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Investigation of effect of variation of cycle parameters on thermodynamic performance of gas-steam combined cycle
Energy 36 (2011) 157e167
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Energy journal homepage: www.elsevier.com/locate/energy
Investigation of effect of variation of cycle parameters on thermodynamic performance of gas-steam combined cycle Sanjay* Department of Mechanical Engineering, National Institute of Technology, Jamshedpur 831 014, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 February 2010 Received in revised form 29 October 2010 Accepted 30 October 2010 Available online 9 December 2010
The paper deals with second law thermodynamic analysis of a basic gas turbine based gas-steam combined cycle. The article investigates the effect of variation of cycle parameters on rational efficiency and component-wise non-dimensionalised exergy destruction of the plant. Component-wise inefficiencies of the combined cycle have been quantified with the objective to pin-point the major sources of exergy destruction. The parameter that affects cycle performance most is the TIT (turbine inlet temperature). TIT should be kept on the higher side, because at lower values, the exergy destruction is higher. The summation of total exergy destruction of all components in percentage terms is lower (44.88%) at TIT of 1800 K & rp,c ¼ 23, as compared to that at TIT ¼ 1700 K. The sum total of rational efficiency of gas turbine and steam turbine is found to be higher (54.91%) at TIT ¼ 1800 K & rp,c ¼ 23, as compared to that at TIT ¼ 1700 K. Compressor pressure ratio also affects the exergy performance. The sum total of exergy destruction of all components of the combined cycle plant is lower (44.17%) at higher value of compressor pressure ratio (23)& TIT ¼ 1700 K, as compared to that at compressor pressure ratio (16). Also exergy destruction is minimized with the adoption of multi-pressure-reheat steam generator configuration. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Cooled gas turbine Exergy destruction Parametric analysis Exergy Combined cycle Rational efficiency
1. Introduction The rising cost of energy and the global warming in recent years has highlighted the need to develop energy conversion systems with improved efficiency and reduced emissions. The availability of fuels has played an important role in the development and prosperity of a nation and their best utilisation is a method to conserve them. Waste heat recovery from gas turbine exhaust improves plant performance significantly, and employing ST (steam turbine) cycles provide the best performance in general. Heat of GT (gas turbine) exhaust is recovered in a HRSG (heat-recovery steam generator) to generate steam for the bottoming ST cycle. This scheme is widely called a combined cycle power generation system. These gas turbine based combined cycle power plants have become the mainstay in providing electrical power worldwide. Most of these combined cycle plants burn natural gas as fuel and the output of such gas turbines for power generation has been projected [1] to increase from around 570 GW in 1999e2035 GW in 2020; an increase of over 6%/yr. This increase in power demand will be met by large combined cycle based on gas turbine plant, which necessitates for studying the thermodynamics of these workhorses.
* Tel.: þ916572373813; fax: þ916572373246. E-mail address: [email protected]. 0360-5442/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.10.058
Second law analysis of these power plants has been used to pinpoint the sources and quantify their component-wise exergy destruction. 2. System configuration The gas turbine based combined cycle, also called the gas-steam combined cycle has components such as axial flow compressors, combustion-chamber, cooled expansion turbine, heat-recovery steam generator, steam turbine, condenser, deaerator, feedpump etc (Fig. 1). Work in the area of parametric analysis of gas turbine based cycles have been reported by Louis et al. [2], Wu and Louis [3], El-Masri [4,5], Briesh et al. [6], Bolland and Stadaas [7], Bolland [8], Chiesa and Macchi [9], and Dechamps [10], A.M. Bassily[11], B.Zaporowski, and R. Szczerbowski [12], Kaushik et al. [13] and Cziesla et al. [14]. Studies related to exergy analysis of energy conversion cycles have earlier been carried out by many researchers. Svend and Ruyck [15] in their work have discussed the optimal cycle layout technique for evaporative gas turbine cycle. The feasibility of each cycle has been discussed by comparison of results of exergy destruction and exergetic efficiency. Aspen þ has been used for analysis of the cycles. The paper suggests various methods of better utilisation of intercooler heat, the aftercooler heat and the turbine exhaust heat.
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Nomenclature a a,b,c cp F Fsa gt Gr h DHr _ m Q rp R p s S St t T TIT W
ratio of mass of coolant to mass of gas flow constants specific heat (kJ-kg1 K1) factor correction factor to account actual blade surface gas turbine Gibbs free energy function ¼ 43890 kJ kg1 specific enthalpy (kJ kg1) lower heating value (kJ kg1) mass flow rate (kg.s1) heat energy transfer (W) cycle pressure ratio gas constant (kJ-kg1K1) pressure (bar) specific entropy (kJ kg1 K1) blade perimeter (m) average Stanton number ¼ hg =cp;g $rg $Cg ¼ 0.005 pitch of blade (m) temperature (K) turbine inlet temperature (K) ¼ combustor exit temperature work (kJ s1)
Greek symbols thermodynamic property function gas flow discharge angle (degree) rational efficiency (%) exergy per unit mass of gas (kJ kg1) exergy (kJ s1) effectiveness (%) ¼ Tc$e Tc;i =Tb Tc;i efficiency (%) specific volume (m3 kg1)
f a hrat u U 3 h y
Subscripts a air, ambient b blade c coolant
Lior and Zhang [16] in their work have discussed energy and exergy based performance criteria, and second law efficiency of energy systems. Hammond [17] in his work has discussed the thermodynamic methods of (energy and exergy) analysis employed to illustrate energy use in industry and the scope for increasing energy efficiency, as well as the extent of exergetic ‘improvement potential’. It [17] has been concluded that poor thermodynamic performance is principally the result of exergy destruction in combustion and heattransfer processes. Marrero et al. [18] in their work have discussed second law analysis and optimisation of combined triple power cycle. Buther and Reddy [19] in their work have evaluated the performance of a waste heat-recovery power generation system based on second law analysis and investigated their various operating conditions. The temperature profiles across the HRSG, network output, second law efficiency and entropy generation number are simulated for various operating conditions. Verma et al., Ivar et al. and Deng et al. [20e22] have also done extensive work in this field. Based on mathematical modeling of the various components of combined cycle plant reported in the author’s [23e25] articles, this paper discusses rational efficiency and non-dimensional componentwise exergy destruction for a cooled gas turbine based combined cycle plant. The mathematical equations used in the analysis of the cycle components are discussed in the following sections.
comp comb cond D e f g gen gt hrsg hp i in ip j lp net P p plant pt s st w
compressor combustor condensate destruction exit fuel gas alternator gas turbine heat-recovery steam generator high pressure (steam) inlet, stage of compressor inlet intermediate pressure (steam) coolant bleed points low pressure (steam) difference between two values product pressure combined cycle plant polytropic steam steam cycle water
Acronym 3PR Triple pressure-reheat HRSG/bottoming cycle configuration AFC Air-film cooling BFP Boiler feedpump C Compressor CC Combustion-chamber GT Gas turbine HPD High pressure drum HPST High pressure steam turbine IPD Intermediate pressure drum IPST Intermediate pressure steam turbine LPD Low pressure drum LPST Low pressure steam turbine
3. Component modeling and governing equations The gas-steam combined cycle includes axial flow compressors, combustion-chamber, cooled expansion turbine, heat-recovery steam generator, steam turbine, condenser, deaerator, feedpump. 3.1. Gas model The specific heat of gas at constant pressure is assumed to be a function of temperature, given by the polynomial adopted from the work of Toulounkain and Tadash [26]. For the temperature range of 250e599 K
cp;a ¼ 1:0232041:76021104 $Tþ4:0205107 $T2 4:872721011 $T3
(1a)
For the temperature range of 600e1500 K
cp;a ¼ 0:8743343:22814104 $Tþ3:58694108 $T2 1:991961011 $T3
(1b)
Thus, the enthalpy, entropy and exergy of gas can be calculated using the above polynomial in the following equations
Sanjay / Energy 36 (2011) 157e167
159
Fig. 1. Schematic of a cooled gas turbine based combined cycle plant.
