A study of organic working fluids of an organic Rankine cycle for solar concentrating power plant

1

INTRODUCTION

Since the industrial revolution, energy demand is increasing. In recent decades the growth of this demand has been intensified by the rise of new indus trial countries like China, India, Brazil and others.

This growth in demand is accompanied by a decrease in reserves of fossil fuels on which mankind counts most for its supply. According to the latest statistics from the International Energy Agency (IEA) [1] as shown in Fig. 1. World energy consumption has increased from 6107 Mtoe in 1973 to 12717 Mtoe in 2012. By analyzing the numbers of 2012 we find that fossil fuels represent 81.1% of global consumption with 21.4% for natural gas, 27.3% for coal and 32.4%

for oil.

To face this problem a lot of attention is given to alternative energy sources such as wind, geothermal and solar energy. This last source of energy offers a wide range of applications; solar energy can be used in agriculture [2], in photovoltaic [3], in solar lighting systems [4] and in solar thermal applications.

Solar thermal applications are those that convert solar radiation into heat. We find applications as solar heating and cooling, water desalination and electricity production.

Solar energy is used to provide the heat require ment for the thermal power generation system such as in the case of the Brayton cycle, the Stirling cycle and particularly in the case of Rankine cycle [5]. However, the use of conventional Rankine cycle requires work ing with high temperatures. The use of organic Rank ine cycle (ORC) allows the exploitation of low temper ature heat sources.

1The article is published in the original.

This study aims to design an ORC installation of 333 kWe that will be coupled to a solar field using cylindroparabolic concentrators. As a first step we will use seven different working fluids which are all hydrocarbons. Then we will use the binary mixtures of these fluids and for each mixture we will change its composition in steps of 10%. The installation will be dimensioned according to four different configura tions of the studied cycle. The obtained efficiencies will be presented and discussed. For the pure fluids results, a parametric analysis will be done to find the parameter that most influences the performance of this family of fluids. All thermodynamic fluids proper ties used in this study and all Ts diagrams presented in this work were taken from REFPROP 9 a software developed by NIST. This software is often encountered in studies of ORC plants [6–9].

ORGANIC RANKINE CYCLE

In a thermodynamic point of view, the organic Rankine cycle is identical to the conventional Rankine cycle. It consists of four elementary transformations which are: isentropic compression which takes place in a pump, an isobaric heating accompanied by an evaporation which takes place in an evaporator, an isentropic expansion which takes place in the turbine and an isobaric cooling accompanied by a condensa tion which takes place in the condenser.

The working fluid used in the classic Rankine cycle is water. The use of water has several problems, which are:

—The turbines used are complex and therefore expensive;

A Study of Organic Working Fluids of an Organic Rankine Cycle for Solar Concentrating Power Plant ¹

D. Saifaoui

, Y. Elmaanaoui

, and A. Faik

aDepartment of Physics, Faculty of Sciences Ain Chock, University of Hassan II Casablanca, Morocco

bResearch Institute of Solar Energy and New Energy, Rabat, Morocco email: ddsaifaoui@gmail.com

Received January 06, 2014

Abstract—This work is a comparative study between four different configurations of an organic Rankine cycle (ORC) in order to find the configuration that gives the best performances. This study also made a com parison between seven organic fluids used as working fluids in the four ORC configurations. These fluids are all hydrocarbons. Then we made a parametric analysis of the results obtained in this first part. In a second part, we developed the binary mixtures of the seven pure hydrocarbons with the NIST software REFPROP 9 and we used them in our four ORC configurations. The obtained results are given and discussed.

DOI: 10.3103/S0003701X14030128

SOLAR

ENGINEERING

—Partial condensation at the end of the expansion which causes erosion of the turbine’s blades [10];

—To avoid the partial condensation a superheater is used [10]. This increase the hot source temperature;

—Working with water requires working with high pressures [11];

—The use of water only allows the installation of large power plants.

The use of organic fluids instead of water allows avoiding these problems. Indeed, the organic fluids allow the installation of plants of some kW up to some MW [12]. Also, they allow the exploitation of low tem perature heat sources [6, 7, 13]. At the end of the expansion, organic fluids are still hot, that not only helps to prevent partial condensation but also to har ness this hot vapor in a regenerator [11].

Organic Fluids

Many organic fluids have been used in the ORC plants. This number has come down to 50 fluids [13].

