Impact of molecular structure of working fluids on performance of organic Rankine cycles (ORCs)

Abstract

Organic Rankine cycle (ORC) power plants are the most mature and economically competitive technology used for converting low- and medium-temperature heat to electricity, especially for renewable energy sources such as geothermal and solar thermal. This paper analyzes the performance of four types of ORC plants (subcritical and supercritical cycles, both with and without heat recuperator) optimized for maximum utilization or exergetic efficiency. The analysis was performed for 13 working fluids, heat source temperatures from 100 to 230 °C, and for cycles with either a wet cooling tower or an air cooled condenser. The primary objective of this work was to investigate the effect of the molecular structure of the working fluids on the efficiency of ORC plants. Using group contribution methods, a number of thermodynamic properties of working fluids can be easily evaluated based on their molecular structures. We show that using two of such properties, namely, the reduced ideal gas heat capacity C⁰_p/R and the critical temperature of the working fluid, one can accurately predict a number of ORC performance metrics including: (1) maximum utilization efficiency of the ORC plant and the heat source temperature at which it is achieved, (2) sensitivity of utilization efficiency to changes in the heat source temperature, and (3) increase in both thermal efficiency and heat source outlet temperature due to addition of heat recuperator.

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1. Introduction

In contrast to fossil fuels, thermal energy from renewable sources is available mostly at low temperatures, typically below 250 °C. Low-temperature renewable resources including geothermal and solar energy are widespread and, together with waste heat available from industrial processes, can provide a significant portion of the U.S. energy demand.^1,2 These resources can be used directly to provide heat, or to generate electricity by employing an appropriate thermal power cycle. While low-temperature thermal energy is better aligned thermodynamically with low-temperature uses such as direct-use applications,³ the limitations in transporting thermal energy over very long distances coupled with the increased emphasis in many countries on generating electricity sustainably have created a demand for electricity generation from low-grade heat.

The most widely recognized and commercially mature technology for converting low-temperature heat to electricity is the organic Rankine cycle (ORC). ORC plants feature a design similar to conventional Rankine cycle plants, but use low-boiling point organic working fluids instead of water. Because of that, ORC plants achieve higher efficiency than steam cycles at low heat source temperatures.⁴ Expanders in small ORC plants are also simpler and more efficient than comparable steam turbines, which makes ORC a popular choice for small (<20 MW_e) biomass boilers and waste heat recovery applications.

Increased implementation of ORC technology has been supported by research aimed at improving ORC plant performance through design modifications. Recent studies have focused on the selection of both pure working fluids^5–9 and multicomponent fluid mixtures,^10–12 high-temperature ORCs for waste heat recovery¹³ and biomass boilers,¹⁴ and hybrid plants using more than one source of heat.^15,16

In several earlier investigations, ORC plants were optimized either to maximize their utilization (exergetic) efficiency or, if cost information was available, to either minimize their levelized cost of electricity (LCOE),^4,7,17,18 minimize the total specific cost of the plant,¹⁹ or maximize the net present value (NPV).²⁰ These studies compared the optimal operating parameters and various performance metrics of several organic working fluids and made recommendations for optimal cycle configurations. In addition, researchers performed parametric studies of ORCs to understand the impact of individual design parameters and to develop generalized design rules.²¹

A number of studies have made a distinction between so-called wet and dry working fluids. With wet working fluids, the saturated vapor curve has a negative slope in temperature–entropy coordinates and thus an expansion process from saturated vapor produces a vapor–liquid mixture. For dry working fluids, the saturation curve shows a positive slope over most of the range of interest and the expansion yields superheated vapor. Fluids with nearly vertical saturated vapor lines are called “isentropic” fluids. This difference in behavior of various working fluids has been linked to their molecular complexity and quantified using molecular mass, acentric factor, reduced ideal gas heat capacity, or directly by the slope of vapor saturation line.^13,22–25 Working fluids with dry expansion characteristics were shown to require less turbine inlet superheat^22,25 and provide higher thermal efficiency in cycles using heat recuperators.^13,21

Prior studies have also investigated other working fluid selection criteria, which can be used to identify next-generation working fluids. For example, working fluids with low molecular entropies were shown to yield higher thermal efficiencies in ORCs.⁸ Thermodynamic properties including compressibility factor, ideal gas isobaric heat capacity, critical temperature, liquid heat capacity, molecular weight, and heat of vaporization were linked to the specific work of the turbine and pump, size of the turbine, ORC efficiency, and optimal heat source temperature.^22,24,26,27 Another approach successfully used to identify promising working fluids is computer-aided molecular design (CAMD). This method was used to analyze the impact of molecular properties, identify working fluids with the highest power output at specific conditions,^9,23 and assess the uncertainty associated with such predictions.⁹

The majority of previous studies looked at performance of multiple working fluids at one, specific set of heat source and sink temperatures. In this paper, we explore a wide range of heat source temperatures (100–230 °C), several cycle configurations and heat rejection conditions. Furthermore, this work goes beyond a mere parametric study given its main objective to investigate and possibly correlate the thermodynamic properties of working fluids with their performance in ORCs. With such correlations, it should be possible to predict the efficiency of plants using new working fluids, some of which may not have adequately characterized thermodynamic property data available for full cycle simulation. For example, accurate equations of state (EOS) may not be available to develop precise numerical models of ORC performance. We hope to show that with the knowledge of only two thermodynamic parameters of a working fluid, namely, the reduced ideal gas heat capacity C⁰_p/R and critical temperature T_c, it is possible to estimate several ORC plant performance metrics. Both C⁰_p/R and T_c have been tabulated for many substances and are widely available. Furthermore, they can be estimated for the remaining working fluids using group contribution methods, e.g., by Joback and Reid^28,29 and Constantinou and Gani.^29,30

This work builds on the existing research by providing a simple method to evaluate performance of optimized ORC plants based on the structural formulas of working fluids. Whereas several earlier papers identified trends between fluid properties and ORC performance, we provided numerical correlations between them. The new correlations can be used to assess ORC performance at, or near, the optimal heat source temperature for the considered types of working fluids.

