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Exergy analysis of gas turbine trigeneration system forcombined production of power heat and refrigeration

Abdul Khaliq*

Department of Mechanical Engineering, Faculty of Engineering and Technology, Jamia Millia Islamia, New Delhi 110025, India

a r t i c l e i n f o

Article history:

Received 31 August 2007

Received in revised form

30 May 2008

Accepted 21 June 2008

Published online 28 June 2008

Keywords:

Trigeneration

Gas turbine

Absorption system

Heat recovery

Calculation

Thermodynamic cycle

Exergy

* Tel./fax: þ91 11 26328717.E-mail address: abd_khaliq2001@yahoo.c

0140-7007/$ – see front matter ª 2008 Elsevidoi:10.1016/j.ijrefrig.2008.06.007

a b s t r a c t

A conceptual trigeneration system is proposed based on the conventional gas turbine cycle

for the high temperature heat addition while adopting the heat recovery steam generator

for process heat and vapor absorption refrigeration for the cold production. Combined first

and second law approach is applied and computational analysis is performed to investigate

the effects of overall pressure ratio, turbine inlet temperature, pressure drop in combustor

and heat recovery steam generator, and evaporator temperature on the exergy destruction

in each component, first law efficiency, electrical to thermal energy ratio, and second law

efficiency of the system. Thermodynamic analysis indicates that exergy destruction in

combustion chamber and HRSG is significantly affected by the pressure ratio and turbine

inlet temperature, and not at all affected by pressure drop and evaporator temperature.

The process heat pressure and evaporator temperature causes significant exergy destruc-

tion in various components of vapor absorption refrigeration cycle and HRSG. It also indi-

cates that maximum exergy is destroyed during the combustion and steam generation

process; which represents over 80% of the total exergy destruction in the overall system.

The first law efficiency, electrical to thermal energy ratio and second law efficiency of

the trigeneration, cogeneration, and gas turbine cycle significantly varies with the change

in overall pressure ratio and turbine inlet temperature, but the change in pressure drop,

process heat pressure, and evaporator temperature shows small variations in these param-

eters. Decision makers should find the methodology contained in this paper useful in the

comparison and selection of advanced heat recovery systems.

ª 2008 Elsevier Ltd and IIR. All rights reserved.

Systeme de trigeneration a turbine a gaz utilise pour produirede I’ energie, du chauffage et du froid : analyse de I’ exergie

Mots cles : Trigeneration ; Turbine a gaz ; Systeme a absorption ; Recuperation de chaleur ; Calcul ; Cycle thermodynamique ; Exergie

o.iner Ltd and IIR. All rights reserved.

Nomenclature

A fuel to air ratioð _mf= _maÞ_E exergy rate [kJ s�1]_Hf heat supplied by fuel [kJ s�1]

DHr heat of reaction of fuel [kJ kg�1 of fuel]_Q energy rate [kJ s�1]

R gas constant [kJ kg�1 K�1]

RET electrical to thermal energy ratio

T temperature [K, �C]

TIT turbine inlet temperature [K]_W work rate [kJ s�1]

Cp specific heat at constant pressure [kJ kg�1 K�1]

CV specific heat at constant volume [kJ kg�1 K�1]

e specific exergy [kJ kg�1]

f solution circulation ratio

Dgr Gibbs function of fuel [kJ kg�1 of fuel]

h enthalpy [kJ kg�1]_m mass flow rate [kg s�1]

p pressure [bar]

pp pinch point [�C]

pp process heat pressure [bar]

qP specific process heat production [-]

s specific entropy [kJ kg�1 K�1]

w specific cycle power output [-]

Greek symbols

b pressure drop factor

h efficiency [%]

hI first law efficiency [%]

hII second law efficiency [%]

g specific heat ratio [-]

j specific exergy [kJ kg�1 (refrigerant)]

q maximum to minimum temperature ratio

pT pressure ratio [-]

pC pressure ratio [-]

Subscripts

A absorber

C compressor

CC combustion chamber

Con condenser

D destruction

E evaporator

G generator

GT gas turbine cycle

HE solution–solution heat exchanger of absorption

system

P product, process

Q heat

R reactant

T turbine

a air

w water

av average

cog cogeneration cycle

c0 condensate

el electrical

f fuel, saturated liquid

g superheated vapor

max maximum

r refrigerant

s solution

tri trigeneration cycle

sp solution pump

1, 2, 3,., a, b,. state points in the Fig. 1

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5 535

1. Introduction

Cogeneration is an engineering concept involving the produc-

tion of both electricity and useful thermal energy in one

operation, thereby utilizing fuel more efficiently than if the

desired products were produced separately. The requirements

of cogeneration may be met in many ways ranging from steam

and gas turbines to fuel cells and Stirlingengines. The disadvan-

tage of the above mentioned conventional cogeneration system

is that to get high energetic and economic efficiency is subject to

such an application where the need for both heat and electric

power is balanced throughout the year. There is no balanced

need for electricity and heat in most practical applications of

conventional cogeneration units. What more, there is a great

demand of cooling for technological purposes or air-condition-

ing in different objects. From the energetic and economic point

of view, the most efficient utilization of the primary energy is in

such case possible by such cogeneration systems that are able

to produce simultaneously power, heat, and also cold with the

possibility of output ratios of individual energy flows. These

combined energy systems may be named as trigeneration

which is a combined production of electricity, heat, and cold.

