Advanced Exergy Analysis for Chemically Reacting Systems - Application to a Simple Open Gas-Turbine System

*This paper is an updated version of a paper published in the ECOS08 proceedings. It is printed here with permission of the authors and organizers. **Corresponding Author Vol. 12 (No. 3) / 105

Int. J. of Thermodynamics Vol. 12 (No. 3), pp. 105-111, 2009 ISSN 1301-9724 www.icatweb.org/journal.htm

Advanced Exergy Analysis for Chemically Reacting Systems – Application to a Simple Open Gas-Turbine System*

Tatiana Morosuk 1**, George Tsatsaronis 2

1 Institute of Marine Propulsion Plants Operation, Maritime Academy of Szczecin, Poland 2 Institute for Energy Engineering, Technische Universität Berlin, Germany

E-mail: [email protected]; 2 [email protected]

Abstract A conventional exergy analysis has some limitations, which are significantly reduced by an advanced exergy analysis. The latter evaluates: (a) the interactions among components of the overall system (splitting the exergy destruction into endogenous and exogenous parts); and, (b) the real potential for improving a system component (splitting the exergy destruction into unavoidable and avoidable parts). The main role of an advanced exergy analysis is to provide engineers with additional information useful for improving the design and operation of energy conversion systems. This information cannot be supplied by any other approach. In previous publications, approaches were presented that were appropriate for application to closed thermodynamic cycles, without chemical reactions (e.g., refrigeration cycles). Here a general approach is discussed that could be applied to systems with chemical reactions. Application of this approach to a simple gas-turbine system reveals the potential for improvement and the interactions among the system components. Keywords: Exergy analysis, exergy destruction, avoidable exergy destruction, endogenous exergy destruction, gas-turbine system.

1. Introduction

A conventional exergy analysis identifies the magnitude and the location of the real thermodynamic inefficiencies (Bejan et al., 1996). However, in revealing the causes of these inefficiencies a conventional analysis fails to identify the contributions by the other components to the exergy destruction within the component being considered. Knowledge of the interactions among components and of the potential for improving each important component is very useful in improving the overall system (Tsatsaronis, 1999a).

Splitting the exergy destruction within each component of an energy conversion system into endogenous/exogenous parts ( += EN

k,Dk,D EE EXk,DE ) and unavoidable/ avoidable

parts ( k,DE = AVk,D

UNk,D EE + ), and combining the two ap-

proaches of splitting the exergy destruction (EX,AV

k,DEN,AV

k,DEX,UN

k,DEN,UN

k,Dk,D EEEEE +++= ) enhances an exergy analysis and improves the quality of the conclusions obtained from it (Tsatsaronis and Park, 2002; Cziesla et al., 2006; Morosuk and Tsatsaronis, 2006a, 2006b, 2008; Tsatsaronis et al., 2006; Kelly, 2008; Tsatsaronis and Morosuk, 2007). These parts of exergy destruction are defined as follows.

The endogenous part of exergy destruction ( ENk,DE ) is

associated only with the irreversibilities occurring in the k th component when all other components operate in an ideal way and the component being considered operates with its current efficiency.

The exogenous part of exergy destruction ( EXk,DE ) is

caused within the k th component by the irreversibilities that occur in the remaining components.

To better understand the interactions among components, the exogenous exergy destruction within the k th component should also be split.

Splitting the exogenous exergy destruction within the k th component ( r,EX

k,DE ) reveals the effect that the irreversibility within the r th component has on the exergy destruction within the k th component. The sum of all

r,EXk,DE terms is lower than the exogenous exergy

destruction within the k th component. The difference is caused by the simultaneous interactions of all (n–1) components. This difference, the mexogenous exergy destruction ( mexo

k,DE ) is calculated from (Tsatsaronis and Morosuk, 2007)

∑−

≠=

−=1

1

n

krr

r,EXk,D

EXk,D

mexok,D EEE (1)

where n denotes the total number of system components and r refers to all but the k th system component.

