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Mathematical modeling and simulation of a cogeneration plant
Applied Thermal Engineering 30 (2010) 2545e2554
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Mathematical modeling and simulation of a cogeneration plant B.T. Aklilu*, S.I. Gilani Department of Mechanical Engineering, Universiti Teknologi PETRONAS, 31750 Tronoh, Malaysia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 June 2009 Accepted 6 July 2010 Available online 14 July 2010
This work aims to develop mathematical models to simulate a single shaft gas turbine based cogeneration plant with variable geometry compressor. At off-design the variable vanes are re-staggered to improve the cogeneration performance. Two modes of operation are identified with the first mode being for part load of less than 50% running to meet the part load demand. This is achieved by controlling the fuel flow and air bleeding at the downstream of the compressor to avoid surge formation. The second mode of operation is for part load greater than 50%. It is running to meet both the part load demand and the exhaust gas temperature set value by simultaneously regulating the fuel flow and the variable vanes opening. To accommodate change of compressor parameters during variable vanes re-stagger correction coefficients are introduced. A behavior of a 4.2 MW power generating cogeneration plant is simulated. The effect of variation of power and ambient temperature on cogeneration parameters like fuel consumption, temperature, pressure, variable vanes opening, efficiency and steam generated is studied. Comparison between the field data and the simulation results is in good agreement. To support the calculations required for off-design analysis, a computer program is developed in MatLAB environment. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Modeling and simulation Part load Variable vanes Single shaft gas turbine Cogeneration performance
1. Introduction The successive energy crises have stimulated the study of more efficient ways for the use of the available energy in fuels. As a consequence new technical plants have been conceived seeking primary energy conservation. One way to conserve energy is to extend power plants to a cogeneration plant. Cogeneration may be defined as the simultaneous production of electrical or mechanical energy and useful thermal energy from a single energy source, by capturing or applying heat from an exhaust gas that would otherwise be rejected to the environment. Cogeneration plant can operate at efficiencies greater than those achieved when heat and power are produced in separate or distinct processes. Therefore, the widespread use of cogeneration in power generation has produced a significant quantity of work on modeling and simulation for different purposes such as for performance prediction, fault detection and diagnosis and optimization of emission. Furthermore, to better monitor and control a cogeneration, a complete analysis for prediction of its performance is required with accompanying mathematical description. Often it is not possible to perform test bed experiments on turbine systems due to safety and cost related issues. Therefore, mathematical models of these complex systems have to be developed which simulate the actual
* Corresponding author. Tel.: þ60 1 75655752; fax: þ60 5 365 6461. E-mail address: [email protected] (B.T. Aklilu). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.07.005
cogeneration system operation over a range of different operating scenarios. The cogeneration considered for this study is a gas turbine based engine. The main units are the gas turbine and the heat recovery steam generator (HRSG). A variety of techniques have been employed for modeling the gas turbine mathematically. These include thermodynamic models, stage by stage, row by row and overall component maps. The technique employed depends on the turbine engine application and available information. To study a cogeneration or gas turbine many different steady state models have been developed in the past. Among these, fixed geometry gas turbines or gas turbine based cogenerations were studied for different purposes [1e5]. A study of the effects of the design parameters on the performance of a fixed geometry co-turbo shaft engine using component maps was carried out by Okelah [1]. Al-Hamdan and Ebaid [2] have modeled and simulated an ideal single shaft gas turbine engine. Zhang and Cai [3] using generalized component performance maps analytically studied the generalized characteristics of single shaft gas turbine and its cogeneration. The general characteristics of single shaft microturbine set at variable speed operation and its optimization were studied by Wang et al. [4]. Najjar [5] compared the performance of single and double shaft gas turbine engines and their cogeneration. The most prominent books by Cohen et al. [6] and Walsh and Fletcher [7] have explained in general how to model a gas turbine using component matching method. They also described the importance of
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variable vanes (variable inlet guide vanes and variable stator vanes) of a compressor as an alternative approach to avoid surging phenomenon during start up and at low speed (part load) gas turbine operation. Furthermore variable vanes are closed at low speed to reduce the mass flow passed by the front stages for that given speed, which raises the surge line. Bleed valves may also be used to maintain an acceptable part speed surge margin instead of variable geometry compressors. However they incur a far more severe specific fuel consumption penalty. This is because, the bleed valve flow can be up to 25% of the main stream and has had considerable work input, is either damped overboard or into a bypass duct (Walsh and Fletcher [7]). Other models that consider the effect of compressor and turbine variable vanes for different purposes are studied [8e11]. Kim et al. [8] compared the part load performance of single and two shaft engines and their potential of modulating variable inlet guide vanes to level-up the heat recovery capacity using stage stacking method. Kim and Hwang [9] studied the part load performance analysis of recuperated gas turbines considering engine configuration and operation strategy to maintain the exhaust gas temperature as high as possible. Using generalized stage characteristics and stage staking method, Muir et al. [10] have studied a variable geometry double spool engine for health monitoring of Canadian Navy engines. The variable vanes of the compressor are regulated based on the shaft speed to avoid unstable operating condition. Similarly, Bringhenti and Barbosa [11] simulated double shaft gas turbine having variable geometry compressor and turbine to search for better performance operation. As mentioned earlier, the performance of the gas turbine or cogeneration is strongly influenced by a part load and compressor variable vanes setting. However, the operation mode of a single shaft turbine with variable vanes compressor working in a cogeneration plant to maintain the exhaust gas temperature at the set value, considering the effect of ambient temperature and part load changes, has not been studied thoroughly. Therefore, this paper studied modified component based mathematical modeling of a single shaft gas turbine cogeneration plant. In ordered to achieve the objective the following issues are addressed. The design point of the cogeneration is determined. The compressor and turbine models are developed. For load less than 50% the amount of air blowdown at the down stream of the compressor as a function of terminal power output is developed. For load greater than 50% compressor parameters’ correction coefficients are developed as a function of VVs percentage opening. Mathematical model of other main components such as combustor, air inlet exhaust ducts, and HRSG are developed. Finally the component models are integrated by simulation model to get the overall cogeneration model. A real plant is modeled mathematically and simulated to study the effects of variations of power and ambient temperature on the cogeneration parameters such as fuel, temperature, pressure and variable vanes opening. Comparisons between field data and simulation results demonstrate a good agreement. To support the huge amount of calculations required for off-design analysis, a computer program has been developed in MatLAB environment. 2. Cogeneration component modeling The main components that determine the overall performance of a cogeneration plant are air intake, compressor, combustion chamber, turbine, exhaust duct and heat recovery steam generator (HRSG). The mathematical model for each component is created using thermodynamic laws, mass conservation, maps and empirical correlations. A schematic diagram of the gas turbine engine showing these components is shown in Fig. 1.
2.1. Modeling assumptions In order to develop the cogeneration model, it is assumed that the air intake and exhaust duct losses, combustion chamber pressure loss and pressure loss in the HRSG gas side are constant. It is also assumed that the process is steady state and adiabatic. Combustion consumes approximately one-fourth of the total compressed air to completely burn the supplied fuel. The excess air is used to cool the combustion chamber and mixes with the combustion products to reduce the gas temperature at inlet to the first stage of turbine. This results in the turbine inlet temperature to be below 1300 K. Moreover, the highest allowable gas inlet temperature with uncooled blades is 1250e1300 K [12]. The inlet temperatures are within uncooled turbine blades range and require a little cooling. Hence, the blade cooling effect is marginalized. 2.2. Air intake model The air intake entry relationships, for temperature Ta and pressure pa are given in Eqs. (1) and (2). Flow is drawn into the gas turbine and accelerated to the inlet velocity from a stagnation condition far from the inlet. The Mach number is nearly zero at the inlet and therefore the ambient static and total properties are equal.
