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CHARACTERISTICS CHARTS FOR PRELIMINARY
DESIGN AND SELECTION OF
A GAS TURBINE COGENERATION PLANT
K.Sarabchi & G.T.Polley
Department of Chemical Engineering
UMIST
Manchester,United kingdom
ABSTRACT
The important and well-established
performance criteria for assessment of a gas
turbine cogeneration plant (GTCP) were
examined. It was found that expressions could be
derived for these criteria in terms of two key
parameters: work efficiency and boiler efficiency.
Three characteristics charts were then
constructed. These covered gas turbine
analysis,boiler analysis and GTCP performance
analysis respectively. It is then demonstrated how
these charts may be used as an effective tool for
both performance prediction and preliminary
design analysis.
Thermodynamic design of a GTCP as an
integrated system is also investigated and
discussed.
NOMENCLATURE
Pb = Recovery boiler pressure (bar)
co = Specific heat of air (taken as.1.005
KJ/Kg.k)
egg = Specific heat of combustion gases (taken as
1.147 KJ/Kg.K)
f = Fuel air ratio
111111111 11[1)1 11111111
'
FESR = Fuel energy saving ratio
h = Specific enthalpy (KJ/Kg)
Kg = Specific heat ratio of air (taken as 1.4)
kg = Specific heat ratio of combustion gases
(taken as 1.333)
LHV = Lower heating value of fuel (taken as
50010 KJ/ICg for methane)
= Mass flow rate of air(Kg/s)
Trif = Mass flow rate of fuel (Kg/s)
• = Energy rate of fuel input (KW)
Q.6 = Energy rate of fuel for separate generation
of heat and power (KW)
• = Energy rate of turbine exhaust gas (KW)
Qh = Process heat rate (KW)
• = Heat to power ratio
• = Price ratio of heat to power (taken as 1/3)
r = Compressor pressure ratio
T = Temperature (K or C)
• = Saturation temperature at process steam
pressure
wo, = Specific net work (KJ/ICg air)
= Net power (KW)
• Tpp = Pinch point temperature difference
= Thermal efficiency of a conventional
"power only" plant (taken as 0.40)
nog = Economic efficiency
flu = Fuel utilization efficiency
Tit = Efficiency of a "heat only"boiler (taken as
Presented at the International Gas Turbine and Aeroengine Congress and Exposition
Houston, Texas - June 5-8, 1995
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Fig.1 Flow Diagram of A Gas
Turbine Cogeneration Plant
Fig.2 Temperature Profile In
Waste Heat Recovery Boiler
Whilst, Fig.2 shows temperature- enthalpy
diagram in the recovery boiler.
A distinguishing feature of this work is the
examination of the optimum design condition
required for a GTCP if it is to be designed and
optimized as an integrated system. To achieve
this a pictorial representation of GTCP
performance criteria is introduced. It can be used
as an effective tool for both performance
prediction and for preliminary design. Decision
makers should find the methodology and charts
useful for quickly identifying relevant design
parameters and estimating main performance
criteria.
With cogeneration there are a number of
important parameters and measures of system
performance. These are defined and examined
first.
0.90)
= Compressor polytropic efficiency (taken as
0.9)
= Turbine polytropic efficiency (taken as 0.9)
TIth = Recovery boiler efficiency
= Work efficiency
INTRODUCTION
Using gas turbines for the simultaneous raising
of heat and power on industrial sites is becoming
of increasing economic and environmental
importance. The most common method of
integrating a gas turbine into an industrial facility
is through the use of the exhaust energy for
steam production. It is that option that is
considered here. Other applications such as where
the exhaust gas energy has been used for drying
or process fluid heating as a source of preheated
combustion air for process heaters and boilers is
the subject of ongoing work.
This paper deals with the thermodynamic
aspects of a GTCP in which process steam is
produced in an unfired and single pressure waste
heat recovery boiler.
Fig.1 shows the schematic diagram of a GTCP.
