Exergoeconomic performance optimization of an endoreversible intercooled regenerated Brayton cogeneration plant Part 1: Thermodynamic model and parameter analyses

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I
NTERNATIONAL
J
OURNAL OF

E
NERGY AND
E
NVIRONMENT



Volume 2, Issue 2, 2011 pp.199-210

Journal homepage: www.IJEE.IEEFoundation.org


ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved.
Exergoeconomic performance optimization of an
endoreversible intercooled regenerated Brayton
cogeneration plant
Part 1: Thermodynamic model and parameter analyses


Lingen Chen, Bo Yang, Fengrui Sun


Postgraduate School, Naval University of Engineering, Wuhan 430033, P. R. China.


Abstract
A thermodynamic model of an endoreversible intercooled regenerative Brayton heat and power
cogeneration plant coupled to constant-temperature heat reservoirs is established by using finite time
thermodynamics in Part 1 of this paper. The heat resistance losses in the hot-, cold- and consumer-side
heat exchangers, the intercooler and the regenerator are taken into account. The finite time
exergoeconomic performance of the cogeneration plant is investigated. The analytical formulae about
dimensionless profit rate and exergetic efficiency are derived. The numerical examples show that there
exists an optimal value of intercooling pressure ratio which leads to an optimal value of dimensionless
profit rate for the fixed total pressure ratio. There also exists an optimal total pressure ratio which leads
to a maximum profit rate for the variable total pressure ratio. The effects of intercooling, regeneration
and the ratio of the hot-side heat reservoir temperature to environment temperature on dimensionless
profit rate and the corresponding exergetic efficiency are analyzed. At last, it is found that there exists an
optimal consumer-side temperature which leads to a double-maximum dimensionless profit rate. The
profit rate of the model cycle is optimized by optimal allocation of the heat conductance of the heat
exchangers in Part 2 of this paper.
Copyright © 2011 International Energy and Environment Foundation - All rights reserved.

Keywords: Finite time thermodynamics, Endoreversible intercooled regenerative Brayton cogeneration
plant, Exergoeconomic performance, Profit rate, Exergetic efficiency.



1. Introduction
The heat and power cogeneration plants are more advantageous in terms of energy and exergy
efficiencies than plants which produce heat and power separately [1]. It is important to determine the
optimal design parameters of the cogeneration plants. By using classical thermodynamics, Rosen et al.
[2] performed energy and exergy analyses for cogeneration-based district energy systems, and exergy
methods are employed to evaluated overall and component efficiencies and to identify and assess
thermodynamic losses. Khaliq [3] performed the exergy analysis of a gas turbine trigeneration system for
combined production of power heat and refrigeration and investigated the effects of overall pressure
ratio, turbine inlet temperature and pressure drop on the exergy destruction. Reddy and Butcher [4]
investigated the exergetic efficiency performance of a natural gas-fired intercooled reheat gas turbine
cogeneration system and analyzed the effects of intercooling, reheat and total pressure ratio on the
International Journal of Energy and Environment (IJEE), Volume 2, Issue 2, 2011, pp.199-210
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved.

