0.03 < 1/V < 0.06 1/V < 0.01

Hexane, cyclohexane MM, toluene R227ea, R1270, R290, R134a, R236fa, cyclopropane, R600, R245fa, R601, R717, R123, hexane, cyclopentane

0.01 < 1/V < 0.03 0.03 < 1/V < 0.06

MM, cyclohexane, toluene

1/V < 0.01

0.01 < 1/V < 0.03 0.03 < 1/V < 0.06

e R227ea, R1270, R290, R134a, R236fa, cyclopropane, R600, R245fa, R601, R123, R717, hexane, cyclopentane MM, cyclohexane, toluene

e R227ea, R1270, R290, R134a, R236fa, cyclopropane, R600, R245fa, R717, R601, R123, hexane, cyclopentane MM, cyclohexane, toluene

e

e

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73

Table 7 Descriptions of theoretical working fluids located on the Pareto fronts of Figs. 10, 12, 14, 16 and 18. Note: the values in the cells show the ranges of acentric factor (u) for the specified Tc and cop;c . Tc/Tsource

Geothermal (Fig. 10)

Low-temperature solar (Fig. 12)

cop;c (kJ/kmol$K)

cop;c (kJ/kmol$K)

110 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 Tc/Tsource

0.0e0.3 0.0e0.3 0.0e0.2 0.0e0.2 0.0e0.1 0.0e0.1 0.0e0.1 0.0e0.1 0.0e0.1 0.0e0.1 0.0e0.1

0.5e0.8 0.4e0.8 0.3e0.7 0.3e0.5 0.0e0.4 0.0e0.3 0.0e0.3

210

110

160

210

0.4e0.7 0.3e0.5 0.2e0.4 0.1e0.3 0.0e0.2

0.0e0.3 0.0e0.3 0.0e0.2 0.0e0.2 0.0e0.2 0.0e0.1 0.0e0.1 0.0e0.1 0.0e0.1 0.0e0.0 0.0e0.0

0.5e0.8 0.4e0.8 0.3e0.6 0.3e0.5 0.0e0.4 0.0e0.3 0.0e0.2

0.3e0.6 0.2e0.4 0.1e0.3 0.0e0.2 0.0e0.1

Low-temperature waste heat recovery (Fig. 14)

High-temperature waste heat recovery (Fig. 16)

High-temperature solar/biomass (Fig. 18)

cop;c (kJ/kmol$K)

cop;c (kJ/kmol$K)

cop;c (kJ/kmol$K)

110 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55

160

0.0e0.2 0.0e0.2 0.0e0.2 0.0e0.1 0.0e0.1 0.0e0.1 0.0e0.1 0.0e0.0 0.0e0.0 0.0e0.0 0.0e0.0

160

0.0e0.4 0.0e0.4 0.0e0.4 0.0e0.3 0.0e0.2 0.0e0.1 0.0e0.0

210

0.2e0.3 0.1e0.2 0.1e0.1 0.0e0.0 0.0e0.0

110 0.0e0.0 0.0e0.0 0.0e0.0 0.0e0.0 0.0e0.0 0.0e0.0 0.0e0.0

160

0.0e0.3 0.0e0.2 0.0e0.2 0.0e0.1 0.0e0.1 0.0e0.0 0.0e0.0

210

0.2e0.3 0.1e0.2 0.0e0.1 0.0e0.0 0.0e0.0

110 0.0e0.0 0.0e0.0 0.0e0.0 0.1e0.1 0.1e0.1

160

210

0.0e0.3 0.0e0.3 0.0e0.2 0.0e0.1 0.0e0.0 0.0e0.0

0.2e0.3 0.1e0.2 0.1e0.1 0.0e0.0 0.0e0.0

methodology of Brown et al. [4] a new empirical correlation allowing for calculating the critical density as a function of the critical ideal gas specific heat is developed. The results show that simple hydrocarbon (HC) working fluids, such as propane, butane, pentane, and cyclopropane provide good thermodynamic performance for low-temperature organic Rankine cycle (ORC) applications while at the same time also possessing good environmental characteristics, low cost, and low toxicity values. One of their largest drawbacks, however, is their flammability. In addition to these HCs, more complex non halocarbon containing working fluids such as hexamethyldisiloxane (MM), cyclohexane, and toluene are appropriate for higher temperature ORC applications.

The parametric study contained herein suggests a working fluid's critical temperature and its critical ideal gas molar heat capacity have the largest impact on the cycle efficiency and volumetric work output, with “ideal” working fluids for high efficiency possessing critical temperatures on the order of 100%e150% of the source temperature and possessing intermediate values of critical ideal gas molar heat capacity. The parametric study further suggests there are “theoretical” fluids for intermediate to higher temperature ORC applications which would yield better thermodynamic performance than commonly used working fluids. Further studies are needed to determine if indeed there are already existing working fluids which possess similar thermodynamic parameters

Fig. 19. Efficiency (hþIHX) and volumetric work output (V) as a function of Tc of the real working fluids shown on Fig. 16 and Table 6 for the high-temperature waste heat recovery ORC application.

Fig. 20. Efficiency (hþIHX) and volumetric work output (V) as a function of cop;c of the real working fluids shown on Fig. 16 and Table 6 for the high-temperature waste heat recovery ORC application.

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