The paper begins by introducing various ORC plant configurations and performance metrics in Sections 2 and 3. Section 4 describes the numerical models of ORC plants used in this analysis, and Section 5 contains the results of these models. In Section 5.1, detailed results are presented for four ORC plant configurations and heat source temperatures from 100 °C to 230 °C using a single working fluid, R134a. The conclusions are then generalized in Section 5.2 using results for 13 working fluids. Building on these results, various performance metrics of ORC plants are correlated with the thermophysical properties of working fluids in Section 6. Lastly, Section 7 quantifies the sensitivity of ORC plants to the heat rejection conditions. An overview of the main steps of the methodology is provided in Table 1.

Table 1 Overview of main steps of the methodology

I. Development of numerical models of ORC plants in Aspen HYSYS software

a. Define ORC performance metrics

b. Specify component properties and model constraints

c. Create 4 models of ORC plants (subcritical and supercritical; with and without recuperator)

d. Implement optimization procedure to maximize utilization efficiency η_u

II. Evaluation of ORC performance for multiple working fluids

a. Select a representative set of 13 working fluids

b. Run calculations for all working fluids and heat source temperatures from 100 to 230 °C

c. Evaluate maximum utilization efficiency and optimum heat source temperature for each working fluid

III. Correlation of performance metrics of ORCs with working fluid properties

a. Identify key working fluid properties (T_c and C⁰_p/R)

b. Correlate main ORC performance metrics ( and ) with working fluid properties

c. Correlate effects of using heat recuperator with working fluid properties

IV. Assessment of the impact of heat sink temperature on ORC performance

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2. Types of organic Rankine cycle (ORC) plants

The principle of operation of a basic ORC plant is well-known and is presented in Fig. 1A. Thermal energy carried by a heat source fluid (hs) is transferred in a primary heat exchanger to a low-boiling-point working fluid (wf). The working fluid vapor passes through a turbine where it expands and produces work. It is then cooled and condensed at a low pressure by dissipating heat to the cooling fluid (cf). After that, working fluid is pressurized by a pump, and eventually returned to the primary heat exchanger. This cycle is presented in temperature–entropy (T–s) coordinates in Fig. 2A. The ORC shown in Fig. 1A and 2A is referred to as a subcritical (Sub) ORC, because the maximum pressure of working fluid is below its critical pressure P_c. The isothermal evaporation of working fluid in subcritical ORCs results in a large temperature mismatch between the heat source and the working fluid. This means that the log-mean temperature difference is large, which results in high irreversibility for the heat transfer process and reduces the maximum work potential (exergy).³¹ To reduce this irreversibility and improve turbine power output, the maximum pressure in ORC can be increased above working fluid critical pressure. Such cycles are referred to as supercritical (Sc) ORC, and an example is of such cycle is presented in Fig. 2B. As a result of a higher maximum cycle pressure, the work consumed by the pump in supercritical ORC is significantly higher compared to a subcritical ORC, partially offsetting the increased turbine output.²²

Fig. 1 Schematics of organic Rankine cycle (ORC) plants. (A) ORC plant with no recuperator (NR). (B) ORC plant with a heat recuperator (R).

Fig. 2 Temperature–entropy (T–s) diagrams of ORC. (A) Subcritical cycle with no recuperator (Sub-NR) using R-134a. (B) Supercritical cycle with a recuperator (Sc-R) using R-227ea.

ORC plants may use an additional heat exchanger called a recuperator, where feasible. This component is an internal heat exchanger, as shown in Fig. 1B, and its effects are presented on a T–s diagram in Fig. 2B. If the vapor at turbine exit (2) is superheated, a recuperator might be used to transfer a fraction of the vapor sensible heat (2 → 3) to the liquid (5 → 6) before it enters the primary heat exchanger. By doing that, the addition of recuperator results in increases of both the temperature of the heat source fluid leaving ORC plant T_hs,out and the thermal efficiency of the cycle.^13,32 However, a sufficient degree of superheat must be available for the recuperator to be practically feasible. In this work, cycles with recuperators are designated with (R) and cycles with no recuperators are abbreviated as (NR).

3. Performance metrics of ORC

Three types of efficiency are used in this analysis: utilization efficiency η_u, thermal efficiency η_th and, as a reference, thermal efficiency of an ideal triangular cycle η_th,tri. Utilization efficiency, also referred to as exergetic (or Second Law) efficiency, is defined as the ratio of the net power output of the plant to the exergy rate of the incoming heat source fluid:³³where ṁ_hs is the mass flow rate of the heat source fluid, h_hs and s_hs are its entropy and enthalpy, and the subscript 0 refers to the dead state (ambient) conditions. Utilization efficiency quantifies what fraction of the heat source thermodynamic potential is converted into useful work. As such, it can be used as a primary performance metric of ORC units, in which the heat source fluid leaving the plant is not used for any other purpose such as, e.g., district heating.

Thermal efficiency is the ratio of the net power output to the thermal power input into the cycle:

Thermal efficiency determines what fraction of the heat withdrawn from the heat source is converted into electricity. It does not, however, quantify how much heat is taken out from the heat source fluid. Because of that, high thermal efficiency does not always correspond to high net power output. Thermal efficiency is a suitable performance metric for combined heat and power (CHP) plants, which utilize the partially cooled fluid leaving the ORC plant for direct use applications.

Lastly, the triangular (or trilateral) cycle is used as a reference ideal cycle, against which the thermal efficiencies of ORC plants can be compared.³⁴ Triangular cycle is an equivalent of a Carnot cycle for heat sources with a finite and constant heat capacity, i.e., non-isothermal heat transfer. The temperature of the heat source in an ideal triangular cycle is brought to the dead state temperature T₀ by reversible heat transfer to the working fluid. Thermal efficiency of ideal triangular cycle is expressed as:³⁴

where all temperatures are absolute. The ratio of η_th to η_th,tri is referred to as relative efficiency η_rel.³⁴

4. ORC models

4.1. Structure and assumptions of ORC models

The models of ORC plants used in this analysis were created with a goal to provide realistic performance figures and a fair comparison basis for different working fluids. The ORC plants were modeled in Aspen HYSYS v8.4 using thermodynamic properties from REFPROP v8.0 equations of state (EOS).³⁵ Four different configurations of ORC plants were considered:

• Subcritical ORC with no heat recuperator (Sub-NR).

• Subcritical ORC including heat recuperator (Sub-R).

• Supercritical ORC with no heat recuperator (Sc-NR).

• Supercritical ORC including heat recuperator (Sc-R).

