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.

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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).

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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

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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

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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

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(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

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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.

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-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)

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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,

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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

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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

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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 - ~ )

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( 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

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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.

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