Unavoidable ( UNk,DE ) is the part of exergy destruction

within one system component that cannot be eliminated even if the best available technology in the near future would be applied.

The avoidable ( AVk,DE ) exergy destruction is the

difference between total and unavoidable exergy destruction and represents the real potential for improving the system component.

By combining the two approaches for splitting exergy destruction we obtain

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Figure 1: O

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exogenous n that can bet being con

(single crespectively.

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able exogenouenous parts of mmarizes all ohin the k th .

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999a, 1999b; 2006) as w

s (Morosuk anis et al., 2006; Kelly et alergy destruction takes placeroblem becau

be defined forring approachsatsaronis et ae a new gener

easier than gy conversiohe following the approach

Tsatsaronis, 20atsaronis and Movercomes theexergy analy

ch could havend complexity

ting conditioniled exergy aonsidered opeon in each sy

Options for sp

ogenous ( UDE

s ( EX,UNk,DE )

genous ( AVk,DE

( EX,AVk,DE ) p

e reduced bynsidered, or components

ogenous partalso be appliedus, and, more exergy destru

options for splcomponent (

g exergy destered the spliable and a

Tsatsaronis well as into nd Tsatsaroni

6; Kelly, 2008l., 2009). Thion in a com

e in the remainuse no idear the reaction

h” was develoal., 2006; Kellral approach the engineer

on systems. has some slused for refri

006a, 2006b, 2Morosuk, 200e most importaysis (Tsatsarone some limitay of the over

ns analysis is coerating at realystem compon

plitting the exe

EN,UNk,D ) and

parts of exe

EN,Vk ) and

parts of exey improving

the remainor subsyst

t of the exed to the splittimportantly,

uction. litting the exe(Tsatsaronis

truction itting of exeavoidable pand Park, 20endogenous

is, 2006a, 200; Tsatsaronis

he calculationmponent whenning compone

al (“theoreticprocess. The ped to overcoly, 2008; Kellyis presented t

ring approachThe appro

light differenigeration syste2008; Tsatsaro7). The approant limitationnis, 1999a). Tations associaall system un

onducted for l conditions. Tnent is calcula

ergy destructi

the

ergy

the

ergy the

ning tem

ergy ting the

ergy and

ergy parts 002; and

06b, and

n of n a ents al”) so-

ome y at that

h to oach nces ems onis oach s of The ated nder

the The ated

separaFigurediagra2R, 3R

Figur

Ththis syTable

E AC,D

E CC,D

and

GT,DE

Thinformoveralrespec

ForoveralMW, tthe expthe prethe temthe re0.09. T

Rfuelm

exergy

consta

const,

tot,PE

ion within the

Int. Centre

ately. For thee 2, the real om in Figure 3

R, 4R and 5R

re 2: Schemati

he results fromystem are sum2 with

EE AC,FC −=

EE CC,FC −=

GT,FT EE −=

his analysis, mation with re

l system andct to the interar illustration l gas-turbine the isentropicpander are Aηessure ratio inmperature at tlative pressurThe resulting

= 5.489 kg/s y analysis d

ant the ratio o

and the net p

netW= = 100

k th compone

for Applied T

e simple gas-operating con3. The real pr(Figure 3 and

ic of a simple

m the convenmmarized in

WACAC,P −=

(3 EEE CC,P −=

(GT,P EE −= 4

however, espect to the pd the single ctions among purposes, w

system generac efficiencies

=AC 0.88 andn the expandethe inlet to thre drop in thmass flow ra

and Rcgm = 2

discussed in

f the mass flo

power genera0 MW = const

ent in an advan

Thermodynam

-turbine systenditions are girocess consistTable 1).

gas-turbine p

ntional exergythe first four

( )12 EE − ,

)24 EE − ,

) GTWE −5 .

does not ppotential for icomponents, the componen

we have assumates net poweof the air com

d =GTη 0.91,r amounts to

he expander ishe combustionates are R

airm

253.2 kg/s. In the followin

ow rates, Rfu

Ra

mm

ated by the ovt.

