thermodynamic optimization of several (heat recovery...

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Energy xxx (2015) 1e11

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Energy

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Thermodynamic optimization of several (heat recovery steamgenerator) HRSG configurations for a range of exhaust gastemperatures

Mahmoud Nadir a, *, Adel Ghenaiet b

a Laboratory of Energetic Mechanics and Engineering (LEMI), Faculty of Engineering, University of Boumerdes, Independence Avenue, Boumerdes, 35000,Algeriab Faculty of Mechanical and Process Engineering, University of Sciences and Technologies Houari Boumediene, BP 32 EL e Alia, Bab Ezzouar, 16111, Algiers,Algeria

a r t i c l e i n f o

Article history:Received 24 October 2014Received in revised form20 February 2015Accepted 21 April 2015Available online xxx

Keywords:HRSG (heat recovery steam generator)Exhaust gas temperatureCombined cycle performanceOptimizationPSO (Particle Swarm Optimization)technique

* Corresponding author.E-mail addresses: [email protected]

com (A. Ghenaiet).

http://dx.doi.org/10.1016/j.energy.2015.04.0230360-5442/© 2015 Elsevier Ltd. All rights reserved.

Please cite this article in press as: Nadir Mconfigurations for a range of exhaust gas te

a b s t r a c t

Design optimization of a (heat recovery steam generator) HRSG is essential due to its direct impact onlarge power generation combined cycles. This study is aimed at giving a thermodynamic comparisonbetween the optimums of three configurations of HRSG operating at exhaust gas temperature (TOT) from350 �C to 650 �C. The optimization results, using PSO (Particle Swarm Optimization) method, show thatadding 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 workindependently of TOT. For a given value of 600 �C representative of TOT of recent gas turbines, anaddition of a pressure level is shown to increase the specific work of about 17 kJ/kg, representing abenefit of about 10% for the steam cycle, whereas a third pressure level results in 8 kJ/kg increase in thespecific work, corresponding to 4% in the steam cycle.

© 2015 Elsevier Ltd. All rights reserved.

1. Introduction

Among improvements made to reduce the fuel consumptionand the greenhouse gas emissions of the (gas turbines) GT, espe-cially CO2, the introduction of the (combined cycle) CC as a favoritefacility for electricity generation, reaching a thermal efficiency of60%. The bottoming steam cycle provides about 30e40 % of theoverall generated power, and any improvement could mainly bedone through optimizing HRSG (heat recovery steam generator).In this context several studies were done, such as the one ofFranco and Casarosa [1] who investigated the possibility ofincreasing efficiency of CC for 60% and compared between HRSG

(M. Nadir), ag1964@yahoo.

, Ghenaiet A, Thermodynammperatures, Energy (2015), h

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 workto show the importance of GT reheat in improving the CC globalperformance, especially the specific work. Also, Sanjay et al. [3]studied the effect of reheated expansion when turbine bladesare cooled by a steam fraction extracted from HRSG. They showedthat with three pressure levels and steam reheat the thermal ef-ficiency may reach 62%. Bassily [4,5] optimized the whole CC inwhich the steam cycle is reheated at two and three pressure levels,resulting in an efficiency enhancement of 1.9e2.1 % compared tothe design case. Polyzakis et al. [6] optimized and compared be-tween the simple, intercooled, reheated and intercooled-reheatedGT when coupled to a simple steam cycle, and concluded that thereheat is the most suitable solution. Godoy et al. [7] optimized CCsimple steam cycle by maximizing its exergetic efficiency for awide range of power with the determination of HRSG optimalsurface.

ic optimization of several (heat recovery steam generator) HRSGttp://dx.doi.org/10.1016/j.energy.2015.04.023

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Delta:1_surname

mailto:[email protected]



www.sciencedirect.com/science/journal/03605442

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http://dx.doi.org/10.1016/j.energy.2015.04.023