T1 ¼ Toa ¼ Ta
(1)
p1 ¼ poa ¼ pa
(2)
Furthermore, the air inlet duct is assumed to be an adiabatic duct in which total temperature is conserved and fluid friction is assumed constant. Hence the inlet duct entry and exit relationships for temperature T1 and pressure p1 are determined by Eqs. (3) and (4), respectively.
p2 ¼ p1 ð1 pi Þ
(3)
T2 ¼ T1
(4)
2.3. Compressor model and analysis Performance maps and design point data of both the compressor and the turbine are not readily available. Therefore, first the design point data were determined using the manufacturer’s unconventional map data and thermodynamic laws. Once the design point data were obtained using scaling law, the performance of the compressor and the turbine was developed, according to the details provided in Ref. [13]. The scaled performance maps of the compressor are shown in Fig. 2. This map is fully described mathematically by a number of dimensionless parameters or normalized parameters [2] as given in Eqs. (5)e(9):
sc d2 po2
¼
!1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi _ a cpa To2 po3 ga 1=ga m 1 1 dN pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 po2 2p hc d2 po1 cpa To2 pffiffiffi
_ a q po3 sc N m ¼ f hc ; pffiffiffi; ; d q d po2
(5)
! (6)
The compression power Wc is given by:
Wc ¼ d2 po2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffi m _ a cpa To2 1 po3 ðga 1Þ=ga 1 cpa To2 hc po2 d2 po2
(7)
B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
2547
Fig. 1. Schematic representation of a single shaft gas turbine based cogeneration plant.
where
q ¼
T Tref
(8a)
p pref
(8b)
and
d¼
The compressor total exit temperature To3 is determined using the compressor property ratio relationships:
To3 ¼ To2 þ
po3 ðga 1Þ=ga 1 hc po2
To2
(9)
The specific heat of air is given by Eq. (10) and taken from [11].
cpa ¼ A0 þ A1TZ þ A2TZ 2 þ A3TZ 3 þ A4TZ 4 þ A5TZ 5 þ A6TZ 6 þ A7TZ 7 þ A8TZ 8
ð10Þ
The specific heat ratio for ideal gas is a function of temperature and given by:
ga ¼
cpa cpa R
(11)
The constants A0, A1, A2, ., A8 are given in Table 1. 2.3.1. Compressor variable vanes system The Variable Vanes (VVs) system position varies depending on the gas turbine output set values. This change of vanes position varies the effective volume of air which enters the compressor rotor. The axial compressor used in the gas turbine’s VVs system consists
a 16
of a single row of variable Inlet Guide Vanes (IGVs) and three rows of Variable Stator Vanes (VSVs). This cogeneration has two modes of operation, that is, when the load is less than 50% and when it is greater than 50%. For load that is less than 50%, the cogeneration runs to meet the power demand and during this mode of operation the VVs are fully opened while the bleed valve is regulated. For load that is greater than 50%, the bleed valve is fully closed while the VVs are regulated to maintain the exhaust gas temperature at the set point, and the fuel flow regulated to meet the part load. For the first mode of operation the bleed valve opening is regulated. It is designed to prevent engine surge by reducing backpressure imposed on the engine compressor during starting, shut down and low load operation. Furthermore, in this mode, VVs are opened fully (100%) whereas the compressor downstream air flow is regulated with the help of bleed valve [14]. The controlled parameter is the part load and a decreasing linear percentage bleed is assumed. After a number of iteration and validation with different sets of data, the following correlation is selected:
_b ¼ m
(12)
For each position of the VVs for the second mode of operation, its performance map is changing. In order to accommodate this change, correction coefficient models are developed. The gas turbine data is monitored and stored by Turbotronic device that does not monitor the absolute VVs angle but rather monitors the VVs percentage opening. To overcome the unavailability of VVs absolute angle opening, modeling was done based on VVs percentage opening. To find the correction coefficient’s trend, a fixed geometry compressor was simulated for a set of experimental data. Once simulated, the compressor’s actual to simulated pressure ratio versus the
b 0.95
14
0.9
1.2
12
0.85
1.1
10
E ffi ci ency
Pressure ratio
_ net W þ 13:5 400
1
8
0.8 1 0.75
0.7
6
0.6
0.9 4
0.7
0.7
0.8
0.65
0.5
0.3
0
5
10 15 Corrected flow [kg/s]
1.2
0.4
0.3 0.4
0
1.1 0.9
0.5
0.6
2
0.8
20
25
0
5
10 15 Corrected flow [kg/s]
20
25
Fig. 2. Taurus 60 compressor maps for relative speed varying between 0.3 and 1.2 [13]. (a) Pressure ratio versus corrected flow. (b) Efficiency versus corrected flow.
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The combustor exit pressure is given by:
Table 1 Constants required to calculate cp of air and kerosene [7].
po4 ¼ po3 ð1 pcc Þ
Constants A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
0.992313 0.236688 1.852148 6.083152 8.893933 7.097112 3.234725 0.794571 0.081873 0.422178 0.000491
B0 B1 B2 B3 B4 B5 B6 B7 B8 B9
0.718874 8.747481 15.863157 17.254096 10.233795 3.081778 0.361112 0.003919 0.055593 0.0016079
percentage VVs openings was plotted and a negative linear slope trend was obtained. After a number of iterations and validations correction coefficients were obtained as shown in Eqs. (13) and (14), the compressor flow correction coefficient coincides with the pressure ratio correction coefficient whereas the efficiency correction coefficient is different and is modeled as:
_ acco ¼ 2:90667 103 a þ 0:819787 prcco ¼ m
(13)
hcco ¼ 1:66667 104 a þ 0:9896667
(14)
For each VVs percentage opening, the new compressor performance map is obtained by multiplying the design point performance map parameters with their respective correction coefficients. Using the modified compressor performance map the rest of the parameters can be easily determined if any of the two dimensionless parameters are known.
The combustion chamber is SoLoNOx type. It is a lean premix low emission combustion system designed to provide combustion reaction temperatures low enough to minimize NOx formation and high enough to minimize CO emission. For calculating the combustor exit temperature and fueleair ratio, constant pressure loss is assumed. Walsh and Fletcher [7] provided curve fits for specific heat as functions of temperature and fueleair ratio (FAR) at one atmosphere. The gas constant is also given as a function of FAR. The equations are as follows:
_ cpg ðTo4 To3 Þ DH34 m ¼ ¼ f _a m LHVhcc LHVhcc
(15)
For calculation within 1% accuracy loss for natural gas, cpg at the mean temperature is evaluated by:
cpg ¼
1:0001 þ 0:9248 FAR 2:2078 FAR2 cpl
(16)
where cpl in [kJ/kg K] of combustion products of liquid fuel (kerosene) in dry air is given by:
cpl ¼ A0 þ A1TZ þ A2TZ 2 þ A3TZ 3 þ A4TZ 4 þ A5TZ 5 þ A6TZ 6 þ A7TZ 7 þ A8TZ 8 þ ðFAR=ð1 þ FARÞÞ B0 þ B1TZ þ B2TZ 2 ð17Þ þ B3TZ 3 þ B4TZ 4 þ B5TZ 5 þ B6TZ 6 þ B7TZ 7 where TZ ¼ T/1000. Once the FAR is determined, the gas constant can be obtained using the following expression:
R ¼ 287:05 þ 212:85FAR 197:89FAR2
Solving the exact exit temperature with an assumed initial value at the given ambient conditions and power output, results in a non linear equation that is solved for FAR numerically using Newton Raphson’s method. 2.5. Turbine modeling and analysis The performance characteristics of a turbine, like that of a compressor, are described mathematically by a number of fully dimensionless parameters or normalized parameters [2]. Equation (20) is in complete dimensionless form and equation (21) is the general form.
st d2 po4
1 dN h pffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2p t cp To4
!1
mg
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi cpg To3 po5 ðgg 1Þ=gg 1 po4 d2 po3 (20)
pffiffiffi
_ g q po4 st N m ¼ f ht ; pffiffiffi; ; d q d po5
! (21)
where
q ¼
T Tref
(22a)
p pref
(22b)
and
d¼
The expansion power Wt and the final stagnation temperature To5 in the expansion process are calculated as follows:
2.4. Combustion chamber modeling and analysis
FAR ¼
(19)
(18)
Wt ¼ d2 po4
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffi m _ g cpg To4 po5 ðgg 1Þ=gg h cpg To4 1 t po4 d2 po4
po5 ðgg 1Þ=gg To5 ¼ To3 To3 ht 1 po4
(23)
(24)
If any two dimensionless parameters are known, the rest of the parameters can be easily determined with the help of performance maps indicated in Fig. 3 and Eqs. (20)e(24). 2.6. Heat recovery steam generator model and analysis The HRSG in this study is a natural circulation water tube type producing saturated steam [15]. Therefore, it consists of two primary coils; evaporator and economizer. Fig. 4 shows the temperature energy diagram of evaporator and economizer in counter flow model of the HRSG. The exhaust gas is supplied to the gas side of the evaporator at temperature Tg5. Exhaust gas comes out of the evaporator at Tg6 and enters at the same temperature to the economizer. The exhaust gas comes out of the economizer at a temperature Tg7 and is rejected to the atmosphere. Applying energy balance on the evaporator between the steam and the exhaust gas streams and simplifying gives:
Tg5 Tsat UA ln ¼ _ g cpgev m Tg6 Tsat
(25)
Equation (25) indicates that the overall heat transfer coefficient is dependent on the mass flowrate outside the tube, that is, U is _ 0:6 provided that fouling is not severe [16]. proportional to m g
B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
a
b
24
1
0.9 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
20 18 16 14
0.8
Efficiency
C orrected fl ow [kg/s]
22
2549
0.7
0.6
0.5
12 10 0
5
10
15
20
25
30
35
40
45
0.4 0
5
10
15
Pressure ratio
20
25
30
35
40
45
Pressure ratio
Fig. 3. Taurus 60 turbine maps for relative speed varying between 0.3 and 1.2 [13]. (a) Corrected flow versus pressure ratio. (b) Efficiency versus pressure.
