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Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures
Energy xxx (2015) 1e11
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Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures Mahmoud Nadir a, *, Adel Ghenaiet b a
Laboratory of Energetic Mechanics and Engineering (LEMI), Faculty of Engineering, University of Boumerdes, Independence Avenue, Boumerdes, 35000, Algeria Faculty of Mechanical and Process Engineering, University of Sciences and Technologies Houari Boumediene, BP 32 EL e Alia, Bab Ezzouar, 16111, Algiers, Algeria b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 October 2014 Received in revised form 20 February 2015 Accepted 21 April 2015 Available online xxx
Design optimization of a (heat recovery steam generator) HRSG is essential due to its direct impact on large power generation combined cycles. This study is aimed at giving a thermodynamic comparison between the optimums of three configurations of HRSG operating at exhaust gas temperature (TOT) from 350 C to 650 C. The optimization results, using PSO (Particle Swarm Optimization) method, show that adding another pressure level allows achieving a higher pressure at the inlet of high pressure turbine, producing more steam quantities, destroying less exergy and finally producing more specific work independently of TOT. For a given value of 600 C representative of TOT of recent gas turbines, an addition of a pressure level is shown to increase the specific work of about 17 kJ/kg, representing a benefit of about 10% for the steam cycle, whereas a third pressure level results in 8 kJ/kg increase in the specific work, corresponding to 4% in the steam cycle. © 2015 Elsevier Ltd. All rights reserved.
Keywords: HRSG (heat recovery steam generator) Exhaust gas temperature Combined cycle performance Optimization PSO (Particle Swarm Optimization) technique
1. Introduction Among improvements made to reduce the fuel consumption and the greenhouse gas emissions of the (gas turbines) GT, especially CO2, the introduction of the (combined cycle) CC as a favorite facility for electricity generation, reaching a thermal efficiency of 60%. The bottoming steam cycle provides about 30e40 % of the overall generated power, and any improvement could mainly be done through optimizing HRSG (heat recovery steam generator). In this context several studies were done, such as the one of Franco and Casarosa [1] who investigated the possibility of increasing efficiency of CC for 60% and compared between HRSG
* Corresponding author. E-mail addresses: [email protected] (M. Nadir), ag1964@yahoo. com (A. Ghenaiet).
with one, two and three pressure levels with and without reheat, considering three values of TOT (Turbine Outlet Temperature); 700 K, 773 K and 823 K. Khaliq and Kaushik [2] focused their work to show the importance of GT reheat in improving the CC global performance, especially the specific work. Also, Sanjay et al. [3] studied the effect of reheated expansion when turbine blades are cooled by a steam fraction extracted from HRSG. They showed that with three pressure levels and steam reheat the thermal efficiency may reach 62%. Bassily [4,5] optimized the whole CC in which the steam cycle is reheated at two and three pressure levels, resulting in an efficiency enhancement of 1.9e2.1 % compared to the design case. Polyzakis et al. [6] optimized and compared between the simple, intercooled, reheated and intercooled-reheated GT when coupled to a simple steam cycle, and concluded that the reheat is the most suitable solution. Godoy et al. [7] optimized CC simple steam cycle by maximizing its exergetic efficiency for a wide range of power with the determination of HRSG optimal surface.
http://dx.doi.org/10.1016/j.energy.2015.04.023 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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Many other studies focused on the optimization of steam s and Rapuan [8] who cycle alone such as the study of Valde optimized a single pressure level HRSG for TOT equal 545 C. Franco and Russo [9] optimized two and three pressure levels HRSG intended to operate with two types of GT, and demonstrated that it is possible to reach an overall efficiency of 60% by optimizing the steam cycle. Xiang and Chen [10] optimized both at base and part load a reheat three pressure levels HRSG built around GE (General Electric) PG9351FA GT and suggested to use a partial recovery of exhaust gas energy for a temperature exceeding 590 C. Mohagheghi and Shayegan [11] optimized four types of HRSG of one, two and three pressure levels with a reheat for TOT equal 550 C. They showed that addition of a pressure level always leads to improving steam cycle performance. Bracco and Siri [12] optimized a single pressure level HRSG adapted with four GT present on the market, considering several objective functions, and outlined the influence of TOT and mass flow rate on the steam cycle performance. The previous studies have only addressed the thermodynamic optimization, but the maximization of performance may lead to a higher cost of electricity [13,14], and this is why many other authors have considered the economical aspect. Bassily [15] optimized an objective function of net additional revenue for a triple pressure level reheat HRSG adapted to a reheated GT with exhaust gas recuperation. The optimization resulted in an annual saving of 33.7 million US Dollars for a 481 MW power plant. Kotowicz and Bartela [16] analyzed the influence of fuel price variation on the optimal values of design variables of the steam part of a combined cycle. They found that an increase in fuel price required higher optimum pressure in the high and intermediate pressure part, a decrease in the optimum value of pinch point and an increase in the optimum value of steam temperature of the intermediate pressure part. Ahmadi and Dincer [17] studied the effect of fuel cost on optimal design variables of CC and concluded that by increasing fuel price, the values of decision variables in the thermoeconomically optimal design tend to those of the thermodynamically optimal design. Rovira et al. [18] considered the frequent off-design operation of CC and developed a thermoeconomic optimization model in order to minimize the electricity cost. Carapellucci and Giordano [19] undertook a thermoeconomic optimization of several types of HRSG adapted to three types of GT and investigated the effect of fuel price and capacity factor on the electricity cost. The dynamic regime is another important aspect of CC study; it aims at improving the start up, shut down and shifting from one load to another. Many authors took interest in this aspect; Lu [20] has presented a brief review of simulation techniques of CC static and dynamic operation. Alobaid et al. [21,22] have modeled and validated the start up procedure of combined cycle and HRSG with measured data. Benato et al. [23] have proposed a complete procedure of the dynamic behavior and estimated the residual life production of some components. In order to optimize the start up process, some studies [24,25] have combined the dynamic modeling with non linear optimization methods. A synthesis of this review shows that most of previous studies addressed the optimization of one or several HRSG types intended to work with a specific gas turbine (consequently a well defined TOT) and no study optimizes several HRSG configurations for a wide range of TOT. Thus, this paper presents, for a TOT range of 350e650 C, a thermodynamic optimization of three HRSG configurations namely: HRSG with one pressure level with reheat (First level) 1P, two pressure levels with reheat (Second level) 2P and three pressure levels with reheat (Third level) 3P. Concerning the optimization method, one of the most recent methods, which is the PSO (Particle Swarm Optimization) is used in this study.
2. Thermodynamic analysis The diagrams of the three HRSG configurations are shown in Fig. 1, they are of a natural circulation type. The diagrams of temperature-transferred heat corresponding to those of Fig. 1 are given by Fig. 2. For an easy presentation, only the modeling of HRSG with three pressure levels and a reheat is shown. The work produced by the steam cycle per a unit mass of exhaust gas is written as follows:
WSC ¼ ðu1 þ u2 þ u3 ÞWLP þ ðu2 þ u3 ÞWIP þ u3 WHP
(1)
u1, u2 and u3 represent the fractions of steam for the first, second and third pressure level. In general terms, the steady state exergy balance applied for a given control volume is written as follows: X j
! X X T0 mi exi me exe Exd ¼ 0 1 Qj W þ Tj e i
(2)
For 1 kg of exhaust gas, by considering a control volume corresponding to the whole steam cycle and by neglecting the exergy of heat transfer, equation (2) becomes:
Wsc þ ex1 ex11 exd ¼ 0
(3)
The destroyed exergy can be deduced:
exd ¼ Wsc þ ex1 ex11
(4)
It is possible to define the destroyed exergy rate as follows:
exdr ¼
exd exn
(5)
exn represents the net exergy carried into the control volume:
exn ¼ ex1 ex11
(6)
For the third pressure level, the energy balance of evaporator, reheater and superheater, leads to the following:
u3 ðhe
SH 3P
hi
EV 3P Þ
þ u3 ðhe
RH
hi
RH Þ
¼ cp1 TOT cp4 Tg4 (7)
From the energy balance of superheater:
u3 ðhe
SH 3P
he
EV 3P Þ
¼ cp1 TOT cp2 Tg2
(8)
The effectiveness of superheater and reheater is defined by:
ESH
3P
ERH ¼
¼
Tse SH 3P Tse TOT Tse EV
EV 3P
(9)
3P
Tse RH Tsi RH Tg2 Tsi RH
(10)
The definition of pinch point:
Tg4 ¼ Tsi
EV 3P
þ DTP3P
(11)
The temperature of gas leaving the economizer of third level (Tg5) is obtained from energy balance:
u3 ðhe
EC 3P
hi
EC 3P Þ
¼ cp4 Tg4 cp5 Tg5
(12)
Equations 7e12 represent a system of 6 equations with 6 unknowns which are: u3,Tse SH 3P,Tse RH,Tg2,Tg4 and Tg5, which are solved by using a numerical method.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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Fig. 1. Diagrams of HRSGs configurations: a) HRSG 1P, b) HRSG 2P, c) HRSG 3P.
