Thermodynamic analysis of a regenerative organic Rankine cycle using dry fluids

Accepted Manuscript Thermodynamic analysis of a regenerative organic Rankine cycle using dry fluids Alireza Javanshir, Nenad Sarunac, Zahra Razzaghpanah PII: DOI: Reference:

S1359-4311(17)31750-7 http://dx.doi.org/10.1016/j.applthermaleng.2017.05.158 ATE 10473

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

14 March 2017 4 May 2017 27 May 2017

Please cite this article as: A. Javanshir, N. Sarunac, Z. Razzaghpanah, Thermodynamic analysis of a regenerative organic Rankine cycle using dry fluids, Applied Thermal Engineering (2017), doi: http://dx.doi.org/10.1016/ j.applthermaleng.2017.05.158

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Thermodynamic analysis of a regenerative organic Rankine cycle using dry fluids Alireza Javanshir (corresponding

Nenad Sarunac

Zahra Razzaghpanah

author)

Faculty of Mechanical Engineering and

PhD student of Mechanical Engineering and

PhD student of Mechanical Engineering and

Engineering Science, UNC Charlotte

Engineering Science, UNC Charlotte

Engineering Science, UNC Charlotte

Charlotte, NC, USA, Zipcode:28223

Charlotte, NC, USA, Zipcode:28223

Charlotte, NC, USA, Zipcode:28223

Email: [email protected],

Email: [email protected],

Email: [email protected],

Tell:7046871089

Tell:7047732923

Tell:7049544395

Highlights 

Analyzing thermodynamic performance of a regenerative ORC.



Selecting the best working fluid suitable for a regenerative ORC.



Offering new expressions for thermal efficiency of a regenerative ORC.

Keywords: Regenerative Organic Rankine cycle- Dry Working fluids- Thermal efficiency- Subcritical ORCTranscritical ORC Abstract Detailed design, analysis, and optimization of a regenerative Organic Rankine cycle (ORC) using dry working fluids is the main focus of this study. Large number of parametric calculations was performed to evaluate the thermodynamic performance (thermal efficiency and net power output) of the regenerative ORC over a range of operating conditions for fourteen dry working fluids. A systematic method is proposed for selection of optimal working fluid(s) considering the cycle operating conditions and thermophysical properties of the working fluids. Regression analysis was used to develop expressions for thermal efficiency for the subcritical, superheated subcritical, and transcritical regenerative ORC. For all analyzed configurations of the regenerative ORC, the relationship between thermal efficiency and relevant cycle parameters, such as maximum, minimum and evaporation temperatures, is logarithmic. Based on the results, it is concluded that regeneration can decrease the difference in thermal efficiencies for different working fluids. In the case of a regenerative ORC operating with a dry working fluid, thermal efficiency increases as the maximum temperature is increased at constant minimum temperature. The results show that adding regeneration to the cycle does not change the specific net work output. Working fluids Butane, iso-Butane, and R113 offer the highest specific net work output.

2 Nomenclature h

P s T

Specific heat[kJ/kg.K] Enthalpy[kJ/kg] Latent heat[kJ/kg] Mass flow rate [kg/s] Pressure[MPa] Heat rate[kW] Entropy[kJ/kg.K] Temperature[K] Power[kW]

Greek symbols ε

Efficiency Effectiveness

Subscript 1-6 c cr 1. Introduction

State points in the cycle Compressor Critical point

eva f in max min net r reg t th Acronyms EPV-11 FOM GWP Ja ODP ORC TIT

Evaporation Working fluid Inlet Maximum Minimum Net Dimensionless Regeneration Turbine Thermal

Ebsilon Professional V11 Figure of merit Global warming potential Jacob number Ozone depletion potential Organic Rankine cycle Turbine inlet temperature

Due to thermodynamic limitations, heat engines (thermodynamic power cycles) convert about 30 to 40% of the released chemical energy of the fuel to mechanical work, and the rest is rejected as waste heat [1, 2]. Harvesting the waste heat recovered through the exhaust and coolant systems to achieve higher power output is in an efficient way of lowering fuel consumption, and has been the focus of the recent studies [3]. The use of environmental friendly technologies such as Organic Rankine cycle (ORC) is one of the proposed solutions. A smaller scale energy generation capacity ORC systems are employed to generate electrical energy by harvesting the low-grade waste heat [4]. ORC is a Clausius-Rankine cycle utilizing an organic working fluid with low temperature phase change instead of water-steam. The organic working fluid thus allows the Rankine cycle to utilize heat recovered from the low temperature heat sources [5]. The improvement of a regenerative ORC (ORC with recuperator) in conjunction with the simple ORC (ORC without recuperator) to improve its performance has been focus of the recent research work [3]. Algieri et al. [6]studied sub-, trans- and supercritical ORC using dry working fluids and the effect of internal heat recovery. A study by Mago et al. [7] based on combined first and second law of thermodynamics analysis shows that using a dry working fluid for the regenerative ORC would not only reduce the required amount of waste heat needed to generate specified power output, but would also lower the irreversibility by increasing cycle efficiency, compared to the simple ORC. The energy and exergy analysis for the reheat-regenerative Rankine cycle was performed by Acar [8] indicating that,