M. Nadir, A. Ghenaiet / Energy xxx (2015) 1e112

Many other studies focused on the optimization of steamcycle alone such as the study of Vald�es and Rapuan [8] whooptimized a single pressure level HRSG for TOT equal 545 �C.Franco and Russo [9] optimized two and three pressure levelsHRSG intended to operate with two types of GT, and demon-strated that it is possible to reach an overall efficiency of 60% byoptimizing the steam cycle. Xiang and Chen [10] optimized bothat base and part load a reheat three pressure levels HRSG builtaround GE (General Electric) PG9351FA GT and suggested to use apartial recovery of exhaust gas energy for a temperatureexceeding 590 �C. Mohagheghi and Shayegan [11] optimized fourtypes of HRSG of one, two and three pressure levels with a reheatfor TOT equal 550 �C. They showed that addition of a pressurelevel always leads to improving steam cycle performance. Braccoand Siri [12] optimized a single pressure level HRSG adaptedwith four GT present on the market, considering several objectivefunctions, and outlined the influence of TOT and mass flow rateon the steam cycle performance.

The previous studies have only addressed the thermodynamicoptimization, but the maximization of performance may lead to ahigher cost of electricity [13,14], and this is why many other au-thors have considered the economical aspect. Bassily [15] opti-mized an objective function of net additional revenue for a triplepressure level reheat HRSG adapted to a reheated GT with exhaustgas recuperation. The optimization resulted in an annual saving of33.7 million US Dollars for a 481 MW power plant. Kotowicz andBartela [16] analyzed the influence of fuel price variation on theoptimal values of design variables of the steam part of a combinedcycle. They found that an increase in fuel price required higheroptimum pressure in the high and intermediate pressure part, adecrease in the optimum value of pinch point and an increase inthe optimum value of steam temperature of the intermediatepressure part. Ahmadi and Dincer [17] studied the effect of fuelcost on optimal design variables of CC and concluded that byincreasing fuel price, the values of decision variables in the ther-moeconomically optimal design tend to those of the thermody-namically optimal design. Rovira et al. [18] considered thefrequent off-design operation of CC and developed a thermoeco-nomic optimization model in order to minimize the electricitycost. Carapellucci and Giordano [19] undertook a thermoeconomicoptimization of several types of HRSG adapted to three types of GTand investigated the effect of fuel price and capacity factor on theelectricity cost.

The dynamic regime is another important aspect of CC study; itaims at improving the start up, shut down and shifting from oneload to another. Many authors took interest in this aspect; Lu [20]has presented a brief review of simulation techniques of CC staticand dynamic operation. Alobaid et al. [21,22] have modeled andvalidated the start up procedure of combined cycle and HRSG withmeasured data. Benato et al. [23] have proposed a complete pro-cedure of the dynamic behavior and estimated the residual lifeproduction of some components. In order to optimize the start upprocess, some studies [24,25] have combined the dynamicmodeling with non linear optimization methods.

A synthesis of this review shows that most of previous studiesaddressed the optimization of one or several HRSG types intendedto work with a specific gas turbine (consequently a well definedTOT) and no study optimizes several HRSG configurations for awide range of TOT. Thus, this paper presents, for a TOT range of350e650 �C, a thermodynamic optimization of three HRSG con-figurations namely: HRSGwith one pressure level with reheat (Firstlevel) 1P, two pressure levels with reheat (Second level) 2P andthree pressure levels with reheat (Third level) 3P. Concerning theoptimization method, one of the most recent methods, which is thePSO (Particle Swarm Optimization) is used in this study.

Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamconfigurations for a range of exhaust gas temperatures, Energy (2015), h

2. Thermodynamic analysis

The diagrams of the three HRSG configurations are shown inFig. 1, they are of a natural circulation type. The diagrams oftemperature-transferred heat corresponding to those of Fig. 1 aregiven by Fig. 2. For an easy presentation, only themodeling of HRSGwith three pressure levels and a reheat is shown.