The properties of water and steam are based on relations of the (International Association of the Properties of Water and Steam) IAPWS [26]. For the second pressure level, by knowing the steam temperature at evaporator exit (Tse EV 2P), the steam temperature at superheater exit is obtained from the definition of effectiveness:
ESH
2P
¼
Tse
Tse Tg5 Tse EV SH 2P
ESH EV 2P
EV 2P
2P
þ DTP2P
(14)
It is now possible to determine the fraction of steam of the second pressure level from energy balance across both evaporator and superheater:
u2 ðhe
SH 2P
hi
EV 2P Þ
¼ cp5 Tg5 cp7 Tg7
(15)
The gas temperature at the outlet of economizer (Tg8) is obtained from:
ðu3 þ u2 Þðhe
EC 2P
hi
EC 2P Þ
1P
¼
Tse
(13)
The gas temperature at exit of second level evaporator (Tg7) is obtained from relation (14):
Tg7 ¼ Tsi
For the first pressure level, similar relations as for second level still apply. By knowing the evaporator exit steam temperature, the exit temperature of superheater is obtained from the definition of effectiveness:
¼ cp7 Tg7 cp8 Tg8
(16)
SH 1P Tse Tg8 Tse EV
EV 1P
(17)
1P
The gas temperature at the exit of first level evaporator (Tg10) is obtained from the definition of pinch point:
Tg10 ¼ Tsi
EV 1P
þ DTP1P
(18)
The steam fraction of the first pressure level is determined from energy balance across both evaporator and superheater:
u1 ðhe
SH 1P
hi
EV 1P Þ
¼ cp8 Tg8 cp10 Tg10
(19)
The stack exit temperature (Tg11) is obtained from economizer energy balance:
ðu3 þ u2 þ u1 Þðhe
EC 1P
hi
EC 1P Þ
¼ cp10 Tg10 cp11 Tg11
(20)
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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Fig. 2. The temperature-transferred heat diagram: a) HRSG 1P, b) HRSG 2P, c) HRSG 3P.
Once the temperatures of heat exchangers and steam fractions are determined, it is possible to calculate the specific work of steam cycle and the destroyed exergy rate. The performances of CC in terms of specific work, energetic and exegetic efficiency are calculated as follows:
WCC ¼ WGT þ WSC
(21)
hth
CC
¼
WGT þ WSC QGT
(22)
hex
CC
¼
WGT þ WSC ExGT
(23)
3. Optimization This study addresses a global non-linear problem of optimization with constraints, thus, the following illustrates its mathematical formulation and the algorithm of the used PSO method. A problem of optimization is mainly constituted of an objective function, optimization variables and constraints. 3.1. Objective function and optimization variables For a given GT, the values of TOT and specific work are fixed, and hence the optimization of CC only requires the steam cycle specific work per unit mass of exhaust gas to be maximized.
This specific work is considered as the objective function and the fitness function f(X). The vector X(p1,p2,p3,ESH 1P,ESH 2P,ESH 3P, ERH,DTPin 1P,DTPin 2P,DTPin 3P) represents the optimization variables characterizing the HRSG. The optimization results are: the steam fraction at each level (i.e u1, u2 and u3), steam exit temperatures from superheaters and reheater (Tse SH 1P, Tse SH 2P, Tse SH 3P and Tse RH), gas temperatures at heat exchangers inlet and outlet (Tg2,Tg4,Tg5,Tg7,Tg8,Tg10 and Tg11) and the specific work produced by the three vapor turbines (WLP, WIP, WHP). 3.2. Constraints analysis In order to avoid mechanical degradation and deterioration of the aerodynamic performances of the last stages of steam turbine, the steam fraction should be higher than 88% [27]. To maintain a good operation of HRSG and turbine material, the steam pressure and temperature at HRSG exit should not exceed 160 bar and 580 C, respectively [28]. The condensed water in exhaust gas could form a corrosive sulfuric-acid, so the stack temperature should be higher than 80 C to avoid water condensation [29]. In practice, for the pinch point, as it is well known, a null value leads to an infinite surface of economizer then a limit value of 10K is imposed [30]. An effectiveness superheater close to “1” leads to an infinite surface, a maximum value of 0.85 is fixed [31]. To summarize, the optimization problem can be denoted mathematically as follows:
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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8 Maximize f ðXÞ with f ðXÞ ¼ Wsc ðXÞ > > > > X ¼ ðp1 ; p2 ; p3 ; ESH 1P ; ESH 2P ; ESH 3P ; ERH ; DTP1P ; DTP2P ; DTP3P Þ > > > > under the following constraints : > > > > x 0:88 0 > > < Tse SH 1P 853K 0; Tse SH 2P 853K 0 and Tse SH 3P 853K 0 Ts > e RH 853K 0 > > > > Tg11 353K 0 > > > > > DTP1P 10K 0; DTP2P 10K 0 and DTP3P 10K 0 > > > 0:85 0; ESH 2P 0:85 0; ESH 3P 0:85 0 and ERH 0:85 0 E > : SH 1P p3 160bar 0
3.3. PSO algorithm The method of PSO as proposed by Eberhart and Kennedy [32] is inspired from the ability of groups of some species of animals to work as a whole, e.g. birds flocking to a food source. This seeking behavior was associated with that of an optimization search for solutions to non-linear equations in a real-valued search space [33]. PSO algorithm starts with a population of solutions (taken randomly) and looks for an optimum for the problem, making population individuals evolve over generations. In contrast to genetic algorithms in which solutions are coded in chromosomes, PSO population directly represents the solutions, and the research for the best solutions is done by moving these individuals in solutions space, benefitting collectively from the optima detected individually by each particle. Thus, each particle, over generations, adjusts its path towards its own previous best position (Pbest), and towards the best previous best position obtained by any member of its group (Gbest). The performance of each particle is evaluated using the fitness function. The flowchart describing the algorithm is given by Fig. 3 which can be summarized as follows: 1 Create a population “Pop” of N particles uniformly spread across the search space. 2 Each particle k is evaluated using the fitness function “f”. Particles that do not obey the imposed constraints are excluded from the group and randomly replaced by others. 3 If a position Xk of a particle k is the best in terms of fitness function, a position it has never met before, then Pbest is to be updated. 4 Determine the best particle (Gbest) among N particles. 5 Update the speed (vk) of each particle (k) according to the following rule:
vtþ1 ¼ w vtk þ c1 ut1 Pbest k
t k
Xkt þ c2 ut2 Gbest
t k
Xkt
(24)
where w is the inertia weight, c1 and c2 are two positive constants called cognitive and social parameter respectively, u1 and u2 are two uniform random variables on [0,1]. 6 Move the particles to their positions Xktþ1 such as:
Xktþ1 ¼ Xkt þ vtþ1 k 7 Go to second step until a criterion of end is verified.
(25) Fig. 3. PSO method flowchart.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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Fig. 4. Convergence of objective function: a) 1P level, b) 2P level, c) 3P levels.