nced exergy a

mics (ICAT)

em shown iniven on a T-sts of states 1,

power system.

y analysis ofr columns of

provide anyimproving the

neither withnts. med that the

er =netW 100mpressor and, respectively,

14 p/p = 15,s 1500 K, andn chamber is= 247.8 kg/s,

the advancedng, we keep

uel

Rir = 45.14 =

verall system,

analysis.

n s ,

f f

y e h

e 0 d , ,

d s ,

d p

=

,

Int. J. of Thermodynamics (IJoT) Vol. 12 (No. 3) / 107

Figure 3: Real, theoretical, unavoidable and hybrid processes for simple gas-turbine power system showed in Figure 2: air , fuel, combustion gases.

Table 1. Thermodynamic data for the real (R), theoretical (T), unavoidable (U) and hybrid processes (H) of the simple gas-turbine power system.

Stre

am

T

[K] p

[bar

]

ePH

[MJ/

kg]

eCH

[MJ/

kg]

e [M

J/kg

]

1 298 1.013 0 0 0 2T 636 15.2 0.350 0 0.350 2H2 652 16.71 0.368 0 0.368 2U 662 15.35 0.366 0 0.366 2H1 680 15.2 0.376 0 0.376 2R 698 16.71 0.396 0 0.396 3T 298 15.2 0.418 51.38 51.8 3U 298 15.5 0.421 51.38 51.8 3R 298 18 0.445 51.38 51.83 4U 2100 15.2 1.878 0.020 1.898 4R= 4T

1500 15.2 1.113 0.005 1.119

5U 943 1.025 0.629 0.020 0.649 5R 859 1.025 0.281 0.005 0.286 5T 1216 1.013 0.228 0.005 0.233

For calculating the values of unavoidable

irreversibilities within each system component, we assumed conditions that cannot be realized in the next decade:

=UNACη 0.93, =UN

GTη 0.96, an adiabatic combustion process with T4=2100 K and a relative pressure drop in the combustion chamber of 0.01.

The composition of the combustion gases for the process with only unavoidable irreversibilities is different than the composition of combustion gases for the real process. Therefore, for showing the process with unavoidable irreversibilities we need four more isobaric lines p2,U, p3,U, p4,U and p5,U (Figure 3).

For calculating the value of the unavoidable exergy destruction within the k th component, the following procedure is used (detailed description is given in Tsatsaronis and Park, 2002; Cziesla et al., 2006).

UN

k,P

k,Dk,D

UNk,D E

EEE ⎟

⎟⎠

⎞⎜⎜⎝

⎛= (2)

where the value UN

k,P

k,D

EE

⎟⎟⎠

⎞⎜⎜⎝

⎛ should be calculated using the

process with unavoidable irreversibilities.

The values UN

k,P

k,D

EE

⎟⎟⎠

⎞⎜⎜⎝

⎛ are given in Table 2 and the

values UNk,DE and AV

k,DE are presented in Table 3. The exergetic efficiency of the overall gas-turbine power system operating at the given pressure ratio and at conditions that are associated with unavoidable exergy destruction is

=UNtotε 40.4%. Thus the potential for improving the overall

efficiency of such a system (without an air preheater) and at the given pressure ratio of about 15 is approximately 5 percentage points.

2.2. Theoretical operating conditions

For splitting the exergy destruction into endogenous and exogenous parts, and for further splitting the exogenous part of the exergy destruction, we need to describe the theoretical operation conditions for each component of the gas-turbine power system.

The theoretical operational conditions for the air compressor and the gas turbine are similar: 0=T

AC,DE

( 1=TACε or 1=T

ACη ) and 0=TGT,DE ( 1=T

GTε or 1=TGTη ).