200
performance of the cogeneration plant. Khaliq and Choudhary [5] evaluated the performance of
intercooled reheat regenerative gas turbine cogeneration plant by using the first law (energetic efficiency)
and second law (exergetic efficiency) of thermodynamics and investigated the effects of overall pressure
ratio, cycle temperature ratio and pressure losses on the performance of the cogeneration plant. Vieira et
al. [6] maximized the profit of a complex combined-cycle cogeneration plant using a professional
process simulator which leading to a better compromise between energetic efficiency and cost, and the
results of the exercises show that the optimal plant operating conditions depend nontrivially on the
economic parameters, also the effects of exported steam mass flow rate and DMP (difference marketable
price) on the optimal performances are discussed.
Finite-time thermodynamics (FTT) [7-18] is a powerful tool for analyzing and optimizing performance
of various thermodynamic cycles and devices. In recent years, some authors have performed the
performance analysis and optimization for various cogeneration plants by using finite-time
thermodynamics. Bojic [19] investigated the annual worth of an endoreversible Carnot cycle
cogeneration plant with the sole irreversibility of heat resistance. Sahin et al. [20] performed exergy
output rate optimization for an endoreversible Carnot cycle cogeneration plant and found that the lower
the consumer-side temperature, the better the performance. Erdil et al. [21] optimized the exergetic
output rate and exergetic efficiency of an irreversible combined Carnot cycle cogeneration plant under
various design and operating conditions and found that the optimal performance stayed approximately
constant with consumer-side temperature. Atmaca et al. [22] performed the exergetic output rate, energy
utilization factor (EUF), artificial thermal efficiency and exergetic efficiency optimization of an
irreversible Carnot cycle cogeneration plant. Ust et al. [23] provided a new exergetic performance
criterion, exergy density, which includes the consideration of the system sizes, and investigated the
general and optimal performances of an irreversible Carnot cycle cogeneration plant. In industry,
Brayton cycle is widely used and some authors are interested in the cogeneration plants composed of
various Brayton cycles. Yilmaz [24] optimized the exergy output rate and exergetic efficiency of an
endoreversible simple gas turbine closed-cycle cogeneration plant, investigated the effects of parameters
on exergetic performance and found that the lower the consumer-side temperature, the better the
performance. Hao and Zhang [25, 26] optimized the total useful-energy rate (including power output and
useful heat rate output) and the exergetic output rate of an endoreversible Joule-Brayton cogeneration
cycle by optimizing the pressure ratio and analyzed the effects of parameters on the optimal
performances. Ust et al. [27, 28] proposed a new objective function called the exergetic performance
coefficient (EPC), and optimized an irreversible regenerative gas turbine closed-cycle cogeneration plant
with heat resistance and internal irreversibility [27] and an irreversible Dual cycle cogeneration plant
with heat resistance, heat leakage and internal irreversibility [28].
Exergoeconomic (or thermoeconomic) analysis and optimization [29, 30] is a relatively new method that
combines exergy with conventional concepts from long-run engineering economic optimization to
evaluate and optimize the design and performance of energy systems. Salamon and Nitzan [31]
combined the endoreversible model with exergoeconomic analysis for endoreversible Carnot heat engine
with the only loss of heat resistance. It was termed as finite time exergoeconomic analysis [32-38] to
distinguish it from the endoreversible analysis with pure thermodynamic objectives and the
exergoeconomic analysis with long-run economic optimization. Furthermore, such a method has been
extended to
endoreversible Carnot heat engine with complex heat transfer law
[39], universal
endoreversible heat engine [40], generalized irreversible Carnot heat engine [41], generalized irreversible
Carnot heat pump [42] and
universal irreversible steady flow variable-temperature heat reservoir
heat pump
[43]. On the bases of Refs. [32-38]. Tao et al. [44, 45] performed the finite time
exergoeconomic performance analysis and optimization for an endoreversible simple [44] and
regenerative [45] gas turbine closed-cycle heat and power cogeneration plant coupled to constant
temperature heat reservoirs by optimizing the heat conductance allocations among the hot-, cold- and
consumer-side heat exchangers, the regenerator and the pressure ratio of the compressor.
As to now, there is no work concerning the finite time thermodynamic analysis and optimization for
endoreversible intercooled regenerative Brayton cogeneration cycle in the open literatures. In this paper,
a thermodynamic model of an endoreversible intercooled regenerative Brayton heat and power
cogeneration plant coupled to constant-temperature heat reservoirs is established and the performance
investigation is performed by using finite time exergoeconomic analysis. The intercooling process and
the heat resistance losses in the hot-, cold-, consumer-side heat exchangers and the regenerator are taken
International Journal of Energy and Environment (IJEE), Volume 2, Issue 2, 2011, pp.199-210
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved.