Simulations for heat source temperatures T_hs between 100 °C and 230 °C were run in 10 °C intervals. The base-case simulations were performed for ORC using a wet cooling tower (WCC), with 17 °C wet bulb temperature T₀ providing 20 °C cooling water at the condenser inlet. Additionally, Section 7 presents sensitivity of the net power output to the dry bulb temperature and relative humidity, along with results for ORC using an air-cooled condenser (ACC). In ACC, the increase in air temperature was set at half of the temperature difference between the working fluid condensing temperature and the inlet air dry bulb temperature, which was previously found to maximize the net power output.¹⁷ The dead state conditions for base-case ORC with wet cooling tower were set at 17 °C and 1 bara.

Pinch-point temperature differences of 3 °C were adopted for all heat exchangers with the exception of the ACC.¹⁸ The working fluid pressure drops in heat exchangers were ignored, but should be calculated for each individual plant configuration during more advanced design phases.

The isentropic efficiencies of turbines (dry expansion) and pumps were set at 85% and 75%, respectively. They were assumed to be the same for all working fluids, and the effects of individual fluids properties on the isentropic turbine efficiency were ignored. In addition, the turbine efficiency was decreased if wet expansion occurred. Following the empirical Baumann rule, isentropic efficiency was reduced by 1% for every percentage of average moisture present during expansion.^32,36 In addition, the minimum turbine exhaust vapor quality was set at 0.9 to prevent blade erosion.

To enhance the stability of operation and avoid significant fluctuations in thermodynamic properties occurring near the critical point, the maximum evaporation pressure in subcritical cycles was set at 90% of critical pressure P_c.¹⁷ In supercritical cycles, the minimum high pressure corresponds to 110% of P_c.¹⁷ The summary of the ORC model assumptions is presented in Table 2.

Table 2 Summary of base-case ORC model specifications. Configurations denoted with asterisk are evaluated in sensitivity analysis in Section 7. The reference sources listed in the text and the table provided a rationale for selection of base-case values for each parameter

Design parameter	Value/properties
1. Heat source
Substance	Liquid water
Temperature range	100–230 °C
Pressure	100 bara
2. Heat exchangers
General characteristics	Countercurrent, single pass, split into 50 intervals with equal Δh
2.1. Primary heat exchanger
Pinch point temperature difference	3 °C
Hot end temperature approach	≥5 °C
2.1.1. Subcritical ORC
Maximum turbine inlet pressure	0.9*Pc
Minimum turbine inlet vapor superheat	1 °C
2.1.2. Supercritical ORC
Minimum turbine inlet pressure	1.1*Pc
2.2. Recuperator (in Sub-R and Sc-R configurations)
Pinch point temperature difference	3 °C
2.3. Condenser and heat rejection system
2.3.1. Water-cooled condenser with wet cooling tower (WCC) – base case
Condenser
Pinch point temperature difference	3 °C
Cooling water inlet temperature	20 °C (6–34 °C)*
Cooling water temperature rise	8 °C (ref. 37)
Wet cooling tower
Inlet air dry bulb temperature	24 °C (10–35 °C)*
Relative humidity of entering air	50% (25%, 75%)*
Relative humidity of exiting air	98%
Approach to wet bulb temperature	3 °C (ref. 38)
Wet bulb temperature rise	7 °C
Pressure rise of cooling fan	170 Pa (ref. 18 and 39)
Isentropic efficiency of fan	0.65 (ref. 18)
Isentropic efficiency of circulation pump	0.75
Cooling water pressure drop	1.5 bar
2.3.2. Air-cooled condenser (ACC)*
Inlet air dry bulb temperature	10–35 °C*
Air temperature rise	0.5*(Tcond − Tair,in) (ref. 17)
Power consumption	0.25 kW per kg per s of air flow (ref. 16 and 17)
3. Expander
Isentropic efficiency	85% for vapor-only expansion <85% when liquid present – Baumann rule (ref. 17)
Minimum exhaust vapor quality	0.9 (ref. 17)
Generator efficiency	98% (ref. 17)
4. Working fluid pump
Isentropic efficiency	75% (ref. 32)

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4.2. Optimization

All ORC plants were optimized with a goal of maximizing their utilization efficiency η_u, which is equivalent to maximizing their specific power output (kW_e per kg per s of heat source fluid) for the given heat resource conditions. The BOX method available in Aspen HYSYS was used for this purpose.⁴⁰ This method is based on the complex method by Box,⁴¹ the Downhill Simplex algorithm,⁴² and the BOX algorithm.⁴³ The BOX algorithm is a slow, but robust method of finding the extrema of functions, which can accommodate inequality constraints. The reliability of the optimization method was confirmed by systematically varying the initial values of the optimized variables and running the algorithm. The models always converged to the same solutions, independent of the initial values of the optimized variables.

Different variables were optimized depending on the type of cycle. In subcritical ORC models they included evaporation temperature, condensation pressure, and the turbine inlet superheat, i.e., the difference between turbine inlet temperature and evaporation temperature. In supercritical ORCs, optimized variables were: turbine inlet temperature, turbine inlet pressure and condensing pressure. In all cycles the turbine exhaust vapor quality was constrained by the optimization procedure to values ≥0.9.

4.3. Selection of working fluids

Working fluids were selected based on their availability, cost, and effects on health and environment. They were also chosen to represent a range of critical temperatures (66–174 °C), slopes of vapor saturation line (corresponding to wet, isentropic, and dry expansion), and several families of compounds (HFCs, HCFCs, PFCs, alkanes, and cycloalkanes).

Table 3 lists the fluids investigated in this analysis along with selected properties including: critical temperature (T_c) and pressure (P_c); molar mass (M); reduced ideal gas heat capacity (C⁰_p/R) evaluated at the average of working fluid critical temperature and the heat sink temperature; indication of the type of saturated vapor curve (wet/isentropic/dry); normal boiling point (T_B), ozone depletion potential (ODP), global warming potential (GWP), and fluid safety group according to the ASHRAE classification. The list includes high-GWP refrigerants such as R-134a or R-125 which, although still in common use, are being phased down in the European Union and other countries.^44,45 They are expected to be replaced by the low-GWP compounds listed in Table 3, such as propane, isobutane, and R-152a.