3.3. Combustor model
ZT h ¼
cp ðTÞdT
(2)
Ta
f¼
ZT cp ðTÞ$
dT T
(3)
Ta
For given values of turbine TIT, pressure drop and combustion efficiency, the fuel flow is found from the mass and energy balance, and the exergy destruction is found from the exergy balance as given below
_e m
comb
i h _ iþm _f ¼ m
(9)
comb
s ¼ f Rlnðp=paÞ
(4)
_ e $he m _ i $hi comb _ f $DHr $hcomb ¼ m m
u ¼ h Ta $s ¼ h Ta $f þ R$Ta $lnðp=pa Þ
(5)
_ f $ DGr þ Rf $Ta $ln pf =pa UD;comb ¼ m
Here, all non-reacting gases are arbitrarily assigned zero thermodynamic enthalpy, entropy and exergy at the ambient pressure and temperature, taken as 1 bar and 288 K regardless of chemical composition. Mass and energy balance of each component is done with the assumption that the process is adiabatic. The mechanism of evaluating rational efficiency and exergy destruction used here is exergy balance across control volume of the component/element. The analysis has been made for constant air mass flow rate i.e per kg of air handled by the cycle. 3.2. Compressor model Compression in axial flow compressor is assumed to be polytropic taking the polytropic efficiency as 92% [Ref. Table 1.]. The temperature of air at any section is expressed in terms of local pressure and polytropic efficiency, by the following expression
dT ¼ T
"
R
#
hp;comp $cp;a
dp p
(6)
Compressor work is found from the mass & energy balance whereas, the exergy destruction from exergy balance is given by the following equations:
_ e $he þ Wcomp ¼ m
X
_ c;j hc;j m _ c; i $hc; i m
_ c;i $uc;i UD;comp ¼ Wcomp þ m
X
_ c;j $uc;j m _ c;e $uc;e m
(7) (8)
h
_ e $ue m _ i $ui comb m
(10)
i comb
(11)
Here, the fuel line is assumed to be at pressure ‘pf’ and at ambient temperature. 3.4. Cooled gas turbine model In this work, the gas turbine blades are modeled to be cooled using AFC (air-film cooling) method. The cooling model used for cooled turbine is the refined version of that by Louis et al. [2]. The mass flow rate of coolant required in a blade row is expressed as [24]:
_c m ac ¼ ¼ _ mg
# " Tg;i Tb Stin $cp;g Sg $Fsa 3$cp;c t$cosa Tb Tc;i
(12)
where Sg y 2c, Sg/t$cosa ¼ 3.0, Fs,a ¼ 1.05, a ¼ 45 (for stator), a ¼ 48 (for rotor), Stin ¼ 0.005 Fig. 2 gives the details of expansion process for a cooled turbine stage. Process b1c1 in Fig. 2 depicts cooling due to heat transfer between hot gas and coolant, which takes place at constant pressure line due to which exergy decreases, while process c1d1 depicts drop in temperature due to mixing of coolant with gas which is an irreversible process and also takes place along constant pressure line, which leads to drop in entropy. Process d1a2 in the model denotes a process similar to throttling. The deviation between actual and theoretical value is dependent upon the amount of coolant and temperature of coolant used for
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Table 1 Input data for analysis [24].
_ g;i $ug;i þ UD;gt ¼ m
Parameter
Symbol
Unit
Gas Properties
cp ¼ f (T) Enthalpy h ¼ ⌠cp(T) dT i. Polytropic efficiency (hpc) ¼ 92.0 ii. Mechanical efficiency(hm)) ¼ 98.5 i. Combustor efficiency (hcomb) ¼ 99.5 ii. Pressure loss (ploss) ¼ 2.0% of entry pressure iii. Lower heating value ðDHr Þ ¼ 42.0 iv. Fuel,Natural gas composition: CH4 ¼ 86%, C2H6 ¼ 7% i. Polytropic efficiency (hpt) ¼ 92.0 ii. Exhaust pressure ¼ 1.08 iii. Exhaust hood temperature loss ¼ 4 iv. Turbine blade temperature ¼ 1123 i. Effectiveness ¼ 98.0 ii. Pressure loss ¼ 10% of entry pressure iii. Stack (minimum temperature) ¼ 363.0 iv. ‘hp’ pressure ¼ 160 v. ‘hp’ superheat temperature ¼ 843.0 vi. ‘hp’ steam exhaust pressure ¼ 35 vii. Reheater loss ¼ 3% of entry pressure ix. ‘ip’ superheat temperature ¼ 603.0 x. ‘lp’ pressure ¼ 6.0 viii. ‘ip’ pressure ¼ 34.0 xi. ‘lp’ superheat temperature ¼ 573.0 xii. Deaerator pressure ¼ 2.0 xiii. Condenser pressure ¼ 0.05 xiv. Gas/steam approach temperature difference ¼ 20.0 xv. Pinch-point temperature difference ¼ 10.0 xvi. Pressure of blade coolant steam ¼ 35 i. Isentropic efficiency ¼ 88.0 ‘hp’, 92.0 ip/lp ii. Mechanical efficiency ¼ 98.5 iii. Minimum steam quality at ‘lp’ exhaust ¼ 0.88 Valve throttling loss ¼ 2% of entry pressure Undercooling ¼ 4 Rise in cooling water temperature ¼ 10 Alternator efficiency ¼ 98.5
kJ/kg K
Compressor Combustor
Gas turbine
HRSG (Triple Pressure with reheat)
Steam turbine
Condenser Alternator
% % % % MJ/kg
% bar K K % % K bar K bar % bar K bar K bar bar K
_ c $ uc;i uc;e m _ g;e $ug;e Wgt m
(14)
3.5. HRSG model An unfired HRSG is considered in the configuration. For the parametric study the pressure levels of the HRSG is one of the variables. Six configurations namely 3PR, 3P, 2PR, 2P, 1PR, and 1P based on number of pressure levels and steam reheat have been considered. The selection of steam pressure and temperature for each of these configurations is based on the optimised value to yield maximum steam cycle efficiency, satisfying the minimum stack temperature and quality of steam at ‘lp’ turbine exhaust given in (Table 1) [23]. The detailed optimisation procedure is outlined in Ref. [23]. 3.6. Steam turbine model Steam turbine output and exergy destruction in HP, IP and LP stages are found out by mass, energy and exergy balance as given below.
Wst ¼
stages X
_ s:i $ hs;i hs;e m
(15)
where ðhs;i hs;e Þ ¼ hst ðhs; i hs; e Þisentropic _ s;i ¼ amount of steam entering to the respective main turbine m stages as per configuration. and the exergy balance as:
K bar % % dry
UD;st ¼
% K C %
stages X
_ s:i $ us; i us; e Wst m
(16)
3.7. Condenser model The mass and energy balance give the cooling requirement while exergy balance will yield exergy destruction, as given below:
cooling of blades and the actual value varies with blade-cooling requirements. At TIT 1700 K for air-film cooling cooling, its maximum value is 6% [24]. Turbine work and exergy destruction are given by the mass, energy and exergy balance of gas turbine as under:
h X i _ c , hc;i hc;e _ g;i , hg;i hg;e þ m Wgt ¼ m
X
_ cond; e $he ¼ m _ w;i $hw;i _ s; i $hi m _ w;e $hw;e m m
_ s;i $us;i m _ cond;e $ucond;e UD;cond ¼ m
_ w;e $ue _ w;i $uw;i m þ m
(13)
(17)
(18)
3.8. Feed pump model Polytropic expansion in a row of bladings
en tha l p y , h
p Polytropic expansion
a -b b -c c -d d -a
: Polytropic expansion : Energy loss due to cooling : Energy loss due to mixing : mixing stagnation pressure loss at constant enthalpy Δp : total pressure loss due to mixing
Coolant mixing pressure drop ( Δ p)
d
Wpump ¼
UD;pump ¼
p b
Heat transfer process followed by mixing with coolant, process
The mass, energy and exergy balances yield pump work and exergy destruction as:
p + Δp
X
yw;i $ðpe pi Þ
X _ w;i uw;i uw;e þ Wpump m
(19)
(20)
4. Performance parameters The performance parameters Wgt;net , Wst;net , Wplant , hplant and
Polytropic expansion in next row
hrat are expressed as follows: Wgt;net ¼ Wgt
entropy, s Fig. 2. Expansion path in cooled gas turbine row.
jWcomp j
hm
Wst;net ¼ Wst $hm
jWpump j
hpump
(21) (22)
(26)
Modeling of cycle components and governing equations developed for cycles proposed above have been coded using Cþþ and results obtained. A flowchart of the programme code ‘Simucomb’ illustrating the method of solution has been given in Appendix-I. The input data used in the analysis is given in Table 1.