3 although energy and exergy efficiencies of the closed cycle are the same, a better understanding of the losses in the system is gained by the exergy analysis. Ying et al. [9] proposed a new approach of utilizing solar heat as a heat source to heat the feedwater in the regenerative Rankine cycle. Wang et al. [10] evaluated characteristics of five different types of ORC. Their analysis proves that the regenerative ORC has the lowest rate of exergy destruction, since a portion of the heat from the turbine exhaust is recovered in the recuperator and beneficially used, instead of being rejected in the condenser. Hung et al. [11] reported that implementing a regenerator does not result in a significant thermal efficiency improvement (up to 2-% points) for the ORCs using wet and isentropic working fluids. However, for dry fluids, the thermal efficiency improvement can be higher than 9%-points. Therefore, the wet and isentropic fluids were not analyzed in this study. This study is focused on a regenerative ORC using solar and geothermal heat sources and employing different working fluids. Solar energy driven regenerative ORC has been studied during the past few years. Wang et al. [12] evaluated the effect of thermodynamic characteristics of working fluids on performance of a low temperature solar regenerative ORC power generation system using a flat plate collector for four organic working fluids: R245fa, R123, isobutene, and R134a. A numerical simulation of the heat transfer and power conversion for a low temperature solar thermal electric generation systems was carried out by Gang et al. [13]. Thermal efficiency of about 8.6% and 4.9% for irradiance 750 W/m 2 was reported for the ORC systems with and without regeneration, respectively. However, not many investigations have been conducted on the effect of parameters such as intermediate pressure on performance of the regenerative ORC system. In addition, only a few operating points have been taken into account while investigating an engine waste heat recovery system performance. Many investigations have been made on the performance of a solar powered ORC and working fluid selection [14, 15]. Also, using geothermal heat source for the ORC is focus of many recent studies [1620]. Saleh et al. [20] compared thermal efficiency for different work cycle configurations of geothermal ORC, for 31 working fluids. Chen et al. [21] also studied performance of the subcritical and supercritical ORC with pure working fluids. Performance optimization of the ORC has also been studied by a number of researchers. Roy et al. [5] performed parametric optimization of the regenerative ORC. He et al. [22] proposed a theoretical analysis to determine the optimum evaporation temperature, and Wang et al. [23] developed a theoretical model for thermal efficiency as a function of the Jacob number. Kuo et al. [24] showed that thermal efficiency of a subcritical ORC decreases with an increase in figure of merit (FOM). The proposed form of FOM is, however, applicable to the subcritical ORC cycle only.

4 Various criteria were examined for the working fluid selection procedure. International protocols and agreements impose restrictions on the use working fluids harmful to the environment. Thus, the criteria such as ozone depletion potential, flammability, toxicity and global warming potential (GWP) need to be considered during the working fluid selection process. Papadopoulos et al. [25] selected 15 criteria for the fluid selection; with environmental, safety, physical, chemical and economical properties being the five main groups. The best working fluid is chosen based on the cycle thermal efficiency. Details are provided in [26]. No working fluid satisfies all selection criteria [27], therefore working fluid selection involves tradeoffs between the environmental, safety, physical and chemical properties of a working fluid, and capital investment, manufacturing, and maintenance requirements. The procedure can be divided into two categories: elimination and ranking [28]. First, elimination is employed to discard incompatible working fluids before ranking process is applied. Roedder et al. [29] examined 22 criteria divided into six groups, and then applied a combination of the elimination and ranking methods for selection of the working fluid. Various weights were taken into account for every property of a working fluid. The approach was applied to a two-stage ORC, and iso-Butane was selected as the best working fluid. Selection of working fluids resulting in best performance (thermodynamic efficiency or net specific work output) of the regenerative ORC for the specified operating conditions (maximum temperature and pressure, heat rejection temperature, and others) is a time-consuming and arduous task, especially when a large number of working fluids is being considered. The commonly used approach involves performing a number of parametric calculations over a range of operating parameters for a number of the candidate working fluids. The results are usually presented in a graphical form, for example: for each of the analyzed working fluids efficiency is plotted as a function of the maximum temperature and pressure. The best working fluid is selected by manually inspecting efficiency diagrams for all analyzed fluids. The procedure has to be repeated for the specific net work output because the working fluid giving the highest efficiency does not give the biggest net work output, and vice versa. Also, since the selection process is manual, there is a certain level of subjectivity and potential for error involved. This study considered a regenerative ORC and investigated the effect of dry working fluids on cycle thermal efficiency and power output and over the range of cycle operating conditions with the objective to identify the best working fluid. A systematic, analytical method was developed for selection of best working fluids for a regenerative ORC. The detailed models of the power cycles were developed using Ebsilon Professional V11 (EPV-11) power systems modeling code [30]. EPV-11 is professional software for detailed design, analysis, and optimization of power generation systems. The EPV-11 models were exercised over a range of cycle