For domestic and industrial applications where various kinds

of energy are demanded, this turns out to be a very effective en-

ergy saving system. Maidment and Tozer (2002) have reviewed

a number of trigeneration plants operating in supermarkets.

Bassolsetal. (2002)have presented different examples of trigen-

eration plants in the food industry. All analyzed examples are

using an absorption chilling machine for cold production.

Thermodynamic analysis can be a perfect tool for

identifying the ways for improving the efficiency of fuel

use, and determining the best configuration and equipment

size for a trigeneration plant. Athanasovici et al. (2000) have

presented a unified comparison method for the calculation

of thermodynamic efficiency applied to CHP plants. A

comparison between the separate and combined production

of energy has been performed using the proposed method.

Havelsky (1999) has analyzed the problem of energetic effi-

ciency evaluation of cogeneration system for combined

heat, cold and power production. Equations for energetic

efficiency and primary energy savings have been presented.

Minciuc et al. (2003) presented a method for analyzing

trigeneration systems, and established the limits for the

best energetic performance of gas turbine trigeneration

with absorption chilling machine from thermodynamic

point of view.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5536

As is seen, most of the studies in the above cited

literature have been conducted using the first law of

thermodynamics or energy balance approach. The first

law analysis gives a good answer to the expected

performance of a cycle and it can certainly lead to the as-

sessment of the overall efficiency of the plant; however,

this is concerned only with the conversion of energy, and

therefore it cannot show how or where irreversibilities in

a system or process occur. This is because first law analysis

has inherent limitations: it gives no distinction between

work and heat, and no provision for quantifying the quality

of heat, no accounting for the work lost in a process, and

no information about the optimal conversion of energy.

Thus, while producing the final design result, energy bal-

ance analysis is incapable on its own of locating sources

of losses. Second law analysis gives much more meaningful

evaluation by indicating the association of irreversibilities

or exergy destruction with combustion and heat transfer

processes and allows thermodynamic evaluation of energy

conservation options in power and refrigeration cycles,

and thereby provides an indicator that points the direction

in which engineers should concentrate their efforts to

improve the performance of thermal power and cooling

systems (Wall, 2003; Khaliq and Kaushik, 2004a,b; Aphorn-

ratana and Eames, 1995). Huang (1990) applied the second

law method for the thermodynamic analysis of combustion

gas turbine cogeneration system, and observed the effects

of pinch point temperature and process steam pressure

on the energetic and exergetic performance of the system.

Si-Doek et al. (1996) carried out the exergy analysis of co-

generation system, and tested the effect of the inlet air

temperature and the relative humidity of the inlet air on

the performance of the system. Khaliq and Kaushik

(2004a,b) conducted a second law based thermodynamic

study for the performance evaluation of gas turbine

cogeneration system with reheat and defined the energetic

and exergetic efficiencies. Khaliq and Rajesh (2008) carried

out a combined first and second law analysis of gas turbine

trigeneration system and observed the effect of limited

operating parameters viz. pressure ratio and process heat

pressure only. This paper aims at adding another dimen-

sion to the work of Khaliq and Rajesh (2008) by observing

the effect of some additional parameters that affect cycle

performance greatly like turbine inlet temperature, pres-

sure drops, and refrigeration temperature along with the

effect of pressure ratio and process steam pressure on the

thermodynamic performance parameters of the cycle like

first-law efficiency, electrical to thermal energy ratio,

second-law efficiency, and exergy destruction in each

component of the cycle.

Therefore in this paper, a more general and detailed

analysis of trigeneration system is presented by means of

combined first and second-law analysis. The exergy balance

for the cycle and its components are presented and are

compared to energy balances. The loss mechanisms in

combustion and heat transfer processes in various heat

exchangers are identified, quantified, and broken down into

their sources by component and by thermodynamic

processes. Emphasis is placed on realistic component model-

ing based on current technological constraints.

2. Description of system

Fig. 1 shows the schematic diagram of trigeneration system.

Ambient air is compressed from state 1 to state 2 and is

then supplied to the combustion chamber (CC) where fuel is

burned, producing hot gas at 3. The hot gas is then expanded

to 4 in turbine (T) to a lower pressure and temperature. This

expanded gas is utilized in the HRSG to generate process

heat (QP). The stack gas coming out of HRSG (at 5) is sent to

the generator of vapor absorption system. The refrigerant

(H2O) is separated from LiBr/H2O in the generator by means

of the heat given by the stack gas. The solution circulation

ratio ðf ¼ _ms= _mrÞ depends on the temperature to which the

solution is heated. After refrigerant has reached the desired

temperature it goes through the condenser at 6 and the evap-

orator at 8 through the expansion valve at 7. The water vapor

mixture that enters the evaporator at 8 is boiled and exits the

evaporator in a saturated state at 9. The saturated steam at 9

enters the absorber where it mixes with a weak solution at 15,

generating heat that has to be dissipated to increase the

efficiency of mixing process. The heat released in the con-

denser and in absorber is rejected to the cooling water. The

mixing process results in a strong solution that exits the

absorber at 10 and is pumped to the upper pressure of the

cycle at 11. The high pressure strong solution at 11 is heated

to a higher temperature at 12 in the heat exchanger (HE) using

the counterpass, high pressure, weak solution at 13. The

cooler weak solution exits the heat exchanger (HE) at 14 and

is expanded in the throttling valve (TV), resulting in a low-

pressure, weak solution at 15.