5. Results and discussions The results of parametric analysis of cooled gas turbine based combined cycle are discussed in the subsequent sections. Rational efficiency of gas turbine and steam turbine has been plotted as histogram for various cycle parameters analyzed. Histogram of exergy balance (in %) showing gas turbine rational efficiency, steam turbine rational efficiency and component-wise non-dimensional exergy destruction with reference to input fuel exergy are shown in Fig. 4 through Fig. 6. The gas turbine blade-cooling model adopted from author’s previous work [24] gives results that were validated with results of El-Masri [4] and Horlock et al. [28] with variation in the acceptable range of 2.5e3.5%. The mathematical model for exergy analysis gives results that have been validated with [23] and [27] and found to compare well. Also the results of combined cycle performance modeling have been validated and combined cycle plant efficiency compares well with the work of Bolland [7,8]. Dechamps [10] and S207FB model of combined cycle plant by GE Power [33]. The parameters that have been studied include turbine inlet temperature, compressor pressure ratio, and bottoming cycle B3PR configuration, Air-film cooling.
Combustor fuel consumption (kg of fuel / kg of air handled by the cycle)
0.030
(rp_c=16) (rp_c=23)
0.025
2
1
0
DA
Wst;net _ f $D Gr m
3
BFP
¼
(25)
5
Co n d .
Wst;net
Uf ;input
Wgt;net _ f $DGr m
10
ST
Uf ;input
¼
15
Stack
hrat;st ¼
Wgt;net
B3PR configuration, rp,c=16, AFC
20
HRSG
hrat;gt ¼
TIT=1700K TIT=1800K
25
GT
The concept of power plant ‘rational efficiency’ to provide a criterion for performance based on actual shaft work output from a power plant to the input fuel exergy was first introduced by Szargut and Petela [29]. The concept has been studied by Kotas [30], Moran [31] and Gyftopoulas and Beratta [32]. Rational efficiency of gas turbine and steam turbine is mathematically expressed as:
Exergy destruction
30
CC
(24)
Rational Efficiency
C
Wplant Wplant ¼ ¼ _ f $DHr m Q
35
161
ST
hplant
(23)
GT
Wplant ¼ Wgt;net þ Wst;net $hgen
Rational Efficiency & (Exergy destruction/input fuel exergy) (%)
Sanjay / Energy 36 (2011) 157e167
Combined cycle components Fig. 4. Effect of TIT on rational efficiency and non-dimensionalised exergy destruction for various combined cycle components.
configuration. The effect of variation of these parameters on rational efficiency and component-wise exergy destruction has been discussed. The values of compressor pressure ratio selected for analysis has been adopted from operating parameters of gas turbines namely M501F (rp,c in the range of 16) from Mitsubishi and MS 9001H (rp,c in the range of 23) from General Electric. The value of TIT ¼ 1700 K is the current state-of-the-art of combustor temperature or TIT and the TIT of M501F & MS 9001H falls around this value. The figures include sensitivity analysis showing the effect of variation of parameters under investigation. 5.1. Effect of TIT and rp,c on fuel consumption Fig. 3 illustrates a histogram of the sensitivity of fuel consumption (in kg of fuel/kg of air handled by the cycle) for fixed values of TIT and rp,c in the case of B3PR configuration. It is observed that at a fixed value of rp,c, when TIT is increased, the fuel consumption of the combustor increases proportionately to achieve the desired TIT. On the other hand at the given value of TIT when rp,c is increased, the fuel consumption of the combustor reduces. This is due to elevated temperature at which the air exits the compressor and enters the combustor (because of elevated pressure of the air), thus reducing the fuel consumption to achieve the required TIT. As the percentage of excess air in the combustor of gas turbine is very high, the change in fuel consumption does not affect the fuel-air ratio significantly. Also as fuel consumption is directly dependent on the value of TIT, it has been selected as one of the parameters to be varied to study the performance of the plant.
0.020
5.2. Effect of turbine inlet temperature 0.015
0.010
0.005
0.000 1700K
1800K
Fig. 3. Effect of compressor pressure ratio and TIT on combustor fuel flow rate.
Fig. 4 illustrates sensitivity analysis depicting the effect of variation of TIT on rational efficiency of gas turbine, steam turbine and also non-dimensional component-wise exergy destruction. The histogram is for B3PR configuration at rp,c ¼ 16, Tb1123 K for cooling scheme AFC gas turbine based combined cycle power plant. AFC has been chosen here and also in Figs. 5 and 6 for depicting the results of the analysis, as it is the most promising cooling technique in the case of power turbine based combined cycle plants. Higher TIT results in higher rational efficiency of ST, while lower rational
Sanjay / Energy 36 (2011) 157e167
efficiency of GT, while the quantum of respective network output (in kJ/kg of gas flow) from each of these components are in the reverse order. The sum total of rational efficiency of GT and ST is found to be higher (54.91%) at TIT ¼ 1800 K. Higher exergy destruction (in percentage) in GT, HRSG, ST, condenser and deaerator are observed at higher values of TIT. But exergy destruction is lower (in percentage terms) at higher values of TIT in case of CC and compressor. This relates to the discussion in Leites, Sama and Lior [34] in their work in section 4.2 wherein they have suggested methods to reduce exergy destruction: “heat of reaction to have a positive thermal exergy, the reaction temperature, T, must be greater than To .... Thus, there must be a reaction temperature, greater than To, but less than Teq (reaction equilibrium temperature), where the work effect is optimal and; ” therefore, where the exergy destruction reduces and in conclusion recommends that the increase in the value of TIT should be such that exergy destruction in combustor reduces. Non-dimensional exergy destruction is highest in combustor and is shown to exhibit a higher value (30.5%) at lower value of TIT i.e. 1700 K, as compared to 28.8% at TIT of 1800 K. Also the sum total of exergy loss in all components of the cycle is lower (44.88%) at higher value of TIT ¼ 1800 K. 5.3. Effect of compressor pressure ratio A histogram showing the sensitivity of rational efficiency and component-wise exergy destruction in B3PR combined cycle configuration at TIT ¼ 1700 K for the two values of rp,c i.e 16 and 23 are shown in Fig. 5. Higher value of rp,c demonstrates higher rational efficiency of GT while lower rational efficiency of ST. This is because more gas cycle specific work is delivered at higher rp,c, while the denominator (input fuel exergy) of the expression of rational efficiency is relatively unaltered. Since at higher rp,c, due to lower level of gas cycle exhaust temperature, less heat energy is available in HRSG, the steam turbine output is lesser, resulting in lower rational efficiency. The sum total of rational efficiency of GT and ST is found to be higher (55.74%) at rp,c ¼ 23. The exergy destruction in compressor is more at higher rp,c due to increased compression work input and also increased bleeding of coolant air, due to higher coolant air temperature of respective bleed points and at compressor exit. In combustor, exergy destruction
Rational Efficiency & (Exergy destruction/input fuel exergy) (%)
162
Rational Efficiency 24
B3PR B3P B2PR B2P B1PR B1P
Exergy destruction
23 22 21 20 19 18
rp,c=16 , TIT=1700K Air film cooling (AFC)
6
4
2
0
ST
HRSG
ST
Cond.
Bottoming cycle components Fig. 6. Distribution of rational efficiency and non-dimensionalised exergy destruction of bottoming cycle components for different bottoming cycle configurations.
(29.66%) is lower at higher rp,c ¼ 23. GT exhibits higher level of exergy destruction (6.15%) at higher value of rp,c due to higher expansion ratio resulting in more entropy generation. In HRSG, exergy destruction is higher at lower rp,c. This is attributed to the fact that at lower rp,c, lower expansion ratio provides more heat energy available to HRSG. The exergy destruction in compressor at rp,c ¼ 23 is higher than at rp,c ¼ 16 because at higher compressor pressure ratio, mass of air-coolant bled from compressor exhaust will be more to achieve same cooling effect, due to higher temperature of compressor exit air. GT exergy destruction follows a similar pattern due to the above reasons. The exergy destruction in stack, ST, condenser, BFP and D/A are in the range of 0.18e1.8%. The sum total of exergy destruction of all components of the combined cycle plant is lower (44.17%) at higher value of compressor pressure ratio (23). Hence higher value of rp,c is should be selected to enhance exergy performance of gas turbine based combined cycle plant.
