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Chapter
5
MODELING AND SIMULATION OF THE COMBINED
CYCLE GAS TURBINE POWER PLANT
5.1 Introduction
The design of combined cycle power plants is complicated because of coupling between
two different types of power cycles and the need to identify optimal distribution of power
production between them. This necessitates the need for developing computer simulation
techniques that would enabJe prediction of plant performance at various operating
conditions like with or without inlet air conditioner, different ambient temperature and
humidity conditions etc. In this chapter the details of a modeling procedure for predicting
the performance of a CCGT plant at RGCCPP-NTPC, Kayamkulam is developed. The
over all configuration of the CCGT plant at RGCCPP- NTPC, Kayamkulam is shown in
figure 5.1. The topping cycle of plant consists of two gas turbines of 115 MW capacity of
GE make (frame 9E). The downstream Heat Recovery Steam Generator, HRSG is
unfired, dual pressure units having natural circulation evaporators. The steam turbine is
of BHEL make having a capacity of 129 MW. The task of computer simulation involves
predicting the operating conditions of the system (pressures, temperatures, energy and
mass flow rates) at various mass and energy balances, all equations of state of working
substances and the performance characteristics of the individual components are satisfied.
Therefore, the availability of performance characteristics of the various components
constituting the system is a prerequisite for system simulation.
41
xl.!IEI[]I·.1 A IRI jJ;::. III, I,' 1"" Ivex! 112 13 14 I 5116 17 I e IslQ..1 F Ip I N IL I(J l""I~I,~+~J
PLANT OVERVlEVV P'10'1
Figure 5.1 Overall configuration of the dual pressure CCGT plant at
NTPC, Kayamkulam
The CCGT plant consists of compressors, liquid pumps, turbines and valves besides a
host of heat exchangers of various kinds. The strategy of system simulation is strongly
dependent on the manner in which the characteristics of various components are
available. For the purpose of system simulation, these characteristics are represented by
information flow diagram, which is essentially a block diagram indicating that the output
variables as known functions of the input variables. Often it is possible to rearrange the
functional relationships, and therefore the choice of input and output variables to some
extend are arbitrary. It is therefore possible (and necessary) to choose the input and
output variables judiciously to arrive at an optimal simulation strategy.
Modeling of the CCGT plant consists of four parts as follows,
1. Modeling of physical properties of the working fluids, here"air, combustion gases
42
and steam.
2. Gas turbine and inlet air conditioner modeling i.e. gas cycle modeling
3. Heat Recovery steam generator(HRSG) and
4. Steam turbine modeling i.e. steam cycle modeling.
5.2 Modeling Physical Properties
Here the physical properties of working fluids, air, water and steam are modeled.
5.2.1 Air Properties
The air is modeled as a perfect gas with non-constant specific heat. The variation of
specific heat at constant pressure cp
is normally modeled by several terms of a power
series in temperature T. This expression is used in conjunction with the general
thermodynamic equations to generate a gas table for particular gas.
(5.1)
The constants for the above equation come frorh the modeling work of Capt. John S.
McKinney (USAF) at the Air Force's Aero Propulsion Laboratory [35], and they ate
widely used in the industry. Above equations are valid over temperature range of 166 to
2225 Kelvin and fuel air ratio of O to 0.0676. By using the above equations, air and
combustion products properties functions are developed in visual basic language in the
air property module of the program.
5.2.2 Steam Properties
Water and steam properties are modeled by the formulation released by the International
Association for Properties of Water and Steam (IAPWS). The formulation provided is for
industrial use, and is called "IAPWS Industrial Formulation 1997 for the Thermodynamic
Properties of Water and Steam" [33] abbreviated to "IAPWS Industrial Formulation
1997" (IAPWS-IF97).
43
5.3 Modeling Gas Turbine
The schematic arrangements of gas turbine components for modeling are shown in
figure 5.2. The characteristics of a Gas turbine compressor and turbine are usually given
in the form of relationship between compressor mass flow, pressure ratio and the
efficiency. In the simulation, the pressure ratio of coupled compressor and turbine versus
mass flow is used. The polytropic efficiency of turbine and compressor are user inputs.
The simulation of various components of gas turbine like inlet air conditioner,
compressor, combustion chamber and turbine are discussed in detail below.
AIR I ·,INI,,ET
AIR Irtjected
-- CONDITIONER Water
Exhaust Gas rv--
TURBINE
'
K.