Substituting this in Eq. (25), simplifying and solving for exhaust gas temperature at the exit of the evaporator gives
Tg6 ¼ Tsat þ
Tg5 Tsat
(26)
0:4
eK ðmg Þ
where K ¼ A=cpgev is determined at the design point. Once the evaporator exit gas temperature is calculated, the evaporated duty is calculated from the exhaust gas stream as follow:
Q_ ev
_ g cpgev Tg5 Tg6 ¼ m
(27)
In order to estimate the steam flow, the feedwater temperature leaving the economizer, Tfw2, must be known. Assuming Tfw2 and applying energy balance on the evaporator section between the two streams, the steam produced can be calculated by Eq. (28). However, the actual steam produced is arrived at through series of iteration.
_s ¼ m
Q_ ev
To make sure that Tfw2 is a valid value, the value of (UA) for the economizer at design conditions is computed using the following expression:
hg hfw2 þ xbd hf hfw2
(28)
Q_ ecdesign LMTDecdesign
(30)
The relationship between (UA)design and (UA)off-design is given by Ganapathy [16] as follows:
ðUAÞoffdesign ¼ ðUAÞdesign
_ goffdesign m _ gdesign m
!0:65 (31)
From the economizer duty that is obtained by assuming Tfw2 and Tg6 values, the economizer exhaust gas temperature is calculated by:
Tg7 ¼ Tg6
Q_ eca _ mg cpgec
(32)
Hence, the new economizer LMTD at off-design can be calculated using
Moreover, the economizer assumed duty is calculated by:
_ sþm _ bd hfw2 hfw Q_ eca ¼ m
ðUAÞdesign ¼
(29) LMTDoffdesign ¼
Tg7 Tfw Tg6 Tfw2 " # Tg7 Tfw ln Tg6 Tfw2
(33)
Once the UA and LMTD of economizer are known at off-design conditions, the economizer duty can be calculated as follows:
Q_ ecc ¼ ðUA*LMTDÞoffdesign
(34)
If the economizer’s calculated duty is the same as the assumed value, then the assumed economizer exit temperature and the other parameters are valid, otherwise the procedure needs to be repeated with new Tfw2 value. Fig. 5 shows the algorithm for offdesign analysis of the cogeneration. The following equations are used to calculate the saturated liquid and vapor enthalpies at the saturated temperature [17]:
hf ðTÞ ¼ 2099:3 a1 þ
8 X
! ai TRi1
(35)
i¼2 1=3
hg ðTÞ ¼ 2099:3 1þb1 TR
5=6
þb2 TR
7=8
þb3 TR
þ
8 X
! bi TRi3
i¼4
Fig. 4. Temperature versus energy profile in the HRSG of a cogeneration plant [16].
where TR ¼ ð647:3TÞ=647:3. The values of coefficients ai and bi are given in Table 2.
(36)
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Assume variable vanes percentage opening
Fixed geometry compressor maps
Modify compressor maps at the given VVs
If T5 simulated Tset then VVs VVs old VVs, else VVs VVs old VVs
Assume compressor air flow ma Assume the combustor exit temperature (T4)
ma
ma ,old
m
Solve the set of equations that represent the gas turbine component process
If Wnet simulated then T4 T4,old , T4 T4,old T
Wnet set T, else
No
Is the power produced =part load demand ? Yes No
Is the simulated turbine pressure the same as the set value? Yes No
Is the air flow within the surge and choke margin and/or the exhaust temperature equal to the set value? Yes With T5 and mg as an input and assumed Tfw2 call saturated vapor and liquid enthalpy subroutiens and get hv, hf, hfw2, hfw Apply energy balance on the evaporator and find the steam generated Calculate economizer duty from the feedwater stream (Q ) ec ,a
T fw 2 T fw 2
Apply energy balance on the economizer between the two streams and find Tg7
T fw 2 ,old T fw 2 ,old
T , if Qec ,c T , if Qec ,c
Qec ,a Qec ,a
Calculate the economizer off design duty using the LMTD ( Qec,c ) No
Qec ,a Qec ,c Qec ,c
ter
Yes Calculate all useful parameters Fig. 5. An algorithm of the simulation model for single shaft gas turbine based cogeneration plant.
The water vapor saturation temperature of the drum is obtained at its corresponding drum pressure by interpolating saturated steam data [18]. The data within the drum pressure operating range is stored in the computer simulation program. The following equations are used to evaluate the gas turbine thermal efficiency, HRSG and cogeneration efficiencies, respectively.
ht ¼
Net power produced wnet ¼ _ f LHV m Q_ in
hHRSG ¼
Heat recovered Q_ þ Q_ ev ¼ ec _ f LHV m Q_ in
(37)
(38)
B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554 Table 2 Coefficients of Eqs. (35) and (36) [16].
2551
100
ai
bi
1 2 3 4 5 6 7 8
0.8839230108 2.67172935 6.22640035 13.1789573 1.91322436 68.7937653 124.819906 72.1435404
0.457874342 5.08441288 1.48513244 4.81351884 2.69411792 7.39064542 10.4961689 5.46840036
Simulated Actual
90
VVs opening [%]
i
80 70 60 50
htotal
Power þ Heat recovered Q_ þ Q_ ev ¼ ¼ wnet þ ec _ _ f LHV m Q
(39)
40
in
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Relative load 3. The simulation program
Fig. 6. Percentage VVs opening versus relative load.
WL ¼ Wt Wc
(40)
_ cþm _ f m _b _t ¼ m m
(41)
4. Experimental configuration The test data is obtained from a Taurus 60 gas turbine based cogeneration plant located at the Universiti Teknologi PETRONAS (UTP). It consists of a single shaft gas turbine engine, a generator with accessories, and heat recovery steam generator and auxiliary systems. The Taurus 60 has an ISO rating power production capacity of 5.3 MW with a maximum rotational speed of approximately 14,944 rpm. However it is limited to produce 4.2 MW terminal power output due to high gas turbine inlet ambient temperature. It contains a 12 stage axial flow compressor with an inlet guide vane and three stages of stator vanes, and a three stage turbine. The Taurus 60 turbine’s operation has been recorded using Turbotronic Control System monitoring and reception of data at the UTP’s Control room computer workstations to determine the status of the cogeneration operation including system temperatures,
pressures, vibration levels, VVs percentage opening, power output and fuel flowrate. 5. Results and discussion The actual data for comparison, ambient temperature and power data used for simulation input were collected in active plant that is providing electricity and chilled water produced by steam driven absorption chiller to the campus. In order not to hamper the operation of the plant, experimental rig input variable manipulation could not be done. Therefore, the results show integration of both the effect of change of load and ambient temperature. During the part load variation, the ambient temperature was varying between 25.5 and 34 C. The gas turbine parameter variations during the simulation for both modes of operation, that is, for less than and greater than 50% load, are shown in Figs. 6e11. In each mode the target of the operation is different. The first one involves compressed air bleeding control at the downstream of the compressor while the VVs are opened fully to meet the power demand. In the second mode, the VVs and fuel mass flow are regulated to maintain the exhaust gas temperature at the set value and minimize emission while the bleed valve is closed. As these two modes of operation
1200
Inlet Outlet
1100 Turb ine temperatures [K]
A computer program for simulating a cogeneration plant should basically satisfy matching conditions analytically between the various components to produce the matching point. This simulation program is a component based modeling subroutines suitable for steady state modeling of a single shaft gas turbine for cogeneration application. The externally applied conditions are load and the surrounding conditions ambient pressure and temperature. With these inputs the simulation model will enable the operating point of each cogeneration component inlet and outlet properties to be found with one pass through the cogeneration calculation. However, a valid point is obtained after a number of iteration. Once gas turbine valid point is obtained, HRSG and cogeneration performance could be predicted. Fig. 5 shows detail of the simulation algorithm. The variable vanes percentage angle opening and fuel injected into the combustion chamber are regulated to control the required exhaust gas temperature and part load, respectively. For the simulation, 12 C and 8 C pinch point and approach point temperature differences are used, respectively. The program contains thermodynamic data for air, steam/water and combustion products so that it can predict the specific heats of air, enthalpy of steam/water and combustion gases at different temperatures. The matching conditions at steady state conditions for constant shaft speed are the work and flow compatibilities;
1000 900 800 700 600
0.2
0.3
0.4
0.5 0.6 0.7 Relative load
0.8
Fig. 7. Turbine temperatures versus relative load.