The following assumptions are made for the theoretical combustion chamber:

• The thermodynamic properties of the combustion gas and the composition of it remain the same as in the real operating conditions (state 4T = state 4R),

• The pressure drop in the combustion chamber is zero, p2 = p4,

• State 4T(=4R) should be the result of the chemical reaction between the streams at states 2T and 3T,

• The excess air at theoretical conditions is equal to the

excess air in the real process: Rfuel

Rair

Tfuel

Tair

mm

mm

= , and

108

•

Figsys

anyful

(Fi

com•

E2

or

Te2

•

nW

wit

con

and

befandbal

com

(EX

genmacon

can

DEtheandKe

8 / Vol. 12 (No

With respectsystem is splcombination chamber whi(Figure 4).

gure 4: Sub-stem.

In general ay chemical refilled.

The theoretigure 3).

The conditimbination of t Since we cabalances simchamber, we

TT EE 432 =+

TTairT em +⋅ 3

In addition, wTcg

TGTnet mw ⋅=

th netW = 100For the gas

nditions we h

d Tcgm = 160.3

It is apparentfore, the overd, therefore, lance. If the ov

mponents, weA throttling

X) with EXη =For a heat

nerator, for achine (Morondition E k,D =

We concludennot always b

tot,D = 0 andeoretical operad Tsatsaroniselly, 2008) wit

o. 3)

t to mass ballit into two suof the air com

ile sub-system

-systems of

a new subsysteactor in whic

tical process

ion 0=TCC,DE

the following annot fulfill t

multaneously f fulfill only th

T4 ,

TTfuel em ⋅=⋅ 4

we fulfill the fTair

TAC

Tg mw ⋅−

0 MW. s-turbine syst

have: Tairm = 1

3 kg/s.

t that Tair mm +

rall system iwe do not

erall system would use thvalve should

=1 (Morosuk at exchanger example for

osuk and Tsmin= is poss

e that the ovebe described ad tot,Dε = 1)ational conditi, 2006a, 200th minE T

k,D =

lances, the gaub-systems: sumpressor with

m II consists on

a simple ga

tem should bech the mass b

is 1 – 2T –

0 can be achtwo equationsthe mass, enefor the theorehe exergy bala

Tcgm⋅ ,

following bala

tem at theor119.8 kg/s, m

Tcg

Tfuel mm ≠ . A

s split into tneed to con

m would cone following pr

d be replaced and Tsatsaron

(including an absorpti

satsaronis, 20ible, with pTΔ

erall energy coat ideal opera). When this ions should b

06b; Tsatsaronn and T

k maε =

as-turbine powub-system I is h the combustnly of the turb

as-turbine po

e introduced aalance cannot

4T (2T+3T) –

hieved througs (3) and (5).ergy and exe

etical combustance:

ance

retical operatTfuelm = 2.654 k

As we mentiotwo sub-systensider this m

ntain additiorocedures: by an expan

nis, 2006a, 200an absorber ion refrigerat008)), only

pinchT =0. onversion sysating condition

is not possie used (Moronis et al., 20ax .

wer the

tion bine

wer

after t be

– 5T

gh a

ergy tion

(3)

(4)

(5)

ting kg/s

oned ems, mass

onal

nder 08).

or tion the

tem ns (ible, osuk 006;

2.3. HFor

endogeendogeproceswith itall oththis cbeing unavoiby-stepsystem(the ueach c

Fordestrucprocesproceswhile operat

• Air pro• Co pro• Ga pro

Thshouldprocescomprdescribwith oexergy

2E + ε

where chamb

Th

Tablecalculaadvanc

Toexergythe fol

E,UNk,DE

ThE,AV

k,DE 2.4. H

Fordestruchybridevery to be i

Int. Centre

Hybrid procesr splitting enous/exogenenous/unavoidsses in which ts real efficien

her componentase, the exer

considered idable endogep introducing

m component unavoidable eomponent. r calculating ction within ssses - 1 shoulss only one cothe remaininging conditions

r compressor ocess 1 –2H1 –ombustion chaocess 1 –2H2 –as turbine ( E

DEocess 1 –2T – 4

e mass flow d be calculatedss with irreressor or onlbed by Eqs. only irreversiby balance in th

