2003-exergy analysis of renewable energy sources

7/29/2019 2003-Exergy Analysis of Renewable Energy Sources

1/16

Renewable Energy 28 (2003) 295310

www.elsevier.com/locate/renene

Exergy analysis of renewable energy sources

Christopher Koroneos *, Thomas Spachos,Nikolaos Moussiopoulos

Laboratory of Heat Transfer and Environmental Engineering, Aristotle University Thessaloniki, 54006

Thessaloniki, Greece

Received 13 March 2001; accepted 22 May 2001

Abstract

Oil crises in the past years made more obvious the dependency of economies on fossil fuels.As a consequence, the need for new energy sources became more urgent. Renewable energysources could provide a solution to the problem, as they are inexhaustible and have less adverse

impacts on the environment than fossil fuels. Yet, renewable energy sources technology hasnot reached a high standard at which it can be considered competitive to fossil fuels. Thepresent study deals with the exergy analysis of solar energy, wind power and geothermalenergy. That is, the actual use of energy from the existing available energy is discussed. Inaddition, renewable energy sources are compared with the non-renewable energy sources onthe basis of efficiency. 2002 Published by Elsevier Science Ltd.

Keywords: Exergy; Renewable energy sources; Environment

1. Introduction

As fossil fuels such as oil and coal are being depleted, the need for using renewableenergy sources (RES) is becoming more and more urgent. Support for this viewbecomes greater as RES technologies, besides being beneficial for the environment,become economically sustainable.

The present study makes use of the concept of exergy for the analysis of RES,in addition to the energy analysis, which is based on the first law of thermodynamicsand which provides a qualitative evaluation of the losses in the different components

* Corresponding author. Tel.: +30-31-995968; fax: +30-31-996012.

E-mail address: [email protected] (C. Koroneos).

0960-1481/03/$ - see front matter 2002 Published by Elsevier Science Ltd.

PII: S 0 9 6 0 - 1 4 8 1 ( 0 1 ) 0 0 1 2 5 - 2


2/16

296 C. Koroneos et al. / Renewable Energy 28 (2003) 295310

of the system. The exergy analysis, based on the second law of thermodynamics,

provides a clearer view of the energy losses in the system, as it presents quantitative

and qualitative evaluation of the different losses.

2. The exergy concept

Exergy is defined as:

Exergy is the property of the system, which gives the maximum power that

can be distracted from the system, when it is brought to a thermodynamic equilib-

rium state from a reference state [1].

The exergy transfer can be associated with mass flow, with work interaction andwith heat interaction [2]. Dynamic and kinetic exergy are two more forms of exergy

that exist in RES technology.

The exergy associated with heat interaction is given by the equation [3]:

EA

TT0T Qi dA, (1)

where A is the heat exchange surface, T0 is the ambient temperature, Tis the tempera-

ture at which the heat transfer takes place and Qi is the heat transfer rate.

The exergy associated with mass flow is divided to chemical, physical and mixingexergy. Chemical exergy is given by [4]:

Ex0chem,in

j1

vjExchem,refjrG0i , (2)

where vj is the specific volume of the jth component and rG0i is the reaction exergy

so as to bring the component to the reference state, and is equal to the standard

Gibbs energy change. n is the number of components and 0 is the reference condition.

Physical exergy, which is defined as the work obtained when the working fluidis brought from the reference condition to the ambient condition, is given by:

Exphysactual0 F n

i1

xiHFiT0

n

i1

xiSFi G

n

i1

xiHGi T0

n

i1

xiSGi , (3)

where H is the enthalpy, S is the entropy and x the molar ratio of the ith component.

F refers to the liquid phase whereas G refers to the vapor phase, as changes in

composition may occur.

Finally, mixing exergy, which has always a negative value, may be calculated

using algorithms for the mixing enthalpy and entropy:

ExmixmixHT0mixS. (4)


3/16


4/16


Fig.

1.

Sketchof

asolarpowersystem.


5/16

299C. Koroneos et al. / Renewable Energy 28 (2003) 295310

nbWnet/Exlu, (9)

where Wnet is the net work produced by the heat exchanger and Exlu is the available

exergy of the working fluid of the heat engine cycle. It is given by the equation:ExluQu[1T0/TR0], (10)

where Qu is the useful transferred heat and TR0 is the ambient temperature of the

Rankine cycle.

The total efficiency of the system is the product of the two separate efficienciesof the subsystems:

ntotWnet/Exi. (11)

Table 1 presents numerical data from the exergetic analysis of the system. Thefirst column gives the input exergy of each component, while the second columngives the output exergy. The difference between the input exergy and the output

exergy is the exergy loss, which is presented in the third column. The fourth column

gives the % exergy loss:

ExlossExinExout

Exin100%.

Finally, the fifth column gives the efficiency of each component based on the secondlaw of thermodynamics:

nExout

Exin100%.

Fig. 2 presents the exergy losses occurring in the different components of the sys-

tem.