(rp,c=16) (rp,c=23)
Exergy destruction
35
B3PR configuration, TIT=1700K, AFC 30 25 20 15 7 6 5 4 3
Fig. 6. depicts the effect of HRSG configuration (B1P to B3PR) on the rational efficiency of ST and exergy destruction of bottoming cycle components at rp,c ¼ 16, TIT ¼ 1700 K and Tb1123 K for AFC scheme. Rational efficiency of steam turbine is sensitive to the type of bottoming cycle configuration of the combined cycle plant. The decreasing order of value of rational efficiency of steam turbine is found as B3PR, B3P, B2PR, B2P, B1PR and B1P. This is because best utilisation of heat energy in bottoming (steam) cycle is exhibited in case of B3PR configuration. The distribution of exergy destruction is also observed to be sensitive to type of bottoming cycle configuration. In all bottoming cycle components (HRSG, ST, Condenser) it is observed that component-wise exergy destruction is lower in reheated configuration with respect to the same configuration without reheat.
2 1
6. Conclusions DA
BFP
Cond.
ST
Stack
HRS G
GT
CC
C
ST
0
GT
Rational Efficiency & (Exergy destruction/input fuel exergy) (%)
5.4. Effect of HRSG configuration (B1P to B3PR) Rational efficiency
Combined cycle components Fig. 5. Effect on rational efficiency and non-dimensionalised exergy destruction of combined cycle components for variation in compressor pressure ratio.
Based on the parametric exergy analysis of gas turbine based combined cycle following conclusions have been drawn: 1) Fuel consumption in the combustor of a gas turbine is directly dependent on desired turbine inlet temperature.
Sanjay / Energy 36 (2011) 157e167
2) The maximum exergy destruction has been found in combustor followed by gas turbine and compressor. Hence combustor should be the focus of further study. 3) Higher exergy destruction is observed in major components like compressor, combustor, and stack at lower values of turbine inlet temperature suggesting the adoption of higher turbine inlet temperature to reduce exergy destruction in these components. Sensitivity analysis shows that higher value of turbine inlet temperature reduces exergy destruction in combustor. It is hence concluded that turbine inlet temperature may be increased, to enhance exergy performance of combined cycle, keeping in mind the technological/metallurgical limits. 4) The sum total of rational efficiency of gas turbine and steam turbine is found to be higher at higher values of compressor pressure ratio and turbine inlet temperature.
163
5) Rational efficiency of steam turbine is sensitive to the type of bottoming cycle configuration of the combined cycle plant. The decreasing order of value of rational efficiency of steam turbine is found as B3PR, B3P, B2PR, B2P, B1PR and B1P indicating B3PR to be the superior configuration. 6) The distribution of exergy destruction is also is found to be sensitive to the type of bottoming cycle configuration. In all studied bottoming cycle components (heat-recovery steam generator, steam turbine & condenser) it is observed that component exergy loss is lower for reheated configuration with respect to the same configuration without reheat, thus indicating the selection of reheated bottoming cycle configuration for superior second law performance of the cycle.
Appendix Start ‘SimuComb’
Select the Basic Gas Turbine module, BGT
Menu to select the gas turbine blade cooling means
Input plant parameters e.g. rpc, TIT, Tci, Tb, Tstack, ps, Ts, cooling means etc.
Compressor module Start
Input parameters Compressor, C
Input parameters
Calculate compressor work etc. Return computed results to datafile
A
Air properties data module
164
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A
Basic Gas Turbine module BGT
Start
Input parameters and read data (compressor module results) from datafile
Call functions CC, steam, air & gas properties data
Compute No. of stages in Gas turbine, and blade coolant flow requirements
Call functions to compute GT work, GT net work, mf, GT efficiency, component exergy and exergy losses, GT exhaust gas temperature etc.
Return computed results to datafile
HRSG/ST module (1P, 1PR, 2P, 2PR, 3P, 3PR)
Start program for configuration selected
Input parameters pinch point allowable stack temperature etc. and read data from datafile
Compute the dryness fraction of steam at the exit of each ST stage i.e hp, ip and lp
B
Program to read steam property from database/ datafile
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165
HRSG/ST module (1P, 1PR, 2P, 2PR, 3P, 3PR) B
Program to compute mass of steam generated in HRSG using optimisation technique
Read all pinch point temp. difference, min. stack temp, min. quality of steam, etc.
Input trail value of mass of steam generated
Compute mass of steam generated in hp, ip and lp drum using iterative procedure
Is Tg,stack >= 80oC & Tpp,ip= 10.0
No
Yes Call functions to compute ST work , pump work, net ST work, bottoming cycle efficiency, component wise exergy and exergy loss etc.
Return computed results to datafile
C
166
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C
Combined cycle plant performance analysis module
Call function to read data stored as computed results for the GT module
Call function to read data stored as computed results for the HRSG/GT
module
Compute results for overall performance of combined cycle / cogeneration plant and component specific exergy and exergy loss
Print results of overall performance of combined cycle / cogeneration plant and component specific exergy and exergy loss
END
Program to read computed results stored in data files
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167
Basic gas turbine module (BGT)
Input parameters and read data (compressor module results) from datafile
Call functions CC, air, steam, & gas properties data
Compute No. of stages in GT, and blade coolant requirements
Call functions to compute GT work, GT net work, mf, GT efficiency, component exergy and exergy losses, GT exhaust gas temperature etc.
Return computed results to datafile
References [1] Pilavachi PA. Mini- and micro-gas turbines for combined heat and power. Applied Thermal Engineering 2002;22:2003e14. [2] Louis JF, Hiraoka K, El-Masri MA. A comparative study of influence of different means of turbine cooling on gas turbine performance. ASME 1983;83-GT-180. Paper no. [3] Chaun Shao Wu, Louis JF. A comparative study of the influence of different means of cooling on the performance of combined (Gas and steam turbines) cycle. Transactions of ASME Journal of Engineering for Gas Turbines and Power 1984;106:750e5. [4] El-Masri MA. GASCAN- An interactive code for thermal analysis of gas turbine systems. Transactions of ASME, Journal of Engineering for Gas Turbines and Power 1988;110:201e9. [5] El-Masri MA. On thermodynamic of gas turbines cycle e part-2 e a model for expansion in cooled turbines. Transactions of ASME, Journal of Engineering for Gas Turbines and Power 1986;108:151e9. [6] Briesh MS, Bannister RL, Diakunchak IS, Huber DJ. A combined cycle designed to achieve greater than 60 percent efficiency. ASME Journal of Engineering For Gas Turbine And Power 1995;117:734e41. [7] Bolland O, Stadaas JF. Comparative Evaluation of combined cycles and gas turbine systems with injections, steam injection and recuperation. ASME Journal of Engineering for Gas Turbine and Power 1995;117:138e45. [8] Bolland O. A comparative evaluation of advanced combined cycle alternatives. ASME Journal of Engineering for Gas Turbine and Power 1991;113:190e7. [9] Chiesa, Macchi. A thermodynamic analysis of different options to break 60% electrical efficiency in combined cycle power plants. ASME Journal of Engineering for Gas Turbine Power 2004;126:770e85. [10] Dechamps PJ. Advanced combined cycle alternatives with latest gas turbines. ASME Journal of Engineering for Gas Turbine and Power 1998;120:350e7. [11] Bassily M. Modeling, numerical optimization, and irreversibility reduction of a triple- pressure reheat combined cycle. Energy 2007;32:778e94. [12 Zaporowski Bolesaw, Szczerbowski Radoslaw. Energy analysis of technological systems of natural gas fired combined heat-and-power plants. Applied Energy 2003;75:43e50. [13] .Kaushik C, Tyagi SK, Singhal MK. Parametric study of an irreversible regenerative Brayton cycle with isothermal heat addition. Energy Conversion and Management 2003;44:2013e25. [14] Cziesla Frank, Tsatsaronis George, Gao Zengliang. Avoidable thermodynamic inefficiencies and costs in an externally fired combined cycle power plant. Energy 2006;31:1472e89. [15] Bram Svend, de Ruyck Jacques. Exergy analysis tools for ASPEN applied to evaporative cycle design. Energy Conversion and Management 1997;38 (15e17):1613e24.