0.9
1
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B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
12
Simulated Actual
Fuel consumption [kg/sec]
11 Compressor pressure ratio
0.35
Simulated Actual
10 9 8
0.3
0.25
0.2
0.15
7 6
0.1
0.2
0.3
0.4
0.5 0.6 0.7 Relative load
0.8
0.9
1
0.2
0.3
0.4
0.5 0.6 0.7 Relative load
0.8
0.9
1
Fig. 10. Fuel consumption versus relative load.
Fig. 8. Compressor pressure ratio versus relative load.
targets are different when the load reaches 50%, there is a sudden ramp up of parameters that is manifested. Furthermore, when the power reaches above 50% load, the combustion chamber SoLoNOx low emission operation begins. The T5 set point is ramped up and variable vanes modulated as necessary to maintain the turbine exit temperature, T5, to the set point. This set point will vary slightly, depending on the emissions requirement. Fig. 6 shows the variation of the compressor VVs opening. As the load continues to increase for more than 50%, in the low emissions range, the VVs are allowed to open as needed to maintain the set point temperature, T5. This temperature variation with part load is shown in Fig. 7. For part load greater than 50%, the exhaust temperature is maintained constant and is used to recover heat in the HRSG. For load less than 50% the VVs are fully opened and the exhaust gas temperature increases slightly as part load increases. The engine is running mostly in the second mode, hence it delivers low emission and high exhaust gas temperature Fig. 8 shows compressor exit pressure variation with part load. The compressor exit is increasing as the part load increases. The possible cause for the small discrepancies between the simulated and the actual data for load less than 50% is the constants in the linear air bleed assumption. The variation of the exhaust gas mass
flow with part load is shown in Fig. 9. It is increasing as the part load increases in its corresponding mode. Fig. 10 shows the variation of fuel consumption with part load. The fuel consumption is observed to increase as part load increases. Basically, in the first mode, a certain fraction of the air is bypassed by the combustion chamber and turbine and useful energy damped to avoid surge in the compressor. The fuel consumption in the first mode is smaller than the second mode operation. Furthermore, air mass flowrate in their relative corresponding operating mode is almost the same. As a result, in the first mode of operation, relatively higher pressure ratio is required to meet the required part load and to compensate the damped energy. The abrupt jumps happened due to change of operation mode at 50% load and the slight inclination is due to unavailability of continuous data. The gas turbine efficiency, plotted in Fig. 11, shows an increase with the relative power. This is expected and the maximum efficiency is around 0.29. As the specific fuel consumption is inversely proportional to efficiency, it is decreasing with the increase of relative load. The input to the HRSG is the exhaust gas mass flow which varies with the part load. Basically, the HRSG starts to work at 50% and above part load. Furthermore, it is not operating at full load and
22
Exhaust gas flow [kg/s]
20 19 18 17 16 15
0.2
0.3
0.4
0.5 0.6 0.7 Relative load
0.8
Fig. 9. Exhaust gas mass flow versus relative load.
0.9
1
0.4
Efficiency
1
0.2
Efficiency
Specfic fuel consumption [kg/kWh]
2 21
Sfc
0
0.2
0.4
0.6 Relative load
0.8
1
0
Fig. 11. Simulated specific fuel consumption and efficiency versus relative load.
B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
6. Conclusions
Actual Simulated
Steam production rate [Tons/hr]
10 8 6 4 2 0 1
100 80
0.8 0.6 Rela tiv e loa d
ni ope ter r e Div 60
0.4
40
ng
[% ]
Fig. 12. Variation of steam production with relative load and diverter damper opening.
therefore the exhaust gas mass flow entering the HRSG is controlled by the diverter damper. Hence, the other parameter that controls the amount of steam production other than the part load is the diverter damper opening. Fig. 12 shows the turbine relative part load and diverter damper opening increase and the steam production increase at the constant exhaust gas temperature. For comparison the actual steam produced is included. This effect also increases the HRSG efficiency and correspondingly the total cogeneration efficiency as indicated in Fig. 13. In this case the plant thermal load demand is not high; as a result the diverter damper is not opened fully. This condition results in some unrecovered turbine exhaust energy, thereby causing a reduction in overall system energy efficiency.
Cogen effeiciency
Turbine efficiency
HRSG efficiency
Acknowledgements The authors would like to thank UTP for providing all the necessary supports to conduct this study. Nomenclature
T p N d
h _ m VVs _ W cp R Q_ ecc cpgec cpgev x pr
0.8
Efficiency
A mathematical model representing a single shaft gas turbine based cogeneration plant is developed. Two modes of operation are identified. One is for part load less than 50% where it is running to meet the part load demand. The other one is for part load greater than 50% load to meet both the power demand and maintain the set point exhaust gas temperature. The model is generic and it can predict a single shaft based cogeneration plant for a wide range of ambient temperature. However, when the data collected for input and validation purpose the ambient temperature was varying between 25 C and 34 C. The assumed correction coefficients for compressor VVs are accurate and valid as the comparisons of the simulated values are in good agreement with the actual data. Here, the set of equations that represent the processes are solved with the help of computer and using in house developed tool in MatLAB environment. Representative numerical results are presented to validate the model against experimental data and the estimated cogeneration behavior is in a good agreement with the actual data set. Based on these findings, it is concluded that the developed model is suitable for simulation of single shaft gas turbine and its cogeneration plant. The model is a useful tool for preparing the operating strategy of the plant. The change of ambient temperature, part load and the like on the entire operation can be predicted.
g p
1
0.6
a h LHV U A LMTD
0.4 0.2 0 1
100 80
0.8
Relativ
2553
60
0.6
e loa d
0.4
40
Div
g [% e nin p o r erte
]
Fig. 13. Simulated efficiencies variation with respect to relative load and diverter damper opening.
s
Q_ eca
temperature pressure speed diameter efficiency mass flow variable vanes power specific heat at constant pressure characteristic gas constant specific heat ratio fraction of pressure drop economizer calculated duty specific heat of gas in economizer specific heat of gas in evaporator fraction pressure ratio VVs percentage opening enthalpy lower heating value overall heat transfer coefficient surface area log mean temperature difference torque economizer assumed duty
Subscripts o total property b bleed a air f fuel or saturated liquid water
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B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
g gas or saturated water vapor i inlet c compressor t turbine L load cco correction coefficient cc combustion chamber 1,2,3,4,5,6,7 designate inlet and exit points fw feedwater S steam produced sat saturated bd blowdown l liquid fw2 feedwater state leaving economizer
References [1] Mohamed Rafat Sayed Okelah, Optimization of the design parameters of a coturboshaft gas turbine engine as a heavy equipment power plant, PhD thesis, Carleton University, Ottawa, Ontario, 1980. [2] Qusai Z. Al-Hamadan, Munzer S.Y. Ebaid, Modelling and simulation of a gas turbine engine for power generation, ASME Journal of Engineering for Gas Turbines and Power 128 (2006) 302e310. [3] Na Zhang, Ruixin Cai, Analytical solutions and typical characteristics of partload performances of a single shaft gas turbine and its cogeneration, Energy Conversion and Management 43 (2002) 1323e1337. [4] Wei Wang, Ruixin Cai, Na Zhang, General characteristics of single shaft microturbine set at variable speed operation and its optimization, Applied Thermal Engineering 24 (2004) 1851e1863.