As can be seen from the results, the exergy losses in the collectorreceiver subsys-

Table 1

Exergetic analysis of a solar thermal power system [5]

Subsystem Exergy received Exergy Exergy loss Exergy loss Second law

(kW) delivered (kW) (kW) (%) ef ficiency

(1) (2) (3) (4) (5)

Collector Exi=270.82 Exc=78.82 I1=192.19 70.96 29.03

Receiver Exc=78.82 Exu=53.768 I2=24.862 31.618 68.38

Collector Exi=270.82 Exu=53.768 I1,2=217.05 80.146 19.854

receiver

Boiler heat Exu=53.77 Exu=51.845 Ihx=1.92 3.577 96.424

exchanger

Heat engine Exlu=51.845 W=34.511 I3=17.334 33.434 66.566

Total system Exi=270.82 W=34.511 I=236.30 87.254 12.743


6/16


Fig. 2. Losses in the different components of the solar power plant.

tem have the greatest value. An energetic analysis would show that the percentageenergy lost in the heat engine subsystem (72.37%) is greater than that lost in thecollectorreceiver subsystem (56.30%) [5]. The high exergy losses in the collectorreceiver subsystem are due to the fact that the lost energy is of great quality in this

subsystem, while in the heat engine subsystem the lost energy is of low quality.

2.2. Exergetic analysis of wind power systems

The efficiency of a wind turbine depends on its type (i.e., if it is of horizontal orvertical axis), on the rotor diameter and on the wind speed.

Wind turbines are classified according to their nominal power. Table 2 represents

Table 2

Power produced (kW) from three wind turbines for different wind speeds [6]

Wind speed (m/s) Turbine type

600 kW/48 m 750 kW/48 m 1 MW/60 m

5 52 48 86

6 93 95 150

7 153 168 248

8 235 259 385

9 329 362 535


7/16


8/16


Fig. 4. Change of the produced power per rotor surface for three different wind turbines, in relation to

the wind speed change.

Fig. 5. Utilization of the winds potential in relation to the wind speed.

is given by the product 1/2rv3, where r is the density of the wind, which is takenequal to 1.225 kg/m3, and v is the wind speed.

It is understandable that wind turbines cannot take advantage of the total power

of the wind (Figs. 5 and 6). According to Betzs law, wind turbine can take advantageof up to 60% of the power of the wind. Nevertheless, in practice, their efficiency isabout 40% for quite high wind speeds. The rest of the energy density of the wind


9/16


Fig. 6. Exergy losses in the different components of a wind turbine.

not obtainable is exergy loss. This exergy loss appears mainly as heat. It is attributed

to the friction between the rotor shaft and the bearings, the heat that the cooling

fluid abducts from the gearbox, the heat that the cooling fluid of the generator abductsfrom it and the thyristors, which assist in smooth starting of the turbine and which

lose 12% of the energy that passes through them.

2.3. Exergy analysis of geothermal power systems

Geothermal steam can be used for electricity production (Fig. 7).

The geothermal fluid (point 1) expands directly in the turbine T, producing workthat is partially needed for the movement of the two compressors of non-condensed

steam. Point 2 is the end of the expansion and is determined by the conditions

imposed in the first mixing condenser M1. Its working pressure is much lower thanatmospheric in order to maximize the produced work. A saturated mixture of CO2steam exits from the top of the condenser (point 3), while the condensed steam exits

from the bottom (point 2w) at the same pressure. The CO2steam mixture is com-pressed and then it is sent to another mixing condenser M2 (point 4) which worksat a higher pressure. The uncondensed substances exit from the top of the second

compressor (point 5) and are disposed to the environment (point 6). The water leav-

ing the second condenser (point 3w) is mixed with the water coming from the firstcondenser and the mixture is pumped to the cooling tower (point 5w). The cooling

water is then re-entered in the mixing condensers and the redundant water is disposed

in the reservoir [7].

The specific exergy (ex) of a fluid is [8]:

ex

i yi(hi

h0i)

T0i yi(si

s0i)

i yiex

ch

i

RT0i y

i ln(giyi), (12)

where y is the molar ratio, h is the enthalpy, T0 is the ambient temperature, s is the


10/16


Fig. 7. Sketch of a geothermal power plant. T: turbine, A: alternator, C1: first compressor, C2: second

compressor, M1: first mixing condenser, M2: second mixing condenser, P: pump, CT: cooling tower.

entropy, R is the gas constant and g is the chemical reactivity coefficient. Thesubscript i refers to the component, the subscript 0 refers to the ambient conditions

and exchi is the chemical exergy of the ith component.

In order to calculate the exergy, the reference condition of each chemical substance

is considered to be at the temperature of 25C and pressure of 1 atm. The evaluation

of exergy losses can be compared with the indirect evaluation of losses, which is

the output exergy minus the input exergy. The exergy loss in our system is:

exergy lossm1{ex1exair(P0, T0)}W, (13)

where m1 is the mass flow rate at point 1, ex1 is the exergy of the geothermal fluidat point 1, exair(P0, T0) is the exergy of the air at ambient conditions and W is the

produced work.

Finally, the efficiency of the geothermal plant is defined as the ratio of the pro-duced power to the exergy of the input geothermal fluid. That is:

nxW

m1{ex1exair(P0, T0)}. (14)

Table 3 presents the results of the exergy analysis for the geothermal power plantunder consideration.