The choice of the working fluid is based on several parameters. These parameters are discussed in the fol lowing sections.

Fluids types. A distinction between three types of fluids is made according to the sign of the slope of the saturation curve in the T–s diagram. Since the slope dT/ds can tend to infinity we calculate its reverse ds/dT. The three possible cases are: if ds/dT < 0 we speak about a wet fluid such as water; if ds/dT > 0 we speak about a dry fluid such as nonane; if ds/dT = 0 we speak about an isentropic fluid such as R11. These cases are summarized in Fig. 2.

At the end of the expansion of wet fluid partial con densation occurs, this doesn’t occur for the other two types. In ORC plants, dry and isentropic fluids are used.

Natural

Cool/peat

12 717 Mtoe 6 107 Mtoe

Oil 46.1%

24.6%

Other*

0.1%

Biofuels and waste

10.5%

Hydro 1.8%

Nuclear 0.9%

gas 16.0%

Oil 32.4%

1973 2010

Cool/peat 27.3%

Other*

0.9%

Biofuels and waste

10.0%

Hydro 2.3%

Nuclear 5.7%

Natural gas 21.4%

Fig. 1. Evolution and distribution of global energy consumption in 1973 and 2012 [1].

400 300 200 100 0

3 6 9

Entropy, kJ/kg K

Temperature, °C

400 300 200 100

–1 0 2

Entropy, kJ/kg K

Temperature, °C

400 300 200 100

0 1 2

Entropy, kJ/kg K

Temperature, °C

0

–2 1

Fig. 2. Three types of the working fluids: wet (water), dry (nonane) and isentropic (R11).

Critical and solidification temperatures. The cho sen working fluid must allow the condensation and evaporation to occur. For this, the solidification tem perature must be smaller than that of condensation and the critical temperature must be higher than that of evaporation.

Chemical properties. Unlike water, organic fluids suffer from chemical deterioration and decomposition at high temperatures [14]. So, the highest temperature of the cycle is limited by the decomposition limit of the fluid temperature.

The organic fluid used must not be corrosive, and must be compatible with the material constituting the various components of the installation. Also, the fluid must not be toxic or flammable.

Environmental aspect. Regarding the environmen tal aspect one should pay attention to three key param eters which are: the potential to deplete the ozone layer (ODP), the global warming potential (GWP) and life in the atmosphere (ALT) [13].

Chosen fluids in this study. In this study we have set a condensation temperature of 40 ° C and an evaporation temperature of 260 ° C to make the choice of our hydro carbons. However, some hydrocarbons that met these

two conditions showed very low pressures at 40 ° C, this has led us to establish a minimum condensing pressure of 0.01 bars. At the end, we selected seven hydrocarbons that meet our requirements; these fluids as well as some of their parameters are shown in Table 1.

The Different Cycle Configurations

In this study we have chosen to work with four dif ferent configurations of the organic Rankine cycle in order to find the best one. The thermodynamic cycles of the four configurations are given in Fig. 3.

The first configuration uses the simple cycle. It consists of the four basic transformations which have already been discussed. The installation in this case consists of a pump, a turbine, a condenser and an evaporator, Fig. 4a. The second configuration is iden tical to the first one in the thermodynamic cycle. The difference between the two lies in the introduction of a regenerator between the turbine and the condenser.

This is done to use the energy contained in the vapor that comes out from the turbine to warm up the work ing fluid (liquid) compressed and before introducing it into the evaporator, Fig. 4b. The third configuration differs from the simple cycle by the superheating that

Fluid name CAS N° Chemical

formula Tc, °C Condensation pressure

at 40°C, bar Molar mass, kg/m³

Toluene 108883 C₇H₈ 318.6 0.078923 92.138

Benzene 71432 C₆H₆ 288.87 0.24389 78.112

Cyclohexane 110827 C₆H₁₂ 280.49 0.24646 84.161

Methyl cyclohexane 108872 C₇H₁₄ 299.05 0.12203 98.186

Nonane 111842 C₉H₂₀ 321.4 0.014136 128.26

Octane 111659 C₈H₁₈ 296.17 0.041263 114.23

Propyl cyclohexane 1678928 C₉H₁₈ 357.65 0.013266 126.24

400

200

0

–1 0 1

Entropy, kJ/kg K

Temperature, °C

–2 2

1 2

3 4 2 '

4 '

400

200

0

–1 0 1

Entropy, kJ/kg K

Temperature, °C

–2 2

1 2

3 4 2 '

4 '

3 '

Fig. 3. Simple cycle and cycle with regenerator (left) cycle with superheater and cycle with regenerator and superheater (right).

takes place after the end of the evaporation. A super heater in this configuration is inserted between the evaporator and the turbine; Fig. 4c. The fourth and final configuration uses the previous two modifica tions at the same time. A superheater in this configu ration is inserted between the evaporator and the tur bine and a regenerator is inserted between the turbine and the condenser; Fig. 4d.