[5] Yousef S.H. Najjar, Comparison of performance for cogeneration systems using single or twin shaft gas turbine engines, Applied Thermal Engineering 17 (1997) 113e124. [6] H. Cohen, G.F.C. Rogers, H.I.H. Saravanamuttoo, Gas Turbine Theory, fourth ed. Longman Group, 1996. [7] P. Walsh, P. Fletcher, Gas Turbine Performance. Blackwell, England, 2004. [8] J.H. Kim, T.S. Kim, J.L. Sohn, S.T. Ro, Comparative analysis of off-design performance characteristics of single and two shaft industrial gas turbines, Transaction of ASME 125 (2003) 954e960. [9] T.S. Kim, S.H. Hwang, Part load performance analysis of recuperated gas turbines considering engine configuration and operation strategy, Energy 31 (2006) 260e277. [10] D.E. Muir, H.I.H. Saravanamuttoo, D.J. Marshall, Health monitoring of variable geometry gas turbines for the Canadian Navy, ASME Journal of Engineering for Gas Turbines and Power 111 (1989) 244e250. [11] C. Bringhenti, J.R. Barbosa, Methodology for gas turbine performance improvement using variable-geometry compressors and turbines, Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy 218 (2004) 541e549. [12] S.L. Dixons, Fluid Mechanics, Thermodynamics of Turbomachinery, fifth ed. Elsevier ButterwortheHeinemann, London, 2004. [13] Syed Ihtsham-ul-Haq Gilani, Aklilu Tesfamichael Baheta, Mohad. Amin A. Majid, Thermodynamics approach to determine a gas turbine components design data and scaling method for performance map generation, in: International Conference on Plant Equipment and Reliability, Selangor, Malaysia, 2008. [14] UTP Cogeneration/District Cooling Project, Installation and Maintenance Instructions, vol. 2, Solar Turbines Incorporated, 2001. [15] UTP Cogeneration/District Cooling Project, General Description of System Plant, vol. 1. [16] V. Ganapathy, Industrial Boilers and Heat Recovery Steam Generators Design, Applications and Calculations. Marcel Dekker Inc., New York, 2003. [17] Da-Wen Sun, Thermodynamic design data and optimum design maps for absorption refrigeration systems, Applied Thermal Engineering 17 (1996) 211e221. [18] Sonntag, Borgnakke, Van Wylen, Fundamentals of Thermodynamics. John Wiley & Sons, Inc, New York, 1998.
Contents lists available at ScienceDirect
Applied Thermal Engineering journal homepage: www.elsevier.com/locate/apthermeng
Mathematical modeling and simulation of a cogeneration plant B.T. Aklilu*, S.I. Gilani Department of Mechanical Engineering, Universiti Teknologi PETRONAS, 31750 Tronoh, Malaysia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 June 2009 Accepted 6 July 2010 Available online 14 July 2010
This work aims to develop mathematical models to simulate a single shaft gas turbine based cogeneration plant with variable geometry compressor. At off-design the variable vanes are re-staggered to improve the cogeneration performance. Two modes of operation are identified with the first mode being for part load of less than 50% running to meet the part load demand. This is achieved by controlling the fuel flow and air bleeding at the downstream of the compressor to avoid surge formation. The second mode of operation is for part load greater than 50%. It is running to meet both the part load demand and the exhaust gas temperature set value by simultaneously regulating the fuel flow and the variable vanes opening. To accommodate change of compressor parameters during variable vanes re-stagger correction coefficients are introduced. A behavior of a 4.2 MW power generating cogeneration plant is simulated. The effect of variation of power and ambient temperature on cogeneration parameters like fuel consumption, temperature, pressure, variable vanes opening, efficiency and steam generated is studied. Comparison between the field data and the simulation results is in good agreement. To support the calculations required for off-design analysis, a computer program is developed in MatLAB environment. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Modeling and simulation Part load Variable vanes Single shaft gas turbine Cogeneration performance
1. Introduction The successive energy crises have stimulated the study of more efficient ways for the use of the available energy in fuels. As a consequence new technical plants have been conceived seeking primary energy conservation. One way to conserve energy is to extend power plants to a cogeneration plant. Cogeneration may be defined as the simultaneous production of electrical or mechanical energy and useful thermal energy from a single energy source, by capturing or applying heat from an exhaust gas that would otherwise be rejected to the environment. Cogeneration plant can operate at efficiencies greater than those achieved when heat and power are produced in separate or distinct processes. Therefore, the widespread use of cogeneration in power generation has produced a significant quantity of work on modeling and simulation for different purposes such as for performance prediction, fault detection and diagnosis and optimization of emission. Furthermore, to better monitor and control a cogeneration, a complete analysis for prediction of its performance is required with accompanying mathematical description. Often it is not possible to perform test bed experiments on turbine systems due to safety and cost related issues. Therefore, mathematical models of these complex systems have to be developed which simulate the actual
* Corresponding author. Tel.: þ60 1 75655752; fax: þ60 5 365 6461. E-mail address: [email protected] (B.T. Aklilu). 1359-4311/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.applthermaleng.2010.07.005
cogeneration system operation over a range of different operating scenarios. The cogeneration considered for this study is a gas turbine based engine. The main units are the gas turbine and the heat recovery steam generator (HRSG). A variety of techniques have been employed for modeling the gas turbine mathematically. These include thermodynamic models, stage by stage, row by row and overall component maps. The technique employed depends on the turbine engine application and available information. To study a cogeneration or gas turbine many different steady state models have been developed in the past. Among these, fixed geometry gas turbines or gas turbine based cogenerations were studied for different purposes [1e5]. A study of the effects of the design parameters on the performance of a fixed geometry co-turbo shaft engine using component maps was carried out by Okelah [1]. Al-Hamdan and Ebaid [2] have modeled and simulated an ideal single shaft gas turbine engine. Zhang and Cai [3] using generalized component performance maps analytically studied the generalized characteristics of single shaft gas turbine and its cogeneration. The general characteristics of single shaft microturbine set at variable speed operation and its optimization were studied by Wang et al. [4]. Najjar [5] compared the performance of single and double shaft gas turbine engines and their cogeneration. The most prominent books by Cohen et al. [6] and Walsh and Fletcher [7] have explained in general how to model a gas turbine using component matching method. They also described the importance of
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B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
variable vanes (variable inlet guide vanes and variable stator vanes) of a compressor as an alternative approach to avoid surging phenomenon during start up and at low speed (part load) gas turbine operation. Furthermore variable vanes are closed at low speed to reduce the mass flow passed by the front stages for that given speed, which raises the surge line. Bleed valves may also be used to maintain an acceptable part speed surge margin instead of variable geometry compressors. However they incur a far more severe specific fuel consumption penalty. This is because, the bleed valve flow can be up to 25% of the main stream and has had considerable work input, is either damped overboard or into a bypass duct (Walsh and Fletcher [7]). Other models that consider the effect of compressor and turbine variable vanes for different purposes are studied [8e11]. Kim et al. [8] compared the part load performance of single and two shaft engines and their potential of modulating variable inlet guide vanes to level-up the heat recovery capacity using stage stacking method. Kim and Hwang [9] studied the part load performance analysis of recuperated gas turbines considering engine configuration and operation strategy to maintain the exhaust gas temperature as high as possible. Using generalized stage characteristics and stage staking method, Muir et al. [10] have studied a variable geometry double spool engine for health monitoring of Canadian Navy engines. The variable vanes of the compressor are regulated based on the shaft speed to avoid unstable operating condition. Similarly, Bringhenti and Barbosa [11] simulated double shaft gas turbine having variable geometry compressor and turbine to search for better performance operation. As mentioned earlier, the performance of the gas turbine or cogeneration is strongly influenced by a part load and compressor variable vanes setting. However, the operation mode of a single shaft turbine with variable vanes compressor working in a cogeneration plant to maintain the exhaust gas temperature at the set value, considering the effect of ambient temperature and part load changes, has not been studied thoroughly. Therefore, this paper studied modified component based mathematical modeling of a single shaft gas turbine cogeneration plant. In ordered to achieve the objective the following issues are addressed. The design point of the cogeneration is determined. The compressor and turbine models are developed. For load less than 50% the amount of air blowdown at the down stream of the compressor as a function of terminal power output is developed. For load greater than 50% compressor parameters’ correction coefficients are developed as a function of VVs percentage opening. Mathematical model of other main components such as combustor, air inlet exhaust ducts, and HRSG are developed. Finally the component models are integrated by simulation model to get the overall cogeneration model. A real plant is modeled mathematically and simulated to study the effects of variations of power and ambient temperature on the cogeneration parameters such as fuel, temperature, pressure and variable vanes opening. Comparisons between field data and simulation results demonstrate a good agreement. To support the huge amount of calculations required for off-design analysis, a computer program has been developed in MatLAB environment. 2. Cogeneration component modeling The main components that determine the overall performance of a cogeneration plant are air intake, compressor, combustion chamber, turbine, exhaust duct and heat recovery steam generator (HRSG). The mathematical model for each component is created using thermodynamic laws, mass conservation, maps and empirical correlations. A schematic diagram of the gas turbine engine showing these components is shown in Fig. 1.