201
into account. The analytical formulae about dimensionless profit rate and exergetic efficiency are
deduced. The two cases with fixed and variable total pressure ratios are discussed, and the effects of
design parameters on general and optimal performances of the cogeneration plant are analyzed by
detailed numerical examples. The intercooling pressure ratio and the total pressure ratio are optimized,
and the corresponding exergetic efficiency is obtained.

2. Cycle model
The T-s diagram of the heat and power cogeneration plant composed of an endoreversible intercooled
regenerative Brayton closed-cycle coupled to constant-temperature heat reservoirs is shown in Figure 1.
Processes 1-2 and 3-4 are isentropic adiabatic compression process in the low- and high-pressure
compressors, while the process 5-6 is isentropic adiabatic expansion process in the turbine. Process 2-3 is
an isobaric intercooling process in the intercooler. Process 4-7 is an isobaric absorbed heat process and
process 6-8 is an isobaric evolved heat process in the regenerator. Process 7-5 is an isobaric absorbed
heat process in the hot-side heat exchanger and process 9-1 is an isobaric evolved heat process in the
cold-side heat exchanger. Process 8-9 is an isobaric evolved heat process in the consumer-side heat
exchanger.



Figure 1. T-s diagram for the cycle model

Assuming that the working fluid used in the cycle is an ideal gas with constant thermal capacity rate
(mass flow rate and specific heat product)
wf
C
. The hot-, cold- and consumer-side heat reservoir
temperatures are
H
T
,
L
T
and
K
T
respectively, and the intercooling fluid temperature is
I
T
. The heat
exchangers between the working fluid and the heat reservoirs, the regenerator and the intercooler are
counter-flow. The conductances (heat transfer surface area and heat transfer coefficient product) of the
hot-, cold- and consumer-side heat exchangers, the intercooler and the regenerator are
,,,,
H LKIR
UUUUU
, respectively. According to the heat transfer processes, the properties of working
fluid and the theory of heat exchangers, the rate (
H
Q
) of heat transfer from heat source to the working
fluid, the rate (
L
Q
) of heat transfer from the working fluid to the heat sink, the rate (
K
Q
) of heat transfer
from the working fluid to the heat consuming device, the rate (
I
Q
) of heat exchanged in the intercooler,
and the rate (
R
Q
) of heat regenerated in the regenerator are, respectively, given by:

[]
57
57 7
75
()
() ( )
ln ( ) ( )
HH wf wfHH
HH
TT
QU CTTCETT
TTTT
−
==−=−
−−
(1)

[]
91
91 9
91
()
() ( )
ln ( ) ( )
L LwfwfLL
LL
TT
QU CTT CETT
TT TT
−
==−=−
−−
(2)

International Journal of Energy and Environment (IJEE), Volume 2, Issue 2, 2011, pp.199-210
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved.

202
[]
89
89 8
89
()
() ( )
ln ( ) ( )
K KwfwfKK
KK
TT
QU CTT CETT
TT TT
−
==−=−
−−
(3)

[]
23
23 2
23
()
() ()
ln ( ) ( )
I IwfwfII
II
TT
QU CTT CETT
TT TT
−
==−=−
−−
(4)

74 68 64
()() ()
Rwf wf wfR
QCTT CTT CETT
=−=−= −
(5)

where
H
E
,
L
E
,
K
E
,
I
E
and
R
E
are the effectivenesses of the hot-, cold-, consumer-side heat exchangers,
the intercooler and the regenerator, respectively, and are defined as:

1exp( ), 1exp( ), 1exp( )
1exp( ), ( 1)
H HL LK K
IIRRR
ENENEN
ENENN
=− − =− − =− −
=− − = +
(6)

where
(,,,,)
i
Ni HLKIR
=
are the numbers of heat transfer units of the hot-, cold-, consumer-side heat
exchangers, the intercooler and the regenerator, respectively, and are defined as:
/
iiwf
NUC
=
.
Defining that the working fluid isentropic temperature ratios for the low-pressure compressor and the
total compression process are
x
and
y
, i.e.
21 56
,
x TTy TT
= =
. According to the properties of
endoreversible cycle, one has:

(1) (1) 1
143
,,
kk kk
x yTTyx
ππ
−− −
== =
(7)

where
1
π
is the intercooling pressure ratio which satisfies
1
1
π
≥
, and
π
is the total pressure ratio which
satisfies
1
π π
≥
.
k
is the specific heat ratio of working fluid.

3. Formulae about dimensionless profit rate and exergetic efficiency
Assuming that the environment temperature is
0
T
, the total rate of exergy input of the cogeneration plant
is:
000
(1 ) (1 ) (1 )
H HHLLII
e Q TT Q TT Q TT
=− −− −−
(8)

According to the first law of thermodynamics, the power output (the exergy output rate of power) of the
cogeneration plant is:

H LIK
PQ Q Q Q
=−−−
(9)

The entropy generation rate (
σ
) of the cogeneration plant is:

L LIIKKHH
QT QT QT Q T
σ
=++ −
(10)

From the exergy balance for the cogeneration plant, one has:

0
HK
ePeT
σ
=+ +
(11)

where
K
e
is thermal exergy output rate, i.e. the exergy output rate of process heat, and
0
T
σ
is the exergy
loss rate.
Combining equations (8)-(11) yields the thermal exergy output rate:

0
(1 )
K KK
eQ TT
=−
(12)

Assuming that the prices of exergy input rate, power output and thermal exergy output rate are
H
ϕ
,
P
ϕ

and
K
ϕ
, respectively, and the profit rate of cogeneration plant is defined as:

International Journal of Energy and Environment (IJEE), Volume 2, Issue 2, 2011, pp.199-210
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved.

203
P KK HH
Pe e
ϕ ϕϕ
Π= + −
(13)

when
P KH
ϕ ϕϕ
==
, equation (13) becomes:

0
()
PKH P
Pe e T
ϕ ϕσ
Π= + − =−
(14)

The maximum profit rate objective is equivalent to a minimum entropy generation rate objective in this
case.
When
P K
ϕ ϕ
=
and
0
HP
ϕ ϕ
→
, equation (13) becomes:

()
PK
Pe
ϕ
Π= +
(15)

The maximum profit rate objective is equivalent to a maximum total exergy output rate objective in this
case.
Combining equations (1)-(5) with (7)-(12) yields the inlet temperature (
1
T
) of the low-pressure
compressor:

23 14 4 4 3 123
1
4235414
2( )2()( )
2[ ( )]
I IRRLLKKHH
RR
yccET cc c yE xy cE ET cET xcccE T
T
xy cE yccc c cc yE
−+ + − + +
=
−+ −−
(16)

where
1
2(1 )
R
cE
=−
,
2
1
K
cE
=−
,
3
1
L
cE
=−
,
4
1
H
cE
= −
, and
5
1
I
cE
= −
.
The power output is:

2
23 1 3 23 51
4212314
13
234
[(1)( ) (
)] (1 )[ ( ) ( )]
(1 )( )
(1 )
wf H K H R L L K K R
I IwfRLKLIKIwf
KK R LL K
KR
C E T xc c T E xy T E T c E T c c y E xc T
E T xc C E c E T T T c c E T xT T xc C
ET E T ET cT
P
xc c c T E
−− − − + +
−− −+ −−
−−−
=
−
(17)

The thermal exergy output rate is:

01 3
23
()( )
wf K K L L K
K
K
CET T T ET cT
e
ccT
−−−
=
(18)

Defining price ratios:
,
P HKH
ab
ϕ ϕϕϕ
==
, and
Π
can be nondimensionalized by using
0Hwf
CT
ϕ
:

0
00
(1) (1)
K
PKKHH
Hwf wf
aPbeT
Pe e
CT CT
σ
ϕϕ ϕ
ϕ
−+− −
+−
Π= =
(19)

The exergetic efficiency (
ex
η
) is defined as the ratio of total exergy output rate to total exergy input rate:

0
KK
ex
HK
Pe Pe
ePeT
η
σ
++
==
++
(20)

where
13 1 1 323
2
23 1 3 23 51 23
4
{ ( )/( ) ( )/ ( )/( )
[(1)( ) ( )]/[
(1 )]}
wf L L L I I I K L L K K
HHR LLKK R II
HR
CETT cT ExTT T ETET cT ccT
E xccT E xyT ET cET ccyE xcT ET xcc
cT E
σ
=− +−+−− −
−− − − + +
−
.

According to equation (19), the dimensionless profit rate (
Π
) of the endoreversible intercooled
regenerative Brayton cogeneration plant coupled to constant-temperature heat reservoirs is the function
International Journal of Energy and Environment (IJEE), Volume 2, Issue 2, 2011, pp.199-210
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved.

204
of the intercooling pressure ratio (
1
π
) and the total pressure ratio (
π
) when the other boundary condition
parameters (
H
T
,
L
T
,
I
T
,
K
T
,
0
T
,
wf
C
,
H
E
,
L
E
,
K
E
,
I
E
,
R
E
) are fixed.
4. Numerical examples
To see how the parameters influence the dimensionless profit rate, detailed numerical examples are
provided. Defining four temperature ratios:
10H
TT
τ
=
,
20L
TT
τ
=
,
30I
TT
τ
=
, and
40K
TT
τ
=
, which are
the ratios of the hot-, cold- and consumer-side heat reservoir temperatures and intercooling fluid
temperature to environment temperature, respectively. In the calculations,
1.4
k
=
,
1.0 /
wf
CkWK
=
,
23
1
τ τ
==
and
4
1.2
τ
=
are set. According to analysis in Ref. [46],
10
a
=
and
6
b
=
are set.

4.1 The total pressure ratio is fixed
Assuming that
1
18 (1 18)
π π
=<≤
. The effect of
R
E
on the characteristic of
Π
versus
1
π
with
0.8
HLIK
EEEE
=== =
and
1
5.0
τ
=
is shown in Figure 2. The effect of
I
E
on the characteristic of
Π

and
ex
η
versus
1
π
with
0.8
HLRK
EEEE
=== =
and
1
5.0
τ
=
is shown in Figure 3.


Figure 2. Effect of
R
E
on the characteristic of
Π

versus
1
π


Figure 3. Effect of
I
E
on the characteristic of
Π

versus
1
π


It can be seen from Figure 2 that there exists an optimal value of intercooling pressure ratio (
1
()
opt
π
Π
)
which corresponds to an optimal value of dimensionless profit rate (
opt
Π
). Also there exists a critical
intercooling pressure ratio (
11
()
c
π
). When
111
()
c
π π
<
, the calculation illustrates that the outlet temperature
of turbine is lower than the outlet temperature of high-pressure compressor, i.e.
64
TT
<
, and the
regenerative process will lead to heat loss in this case, and
Π
decreases with the increase of
R
E
. When
111
()
c
π π
>
, one has
64
TT
>
, and
Π
increases with the increase of
R
E
. The calculation illustrates that
when the fixed
π
is large, the critical point (
11
()
c
π
) will reach the right-side of the curve.
It can be seen from Figure 3 that there exists another critical intercooling pressure ratio (
12
()
c
π
). The
calculation illustrates that with the increase of
I
E
,
K
e
decreases rapidly,
H
e
increases rapidly, and
P

changes slowly. When
112
()
c
π π
>
,
Π
decreases with the increase of
I
E
. When
112
()
c
π π
<
,
Π
increases
with the increase of
I
E
. The calculation illustrates that no matter that the fixed
π
is large or small, the
critical point (
12
()
c
π
) will be always at the right-side of the peak value of the curve.