3. Thermodynamic analysis

3.1. Power output

The net power output of a cycle is given as

_Wnet ¼�

_ma þ _mf

�ðh3 � h4Þ � _maðh2 � h1Þ (1)

Assuming air to be an ideal gas with constant specific heats,

Eq. (1) may be written as

_Wnet ¼�

_ma þ _mf

�CPðT3 � T4Þ � _maCPðT2 � T1Þ (2)

Turbine and compressor isentropic efficiencies may be de-

fined as

hT ¼T3 � T4

T3 � T4sand hC ¼

T2s � T1

T2 � T1(3)

Using the isentropic relations for the conversion of temper-

ature ratio into the pressure ratio across the turbine and com-

pressor as

T2s

T1¼�p2

p1

�ðg�1g Þ

andT3

T4s¼�p3

p4

�ðg�1g Þ

(4)

After substituting the Eqs. (3) and (4) into Eq. (2) and dividing

across by ð _maCpT1Þ, the specific net power output of the cycle

may be reported as;

wnet ¼_Wnet

_maCPT1¼ ð1þAÞqhTjT �

�jC

hC

�(5)

3

GeneratorTG= 80°C

CondenserTC= 35°C

AbsorberTA= 35°C

EvaporatorTE

HEExpansionValve

ThrottlingValvePump

5’, 125°C

mG.

6

7

8

9

10

11 14

15

13, (ms – mr)..

mr.

12, ms.

f, 30°C

e, 25°C

mA.

mE.

mC.

c, 25°C

d, 10°C

b, 30°C

a, 25°C

CC

Fuel

C

2

5

T

41

ProcessSteam

CondensateReturn

.QP

.Wnet

.Wel

17

16

.Qin

Fig. 1 – Schematic diagram of the gas turbine trigeneration system for combined heat cold and power production.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5 537

Where, q ¼ Tmax=T1, jC ¼ paC � 1, jT ¼ 1� ð1=pa

TÞ, A ¼ _mf= _ma

pC are the compressor compression ratio, pT is the turbine ex-

pansion ratio, and a ¼ ðg� 1=gÞThe electrical power output of the system is given by

_Wel ¼ hg_Wnet (6)

where hg is the mechanical to electrical conversion efficiency.

3.2. Energy input

The total heat input to the cycle is given by

_Q in ¼ _ma½ð1þ AÞh3 � h2� ¼ _maCp½ð1þAÞT3 � T2� (7)

where A is the fuel to air ratio.

After dividing across Eq. (7) by ð _maCpT1Þ, Eq. (7) may be

written as

_Q in

_maCPT1¼�ð1þ AÞT3

T1� T2

T1

�(8)

After using Eq. (3) into Eq. (8), the specific heat input to the

cycle is given by

qin ¼_Q in

_maCPT1¼�ð1þAÞq� jC

hC

�(9)

The specific exergy corresponding to the specific heat input

qin defined in Eq. (9) may be explained as the amount of exergy

associated with the heat input to the system and may be de-

fined as

ein ¼ qin

�1� T0

Tin

�(10)

Energy of fuel input, _Qf , may be obtained from

_Qf ¼_Q in

hCC

(11)

Where hCC is the combustion chamber efficiency.

3.3. Process heat production

The amount of process heat rate ð _QPÞ produced is given by

_QP ¼�

_ma þ _mf

�ðh4 � h5Þ (12)

Assuming ideal gas with constant specific heat, Eq. (12) may

be written as

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5538

_QP ¼ _mað1þAÞ½T3 � T3ð1� T4=T3Þ � T5� (13)

Using Eqs. (3) and (4) into Eq. (13), and dividing across by

ð _maCPT1Þ, the specific process heat may be obtained as

qP ¼_QP

_maCPT1¼ ½q� qhTjT � s� (14)

where s ¼ T5=T1, and T5 ¼ ðTP þ ppÞ � ½T4 � ðTP þ ppÞ��hf � hc=hg � hf

.

3.4. Refrigeration or cold production

The amount of cold produced ð _QEÞ may be obtained after

applying the energy balance on evaporator as

_QE ¼ _mrðh9 � h8Þ ¼ _mEðhc � hdÞ (15)

The enthalpy and entropy values of LiBr–H2O mixture at in-

let and outlet of the evaporator of vapor absorption refrigera-

tion can be obtained from Chua et al. (2000).