5 operating conditions and for multitude of working fluids to generate results (simulation results) on cycle performance parameters. The regression analysis was applied to the simulation results to develop analytical correlations for thermal efficiency and specific net work output for the following working cycles: subcritical, superheated subcritical, and transcritical regenerative ORC. Using these analytical correlations in conjunction with the extremum seeking algorithm allows non-subjective and exact determination of the best working fluid for the selected cycle operating conditions, as well as construction of performance maps which provide visual and easy-to-interpret information on cycle performance and best working fluids. 2. Thermodynamic modeling and working fluid properties Thermodynamic modeling of work cycles was performed to determine theoretical expressions for cycle efficiency and net work output. The functional form of these theoretical expressions is used as a basis for analytical correlations. Both the regenerative ORC and regenerative Rankine cycles employ five thermodynamic processes: pressure increase of the evaporator inlet, evaporation, expansion in the turbine (expander), condensation, and preheat of the pump outlet by the turbine outlet (regeneration). Figure 1 is an illustration of the regenerative ORC presenting the main system components: feed pump, evaporator, turbine, condenser, and regenerator. The feed pump delivers working fluid to the regenerator to be preheated by the turbine exhaust flow stream and sends it to the approximately constant pressure evaporator to be evaporated using the externally supplied heat. Some ORC designs might also implement a superheater to superheat the working fluid before it is expanded in the turbine (expander) driving an electric generator. The lowpressure, low-temperature working fluid leaving the turbine is cooled in the regenerator and condensed in the condenser to reach the saturated liquid (or slightly subcooled) state. The pressure of the working fluid leaving the condenser is increased by the feed pump, completing the work cycle.

Figure 1: Schematic of the regenerative ORC.

6 Figure 2 presents schematics of the subcritical and transcritical regenerative ORC cycles. In the superheated subcritical cycle, the working fluid is superheated in the superheater after phase change in the evaporator prior to entering the turbine. In the transcritical cycle working fluid remains as a homogeneous supercritical fluid throughout the part of the cycle where working pressure is above the critical pressure. As pressure is reduced during expansion is the turbine, working fluid exits the turbine at the subcritical pressure and undergoes phase change in the condenser. Subcritical regenerative ORC with and without superheat was analyzed in this study.

A) Subcritical without superheat

B) Subcritical with superheat

C) Transcritical

Figure 2: T-s diagram for the regenerative ORC. 2.1. Thermodynamic and Environmental Properties of Working Fluids The performance of the regenerative ORC is significantly affected by the choice of working fluid. In order to establish a procedure for selecting the appropriate working fluid, the analysis was performed for 14 working fluids listed in Table 1. The slope of the saturated vapor curve in a T-s diagram divides working fluids into the three main categories: dry fluids for the positive slope vapor curve, wet fluids for the negative slope vapor curve, and isentropic for the infinite slope vapor curve. T-s diagrams for these working fluid categories are presented in Figure ‎3. The slope of the saturated vapor curve, as one of the key thermo-physical property of the working fluid [31], plays an important role on thermal efficiency and equipment arrangement of an ORC [11]. By superheating the wet working fluid, vapor quality at the turbine exhaust is increased and erosion damage to the blading is reduced [32]. However, the same does not apply to the dry fluids where turbine discharge is in the superheated region. This is because superheat increases the amount of rejected heat and condenser loading without a significant effect on the turbine power output. Therefore, for dry working fluids, saturated steam conditions at the turbine inlet result in the highest cycle thermal efficiency [33, 34]. Lowering temperature of the working fluid prior to the condenser by implementing a regenerator located downstream of the turbine is an effective option for increasing thermal efficiency of the ORC employing

7 dry working fluids. The recovered heat is transferred to the evaporator and used to increase temperature of the working fluid prior to entering the evaporator [35]. Hung et al. [11] reported that implementing a regenerator does not result in a significant thermal efficiency improvement (up to 2%- points) for the ORCs using wet and isentropic working fluids. Therefore, the wet and isentropic fluids were not analyzed in this study. For dry fluids regeneration may improve thermal efficiency by more than 9%points.

Figure 3: Comparison of wet, dry and isentropic fluids. Selection of the appropriate working fluid should be carefully performed based on its physical properties since, as mentioned before, performance of the regenerative ORC is significantly affected by thermophysical properties of the working fluid. Table ‎1 presents properties of 14 working fluids investigated in this study. The first nine working fluids listed in Table 1 have the potential to be used in regenerative ORC as they are not toxic. Butane and iso-Butane they are, despite their flammability, used as working fluids in geothermal cycles; R113 and R114 are chlorofluorocarbons (CFCs) with a strong ozone depletion potential. The remaining five working fluids are flammable or toxic. All 14 working fluids were analyzed in this study to develop correlations for cycle thermal efficiency and work output valid over a wide range of thermo-physical properties of working fluids. It can be noted that organic fluids have a significantly lower critical pressure and temperature, and higher molar mass compared to water (21.8 MPa and 374 °C, 18.015 kg/kmol). Since the environmental and safety characteristics of working fluids affect both plant operators’ health and environment, Table 1 also presents environmental and safety data, such as global warming potential (GWP), ozone depletion potential (ODP), toxicity, flammability and corrosiveness for the working fluids evaluated in this study. Carbon dioxide (CO 2) with GWP of 1 is set to be the scale of comparison. Thus, the effect on global warming for a fluid with GWP of 2 is two times stronger compared to the CO 2.