PERFORMANCE CRITERIA
Work Efficiency
Work efficiency for a cogeneration system is
defined as the ratio of electrical power
extracted from the system to the energy of fuel
input. This is equivalent to the thermal efficiency
of a heat engine used solely for the production of
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power. It is given by the equation:
71w—
lirnet
Qj
cogeneration system is defined as the ratio of the
total useful energy output (process heat+power)
to the energy of fuel input. It is given by the
expression:
(1)
fu
Ti'Ulu
Where,
(2;.=m; LHV
Wnet+Qh
Q.r
(5)
(2)
The individual expressions for fuel utilization
efficiency, work efficiency, and heat to .power
ratio can be combined to give:
Specific Net Work
Specific net work is defined as the net power
output of the system per unit mass flow rate of
inlet air. It is given by
n fu =n,„(i+Rhp )
(6)
•
W net _
— wnet
Ina
Economic Efficiency
(3)
Although fuel utilization efficiency is probably
the most widely used criteria for cogeneration
system evaluation it suffers from a major
drawback. As with all of the performance
measures considered so far it is based solely on
thermodynamics and makes no recognition of
economics.
One way around this problem is the use of an
economic efficiency which introduces the ratio of
heat to power values. This efficiency is given by
the equation:
Work efficiency and specific net work provide
the two key parameters for the optimization of
gas turbine power plant design. The former is
related to fuel consumption and hence, operating
cost. The latter is related to equipment size. The
higher the specific net work the smaller is the
size of components required for a given power
output and hence, the lower the capital cost.
Heat To Power Ratio
A key factor in the design of a cogeneration
scheme is the system's heat power ratio. This is
the ratio of heat successfully absorbed by the
process to the power output of the power
generation system. It is given by the expression:
Oh
Rhp—
Ti
—
wnec +Rv• Oh
0?
(7)
The economic efficiency is useful in the
evaluation of the potential benefits of
cogeneration and can be used in a number of
ways. For instance, consider the case in which
the value of power is set at y (say, the current
purchase price), that of heat at x (say the current
steam raising cost) and the price of fuel is z.
Then the value of the cogeneration is:
(4)
net
Fuel Utilization Efficiency
The fuel utilization efficiency for a
3
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V= W72.9 t
y+ Qi; . x
A typical heat to power price ratio is: .33 (and
that is the value assumed in the examples
described below). However, different values may
be ascribed to different situations (for example
when local tariffs or sales prices have been
negotiated) and no value can be considered
general.
Economic efficiency can be related to work
efficiency and heat to power ratio through the
expression:
( 8)
the cost of cogeneration is:
C=Qt. z
(9)
and for breakeven:
71„0=1191(l+R,. Rhp )
Q. nnet• Y +Qh• X
(14)
(10)
and to fuel utilization efficiency through:
Or,
1+R,. Rhp)
z _ w Rv• Oh.
11 eco =71
0;
In order to have an operating advantage we
need:
5
eco-
z
(12)
z+ e
i+Rhp
(15)
Fuel Energy Saying Ratio
Another performance criteria developed for
cogeneration systems involves a comparison
between the fuel energy required to meet the
given loads of electricity and heat in the
cogeneration plant with that required in a
separate conventional plants (say in a power
station of efficiency of ti e and a "heat only"
boiler of efficiency nhb ). Then the fuel energy
saved is
In reality, a company would have to include a
consideration of both required investment and
necessary return on investment in its cost
appraisal. This can conveniently be allowed for
through the adjustment of fuel price. A required
"added value" (e) can be incorporated. Then, the
required minimum economic efficiency is given
by:
(T lecc) required
fu‘
FESR=
Of
s-Of
t
(16)
Vf,s
Where,
Wnec+—
Oh
Tie
rib
(13)
4
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(17)
hp
And
of. _ Wnet +Oh
(18)
(24)
111v
Now, using Eq.(23) in Eqs(6),(14),and(19)
fu
we can introduce the expressions for fuel
utilization efficiency , economic efficiency, and
fuel energy saving ratio:
FESR can be related to work efficiency and
heat to power ratio through the expression:
ru'r1rb"1 ty (1 - nrb)
FESR-1-
le
• lib (1 +Rhp)
(25)
(19)
ntu (11213 +1e' Rhp)
oco =Rv • r
If we assume rj hb = 0.9 and it = 0.4 then
FESR may be written in the form
FESR=1-
FESR - 1-
1 +R
(20)
(21)
The energy balance equation for the gas
turbine section of a GTCP may be written as
(22)
Inserting Eq.(22) into Eq.(21) gives
Oh
ar - Wi;ec
R
1- T1 w
(26)
(27)
to produce equations that are solely in terms of
work efficiency and recovery boiler efficiency.