The exergy associated with the coldð _EEÞ or exergy of refrig-

eration may be defined as the refrigeration capacity divided by

the coefficient of performance of a Carnot refrigeration cycle

operating between the ambient and cycle temperatures and

is given by Tamm et al. (2004)

_EE ¼ _QE

�T0 � TE

TE

�(16)

3.5. Fuel utilization efficiency (first law or energeticefficiency)

The ratioof all the useful energy extracted from the system (elec-

tricity, process heat, and cold) to the energy of fuel input is

known as the fuel utilization efficiency ðhIÞwhich is also known

asthefirst lawefficiencyorenergetic efficiency.Accordingtothis

definition, ðhIÞ is then given by the following expression

hI ¼ð _Wel þ _QP þ _QE � _QSPÞ

_Qf

(17)

Where _QSP ¼ rate of energy consumed by the solution pump and

is given by

_QSP ¼ _msðh11 � h10Þ (18)

Using Eqs. (6), (7) and (11), Eq. (17) may be written as

hI ¼ hCC

�hghth þ

ð _QP þ _QE � _QSPÞ_Q in

�(19)

where hCC ¼ combustion chamber efficiency, hg ¼ electrical con-

version efficiency,

hth ¼ Gas turbine cycle thermal efficiency ¼ _Wnet= _Q in (20)

3.6. Electrical to thermal energy ratio (first law orenergetic efficiency)

The cost effectiveness of any trigeneration system is directly

related to the amount of power it can produce for a given

amount of process heat and cold needed. Thus the electrical

to thermal energy ratio (RET) is an important parameter used

to assess the performance of such a system. Making use of

Eqs. (5), (7), (14) and (15), (RET) for a given system may be

reported as

RET ¼ _Wel=�

_QP þ _QE

�

¼_maCP½ð1þAÞTmaxhTjT � T1jC

hC

ihg

maCPð1þAÞðTmax � hTjTTmax � T5Þ þ _mrðh9 � h8Þð21Þ

3.7. Second law efficiency (exergetic efficiency)

An efficiency is a ratio of output to input. If we consider both

output and input in terms of energy, we have the so-called

first law efficiency. Since exergy is more valuable than energy

according to the second law of thermodynamics (Khaliq and

Kaushik, 2004a,b), it is useful to consider both output and in-

put in terms of exergy as shown in Khaliq and Kaushik,

2004a,b. By definition, the second law efficiency is then given

by the following expression

hII ¼ _Wel þ_EP þ _EE

_Ef

(22)

_Wel is exergy content of electrical power, _EP is the exergy con-

tent of process heat, _Ef is the exergy content of fuel input, and_EE is the exergy content of cold.

The exergy content of fuel and process heat may be

obtained after using the exergy factor 3f and 3P as

3f ¼_Ef

_Qf

; 3P ¼_EP

_QP

(23)

For most of the fuels, the exergy factor 3f is close to unity. For

process heat, the exergy factor 3P is always less than unity, but

it increases with the pressure of process heat produced. From

Khaliq and Kaushik (2004a,b), 3P for our system is given by

3P ¼ 1�T0

�sg � sc

��hg � hc

� (24)

The exergy content of cold may be obtained after using Eq.

(16) for given cold and refrigeration temperature.

3.8. Turbine expansion ratio

The turbine expansion ratio may be expressed in terms of the

compressor compression ratio and pressure drop to be used in

each of the heat transfer device involved in gas turbines. If pin

and pout are inlet pressure and outlet pressure for each heat

transfer device, then

pout ¼ bpin (25)

and

b ¼ 1��pin � pout

�pin

¼ 1��

Dpp

�

The quantity ðDp=pÞ is known as the relative pressure drop.

b maybecalledthepressuredropfactor.FromFig.1,wethushave

p3 ¼ b23p2 (26)

p5 ¼ b45p4 (27)

where b23 is the pressure drop factor for the combustion cham-

ber, b45 is the pressure drop factor for the HRSG.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5 539

Combining the Eqs. (25) and (26), we have

p3

p4¼ b23b45pC ¼ pT (28)

4. Exergy destruction model

An exergy analysis is the combination of the first and second

laws of thermodynamics. In an exergy analysis, the time rate

of heat does not have the same value as the power, and the

losses represent the real losses of work. When analyzing novel

and complex thermal systems, however, such experience

needs to be supplemented by more rigorous quantitative ana-

lytical tools; exergy analysis provides those tools.

If the system operates in a steady state, steady flow condi-

tion and all the non-reacting gases are arbitrarily assigned as

zero thermomechanical enthalpy, entropy and exergy at the

condition of ambient pressure and temperature regardless of

their chemical composition, then the entropy of mixing differ-

ent gaseous components can be neglected, and the general

exergy-balance equation is given by (Bejan, 2002).

_EW ¼Xn

i¼1

�_EQ

�iþX

in

_me�Xout

_me� _ED (29)

For single stream flow

_EW ¼ _EQ þ _mein � _meout � _meD (30)

where

e ¼ ðh� haÞ � Taðs� saÞ (31)

and

s ¼ CP lnTTa� R ln

ppa

(32)

Fig. 2 – Effect of variation of pressure ratio on first law efficiency,

The thermodynamic losses in each component of trigener-

ation may be obtained with the application of exergy destruc-

tion model and may appear in the form of following

equations:

_ED;C ¼ _WC þ _maðe2 � e1Þ (33)

_ED;CC ¼ _mf efCCþ _ma½ð1þ AÞe2 � e3� (34)

efCC¼ Dgr þ RfTa ln

pf

pa(35)

Dgr ¼ DHr � TavðsP � sRÞ (36)

where ðsP � sRÞ is the entropy change during combustion

process and is given as

sP � sR ¼�CP ln

T3

T2� Ra ln

p3

p2

�(37)

_ED;T ¼ _m4ðe3 � e4Þ � _WT (38)