8

Table 1: Physical, safety and environmental data of the working fluids. Physical Data Fluid

Molar mass

Tcr

Pcr

(kg/kmol)

(°C)

(MPa)

Environmental and Safety Data Type

GWP

ODP

Toxicity

Flammability

Corrosiveness

1

R113

187.38

214.06

3.39

Dry

6130

0.8

NO

NO

NO

2

R114

170.92

145.68

3.25

Dry

10.04

1

NO

NO

NO

3

R227ea

170.03

101.75

2.92

Dry

3220

0

NO

NO

NO

4

R236ea

152.04

139.29

3.50

Dry

9810

0

NO

NO

NO

5

R236fa

152.04

124.92

3.20

Dry

1300

0

NO

NO

NO

6

R245fa

134.05

154.01

3.65

Dry

1030

0

NO

NO

NO

7

RC318

200.3

115.23

2.77

Dry

8200

0

NO

NO

NO

8

Butane

58.122

151.98

3.79

Dry

3

0

NO

YES

NO

9

Iso-Butane

58.122

134.66

3.62

Dry

3

0

NO

YES

NO

10

R123

152.93

183.68

3.66

Dry

77

0.02

YES

NO

NO

11

Isopentane

72.149

187.2

3.37

Dry

5

0

YES

YES

NO

12

Pentane

72.149

196.55

3.37

Dry

5

0

YES

YES

NO

13

n-Hexane

86.18

234.45

3.02

Dry

900

0

YES

YES

NO

14

R245ca

134.047

174.42

3.94

Dry

693

0

YES

YES

NO

The restrictions and laws imposed by the Montreal and the Kyoto protocols requiring the countries end production of ozone-depleting substances prevents us from considering fluids with ODP higher than zero [36, 37]. The properties in Table 1 were obtained from the GESTIS database [38]. 2.2. Calculation of Thermal Efficiency The analysis of the cycle performance was performed by neglecting the friction and heat losses in the pipes and heat exchangers, and assuming adiabatic turbine and feed pump. The heat input to the cycle is calculated as: (1) The net power output is: (2) For ideal gas: (2a) The temperature at point 3 and 5 are calculated by:

9 (3) (4) (5) Where

denotes regenerator effectiveness.

The thermal efficiency of the cycle

is defined as: (6)

3. Results and discussion 3.1. The Effect of Operating Conditions on Performance of a Regenerative ORC Thermal efficiency of a regenerative ORC was determined over a range of operating conditions for nine working fluids from Table 1. Cycle parameters used in the calculations are presented in Table 2. The temperature difference of 10°C between the turbine inlet temperature (TIT) and the heat source temperature was used in the analysis. The maximum pressure of the cycle was set to 2 MPa, which is lower than critical pressure of all working fluids used in the analysis. Thus, ORC is operated as a subcritical cycle with and without superheat. The maximum temperature was varied between the saturation temperature at maximum pressure of 2MPa and 250°C. However, since the upper temperature limit for some working fluids (R236ea for example) is lower than 250°C, cycle analysis for these fluids was performed for lower maximum temperature. The steady state conditions and negligible pressure drop in heat exchangers have been assumed in this study. Table 2: Cycle parameters. Parameter

Value

Maximum pressure, P4 (MPa)

2

Maximum temperature, T 4 (°C)

85-250

Minimum temperature, T 1 (°C)

2-30

Turbine isentropic efficiency,

(%)

0.85

Pump isentropic efficiency (%)

0.8

Regenerator effectiveness

0.85

Mass flow rate,

(kg/s)

35

Generator efficiency (%)

0.975

Turbine mechanical efficiency (%)

0.99

Minimum pressure (MPa)

Saturation pressure at minimum temperature

10 Thermal efficiency of a regenerative ORC for nine working fluids is presented in Figure 4. The contour graphs are plotted in terms of the minimum and maximum cycle temperature, Tmin and Tmax for Pmax = 2 MPa.

A) Thermal efficiency scale (%)

B) R113 (CFC)

C) R114 (CFC)

D) R227ea

E) R236ea

F) R236fa

G) R245fa

H) RC318

I) Butane (flammable)

J) iso-Butane (flammable)

Figure 4: Thermal efficiency of a regenerative ORC for different working fluids and P max = 2 MPa.

11 The results show that the regenerative ORCs operating with R113 and R227ea have the highest and lowest thermal efficiencies, respectively compared to the regenerative ORCs using other working fluids. For example, a regenerative ORC operating with R113 and R227ea at Tmin=10°C and Tmax=180°C, has thermal efficiency of 25% and 18%, respectively. For the maximum temperature lower than 175°C, lower than 23%, while for the maximum temperature in the 175 °C to 250°C range,

is

reaches 29%.