Fig. 4 shows an example of the objective function convergence. For the initial number of individuals chosen higher than 100, the objective function converges after 43 iterations for 1P, 4 iterations for 2P and 7 iterations for 3P. Also these curves reveal that the initial number of individuals has an impact on the convergence speed, but this is not a general rule as demonstrated by Bratton and Kennedy [33]. Calculations were performed on a personal computer i3 CPU 2 Gb RAM. The calculation time for 50 iterations for the three configurations is given in Table 1. For N ¼ 100, the computing time is less than 1 min and this can be considered in favor of this method. 4. Results and discussion To confirm the validity of the proposed model, the results are compared with three pressure levels and reheat steam cycle built around the GE PG9371FB. The main characteristics of this combined cycle are listed in Table 2. The comparison between the results of
Table 1 Computing time.
1P 2P 3P
N ¼ 50
N ¼ 100
N ¼ 200
N ¼ 300
21 s 23 s 33 s
39 s 54 s 48 s
58 s 91 s 89 s
77 s 125 s 110 s
the model and the real data is presented in Table 3. The latter shows that the calculated values are close to the real data and that the difference between them is acceptable. The light difference is due to some aspects not considered by the present model such as auxiliary equipment consumption. Fig. 5 gives, for several TOTs, the evolutions of the optimal values of pressure at inlet of HP (High pressure) turbine. As shown, the
Table 2 Main data of gas turbine PG9371FB [34]. Parameter (unit) Gas turbine Pressure ratio Turbine inlet temperature ( C) Exhaust gas mass flow rate (kg/s) Exhaust gas temperature ( C) Net output (MW) Steam cycle 1st level pressure (bar) 2nd level pressure (bar) 3rd level pressure (bar) 1st level steam mass flow rate (kg/s) 2nd level steam mass flow rate (kg/s) 3rd level steam mass flow rate (kg/s) Maximal steam cycle temperature ( C) Stack temperature ( C) Condenser pressure (bar) Net output (MW)
Value 18.5 1427 657.5 644 285.3 4.2 25.3 142.5 12.63 12.76 86.7 565 96 0.12 145.5
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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Table 3 Model validation. Parameter (unit)
Real data
Model results
Power (MW) 1st level mass flow rate (kg/s) 2nd level mass flow rate (kg/s) 3rd level mass flow rate (kg/s) Maximal steam cycle temperature ( C) Stack temperature ( C)
145.5 12.63 12.76 86.7 565 96
146.21 13.01 13.51 88.07 564.9 94.8
optimum of pressure at HP turbine inlet cannot reach the limit of 160 bar for given values of TOT: 580 C for 1P, 540 C for 2P and 500 C for 3P due to the fact that a low TOT value leads to a low superheated steam temperature and subsequently a low steam fraction that should remain above 0.88. Above these values of TOT the optimum inlet pressure at HP turbine reaches its limit and becomes constant due to imposed constraint. In fact, this value is reached because of reheat that allows obtaining higher steam fraction, but in contrary for HRSG without reheat such pressure values are not reached, and this leads to low steam fractions. Fig. 5 also shows that, for a given TOT value, adding a pressure level permits reaching higher optimal pressure at HP turbine inlet. This result is practically justified as follows: The maximal pressure of the cycle is constrained by the steam fraction in the last stages of LP (Low pressure) turbine which must be higher than 88%. For a given temperature at turbine inlet, the use of high pressures leads to low steam fractions at the expansion end. Consequently, one have recourse to reheat in order to increase the steam fraction (and the pressure at turbine inlet). Fig. 6 shows that the steam temperatures after reheat in case of 3P are higher than the ones obtained in cases of 2P and 1P, and this justifies the fact that for a given TOT, using 3P allows reaching higher pressures than in the cases of 2P and 1P. Unlike the boilers where a reheat can produce higher temperatures and therefore high pressures, in the case of HRSG the reheat of steam is constrained by TOT that leads to lower reheat temperatures (Fig. 6), and this is why the optimum pressures at inlet of HP steam turbine are relatively lower when using lower TOT values. Fig. 7 shows that the pinch point tends to its minimal value of 10K whatever the value of TOT which is in accordance with that given by Mohagheghi and Shayegan [11], who optimized several models of HRSG for TOT equal 550 C and showed that the pinch point takes the lowest value.
Fig. 5. Optimum pressure at inlet of HP turbine versus TOT.
Fig. 6. Steam temperature at exit of reheater.
Fig. 7. Optimum pinch point versus TOT.
Fig. 8. Optimum superheater effectiveness versus TOT.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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Fig. 9. Steam temperature at inlet HP turbine: a) HRSG 1P, b) HRSG 2P, c) HRSG 3P.
The superheater effectiveness keeps its maximum value, but marks a drop for TOT higher than 600 C due to constraint of maximal steam temperature of 580 C (Fig. 8). This result is argued by Fig. 9 which compares between the cases with and without imposed constraint on the maximal steam cycle temperature. For the three types of HRSG and values of TOT less or equal 600 C, the curves are practically the same, this means that the temperature at outlet of superheater is at its maximal value, and the superheater effectiveness takes its maximal value of 0.85. According to Fig. 9 when the constraint of maximal steam cycle temperature is ignored, the limit of 580 C is exceeded from TOT ¼ 600 C, and this is why above this temperature, the effectiveness must have a low value to keep the steam temperature of highest level under its required limit. Fig. 10 shows a comparison of obtained specific work for three HRSG configurations. As seen, for all TOT values, HRSG 3P leads to a higher value of specific work than HRSG 2P and 1P, respectively. Adding a pressure level is always interesting whatever the TOT values. These curves also reveal that the steam cycle is strongly influenced by TOT, and there is a considerable increase in the specific work with it. For TOT equal 600 C, which is representative of modern gas turbines, the addition of a pressure level (2P) seems to increase the specific work of about 17 kJ/kg, which represents a benefit of about 10% for the steam cycle. For the same temperature, a
third level of pressure (3P) adds about 8 kJ/kg which corresponds to a benefit of 4% in the steam cycle specific work, and in overall there is an increase of 25 kJ/kg which is equivalent to 14% and it is a significant percentage. For example, a CC in which the gas cycle
Fig. 10. Steam cycle specific work versus TOT.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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Fig. 11. Optimal total steam fractions versus TOT.
participates with 65% in the produced power, an increase of about 14% in the steam cycle corresponds to about 5% of specific work increase in the entire CC. If the gas cycle has a thermal efficiency of 36%, when TOT is equal to 600 C, the combined cycle with 1P may have an overall efficiency of 55% and subsequently an increase of 25 kJ/kg in steam cycle specific work corresponds to a 3% of improvement in the overall thermal efficiency reaching a value of 58%. The total optimal steam fractions produced by the three types of HRSG are given by Fig. 11. HRSG 3P allows to produce more steam as compared with HRSG 2Pand HRSG 1P, and this applies to all the values of TOT. This result supports the one presented by Fig. 10 which comes to the conclusion that the specific work achieved by 3P is higher than in 2P and 1P. For example, for TOT equal 600 C, the produced optimal total steam fractions are 13.3%, 14.8% and 16.4% for 1P, 2P and 3P respectively, but, an additional steam quantity usually leads to a higher HRSG size and this would consequently impact the economic aspect. Fig. 12 shows, for HRSG 2P and 3P, the repartition of steam fractions on their different pressure levels. For HP level, the steam fractions seem to be much higher than IP (Intermediate pressure) and LP levels, particularly when considering high TOT values. For instance, for 600 C, the fractions of the 1st and 2nd level represent
9
Fig. 13. Destroyed exergy rate of steam cycle.
about 1/8 and 1/7 respectively, in relation to the total fraction of 3P. For HRSG 2P and for the same TOT, the fraction of the 1st level represents about 1/5 in relation to the total fraction of 2P. The evolution of destroyed exergy with TOT is illustrated by Fig. 13. It is clear that for HRSG with the highest pressure level, the destroyed exergy is the lowest. For all TOT values, steam cycle with three pressure levels destroys less exergy as compared with 2P and 1P. Steam cycle with one pressure level destroys more exergy namely for low TOT, where for example for values less than 450 C it destroys more than 40% of the exergy supplied at the HRSG. Also, this figure shows that the destroyed exergy rate decreases when TOT is increased. To summarize, the pinch point tends to the lowest possible value and the superheater effectiveness tends to the highest possible value, but they are limited by the heat exchange area. This result has already been shown by other studies considering a single TOT value. However, the present study has shown that for TOT higher than 600 C, superheater effectiveness is also constrained by the maximal steam cycle temperature. Adding another pressure level allows achieving higher pressure, producing more steam quantities, destroying less exergy and finally producing more specific work.