_ED;HRSG ¼ _m4ðe4 � e5Þ � _mwðe16 � e17Þ (39)

_ED;G ¼ _mr½fj12 � ðf � 1Þj13 � j6� þ _mað1þAÞðe5 � e50 Þ (40)

_ED;Con ¼ _mCðja � jbÞ þ _mrðj6 � j7Þ (41)

_ED;EV ¼ _mrðj7 � j8Þ (42)

_ED;E ¼ _mrðj8 � j9Þ þ _mEðjc � jdÞ (43)

_ED;A ¼ _mA

�je � jf

þ _mr½j9 þ ðf � 1Þj15 � fj10� (44)

_ED;HE ¼ _mrðf � 1Þðj13 � j14Þ þ _mrðj11 � j12Þ (45)

second law efficiency and electrical to thermal energy ratio.

Fig. 3 – Effect of variation of Turbine inlet temperature on first law efficiency, second law efficiency and electrical to thermal

energy ratio.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5540

_ED;TV ¼ _mrðf � 1Þðj14 � j15Þ (46)

The terms used in Eqs. (1)–(46) have been defined in

nomenclature.

Fig. 4 – Effect of variation of % pressure drop on first law efficie

ratio.

5. Results and discussion

The effects of pressure ratio across the compressor (pC), tur-

bine inlet temperature (TIT), percentage pressure drop

ncy, second law efficiency and electrical to thermal energy

Fig. 5 – Effect of variation of process heat pressure on first law efficiency, second law efficiency and electrical to thermal

energy ratio.

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5 541

(Dp/p), process heat pressure ( pp), and evaporator tempera-

ture (TE) on the first law efficiency and electrical to thermal en-

ergy ratio (RET) is obtained by energy balance approach or the

first law analysis of the cycle. However, the exergy destruction

Fig. 6 – Effect of variation of evaporator temperature on first law

energy ratio.

or thermodynamic losses in each component, and the second

law efficiency of the trigeneration cycle have also been inves-

tigated under the exergy-balance approach or the second law

analysis of the cycle. To examine the effect of these operating

efficiency, second law efficiency and electrical to thermal

Table 1 – Effect of variation of pressure ratio on exergy destruction in different components of the cycle for TIT [ 1500 K,Dp/p [ 4%, pP [ 5 bar, TE [ 5 8C, patm [ 1 bar, Tatm [ 298 K

pC ED,C (kW) ED,CC (kW) ED,T (kW) ED,HRSG (kW) ED,G (kW) ED,Con (kW) ED, EV (kW) ED,E (kW) ED,A (kW) ED,HE (kW)

4 505.83 11679.23 403.92 5624.81 271.76 38.97 3.3 54.7 62.6 15.8

8 686.14 9540.50 676.58 3549.75 271.76 38.97 3.3 54.7 62.6 15.8

12 774.92 8299.00 858.00 2623.90 271.76 38.97 3.3 54.7 62.6 15.8

16 831.60 7415.26 997.83 2077.80 271.76 38.97 3.3 54.7 62.6 15.8

20 872.18 6737.90 1111.16 1711.60 271.76 38.97 3.3 54.7 62.6 15.8

24 903.60 6175.30 1208.30 1446.45 271.76 38.97 3.3 54.7 62.6 15.8

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5542

variables on the performance parameters of the system,

operating under different conditions, the following common

characteristics were chosen.

The compressor isentropic efficiency (hC) is 85%, the

turbine isentropic efficiency (hT) is 90%, the efficiency of com-

bustion chamber (hCC) is 95%, electrical conversion efficiency

(hg) is 95%, pressure drop in combustion chamber is 4%, the

pinch point is 25 �C, the pressure drop in HRSG is 2%, the con-

densate return is saturated water at process steam pressure,

the temperature of inlet water at condenser, evaporator and

absorber is 25 �C. The fuel is methane gas which has a lower

heating value of 50,016 kJ kg�1, the ambient pressure and

temperature are, respectively, 1 bar and 298 K (Minciuc et al.,

2003; Khaliq and Kaushik, 2004a,b; El-Masri, 1988).

Fig. 2 shows the variation of first law efficiency (hI), second

law efficiency (hII) and electrical to thermal energy ratio (RET)

for cogeneration and trigeneration cycles with a change in

compressor pressure ratio (pC) for fixed values of

[TIT¼ 1500 K, pP¼ 5 bar, Dp/p¼ 4%, TE¼ 5 �C]. As the pressure

ratio (pC) increases the compressor work increases, raising

the temperature at compressor outlet. Increase in pressure

ratio also increases the turbine work. The net work output first

increases and then decreases as at high pressure ratio com-

pressor work increases rapidly. As the pressure ratio increases

the air temperature at the inlet of combustion chamber

increases which results in decreasing the heat added to the

cycle. The ratio of net work output to the heat added repre-

sents the first law efficiency of the gas turbine cycle (hI, GT).