[16] Lior Noam, Zhang Na. Energy, exergy, and second law performance criteria. Energy 2007;32:281e96. [17] Hammond Geoffrey P. Industrial energy analysis, thermodynamics and sustainability. Applied Energy 2007;84:675e700. [18] Marrero IO, Lafsaker AM, Razani A, Kim KJ. Second law analysis and optimisation of combined triple power cycle. Energy Conversion and Management 2002;43(4):557e73. [19] Butcher CJ, Reddy BV. Second law analysis of a waste heat recovery based power generation system. International Journal of Heat and Mass Transfer 2007;50:2355e63. [20] Verma A, Rao AD, Samuelsen GS. Sensitivity analysis of a Vision 21 coal based zero emission power plant. Journal of Power Sources 2006;158:417e27. [21] Ertesvag Ivar S. Sensitivity of chemical exergy for atmospheric gases and gaseous fuels to variations in ambient conditions. Energy Conversion and Management 2007;48(7):1983e95. [22] Sue Deng-Chern, Chuang Chia-Chin. Engineering design and exergy analyses for combustion gas turbine based power generation system. Energy 2004;29: 1183e205. [23] Sanjay, Singh Onkar, .Prasad BN. Energy and exergy analysis of steam cooled reheat gas-steam combined cycle. Applied Thermal Engineering 2007;27:2779e90. [24] Sanjay, Singh Onkar, .Prasad BN. Influence of different means of turbine blade cooling on the thermodynamic performance of combined cycle. Applied Thermal Engineering 2008;28:2315e26. [25] Sanjay, Singh Onkar, .Prasad BN. Comparative performance analysis of Cogeneration gas turbine cycle for different blade cooling means. International Journal of Thermal Sciences July 2009;48(7):1432e40. [26] Touloukian YS, Tadash Makita. The TPRC Data Series. Thermo-physical properties of matter, vol. 6. New York, Washington: IFI/PLENUNM; 1970. [27] El-Masri MA. Exergy analysis of combined cycles: part 1- air-cooled Braytoncycle gas turbines. ASME Journal of Engineering for Gas Turbine Power 1987;109:228e36. [28] Horlock JH, Watson DT, Jones TV. Limitation on gas turbines performance imposed by large turbine cooling flows. ASME Journal of Engineering of Gas Turbine Power 2001;123:487e94. [29] Szargut J, Petela R. Egzergia. Warsaw: Naukowa-Technicze; 1965 [in Polish]. [30] Kotas TJ. The exergy method of thermal power analysis. Butterworth; 1985. [31] Moran MJ. Availability analysis: a guide to efficient energy use. New York: ASME Press; 1989. [32] Gyftopoulos EP, Beretta GP. Thermodynamics, foundation and applications. NewYork: MacMillan; 1991. [33] Gas turbine world, vol. 32. Pequot Publishing Inc; 2001 (1). [34] Leites IL, Sama DA, Lior N. The theory and practice of energy saving in the chemical industry: some methods for reducing thermodynamic irreversibility in chemical technology processes. Energy 2003;28:55e97.
Contents lists available at ScienceDirect
Energy journal homepage: www.elsevier.com/locate/energy
Investigation of effect of variation of cycle parameters on thermodynamic performance of gas-steam combined cycle Sanjay* Department of Mechanical Engineering, National Institute of Technology, Jamshedpur 831 014, India
a r t i c l e i n f o
a b s t r a c t
Article history: Received 12 February 2010 Received in revised form 29 October 2010 Accepted 30 October 2010 Available online 9 December 2010
The paper deals with second law thermodynamic analysis of a basic gas turbine based gas-steam combined cycle. The article investigates the effect of variation of cycle parameters on rational efficiency and component-wise non-dimensionalised exergy destruction of the plant. Component-wise inefficiencies of the combined cycle have been quantified with the objective to pin-point the major sources of exergy destruction. The parameter that affects cycle performance most is the TIT (turbine inlet temperature). TIT should be kept on the higher side, because at lower values, the exergy destruction is higher. The summation of total exergy destruction of all components in percentage terms is lower (44.88%) at TIT of 1800 K & rp,c ¼ 23, as compared to that at TIT ¼ 1700 K. The sum total of rational efficiency of gas turbine and steam turbine is found to be higher (54.91%) at TIT ¼ 1800 K & rp,c ¼ 23, as compared to that at TIT ¼ 1700 K. Compressor pressure ratio also affects the exergy performance. The sum total of exergy destruction of all components of the combined cycle plant is lower (44.17%) at higher value of compressor pressure ratio (23)& TIT ¼ 1700 K, as compared to that at compressor pressure ratio (16). Also exergy destruction is minimized with the adoption of multi-pressure-reheat steam generator configuration. Ó 2010 Elsevier Ltd. All rights reserved.
Keywords: Cooled gas turbine Exergy destruction Parametric analysis Exergy Combined cycle Rational efficiency
1. Introduction The rising cost of energy and the global warming in recent years has highlighted the need to develop energy conversion systems with improved efficiency and reduced emissions. The availability of fuels has played an important role in the development and prosperity of a nation and their best utilisation is a method to conserve them. Waste heat recovery from gas turbine exhaust improves plant performance significantly, and employing ST (steam turbine) cycles provide the best performance in general. Heat of GT (gas turbine) exhaust is recovered in a HRSG (heat-recovery steam generator) to generate steam for the bottoming ST cycle. This scheme is widely called a combined cycle power generation system. These gas turbine based combined cycle power plants have become the mainstay in providing electrical power worldwide. Most of these combined cycle plants burn natural gas as fuel and the output of such gas turbines for power generation has been projected [1] to increase from around 570 GW in 1999e2035 GW in 2020; an increase of over 6%/yr. This increase in power demand will be met by large combined cycle based on gas turbine plant, which necessitates for studying the thermodynamics of these workhorses.
* Tel.: þ916572373813; fax: þ916572373246. E-mail address: [email protected]. 0360-5442/$ e see front matter Ó 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.energy.2010.10.058
Second law analysis of these power plants has been used to pinpoint the sources and quantify their component-wise exergy destruction. 2. System configuration The gas turbine based combined cycle, also called the gas-steam combined cycle has components such as axial flow compressors, combustion-chamber, cooled expansion turbine, heat-recovery steam generator, steam turbine, condenser, deaerator, feedpump etc (Fig. 1). Work in the area of parametric analysis of gas turbine based cycles have been reported by Louis et al. [2], Wu and Louis [3], El-Masri [4,5], Briesh et al. [6], Bolland and Stadaas [7], Bolland [8], Chiesa and Macchi [9], and Dechamps [10], A.M. Bassily[11], B.Zaporowski, and R. Szczerbowski [12], Kaushik et al. [13] and Cziesla et al. [14]. Studies related to exergy analysis of energy conversion cycles have earlier been carried out by many researchers. Svend and Ruyck [15] in their work have discussed the optimal cycle layout technique for evaporative gas turbine cycle. The feasibility of each cycle has been discussed by comparison of results of exergy destruction and exergetic efficiency. Aspen þ has been used for analysis of the cycles. The paper suggests various methods of better utilisation of intercooler heat, the aftercooler heat and the turbine exhaust heat.
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Sanjay / Energy 36 (2011) 157e167
Nomenclature a a,b,c cp F Fsa gt Gr h DHr _ m Q rp R p s S St t T TIT W
ratio of mass of coolant to mass of gas flow constants specific heat (kJ-kg1 K1) factor correction factor to account actual blade surface gas turbine Gibbs free energy function ¼ 43890 kJ kg1 specific enthalpy (kJ kg1) lower heating value (kJ kg1) mass flow rate (kg.s1) heat energy transfer (W) cycle pressure ratio gas constant (kJ-kg1K1) pressure (bar) specific entropy (kJ kg1 K1) blade perimeter (m) average Stanton number ¼ hg =cp;g $rg $Cg ¼ 0.005 pitch of blade (m) temperature (K) turbine inlet temperature (K) ¼ combustor exit temperature work (kJ s1)
Greek symbols thermodynamic property function gas flow discharge angle (degree) rational efficiency (%) exergy per unit mass of gas (kJ kg1) exergy (kJ s1) effectiveness (%) ¼ Tc$e Tc;i =Tb Tc;i efficiency (%) specific volume (m3 kg1)
f a hrat u U 3 h y
Subscripts a air, ambient b blade c coolant
Lior and Zhang [16] in their work have discussed energy and exergy based performance criteria, and second law efficiency of energy systems. Hammond [17] in his work has discussed the thermodynamic methods of (energy and exergy) analysis employed to illustrate energy use in industry and the scope for increasing energy efficiency, as well as the extent of exergetic ‘improvement potential’. It [17] has been concluded that poor thermodynamic performance is principally the result of exergy destruction in combustion and heattransfer processes. Marrero et al. [18] in their work have discussed second law analysis and optimisation of combined triple power cycle. Buther and Reddy [19] in their work have evaluated the performance of a waste heat-recovery power generation system based on second law analysis and investigated their various operating conditions. The temperature profiles across the HRSG, network output, second law efficiency and entropy generation number are simulated for various operating conditions. Verma et al., Ivar et al. and Deng et al. [20e22] have also done extensive work in this field. Based on mathematical modeling of the various components of combined cycle plant reported in the author’s [23e25] articles, this paper discusses rational efficiency and non-dimensional componentwise exergy destruction for a cooled gas turbine based combined cycle plant. The mathematical equations used in the analysis of the cycle components are discussed in the following sections.