Working fluids R113 and R114 are giving the highest thermal efficiency 29% and 23%, respectively. However, R113 and R114 are chlorofluorocarbons (CFCs) and they have been phased-out and prohibited for use in power generation [36]. Regeneration may result in a smaller difference in thermal efficiency between different working fluids. For example, at 150°C thermal efficiency of a regenerative ORC operating with R245fa is just 1%-point higher compared to the regenerative ORC operating with RC318. For a simple ORC, this difference is larger than 5%-points [39]. Figure 4 shows that for all analyzed dry working fluids thermal efficiency

of a regenerative ORC

increases as the maximum temperature is increased at the constant minimum temperature. For example, for Tmin =15°C and R113 (Figure 4B), increasing the maximum temperature from 180°C to 250°C results in an increase in thermal efficiency from 24% to 27%. In contrast, for the case of a simple ORC, depending on the operating conditions, thermal efficiency of the cycle operating with dry fluids may increase or decrease [39]. For dry working fluids and certain cycle operating conditions, isobaric lines in T-s diagram converge with temperature, thus for a simple ORC thermal efficiency decreases as the maximum cycle temperature is increased. In many applications such as solar or geothermal where ORC is chosen as a bottoming cycle, the cycle power output is more important than its thermal efficiency. The specific net work output for nine working fluids is presented in Figure 5 over the range of operating conditions. Since the turbine inlet, turbine outlet, pump inlet, and pump outlet conditions are not affected by regeneration, adding regeneration to the ORC does not change the specific net work output. The highest specific net work output is for a regenerative ORC system operating with Butane followed by iso-Butane and R113. However, R-113 and R-114 are CFCs and they have been phased-out [36]. The difference in specific net work output for the ORC operating with Butane and iso-Butane is higher than 15% (20 kJ/kg). Eqn. (2a), Figure 5 and previous study performed by the authors [39] show that working fluids with higher Cp, produce higher net work output. Specific heat capacity of dry working fluids Butane, R236ea, R245fa, and RC318 at 2MPa is shown in Figure 6.

12

A) specific net work scale (kJ/kg)

B) R113 (CFC)

C) R114 (CFC)

D) R227ea

E) R236ea

F) R236fa

G) R245fa

H) RC318

I) Butane (flammable)

J) iso-Butane (flammable)

Figure 5. Net specific work output of a regenerative ORC for different working fluids and Pmax = 2 MPa.

13

Figure 6. Cp-T diagram for different working fluids at 2 MPa. 3.2. Correlations for thermal efficiency for the subcritical, superheated subcritical, and transcritical ORC A systematic, analytical method was developed for selection of best working fluids for a regenerative ORC. The detailed models of the power cycles were developed using Ebsilon Professional V11 (EPV-11) power systems modeling code [30]. The EPV-11 models were exercised over a range of operating conditions and multitude of working fluids to generate simulation results on cycle performance parameters. The regression analysis was applied to the simulation results to develop analytical correlations for thermal efficiency th and specific net work output wnet as functions of the relevant cycle operating parameters, such as: Tmax, Tmin or Teva at constant regenerator effectiveness reg, turbine isentropic efficiency t and critical temperature Tcr. The analysis was performed for the subcritical, superheated subcritical, and transcritical regenerative ORC. 3.2.1. Subcritical ORC without Superheat For the regenerative ORC without a superheat, shown in Figure 2.A, a logarithmic relationship between Tmax/Tmin and

represented by Eqn. (7) was used in regression analysis. For the ORC cycle without a

superheat, maximum temperature Tmax is equal to the evaporation temperature Teva (Tmax = Teva). (7) Coefficients c1 and c2 were determined by regressing performance data (EPV-11 simulation results) obtained for the regenerative ORC for 14 working fluids presented in Table 1, 31 evaporation temperatures (40 to 100 °C), 5 regenerator effectiveness values (0.75 to 0.95), and 15 condensation temperatures (2 to 30 °C), and 5 turbine isentropic efficiency values (0.55 to 0.95), for the total of 162,750 cases. The regression analysis gives a linear relationship for coefficients c1 and c2 in terms of

14 represented by Eqns. (8 and 9). Coefficients c1 and c2 are also presented in a graphical form in Figures 7A and 7B. (8) (9) Figure 7C, shows excellent agreement between the correlation (Eqn. 7) and EPV-11 simulation results. Since c1 and c2 are positive, thermal efficiency increases as the Tmax/Tmin ratio is increased, i.e., the maximum (evaporation) temperature is increased, and/or the minimum (heat rejection) temperature is decreased. Correlations for c1 and c2 and Figures 7A and 7B show that thermal efficiency is a linear function of turbine efficiency t and exponential function of regenerator effectiveness

with turbine

efficiency being a dominant factor.

(A)

(B)

(C)

Figure 7: A) c1 in Eqn. (7), B) c2 in Eqn. (7), C) Comparison between Eqn. (7) and simulation results for a subcritical ORC without superheat The average relative error for all analyzed cases is 0.005024. The relative error was defined as: (10) 3.2.2. Subcritical ORC with Superheat For the regenerative ORC with superheat, shown in Figure 2.B, both the evaporation Teva and maximum Tmax temperatures affect efficiency. Logarithmic relationship between Teva/Tmin and

represented by

Eqn. (11) was used in regression analysis, where coefficients c1 and c2 are functions of Tmax. (11)

15 To incorporate the effect Tmax, the number of analyzed cases was increased to 14 working fluids, 8 condensation temperatures (2 to 30°C), 11 evaporation temperatures (40 to 60°C), 5 regenerator effectiveness values (0.75 to 0.95), 9 maximum temperatures between (62 to 94°C), and 5 turbine isentropic efficiency values (0.55 to 0.95), for the total of 277,200 cases. The regression analysis gives a linear relationship for coefficients c1 and c2 in terms of Tmax and

of the following form: (12) (13)

The coefficients c1 and c2 for Tmax=94°C are presented in a graphical form in Figures 8A, 8B, 8C and 8D. Figure 8E, shows excellent agreement between the correlation given by Eqn. (11) and EPV-11 simulation results. The average relative error for all analyzed cases is 0.015178.