Hence, as pC increases, the first law efficiency of the gas

turbine cycle increases. Fig. 2 also shows the variation of

second law efficiency which is a more accurate measure of

thermodynamic performance. Since the quality of fuel, i.e.,

exergy associated with the heat addition is higher than heat-

ing value or energy of fuel, the exergy of fuel would increase

while bringing it from ambient pressure to combustion

Table 2 – Effect of variation of TIT on exergy destruction in difpP [ 5 bar, TE [ 5 8C, patm [ 1 bar, Tatm [ 298 K

TIT (K) ED,C (kW) ED,CC (kW) ED,T (kW) ED,HRSG (kW) ED,G (kW

1200 831.6 4481.10 989.68 771.21 271.76

1300 831.6 5844.47 991.68 1154.2 271.76

1400 831.6 6645.70 1046.83 1540.1 271.76

1500 831.6 7415.26 997.83 2077.6 271.76

1600 831.6 8162.90 998.50 2607.1 271.76

1700 831.6 8901.20 999.80 3174.3 271.76

1800 831.6 9597.70 1001.56 3775.8 271.76

pressure at ambient temperature. Hence exergy associated

with the heat addition will be equal to exergy associated

with the heating value of fuel plus exergy increase, i.e.,

mechanical exergy due to increase of pressure of fuel from

ambient to combustion state. Therefore, the second law effi-

ciency is slightly lower than the first law efficiency of the

gas turbine cycle. The first law efficiency of cogeneration cycle

(hI,cog) is higher than first law efficiency of gas turbine cycle

(hI,GT) because the gas turbine exhaust is utilized to produce

the process heat. The second law efficiency for cogeneration

cycle (hII,cog) is higher than the second law efficiency for gas

turbine cycle (hII,GT) but the difference between the second

law efficiency for cogeneration cycle and gas turbine cycle is

less as compared to the difference between the first law effi-

ciency of both cycles because the exergy associated with the

process heat will be less than the energy of the process heat.

The first law efficiency of trigeneration cycle (hI,tri) is higher

than the first law efficiency of cogeneration cycle and the first

law efficiency of cogeneration cycle is higher than the first law

efficiency of gas turbine cycle (hI, GT). This is because the flue

gases are utilized to produce the cold in the same plant. The

second law efficiency for trigeneration cycle (hII,tri) is slightly

higher than the second law efficiency for cogeneration cycle

(hII,cog) because exergy associated with cooling load is very

small. The electrical to thermal energy ratio (RET) for cogenera-

tion and trigeneration cycle increases as the net work output

increases, process heat decreases and cooling load remains

same with increase in pressure ratio.

Fig. 3 shows the variation of first law efficiency (hI), second

law efficiency (hII) and electrical to thermal energy ratio (RET)

with respect to the change in TIT for [pC¼ 16, pP¼ 5 bar,

Dp/p¼ 4%, TE¼ 5 �C]. It is found that the first law efficiency in-

creases with the increase in TIT. This is because increasing

TIT leads to significant increase in net work output and insig-

nificant increase in heat addition of cycle. Therefore first law

ferent components of the cycle for pC [ 16, Dp/p [ 4%,

) ED,Con (kW) ED,EV (kW) ED,E (kW) ED,A (kW) ED,HE (kW)

38.97 3.3 54.7 62.6 15.8

38.97 3.3 54.7 62.6 15.8

38.97 3.3 54.7 62.6 15.8

38.97 3.3 54.7 62.6 15.8

38.97 3.3 54.7 62.6 15.8

38.97 3.3 54.7 62.6 15.8

38.97 3.3 54.7 62.6 15.8

Table 3 – Effect of variation of percentage pressure drop in combustion chamber on exergy destruction in differentcomponents of the cycle for pC [ 16, TIT [ 1500 K, pP [ 5 bar, TE [ 5 8C, patm [ 1 bar, Tatm [ 298 K

%Dp/p ED,C (kW) ED,CC (kW) ED,T (kW) ED,HRSG (kW) ED,G (kW) ED,Con (kW) ED,EV (kW) ED,E (kW) ED,A (kW) ED,HE (kW)

4 831.6 7415.26 997.83 2077.8 271.76 38.97 3.3 54.7 62.6 15.8

6 831.6 7473.30 986.08 2115.0 271.76 38.97 3.3 54.7 62.6 15.8

8 831.6 7533.02 975.10 2153.0 271.76 38.97 3.3 54.7 62.6 15.8

10 831.6 7593.30 964.75 2192.4 271.76 38.97 3.3 54.7 62.6 15.8

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5 543

efficiency increases with increase in TIT. It also shows the

variation of second law efficiency for all three cycles which

increases with TIT and it is observed that the second law

efficiency of the cycle is slightly lower than the first law effi-

ciency. The difference between the second law efficiency for

trigeneration, cogeneration and gas turbine cycles is less as

compared to the difference in first law efficiency of all these

cycles because the exergy associated with cold is much less

than the energy of cold, and the exergy associated with

process heat is lower than the energy of process heat. It is

also seen from Fig. 3 that the turbine inlet temperature does

not have significant effect on electrical to thermal energy ratio

for cogeneration and trigeneration cycles because increase in

TIT causes significant increase in power output, process heat

and cold, and the improvement in power output is greater

than the improvement in process heat and cold.

The performance of our system operating with relative

pressure drops (4–10%) in combustion chamber and 2% pres-

sure drop in HRSG is shown in Fig. 4. It is observed that the first

and second law efficiencies for all three cycles is more or less

independent of pressure drop, only second law efficiency of

the gas turbine slightly decreases when the pressure drop

increases.