Table 3 Working fluids used in ORCs and their selected properties^46–51

Name	Formula	T c (°C)	P c (bar)	M (g mol^−1)	C ^0p/R	Fluid type	T B (°C)	ODP	GWP (100 yr)	Safety group
R-125	CF3CHF2	66.0	36.2	120.0	11.8	Wet	−48.1	0	3500	A1
R-218	CF3CF2CF3	71.9	26.4	188.0	18.5	Dry	−37.8	0	8830	A1
R-143a	CF3CH3	72.7	37.6	84.0	9.8	Wet	−47.2	0	4470	A2
R-32	CH2F2	78.1	57.8	52.0	5.4	Wet	−51.7	0	675	A2
Propane	CH3CH2CH3	96.7	42.5	44.1	9.6	Wet	−42.1	0	3	A3
R-134a	CF3CH2F	101.1	40.6	102.0	11.0	Isentropic	−26.1	0	1430	A1
R-227ea	CF3CHFCF3	102.8	29.3	170.0	17.5	Dry	−16.4	0	3220	A1
R-152a	CHF2CH3	113.3	45.2	66.1	8.9	Wet	−24.0	0	124	A2
Cyclopropane	cyclo-C3H6	125.2	55.8	42.1	7.9	Wet	−32.5	0	20	—
Isobutane	CH(CH3)3	134.7	36.3	58.1	13.4	Dry	−11.8	0	20	A3
R-142b	CClF2CH3	137.1	40.6	100.5	11.1	Isentropic	−9.1	0.07	2310	A2
R-236ea	CF3CHFCHF2	139.3	34.2	152.0	17.0	Dry	6.2	0	1370	—
R-245ca	CHF2CF2CH2F	174.4	39.3	134.1	16.7	Dry	25.1	0	693	A1

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As indicated by the normal boiling point, none of the working fluids would create vacuum in the condenser as long as condensing temperature exceeds 25 °C. This conservative design reduces the risk of air leakage into the system, and thus potential performance issues. In ASHRAE 34 standard, ‘A’ denotes low toxicity and ‘1’, ‘2’, and ‘3’ indicate no flame propagation, lower flammability, and higher flammability, respectively.⁴⁶ It should be noted that R236ea has not been considered for supercritical configurations due to the limited range of EOS implemented in the REFPROP database.

As shown in Fig. 3, reduced ideal gas heat capacity C⁰_p/R and critical temperature T_c describe the shape of binodal coexistence curve on a T–s diagram. C⁰_p/R is related to the slope of vapor saturation line on a T–s diagram and therefore affects the phase composition at turbine exhaust. Fluids with low C⁰_p/R (<11) have a conventional Gaussian-like saturation curve, and expansion of saturated vapor usually results in a 2-phase mixture. Such working fluids are referred to as ‘wet’ and are represented in Fig. 3 by R-32 and R-152a. ‘Dry’ fluids such as R-227ea have high C⁰_p/R (>11) and retrograde vapor saturation lines resulting in superheated vapor at the turbine exhaust. We found that fluids with C⁰_p/R of approximately 11 have nearly vertical (isentropic) vapor saturation lines.

Fig. 3 Example of four working fluids representing a range of reduced ideal gas heat capacities C⁰_p/R.

5. Results

5.1. Detailed results for a selected working fluid – R134a

This section provides detailed results of numerical ORC models for a representative working fluid, R-134a. Our conclusions, however, are broader and representative of the range of fluids investigated in this work. The main goals of this section are to provide a context for the more generalized results presented in later sections and show the operating parameters corresponding to the optimized ORC configurations. In addition, this chapter highlights the differences in the characteristics of the four analyzed ORC configurations.

The selected parameters of optimized ORCs are presented in Fig. 4A–F using R-134a. Fig. 4A shows, that supercritical cycles provide higher power output than subcritical ORC at medium and high heat source temperatures T_hs (e.g., for R134a > 140 °C). This was not true at lower source temperatures less than 20 to 40 °C above the working fluid critical temperature T_c. The increased net power output of supercritical cycles translates into higher utilization efficiency presented in Fig. 4B. For R-134a the utilization efficiencies for subcritical and supercritical ORC achieve their respective maxima at heat source temperatures of 175 °C and 250 °C, respectively. These optimum heat source temperatures maximizing the utilization efficiency are denoted as .

Fig. 4 (A–F) Selected parameters of four ORC plant configurations using R-134a are presented as functions of the heat source temperature. The net power output in (A) is expressed per unit mass flow rate of the heat source fluid.

In addition to higher utilization efficiency, supercritical cycles typically provide higher thermal efficiency than subcritical ORC, as shown in Fig. 4C. As a direct consequence of that, supercritical cycles can provide increased heat source outlet temperatures despite higher power outputs. In other words, supercritical ORCs not only produce more power than subcritical cycles, but often do so while withdrawing less thermal energy from the heat source.

In the majority of the optimized cycles the heat source fluid is cooled to low temperatures, which may be troublesome in some applications. For example, in geothermal power plants excessive cooling of brine may induce scaling, especially of silica compounds, and reduce the heat transfer coefficient of the primary heat exchanger. In waste heat recovery applications, cooling gaseous heat sources below their dew points would lead to condensation of corrosive liquids necessitating the use of more expensive materials. These issues can be alleviated by installing a heat recuperator. Fig. 4C and D show that the addition of heat recuperator results in increased thermal efficiency and heat source outlet temperature. The positive effects of using a recuperator increase with heat input temperature and are higher in subcritical cycles compared to supercritical cycles.

The optimal turbine inlet pressures are presented in Fig. 4E. In subcritical cycles, turbine inlet pressure increases with the heat source temperature T_hs until it reaches the maximum allowable reduced pressure P_r of 0.9. In supercritical cycles, optimum turbine inlet pressure corresponds to the minimum allowed P_r of 1.1 at low T_hs and increases at higher T_hs (>140 °C for R-134a). The nearly linear increase in pressure for supercritical ORC from 140 to 200 °C is an extension of the same trend for subcritical cycle from 100 to 130 °C.

The implementation of the Baumann rule generally resulted in avoiding wet turbine expansions. In subcritical ORC, all optimized configurations have either saturated or superheated vapor at turbine exhaust. At low T_hs (for R-134a < 130 °C), the optimization procedure selected a sufficient turbine inlet superheat to obtain saturated vapor at turbine exhaust. At higher T_hs, the turbine exhaust temperature increases nearly linearly with the T_hs, as shown in Fig. 4F. In supercritical ORCs, there can be moisture present in turbine's exhaust if the T_hs is very low (e.g., for R-134a < 130 °C). In these cases, however, supercritical cycles provide lower power output than subcritical ORC and therefore would not be selected over the basic subcritical cycle.