2.1. Modeling assumptions In order to develop the cogeneration model, it is assumed that the air intake and exhaust duct losses, combustion chamber pressure loss and pressure loss in the HRSG gas side are constant. It is also assumed that the process is steady state and adiabatic. Combustion consumes approximately one-fourth of the total compressed air to completely burn the supplied fuel. The excess air is used to cool the combustion chamber and mixes with the combustion products to reduce the gas temperature at inlet to the first stage of turbine. This results in the turbine inlet temperature to be below 1300 K. Moreover, the highest allowable gas inlet temperature with uncooled blades is 1250e1300 K [12]. The inlet temperatures are within uncooled turbine blades range and require a little cooling. Hence, the blade cooling effect is marginalized. 2.2. Air intake model The air intake entry relationships, for temperature Ta and pressure pa are given in Eqs. (1) and (2). Flow is drawn into the gas turbine and accelerated to the inlet velocity from a stagnation condition far from the inlet. The Mach number is nearly zero at the inlet and therefore the ambient static and total properties are equal.
T1 ¼ Toa ¼ Ta
(1)
p1 ¼ poa ¼ pa
(2)
Furthermore, the air inlet duct is assumed to be an adiabatic duct in which total temperature is conserved and fluid friction is assumed constant. Hence the inlet duct entry and exit relationships for temperature T1 and pressure p1 are determined by Eqs. (3) and (4), respectively.
p2 ¼ p1 ð1 pi Þ
(3)
T2 ¼ T1
(4)
2.3. Compressor model and analysis Performance maps and design point data of both the compressor and the turbine are not readily available. Therefore, first the design point data were determined using the manufacturer’s unconventional map data and thermodynamic laws. Once the design point data were obtained using scaling law, the performance of the compressor and the turbine was developed, according to the details provided in Ref. [13]. The scaled performance maps of the compressor are shown in Fig. 2. This map is fully described mathematically by a number of dimensionless parameters or normalized parameters [2] as given in Eqs. (5)e(9):
sc d2 po2
¼
!1 pffiffiffiffiffiffiffiffiffiffiffiffiffiffi _ a cpa To2 po3 ga 1=ga m 1 1 dN pffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1 po2 2p hc d2 po1 cpa To2 pffiffiffi
_ a q po3 sc N m ¼ f hc ; pffiffiffi; ; d q d po2
(5)
! (6)
The compression power Wc is given by:
Wc ¼ d2 po2
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffi m _ a cpa To2 1 po3 ðga 1Þ=ga 1 cpa To2 hc po2 d2 po2
(7)
B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
2547
Fig. 1. Schematic representation of a single shaft gas turbine based cogeneration plant.
where
q ¼
T Tref
(8a)
p pref
(8b)
and
d¼
The compressor total exit temperature To3 is determined using the compressor property ratio relationships:
To3 ¼ To2 þ
po3 ðga 1Þ=ga 1 hc po2
To2
(9)
The specific heat of air is given by Eq. (10) and taken from [11].
cpa ¼ A0 þ A1TZ þ A2TZ 2 þ A3TZ 3 þ A4TZ 4 þ A5TZ 5 þ A6TZ 6 þ A7TZ 7 þ A8TZ 8
ð10Þ
The specific heat ratio for ideal gas is a function of temperature and given by:
ga ¼
cpa cpa R
(11)
The constants A0, A1, A2, ., A8 are given in Table 1. 2.3.1. Compressor variable vanes system The Variable Vanes (VVs) system position varies depending on the gas turbine output set values. This change of vanes position varies the effective volume of air which enters the compressor rotor. The axial compressor used in the gas turbine’s VVs system consists
a 16
of a single row of variable Inlet Guide Vanes (IGVs) and three rows of Variable Stator Vanes (VSVs). This cogeneration has two modes of operation, that is, when the load is less than 50% and when it is greater than 50%. For load that is less than 50%, the cogeneration runs to meet the power demand and during this mode of operation the VVs are fully opened while the bleed valve is regulated. For load that is greater than 50%, the bleed valve is fully closed while the VVs are regulated to maintain the exhaust gas temperature at the set point, and the fuel flow regulated to meet the part load. For the first mode of operation the bleed valve opening is regulated. It is designed to prevent engine surge by reducing backpressure imposed on the engine compressor during starting, shut down and low load operation. Furthermore, in this mode, VVs are opened fully (100%) whereas the compressor downstream air flow is regulated with the help of bleed valve [14]. The controlled parameter is the part load and a decreasing linear percentage bleed is assumed. After a number of iteration and validation with different sets of data, the following correlation is selected:
_b ¼ m
(12)
For each position of the VVs for the second mode of operation, its performance map is changing. In order to accommodate this change, correction coefficient models are developed. The gas turbine data is monitored and stored by Turbotronic device that does not monitor the absolute VVs angle but rather monitors the VVs percentage opening. To overcome the unavailability of VVs absolute angle opening, modeling was done based on VVs percentage opening. To find the correction coefficient’s trend, a fixed geometry compressor was simulated for a set of experimental data. Once simulated, the compressor’s actual to simulated pressure ratio versus the
b 0.95
14
0.9
1.2
12
0.85
1.1
10
E ffi ci ency
Pressure ratio
_ net W þ 13:5 400
1
8
0.8 1 0.75
0.7
6
0.6
0.9 4
0.7
0.7
0.8
0.65
0.5
0.3
0
5
10 15 Corrected flow [kg/s]
1.2
0.4
0.3 0.4
0
1.1 0.9
0.5
0.6
2
0.8
20
25
0
5
10 15 Corrected flow [kg/s]
20
25
Fig. 2. Taurus 60 compressor maps for relative speed varying between 0.3 and 1.2 [13]. (a) Pressure ratio versus corrected flow. (b) Efficiency versus corrected flow.
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B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
The combustor exit pressure is given by:
Table 1 Constants required to calculate cp of air and kerosene [7].
po4 ¼ po3 ð1 pcc Þ
Constants A0 A1 A2 A3 A4 A5 A6 A7 A8 A9 A10
0.992313 0.236688 1.852148 6.083152 8.893933 7.097112 3.234725 0.794571 0.081873 0.422178 0.000491
B0 B1 B2 B3 B4 B5 B6 B7 B8 B9
0.718874 8.747481 15.863157 17.254096 10.233795 3.081778 0.361112 0.003919 0.055593 0.0016079
percentage VVs openings was plotted and a negative linear slope trend was obtained. After a number of iterations and validations correction coefficients were obtained as shown in Eqs. (13) and (14), the compressor flow correction coefficient coincides with the pressure ratio correction coefficient whereas the efficiency correction coefficient is different and is modeled as:
_ acco ¼ 2:90667 103 a þ 0:819787 prcco ¼ m
(13)
hcco ¼ 1:66667 104 a þ 0:9896667
(14)
For each VVs percentage opening, the new compressor performance map is obtained by multiplying the design point performance map parameters with their respective correction coefficients. Using the modified compressor performance map the rest of the parameters can be easily determined if any of the two dimensionless parameters are known.
The combustion chamber is SoLoNOx type. It is a lean premix low emission combustion system designed to provide combustion reaction temperatures low enough to minimize NOx formation and high enough to minimize CO emission. For calculating the combustor exit temperature and fueleair ratio, constant pressure loss is assumed. Walsh and Fletcher [7] provided curve fits for specific heat as functions of temperature and fueleair ratio (FAR) at one atmosphere. The gas constant is also given as a function of FAR. The equations are as follows:
_ cpg ðTo4 To3 Þ DH34 m ¼ ¼ f _a m LHVhcc LHVhcc
(15)
For calculation within 1% accuracy loss for natural gas, cpg at the mean temperature is evaluated by:
cpg ¼
1:0001 þ 0:9248 FAR 2:2078 FAR2 cpl
(16)
where cpl in [kJ/kg K] of combustion products of liquid fuel (kerosene) in dry air is given by:
cpl ¼ A0 þ A1TZ þ A2TZ 2 þ A3TZ 3 þ A4TZ 4 þ A5TZ 5 þ A6TZ 6 þ A7TZ 7 þ A8TZ 8 þ ðFAR=ð1 þ FARÞÞ B0 þ B1TZ þ B2TZ 2 ð17Þ þ B3TZ 3 þ B4TZ 4 þ B5TZ 5 þ B6TZ 6 þ B7TZ 7 where TZ ¼ T/1000. Once the FAR is determined, the gas constant can be obtained using the following expression:
R ¼ 287:05 þ 212:85FAR 197:89FAR2
Solving the exact exit temperature with an assumed initial value at the given ambient conditions and power output, results in a non linear equation that is solved for FAR numerically using Newton Raphson’s method. 2.5. Turbine modeling and analysis The performance characteristics of a turbine, like that of a compressor, are described mathematically by a number of fully dimensionless parameters or normalized parameters [2]. Equation (20) is in complete dimensionless form and equation (21) is the general form.