The effect of process heat pressure ( pP) for fixed values of

[pC¼ 16, Dp/p¼ 4%, TIT¼ 1500 K, TE¼ 5 �C] on the first law

efficiency, electrical to thermal energy ratio, and second law

efficiency of cogeneration and trigeneration systems is shown

in Fig. 5. It is found that the first law efficiency of cogeneration

decreases with an increase in the pressure of process heat. This

is because the amount of process heat decreases significantly

with process heat pressure. The first law efficiency of trigener-

ation cycle also decreases with increase in process heat

pressure. This is because the increase in cold is relatively

smaller than decrease in amount of process heat with the in-

crease in process heat pressure. It is found that in cogeneration,

the second law efficiency increases with the increase in pres-

sure of process heat if turbine exhaust temperature is relatively

high. For trigeneration, the second law efficiency also increases

with the increase in process heat pressure same as

Table 4 – Effect of variation of process heat pressure on exergy dTIT [ 1500 K, Dp/p [ 4%, TE [ 5 8C, patm [ 1 bar, Tatm [ 298 K

pP (bar) ED,C (kW) ED,CC (kW) ED,T (kW) ED,HRSG (kW) ED,G (kW

5 831.6 7415.26 997.83 2077.80 271.76

10 831.6 7415.26 997.83 1629.55 430.43

15 831.6 7415.26 997.83 1383.26 469.63

20 831.6 7415.26 997.83 1229.08 685.50

25 831.6 7415.26 997.83 1093.10 782.74

cogeneration but the second law efficiency for trigeneration is

slightly higher than cogeneration because the exergy associ-

ated with cold at evaporator temperature is very small as com-

pared to the exergy associated with power output and process

heat. Fig. 5 further shows that the electrical to thermal energy

ratio for cogeneration increases with increase in process heat

pressure. This is expected because a higher pressure ratio for

process heat will increase the temperature of gas mixture at

the pinch point. The result is that the flue gas temperature

will be higher. Consequently less process heat will be produced

at a higher pressure of process heat. The electrical to thermal

energy ratio for trigeneration is more or less constant with

the increase in process heat pressure. This is because at higher

process heat pressure, more cold will be produced due to

increase in the gas temperature at the generator inlet.

Fig. 6 shows the variation of first law efficiency, second law

efficiency, and electrical to thermal energy ratio with the

increase in evaporator temperature. The first law efficiency,

second law efficiency of gas turbine cycle and first law effi-

ciency, second law efficiency, and electrical to thermal energy

ratio of cogeneration system is independent of evaporator

temperature. First law efficiency of trigeneration cycle slightly

increases with the increase in evaporator temperature. This is

because at higher evaporator temperature, the cooling load

will be higher. The second law efficiency for trigeneration

cycle also increases with the increase in evaporator tempera-

ture but the magnitude of increase is small as the exergy

associated with the cold is very small. The electrical to ther-

mal energy ratio for trigeneration decreases with the increase

in evaporator temperature due to increase in cold.

Table 1 shows the variation of magnitude of exergy de-

struction in each component of the system with the change

in pressure ratio (pC) for fixed values of Dp/p¼ 4%,

TIT¼ 1500 K, pP¼ 5 bar, TE¼ 5 �C. It is found that the exergy

destruction in the combustion process dominates. It repre-

sents over 60% of the total exergy destruction in the overall

system. As the pressure ratio increases the exergy destruction

in the combustion chamber decreases significantly. This is be-

cause the increase in pressure ratio implies lower difference

estruction in different components of the cycle for pC [ 16,

) ED,Con (kW) ED,EV (kW) ED,E (kW) ED,A (kW) ED,HE (kW)

38.97 3.3 54.7 62.6 15.8

60.06 5.1 84.0 96.1 24.3

73.58 6.2 103.3 118.2 29.8

84.18 7.1 118.2 135.2 34.1

92.68 7.8 130.1 148.8 37.6

Table 5 – Effect of variation of evaporator temperature on exergy destruction in different components of the cycle forpC [ 16, TIT [ 1500 K, Dp/p [ 4%, pP [ 5 bar, patm [ 1 bar, Tatm [ 298 K

TE (�C) ED,C (kW) ED,CC (kW) ED,T (kW) ED,HRSG (kW) ED,G (kW) ED,Con (kW) ED,EV (kW) ED,E (kW) ED,A (kW) ED,HE (kW)

2 831.6 7415.26 997.83 2077.80 262.10 35.88 3.8 63.1 49.6 24.7

5 831.6 7415.26 997.83 2077.80 271.76 38.97 3.3 54.7 62.6 15.8

8 831.6 7415.26 997.83 2077.80 275.30 40.96 2.7 43.5 64.0 12.8

10 831.6 7415.26 997.83 2077.80 279.10 41.54 2.4 34.4 69.5 9.3

12 831.6 7415.26 997.83 2077.80 282.30 41.99 2.1 24.5 76.0 8.0

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5544

of exergy between the combustion products and compressed

air but its difference with exergy carried by fuel drops. It is

further shown that as the pressure ratio increases the exergy

destruction in HRSG decreases. This is because the higher

pressure ratio results in higher exergy of combustion products

and lower turbine exhaust exergy which leads to the higher

turbine output.