(A)

(B)

(D) Figure 8: A) c1-

(C)

(E) in Eqn. (11), B) c2-

in Eqn. (11), C) c1-Tmax in Eqn. (11), D) c2-Tmax in Eqn. (11),

E) Comparison between Eqn. (11) and simulation results for a subcritical ORC with superheat

16 Since c1 and c2 are positive, increasing the Teva/Tmin gives higher efficiency. Correlations for c1 and c2 and Figures 8A, 8B, 8C and 8D also show that thermal efficiency is a linear function of the maximum temperature Tmax, turbine efficiency

and exponential function of regenerator effectiveness

, with

maximum temperature and turbine efficiency being dominant factors.

3.2.3. Transcritical ORC Based on the results of a previous study performed by the authors [39], for a constant minimum and maximum temperature and maximum pressure Pmax ≥ Pcr, thermal efficiency remains approximately constant. Thus, at constant Tmin and Tmax, increasing Pmax in the supercritical region does not have a significant effect on thermal efficiency. Thus, for the transcritical regenerative ORC shown in Figure 2.C, Pmax = Pcr was assumed. Correlation between thermal efficiency and Tmax/Tmin given by Eqn. (14) was used in the regression analysis. (14) Coefficients c1 and c2 were determined by performing regression analysis of the cycle performance data (EPV-11 simulation results) obtained for 14 working fluids presented in Table 1, 41 values of Tr (1 to 1.2), 5 regenerator effectiveness values (0.75 to 0.95), and 15 condensation temperatures (2 to 30°C), 5 turbine isentropic efficiency values (0.55 to 0.95), for the total of 215,250 cases. The regression analysis gives a first and second order relationship for coefficients c1 and c2 in terms of the dimensionless maximum temperature Tr, and first order (linear) in terms of regenerator effectiveness of the following form: (15) (16) (17) Coefficients c1 and c2 are also presented in a graphical form in Figures 9A, 9B and 9C. Figure 9D, shows excellent agreement between the correlation given by Eqn. (14) and EPV-11 simulation results. The average relative error for all analyzed cases is 0.01026.

17

(A)

(B)

(C)

(D)

Figure 9: A) c1-Tr in Eqn. (14), B) c2-Tr in Eqn. (14), C) c1-

in Eqn. (14), D) Comparison between Eqn.

(14) and simulation results for transcritical ORC Since c1 and c2 are positive, incresing the Tmax/Tmin results in higher thermal efficiency. Correlations for c1 and c2 and Figures 9A, 8B and 8C also show that thermal efficiency is a linear function of the turbine efficiency

, with maximum temperature and turbine efficiency being dominant factors.

Correlations (Eqns. (7), (11) and (14)) may be used for a quick, systematic and precise determination of thermodynamic performance of the analyzed work cycles in terms of the cycle operating parameters for a working fluid(s) of interest, or selection of the best working fluid without the need for preforming tedious parametric calculations and results analysis. Also, developed correlations and thermodynamic expressions allow determination of the effect of working fluid properties, such as specific heat, latent heat of evaporation, and critical temperature on cycle performance, as illustrated in Section 3.5. Such analysis can be used to investigate and predict cycle performance for mixtures of different working fluids.

18 3.3. Validation of results for a regenerative ORC 3.3.1. Subcritical ORC without superheat Values of thermal efficiency obtained by the EPV-11 model of the regenerative ORC, and correlation developed in Section 3.2.1 represented by Eqn. (7) were compared to the results reported by Wang et al. [40]. Cycle parameters used in the calculations are summarized in Table 3. The temperature difference between TIT and the heat source temperature of 10°C was used in the calculations. Table 3: Cycle parameters for regenerative ORC. Parameter

Value

Maximum pressure, P4 (MPa)

Saturation pressure at minimum temperature

Turbine isentropic efficiency,

0.8

Pump isentropic efficiency

0.9

Regenerator effectiveness

0.55

Minimum pressure (MPa)

Saturation pressure at minimum temperature

The simple and regenerative ORC having the net power output of 10 kW were analyzed in [40] using a custom-written Matlab code. Physical properties of the working fluids were provided by the REFPROP code developed by NIST. The results for seven working fluids are compared in Table 4. Table 4: Comparison of results for a subcritical regenerative ORC without superheat.