st d2 po4
1 dN h pffiffiffiffiffiffiffiffiffiffiffiffi ¼ 2p t cp To4
!1
mg
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi cpg To3 po5 ðgg 1Þ=gg 1 po4 d2 po3 (20)
pffiffiffi
_ g q po4 st N m ¼ f ht ; pffiffiffi; ; d q d po5
! (21)
where
q ¼
T Tref
(22a)
p pref
(22b)
and
d¼
The expansion power Wt and the final stagnation temperature To5 in the expansion process are calculated as follows:
2.4. Combustion chamber modeling and analysis
FAR ¼
(19)
(18)
Wt ¼ d2 po4
pffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffi m _ g cpg To4 po5 ðgg 1Þ=gg h cpg To4 1 t po4 d2 po4
po5 ðgg 1Þ=gg To5 ¼ To3 To3 ht 1 po4
(23)
(24)
If any two dimensionless parameters are known, the rest of the parameters can be easily determined with the help of performance maps indicated in Fig. 3 and Eqs. (20)e(24). 2.6. Heat recovery steam generator model and analysis The HRSG in this study is a natural circulation water tube type producing saturated steam [15]. Therefore, it consists of two primary coils; evaporator and economizer. Fig. 4 shows the temperature energy diagram of evaporator and economizer in counter flow model of the HRSG. The exhaust gas is supplied to the gas side of the evaporator at temperature Tg5. Exhaust gas comes out of the evaporator at Tg6 and enters at the same temperature to the economizer. The exhaust gas comes out of the economizer at a temperature Tg7 and is rejected to the atmosphere. Applying energy balance on the evaporator between the steam and the exhaust gas streams and simplifying gives:
Tg5 Tsat UA ln ¼ _ g cpgev m Tg6 Tsat
(25)
Equation (25) indicates that the overall heat transfer coefficient is dependent on the mass flowrate outside the tube, that is, U is _ 0:6 provided that fouling is not severe [16]. proportional to m g
B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
a
b
24
1
0.9 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2
20 18 16 14
0.8
Efficiency
C orrected fl ow [kg/s]
22
2549
0.7
0.6
0.5
12 10 0
5
10
15
20
25
30
35
40
45
0.4 0
5
10
15
Pressure ratio
20
25
30
35
40
45
Pressure ratio
Fig. 3. Taurus 60 turbine maps for relative speed varying between 0.3 and 1.2 [13]. (a) Corrected flow versus pressure ratio. (b) Efficiency versus pressure.
Substituting this in Eq. (25), simplifying and solving for exhaust gas temperature at the exit of the evaporator gives
Tg6 ¼ Tsat þ
Tg5 Tsat
(26)
0:4
eK ðmg Þ
where K ¼ A=cpgev is determined at the design point. Once the evaporator exit gas temperature is calculated, the evaporated duty is calculated from the exhaust gas stream as follow:
Q_ ev
_ g cpgev Tg5 Tg6 ¼ m
(27)
In order to estimate the steam flow, the feedwater temperature leaving the economizer, Tfw2, must be known. Assuming Tfw2 and applying energy balance on the evaporator section between the two streams, the steam produced can be calculated by Eq. (28). However, the actual steam produced is arrived at through series of iteration.
_s ¼ m
Q_ ev
To make sure that Tfw2 is a valid value, the value of (UA) for the economizer at design conditions is computed using the following expression:
hg hfw2 þ xbd hf hfw2
(28)
Q_ ecdesign LMTDecdesign
(30)
The relationship between (UA)design and (UA)off-design is given by Ganapathy [16] as follows:
ðUAÞoffdesign ¼ ðUAÞdesign
_ goffdesign m _ gdesign m
!0:65 (31)
From the economizer duty that is obtained by assuming Tfw2 and Tg6 values, the economizer exhaust gas temperature is calculated by:
Tg7 ¼ Tg6
Q_ eca _ mg cpgec
(32)
Hence, the new economizer LMTD at off-design can be calculated using
Moreover, the economizer assumed duty is calculated by:
_ sþm _ bd hfw2 hfw Q_ eca ¼ m
ðUAÞdesign ¼
(29) LMTDoffdesign ¼
Tg7 Tfw Tg6 Tfw2 " # Tg7 Tfw ln Tg6 Tfw2
(33)
Once the UA and LMTD of economizer are known at off-design conditions, the economizer duty can be calculated as follows:
Q_ ecc ¼ ðUA*LMTDÞoffdesign
(34)
If the economizer’s calculated duty is the same as the assumed value, then the assumed economizer exit temperature and the other parameters are valid, otherwise the procedure needs to be repeated with new Tfw2 value. Fig. 5 shows the algorithm for offdesign analysis of the cogeneration. The following equations are used to calculate the saturated liquid and vapor enthalpies at the saturated temperature [17]:
hf ðTÞ ¼ 2099:3 a1 þ
8 X
! ai TRi1
(35)
i¼2 1=3
hg ðTÞ ¼ 2099:3 1þb1 TR
5=6
þb2 TR
7=8
þb3 TR
þ
8 X
! bi TRi3
i¼4
Fig. 4. Temperature versus energy profile in the HRSG of a cogeneration plant [16].
where TR ¼ ð647:3TÞ=647:3. The values of coefficients ai and bi are given in Table 2.
(36)
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B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
Assume variable vanes percentage opening
Fixed geometry compressor maps
Modify compressor maps at the given VVs
If T5 simulated Tset then VVs VVs old VVs, else VVs VVs old VVs
Assume compressor air flow ma Assume the combustor exit temperature (T4)
ma
ma ,old
m
Solve the set of equations that represent the gas turbine component process
If Wnet simulated then T4 T4,old , T4 T4,old T
Wnet set T, else
No
Is the power produced =part load demand ? Yes No
Is the simulated turbine pressure the same as the set value? Yes No
Is the air flow within the surge and choke margin and/or the exhaust temperature equal to the set value? Yes With T5 and mg as an input and assumed Tfw2 call saturated vapor and liquid enthalpy subroutiens and get hv, hf, hfw2, hfw Apply energy balance on the evaporator and find the steam generated Calculate economizer duty from the feedwater stream (Q ) ec ,a
T fw 2 T fw 2
Apply energy balance on the economizer between the two streams and find Tg7
T fw 2 ,old T fw 2 ,old
T , if Qec ,c T , if Qec ,c
Qec ,a Qec ,a
Calculate the economizer off design duty using the LMTD ( Qec,c ) No
Qec ,a Qec ,c Qec ,c
ter
Yes Calculate all useful parameters Fig. 5. An algorithm of the simulation model for single shaft gas turbine based cogeneration plant.
The water vapor saturation temperature of the drum is obtained at its corresponding drum pressure by interpolating saturated steam data [18]. The data within the drum pressure operating range is stored in the computer simulation program. The following equations are used to evaluate the gas turbine thermal efficiency, HRSG and cogeneration efficiencies, respectively.
ht ¼
Net power produced wnet ¼ _ f LHV m Q_ in
hHRSG ¼
Heat recovered Q_ þ Q_ ev ¼ ec _ f LHV m Q_ in
(37)
(38)
B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554 Table 2 Coefficients of Eqs. (35) and (36) [16].
2551
100
ai
bi
1 2 3 4 5 6 7 8
0.8839230108 2.67172935 6.22640035 13.1789573 1.91322436 68.7937653 124.819906 72.1435404
0.457874342 5.08441288 1.48513244 4.81351884 2.69411792 7.39064542 10.4961689 5.46840036
Simulated Actual
90
VVs opening [%]
i
80 70 60 50
htotal
Power þ Heat recovered Q_ þ Q_ ev ¼ ¼ wnet þ ec _ _ f LHV m Q
(39)
40
in
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Relative load 3. The simulation program
Fig. 6. Percentage VVs opening versus relative load.