Fig. 12. Steam fractions of different levels: a) HRSG 2P, b) HRSG 3P.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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M. Nadir, A. Ghenaiet / Energy xxx (2015) 1e11
5. Conclusion A thermodynamic optimization has been undertaken for different HRSG configuration 1P, 2P and 3P with reheat, considering several values of exhaust gas temperature and several constraints that represent the state of art of combined cycles. The results show that adding another level of pressure leads to improving the steam cycle performance independently of TOT. Concerning the optimization method, PSO algorithm was used successfully in HRSG optimization, moreover, this method is easy to implement comparing with the other methods. Concerning the design parameters, the following conclusions can also be drawn: Adding a pressure level, allows reaching higher optimal pressures and producing higher steam fractions for all considered TOTs. Steam fractions at LP and IP levels are lower than those of HP level. Optimal superheater effectiveness tends to a maximum, but it is constrained by the limit of temperature. Pinch point tends to its lowest value, but it is constrained by the exchange area. References [1] Franco A, Casarosa C. On some perspectives for increasing the efficiency of combined cycle power plants. Appl Therm Eng 2002;22:1501e18. [2] Khaliq A, Kaushik SC. Second-law based thermodynamic analysis of Brayton/Rankine combined power cycle with reheat. Appl Energy 2004;78: 179e97. [3] Sanjay Y, Singh Onkar, Prasad BN. Energy and exergy analysis of steam cooled reheat gasesteam combined cycle. Appl Therm Eng 2007;27: 2779e90. [4] Bassily AM. Modeling, numerical optimization, and irreversibility reduction of a dual-pressure reheat combined cycle. Energy 2005;81:127e51. [5] Bassily AM. Modeling, numerical optimization, and irreversibility reduction of a triple-pressure reheat combined cycle. Energy 2007;32:778e94. [6] Polyzakis AL, Koroneos C, Xydi G. Optimum gas turbine cycle for combined cycle power plant. Energy Convers Manag 2008;49:551e63. [7] Godoy E, Scenna NJ, Benz SJ. Families of optimal thermodynamic solutions for combined cycle gas turbine (CCGT) power plants. Appl Therm Eng 2010;30: 569e76. s M, Rapuan JL. Optimization of heat recovery steam generator for [8] Valde combined cycle power plants. Appl Therm Eng 2001;21:1149e59. [9] Franco A, Russo A. Combined cycle plant efficiency increase based on the optimization of the heat recovery steam generator operating parameters. Int J Therm Sci 2002;41:843e59. [10] Xiang W, Chen Y. Performance improvement of combined cycle power plant based on the optimization of the bottom cycle and heat recuperation. J Therm Sci 2007;16:84e9. [11] Mohagheghi M, Shayegan J. Thermodynamic optimization of design variables and heat exchangers layout in HRSGs for CCGT, using genetic algorithm. Appl Therm Eng 2009;29:290e9. [12] Bracco S, Siri S. Exergetic optimization of single level combined gas-steam power plants considering different objective functions. Energy 2010;35: 5365e73. s M, Duran MD, Rovira A. Thermoeconomic optimization of combined [13] Valde cycle gas turbine power plants using genetic algorithms. Appl Therm Eng 2003;23:2169e82. [14] Koch C, Cziesla F, Tsatsaronis G. Optimization of combined cycle power plants using evolutionary algorithms. Chem Eng Process 2007;46:1151e9. [15] Bassily AM. Analysis and cost optimization of the triple-pressure steam-reheat gas-reheat gas-recuperated combined power cycle. Int J Energy Res 2008;32: 116e34. [16] Kotowicz J, Bartela Q. The influence of economic parameters on the optimal values of the design variables of a combined cycle plant. Energy 2010;35: 911e9. [17] Ahmadi P, Dincer I. Thermodynamic analysis and thermoeconomic optimization of a dual pressure combined cycle power plant with a supplementary firing unit. Energy Convers Manag 2011;52:2296e308. nchez C, Mun ~ oz M, Valde s M, Dura n MD. Thermoeconomic opti[18] Rovira A, Sa mization of heat recovery steam generators of combined cycle gas turbine power plants considering off-design operation. Energy Convers Manag 2011;52:1840e9.
[19] Carapellucci R, Giordano L. A comparison between exergetic and economic criteria for optimizing the heat recovery steam generators of gas-steam power plants. Energy 2013;58:458e72. [20] Lu S. Dynamic modelling and simulation of power plant systems. Proc Institution Mech Eng J Power Energy Part A 1999;213:7e22. €hle J, Epple B, Kim H. Modeling and investigation [21] Alobaid F, Postler R, Stro start-up procedures of a combined cycle power plant. Appl Energy 2008;85: 1173e89. [22] Alobaid F, Karne K, Belz J, Epple B, Kim H. Numerical and experimental study of a heat recovery steam generator during start-up procedure. Energy 2014;64:1057e70. [23] Benato A, Stoppato A, Bracco S. Combined cycle power plants: a comparison between two different dynamic models to evaluate transient behaviour and residual life. Energy Convers Manag 2014;87:1269e80. guen H, Dumur D, Faille D, Davelaar F. Design of a combined cycle [24] Tica A, Gue power plant model for optimization. Appl Energy 2012;98:256e65. [25] Shirakawa M, Nakamoto M, Hosaka S. Dynamic simulation and optimization of start-up processes in combined cycle power plants. JSME Int J 2005;48: 122e8. [26] Wagner W, Kretzschmar HJ. International steam tables properties of water and steam based on the industrial formulation IAPWS-IF97. Springer; 2008. [27] Sonntag RE, Borgenakke C, VanWylen GJ. Fundamentals of thermodynamics. 5th ed., vol. 356e57. New York: John Wiley & Sons,Inc; 1998. [28] Chase DL, Kehoe PT. GE combined-cycle product line and performance. Report GER-3574g. Schenectady. NY: GE Power Systems; 2000. [29] Dick E, De Paepe M. Steam-injected gas-turbine: cycle analysis and feasibility of water recuperation. Eur J Mech Eng 1997;42(2):67e77. [30] Jury W, Searies DE. Process optimization of an integrated combined cycle e the impact & benefit of sequential combustion. In: Proceedings of international gas turbine and aeroengine congress and exhibition, Orlando, Crida, FL 2e5 June 1997. [31] Bhargava RK, Bianchi M, De Pascale A, Negri di Montenegro G, Peretto A. Gas turbine based power cycles e a state-of-the-art review. In: International conference on power engineering-2007; October 23e27, 2007 [Hangzhou, China]. [32] Eberhart R, Kennedy J. A new optimizer using particle swarm theory. MHS 95. In: Proceedings of the sixth international symposium on micro machine and human science; October 1995. p. 39e43. [33] Bratton D, Kennedy J. Defining a standard for particle swarm optimization. In: Proceedings of the 2007 IEEE swarm intelligence symposium (SIS); 2007. nchez D, Chacartegui R, Mun ~ oz JM, Mun ~ oz A, Sanchez T. Performance [34] Sa analysis of a heavy duty combined cycle power plant burning various syngas fuels. Int J Hydrogen Energy 2010;35:337e45.