The Modeling Equations

For the design of the four installations it is neces sary to take into consideration the efficiencies of the equipment used. We took the most encountered effi ciencies in the literature. These efficiencies are sum marized in Table 2.

The isentropic efficiency of the pump reflects the fact that the compression of the working fluid is not isentropic; the pump will consume more energy in the real case to arrive at the same pressure as in the theo retical case. Similarly, the isentropic efficiency of the turbine reflects the fact that the expansion of the work ing fluid is not isentropic, this expansion will provide less work in the real case as in the theoretical case.

The role of the pump is to ensure the compression of the working fluid from the low pressure to the high pressure. This is done by receiving a work; this work received is equal to:

(1) In the turbine occurs the expansion of the working fluid which drops from the high to the low pressures.

This is accompanied by a delivering of a work. The work provided is equal to:

(2) In the evaporator occurs the preheating of the com pressed working fluid to the evaporation temperature.

w

= w

= m·

( h

– h

) with h

h

( h

– h

)

η

.

+

=

w

= m·

( h

– h

) with h

= h

– ( h

– h

)η

,

Then the preheated fluid undergoes evaporation. The amount of heat exchanged with the heat source is equal to:

(3) In the condenser occurs the cooling of the expanded working fluid in the turbine to the conden sation temperature. Then the cooling fluid undergoes condensation. The amount of heat exchanged with the cold source is equal to:

(4) The amount of heat that is rejected by the working fluid during cooling and before condensation is used by the regenerator to warm up the working fluid that leaves the pump. This amount of heat is equal to:

(5) In the case where we add a superheater it absorbs a quantity of heat equal to:

(6) The efficiency expression for the four configura tions of the cycle remains the same; it’s equal to:

(7) However, the expressions of the turbine work (w

) and the amount of the heat absorbed differ from a con figuration to another. Table 3 gives these expressions for the four configurations.

Q

= m·

( h

– h

) .

Q

= m·

( h

– h

) .

Q

= m·

( h

– h

) = Q

= m·

( h

– h

) .

Q

= m·

( h

– h

) .

η w

– w

Q

= .

(a)

regenerator superheater

Evaporator

Turbine Pump

Condenser

Cycle with regenerator and superheater

(d)

Cycle with superheater (c)

Cycle with superheater

(b)

Cycle simple 1

2 ' 3

4 1

1 1

2 '' 3

2 4

Turbine superheater Evaporator

regenerator Pump

2

Condenser

4 '

Condenser Pump 2

2'

3

4

Turbine

Turbine Evaporator Evaporator

2 2 ' 3

4

Pump Condenser

Fig. 4. The four studied ORC configurations.

Table 2. Components efficiencies

Generator efficiency 0.95

Turbine efficiency 0.75

Isentropic efficiency of the turbine 0.8 Isentropic efficiency of the pump 0.8

4 '

RESULTS AND DISCUSSIONS

The equations we just discussed have been intro duced to an Excel sheet that will serve as a model for the comparison between the four configurations of the cycle, between the seven pure fluids and between there binary mixtures.

In this study we chose to work with a condensing temperature of 40 ° C, an evaporation temperature of 260 ° C and the maximum superheating temperature is 300 ° C.

Pure Fluids Case

Obtained results. The efficiencies recorded by the seven pure fluids in the four configurations were sum marized in Table 4. Benzene showed the highest effi ciencies in the case of Simple cycle (16.82%) and cycle with superheater (16.93%). Nonane recorded the

worst performance in these two configurations (simple cycle: 13.71% cycle with superheater: 13.18%). On the other hand, propylcyclohexane recorded the best returns in the case of cycle with regenerator (21.86%) and cycle with regenerator and superheater (23.31%).

And benzene showed the worst performance in these two configurations (cycle with regenerator: 19.33%

cycle with regenerator and superheater: 21.56%).