COMPRESSOR
v
COMBUSTION
CHAMBER Water
Injection
Figure 5.2 Schematic arrangements of gas turbine components for modeling
5.3.1 Inlet Air Conditioner
As shown in figure 5.3 the inputs to the air conditioner are the ambient air and injected
water. The injected water is modeled as to get evaporated inside the air conditioner, so
that the air becomes 100% humid at outlet, thus causing cooling. By energy·balance per
44
unit masS of dry air following equation (5.2) is obtained:
Air Inlet
Injected Water Unevapourated Water
Figure 5.3 Schematic diagram of inlet air conditioner
(h. + wh )0 + (m . .h . ')0air w water 111) water 111)
(5.2)
Equation 5.2 is an implicit function of outlet temperature of the air conditioner, which
is solved by iteration.
For evaporative cooler same inlet air conditioner module as above is used except the
un evaporated component of water at the outlet of inlet air conditioner. Air at outlet is
assumed always saturated and outlet temperature is calculated by iteration similar to
above. Injected water temperature is assumed equal to the adiabatic saturation
temperature calculated by iteration above.
For absorption/mechanical chillers the inlet air conditioner is replaced with a cooling
coiL Temperature at the outlet of cooling coil is user specified. If this temperature is
above the dew point of the air at inlet of cooling coil then there is no water
45
condensation on coils and thus no un evaporated water removal. If the specified
outlet temperature is below the dew point of the air at inlet of cooling coil then there
is water condensation on coils and this condensed water is assumed to be removed
from air before it enters the compressor. In this case air entering the compressor is
fully saturated. The cooler load is the enthalpy difference of air at inlet and outlet of
cooling coil.
COP of the refrigerate system is user specified. Cooling coil load calculated above
multiplied by COP gives the actual energy input to the refrigerate system. For
mechanical refrigeration energy input to the mechanical chiller is in the form of
electricity and is directly subtracted from the combined cycle plant generator output.
Incase of vapor absorption system the energy input to the refrigerate system is in the
form of heat energy. This heat energy is assumed to be taken from the low pressure
steam generated at HRSG. The equivalent amount of LP steam is deducted from
steam turbine simulation module before calculating the steam turbine output.
5.3.2 Compressor
Assuming equal pressure 'rise in all stages, the pressure ratio. across a stage is given by
equation 5 .3
P .
(P . )(I I No of stages)ratio stage = ratio compressor
Across a compressor stage the temperature rise is:
(p ratio ) (y-1) I (r 11c )
stage
And corresponding work done is given by
Wstage = �air "". hiair + Chi water - hi water) m1 water
(5.3)
(5.4)
(5.5)
Toe above equation holds true if the physical properties of working fluids is �onstant. But
46
in practice they vary with temperature artd pressure. To account for this we assume that
the total pressure rise is occurring through a large number of stages, say 1000. The
pressure and temperature rise across a stage is very small so that the properties of
working fluid are assumed constant. In this way, the above equations are evaluated across
all stages and the summation of work across all stages gives the total compressor work.
In an over-spray condition, un-evaporated water will be present inside the compressor as
the inlet air is fully saturated. As air is compressed adiabatically the temperature of air
increase thus bringing down the saturation, which promotes further evaporation of water
between stages. For modeling this, after compression of air at outlet of each stage, the un
evaporated water at inlet of stage is being mixed with the compressed air adiabatically.
Similar to inlet air conditioner writing the enthalpy balance,
h2 air + Ml water h 2 .water + Ml_ water_ unevap hl _water_ unevap
±= hx air + M x water hx water +
(Ml water unevap - ( M x water - Ml water)) h x _water_ unevap (5.6)
Where hx air, hx water are enthalpy of air and evaporated water after adiabatic mixing at
outlet of stage.
By mass balance amount of un-evaporated water at outlet after adiabatic saturation can be
found by equation 5.7
w�ed ==�_mter_urmrp- (�mter- �mter) (5.7)
Now the R.H.S of energy balance equation 5.6 is an implicit function of outlet
temperature of stage. This temperature is solved by bisection iteration in the program
module. This gives the inlet temperature for next stage and this continues until all water
is evaporated.
5.3.3 Combustor
Input to combustion chamber includes the pressure loss, combustion efficiency; heat loss
47
etc. The fuel naphtha is modeled as (CH2)n. Two options are provided for the user in the
combustor module, namely 1) specified fuel mass flow rate, and 2) specified firing
temperature. If one is specified, then the other can be calculated. Applying energy
balance across the combustor for unit mass of dry air,
hair2 + W.hwater2 + FA.LCV ·1lcomb = hair3 + W.hwater3 (5.8)
Above equation is iteratively solved for FA or Turbine Inlet Temperature, TIT as per the
specified condition.