5.2. Generalized results for multiple working fluids

Having reviewed the detailed findings for R-134a, this section presents more general results for all 13 working fluids listed in Table 3. These results are then used in the next section to correlate the performance of ORCs with working fluid properties. The results presented in this section were validated using published values from an earlier study.¹⁷

Fig. 5 and 6 show the utilization efficiencies η_u of various working fluids as functions of heat source temperature T_hs for Sub-NR and Sc-NR cycles, respectively. Dotted and dashed lines mark the composite curves of maximum η_u for Sub-NR and Sc-NR cycles. The most efficient Sc-NR cycles provide between 1% and 17% higher η_u compared to the best Sub-NR cycles. The η_u curves for supercritical ORC are also less convex compared to the subcritical cycle. As a result, a single working fluid may be used near-optimally in a supercritical ORC over a broader range of heat source temperatures without sacrificing much in utilization efficiency. Fluids with high reduced ideal gas heat capacities C⁰_p/R (R-218, R-227ea, R-236ea, R-245ca) yield higher η_u compared to fluids with low C⁰_p/R (R-32, R-152a, cyclopropane), particularly in the subcritical cycle, for any given heat source temperature.

Fig. 5 Utilization efficiency of subcritical ORC with no recuperator (Sub-NR) using various working fluids. Filled markers are cases where turbine reduced inlet pressure P_r reached 0.9; open markers are cycles with optimal P_r < 0.9. Dead state conditions are 17 °C and 1 bara.

Fig. 6 Utilization efficiency of supercritical ORC with no recuperator (Sc-NR) using various working fluids. Filled markers are cases where optimal reduced turbine inlet pressure P_r is 1.1; open markers are cycles with P_r > 1.1. Dead state conditions are 17 °C and 1 bara.

The composite curves of maximum utilization efficiency ‘Max Sub-NR’ and ‘Max Sc-NR’ are composed of results for eight best performing working fluids. However, four fluids (R218, R227ea, isobutane, and R-245ca) are sufficient to provide very high utilization efficiencies across the considered temperature spectrum. Some of the low-GWP fluids (isobutane, R-142b, R-152a) perform well at heat source temperatures between 160 and 200 °C, but they cannot match the performance of R-227ea and R-218 at low heat source temperatures and R-245ca above 200 °C.

Fig. 5 and 6 show that each working fluid achieves its maximum utilization efficiency at a particular heat source temperature. At these conditions, the optimal reduced turbine inlet pressure P_r in subcritical ORC is 0.9 for each working fluid. This high evaporation pressure reduces exergy loss in the primary heat exchanger by providing a better temperature match in preheater and a lower enthalpy of vaporization. Depending on the working fluid used, P_r of 0.9 was achieved at absolute heat source temperatures of at least 1.06*T_c to 1.09*T_c. For supercritical ORCs to reach high efficiency operation, the situation was different than for subcritical cycles. We found that working fluids in supercritical ORCs reached their peak performance at conditions, where optimal P_r was above 1.1.

The utilization efficiencies of the top-performing cycles with recuperators are not shown in Fig. 5 and 6 because they are typically only 0.5% lower than for cycles without a recuperator. This small drop in power output is a combination of two factors: (1) a larger decrease in power due to shifting the location of the pinch point in the condenser leading to an increase in condensing pressure, and (2) a smaller increase in power due to the lower condenser duty and the resulting lower parasitic power consumption of the cooling tower. In actual plants, the power output of cycles with a recuperator would be even lower due to the pressure loss in the recuperator and resulting increased turbine backpressure. Depending on the working used, each 0.1 bar increase in turbine backpressure would cause between 0.2% (for R-32) to 1.6% (for R-245ca) drop in utilization efficiency. The effects of pressure loss in recuperator would be more significant for fluids with high critical temperatures, which typically have low condensing pressures and high turbine exhaust volumetric flow rates.

Fig. 7 shows the thermal efficiency of ORC plants with the highest utilization efficiencies. ORC plants using a heat recuperator were included if the equivalent non-recuperated cycles had sufficiently hot turbine exhaust gases to transfer heat to the pressurized liquid working fluid. Thermal efficiency of ORC plants with a recuperator was on average 6.5% higher compared to equivalent cycles without recuperator. The increase in thermal efficiency was particularly high for dry fluids with high C⁰_p/R and for heat source temperatures T_hs much above fluid critical temperature T_c. As we will show in the next section, the effects of adding a heat recuperator can be in fact predicted based on these three parameters: C⁰_p/R, T_c, and T_hs.

Fig. 7 Thermal efficiency of sub- and supercritical ORC with and without heat recuperator as a function of heat source temperature T_hs. Results are presented only for working fluids with the highest utilization efficiency for each T_hs.

The thermal efficiencies of ORC cycles were approximated in Fig. 7 with the following linear trend:

η_th = 9.09 × 10⁻⁴ × T_hs − 0.03 (4)

where T_hs is the heat source temperature in °C and the efficiency is given as a fraction. The fitted trend has a regression coefficient R² of 0.95 and a standard deviation of 0.8%. The thermal efficiencies of 5% to 19% presented in Fig. 7 correspond to relative efficiencies η_rel of 42% to 73% with an average of 63%. This figure is consistent with the reported 61% average relative efficiency of three existing ORC geothermal power plants using wet cooling towers.³⁴ The relative efficiency of ORC plants increases with T_hs, as the parasitic power losses and other irreversibilities contribute a smaller fraction of the heat input to the cycle.