Nomenclature cp: Specific heat capacity [kJ/kg K] E: Effectiveness of exchanger Ex: Exergy [kJ] ex: Specific exergy [kJ/kg] f: Fitness function Gbest: Global best solution h: Steam or water specific enthalpy [kJ/kg] N: Number of particles in population Pbest: Best solution for each particle Q: Heat supplied [kJ/kg] T: Temperature [K] p: Pressure [bar] Pop: Population V: speed of particle vector W: Inertia weight W: Specific work [kJ/kg] x: Vapor fraction at turbine exit X: Optimization variables vector DTP: Pinch point [K] h: Efficiency u: Steam to gas ratio Subscripts d: Destroyed dr: Destroyed rate e: Exit EC: Economizer EV: Evaporator g: Gas HP: High pressure i: Inlet j: Thermal exchange frontier with the outside environment
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M. Nadir, A. Ghenaiet / Energy xxx (2015) 1e11 IP: Intermediate pressure K: Particle LP: Low pressure max: Maximal N: Net RH: Reheater S: Steam SC: Steam cycle SH: Superheater T: Iteration or generation th: Thermal 1P: First level 2P: Second level 3P: Third level
11
0: reference environment condition 1e11: Gas station at different heat exchangers Abbreviations CC: Combined cycle GT: Gas turbine HRSG: Heat recovery steam generator IAPWS: International Association for the Properties of Water and Steam TOT: Turbine outlet temperature 1P: Reheat one pressure level HSRG 2P: Reheat two pressures level HSRG 3P: Reheat three pressures level HSRG
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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Energy journal homepage: www.elsevier.com/locate/energy
Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures Mahmoud Nadir a, *, Adel Ghenaiet b a
Laboratory of Energetic Mechanics and Engineering (LEMI), Faculty of Engineering, University of Boumerdes, Independence Avenue, Boumerdes, 35000, Algeria Faculty of Mechanical and Process Engineering, University of Sciences and Technologies Houari Boumediene, BP 32 EL e Alia, Bab Ezzouar, 16111, Algiers, Algeria b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 24 October 2014 Received in revised form 20 February 2015 Accepted 21 April 2015 Available online xxx
Design optimization of a (heat recovery steam generator) HRSG is essential due to its direct impact on large power generation combined cycles. This study is aimed at giving a thermodynamic comparison between the optimums of three configurations of HRSG operating at exhaust gas temperature (TOT) from 350 C to 650 C. The optimization results, using PSO (Particle Swarm Optimization) method, show that adding another pressure level allows achieving a higher pressure at the inlet of high pressure turbine, producing more steam quantities, destroying less exergy and finally producing more specific work independently of TOT. For a given value of 600 C representative of TOT of recent gas turbines, an addition of a pressure level is shown to increase the specific work of about 17 kJ/kg, representing a benefit of about 10% for the steam cycle, whereas a third pressure level results in 8 kJ/kg increase in the specific work, corresponding to 4% in the steam cycle. © 2015 Elsevier Ltd. All rights reserved.
Keywords: HRSG (heat recovery steam generator) Exhaust gas temperature Combined cycle performance Optimization PSO (Particle Swarm Optimization) technique
1. Introduction Among improvements made to reduce the fuel consumption and the greenhouse gas emissions of the (gas turbines) GT, especially CO2, the introduction of the (combined cycle) CC as a favorite facility for electricity generation, reaching a thermal efficiency of 60%. The bottoming steam cycle provides about 30e40 % of the overall generated power, and any improvement could mainly be done through optimizing HRSG (heat recovery steam generator). In this context several studies were done, such as the one of Franco and Casarosa [1] who investigated the possibility of increasing efficiency of CC for 60% and compared between HRSG
* Corresponding author. E-mail addresses: [email protected] (M. Nadir), ag1964@yahoo. com (A. Ghenaiet).
with one, two and three pressure levels with and without reheat, considering three values of TOT (Turbine Outlet Temperature); 700 K, 773 K and 823 K. Khaliq and Kaushik [2] focused their work to show the importance of GT reheat in improving the CC global performance, especially the specific work. Also, Sanjay et al. [3] studied the effect of reheated expansion when turbine blades are cooled by a steam fraction extracted from HRSG. They showed that with three pressure levels and steam reheat the thermal efficiency may reach 62%. Bassily [4,5] optimized the whole CC in which the steam cycle is reheated at two and three pressure levels, resulting in an efficiency enhancement of 1.9e2.1 % compared to the design case. Polyzakis et al. [6] optimized and compared between the simple, intercooled, reheated and intercooled-reheated GT when coupled to a simple steam cycle, and concluded that the reheat is the most suitable solution. Godoy et al. [7] optimized CC simple steam cycle by maximizing its exergetic efficiency for a wide range of power with the determination of HRSG optimal surface.
http://dx.doi.org/10.1016/j.energy.2015.04.023 0360-5442/© 2015 Elsevier Ltd. All rights reserved.
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M. Nadir, A. Ghenaiet / Energy xxx (2015) 1e11
Many other studies focused on the optimization of steam s and Rapuan [8] who cycle alone such as the study of Valde optimized a single pressure level HRSG for TOT equal 545 C. Franco and Russo [9] optimized two and three pressure levels HRSG intended to operate with two types of GT, and demonstrated that it is possible to reach an overall efficiency of 60% by optimizing the steam cycle. Xiang and Chen [10] optimized both at base and part load a reheat three pressure levels HRSG built around GE (General Electric) PG9351FA GT and suggested to use a partial recovery of exhaust gas energy for a temperature exceeding 590 C. Mohagheghi and Shayegan [11] optimized four types of HRSG of one, two and three pressure levels with a reheat for TOT equal 550 C. They showed that addition of a pressure level always leads to improving steam cycle performance. Bracco and Siri [12] optimized a single pressure level HRSG adapted with four GT present on the market, considering several objective functions, and outlined the influence of TOT and mass flow rate on the steam cycle performance. The previous studies have only addressed the thermodynamic optimization, but the maximization of performance may lead to a higher cost of electricity [13,14], and this is why many other authors have considered the economical aspect. Bassily [15] optimized an objective function of net additional revenue for a triple pressure level reheat HRSG adapted to a reheated GT with exhaust gas recuperation. The optimization resulted in an annual saving of 33.7 million US Dollars for a 481 MW power plant. Kotowicz and Bartela [16] analyzed the influence of fuel price variation on the optimal values of design variables of the steam part of a combined cycle. They found that an increase in fuel price required higher optimum pressure in the high and intermediate pressure part, a decrease in the optimum value of pinch point and an increase in the optimum value of steam temperature of the intermediate pressure part. Ahmadi and Dincer [17] studied the effect of fuel cost on optimal design variables of CC and concluded that by increasing fuel price, the values of decision variables in the thermoeconomically optimal design tend to those of the thermodynamically optimal design. Rovira et al. [18] considered the frequent off-design operation of CC and developed a thermoeconomic optimization model in order to minimize the electricity cost. Carapellucci and Giordano [19] undertook a thermoeconomic optimization of several types of HRSG adapted to three types of GT and investigated the effect of fuel price and capacity factor on the electricity cost. The dynamic regime is another important aspect of CC study; it aims at improving the start up, shut down and shifting from one load to another. Many authors took interest in this aspect; Lu [20] has presented a brief review of simulation techniques of CC static and dynamic operation. Alobaid et al. [21,22] have modeled and validated the start up procedure of combined cycle and HRSG with measured data. Benato et al. [23] have proposed a complete procedure of the dynamic behavior and estimated the residual life production of some components. In order to optimize the start up process, some studies [24,25] have combined the dynamic modeling with non linear optimization methods. A synthesis of this review shows that most of previous studies addressed the optimization of one or several HRSG types intended to work with a specific gas turbine (consequently a well defined TOT) and no study optimizes several HRSG configurations for a wide range of TOT. Thus, this paper presents, for a TOT range of 350e650 C, a thermodynamic optimization of three HRSG configurations namely: HRSG with one pressure level with reheat (First level) 1P, two pressure levels with reheat (Second level) 2P and three pressure levels with reheat (Third level) 3P. Concerning the optimization method, one of the most recent methods, which is the PSO (Particle Swarm Optimization) is used in this study.