The work produced by the steam cycle per a unit mass ofexhaust gas is written as follows:

WSC ¼ ðu1 þ u2 þ u3ÞWLP þ ðu2 þ u3ÞWIP þ u3WHP (1)

u1, u2 and u3 represent the fractions of steam for the first, sec-ond and third pressure level.

In general terms, the steady state exergy balance applied for agiven control volume is written as follows:

Xj

1� T0

Tj

!Qj �W þ

Xi

miexi �Xe

meexe � Exd ¼ 0 (2)

For 1 kg of exhaust gas, by considering a control volume cor-responding to the whole steam cycle and by neglecting the exergyof 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 ¼exdexn

(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:

u3ðhe SH 3P � hi EV 3PÞ þ u3ðhe RH � hi RHÞ ¼ cp1TOT � cp4Tg4(7)

From the energy balance of superheater:

u3ðhe SH 3P � he EV 3PÞ ¼ cp1TOT � cp2Tg2 (8)

The effectiveness of superheater and reheater is defined by:

ESH 3P ¼ Tse SH 3P � Tse EV 3P

TOT � Tse EV 3P(9)

ERH ¼ 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:

u3ðhe EC 3P � hi EC 3PÞ ¼ cp4 Tg4 � cp5Tg5 (12)

Equations 7e12 represent a system of 6 equations with 6 un-knowns which are: u3,Tse SH 3P,Tse RH,Tg2,Tg4 and Tg5, which aresolved by using a numerical method.


Fig. 1. Diagrams of HRSGs configurations: a) HRSG 1P, b) HRSG 2P, c) HRSG 3P.

M. Nadir, A. Ghenaiet / Energy xxx (2015) 1e11 3

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 tempera-ture at evaporator exit (Tse EV 2P), the steam temperature at super-heater exit is obtained from the definition of effectiveness:


Tg5 � Tse EV 2P(13)

The gas temperature at exit of second level evaporator (Tg7) isobtained from relation (14):


It is now possible to determine the fraction of steam of thesecond pressure level from energy balance across both evaporatorand superheater:

u2ðhe SH 2P � hi EV 2PÞ ¼ cp5Tg5 � cp7Tg7 (15)

The gas temperature at the outlet of economizer (Tg8) is ob-tained from:

ðu3 þ u2Þðhe EC 2P � hi EC 2PÞ ¼ cp7Tg7 � cp8Tg8 (16)


For the first pressure level, similar relations as for second levelstill apply. By knowing the evaporator exit steam temperature, theexit temperature of superheater is obtained from the definition ofeffectiveness:


Tg8 � Tse EV 1P(17)

The gas temperature at the exit of first level evaporator (Tg10) isobtained from the definition of pinch point:


The steam fraction of the first pressure level is determined fromenergy balance across both evaporator and superheater:

u1ðhe SH 1P � hi EV 1PÞ ¼ cp8Tg8 � cp10Tg10 (19)

The stack exit temperature (Tg11) is obtained from economizerenergy balance:

ðu3 þu2 þu1Þðhe EC 1P � hi EC 1PÞ ¼ cp10Tg10 � cp11Tg11 (20)


Fig. 2. The temperature-transferred heat diagram: a) HRSG 1P, b) HRSG 2P, c) HRSG 3P.


Once the temperatures of heat exchangers and steam fractionsare determined, it is possible to calculate the specific work of steamcycle and the destroyed exergy rate.

The performances of CC in terms of specific work, energetic andexegetic efficiency are calculated as follows:

WCC ¼ WGT þWSC (21)

hth CC ¼ WGT þWSC

QGT(22)

hex CC ¼ WGT þWSC

ExGT(23)

3. Optimization

This study addresses a global non-linear problem of optimiza-tion with constraints, thus, the following illustrates its mathemat-ical formulation and the algorithm of the used PSO method. Aproblem of optimization is mainly constituted of an objectivefunction, 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 cyclespecific work per unit mass of exhaust gas to be maximized.