Fluid

P4(MPa)

T4(K)

T1(K)

P1(MPa)

Mass flow rate (kg/s)

Thermal Efficiency from [40](%)

Thermal Efficiency from EPV11 Model

Thermal Efficiency from Eqn. (7)

Relative Error Between [40] and EPV-11 Model (%)

Relative Error Between [40] and Eqn. (7) (%)

R245fa

1.4923

380.90

304.44

0.1874

0.498

9.51

9.44

9.45

0.73

0.68

R245ca

1.4923

395.05

315.56

0.1882

0.481

9.61

9.62

9.55

0.10

0.62

R236ea

1.7231

377.51

300.00

0.2196

0.597

9.55

9.52

9.64

0.31

1.01

R114

1.8154

385.81

300.00

0.2275

0.672

10.22

10.22

10.29

0.00

0.68

R113

1.7692

444.74

346.67

0.2223

0.619

10.35

10.34

10.32

0.09

0.27

Butane

2.0000

387.51

300.00

0.2580

0.233

10.46

10.43

10.5

0.28

0.38

R123

1.5385

406.00

320.00

0.1926

0.545

10.00

9.98

9.94

0.20

0.60

As shown in Table 4, thermal efficiency values obtained by the EPV-11 model and the correlation for the subcritical ORC without superheat represented by Eqn. (7) are in the excellent agreement with the results from [40]. The relative error between the results from Eqn. (7) and [40] is in the 0.27 and 1.01% range, while the relative error between the results from EPV-11 model and [40] is in the 0.00 and 0.73% range.

19 The difference in thermal efficiency values obtained by using different working fluids are relatively small. The values of thermal efficiency presented in Table 4 range from 9.44 to 10.43%, i.e. about 1%point. 3.3.2. Subcritical ORC with superheat Values of thermal efficiency obtained by the EPV-11 model of the regenerative ORC, and correlation developed in Section 3.2.2 represented by Eqn. (11) were compared to the results reported by Peris et al. [41], who designed, built, and tested a regenerative ORC in the superheated subcritical region using R245fa. The reported experimental uncertainty in thermal efficiency is ±4.55% for the net power output in the 6.85 to 16.93kW range. Comparison of thermal efficiency values determined by Peris at al., Ref. [41] and calculated in this study by using EPV-11 model of the cycle and Eqn. (11) is presented in Table 5 over a range of operating conditions.

Table 5: Comparison of results for a subcritical regenerative ORC with superheat.

P4(MPa)

T4(K)

P1(MPa)

Mass flow rate(kg/s)

Thermal Efficiency from [41](%)

Thermal Efficiency from EPV11 model

Thermal Efficiency from Eqn. (11)

Relative error Between [41] and EPV-11 model(%)

Relative error Between [41] and Eqn. (11) (%)

1

1.41

395.42

0.25

0.39

7.16

7.30

7.33

2.02

2.44

2

1.63

402.99

0.26

0.47

8.38

8.69

8.61

3.74

2.79

3

1.76

406.54

0.26

0.52

9.00

9.37

9.30

4.09

3.31

4

1.90

410.03

0.27

0.58

9.94

10.34

10.25

3.99

3.08

5

1.94

411.03

0.26

0.59

10.00

10.49

10.42

4.90

4.21

6

1.96

411.26

0.25

0.60

10.49

10.97

10.77

4.59

2.71

7

2.01

412.55

0.23

0.62

10.83

11.20

11.25

3.47

3.91

8

2.03

413.12

0.23

0.64

10.90

11.35

11.30

4.12

3.66

Considering experimental uncertainty, results obtained from EPV-11 model and Eqn. (11) are in a good agreement with results from [41]. The relative error between results from Eqn. (11) and Ref. [41] is in the 2.44% and 4.21% range, while the relative error between results from EPV-11 model and Ref. [41] is in the 2.02% and 4.90% range. 3.4. Comparison of a simple and regenerative ORC Values of thermal efficiency obtained for the simple and regenerative ORCs for Pmax of 0.3 and 4.1 MPa and Butane as a working fluid are compared in Figure 9. As discussed in Section 3.1, thermal efficiency of a regenerative ORC increases as Tmax is increased at constant Tmin and Pmax. However, thermal

20 efficiency of a simple ORC using dry working fluid such as Butane decreases as Tmax is increased at constant Tmin and Pmax. This difference in trends may be explained by the slope of isobaric lines in the superheated region of the T-s diagram. Convergence or divergence of isobaric curves results in the increase or decrease of thermal efficiency with temperature. More details are provided in [39]. At Tmax = 250 °C and Pmax = 4.1 MPa, thermal efficiency of the regenerative ORC is 8%-points higher compared to the simple ORC. For Pmax = 0.3 MPa this difference is 4%-points. The difference between thermal efficiencies of the regenerative and simple ORCs increases as Tmax increases. In the supercritical region, increasing Tmax increases the turbine exhaust temperature, thus more exhaust heat is available to be recovered by the regenerator, making regeneration more effective and resulting in higher efficiency.

Figure 10. Comparison of thermal efficiency of regenerative to simple ORC for butane.

3.5. Effect of working fluid properties on thermal efficiency and specific net work output. Correlations developed in this study can be used to investigate effects of the working fluid properties on performance of the regenerative ORC. Eqns. (7) and (11) show that in a subcritical region, properties of the working fluid do not affect thermal efficiency. However, Eqn. (14) shows that in the supercritical region, thermal efficiency is affected by the critical temperature. It can be shown that the first derivative of Eqn. (14) in the supercritical region is positive (Eqn. (18)), meaning that at constant maximum and minimum temperatures, working fluids with higher critical temperature give higher thermal efficiency.