6. Correlations between ORC performance and working fluid properties

Given the large number of potential ORC working fluids, it is useful to develop guidelines for their selection. Such guidelines could help to pre-screen fluids for applications at various heat source temperatures. This insight would be particularly helpful in analyzing less common fluids, for which the EOS are unavailable or inaccurate, making numerical modeling unreliable and plant design challenging. In this section, we present correlations for evaluating a number of ORC performance metrics based on the heat source temperature T_hs, the working fluid critical temperature T_c, and the reduced ideal gas heat capacity C⁰_p/R. This is the main and most novel contribution of this work. C⁰_p/R and T_c were identified as the most relevant fluid properties based on: (1) their ability to describe the shape of the coexistence curve on a T–s diagram; (2) the use of C⁰_p/R in equation of state formulas for changes in reduced enthalpy and entropy between two thermodynamic states;⁵² and (3) ease and accuracy of evaluating these properties based on molecular structure of fluid.^28–30

The following analysis is split into two parts. The first discusses predictive methods for assessing utilization efficiency of ORC plants without a recuperator. This analysis includes developed correlations for the following performance metrics: maximum utilization efficiency , heat source temperature at which utilization efficiency is maximized , and sensitivity of utilization efficiency to the changes in heat source temperature. The second section provides correlations for assessing the impacts of heat recuperators on thermodynamic performance of ORCs. The two main objectives of heat recuperators are to increase thermal efficiency and reduce excess cooling of the heat source fluid, as might be important from a chemical scaling perspective. Therefore, we correlated working fluid properties with the changes in thermal efficiency η_th and heat source outlet temperature T_hs,out due to installing heat recuperators. The developed correlations are valid for the types of considered working fluids (halogenated and non-halogenated alkanes) with values of T_c from 66 to 174 °C and C⁰_p/R from 5.4 to 18.5, as listed in Table 3. The follow-up work based on this study found, however, that similar correlations could be developed for other types of working fluids including fluorinated alkenes, siloxanes, and ethers.⁵³

6.1. Correlations for assessing utilization efficiency

Fig. 5 and 6 demonstrated, that each working fluid achieves its maximum utilization efficiency at a particular heat source temperature . The following analysis shows that it is possible to predict both and based on the molecular structure of the working fluid.

Fig. 8 illustrates that the optimal heat source temperature is strongly correlated with C⁰_p/R and T_c of the working fluid. Knowing both C⁰_p/R and T_c, one can accurately determine for various heat rejection conditions. Supercritical cycles achieve their maximum utilization efficiencies at much higher heat source temperatures than subcritical ORC, especially when using wet working fluids such as R-32 or R-152a. The results for subcritical and supercritical cycles were approximated in Fig. 8 with linear trends, providing reasonable R² values of 0.9 and 0.87 and standard deviations of 6.4 °C and 15.3 °C, respectively. The fitted linear trends are described by eqn (A-1) in the Appendix. The scatter in results presented in Fig. 8 is partially due to the assumption of an equal condenser pinch-point temperature difference for all working fluids. This assumption led to small variations in the condensing temperatures of individual fluids, a result of unequal vapor superheat at condenser inlet. The impact of this scatter is small, because the utilization efficiency curves presented in Fig. 5 and 6 are relatively flat near their maxima. If fact, utilization efficiencies at heat source temperatures predicted by the linear trends in Fig. 8 are on average only 0.4% lower compared to obtained at .

Fig. 8 Heat source temperature increment above critical temperature at which the utilization efficiency is maximized for various working fluids presented as functions of reduced ideal gas heat capacity C⁰_p/R.

In this work, C⁰_p/R of each working fluid was evaluated at a representative temperature corresponding to the arithmetic average of the heat sink temperature and fluid critical temperature. This temperature was selected to be consistent with the average slope of the vapor saturation line along turbine expansion path. The reduced ideal gas heat capacity proved to be a much better predictor of than acentric factor or molar mass, for which equivalent correlations yielded R² values of only 0.18 and 0.55, respectively.

Molecular structure of working fluid determines not only the optimal heat source temperature , but also the maximum utilization efficiency achieved at . Fig. 5 showed that dry fluids with C⁰_p/R >11 (e.g., R-218, R-227ea, R-236ea, R-245ca) achieve higher peak utilization efficiencies than wet fluids characterized by low C⁰_p/R <11 (e.g., R-32, cyclopropane, R-152a). The value of is, in fact, strongly correlated with and C⁰_p/R for both subcritical and supercritical ORCs. This correlation, shown in Fig. 9, indicates that for working fluids with comparable , the maximum utilization efficiency increases with C⁰_p/R. This is largely a result of a better temperature match in the primary heat exchanger achieved at by dry fluids (C⁰_p/R > 11) as compared to wet fluids (C⁰_p/R < 11). In Fig. 9, the results from the ORC models are represented by the markers and are approximated using fitted trends linear in and C⁰_p/R. These fitted correlations described by eqn (A-2) in the Appendix provide reasonable regression coefficients R² of 0.96 and 0.93 for subcritical and supercritical ORCs, respectively. The R² values indicate that 93% to 96% of the variability in can be explained by the and C⁰_p/R of the examined fluids. The variations in alone could account for only 79% to 84% of the variability in , which emphasizes the importance of C⁰_p/R as a predictor of working fluid performance in ORC.

Fig. 9 Maximum utilization efficiency achieved by ORCs as a function of the optimal heat source temperature and the reduced ideal gas heat capacity C⁰_p/R of the working fluid. Left: subcritical ORC with no heat recuperator (Sub-NR); right: supercritical ORC with no heat recuperator (Sc-NR). Markers represent results for individual working fluids and the surface is a fitted linear correlation.

The optimal heat source temperature used as abscissa in Fig. 9 is an empirical function of T_c and C⁰_p/R, which was illustrated in Fig. 8. Because of that, the can also be correlated directly with the working fluid properties: T_c and C⁰_p/R. The correlation between , T_c, and C⁰_p/R is presented in Fig. 10 for both subcritical and supercritical ORCs. The results from models are represented by markers. The fitted trends shown in Fig. 9 are described by eqn (A-3) in the Appendix and provide reasonable R² values of 0.96 and 0.93 for Sub-NR and Sc-NR cycles, respectively.

Fig. 10 Maximum utilization efficiency achieved by ORC as a function of the critical temperature T_c and the reduced ideal gas heat capacity C⁰_p/R of the working fluid. Left: subcritical ORC with no heat recuperator (Sub-NR); right: supercritical ORC with no heat recuperator (Sc-NR). Markers represent results for individual working fluids and the surface is a fitted linear correlation.