4.2 The total pressure ratio is variable
The effects of
1
τ
on the characteristics of the optimal dimensionless profit rate (
opt
Π
) and the
corresponding exergetic efficiency (
()
opt
ex
η
Π
) versus
π
is shown in Figure 4. It can be seen that there
exists an optimal value of total pressure ratio (
max
()
π
Π
) (The value of the intercooling pressure ratio is also
International Journal of Energy and Environment (IJEE), Volume 2, Issue 2, 2011, pp.199-210
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved.

205
optimal in this case) which corresponds to a maximum value of dimensionless profit rate (
max
Π
).
()
opt
ex
η
Π

also exists a extremum with respect to
π
. With the increase of
1
τ
,
opt
Π
and
()
opt
ex
η
Π
increase. Figure 5
shows the effect of
1
τ
on the characteristic of the optimal intercooling pressure ratio (
1
()
opt
π
Π
) versus
π
.
It indicates that
1
()
opt
π
Π
increases with the increase of
π
, and approximately stays constant for different
1
τ
.


Figure 4. Effects of
1
τ
on the characteristics of
opt
Π
and
()
opt
ex
η
Π
versus
π



Figure 5. Effect of
1
τ
on the characteristic of
1
()
opt
π
Π
versus
π


Figure 6. shows the effects of
R
E
on the characteristics of
opt
Π
and
()
opt
ex
η
Π
versus
π
. It can be seen that
there exists a critical total pressure ratio (
c
π
). When
c
π π
<
,
opt
Π
increases with the increase of
R
E
.
When
c
π π
>
, the calculation illustrates that the outlet temperature of turbine is lower than the outlet
temperature of high-pressure compressor, i.e.
64
TT
<
, and the regenerative process will lead to heat loss
in this case,
opt
Π
decreases with the increase of
R
E
. The effect of
R
E
on
()
opt
ex
η
Π
is similar to that of
R
E

on
opt
Π
. Figure 7 shows the effect of
R
E
on the characteristic of
1
()
opt
π
Π
versus
π
. It indicates that
1
()
opt
π
Π
increases with the increase of
R
E
.



Figure 6. Effects of
R
E
on the characteristics of
opt
Π
and
()
opt
ex
η
Π
versus
π



Figure 7. Effect of
R
E
on the characteristic of
1
()
opt
π
Π
versus
π


4.3 Dimensionless profit rate versus exergetic efficiency characteristic
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206
Figure 8 shows the characteristic of
opt
Π
versus
()
opt
ex
η
Π
with
0.8
HLIRK
EEEEE
= == = =
and
1
5.0
τ
=
.
One can find that the characteristic is loop-shaped. There exist a maximum dimensionless profit rate
(
max
Π
) and the corresponding exergetic efficiency (
max
()
ex
η
Π
), and
max
()
ex
η
Π
is termed as the finite time
exergoeconomic performance limit to distinguish it from the finite time thermodynamic performance
limit at maximum thermodynamic output. The calculation illustrates that the curve is always not closed.



Figure 8. Characteristic of
opt
Π
versus
()
opt
ex
η
Π


4.4 The effect of consumer-side temperature
It can be seen from equation (19) that the effect of consumer-side temperature (
4
τ
) on exergoeconomic
performance of the cogeneration plant is complex. Figures 9 and 10 show the characteristics of the
maximum dimensionless profit rate (
max
Π
), the corresponding exergetic efficiency (
max
()
ex
η
Π
), the optimal
total pressure ratio (
max
π
Π
) and the optimal intercooling pressure ratio (
max
1
()
π
Π
) versus
4
τ
with
0.8
HLIRK
EEEEE
==== =
and
1
5.0
τ
=
. It can be seen from Figure 9 that there exists an optimal value
of consumer-side temperature which corresponds to a double-maximum value of dimensionless profit
rate.
max
()
ex
η
Π
also exists a extremum with respect to
4
τ
. It can be seen from Figure 10 that with the
increase of
4
τ
,
max
1
()
π
Π
decreases, and
max
π
Π
increases first, and then decreases, but the value of
max
π
Π

changes slightly.