The difference between the maximum and mini mum efficiencies of the seven fluids for the simple cycle was 3.11%, for the cycle with superheater was 3.75%, for the cycle with regenerator was 2.53% and it was 0.96% for the cycle with regenerator and super heater; the seven fluids had efficiencies close to each other in the configuration of the cycle with regenerator and superheater.

The best efficiencies of the seven fluids were all recorded in the configuration of the cycle with regen erator and superheater, which is the best of the four configurations. Table 5 shows the efficiency gains we have achieved with the introduction of each modifica tion to the simple cycle.

The first observation to make is that the super heater decreases the efficiency of fluids (except ben zene) this confirms the work [1]. The other two changes have increased the efficiency of the seven flu ids. Increases in efficiency were very large with the introduction of the regenerator and superheater, the biggest gain was recorded by nonane in this configura

the heat absorbed in the four configurations

Configuration W_t Q_absorbed

Simple cycle W₃₄ Q₂₃

Cycle with superheater W_3'4 Q_23' Cycle with regenerator W₃₄ Q_2''3 Cycle with regenerator and superheater W_3'4 Q_2''3'

Table 4. Results obtained for the seven fluids in the four ORC configurations Cycle efficiency in % fluid name fluid number simple with

superheater

with regenerator

with regenerator and superheater

Toluene 1 16.66 16.52 20.47 22.25

Benzene 2 16.82 16.93 19.33 21.56

Cyclohexane 3 15.27 14.98 19.88 22.35

Methyl cyclohexane 4 14.55 14.09 21.10 22.92

Nonane 5 13.71 13.18 21.51 23.02

Octane 6 13.72 13.23 21.08 22.83

Propyl cyclohexane 7 14.32 13.75 21.86 23.31

Table 5. Results obtained for the seven fluids in the four ORC configurations Gain in efficiency made

by superheater

Gain in efficiency made by regenerator

Gain in efficiency made by regenerator and superheater

Toluene –0.14 3.81 5.59

Benzene 0.11 2.51 4.74

Cyclohexane –0.29 4.61 7.08

Methyl cyclohexane –0.46 6.55 8.37

Nonane –0.53 7.8 9.31

Octane –0.49 7.36 9.11

Propylcyclohexane –0.57 7.54 8.99

tion and has reached to 9.31%. The two curves of Fig. 5 show the analysis of the gains made by each modification depending on ds/dT. In the cases of the cycle with regenerator and the cycle with regenerator and superheater it’s clear that the bigger ds/dT is the bigger the gain in efficiency that a fluid will make is.

Also, for the same ds/dT, the gain achieved by regen erator and superheater is always greater than that achieved by regenerator only. In the case of the cycle with superheater, the efficiency losses increase as ds/dT increases.

Parametric analysis of the results. In this section we propose to analyze the results obtained in the previous section based on four parameters that are temperature, pressure and density of the critical point and ds/dT.

The values of these parameters for the seven fluids sub jects of this study are given in Table 6.

In case these parameters are not sufficient to make a correct interpretation of the results other parameters will be used. Figures 6, 7, 8 and 9 show the results of the analysis that has been made.

10 8 6 4 2

4.0 3.0 2.0 ds/dT in J/K² kg 1.0

0

Cycle with regenerator and superheater Cycle with regenerator

Gain in efficiency in %

1 2

3 4

5 7 6

0.2 0.1 –0.2 –0.3 –0.5

4.0 3.0

2.0 ds/dT in J/K² kg 1.0

Gain in efficiency in %

1 2

3

4 6 5 7 1

2

3 4 7 6 5

1E–15 –0.1 –0.4 –0.6 –0.7 0

Fig. 5. Variation of the gain in efficiency with ds/dT for the cycles with regenerator and with regenerator and superheater (left) and for the cycle with superheater (right).