This specific work is considered as the objective function andthe 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 vari-ables characterizing the HRSG. The optimization results are: thesteam fraction at each level (i.e u1, u2 and u3), steam exittemperatures from superheaters and reheater (Tse SH 1P,Tse SH 2P, Tse SH 3P and Tse RH), gas temperatures at heat ex-changers inlet and outlet (Tg2,Tg4,Tg5,Tg7,Tg8,Tg10 and Tg11) and thespecific work produced by the three vapor turbines (WLP, WIP,WHP).

3.2. Constraints analysis

In order to avoid mechanical degradation and deterioration ofthe aerodynamic performances of the last stages of steam turbine,the steam fraction should be higher than 88% [27]. To maintain agood operation of HRSG and turbine material, the steam pressureand temperature at HRSG exit should not exceed 160 bar and580 �C, respectively [28]. The condensedwater in exhaust gas couldform a corrosive sulfuric-acid, so the stack temperature should behigher than 80 �C to avoid water condensation [29]. In practice, forthe pinch point, as it is well known, a null value leads to an infinitesurface of economizer then a limit value of 10K is imposed [30]. Aneffectiveness superheater close to “1” leads to an infinite surface, amaximum value of 0.85 is fixed [31].

To summarize, the optimization problem can be denotedmathematically as follows:


Fig. 3. PSO method flowchart.

8>>>>>>>>>>>>>><>>>>>>>>>>>>>>:

Maximize f ðXÞ with f ðXÞ ¼ WscðXÞX ¼ ðp1; p2; p3; ESH 1P ; ESH 2P ; ESH 3P ; ERH;DTP1P ;DTP2P ;DTP3PÞunder the following constraints :x� 0:88 � 0Tse SH 1P � 853K � 0; Tse SH 2P � 853K � 0 and Tse SH 3P � 853K � 0Tse RH � 853K � 0Tg11 � 353K � 0DTP1P � 10K � 0;DTP2P � 10K � 0 and DTP3P � 10K � 0ESH 1P � 0:85 � 0; ESH 2P � 0:85 � 0; ESH 3P � 0:85 � 0 and ERH � 0:85 � 0p3 � 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 animalsto work as a whole, e.g. birds flocking to a food source. Thisseeking behavior was associated with that of an optimizationsearch for solutions to non-linear equations in a real-valuedsearch space [33]. PSO algorithm starts with a population of so-lutions (taken randomly) and looks for an optimum for theproblem, making population individuals evolve over generations.In contrast to genetic algorithms in which solutions are coded inchromosomes, PSO population directly represents the solutions,and the research for the best solutions is done by moving theseindividuals in solutions space, benefitting collectively from theoptima detected individually by each particle. Thus, each particle,over generations, adjusts its path towards its own previous bestposition (Pbest), and towards the best previous best position ob-tained by any member of its group (Gbest). The performance ofeach particle is evaluated using the fitness function. The flow-chart describing the algorithm is given by Fig. 3 which can besummarized as follows:

1 Create a population “Pop” of N particles uniformly spread acrossthe search space.

2 Each particle k is evaluated using the fitness function “f”. Par-ticles that do not obey the imposed constraints are excludedfrom the group and randomly replaced by others.

3 If a position Xk of a particle k is the best in terms of fitnessfunction, a position it has never met before, then Pbest is to beupdated.

4 Determine the best particle (Gbest) among N particles.5 Update the speed (vk) of each particle (k) according to the

following rule:

vtþ1k ¼ w vtk þ c1u

t1�Pbest

tk � Xt

k

�þ c2ut2

�Gbest

tk � Xt

k

�(24)

where w is the inertia weight, c1 and c2 are two positive constantscalled cognitive and social parameter respectively, u1 and u2 aretwo uniform random variables on [0,1].