2. Thermodynamic analysis The diagrams of the three HRSG configurations are shown in Fig. 1, they are of a natural circulation type. The diagrams of temperature-transferred heat corresponding to those of Fig. 1 are given by Fig. 2. For an easy presentation, only the modeling of HRSG with three pressure levels and a reheat is shown. The work produced by the steam cycle per a unit mass of exhaust gas is written as follows:
WSC ¼ ðu1 þ u2 þ u3 ÞWLP þ ðu2 þ u3 ÞWIP þ u3 WHP
(1)
u1, u2 and u3 represent the fractions of steam for the first, second and third pressure level. In general terms, the steady state exergy balance applied for a given control volume is written as follows: X j
! X X T0 mi exi me exe Exd ¼ 0 1 Qj W þ Tj e i
(2)
For 1 kg of exhaust gas, by considering a control volume corresponding to the whole steam cycle and by neglecting the exergy of heat transfer, equation (2) becomes:
Wsc þ ex1 ex11 exd ¼ 0
(3)
The destroyed exergy can be deduced:
exd ¼ Wsc þ ex1 ex11
(4)
It is possible to define the destroyed exergy rate as follows:
exdr ¼
exd exn
(5)
exn represents the net exergy carried into the control volume:
exn ¼ ex1 ex11
(6)
For the third pressure level, the energy balance of evaporator, reheater and superheater, leads to the following:
u3 ðhe
SH 3P
hi
EV 3P Þ
þ u3 ðhe
RH
hi
RH Þ
¼ cp1 TOT cp4 Tg4 (7)
From the energy balance of superheater:
u3 ðhe
SH 3P
he
EV 3P Þ
¼ cp1 TOT cp2 Tg2
(8)
The effectiveness of superheater and reheater is defined by:
ESH
3P
ERH ¼
¼
Tse SH 3P Tse TOT Tse EV
EV 3P
(9)
3P
Tse RH Tsi RH Tg2 Tsi RH
(10)
The definition of pinch point:
Tg4 ¼ Tsi
EV 3P
þ DTP3P
(11)
The temperature of gas leaving the economizer of third level (Tg5) is obtained from energy balance:
u3 ðhe
EC 3P
hi
EC 3P Þ
¼ cp4 Tg4 cp5 Tg5
(12)
Equations 7e12 represent a system of 6 equations with 6 unknowns which are: u3,Tse SH 3P,Tse RH,Tg2,Tg4 and Tg5, which are solved by using a numerical method.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
M. Nadir, A. Ghenaiet / Energy xxx (2015) 1e11
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Fig. 1. Diagrams of HRSGs configurations: a) HRSG 1P, b) HRSG 2P, c) HRSG 3P.
The properties of water and steam are based on relations of the (International Association of the Properties of Water and Steam) IAPWS [26]. For the second pressure level, by knowing the steam temperature at evaporator exit (Tse EV 2P), the steam temperature at superheater exit is obtained from the definition of effectiveness:
ESH
2P
¼
Tse
Tse Tg5 Tse EV SH 2P
ESH EV 2P
EV 2P
2P
þ DTP2P
(14)
It is now possible to determine the fraction of steam of the second pressure level from energy balance across both evaporator and superheater:
u2 ðhe
SH 2P
hi
EV 2P Þ
¼ cp5 Tg5 cp7 Tg7
(15)
The gas temperature at the outlet of economizer (Tg8) is obtained from:
ðu3 þ u2 Þðhe
EC 2P
hi
EC 2P Þ
1P
¼
Tse
(13)
The gas temperature at exit of second level evaporator (Tg7) is obtained from relation (14):
Tg7 ¼ Tsi
For the first pressure level, similar relations as for second level still apply. By knowing the evaporator exit steam temperature, the exit temperature of superheater is obtained from the definition of effectiveness:
¼ cp7 Tg7 cp8 Tg8
(16)
SH 1P Tse Tg8 Tse EV
EV 1P
(17)
1P
The gas temperature at the exit of first level evaporator (Tg10) is obtained from the definition of pinch point:
Tg10 ¼ Tsi
EV 1P
þ DTP1P
(18)
The steam fraction of the first pressure level is determined from energy balance across both evaporator and superheater:
u1 ðhe
SH 1P
hi
EV 1P Þ
¼ cp8 Tg8 cp10 Tg10
(19)
The stack exit temperature (Tg11) is obtained from economizer energy balance:
ðu3 þ u2 þ u1 Þðhe
EC 1P
hi
EC 1P Þ
¼ cp10 Tg10 cp11 Tg11
(20)
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Fig. 2. The temperature-transferred heat diagram: a) HRSG 1P, b) HRSG 2P, c) HRSG 3P.
Once the temperatures of heat exchangers and steam fractions are determined, it is possible to calculate the specific work of steam cycle and the destroyed exergy rate. The performances of CC in terms of specific work, energetic and exegetic efficiency are calculated as follows:
WCC ¼ WGT þ WSC
(21)
hth
CC
¼
WGT þ WSC QGT
(22)
hex
CC
¼
WGT þ WSC ExGT
(23)
3. Optimization This study addresses a global non-linear problem of optimization with constraints, thus, the following illustrates its mathematical formulation and the algorithm of the used PSO method. A problem of optimization is mainly constituted of an objective function, optimization variables and constraints. 3.1. Objective function and optimization variables For a given GT, the values of TOT and specific work are fixed, and hence the optimization of CC only requires the steam cycle specific work per unit mass of exhaust gas to be maximized.
This specific work is considered as the objective function and the fitness function f(X). The vector X(p1,p2,p3,ESH 1P,ESH 2P,ESH 3P, ERH,DTPin 1P,DTPin 2P,DTPin 3P) represents the optimization variables characterizing the HRSG. The optimization results are: the steam fraction at each level (i.e u1, u2 and u3), steam exit temperatures from superheaters and reheater (Tse SH 1P, Tse SH 2P, Tse SH 3P and Tse RH), gas temperatures at heat exchangers inlet and outlet (Tg2,Tg4,Tg5,Tg7,Tg8,Tg10 and Tg11) and the specific work produced by the three vapor turbines (WLP, WIP, WHP). 3.2. Constraints analysis In order to avoid mechanical degradation and deterioration of the aerodynamic performances of the last stages of steam turbine, the steam fraction should be higher than 88% [27]. To maintain a good operation of HRSG and turbine material, the steam pressure and temperature at HRSG exit should not exceed 160 bar and 580 C, respectively [28]. The condensed water in exhaust gas could form a corrosive sulfuric-acid, so the stack temperature should be higher than 80 C to avoid water condensation [29]. In practice, for the pinch point, as it is well known, a null value leads to an infinite surface of economizer then a limit value of 10K is imposed [30]. An effectiveness superheater close to “1” leads to an infinite surface, a maximum value of 0.85 is fixed [31]. To summarize, the optimization problem can be denoted mathematically as follows:
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8 Maximize f ðXÞ with f ðXÞ ¼ Wsc ðXÞ > > > > X ¼ ðp1 ; p2 ; p3 ; ESH 1P ; ESH 2P ; ESH 3P ; ERH ; DTP1P ; DTP2P ; DTP3P Þ > > > > under the following constraints : > > > > x 0:88 0 > > < Tse SH 1P 853K 0; Tse SH 2P 853K 0 and Tse SH 3P 853K 0 Ts > e RH 853K 0 > > > > Tg11 353K 0 > > > > > DTP1P 10K 0; DTP2P 10K 0 and DTP3P 10K 0 > > > 0:85 0; ESH 2P 0:85 0; ESH 3P 0:85 0 and ERH 0:85 0 E > : SH 1P p3 160bar 0
3.3. PSO algorithm The method of PSO as proposed by Eberhart and Kennedy [32] is inspired from the ability of groups of some species of animals to work as a whole, e.g. birds flocking to a food source. This seeking behavior was associated with that of an optimization search for solutions to non-linear equations in a real-valued search space [33]. PSO algorithm starts with a population of solutions (taken randomly) and looks for an optimum for the problem, making population individuals evolve over generations. In contrast to genetic algorithms in which solutions are coded in chromosomes, PSO population directly represents the solutions, and the research for the best solutions is done by moving these individuals in solutions space, benefitting collectively from the optima detected individually by each particle. Thus, each particle, over generations, adjusts its path towards its own previous best position (Pbest), and towards the best previous best position obtained by any member of its group (Gbest). The performance of each particle is evaluated using the fitness function. The flowchart describing the algorithm is given by Fig. 3 which can be summarized as follows: 1 Create a population “Pop” of N particles uniformly spread across the search space. 2 Each particle k is evaluated using the fitness function “f”. Particles that do not obey the imposed constraints are excluded from the group and randomly replaced by others. 3 If a position Xk of a particle k is the best in terms of fitness function, a position it has never met before, then Pbest is to be updated. 4 Determine the best particle (Gbest) among N particles. 5 Update the speed (vk) of each particle (k) according to the following rule:
vtþ1 ¼ w vtk þ c1 ut1 Pbest k
t k
Xkt þ c2 ut2 Gbest
t k
Xkt
(24)
where w is the inertia weight, c1 and c2 are two positive constants called cognitive and social parameter respectively, u1 and u2 are two uniform random variables on [0,1]. 6 Move the particles to their positions Xktþ1 such as:
Xktþ1 ¼ Xkt þ vtþ1 k 7 Go to second step until a criterion of end is verified.