comp comb cond D e f g gen gt hrsg hp i in ip j lp net P p plant pt s st w
compressor combustor condensate destruction exit fuel gas alternator gas turbine heat-recovery steam generator high pressure (steam) inlet, stage of compressor inlet intermediate pressure (steam) coolant bleed points low pressure (steam) difference between two values product pressure combined cycle plant polytropic steam steam cycle water
Acronym 3PR Triple pressure-reheat HRSG/bottoming cycle configuration AFC Air-film cooling BFP Boiler feedpump C Compressor CC Combustion-chamber GT Gas turbine HPD High pressure drum HPST High pressure steam turbine IPD Intermediate pressure drum IPST Intermediate pressure steam turbine LPD Low pressure drum LPST Low pressure steam turbine
3. Component modeling and governing equations The gas-steam combined cycle includes axial flow compressors, combustion-chamber, cooled expansion turbine, heat-recovery steam generator, steam turbine, condenser, deaerator, feedpump. 3.1. Gas model The specific heat of gas at constant pressure is assumed to be a function of temperature, given by the polynomial adopted from the work of Toulounkain and Tadash [26]. For the temperature range of 250e599 K
cp;a ¼ 1:0232041:76021104 $Tþ4:0205107 $T2 4:872721011 $T3
(1a)
For the temperature range of 600e1500 K
cp;a ¼ 0:8743343:22814104 $Tþ3:58694108 $T2 1:991961011 $T3
(1b)
Thus, the enthalpy, entropy and exergy of gas can be calculated using the above polynomial in the following equations
Sanjay / Energy 36 (2011) 157e167
159
Fig. 1. Schematic of a cooled gas turbine based combined cycle plant.
3.3. Combustor model
ZT h ¼
cp ðTÞdT
(2)
Ta
f¼
ZT cp ðTÞ$
dT T
(3)
Ta
For given values of turbine TIT, pressure drop and combustion efficiency, the fuel flow is found from the mass and energy balance, and the exergy destruction is found from the exergy balance as given below
_e m
comb
i h _ iþm _f ¼ m
(9)
comb
s ¼ f Rlnðp=paÞ
(4)
_ e $he m _ i $hi comb _ f $DHr $hcomb ¼ m m
u ¼ h Ta $s ¼ h Ta $f þ R$Ta $lnðp=pa Þ
(5)
_ f $ DGr þ Rf $Ta $ln pf =pa UD;comb ¼ m
Here, all non-reacting gases are arbitrarily assigned zero thermodynamic enthalpy, entropy and exergy at the ambient pressure and temperature, taken as 1 bar and 288 K regardless of chemical composition. Mass and energy balance of each component is done with the assumption that the process is adiabatic. The mechanism of evaluating rational efficiency and exergy destruction used here is exergy balance across control volume of the component/element. The analysis has been made for constant air mass flow rate i.e per kg of air handled by the cycle. 3.2. Compressor model Compression in axial flow compressor is assumed to be polytropic taking the polytropic efficiency as 92% [Ref. Table 1.]. The temperature of air at any section is expressed in terms of local pressure and polytropic efficiency, by the following expression
dT ¼ T
"
R
#
hp;comp $cp;a
dp p
(6)
Compressor work is found from the mass & energy balance whereas, the exergy destruction from exergy balance is given by the following equations:
_ e $he þ Wcomp ¼ m
X
_ c;j hc;j m _ c; i $hc; i m
_ c;i $uc;i UD;comp ¼ Wcomp þ m
X
_ c;j $uc;j m _ c;e $uc;e m
(7) (8)
h
_ e $ue m _ i $ui comb m
(10)
i comb
(11)
Here, the fuel line is assumed to be at pressure ‘pf’ and at ambient temperature. 3.4. Cooled gas turbine model In this work, the gas turbine blades are modeled to be cooled using AFC (air-film cooling) method. The cooling model used for cooled turbine is the refined version of that by Louis et al. [2]. The mass flow rate of coolant required in a blade row is expressed as [24]:
_c m ac ¼ ¼ _ mg
# " Tg;i Tb Stin $cp;g Sg $Fsa 3$cp;c t$cosa Tb Tc;i
(12)
where Sg y 2c, Sg/t$cosa ¼ 3.0, Fs,a ¼ 1.05, a ¼ 45 (for stator), a ¼ 48 (for rotor), Stin ¼ 0.005 Fig. 2 gives the details of expansion process for a cooled turbine stage. Process b1c1 in Fig. 2 depicts cooling due to heat transfer between hot gas and coolant, which takes place at constant pressure line due to which exergy decreases, while process c1d1 depicts drop in temperature due to mixing of coolant with gas which is an irreversible process and also takes place along constant pressure line, which leads to drop in entropy. Process d1a2 in the model denotes a process similar to throttling. The deviation between actual and theoretical value is dependent upon the amount of coolant and temperature of coolant used for
160
Sanjay / Energy 36 (2011) 157e167
Table 1 Input data for analysis [24].
_ g;i $ug;i þ UD;gt ¼ m
Parameter
Symbol
Unit
Gas Properties
cp ¼ f (T) Enthalpy h ¼ ⌠cp(T) dT i. Polytropic efficiency (hpc) ¼ 92.0 ii. Mechanical efficiency(hm)) ¼ 98.5 i. Combustor efficiency (hcomb) ¼ 99.5 ii. Pressure loss (ploss) ¼ 2.0% of entry pressure iii. Lower heating value ðDHr Þ ¼ 42.0 iv. Fuel,Natural gas composition: CH4 ¼ 86%, C2H6 ¼ 7% i. Polytropic efficiency (hpt) ¼ 92.0 ii. Exhaust pressure ¼ 1.08 iii. Exhaust hood temperature loss ¼ 4 iv. Turbine blade temperature ¼ 1123 i. Effectiveness ¼ 98.0 ii. Pressure loss ¼ 10% of entry pressure iii. Stack (minimum temperature) ¼ 363.0 iv. ‘hp’ pressure ¼ 160 v. ‘hp’ superheat temperature ¼ 843.0 vi. ‘hp’ steam exhaust pressure ¼ 35 vii. Reheater loss ¼ 3% of entry pressure ix. ‘ip’ superheat temperature ¼ 603.0 x. ‘lp’ pressure ¼ 6.0 viii. ‘ip’ pressure ¼ 34.0 xi. ‘lp’ superheat temperature ¼ 573.0 xii. Deaerator pressure ¼ 2.0 xiii. Condenser pressure ¼ 0.05 xiv. Gas/steam approach temperature difference ¼ 20.0 xv. Pinch-point temperature difference ¼ 10.0 xvi. Pressure of blade coolant steam ¼ 35 i. Isentropic efficiency ¼ 88.0 ‘hp’, 92.0 ip/lp ii. Mechanical efficiency ¼ 98.5 iii. Minimum steam quality at ‘lp’ exhaust ¼ 0.88 Valve throttling loss ¼ 2% of entry pressure Undercooling ¼ 4 Rise in cooling water temperature ¼ 10 Alternator efficiency ¼ 98.5
kJ/kg K
Compressor Combustor
Gas turbine
HRSG (Triple Pressure with reheat)
Steam turbine
Condenser Alternator
% % % % MJ/kg
% bar K K % % K bar K bar % bar K bar K bar bar K
_ c $ uc;i uc;e m _ g;e $ug;e Wgt m
(14)
3.5. HRSG model An unfired HRSG is considered in the configuration. For the parametric study the pressure levels of the HRSG is one of the variables. Six configurations namely 3PR, 3P, 2PR, 2P, 1PR, and 1P based on number of pressure levels and steam reheat have been considered. The selection of steam pressure and temperature for each of these configurations is based on the optimised value to yield maximum steam cycle efficiency, satisfying the minimum stack temperature and quality of steam at ‘lp’ turbine exhaust given in (Table 1) [23]. The detailed optimisation procedure is outlined in Ref. [23]. 3.6. Steam turbine model Steam turbine output and exergy destruction in HP, IP and LP stages are found out by mass, energy and exergy balance as given below.