Exergy losses in different components of the system are depicted in Fig. 8.


11/16


Table 3

Power and losses of a typical geothermal plant in Larderello area [7]

Power

a

(kW) Losses

a

(kW) Losses

b

%

Turbine 55,805 12,011 21.52

First compressor 1367 286 2.96

Second compressor 873 171 1.87

Mixing and feed pump 773 312 1.94

Cooling tower 960 7593 20.36

First condenser 7800 13.98

Second condenser 457 1.76

Second condenser disposal stage 526

Cooling tower disposal stage 2809

Total 51,832 31,965

a Produced power is positive while consumed power is negative.b Power losses plus other losses divided by the turbine power.

Fig. 8. Losses in the different components of a geothermal power plant.

3. Comparison between renewable and non-renewable energy sources

An important difference between RES and fossil fuels lies in the fact that renew-

able energy sources are inexhaustible and of low or zero economic value before

being converted to a useful form. Only their cost restricts the device that is necessaryfor the collection of energy, e.g., construction of the network for the collection of

solar radiation [9].


12/16


13/16


Fig. 10. Net energy produced by renewable and non-renewable energy systems as a function of time

from the start of the plant construction.

Table 4

Net energy converted in relation to the energy invested on main energy systems [9 11]

Efficiency 1a (%) Ef ficiency 2b (%)

Solar thermal 25 52

Natural gas and oil 20 48

Lignite 34

Nuclear cracking 10

Solar electric 3 12.75

Wind electric 39

Geothermal 35.6

Sources: Slesser M, Hounam I. Solar energy breeders. Nature 1976;244:262 and Koening H. Personal

communication, 1980.a Efficiency 1=(Net produced energy/Energy invested)100%.b Efficiency 2=(Output energy/Input energy)100%.


14/16


tioned is that the plants shown in Table 4 have the same life period. In fact, the

lifetime of systems using RES is greater than that of systems using fossil fuels.

The results are presented in graphical form in Figs. 11 and 12.

The basics used for comparison of these systems is the price per produced energyunit in useful form. With this calculation system, the future value of non-renewable

energy sources is reduced.

4. Conclusion

This work deals with three different kinds of system that use renewable energy

sources as input. Specifically, it deals with systems that use solar energy, wind powerand geothermal energy.

From the results it can be seen that some of the systems appear to have high

efficiencies, and in some cases they are greater than the efficiency of systems usingnon-renewable energy sources. In other cases, like the conversion of solar energy to

electricity, the efficiencies are lower, in order to meet the electricity needs of cities.A significant advantage from the usage of renewable energy systems is that they

are environmentally friendly, since they emit very few dangerous pollutants. On the

other hand, their main disadvantage lies in their incapability to take advantage of a

big part of the available energy. This is balanced by the fact that RES are inexhaust-

ible.

Greece is a country that has sunny weather for most of the year. Moreover, its

Fig. 11. Energy converted by a system in relation to the energy invested in it for different kinds of

energy sources.


15/16


Fig. 12. Energy output in relation to the energy input for different kinds of systems and energy sources.

islands, as well as its coasts, sustain the installation of wind turbines for exploitation

of the high wind capacity existing in these areas. Finally, there are some geothermal

fields, which unfortunately remain unexploited. By using these energy sources,Greece could meet a great part of its energy needs, making its dependence on fossil

fuels significantly smaller.

References

[1] Tober E. Theory of exergy analysis. Graduation thesis, University of Twente. Available at

http://www.thw.wb.utwente.nl/topics/exergy/theoryFe.htm.

[2] Cornelisse R. The method of exergy analysis. Dissertation, University of Twente, 1997. Available

at http://www.thw.wb.utwente.nl/topics/exergy/theoryFe.htm.

[3] Baher HD. Definition und Berechnung von Exergie und Anergie. Brennst-Warme-Kraft

1993;17(1):16.

[4] Szargut J, Morris DR, Steward FR. Exergy analysis of thermal, chemical and metallurgical processes.

New York: Hemisphere, 1998.

[5] Singh N, Kayshik SC, Misra RD. Exergetic analysis of a solar thermal power system. Renewable

Energy 2000;19(1-2):13543.

[6] Available at: http://www.windpower.dk/tour/wres/pow/index.htm.

[7] Bettagli N, Bidini G. Larderello-Farinello-Valle Secolo Geothermal Area: exergy analysis of the

transportation network and of the electric power plants. Geothermics 1996;25(1):3 16.

[8] Kotas TJ. The exergy method of thermal plant analysis. London: Butterworth, 1985.


16/16


[9] Edgerton RH. In: Available energy and environmental economics. USA: Lexington Books,

1982:24650.

[10] Beckman WA, Klein SA, Duffie JAA. In: Solar heating design. Wiley-Interscience, 1977:80.

[11] US Department of Energy/US Environmental Protection Agency. Inventory of technologies, methodsand particles for reducing emissions of greenhouse gases [online]. Available at

http://www.energyanalysis.anl.gov.

2003-exergy analysis of renewable energy sources

Documents