(25) Fig. 3. PSO method flowchart.
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M. Nadir, A. Ghenaiet / Energy xxx (2015) 1e11
Fig. 4. Convergence of objective function: a) 1P level, b) 2P level, c) 3P levels.
Fig. 4 shows an example of the objective function convergence. For the initial number of individuals chosen higher than 100, the objective function converges after 43 iterations for 1P, 4 iterations for 2P and 7 iterations for 3P. Also these curves reveal that the initial number of individuals has an impact on the convergence speed, but this is not a general rule as demonstrated by Bratton and Kennedy [33]. Calculations were performed on a personal computer i3 CPU 2 Gb RAM. The calculation time for 50 iterations for the three configurations is given in Table 1. For N ¼ 100, the computing time is less than 1 min and this can be considered in favor of this method. 4. Results and discussion To confirm the validity of the proposed model, the results are compared with three pressure levels and reheat steam cycle built around the GE PG9371FB. The main characteristics of this combined cycle are listed in Table 2. The comparison between the results of
Table 1 Computing time.
1P 2P 3P
N ¼ 50
N ¼ 100
N ¼ 200
N ¼ 300
21 s 23 s 33 s
39 s 54 s 48 s
58 s 91 s 89 s
77 s 125 s 110 s
the model and the real data is presented in Table 3. The latter shows that the calculated values are close to the real data and that the difference between them is acceptable. The light difference is due to some aspects not considered by the present model such as auxiliary equipment consumption. Fig. 5 gives, for several TOTs, the evolutions of the optimal values of pressure at inlet of HP (High pressure) turbine. As shown, the
Table 2 Main data of gas turbine PG9371FB [34]. Parameter (unit) Gas turbine Pressure ratio Turbine inlet temperature ( C) Exhaust gas mass flow rate (kg/s) Exhaust gas temperature ( C) Net output (MW) Steam cycle 1st level pressure (bar) 2nd level pressure (bar) 3rd level pressure (bar) 1st level steam mass flow rate (kg/s) 2nd level steam mass flow rate (kg/s) 3rd level steam mass flow rate (kg/s) Maximal steam cycle temperature ( C) Stack temperature ( C) Condenser pressure (bar) Net output (MW)
Value 18.5 1427 657.5 644 285.3 4.2 25.3 142.5 12.63 12.76 86.7 565 96 0.12 145.5
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Table 3 Model validation. Parameter (unit)
Real data
Model results
Power (MW) 1st level mass flow rate (kg/s) 2nd level mass flow rate (kg/s) 3rd level mass flow rate (kg/s) Maximal steam cycle temperature ( C) Stack temperature ( C)
145.5 12.63 12.76 86.7 565 96
146.21 13.01 13.51 88.07 564.9 94.8
optimum of pressure at HP turbine inlet cannot reach the limit of 160 bar for given values of TOT: 580 C for 1P, 540 C for 2P and 500 C for 3P due to the fact that a low TOT value leads to a low superheated steam temperature and subsequently a low steam fraction that should remain above 0.88. Above these values of TOT the optimum inlet pressure at HP turbine reaches its limit and becomes constant due to imposed constraint. In fact, this value is reached because of reheat that allows obtaining higher steam fraction, but in contrary for HRSG without reheat such pressure values are not reached, and this leads to low steam fractions. Fig. 5 also shows that, for a given TOT value, adding a pressure level permits reaching higher optimal pressure at HP turbine inlet. This result is practically justified as follows: The maximal pressure of the cycle is constrained by the steam fraction in the last stages of LP (Low pressure) turbine which must be higher than 88%. For a given temperature at turbine inlet, the use of high pressures leads to low steam fractions at the expansion end. Consequently, one have recourse to reheat in order to increase the steam fraction (and the pressure at turbine inlet). Fig. 6 shows that the steam temperatures after reheat in case of 3P are higher than the ones obtained in cases of 2P and 1P, and this justifies the fact that for a given TOT, using 3P allows reaching higher pressures than in the cases of 2P and 1P. Unlike the boilers where a reheat can produce higher temperatures and therefore high pressures, in the case of HRSG the reheat of steam is constrained by TOT that leads to lower reheat temperatures (Fig. 6), and this is why the optimum pressures at inlet of HP steam turbine are relatively lower when using lower TOT values. Fig. 7 shows that the pinch point tends to its minimal value of 10K whatever the value of TOT which is in accordance with that given by Mohagheghi and Shayegan [11], who optimized several models of HRSG for TOT equal 550 C and showed that the pinch point takes the lowest value.
Fig. 5. Optimum pressure at inlet of HP turbine versus TOT.
Fig. 6. Steam temperature at exit of reheater.
Fig. 7. Optimum pinch point versus TOT.
Fig. 8. Optimum superheater effectiveness versus TOT.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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Fig. 9. Steam temperature at inlet HP turbine: a) HRSG 1P, b) HRSG 2P, c) HRSG 3P.
The superheater effectiveness keeps its maximum value, but marks a drop for TOT higher than 600 C due to constraint of maximal steam temperature of 580 C (Fig. 8). This result is argued by Fig. 9 which compares between the cases with and without imposed constraint on the maximal steam cycle temperature. For the three types of HRSG and values of TOT less or equal 600 C, the curves are practically the same, this means that the temperature at outlet of superheater is at its maximal value, and the superheater effectiveness takes its maximal value of 0.85. According to Fig. 9 when the constraint of maximal steam cycle temperature is ignored, the limit of 580 C is exceeded from TOT ¼ 600 C, and this is why above this temperature, the effectiveness must have a low value to keep the steam temperature of highest level under its required limit. Fig. 10 shows a comparison of obtained specific work for three HRSG configurations. As seen, for all TOT values, HRSG 3P leads to a higher value of specific work than HRSG 2P and 1P, respectively. Adding a pressure level is always interesting whatever the TOT values. These curves also reveal that the steam cycle is strongly influenced by TOT, and there is a considerable increase in the specific work with it. For TOT equal 600 C, which is representative of modern gas turbines, the addition of a pressure level (2P) seems to increase the specific work of about 17 kJ/kg, which represents a benefit of about 10% for the steam cycle. For the same temperature, a
third level of pressure (3P) adds about 8 kJ/kg which corresponds to a benefit of 4% in the steam cycle specific work, and in overall there is an increase of 25 kJ/kg which is equivalent to 14% and it is a significant percentage. For example, a CC in which the gas cycle
Fig. 10. Steam cycle specific work versus TOT.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
M. Nadir, A. Ghenaiet / Energy xxx (2015) 1e11
Fig. 11. Optimal total steam fractions versus TOT.