Table 6. Parameters for the results analysis

Fluid Tc, °C Pc, bar Dc, kg/m³ ds/dT, J/kg K²

Toluene 318.600 41.263 291.99 1.155

Benzene 288.87 49.063 304.79 0.635

Cyclohexane 280.49 40.75 273 1.573

Methyl cyclohexane 299.05 34.7 267.07 2.316

Nonane 321.4 22.81 232.14 3.026

Octane 296.17 24.97 234.9 2.85

Propyl cyclohexane 357.65 28.6 260.05 2.745

17 16 15 14 13

350 300

Temperature in °C 250

Efficiency in %

5 2 1 3

4 7

6 18

Efficiency depending on Tc 17 16 15 14 13

55 35

Pressure in bar 15

Efficiency in %

5

1 2

3 7 4 6 18

Efficiency depending on Pc 17 16 15 14 13

320 270

Density in kg/m³ 220

Efficiency in %

5

1 2 3 4 7 6 18

Efficiency depending on Dc 17 16 15 14 13

2.0 ds/dT in J/kg K² 0

Rendement en %

5 2 1

3 4 7

6 18

Efficiency depending on ds/dT

Fig. 6. Analysis results of the simple cycle.

First, we can give two major observations: the first is that the seven fluids had a similar behavior in the simple cycle and in cycle with superheater in one hand, and in the cycle with regenerator and cycle with regenerator and superheater in another hand. The second observation is that for the seven fluids in the four configurations, the temperature was not a good parameter to have a clear idea on the behavior of these fluids.

For the simple cycle and the cycle with super heater, a fluid will have a good efficiency if he has a big critical pressure and critical density and a low ds/dT.

For the cycles with regenerator and with regenerator and superheater, the fluids followed the inverse law that they followed in the two first configurations; the efficiency of a fluid is good if his critical pressure and density are low and his ds/dT is big. However, the alignment of the fluids in these two configurations are

16 15 14 13

350 300

Temperature in °C 250

Efficiency in %

5 2 1 3

4 7

6 18

Efficiency depending on Tc

17 16 15 13

55 35

Pressure in bar 15

Efficiency in % 5

1 2 3 7 4 6 18

Efficiency depending on Pc 17 16 15 14 12

320 270

Density in kg/m³ 220

Efficiency in % 5

1 2 3 4 7 6 18

Efficiency depending on Dc

17 16 15 14 12

4 2

ds/dT in J/kg K² 0

Efficiency in % 5

2 1 3

4 7 6 18

Efficiency depending on ds/dT

14 12

13 13

Fig. 7. Analysis results for the cycle with superheater.

21.5 21,0 20.5 20.0

350 300

Temperature in °C 250

Efficiency in %

5 1 2 3

4

7 6

22.0

Efficiency depending on Tc 21.5 21.0 20.5 20.0 19.0

55 35

Pressure in bar 15

Efficiency in %

5

1 2 3 4

7 6 22.0

Efficiency depending on Pc 21.5 21.0 20.5 19.5 19.0

320 270

Density in kg/m³ 220

Efficiency in %

5

1 2 3 4

7 6 22.0

Efficiency depending on Dc

21.5 21.0 20.5 20.0 19.0

2 ds/dT in J/kg K² 0

Efficiency in %

5 1

2 3

4 7

6 22.0

Efficiency depending on ds/dT

19.5 19.0

19.5

20.0

19.5

Fig. 8. Analysis results for the cycle with regenerator.

23.0 22.5 22.0 21.5 21.0

320 Temperature in °C 270

Efficiency in %

5 1 2 3

4 7

6 23.5

Efficiency depending on Tc

23.0 22.5 22.0 21.5 21.0

55 35

Pressure in bar 15

Efficiency in %

5

1 2 3 4 7 6 23.5

Efficiency depending on Pc

23.0 22.5 22.0 21.5 21.0

320 270

Density in kg/m³ 220

Efficiency in %

5

1 2 3 4 7 6 23.5

Efficiency depending on Dc

23.0 22.5 22.0 21.5 21.0

2 ds/dT in J/kg K² 0

Efficiency in %

5 1

2 3

4 7

6 23.5

Efficiency depending on ds/dT

Fig. 9. Analysis results for the cycle with regenerator and superheater.

not as good as in the first two configurations analyzed, especially nonane and octane who are not on the same line as the other fluids. In this case we had to use other parameters to have a clearer view on the behavior of our hydrocarbons in the last two configurations. The results obtained using the pressure difference between the inlet and outlet of the turbine as the analysis parameter was the most satisfying, these results are given in Fig. 10.

For both configurations it is clear that a given fluid has a high performance if he has a small pressure dif ference between the inlet and the outlet of the turbine.