Examination of the performance criteria
relationships derived above shows that although
there are several measures of note, there are only
two degrees of freedom between them. Fix any
two and all are fixed. Know any two and all can
be known.
This observations allows us to set up a quick
and simple means of appraising proposed
cogeneration systems. If we characterize a given
system in terms of work efficiency and boiler
efficiency we can then quickly estimate the heat
to power ratio the system will deliver and both
fuel utilization and economic efficiencies.
Similarly, if we know the heat to power ratio
we require and set an economic efficiency we can
determine the work and boiler efficiencies
required from the scheme. These can then be
compared with the performance of available
systems and a suitable one identified.
All that is needed to develop this technique are
relationships between turbine operating
Heat Recovery Boiler Efficiency
The easiest way of making use of the heat
engine exhaust is through steam raising and
subsequent distribution using a site steam main.
This requires the provision of a heat recovery
boiler. The efficiency of that boiler is given by
the expression:
(if = hnec +0;
1
1
n-_)
rb
+1 w ( —
Tlh
fl e Tip
2. 511 fi, (1 t 4/9Rhp)
02.1 _ T4 -T5
zb- Q v' T4 - Ti
rb+11„,(1 - Rv . nib )
(23)
Or,
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450
0.50
400
0.45
350
0.40
300
0.35
250
0.30
200
0.25
150
[x /fiN ] in dlno )ti om ouT oa ds
EFFICIENCIES
0.55
100
0.20
0
10
20
30
40
50
PRESSURE RATIO
Fig3. Performance Criteria Versus Pressure Ratio
DISCUSSIONS
Results of this work may be suitably discussed
in two parts. First, we introduce graphs which
represent thermodynamic features of designing a
GTCP as an unified or integrated system. Second,
we present charts that may be used for quick
evaluation and identification of GTCP's.
characteristics and work efficiency and between
boiler characteristics and boiler efficiency
Conventional cycle analysis can be used for
this purpose. This allows the examination of the
effect of key operating variables like compressor
pressure ratio, turbine inlet temperature, recovery
boiler pressure and the steam generator pinch
point temperature difference on the performance
of a GTCP. The methodology for this analysis is
straightforward and is given in appendix 1.
1-Graphs Related To Designing Of A GTCP
As An Integrated System
Fig.3 shows the variations of efficiencies and
specific net work with pressure ratio for given
values of turbine inlet temperature, boiler
CHARTS, OBSERVATIONS, AND
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ECONOMI CEFFICIENCIE S
PRESSURE RATIO
Fig.4 Effect Of Boiler Pressure And Pinch Point Temperature Difference On Economic
Efficiencies For 13= 1200 C
Therefore, we conclude that the use of gas
turbine designed for maximum specific net work
for cogeneration scheme, from fuel economy
point of view, is more beneficial than those
designed for maximum thermal efficiency.
Fig.4 represents the effect of boiler pressure
and pinch point temperature on the optimum
pressure ratio. It is observed that , for given
pressure, and pinch point temperature difference.
It is observed that whilst for given turbine inlet
temperature, the optimum pressure ratio for
maximum economic efficiency is between those
for maximum specific net work and maximum
work efficiency, its value is in fact closer to that
required for maximum specific net work.
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200
190
S TACKTEMPERATURE[ C]
180
170
160
150
140
130
LSo C a
I
120
0
10 20 30 40 50 60 70 80 90 100
BOILER PRESSURE[BAR]
Fig.5 Stack Temperature Versus Boiler Pressure
turbine inlet temperature, the maximum economic
efficiency for high boiler pressure (P b = 100 bar)
is achieved at low pressure ratios and hence high
exhaust temperatures. It is also seen that the
optimum pressure ratio, for given turbine inlet
temperature and boiler pressure, does not change
considerably with pinch point temperature
difference. However, dropping the pinch
temperature difference from 4.0 to 20 C will
result in the economic efficiency increasing by
about 1 percent. There is scope here for trading
off boiler capital against fuel cost. This again is
the subject of current work.