participates with 65% in the produced power, an increase of about 14% in the steam cycle corresponds to about 5% of specific work increase in the entire CC. If the gas cycle has a thermal efficiency of 36%, when TOT is equal to 600 C, the combined cycle with 1P may have an overall efficiency of 55% and subsequently an increase of 25 kJ/kg in steam cycle specific work corresponds to a 3% of improvement in the overall thermal efficiency reaching a value of 58%. The total optimal steam fractions produced by the three types of HRSG are given by Fig. 11. HRSG 3P allows to produce more steam as compared with HRSG 2Pand HRSG 1P, and this applies to all the values of TOT. This result supports the one presented by Fig. 10 which comes to the conclusion that the specific work achieved by 3P is higher than in 2P and 1P. For example, for TOT equal 600 C, the produced optimal total steam fractions are 13.3%, 14.8% and 16.4% for 1P, 2P and 3P respectively, but, an additional steam quantity usually leads to a higher HRSG size and this would consequently impact the economic aspect. Fig. 12 shows, for HRSG 2P and 3P, the repartition of steam fractions on their different pressure levels. For HP level, the steam fractions seem to be much higher than IP (Intermediate pressure) and LP levels, particularly when considering high TOT values. For instance, for 600 C, the fractions of the 1st and 2nd level represent
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Fig. 13. Destroyed exergy rate of steam cycle.
about 1/8 and 1/7 respectively, in relation to the total fraction of 3P. For HRSG 2P and for the same TOT, the fraction of the 1st level represents about 1/5 in relation to the total fraction of 2P. The evolution of destroyed exergy with TOT is illustrated by Fig. 13. It is clear that for HRSG with the highest pressure level, the destroyed exergy is the lowest. For all TOT values, steam cycle with three pressure levels destroys less exergy as compared with 2P and 1P. Steam cycle with one pressure level destroys more exergy namely for low TOT, where for example for values less than 450 C it destroys more than 40% of the exergy supplied at the HRSG. Also, this figure shows that the destroyed exergy rate decreases when TOT is increased. To summarize, the pinch point tends to the lowest possible value and the superheater effectiveness tends to the highest possible value, but they are limited by the heat exchange area. This result has already been shown by other studies considering a single TOT value. However, the present study has shown that for TOT higher than 600 C, superheater effectiveness is also constrained by the maximal steam cycle temperature. Adding another pressure level allows achieving higher pressure, producing more steam quantities, destroying less exergy and finally producing more specific work.
Fig. 12. Steam fractions of different levels: a) HRSG 2P, b) HRSG 3P.
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
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5. Conclusion A thermodynamic optimization has been undertaken for different HRSG configuration 1P, 2P and 3P with reheat, considering several values of exhaust gas temperature and several constraints that represent the state of art of combined cycles. The results show that adding another level of pressure leads to improving the steam cycle performance independently of TOT. Concerning the optimization method, PSO algorithm was used successfully in HRSG optimization, moreover, this method is easy to implement comparing with the other methods. Concerning the design parameters, the following conclusions can also be drawn: Adding a pressure level, allows reaching higher optimal pressures and producing higher steam fractions for all considered TOTs. Steam fractions at LP and IP levels are lower than those of HP level. Optimal superheater effectiveness tends to a maximum, but it is constrained by the limit of temperature. Pinch point tends to its lowest value, but it is constrained by the exchange area. References [1] Franco A, Casarosa C. On some perspectives for increasing the efficiency of combined cycle power plants. Appl Therm Eng 2002;22:1501e18. [2] Khaliq A, Kaushik SC. Second-law based thermodynamic analysis of Brayton/Rankine combined power cycle with reheat. Appl Energy 2004;78: 179e97. [3] Sanjay Y, Singh Onkar, Prasad BN. Energy and exergy analysis of steam cooled reheat gasesteam combined cycle. Appl Therm Eng 2007;27: 2779e90. [4] Bassily AM. Modeling, numerical optimization, and irreversibility reduction of a dual-pressure reheat combined cycle. Energy 2005;81:127e51. [5] Bassily AM. Modeling, numerical optimization, and irreversibility reduction of a triple-pressure reheat combined cycle. Energy 2007;32:778e94. [6] Polyzakis AL, Koroneos C, Xydi G. Optimum gas turbine cycle for combined cycle power plant. Energy Convers Manag 2008;49:551e63. [7] Godoy E, Scenna NJ, Benz SJ. Families of optimal thermodynamic solutions for combined cycle gas turbine (CCGT) power plants. Appl Therm Eng 2010;30: 569e76. s M, Rapuan JL. Optimization of heat recovery steam generator for [8] Valde combined cycle power plants. Appl Therm Eng 2001;21:1149e59. [9] Franco A, Russo A. Combined cycle plant efficiency increase based on the optimization of the heat recovery steam generator operating parameters. Int J Therm Sci 2002;41:843e59. [10] Xiang W, Chen Y. Performance improvement of combined cycle power plant based on the optimization of the bottom cycle and heat recuperation. J Therm Sci 2007;16:84e9. [11] Mohagheghi M, Shayegan J. Thermodynamic optimization of design variables and heat exchangers layout in HRSGs for CCGT, using genetic algorithm. Appl Therm Eng 2009;29:290e9. [12] Bracco S, Siri S. Exergetic optimization of single level combined gas-steam power plants considering different objective functions. Energy 2010;35: 5365e73. s M, Duran MD, Rovira A. Thermoeconomic optimization of combined [13] Valde cycle gas turbine power plants using genetic algorithms. Appl Therm Eng 2003;23:2169e82. [14] Koch C, Cziesla F, Tsatsaronis G. Optimization of combined cycle power plants using evolutionary algorithms. Chem Eng Process 2007;46:1151e9. [15] Bassily AM. Analysis and cost optimization of the triple-pressure steam-reheat gas-reheat gas-recuperated combined power cycle. Int J Energy Res 2008;32: 116e34. [16] Kotowicz J, Bartela Q. The influence of economic parameters on the optimal values of the design variables of a combined cycle plant. Energy 2010;35: 911e9. [17] Ahmadi P, Dincer I. Thermodynamic analysis and thermoeconomic optimization of a dual pressure combined cycle power plant with a supplementary firing unit. Energy Convers Manag 2011;52:2296e308. nchez C, Mun ~ oz M, Valde s M, Dura n MD. Thermoeconomic opti[18] Rovira A, Sa mization of heat recovery steam generators of combined cycle gas turbine power plants considering off-design operation. Energy Convers Manag 2011;52:1840e9.
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Nomenclature cp: Specific heat capacity [kJ/kg K] E: Effectiveness of exchanger Ex: Exergy [kJ] ex: Specific exergy [kJ/kg] f: Fitness function Gbest: Global best solution h: Steam or water specific enthalpy [kJ/kg] N: Number of particles in population Pbest: Best solution for each particle Q: Heat supplied [kJ/kg] T: Temperature [K] p: Pressure [bar] Pop: Population V: speed of particle vector W: Inertia weight W: Specific work [kJ/kg] x: Vapor fraction at turbine exit X: Optimization variables vector DTP: Pinch point [K] h: Efficiency u: Steam to gas ratio Subscripts d: Destroyed dr: Destroyed rate e: Exit EC: Economizer EV: Evaporator g: Gas HP: High pressure i: Inlet j: Thermal exchange frontier with the outside environment
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023
M. Nadir, A. Ghenaiet / Energy xxx (2015) 1e11 IP: Intermediate pressure K: Particle LP: Low pressure max: Maximal N: Net RH: Reheater S: Steam SC: Steam cycle SH: Superheater T: Iteration or generation th: Thermal 1P: First level 2P: Second level 3P: Third level
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0: reference environment condition 1e11: Gas station at different heat exchangers Abbreviations CC: Combined cycle GT: Gas turbine HRSG: Heat recovery steam generator IAPWS: International Association for the Properties of Water and Steam TOT: Turbine outlet temperature 1P: Reheat one pressure level HSRG 2P: Reheat two pressures level HSRG 3P: Reheat three pressures level HSRG
Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSG configurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023