Mixtures Case

After using the seven hydrocarbons such working fluids in the four configurations of the organic Rank ine cycle, we are now interested in their binary mix tures. Always using the software REFPROP 9 we developed binary mixtures of the seven pure fluids used in the first part, it gave us 21 mixtures. Each mix ture will be used as working fluid in the four configura tions of the ORC installation. Furthermore, for each configuration the composition of the mixture will be varied with an increment of 10%. The Table 7 gives an example of calculation done for the mixture of ben zene and methyl cyclohexane.

Tables like this were made for the 21 mixtures which allowed us to make our comparison. In total, we calculated 756 efficiencies (21 mixtures, 9 composi tions for each mixture and 4 cycle configurations). The best efficiencies for each mixture and in the four con figurations are shown in Table 8.

The best performance in the case of simple cycle (18.56%) was recorded by the mixtue of benzene and propylcyclohexane at the composition of 70–30%.

This same mixture showed the best performance in the case of the cycle with superheater (18.34%) at the composition of 80–20%.

The best performance in the case of the cycle with regenerator (23.47%) was recorded by the mixture of cyclohexane and propylcyclohexane at the composi tion of 50–50%. This same mixture showed the best performance in the case of the cycle with superheater and regenerator (25.24%) at the composition of 60–

40%.

By the 84 maximum efficiencies of the 21 mixtures analyzing we found that in 69.05% of the cases, the maximum efficiency of a given mixture was greater than the efficiencies of the two pure fluids which con stitute this mixture.

As in the case of pure fluids, the fact of adding a superheater to the simple cycle in the case of mixtures lowers their efficiencies. Only in 7 of 756 cases effi ciency increased.

The largest drop in efficiency due to superheater is equal to 0.63% recorded by the mixture of benzene and propylcyclohexane. The other two modifica tions, as for pure fluids, have increased mixtures effi ciencies. The largest increase was 9.31% recorded by the mixture of octane and nonane.

21.0 20.5 20.0 19.5 19.0

40 20

Pressure in bar 0

Efficiency in %

5 1

2 3 4 7

21.5 6

30 10

22.0

23.0 22.5 22.0 21.5 21.0

40 20

Pressure in bar 0

Efficiency in %

5 1

2 3 7 4

6

30 10

23.5

Fig. 10. Analysis results for the cycles with regenerator (left) and with regenerator and superheater (right) depending on the pressure difference between the inlet and the outlet of the turbine.

Table 7. Results obtained and gain achieved for the benzene and methylcyclohexane mixture

Efficiency in % for the cycle: Gain made by each modification % mixture

composition simple with regenerator

with superheater

with regenerator and superheater

gain by regenerator

gain by super

heater

gain by regener ator and super

heater

b10/mch90 14.87 21.04 14.44 22.9 6.17 –0.43 8.03

b20/mch80 15.17 20.94 14.78 22.85 5.77 –0.39 7.68

b30/mch70 15.44 20.79 15.09 22.75 5.35 –0.35 7.31

b40/mch60 15.67 20.61 15.38 22.63 4.94 –0.29 6.96

b50/mch50 15.88 20.4 15.64 22.46 4.52 –0.24 6.58

b60/mch40 16.06 20.16 15.89 22.28 4.1 –0.17 6.22

b70/mch30 16.23 19.92 16.14 22.09 3.69 –0.09 5.86

b80/mch20 16.4 19.69 16.39 21.9 3.29 –0.01 5.5

b90/mch10 16.58 19.48 16.65 21.72 2.9 0.07 5.14

The fact of using mixtures instead of pure fluids is very beneficial. Indeed, the maximum efficiencies recorded in the case of mixtures are significantly higher than those recorded in the case of pure fluids.

The difference in the maximum efficiencies reached 1.93% in the case of the cycle with superheater and regenerator. Table 9 shows the maximum efficiencies in the case of mixtures and the case of pure fluids.

It may be noted that for 15 of the 21 mixtures, or 71.43% of the cases, the composition of the mixture which gives the greatest efficiency in simple cycle also gives the greatest efficiency in the cycle with super heater. And for 16 of the 21 mixtures, or 76.19% of the cases, the composition of the mixture which gives the

greatest efficiency in the cycle with regenerator also gives the greatest efficiency in the cycle with super heater and regenerator.

CONCLUSIONS

This study showed that adding a superheater to the simple cycle decreases its efficiency as opposed to add ing a regenerator or a regenerator and superheater.