Fig.5 shows stack temperature variation with
boiler pressure for given turbine exhaust
temperature. It is observed that the range of stack
temperature variation with boiler pressure
decreases as turbine exhaust temperature
increases. Therefore, gas turbines with very high
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•
1500
1400
TURBINE INLETTEMPERATURE[ C]
1300
1200
1100
1000
900
800
700
600
0
10
20
PRESSURE RATIO
30
40
Fig.6 (CHART 1) Gas Turbine Characteristic Chart
quickly.
Gas turbine design parameters and performance
criteria may be brought together in a single chart:
CHART 1 (Fig.6). This chart shows the
relationship between turbine inlet temperature,
pressure ratio and various performance
parameters. As stated above, it has been derived
from an analysis of turbine performance.
CHART 2 (Fig.7) presents the recovery boiler
characteristics. It has been derived from an
exhaust temperature (T?600 C) may be equally
and efficiently used for high as well as low
pressure steam generation. Turbines with lower
exhaust temperature are only suitable for
relatively low pressure steam generation.
2- Charts For Ouick Evaluation And
Identification Of A GTCP
Three characteristics charts have been
constructed to evaluate and characterize a GTCP
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0.90
1
0.85
4
BOILER EFFICIENCY
0.80
0.75
0.70
0.65
0.60
0.55
0.50
0
10 20 30 40 50 60 70 80 90 100
BOILER PRESSURE[BAR]
Fig.7 (CHART 2) Boiler Efficiency Versus Boiler Pressure
analysis of boiler performance and allows the
rapid determination of boiler efficiency as a
function of boiler inlet temperature, boiler
pressure, and pinch point temperature difference.
Finally, we develop a chart that links these
using the cogeneration system criteria (heat to
power ratio, fuel utilization efficiency, economic
efficiency, and fuel energy saving ratio). This is
presented as CHART 3 (Fig.8).
APPLICATIONS OF CHARACTERISTICS
CHARTS
The characteristics charts will now be applied
to two cogeneration analysis problems. The first
problem involves a preliminary determination of
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0.50
0.45
WORKEFFIC IENCY
0.40
0.35
0.30
0.25
0.20
0.5
0.6
0.7
0.8
0.9
BOILER EFFICIENCY
Fig.8 (CHART 3) Characteristics Charts For Gas Turbine Cogeneration Plant
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1.0
How effectively can this unit be installed in a
cogeneration scheme in which steam is raised at
a pressure of 20 bar?
a gas turbine characteristics for a cogeneration
scheme. The second involves an investigation of
how suitable a given turbine is for use in a
cogeneration scheme.
Solution:
Examination of Chart 1 shows that the turbine
inlet temperature and pressure ratio are 1170 C
and 16 respectively.
Examination of Chart 2 shows that for a
turbine exhaust temperature of 500 C and a boiler
pressure of 20 bar the boiler efficiency (at boiler
pinch point temperature of 40 C) is 0.64.
Examination of Chart 3 then indicates that the
turbine can be used to provide a heat to power
ratio of around 1.2 and an economic efficiency of
around 0.488. Also, fuel energy saving ratio and
fuel utilization efficiency are around 0.25 and
0.76 respectively.
A comparison of these two examples is
interesting. In the first case we have identified a
need for a turbine inlet temperature of 1200 C
and a work efficiency of 0.33. In the second we
are offered a machine with an inlet temperature
of 1170 C and a work efficiency of 0.35. At
0.488 this machine has a lower economic
efficiency than the machine identified in the first
example. So, economically it is less efficient than
the first machine. Why?
The answer is related to the way in which the
turbine is interfaced with the boiler. In the first
case the turbine exhaust is set at 600 C. In the
second it is dropped to 500 C. This temperature
reduction would be fine for a stand alone power
system. However, for a cogeneration system (with
the chosen boiler temperature approach) it results
in a serious fall off in boiler efficiency. The
Charts clearly demonstrate this.
The boiler efficiency associated with the
second turbine is 0.64. Re-examination of Chart
3 indicates that with this boiler efficiency a work
efficiency of around 0.37 is needed in order to
achieve the required economic efficiency.