5.3.4 Gas Turbine
Assuming equal pressure rise in all stages, the pressure ratio across a stage is given by equation 5.9,
, . )(1 I No of stages)P ratzo stage = (P ratio turbine
Across a turbine stage the te1�perature drop is:
T I T (p . ) (y-1) 17, I r
3 4 = ratio stage
Corresponding work ddne is given by
wstage = �air - h4air + (�water - h4water) m3water
(5.9)
(5.10)
(5.11)
The above equation holds true if the physical properties of working fluids is constant. But
in practice they vary with temperature and pressure. To account for this we assume that
the total pressure drop is occurring through a large number of stages, say 1000. The
pressure and temperature drop across a stage is very small so that the properties of
working fluid are assumed constant. In this way, the above equations evaluated across all
stages and the summation of work across all stages gives the total turbine work. The
blade cooling bleed loss is modeled by bypassing the specified cooling flow across the
48
turbine fIrst stage and adiabatically mixing at downstream of fIrst stage.
5.4 Modeling of Heat Recovery Steam Generator, HRSG
The arrangements of heat exchangers inside the HRSG are shown in figure 5.4. These are
basically cross flow heat exchangers of different configurations provided at various
sections of the boiler to raise water temperature and superheat the steam before entry into
the HP and LP turbines. The modeling of these heat exchangers involves determination of
the pressure and temperatures of outgoing streams for given pressures, temperatures and
flow rates of incoming streams. This is most conveniently done using the effectiveness
concept.
H11 P
C::>ECoI
3Swirl Flasll Extraction
Figure 5.4 Arrangement and designation of heat exchangers inside HRSG
49
The heat exchanger effectiveness is defined as '
Cmin (Ti.. -T. ) "in C,n
It follows that,
Q
(5.12)
(5.13)
The effectiven�ss of these cross flow exchangers requires the calculation of NTU, which
is defined as,
NTU UA
C min (5.14)
This requires the calculation of overall heat transfer coefficient, U. For a cylindrical bare
tube,
1 d 0 =----
U hint di +
ln(do/di) do +
1
2 k hext (5.15)
The inside and outside convective heat transfer coefficients required for above are taken
from correlations available in heat transfer literature. For finned tubes, fin efficiencies are
also taken into account In addition, the pressure drops in heat exchangers are calculated
from standard correlations.
In addition to heat exchangers there are a number of pumps like high pressure boiler feed
50
pump, low pressure boiler feed pump, condensate preheat pump and condensate
extraction pump which feeds water to the heat recovery steam generator i.e. HRSG. The
characteristics curves of the pumps are used to calculate pump mass flow rate and its
efficiency with respect to the pump pressure ratio. While flow rate and efficiency is
directly estimated from the pump characteristics, the work input and outlet temperature
are determined from basic thermodynamic equations.
5.4.lHeat Transfer Coefficients
5.4.1.lConfined Flows
For confined flow inside the tubes, Nusselt number can be calculated by Gnielinski
correlation [43].
[ ] [ ]2/3Nu= (/ /8)Pr Re
n.-1000
1 + d
0
1+12.7�(/ /8)(Pr213 -l) L (5.16)
Where Um is the mean fluid velocity over the tube cross-section and di is the tube
diameter. Its range of validity is:
0.5 < Pr <106
2300 <Ren< 5 x106
The friction factor for smooth tubes is calculated by using the equation recommended by
Filoneko,
5.4.1.2 Gas Side Heat Transfer Coefficient
The hot �ases flow across the tube banks both for finned and un finned -formed by the
various heat exchangers. To estimate the heat transfer coefficient across these _bundles the
51
(5.17)
correlation by Zukauskas [3,65] is used.
Finned tubes
Nuj =O.l92(albt2(sl clut t8
(hj Iclu r{).l4 Re/·65 Pr/36 (PrjlI\,t.251 x 102 < Re < 1.4 x 106
7\T. - 0 0507( / b)0.2 ( / d )0.18 (h / d" )-0.14 0.8 0.4 ( )0.25IVUf -· a s ° f ° Ref Prf Pr/Pr
w (5.18)2 x 104 < Re < 2 x 105
1.1 < a < 4.0
1.03 < b < 2.5
0.07 < hid < 0.715
0.06 < sId < 0.36
Nuf = 0.0081 (a / bt 2(~/ do t.l8 (hf / do r{).14 Ref0.95 Prf0.4 (Pr/Pr
wf25
(5.19)
2 X 105 < Re < 2 x 106
2.2 <a <4.2
1.27 <b <2.2
0.125 < hid < 0.6
0.125 < sId < 0.28
Bare tubes
" (J1I4Nu = C Rem PrO.36 PrD,max "" Pr
s
1000 <ReD, max < 2 x 106
0.7 <Pr <500
The value of constant C for staggered tubes are given as,
(5.20)
For ST I SL<2
For ST I SL>2
C=0.35(ST I SL) 1/5
C=O.4
52
m=0.60
m=0.60
The value of Reynolds number for above correlation is based on the maximum velocity
occurring within the tube bank. For staggered cohfiguration the maximum velocity may
occur at either transverse or diagonal plane. It will occur at diagonal plane if the rows are
placed such that,
Where,
In this case maximum velocity is given by,
Sr Umax= ( )u2 S
D-D
IfU max occurs at transverse plane for staggered configuration, it may be computed as:
5.4.1.3 Fin Efficiency
The fin effidency, T\r is defined as the ratio of actual heat transfer rate to the maximum
heat transfer rate that would occur with a fin of infinite thermal conductivity. This is
determined using standard expressions for cylindrical fins. The overall efficiency of a
finned surface is calculated as,
(5.21)
Where At is the fin area and A is the total heat transfer area.