Configuration of the cycle with regenerator and super heater recorded the best efficiencies for the seven pure fluids and for 21 mixtures; this is the best of the four configurations studied. The best gain in efficiency we have achieved with this configuration has reached 9.31% for pure fluids and for mixtures.

Table 8. The best efficiencies obtained for each mixture

Simple cycle Cycle with superheater Cycle with regenerator Cycle with superheater and regenerator

mixture efficiency

% mixture efficiency

% mixture efficiency

% mixture efficiency

%

t40/b60 17.18 t30/b70 17.2 t90/b10 20.47 t70/b30 22.32

t90/ch10 16.62 t90/ch10 16.47 t90/ch10 20.46 t30/ch70 22.7

t90/mc10 16.5 t90/mc10 16.32 t10/mc90 21.04 t10/mc90 22.86

t90/n10 16.54 t90/n10 16.31 t40/n60 22.29 t40/n60 23.84

t90/o10 16.37 t90/o10 16.16 t30/o70 21.29 t30/o70 22.97

t80/pch20 16.77 t90/pch10 16.52 t30/pch70 22.26 t40/pch60 23.8

b90/ch10 16.65 b90/ch10 16.72 b20/ch80 20.08 b10/ch90 22.36

b90/mch10 16.58 b90/mch10 16.65 b10/mch90 21.04 b10/mch90 22.9

b70/n30 18.27 b80/n20 17.98 b50/n50 23.34 b50/n50 24.99

b80/o20 16.85 b90/o10 16.81 b30/o70 21.91 b30/o70 23.64

b70/pch30 18.56 b80/pch20 18.34 b50/pch50 23.09 b50/pch50 24.77

ch90/mch10 15.28 ch90/mch10 14.96 ch10/mch90 21.05 ch10/mch90 22.92

ch80/n20 17.08 ch80/n20 16.59 ch60/n40 23.2 ch60/n40 25

ch80/o20 15.77 ch80/o20 15.35 ch50/o50 21.76 ch50/o50 23.66

ch70/pch30 17.41 ch70/pch30 16.86 ch50/pch50 23.47 ch60/pch40 25.24

mch80/n20 15.63 mch80/n20 15.08 mch70/n30 22.64 mch70/n30 24.32

mch80/o20 14.75 mch80/o20 14.26 mch70/o30 21.53 mch70/o30 23.3

mch70/pch30 15.77 mch70/pch30 15.19 mch50/pch50 22.97 mch50/pch50 24.57

n40/o60 13.98 n40/o60 13.46 n60/o40 21.65 n60/o40 23.24

n10/pch90 14.24 n10/pch90 13.68 n10/pch90 21.83 n10/pch90 23.28

o20/pch80 14.36 o30/pch70 13.79 o30/pch70 21.96 o30/pch70 23.46

Table 9. Maximum efficiencies for mixture and for pure fluids cases

Simple cycle Cycle with superheater Cycle with regenerator Cycle with regenerator

Mixture case 18.56 18.34 23.47 25.24

Purefluids case 16.82 16.93 21.86 23.31

Difference 1.74 1.41 1.61 1.93

The best performance was recorded by nonane (23.31%) in the case of pure fluids and the mixture of cyclohexane and propyl cyclohexane (25.24%) in the case of mixtures. Maximum efficiencies recorded by the mixtures were larger than those of pure fluids; this proves the importance of working with mixtures instead of pure fluids. In addition, this study showed that the efficiency of a mixture has a 69.05% chance of being greater than the efficiencies of the two pure flu ids which constitute this mixture.

The parametric analysis of efficiencies achieved by pure fluids showed that these fluids behave similarly in the case of simple cycle and the cycle with super heater in one hand, and in the case of the cycle with regenerator and cycle with regenerator and super heater on the other hand. The critical temperature is not a good parameter to have a clear idea on the behavior of fluids in the four configurations.

The law that followed the pure fluids in the case of the simple cycle and the cycle with superheater is reversed in the two other cases. Indeed, for the first two configurations fluids that have big critical pressure and density and a low ds/dT will have high efficiencies and the opposite thing will happen in the two last configu rations.

In the case of the cycles with regenerator and with regenerator and superheater the analysis results were not very satisfying. For both configurations another parameter was added to do the analysis which was the pressure difference between the inlet and the outlet of the turbine. The obtained results with this parameter were much more satisfying. Fluids that have this dif ference small have the best efficiencies.

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