Example 1
The requirements for a cogeneration scheme
have been identified as:
Steam flow rate: 50 t/hr
Steam pressure: 20 bar
Power generation: 22MW
The level of power generation has been set on
the basis of exporting power. The minimum
economic efficiency required from the system is
0.5.
Identify a suitable gas turbine configuration.
Solution:
The system's heat to power ratio is: 1.5
Examination of Chart 3 shows that for this
ratio and economic efficiency we need a system
with a work efficiency of at least 0.33 and a
boiler efficiency of at least 0.75. It also shows
that such a system will have a fuel energy saving
ratio and fuel utilization efficiency of 0.28 and
0.83 respectively.
Examination of Chart 2 shows that for steam
raising at 20 bar at a boiler efficiency of 0.75 the
turbine exhaust temperature must be at least 600
C (at boiler pinch point temperature difference of
40 C).
Finally, examination of Chart 1 shows that for
a work efficiency of 0.33 and a turbine exhaust
temperature of 600 C we need a gas turbine with
an inlet temperature of at least 1200C and a
pressure ratio of II.
Example 2
A turbine having the following characteristics
is offered:
Power generation: 22 MW
Turbine exhaust temperature: 500 C
Thermal efficiency: 0.35
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4
1-
So we see, that whilst the second machine
would be better in a power alone context, the
first is better in a cogeneration context.
Turbine Cogeneration Plant From First And
Second-Law Viewpoints", Proceedings of 1992
ASME Cogen Turbo Power Congress.
CONCLUSION
APPENDIX 1
A pictorial representation for analysis and
selection of a GTCP was introduced as three
important characteristics charts. These charts may
be used in two different ways:
1- If we characterize a GTCP with two
performance criteria (i.e. heat to power ratio and
economic efficiency), then, we can easily
estimate other criteria as well as required design
conditions for gas turbine and recovery boiler to
meet these targets.
2- If a gas turbine is to apply for a
cogeneration scheme, then, we can readily
evaluate its cogeneration performance criteria.
Regarding integrated design of a GTCP it was
shown that using gas turbine designed for
maximum specific net work in a cogeneration
scheme will lead to a better fuel economy rather
than those designed for maximum efficiency.
Analysis procedure
The methodology for calculating of
performance parameters of a gas turbine
cogeneration system is quite straightforward
consisting essentially of the following steps:
1- Compressor and turbine specific net works
may be found front the following equations:
wc =cpa ( T2 T1 )=
-
ica -1
(28)
Cpa. T
1. (r k a . TI P` —1)
W t = Cpg ( T3 — T4 )
(kg-thi pc
( 2 9)
Pr 3
REFERENCES
Horlock, J. H, 1987, Cogeneration: Combined
Heat And Power, Pergamon Press.
Rice, I. G. 1987, "Thermodynamic Evaluation
of Gas Turbine Cogeneration Cycles: Part 1- Heat
Balance Method Analysis", ASME Journal Of
Engineering For Gas Turbine And Power, Vol.
109.
Cal, R, 1987, "Evaluation Criteria For
Cogeneration And Basic Analysis Of Gas Turbine
Cogeneration", Proceedings Of 1987 ASME
Cogen Turbo Power Congress.
Huang, F. F., 1990, "Performance Evaluation
Of Selected Combustion Gas Turbine
Cogeneration Systems Based On First And
Second-Law Analysis", ASME Journal Of
Engineering For Gas Turbine And Power, Vol.
112.
Sarabchi, K, "Parametric Analysis Of Gas
Then,the plant specific net work (KJ/Kg air) is
given by
ki„ t= (1+5) wc - wc
(30)
Where, f denotes fuel - air ratio.
2- the fuel air ratio can be obtained by
applying the first law for combustion equation of
methane.
3- Combining the energy balance equations for
evaporator with that for the evaporation and
economizer sections of recovery boiler gives the
following relation for stack temperature:
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T5 =T4
-
(T4 Tsa C AT ) (
Pr.
-
-
n
1
h12
(31)
-
,
6
,
)
n7-nb
It should be noted that process steam is
considered to be saturated, condensate is assumed
to return at 100 C and the ambient temperature is
assumed to be 15 C.
14
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