Fig. 8 and 10 are the key results of this work. They prove that it is possible to predict the maximum utilization efficiency of ORC plants and the heat source temperature at which it is achieved based on the molecular structure of the working fluid. This work identified T_c and C⁰_p/R as key properties used to predict the working fluid performance in ORC. Both of these parameters can be evaluated based on molecular structures of working fluids using group contribution methods.^28–30T_c and C⁰_p/R were also experimentally measured and tabulated for many working fluids.²⁹

While Fig. 8–10 assess the maximum utilization efficiency and conditions at which it is achieved, they provide no information about the ORC performance at other, non-optimal, heat source temperatures. Fig. 5 showed, that in subcritical ORCs, fluids with high C⁰_p/R (e.g., R-218, R-227ea, R-236ea, R-245ca) achieve high utilization efficiency over a narrow range of heat source temperatures compared to fluids with low C⁰_p/R (e.g., R-32, cyclopropane, R-152a). To provide a measure of ORC performance for near-optimal heat source temperatures, Fig. 11 quantifies the drop in utilization efficiency at heat source temperatures above and below . In Fig. 11, the utilization efficiency of each working fluid in subcritical ORCs is presented for heat source temperatures T_hs 20 °C above and 20 °C below . The utilization efficiencies are expressed as a fraction of the maximum utilization efficiency achieved at , and presented as function of C⁰_p/R. At heat source temperatures 20 °C below , fluids with high C⁰_p/R achieve only 88–92% of their , while fluids with low C⁰_p/R achieve approximately 99% of . For dry fluids, reducing the T_hs by 20 °C below results in a poorer temperature match in the preheater, and thus less heat recovered from the heat source and a lower utilization efficiency. An equivalent drop in T_hs has a much smaller effect on the effectiveness of heat recovery in ORCs using wet working fluids. This discrepancy is due to the difference in optimal configurations of ORC plants using heat input at temperature . Wet fluids require significant vapor superheat at turbine inlet and their optimal evaporation temperature is much below the heat source temperature , whereas dry fluids require little to no superheat, and their optimal evaporation temperature is closer to . Fig. 11 shows, that at heat source temperatures 20 °C above , the decrease in utilization efficiency is far less significant than 20 °C below , but it is also correlated with C⁰_p/R. Polynomial trends fitted to data in Fig. 11 and described by eqn (A-4) in the Appendix have reasonable correlation coefficients R² of 0.97 and 0.86 for 20 °C below and 20 °C above , respectively.

Fig. 11 Percentage of the maximum utilization efficiency achieved by individual working fluids at temperatures 20 °C below and 20 °C above the optimum resource temperature for subcritical ORC without recuperator.

6.2. Correlations for assessing the effects of heat recuperators

In addition to correlating working fluid properties with their performance in ORCs, rules-of-thumb may be useful for evaluating the effects of adding recuperators to ORC plants. This section illustrates that the increase in both the thermal efficiency η_th and the heat source outlet temperature T_hs,out due to the addition of a recuperator to supercritical ORC can be quantified using C⁰_p/R and the difference between the heat source temperature and working fluid critical temperature (T_hs − T_c). These variables are correlated because the increases in η_th and T_hs,out are proportional to the degree of superheat present in turbine exhaust gases. This quantity is, in turn, determined by the turbine inlet temperature, the isentropic efficiency of the turbine, and the reduced ideal gas heat capacity C⁰_p/R. Our results show that the turbine inlet temperature is a near-linear function of T_hs for cycles which can accommodate a recuperator.

Fig. 12 shows the increase in the heat source outlet temperature T_hs,out caused by the addition of a recuperator. This parameter is presented as a function of C⁰_p/R and (T_hs − T_c). In Fig. 12A, results from the models are represented by the markers. They were approximated using a polynomial surface that is first-order in C⁰_p/R and second-order in (T_hs − T_c). This correlation is described by eqn (A-5) in the Appendix and provides a reasonable coefficient of determination R² of 0.91, suggesting that the effects of using heat recuperators can be accurately predicted for other fluids for which the C⁰_p/R and T_c are known and within the ranges covered here. To better illustrate the accuracy of the fitted correlation, Fig. 12B and C show the results from ORC simulation models using markers and dashed lines and from the corresponding predictions of the polynomial correlation using continuous lines. The data was split into two figures (B and C) to enhance the clarity and avoid overlap.

Fig. 12 Increase in the temperature of heat source fluid leaving ORC plant due to addition of a heat recuperator in supercritical ORC. (A) Markers represent results for individual working fluids and the surface is a fitted correlation. (B and C) Results from ORC models (dashed lines with markers) are compared to the fitted correlation from (A) (continuous lines).

In a similar way, the increase in thermal efficiency provided by addition of recuperators to supercritical ORCs was quantified and presented in Fig. 13. The regression coefficient R² for polynomial fitted to the data was 0.9. The observed absolute increase in thermal efficiency of up to 4 percentage points is substantial because most of presented configurations have a base-case thermal efficiency between 10% and 20%.

Fig. 13 Absolute percentage point increase in thermal efficiency due to addition of a heat recuperator to supercritical ORCs. (A): Markers represent results for individual working fluids and the surface is a fitted correlation. (B and C): Results from ORC models (dashed lines with markers) are compared to the fitted correlation from (A) (continuous lines).

Results presented in Fig. 12 and 13 suggest that dry fluids with reduced ideal gas heat capacities above 11 (e.g. isobutane, R-227ea, R-218) and critical temperatures at least 50–70 °C below the heat source temperature would be particularly good candidates for Sc-R cycles used in combined heat and power (CHP) applications.

7. Heat rejection systems

The largest variability in performance of existing ORC plants is caused by the type of heat rejection system used, although the choices of the appropriate working fluid and the cycle operating parameters are also important. All of the ORC simulations discussed so far used a water cooled condenser (WCC) coupled with a wet, mechanical induced draft cooling tower. The inlet air dry bulb temperature was 24 °C, wet bulb temperature T₀ was 17 °C and the relative humidity was 50%. Fig. 14 shows the sensitivity of the net specific power output (in kW_e per kg per s or kJ per kg of heat source fluid flow) to the changes in dry bulb temperature and relative humidity. In addition, it includes results for an ORC plant using an air cooled condenser (ACC). The selected plant configuration uses a Sub-NR R-134a cycle and 150 °C heat source temperature.

Fig. 14 Sensitivity of the net specific power output, kW_e per (kg per s) or kJ per kg of heat source fluid, to changes in dry bulb temperature and relative humidity (RH) for wet cooling tower (WCC) and air cooled condenser (ACC) for Sub-NR cycle using R-134a and heat source temperature of 150 °C.