53
-5.4.1.4 Evaporator Heat Transfer Coefficient
Internal convectibn boiling which occurs irt the evaporator is associated with bubble
formation at the inner surface of tfie heafed tube. The bubble growth and separation are- -
strongly infl1.1enced}by thi flow==-velocity. Tlie process is-=- further co�plicated by the
possibility of existence of differertt two-phase flow patterns. In the evaporator the water
is saturated at entry and only partially evaporated (typical vapor fraction 0.2) when it
leaves it and re enters the evaporator drum. Th� correlation of Chen [20] -that has been
widely recommended in the literature for such situations has been used.
In Chen's correlation the total heat transfer in boiling is contributed by two components,
(5.22)
Where he, the convective boiling component is calculated as,
(5.23)
Where Fis a function of Martinelli parameter (l!Xtt)
Arid hNB, the nucleate boiling component can be estimated as,
. (5.24)
54
S is a function of the local two-phase Reynolds number. The values of F and S as a function of Xtt and ReTP are given below,
F =l.361+0.7788(-1-)xii
S = 0.7194-0.8081 *10-7 ReTP
Where Rerp = Rer F 1.zs
5.4.2 Estimation of Pressure Drop
The pressure drop inside tlie tube is given as,
(11P) . . + (11P). friction turning
Frictional Pressure Drop
(5.25)
The frictional pressure drop results when fluid particles are decelerated due to the presence of structural walls such as tube, channel etc. It is calculated from the conventional Darcy equation [ 61].
(�P) = 4 fL (!_ u 2 )
friction Dh 2 p (5.26)
Where. Dh is the hydraulic diameter and f is fanning friction factor, which can be calculated as,
55
f=_!iRe (For laminar flow)
(For turbulent flow)
Pressure drop due to flow turning:
The pressure drop associated with flow turning is expressed in the form of,
(AfJ) = k(l. pf.]2)twning . 2
(5.27)
Here k is turning loss coefficient, which consists of two factors K90 ° and Ke
k = K90° x Ke
Where K90 ° is loss coefficient for 90°
Ke is correction factor for turning angle [ 61]
5.5 Simulation Procedure for HRSG
The system simulation strategy is obtained by suitably combining the information flow
diagrams of individual components of the system. Due to the non-linear nature of
equations modeling the components, an iterative solution is required. This necessitates
assumption of suitable initial values to start the simulation. The following variables are
initialized and then the simulations of the components are carried out sequentially:
1. HP circuit mass flow
2. LP circuit mass flow
3. CPH pump mass flow
4. Mass flow of LP steam to de aerator
5. HP Superheater-2 inlet temperature
6. Economizer-3 inlet temperature
56
7. Economizer-2 inlet temperature
8. Economizer inlet temperature of section from which swirl flash extraction is taken
As an example, the simulation of one heat exchanger HP super heater is explained below.
As shown in figure 5.5 the flue gas inlet temperature to HP SH-2, steam inlet to HP SH-I
and mass flows are known. Now the inlet steam temperature of HP SH-2 is assumed.
With this assumed HP SH-2 inlet temperature the steam outlet and flue gas outlet
temperature can be found from effectiveness theory and heat exchanger configuration.
From the calculated flue gas temperature the steam outlet and flue gas outlet temperatures
of HP SH-I can be found. Now constrain is that the assumed inlet temperature and
calculated outlet temperature of HP SH-1 should match. This is done by successive
approximation. Similar to this there are eight unknowns to be solved simultaneously. This
is explained as follows:
I T Flue 1 (known) I:
...