43 EECC =ε

CCε is the ber at real operhe values EN

k,DE

3. The valuated because ced exergy an calculate th

y destruction llowing equati

P

DENk,P

EN

EE

E ⎜⎜⎝

⎛=

he results obtaEX are given in

Hybrid procesr splitting tction within

d processes –one of these prreversible:

for Applied T

ses - 1 the exergy

nous parts (odable exogenonly one comncy (or its unats operate in argy destructio

represents enous) exergyg irreversibilienables us to

endogenous)

the endogeystem compold be analyzedomponent is ag componentss:

( ENAC,DE ) –

4T (3T +2H1) –amber ( EN

CC,DE4T (3R +2H2) –

ENGT,D ) –

4T (3T +2T) – 5

rates of air, fd for each hybeversibilities ly in the ga(3)-(5) is usebilities in thehis component

exergetic effirating conditio

Nk as well as th

ues ENk,PE (T

they are neednalysis. e unavoidablwithin a syst

ion UN

k,P

k,D⎟⎟⎠

⎞

ined for UNk,DE

n Table 3.

ses - 2 the exogenoeach system 2 should be

processes, two

Thermodynam

y destructionor into the

nous parts) wmponent is real

avoidable effian ideal/theoron within th

the endogy destructionities successivo calculate theexergy destru

nous part ofnents, the folld (Figure 3). assumed to bes operate at th

– 5T , ) –

– 5T, and

5R.

fuel and combbrid process. F

either only as turbine, thed. For the hy combustion t becomes

ficiency of theons.

he values EXk,DE

Table 2) shoded for the ne

e endogenoutem compone

EN,Nk , EX,UN

k,DE ,

ous part of component, tintroduced (

o components

mics (ICAT)

n into theunavoidable

we use hybridl, i.e. operatesciency) whileetical way. Ine componentgenous (the

n. Thus, step-vely in eache endogenousuction within

f the exergylowing hybridIn each such

e irreversible,he theoretical

bustion gasesFor the hybrid

in the airhe procedureybrid processchamber, the

(6)

e combustion

Xk are given in

ould also bext step of the

s part of theent, we apply

(7)

, EN,AVk,DE and

the exergythe following(Figure 3). Ins are assumed

e e d s e n t e -h s n

y d h , l

s d r e s e

)

n

n

e e

e y

)

d

y g n d

Int. J. of Thermodynamics (IJoT) Vol. 12 (No. 3) / 109

• Air compressor and combustion chamber for calculating the values CC,EX

AC,DE and AC,EXCC,DE – process 1 –2R – 4R (3R

+2R) – 5T, • Air compressor and gas turbine for calculating the

values GT,EXAC,DE and AC,EX

GT,DE – process 1 –2H1 – 4T (3T+2H1) – 5R, and

• Combustion chamber and gas turbine for calculating the values GT,EX

CC,DE and CC,EXGT,DE – process 1 –2H2 – 4R (3R

+2H2) – 5R.

The value of r,EXk,DE (Table 3) is calculated by

ENk,D

r,kk,D

r,EXk,D EEE −= (8)

The values r,kk,DE are given in Table 2.

For splitting the unavoidable exogenous part of the exergy destruction within a system component, we need a procedure similar to the one described by Eqs. (8) and (9)

EN,UNk,D

r,k,UNk,D

r,EX,UNk,D EEE −= (9)

with

UN

k,P

k,Dr,kk,P

r,k,UNk,D E

EEE ⎟

⎟⎠

⎞⎜⎜⎝

⎛= (10)

The values of r,kk,PE are given in Table 2 and the results

are presented in Table 3. 3. Discussion and conclusion

When we evaluate the thermodynamic performance of a system component, it is very helpful to know (a) what part of the exergy destruction is caused by which other component, and (b) what part of the exergy destruction within the component being considered could be avoided. This information is obtained with the aid of theoretical, hybrid and unavoidable processes that are considered together with the real process.