Table 2 shows the variation of magnitude of exergy de-

struction in each component of the system with the change

in turbine inlet temperature (TIT) for fixed values of pC¼ 16,

Dp/p¼ 4%, pP¼ 5 bar, TE¼ 5 �C. As the TIT increases the exergy

destruction in combustion chamber increases because the

mean temperature of heat addition increases. The exergy

destruction in HRSG increases because the temperature

difference between the two heat exchanging fluids (flue gas

and water/steam) increases, and for the given pressure ratio

of the cycle, more process heat is produced due to more steam

generated by HRSG at higher TIT. The exergy destruction in

compressor and turbine is constant. The exergy destruction

in generator, condenser, throttling valve, evaporator,

absorber, and heat exchanger is also constant.

Table 3 shows the variation of magnitude of exergy de-

struction in each component of the system, with respect to

pressure drop in combustion chamber and HRSG [pc¼ 16,

TIT¼ 1500 K, pP¼ 5 bar, TE¼ 5 �C]. It is shown that the exergy

destruction in all components of the system are more or less

independent of pressure losses in combustion chamber. It is

further shown that increase in pressure drop in combustion

chamber causes little increase in exergy destruction in

combustion chamber and HRSG. But the exergy destruction

in turbine decreases insignificantly with the increase in

pressure drop in combustion chamber.

The effect of process heat pressure on exergy destruction

in each component of the system is shown in Table 4. It has

been observed that the exergy destruction in all components

of gas turbine and cogeneration cycle is more or less indepen-

dent of the process heat pressure but increase in process heat

pressure causes significant decrease in the exergy destruction

in HRSG. This is consistent with the fact that larger process

heat pressure will lead to more entropy generation in HRSG.

The exergy of the flue gas coming to the refrigeration cycle in-

creases due to increase in process heat pressure. So, more

exergy is added to the refrigeration cycle. As a result, more

refrigerant will evaporate from the generator. So, exergy de-

struction in each component of refrigeration cycle increases.

It is further observed that the exergy destruction in each com-

ponent of vapor absorption refrigeration increases with

increase in process heat pressure. This is expected because

higher pressure for process heat results in higher flue gas

temperature. Consequently more heat will be added to the

generator and hence mass flow rate of refrigerant increase,

and that would result in higher exergy destruction in each

component of vapor absorption system.

Table 5 shows the variation of magnitude of exergy

destruction in each component of the system with respect to

evaporator temperature [pC¼ 16, TIT¼ 1500 K, pP¼ 5 bar,

Dp/p¼ 4%]. It has been observed that the exergy destruction

in the components of gas turbine cycle and cogeneration cycle

is constant with the increase in evaporator temperature but

there is slight variation of exergy destruction in the compo-

nents of refrigeration cycle.

6. Conclusion

The exergy-balance equation, which is applicable to any ther-

mal system has been applied to the trigeneration cycle for

combined production of power, heat and refrigeration. From

thermodynamic point of view, the combination of gas turbine

with absorption chilling machine in these trigeneration sys-

tems proves to be highly efficient, because the flue gas from

heat recovery steam generator is used as a heat source for

vapor absorption refrigeration as described in this study.

Combined first and second law analysis of the given system

leads to the following conclusions:

1. Maximum exergy is destroyed during the combustion and

steam generation process; it represents over 80% of the to-

tal exergy destruction in the overall system.

2. The exergy destruction in combustion chamber and heat

recovery steam generator decreases significantly with

the increase in pressure ratio but increases significantly

with the increase in turbine inlet temperature.

3. At a given TIT, pressure drop, process heat pressure, and

evaporator temperature, the exergy destruction in com-

pressor and turbine increases with the increase in

pressure ratio.

4. The exergy destruction decreases in HRSG and increases

significantly in the vapor absorption refrigeration compo-

nents with the increase in process heat pressure. The

exergy destruction seems constant in the compressor,

the combustion chamber, and the turbine.

5. The exergy destruction in the generator, the absorber, and

the condenser increases slightly with the evaporator tem-

perature, while it decreases in the throttling valve, the

evaporator and the heat exchanger solution.

6. The first law efficiency of cogeneration and trigeneration

decreases with the increase in pressure ratio but the

i n t e r n a t i o n a l j o u r n a l o f r e f r i g e r a t i o n 3 2 ( 2 0 0 9 ) 5 3 4 – 5 4 5 545

second law efficiency and electrical to thermal energy ra-

tio for these systems increases with the same.

7. The first law efficiency, electrical to thermal energy ratio,

and second law efficiency of cogeneration and trigenera-

tion increases with the increase in turbine inlet

temperature.

8. The first law efficiency, electrical to thermal energy ratio,

and second law efficiency of gas turbine, cogeneration and

trigeneration cycles are not at all affected with the pres-

sure drop in combustion chamber and HRSG.

9. The first law efficiency of cogeneration and trigeneration

decreases slightly with the increase in process heat pres-

sure but the second law efficiency and electrical to

thermal energy ratio increases with the same.

10. The first law efficiency and second law efficiency for co-

generation and trigeneration is found to be almost con-

stant with the variation of evaporator temperature but

the electrical to thermal energy ratio for trigeneration

decreases slightly with the increase in TE.

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