H
p
s
H
Assume
the T
I T Steam 1 (known) I
H
p
s
H
e, cunknowni I
Figure 5.5 Simulation of HP super heater
From the asswned HP steam flow; calculate the HP steam pressure from sliding pressure
curve of steam turbine. With known gas turbine exhaust temperature, flow and assumed
57
I'
inlet steam temperature find the steam outlet temperature; flue-gas outlet temperature and
pressure drop for HP superheater-2. From the outputs of HP superheater-2, we can solve
the HP superheater-1 by effectiveness concept. Similarly, HP evaporator and economizers are solved. Economizers are high-pressure economizers, therefore the
operating pressures are calculated by subtracting the DP from HPBFP outlet pressure,
which is obtained from the characteristics curve. The swirl flash extraction point is taken
from the exit of HP economizer-2 first bank from inlet.
LP circuit is calculated similar to the HP circuit, but with lesser heat exchangers. From
the assumed CPR mass flow, CPHRC pump characteristics and constant inlet CPH inlet
temperature, we can solve the CPH-1 and CPH-2 modules.
The analysis of all the components of the system is thus computed, and checks are made
to ensure that the values of various variables satisfy the following compatibility
conditions.
1. Energy balance of HP drum
2. Energy balance of LP drum
3. CPR inlet energy balance
4. De-aerator energy balance
5. Temperature matching of HP super heater-2 and 1
6. Temperature matching of economizer-3 and 2
7. Temperature matching of economizer-2 and 1
8. Temperature matching of economizer at swirl flash extraction point
Conseque:1;1.tly, the whole task of HRSG simulation reduces to that of obtaining
appropriate values of eight variables so that eight compatibility equations are satisfied.
These variables are then solved by successive approximation.
The solution gives the steam mass flows, flue gas and steams temperatures at various
locations ofHRSG as shown in temperature profile diagram, figure 5.6
58
Figure 5.6 Temperature proille ofHRSG from simulation
5.6 Steam Turbine
The schematic diagram of the steam turbine is shown in 5.7. First HP steam expands
through lIP turbine. Then the HP turbine exhausts mix with LP steam from boiler to enter
into LP turbine. The pressure, temperature and mass flow of HP and LP steam are known
from HRSG simulation. The components characteristics of HP and LP turbines like
pressure ratio and efficiency with mass flow are used to calculate the operating condition£).
The turbine work is calculated by the equation:
W;urbine = llturbine (~isen - ~ )
59
( 5.28)
1
HPT
1
HPSTEAM
2
LPT
3
4
Figure 5.7 Schematic diagram of steam turbine
From HP steam mass flow, the HP turbine pressure ratio and efficiency are calculated
from characteristics curves. Then from simple thermodynamic relation HP turbine work
is calculated. Now at the inlet of LP turbine a constant enthalpy mixer is modeled where
the HP exhaust and LP steam from HRSG mixes to form LP turbine inlet steam at lIP
exhaust pressure. Then similar to HP turbine the LP turbine work is calculated from
known mass flow, efficiency and condenser pressure.
5.7 Validation of the Model
The developed model of the combined cycle power plant was checked by comparing the
model output and designed rated performance values provided by the original equipment
manufacturer. The comparison of predicted and design values are given in table 5.1
60
Table 5.1 Comparison of predicted and design values
FUEL FLOW MWGT MWCC MWST
kg/s RATED COMPUTED RATED COMPUTED RATED COMPUTED
8.3 115.2 115.5 359.577 356.6 129.177 125.3
8.95 124.8 124.84 391.1 386.75 141.5 139.3
Deviation%
8.3 0.2604167 -0.8279172 -3.0013083
8.95 0.0320513 -1.1122475 -1.5547703
FUEL FLOW COMP AIR FLOW HRSG li:XIT TEMP TOTAL STEAM FLOW
kg/s RATED COMPUTED RATED COMPUTED RATED COMPUTED
8.3 394.17 394.3 117.9 120.4 126.61 125.302
8.95 395.833 396.1 117.1 119.6 139.17 135.82
Deviation%
8.3 0.0329807 2.1204411 -1.0330938
8.95 0.0674527 2.1349274 -2.407128
FUEL FLOW GT EFFICENCY CC EFFICENCY GT EXHAUST TEMP
kg/s RATED COMPUTED RATED COMPUTED RATED COMPUTED
8.3 31.6 31.5 49.3 48.6 553 553
8.95 31.63 31.64 49.56 49.01 588 581.5
Deviation%
8.3 -0.3164557 -1.4198783 0
8.95 0.0316156 -1.1097659 -1.1054422
As evident from the data above, the computed and rated values are excellently
matching. Maximum deviation observed is about 3% for the steam turbine values.
61
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