Wst ¼
stages X
_ s:i $ hs;i hs;e m
(15)
where ðhs;i hs;e Þ ¼ hst ðhs; i hs; e Þisentropic _ s;i ¼ amount of steam entering to the respective main turbine m stages as per configuration. and the exergy balance as:
K bar % % dry
UD;st ¼
% K C %
stages X
_ s:i $ us; i us; e Wst m
(16)
3.7. Condenser model The mass and energy balance give the cooling requirement while exergy balance will yield exergy destruction, as given below:
cooling of blades and the actual value varies with blade-cooling requirements. At TIT 1700 K for air-film cooling cooling, its maximum value is 6% [24]. Turbine work and exergy destruction are given by the mass, energy and exergy balance of gas turbine as under:
h X i _ c , hc;i hc;e _ g;i , hg;i hg;e þ m Wgt ¼ m
X
_ cond; e $he ¼ m _ w;i $hw;i _ s; i $hi m _ w;e $hw;e m m
_ s;i $us;i m _ cond;e $ucond;e UD;cond ¼ m
_ w;e $ue _ w;i $uw;i m þ m
(13)
(17)
(18)
3.8. Feed pump model Polytropic expansion in a row of bladings
en tha l p y , h
p Polytropic expansion
a -b b -c c -d d -a
: Polytropic expansion : Energy loss due to cooling : Energy loss due to mixing : mixing stagnation pressure loss at constant enthalpy Δp : total pressure loss due to mixing
Coolant mixing pressure drop ( Δ p)
d
Wpump ¼
UD;pump ¼
p b
Heat transfer process followed by mixing with coolant, process
The mass, energy and exergy balances yield pump work and exergy destruction as:
p + Δp
X
yw;i $ðpe pi Þ
X _ w;i uw;i uw;e þ Wpump m
(19)
(20)
4. Performance parameters The performance parameters Wgt;net , Wst;net , Wplant , hplant and
Polytropic expansion in next row
hrat are expressed as follows: Wgt;net ¼ Wgt
entropy, s Fig. 2. Expansion path in cooled gas turbine row.
jWcomp j
hm
Wst;net ¼ Wst $hm
jWpump j
hpump
(21) (22)
(26)
Modeling of cycle components and governing equations developed for cycles proposed above have been coded using Cþþ and results obtained. A flowchart of the programme code ‘Simucomb’ illustrating the method of solution has been given in Appendix-I. The input data used in the analysis is given in Table 1.
5. Results and discussions The results of parametric analysis of cooled gas turbine based combined cycle are discussed in the subsequent sections. Rational efficiency of gas turbine and steam turbine has been plotted as histogram for various cycle parameters analyzed. Histogram of exergy balance (in %) showing gas turbine rational efficiency, steam turbine rational efficiency and component-wise non-dimensional exergy destruction with reference to input fuel exergy are shown in Fig. 4 through Fig. 6. The gas turbine blade-cooling model adopted from author’s previous work [24] gives results that were validated with results of El-Masri [4] and Horlock et al. [28] with variation in the acceptable range of 2.5e3.5%. The mathematical model for exergy analysis gives results that have been validated with [23] and [27] and found to compare well. Also the results of combined cycle performance modeling have been validated and combined cycle plant efficiency compares well with the work of Bolland [7,8]. Dechamps [10] and S207FB model of combined cycle plant by GE Power [33]. The parameters that have been studied include turbine inlet temperature, compressor pressure ratio, and bottoming cycle B3PR configuration, Air-film cooling.
Combustor fuel consumption (kg of fuel / kg of air handled by the cycle)
0.030
(rp_c=16) (rp_c=23)
0.025
2
1
0
DA
Wst;net _ f $D Gr m
3
BFP
¼
(25)
5
Co n d .
Wst;net
Uf ;input
Wgt;net _ f $DGr m
10
ST
Uf ;input
¼
15
Stack
hrat;st ¼
Wgt;net
B3PR configuration, rp,c=16, AFC
20
HRSG
hrat;gt ¼
TIT=1700K TIT=1800K
25
GT
The concept of power plant ‘rational efficiency’ to provide a criterion for performance based on actual shaft work output from a power plant to the input fuel exergy was first introduced by Szargut and Petela [29]. The concept has been studied by Kotas [30], Moran [31] and Gyftopoulas and Beratta [32]. Rational efficiency of gas turbine and steam turbine is mathematically expressed as:
Exergy destruction
30
CC
(24)
Rational Efficiency
C
Wplant Wplant ¼ ¼ _ f $DHr m Q
35
161
ST
hplant
(23)
GT
Wplant ¼ Wgt;net þ Wst;net $hgen
Rational Efficiency & (Exergy destruction/input fuel exergy) (%)
Sanjay / Energy 36 (2011) 157e167
Combined cycle components Fig. 4. Effect of TIT on rational efficiency and non-dimensionalised exergy destruction for various combined cycle components.
configuration. The effect of variation of these parameters on rational efficiency and component-wise exergy destruction has been discussed. The values of compressor pressure ratio selected for analysis has been adopted from operating parameters of gas turbines namely M501F (rp,c in the range of 16) from Mitsubishi and MS 9001H (rp,c in the range of 23) from General Electric. The value of TIT ¼ 1700 K is the current state-of-the-art of combustor temperature or TIT and the TIT of M501F & MS 9001H falls around this value. The figures include sensitivity analysis showing the effect of variation of parameters under investigation. 5.1. Effect of TIT and rp,c on fuel consumption Fig. 3 illustrates a histogram of the sensitivity of fuel consumption (in kg of fuel/kg of air handled by the cycle) for fixed values of TIT and rp,c in the case of B3PR configuration. It is observed that at a fixed value of rp,c, when TIT is increased, the fuel consumption of the combustor increases proportionately to achieve the desired TIT. On the other hand at the given value of TIT when rp,c is increased, the fuel consumption of the combustor reduces. This is due to elevated temperature at which the air exits the compressor and enters the combustor (because of elevated pressure of the air), thus reducing the fuel consumption to achieve the required TIT. As the percentage of excess air in the combustor of gas turbine is very high, the change in fuel consumption does not affect the fuel-air ratio significantly. Also as fuel consumption is directly dependent on the value of TIT, it has been selected as one of the parameters to be varied to study the performance of the plant.
0.020
5.2. Effect of turbine inlet temperature 0.015
0.010
0.005
0.000 1700K
1800K
Fig. 3. Effect of compressor pressure ratio and TIT on combustor fuel flow rate.