21

(18) As discussed earlier, conditions at the turbine inlet, turbine outlet, pump inlet, and pump outlet are not affected by regeneration, thus adding regeneration to a simple ORC does not change the specific net work output. The previous study performed by the authors [39] gives: (19) (20) (21) Since the first derivatives of wnet with respect to specific heat cp and critical temperature T cr (expressed in dimensionless form as Tr) are positive, Eqn. (22), working fluids with higher Cp or Tcr produce higher net work output. (22) The effect of critical temperature on thermal efficiency (Eqn. (14)) and specific net work output (Eqn. (19)) for

=0.9,

=0.9 and Tmax=250°C is presented in Figure 11.As the results show,

and wnet

increase as critical temperature is increased. An increase in specific heat Cp, results in higher specific net work output, which increase linearly with Cp. Thermal efficiency, however, remains unaffected.

A) Tcr

B) Cp

Figure 11. Effect of critical temperature and specific heat capacity on thermal efficiency and specific net work output of the regenerative ORC in the supercritical region. 4. Conclusions Cycle performance (thermal efficiency and net power output) of the regenerative ORC was studied for fourteen dry working fluids. A thermodynamic analysis of the subcritical, superheated subcritical, and

22 transcritical regenerative ORC was performed using Ebsilon Professional V11 (EPV-11) power systems modeling software. Thermo-physical properties of the working fluids along with their environmental impact and safety properties of such as GWP, ODP, flammability and toxicity were taken into account while choosing the appropriate working fluid. Cycle performance (thermal efficiency and net power output) was the main focus of this study. The results were analyzed to determine correlations for thermal efficiency

in terms of the relevant cycle operating parameters for the subcritical, superheated

subcritical, and transcritical regenerative ORC. In case of the regenerative ORC operating with a dry working fluid,

increases as the maximum

temperature is increased at constant minimum temperature. The results show that adding regeneration to the work cycle does not change the specific net work output. However, regeneration decreases the difference in thermal efficiencies for different working fluids. Working fluids Butane followed by isoButane and R113 offer the highest specific net work output. Also, working fluids with higher Cp, produce higher specific net work output, while working fluids with higher critical temperature produce higher thermal efficiency. Regenerative ORC system operating with R113 and R227ea provide the highest and lowest thermal efficiency compared to the regenerative ORC operating with other working fluids, respectively. However, R113 and R114 are chlorofluorocarbons (CFCs) and they have been phased-out and prohibited for use in power generation. For all three analyzed configurations of the regenerative ORC (subcritical with and without superheat, and transcritical), the relationship between thermal efficiency and relevant cycle parameters, such as Tmax/Tmin and Teva/Tmin, is logarithmic. Also, for analyzed configurations of the regenerative ORC, increasing Tmax/Tmin or Teva/Tmin increases thermal efficiency. The EPV-11 model was validated by comparing its results to the results from the correlations for thermal efficiencies, and results from the literature. Results obtained from EPV-11, Eqn. (7) and Eqn. (11) are in an excellent agreement with results from the literature. Acknowledgments This research was supported by Energy Production and Infrastructure Center (EPIC) at UNC Charlotte and American Public Power Association (APPA). References [1] J.B. Heywood, Internal combustion engine fundamentals, Mcgraw-hill New York, 1988.

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25 Figure captions: (Single column) Figure 1: Schematic of the regenerative ORC. (Two-column) Figure 2: T-s diagram for the regenerative ORC. (Single column) Figure 3: Comparison of wet, dry and isentropic fluids. (Two-column) Figure 4: Thermal efficiency of a regenerative ORC for different working fluids and P max = 2 MPa. (Two-column) Figure 5. Net specific work output of a regenerative ORC for different working fluids and Pmax = 2 MPa. (Single column) Figure 6. Cp-T diagram for different working fluids at 2 MPa. (Two-column) Figure 7: A) c1 in Eqn. (7), B) c2 in Eqn. (7), C) Comparison between Eqn. (7) and simulation results for a subcritical ORC without superheat (Two-column) Figure 8: A) c1-ereg in Eqn. (11), B) c2-ereg in Eqn. (11), C) c1-Tmax in Eqn. (11), D) c2-Tmax in Eqn. (11), E) Comparison between Eqn. (11) and simulation results for a subcritical ORC with superheat (Two-column) Figure 9: A) c1-Tr in Eqn. (14), B) c2-Tr in Eqn. (14), C) c1-ht in Eqn. (14), D) Comparison between Eqn. (14) and simulation results for transcritical ORC (Single column) Figure 10. Comparison of thermal efficiency of regenerative to simple ORC for butane. (1.5-column) Figure 11. Effect of critical temperature and specific heat capacity on thermal efficiency and specific net work output of the regenerative ORC in the supercritical region. Table titles: Table 1: Physical, safety and environmental data of the working fluids. Table 2: Cycle parameters. Table 3: Cycle parameters for regenerative ORC. Table 4: Comparison of results for a subcritical regenerative ORC without superheat. Table 5: Comparison of results for a subcritical regenerative ORC with superheat.

26 Highlights: 

Analyzing thermodynamic performance of regenerative ORC.



Selecting the best working fluid suitable for a regenerative ORC.



Offering new expressions for thermal efficiency of a regenerative ORC.