WL ¼ Wt Wc
(40)
_ cþm _ f m _b _t ¼ m m
(41)
4. Experimental configuration The test data is obtained from a Taurus 60 gas turbine based cogeneration plant located at the Universiti Teknologi PETRONAS (UTP). It consists of a single shaft gas turbine engine, a generator with accessories, and heat recovery steam generator and auxiliary systems. The Taurus 60 has an ISO rating power production capacity of 5.3 MW with a maximum rotational speed of approximately 14,944 rpm. However it is limited to produce 4.2 MW terminal power output due to high gas turbine inlet ambient temperature. It contains a 12 stage axial flow compressor with an inlet guide vane and three stages of stator vanes, and a three stage turbine. The Taurus 60 turbine’s operation has been recorded using Turbotronic Control System monitoring and reception of data at the UTP’s Control room computer workstations to determine the status of the cogeneration operation including system temperatures,
pressures, vibration levels, VVs percentage opening, power output and fuel flowrate. 5. Results and discussion The actual data for comparison, ambient temperature and power data used for simulation input were collected in active plant that is providing electricity and chilled water produced by steam driven absorption chiller to the campus. In order not to hamper the operation of the plant, experimental rig input variable manipulation could not be done. Therefore, the results show integration of both the effect of change of load and ambient temperature. During the part load variation, the ambient temperature was varying between 25.5 and 34 C. The gas turbine parameter variations during the simulation for both modes of operation, that is, for less than and greater than 50% load, are shown in Figs. 6e11. In each mode the target of the operation is different. The first one involves compressed air bleeding control at the downstream of the compressor while the VVs are opened fully to meet the power demand. In the second mode, the VVs and fuel mass flow are regulated to maintain the exhaust gas temperature at the set value and minimize emission while the bleed valve is closed. As these two modes of operation
1200
Inlet Outlet
1100 Turb ine temperatures [K]
A computer program for simulating a cogeneration plant should basically satisfy matching conditions analytically between the various components to produce the matching point. This simulation program is a component based modeling subroutines suitable for steady state modeling of a single shaft gas turbine for cogeneration application. The externally applied conditions are load and the surrounding conditions ambient pressure and temperature. With these inputs the simulation model will enable the operating point of each cogeneration component inlet and outlet properties to be found with one pass through the cogeneration calculation. However, a valid point is obtained after a number of iteration. Once gas turbine valid point is obtained, HRSG and cogeneration performance could be predicted. Fig. 5 shows detail of the simulation algorithm. The variable vanes percentage angle opening and fuel injected into the combustion chamber are regulated to control the required exhaust gas temperature and part load, respectively. For the simulation, 12 C and 8 C pinch point and approach point temperature differences are used, respectively. The program contains thermodynamic data for air, steam/water and combustion products so that it can predict the specific heats of air, enthalpy of steam/water and combustion gases at different temperatures. The matching conditions at steady state conditions for constant shaft speed are the work and flow compatibilities;
1000 900 800 700 600
0.2
0.3
0.4
0.5 0.6 0.7 Relative load
0.8
Fig. 7. Turbine temperatures versus relative load.
0.9
1
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B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
12
Simulated Actual
Fuel consumption [kg/sec]
11 Compressor pressure ratio
0.35
Simulated Actual
10 9 8
0.3
0.25
0.2
0.15
7 6
0.1
0.2
0.3
0.4
0.5 0.6 0.7 Relative load
0.8
0.9
1
0.2
0.3
0.4
0.5 0.6 0.7 Relative load
0.8
0.9
1
Fig. 10. Fuel consumption versus relative load.
Fig. 8. Compressor pressure ratio versus relative load.
targets are different when the load reaches 50%, there is a sudden ramp up of parameters that is manifested. Furthermore, when the power reaches above 50% load, the combustion chamber SoLoNOx low emission operation begins. The T5 set point is ramped up and variable vanes modulated as necessary to maintain the turbine exit temperature, T5, to the set point. This set point will vary slightly, depending on the emissions requirement. Fig. 6 shows the variation of the compressor VVs opening. As the load continues to increase for more than 50%, in the low emissions range, the VVs are allowed to open as needed to maintain the set point temperature, T5. This temperature variation with part load is shown in Fig. 7. For part load greater than 50%, the exhaust temperature is maintained constant and is used to recover heat in the HRSG. For load less than 50% the VVs are fully opened and the exhaust gas temperature increases slightly as part load increases. The engine is running mostly in the second mode, hence it delivers low emission and high exhaust gas temperature Fig. 8 shows compressor exit pressure variation with part load. The compressor exit is increasing as the part load increases. The possible cause for the small discrepancies between the simulated and the actual data for load less than 50% is the constants in the linear air bleed assumption. The variation of the exhaust gas mass
flow with part load is shown in Fig. 9. It is increasing as the part load increases in its corresponding mode. Fig. 10 shows the variation of fuel consumption with part load. The fuel consumption is observed to increase as part load increases. Basically, in the first mode, a certain fraction of the air is bypassed by the combustion chamber and turbine and useful energy damped to avoid surge in the compressor. The fuel consumption in the first mode is smaller than the second mode operation. Furthermore, air mass flowrate in their relative corresponding operating mode is almost the same. As a result, in the first mode of operation, relatively higher pressure ratio is required to meet the required part load and to compensate the damped energy. The abrupt jumps happened due to change of operation mode at 50% load and the slight inclination is due to unavailability of continuous data. The gas turbine efficiency, plotted in Fig. 11, shows an increase with the relative power. This is expected and the maximum efficiency is around 0.29. As the specific fuel consumption is inversely proportional to efficiency, it is decreasing with the increase of relative load. The input to the HRSG is the exhaust gas mass flow which varies with the part load. Basically, the HRSG starts to work at 50% and above part load. Furthermore, it is not operating at full load and
22
Exhaust gas flow [kg/s]
20 19 18 17 16 15
0.2
0.3
0.4
0.5 0.6 0.7 Relative load
0.8
Fig. 9. Exhaust gas mass flow versus relative load.
0.9
1
0.4
Efficiency
1
0.2
Efficiency
Specfic fuel consumption [kg/kWh]
2 21
Sfc
0
0.2
0.4
0.6 Relative load
0.8
1
0
Fig. 11. Simulated specific fuel consumption and efficiency versus relative load.
B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
6. Conclusions
Actual Simulated
Steam production rate [Tons/hr]
10 8 6 4 2 0 1
100 80
0.8 0.6 Rela tiv e loa d
ni ope ter r e Div 60
0.4
40
ng
[% ]
Fig. 12. Variation of steam production with relative load and diverter damper opening.
therefore the exhaust gas mass flow entering the HRSG is controlled by the diverter damper. Hence, the other parameter that controls the amount of steam production other than the part load is the diverter damper opening. Fig. 12 shows the turbine relative part load and diverter damper opening increase and the steam production increase at the constant exhaust gas temperature. For comparison the actual steam produced is included. This effect also increases the HRSG efficiency and correspondingly the total cogeneration efficiency as indicated in Fig. 13. In this case the plant thermal load demand is not high; as a result the diverter damper is not opened fully. This condition results in some unrecovered turbine exhaust energy, thereby causing a reduction in overall system energy efficiency.
Cogen effeiciency
Turbine efficiency
HRSG efficiency
Acknowledgements The authors would like to thank UTP for providing all the necessary supports to conduct this study. Nomenclature
T p N d
h _ m VVs _ W cp R Q_ ecc cpgec cpgev x pr
0.8
Efficiency
A mathematical model representing a single shaft gas turbine based cogeneration plant is developed. Two modes of operation are identified. One is for part load less than 50% where it is running to meet the part load demand. The other one is for part load greater than 50% load to meet both the power demand and maintain the set point exhaust gas temperature. The model is generic and it can predict a single shaft based cogeneration plant for a wide range of ambient temperature. However, when the data collected for input and validation purpose the ambient temperature was varying between 25 C and 34 C. The assumed correction coefficients for compressor VVs are accurate and valid as the comparisons of the simulated values are in good agreement with the actual data. Here, the set of equations that represent the processes are solved with the help of computer and using in house developed tool in MatLAB environment. Representative numerical results are presented to validate the model against experimental data and the estimated cogeneration behavior is in a good agreement with the actual data set. Based on these findings, it is concluded that the developed model is suitable for simulation of single shaft gas turbine and its cogeneration plant. The model is a useful tool for preparing the operating strategy of the plant. The change of ambient temperature, part load and the like on the entire operation can be predicted.
g p
1
0.6
a h LHV U A LMTD
0.4 0.2 0 1
100 80
0.8
Relativ
2553
60
0.6
e loa d
0.4
40
Div
g [% e nin p o r erte
]
Fig. 13. Simulated efficiencies variation with respect to relative load and diverter damper opening.
s
Q_ eca
temperature pressure speed diameter efficiency mass flow variable vanes power specific heat at constant pressure characteristic gas constant specific heat ratio fraction of pressure drop economizer calculated duty specific heat of gas in economizer specific heat of gas in evaporator fraction pressure ratio VVs percentage opening enthalpy lower heating value overall heat transfer coefficient surface area log mean temperature difference torque economizer assumed duty
Subscripts o total property b bleed a air f fuel or saturated liquid water
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B.T. Aklilu, S.I. Gilani / Applied Thermal Engineering 30 (2010) 2545e2554
g gas or saturated water vapor i inlet c compressor t turbine L load cco correction coefficient cc combustion chamber 1,2,3,4,5,6,7 designate inlet and exit points fw feedwater S steam produced sat saturated bd blowdown l liquid fw2 feedwater state leaving economizer
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