Fig. 4 illustrates sensitivity analysis depicting the effect of variation of TIT on rational efficiency of gas turbine, steam turbine and also non-dimensional component-wise exergy destruction. The histogram is for B3PR configuration at rp,c ¼ 16, Tb1123 K for cooling scheme AFC gas turbine based combined cycle power plant. AFC has been chosen here and also in Figs. 5 and 6 for depicting the results of the analysis, as it is the most promising cooling technique in the case of power turbine based combined cycle plants. Higher TIT results in higher rational efficiency of ST, while lower rational
Sanjay / Energy 36 (2011) 157e167
efficiency of GT, while the quantum of respective network output (in kJ/kg of gas flow) from each of these components are in the reverse order. The sum total of rational efficiency of GT and ST is found to be higher (54.91%) at TIT ¼ 1800 K. Higher exergy destruction (in percentage) in GT, HRSG, ST, condenser and deaerator are observed at higher values of TIT. But exergy destruction is lower (in percentage terms) at higher values of TIT in case of CC and compressor. This relates to the discussion in Leites, Sama and Lior [34] in their work in section 4.2 wherein they have suggested methods to reduce exergy destruction: “heat of reaction to have a positive thermal exergy, the reaction temperature, T, must be greater than To .... Thus, there must be a reaction temperature, greater than To, but less than Teq (reaction equilibrium temperature), where the work effect is optimal and; ” therefore, where the exergy destruction reduces and in conclusion recommends that the increase in the value of TIT should be such that exergy destruction in combustor reduces. Non-dimensional exergy destruction is highest in combustor and is shown to exhibit a higher value (30.5%) at lower value of TIT i.e. 1700 K, as compared to 28.8% at TIT of 1800 K. Also the sum total of exergy loss in all components of the cycle is lower (44.88%) at higher value of TIT ¼ 1800 K. 5.3. Effect of compressor pressure ratio A histogram showing the sensitivity of rational efficiency and component-wise exergy destruction in B3PR combined cycle configuration at TIT ¼ 1700 K for the two values of rp,c i.e 16 and 23 are shown in Fig. 5. Higher value of rp,c demonstrates higher rational efficiency of GT while lower rational efficiency of ST. This is because more gas cycle specific work is delivered at higher rp,c, while the denominator (input fuel exergy) of the expression of rational efficiency is relatively unaltered. Since at higher rp,c, due to lower level of gas cycle exhaust temperature, less heat energy is available in HRSG, the steam turbine output is lesser, resulting in lower rational efficiency. The sum total of rational efficiency of GT and ST is found to be higher (55.74%) at rp,c ¼ 23. The exergy destruction in compressor is more at higher rp,c due to increased compression work input and also increased bleeding of coolant air, due to higher coolant air temperature of respective bleed points and at compressor exit. In combustor, exergy destruction
Rational Efficiency & (Exergy destruction/input fuel exergy) (%)
162
Rational Efficiency 24
B3PR B3P B2PR B2P B1PR B1P
Exergy destruction
23 22 21 20 19 18
rp,c=16 , TIT=1700K Air film cooling (AFC)
6
4
2
0
ST
HRSG
ST
Cond.
Bottoming cycle components Fig. 6. Distribution of rational efficiency and non-dimensionalised exergy destruction of bottoming cycle components for different bottoming cycle configurations.
(29.66%) is lower at higher rp,c ¼ 23. GT exhibits higher level of exergy destruction (6.15%) at higher value of rp,c due to higher expansion ratio resulting in more entropy generation. In HRSG, exergy destruction is higher at lower rp,c. This is attributed to the fact that at lower rp,c, lower expansion ratio provides more heat energy available to HRSG. The exergy destruction in compressor at rp,c ¼ 23 is higher than at rp,c ¼ 16 because at higher compressor pressure ratio, mass of air-coolant bled from compressor exhaust will be more to achieve same cooling effect, due to higher temperature of compressor exit air. GT exergy destruction follows a similar pattern due to the above reasons. The exergy destruction in stack, ST, condenser, BFP and D/A are in the range of 0.18e1.8%. The sum total of exergy destruction of all components of the combined cycle plant is lower (44.17%) at higher value of compressor pressure ratio (23). Hence higher value of rp,c is should be selected to enhance exergy performance of gas turbine based combined cycle plant.
(rp,c=16) (rp,c=23)
Exergy destruction
35
B3PR configuration, TIT=1700K, AFC 30 25 20 15 7 6 5 4 3
Fig. 6. depicts the effect of HRSG configuration (B1P to B3PR) on the rational efficiency of ST and exergy destruction of bottoming cycle components at rp,c ¼ 16, TIT ¼ 1700 K and Tb1123 K for AFC scheme. Rational efficiency of steam turbine is sensitive to the type of bottoming cycle configuration of the combined cycle plant. The decreasing order of value of rational efficiency of steam turbine is found as B3PR, B3P, B2PR, B2P, B1PR and B1P. This is because best utilisation of heat energy in bottoming (steam) cycle is exhibited in case of B3PR configuration. The distribution of exergy destruction is also observed to be sensitive to type of bottoming cycle configuration. In all bottoming cycle components (HRSG, ST, Condenser) it is observed that component-wise exergy destruction is lower in reheated configuration with respect to the same configuration without reheat.
2 1
6. Conclusions DA
BFP
Cond.
ST
Stack
HRS G
GT
CC
C
ST
0
GT
Rational Efficiency & (Exergy destruction/input fuel exergy) (%)
5.4. Effect of HRSG configuration (B1P to B3PR) Rational efficiency
Combined cycle components Fig. 5. Effect on rational efficiency and non-dimensionalised exergy destruction of combined cycle components for variation in compressor pressure ratio.
Based on the parametric exergy analysis of gas turbine based combined cycle following conclusions have been drawn: 1) Fuel consumption in the combustor of a gas turbine is directly dependent on desired turbine inlet temperature.
Sanjay / Energy 36 (2011) 157e167
2) The maximum exergy destruction has been found in combustor followed by gas turbine and compressor. Hence combustor should be the focus of further study. 3) Higher exergy destruction is observed in major components like compressor, combustor, and stack at lower values of turbine inlet temperature suggesting the adoption of higher turbine inlet temperature to reduce exergy destruction in these components. Sensitivity analysis shows that higher value of turbine inlet temperature reduces exergy destruction in combustor. It is hence concluded that turbine inlet temperature may be increased, to enhance exergy performance of combined cycle, keeping in mind the technological/metallurgical limits. 4) The sum total of rational efficiency of gas turbine and steam turbine is found to be higher at higher values of compressor pressure ratio and turbine inlet temperature.
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5) Rational efficiency of steam turbine is sensitive to the type of bottoming cycle configuration of the combined cycle plant. The decreasing order of value of rational efficiency of steam turbine is found as B3PR, B3P, B2PR, B2P, B1PR and B1P indicating B3PR to be the superior configuration. 6) The distribution of exergy destruction is also is found to be sensitive to the type of bottoming cycle configuration. In all studied bottoming cycle components (heat-recovery steam generator, steam turbine & condenser) it is observed that component exergy loss is lower for reheated configuration with respect to the same configuration without reheat, thus indicating the selection of reheated bottoming cycle configuration for superior second law performance of the cycle.
Appendix Start ‘SimuComb’
Select the Basic Gas Turbine module, BGT
Menu to select the gas turbine blade cooling means
Input plant parameters e.g. rpc, TIT, Tci, Tb, Tstack, ps, Ts, cooling means etc.
Compressor module Start
Input parameters Compressor, C
Input parameters
Calculate compressor work etc. Return computed results to datafile
A
Air properties data module
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A
Basic Gas Turbine module BGT
Start
Input parameters and read data (compressor module results) from datafile
Call functions CC, steam, air & gas properties data
Compute No. of stages in Gas turbine, and blade coolant flow requirements
Call functions to compute GT work, GT net work, mf, GT efficiency, component exergy and exergy losses, GT exhaust gas temperature etc.
Return computed results to datafile
HRSG/ST module (1P, 1PR, 2P, 2PR, 3P, 3PR)
Start program for configuration selected
Input parameters pinch point allowable stack temperature etc. and read data from datafile
Compute the dryness fraction of steam at the exit of each ST stage i.e hp, ip and lp
B
Program to read steam property from database/ datafile
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165
HRSG/ST module (1P, 1PR, 2P, 2PR, 3P, 3PR) B
Program to compute mass of steam generated in HRSG using optimisation technique
Read all pinch point temp. difference, min. stack temp, min. quality of steam, etc.
Input trail value of mass of steam generated
Compute mass of steam generated in hp, ip and lp drum using iterative procedure
Is Tg,stack >= 80oC & Tpp,ip= 10.0
No
Yes Call functions to compute ST work , pump work, net ST work, bottoming cycle efficiency, component wise exergy and exergy loss etc.
Return computed results to datafile
C
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C
Combined cycle plant performance analysis module
Call function to read data stored as computed results for the GT module
Call function to read data stored as computed results for the HRSG/GT
module
Compute results for overall performance of combined cycle / cogeneration plant and component specific exergy and exergy loss
Print results of overall performance of combined cycle / cogeneration plant and component specific exergy and exergy loss
END
Program to read computed results stored in data files
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167
Basic gas turbine module (BGT)
Input parameters and read data (compressor module results) from datafile
Call functions CC, air, steam, & gas properties data
Compute No. of stages in GT, and blade coolant requirements
Call functions to compute GT work, GT net work, mf, GT efficiency, component exergy and exergy losses, GT exhaust gas temperature etc.
Return computed results to datafile
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