Figure 9. Characteristics of
max
Π
and
max
()
ex
η
Π

versus
4
τ



Figure 10. Characteristics of
max
π
Π
and
max
1
()
π
Π

versus
4
τ


International Journal of Energy and Environment (IJEE), Volume 2, Issue 2, 2011, pp.199-210
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved.

207
5. Conclusion
Finite time exergoeconomic analyses is applied to investigate the exergoeconomic performance of an
endoreversible intercooled regenerative Brayton cogeneration plant coupled to constant-temperature heat
reservoirs. Analytical formulae about dimensionless profit rate and exergetic efficiency are derived. The
effects of intercooling and regeneration on the general and optimal exergoeconomic performance of the
cogeneration cycle are different with the changes of pressure ratios, and it is found that there exist the
critical intercooling pressure ratio and the critical total pressure ratio. Also the optimal intercooling
pressure ratio, the optimal total pressure ratio and corresponding exergetic efficiency are obtained.
Dimensionless profit rate versus exergetic efficiency characteristic is studied and the characteristic is
loop-shaped. At last, the effect of consumer-side temperature on the exergoeconomic performance is
analyzed and it is found that there exists an optimal consumer-side temperature which leads to a double-
maximum dimensionless profit rate. The results obtained in this paper may provide some guidelines for
the optimal design and parameters selection of practical gas turbine cogeneration plant. The
dimensionless profit rate of the model cycle will be optimized by optimal allocation of the heat
conductance of the heat exchangers in Part 2 of this paper [47].

Acknowledgements
This paper is supported by The National Natural Science Foundation of P. R. China (Project No.
10905093), The Program for New Century Excellent Talents in University of P. R. China (Project No.
NCET-04-1006) and The Foundation for the Author of National Excellent Doctoral Dissertation of P. R.
China (Project No. 200136).

Nomenclature
a

price ratio of power output to exergy input rate
b

price ratio of thermal exergy output rate to exergy input rate
C

heat capacity rate (
/kW K
)
E

effectiveness of the heat exchanger
e

exergy flow rate (
kW
)
k

ratio of the specific heats
N

number of heat transfer units
P

power output of the cycle (
kW
)
Q

rate of heat transfer (
kW
)
s

entropy (
/kJ K
)
T

temperature (
K
)
U

heat conductance (
/
kW K
)
x

isentropic temperature ratio for the low-pressure compressor
y

isentropic temperature ratio for the total compression process
Greek symbols
ϕ

price of exergy flow rate (
/dollar kW
)
η

efficiency
Π

profit rate (
dollar
)
1
π

intercooling pressure ratio
π

total pressure ratio
σ

entropy generation rate of the cycle (
/kW K
)
1
τ

ratio of the hot-side heat reservoir temperature to environment temperature
2
τ

ratio of the cold-side heat reservoir temperature to environment temperature
3
τ

ratio of the intercooling fluid temperature to environment temperature
4
τ

ratio of the consumer-side temperature to environment temperature

Subscripts
c

critical value
ex

exergy
H

hot-side
I

intercooler
International Journal of Energy and Environment (IJEE), Volume 2, Issue 2, 2011, pp.199-210
ISSN 2076-2895 (Print), ISSN 2076-2909 (Online) ©2011 International Energy & Environment Foundation. All rights reserved.

208
K

consumer-side
L

cold-side
max

maximum
opt

optimal
R

regenerator
wf

working fluid
0

ambient
1,2,3, 4,5,6,7,8,9

state points of the cycle

dimensionless

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