In moderate climates representative of the Eastern U.S. (15 °C, 70% RH), a cycle with a WCC provides 25% higher power compared to an ACC plant. In warm, dry weather encountered in the Western U.S. (e.g., during an average summer afternoon in Reno, Nevada at 30 °C and 20% RH), power output with WCC can be nearly double of that with ACC. This difference is due to both the higher parasitic power consumption of ACC fans and the increased condensing pressure caused by the ACC. At heat source temperatures below 150 °C, the power advantage of cycles with WCC is even greater than that presented in Fig. 14.

8. Conclusions

This study analyzed four different ORC power plant configurations using heat sources from 100 °C to 230 °C, 13 different working fluids, and 2 types of heat rejection systems. The models employed were optimized for maximum utilization efficiency and validated using results from previous numerical studies¹⁷ and performance data from actual ORC plants.³⁴

The key result of this work was correlating the efficiency of ORC plants with the thermodynamic properties of working fluids. Two selected fluid properties – reduced ideal gas heat capacity C⁰_p/R and critical temperature T_c can be evaluated from data or, for less characterized working fluids, using group contribution methods. The latter approach provides a method for evaluating the ORC plant performance based on the characteristics of the heat source and the heat sink, and the molecular structure of the working fluid. Because of that, the correlations developed in the paper can be used to pre-screen potential ORC working fluids which may not have sufficiently accurate equation of state (EOS) models. We showed that in ORC plants optimized for maximum utilization efficiency, C⁰_p/R and T_c can be used to accurately predict: (1) maximum utilization efficiency for a given working fluid, (2) heat source temperature at which is achieved, (3) sensitivity of utilization efficiency to the changes in heat source temperature, and (4) increase in thermal efficiency and heat source fluid outlet temperature due to addition of a heat recuperator.

Furthermore, we found that supercritical ORC provide up to 17% higher utilization efficiencies and increased thermal efficiencies compared to subcritical ORC. A single working fluid can be also effectively used in supercritical ORC over a broader range of heat source temperatures. Subcritical cycles, on the other hand, experience higher thermal efficiency increase when equipped with heat recuperators.

Adding a recuperator to the top performing sub- and supercritical configurations resulted, on average, in a 0.5% drop in net power output and a 6.5% increase in thermal efficiency. It also increased the temperature of heat source fluid leaving ORC plant, which may help avoid scaling in geothermal ORC plants and condensation of flue gases in many heat recovery applications.

The type of heat rejection system employed in the power cycle has a large impact on the efficiency of an ORC, especially for cycles utilizing low-temperature heat sources. In moderate climates, the use of an air cooled condenser results in only 20% penalty in net power output compared to a wet cooling tower. In warm and arid conditions, this difference increases to as much as 50%.

Appendix

The correlations listed in this section are limited to the ranges of T_c (66 °C to 174 °C) and C⁰_p/R (5.4 to 18.5) evaluated in this work.

The linear trends fitted to data in Fig. 8 are correlated by eqn (A-1):

where constants a and b are: −4.5 and 121.5 for Sub-NR cycle and −9.73 and 250.7 for Sc-NR cycle, respectively.

The linear functions fitted to data in Fig. 9 are described by eqn (A-2):

where constants d, e, and f are listed in Table 4:

Table 4 Coefficients d–f used in eqn (A-2) and the standard deviations σ of the regressed data

	Sub-NR	Sc-NR
d	−0.199	−0.1746
e	2.854 × 10^−3	2.33 × 10^−3
f	8.86 × 10^−3	1.06 × 10^−2
σ	2.3%	1.9%

---

The linear trends fitted to the results in Fig. 10 are described by eqn (A-3):

where constants i, j, and k are listed in Table 5.

Table 5 Coefficients i–k used in eqn (A-3) and the standard deviations σ of the regressed data

	Sub-NR	Sc-NR
i	0.121	0.464
j	3.18 × 10^−3	1.71 × 10^−3
k	−4.7 × 10^−3	−1.11 × 10^−2
σ	2.2%	1.9%

---

The trends fitted to data in Fig. 11 are correlated by eqn (A-4):

where is the fraction of the maximum utilization efficiency, and coefficients l, m, n, and o are listed in Table 6.

Table 6 Coefficients l–o used in eqn (A-4) and the standard deviations σ of the regressed data

	T hs = − 20 °C	T hs = + 20 °C
l	−3.04 × 10^−5	0
m	3.7 × 10^−4	0
n	2.91 × 10^−3	−1.55 × 10^−3
o	1	1.002
σ	0.7%	0.3%

---

The polynomial functions fitted to data in Fig. 12 and 13 are described by eqn (A-5):

where Z is either the increase in heat source outlet temperature T_hs,out or the absolute percentage point increase in thermal efficiency η_th. Constants A–E are listed in Table 7.

Table 7 Coefficients A–E used in eqn (A-5) and the standard deviations σ of the regressed data

Z=	Increase in Ths,out	Percentage point increase in ηth
A	−25.09	−0.03347
B	−0.02852	0.0001015
C	0.3358	0.0007033
D	0.000634	1.332 × 10^−7
E	0.03539	3.179 × 10^−5
σ	3.6 °C	0.4%

---

Nomenclature

C	Heat capacity
E	Exergy
GWP	Global warming potential
h	Specific enthalpy
M	Molar mass or molecular weight
ṁ	Mass flow rate
NR	No recuperator
ODP	Ozone depletion potential
ORC	Organic Rankine cycle(s)
Q̇	Heat flow rate
R	Recuperator
R	Specific gas constant
RH	Relative humidity [%]
s	Specific entropy
Sc	Supercritical ORC
Sub	Subcritical ORC
T	Temperature
Ẇ	Power
η	Efficiency
σ	Standard deviation

Superscripts

0	Ideal gas state
*	Condition corresponding to a maximum utilization efficiency of ORC

Subscripts

B	Normal boiling point (at 1 atm)
c	Critical point of working fluid
cf	Cooling fluid
cond	Condensing
e	Electric power
hs	Heat source fluid
in	Input or inlet
net	Accounting for the parasitic power consumption
out	Outlet
P	Pressure
r	Reduced, i.e., divided by the respective value at the critical point
th	Thermal
tri	Triangular cycle
u	Utilization
wf	Working fluid
0	Dead state

Acknowledgements

The authors are grateful to the Cornell Energy Institute and the Atkinson Center for a Sustainable Future for partial financial support of this research. They would like to express their gratitude to Dr Jakub Kupecki and Dr Koenraad Beckers who provided useful comments on this work. They would also like to thank the anonymous reviewer for several valuable comments that resulted in a significantly improved paper.

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