This paper demonstrates how to define all these processes and how to split the exergy destruction within a system component into its parts unavoidable/avoidable and endogenous/ exogenous as well as unavoidable endogenous, unavoidable exogenous, avoidable endogenous and avoidable exogenous. The system evaluation is based on the last two parts of exergy destruction.

Compared with the conventional exergy analysis of a simple gas-turbine power system we obtain the following additional information with the aid of an advanced exergy analysis:

1. The potential for improving the efficiency of the overall system is approximately 5 percentage points because over 70% of the exergy destruction in the overall system is unavoidable.

2. Only one fourth of the exergy destruction in the combustion chamber is avoidable. For the combustion chamber, the avoidable endogenous exergy destruction (to be reduced, for example, by increasing the temperature T4) is four times higher than the avoidable exogenous exergy destruction (to be reduced through improvements in the air compressor and the expander).

3. Over 50% of the exergy destruction in the air compressor is exogenous whereas this percentage is

approximately 27% for the expander and 22% for the combustion chamber.

4. An improvement in the expander would affect not only the endogenous avoidable exergy destruction of this component but also the exogenous avoidable exergy destruction within the combustion chamber. Nomenclature

E exergy rate [W] e specific exergy [J/kg] m mass flow rate [kg/s] p pressure [bar]

Q heat rate [W]

gens specific entropy generation [J/kg·K] T temperature [K] W power [W]

Greek symbols

Δ difference ε exergetic efficiency η isentropic efficiency

Abbreviations

AC air compressor CC combustion chamber GT gas turbine (expander)

Subscripts

D destruction F fuel H point of a hybrid process k k th component P product R point of a real process U point of a process with unavoidable exergy destruction T point of a theoretical process tot overall system 0 thermodynamic environment

Superscripts

AV avoidable ch chemical exergy EN endogenous EX exogenous k k th component mexo mexogenous n number of components ph physical exergy r r th component (different from the k th component being considered) R real operation conditions T theoretical operation conditions UN unavoidable

110 / Vol. 12 (No. 3) Int. Centre for Applied Thermodynamics (ICAT)

Ta

ble

2: D

ata

obta

ined

from

the

conv

entio

nal e

xerg

y an

alys

is a

nd so

me

data

for t

he a

dvan

ced

exer

gy a

naly

sis.

Tabl

e 3:

Con

vent

iona

l and

adv

ance

d ex

ergy

ana

lyse

s for

the

sim

ple

gas-

turb

ine

pow

er sy

stem

.

Int. J. of Thermodynamics (IJoT) Vol. 12 (No. 3) / 111

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Morosuk, T. and Tsatsaronis, G., 2008, “New approach to the exergy analysis of absorption refrigeration machines”, Energy Int. J., Vol. 33, pp. 890-907. Tsatsaronis, G., 1999a, “Strengths and limitations of exergy analysis”, Thermodynamic optimization of complex energy systems, Bejan, A. and Mamut, E., eds., Dordrecht: Kluwer Academic Publishers, pp. 93–100. Tsatsaronis, G., 1999b, “Design optimization using exergoeconomics”, Thermodynamic optimization of complex energy systems, Bejan, A. and Mamut, E., eds., Dordrecht: Kluwer Academic Publishers, pp.101–117. Tsatsaronis, G., Kelly, S. and Morosuk, T., 2006, “Endogenous and exogenous exergy destruction in thermal systems”, Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Chicago, USA, CD-ROM, file 2006-13675. Tsatsaronis, G. and Morosuk, T., 2007, “Advanced exergoeconomic evaluation and its application to compression refrigeration machines”, Proceedings of the ASME International Mechanical Engineering Congress and Exposition, Seattle, USA, CD-ROM, file 2007-41202. Tsatsaronis, G. and Park, M.H., 2002, “On avoidable and unavoidable exergy destructions and investment costs in thermal systems”, Energy Conversion and Management, Vol. 43, pp.1259–1270.