6 Move the particles to their positions Xtþ1k such as:

Xtþ1k ¼ Xt

k þ vtþ1k (25)

7 Go to second step until a criterion of end is verified.

Please cite this article in press as: Nadir M, Ghenaiet A, Thermodynamic optimization of several (heat recovery steam generator) HRSGconfigurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023

Fig. 4. Convergence of objective function: a) 1P level, b) 2P level, c) 3P levels.

Table 2Main data of gas turbine PG9371FB [34].

Parameter (unit) Value

Gas turbinePressure ratio 18.5Turbine inlet temperature (�C) 1427Exhaust gas mass flow rate (kg/s) 657.5Exhaust gas temperature (�C) 644Net output (MW) 285.3

Steam cycle1st level pressure (bar) 4.2


Fig. 4 shows an example of the objective function convergence.For the initial number of individuals chosen higher than 100, theobjective function converges after 43 iterations for 1P, 4 iterationsfor 2P and 7 iterations for 3P. Also these curves reveal that the initialnumber of individuals has an impact on the convergence speed, butthis is not a general rule as demonstrated by Bratton and Kennedy[33].

Calculations were performed on a personal computer i3 CPU2 Gb RAM. The calculation time for 50 iterations for the threeconfigurations is given in Table 1. For N ¼ 100, the computing timeis less than 1 min and this can be considered in favor of thismethod.

4. Results and discussion

To confirm the validity of the proposed model, the results arecompared with three pressure levels and reheat steam cycle builtaround the GE PG9371FB. Themain characteristics of this combinedcycle are listed in Table 2. The comparison between the results of

Table 1Computing time.

N ¼ 50 N ¼ 100 N ¼ 200 N ¼ 300

1P 21 s 39 s 58 s 77 s2P 23 s 54 s 91 s 125 s3P 33 s 48 s 89 s 110 s


themodel and the real data is presented in Table 3. The latter showsthat the calculated values are close to the real data and that thedifference between them is acceptable. The light difference is dueto some aspects not considered by the present model such asauxiliary equipment consumption.

Fig. 5 gives, for several TOTs, the evolutions of the optimal valuesof pressure at inlet of HP (High pressure) turbine. As shown, the

2nd level pressure (bar) 25.33rd level pressure (bar) 142.51st level steam mass flow rate (kg/s) 12.632nd level steam mass flow rate (kg/s) 12.763rd level steam mass flow rate (kg/s) 86.7Maximal steam cycle temperature (�C) 565Stack temperature (�C) 96Condenser pressure (bar) 0.12Net output (MW) 145.5


Fig. 6. Steam temperature at exit of reheater.

Fig. 7. Optimum pinch point versus TOT.

Table 3Model validation.

Parameter (unit) Real data Model results

Power (MW) 145.5 146.211st level mass flow rate (kg/s) 12.63 13.012nd level mass flow rate (kg/s) 12.76 13.513rd level mass flow rate (kg/s) 86.7 88.07Maximal steam cycle temperature (�C) 565 564.9Stack temperature (�C) 96 94.8


optimum of pressure at HP turbine inlet cannot reach the limit of160 bar for given values of TOT: 580 �C for 1P, 540 �C for 2P and500 �C for 3P due to the fact that a low TOT value leads to a lowsuperheated steam temperature and subsequently a low steamfraction that should remain above 0.88. Above these values of TOTthe optimum inlet pressure at HP turbine reaches its limit andbecomes constant due to imposed constraint. In fact, this value isreached because of reheat that allows obtaining higher steamfraction, but in contrary for HRSG without reheat such pressurevalues are not reached, and this leads to low steam fractions. Fig. 5also shows that, for a given TOT value, adding a pressure levelpermits reaching higher optimal pressure at HP turbine inlet.

This result is practically justified as follows: The maximalpressure of the cycle is constrained by the steam fraction in the laststages of LP (Low pressure) turbine which must be higher than 88%.For a given temperature at turbine inlet, the use of high pressuresleads 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 steamtemperatures after reheat in case of 3P are higher than the onesobtained in cases of 2P and 1P, and this justifies the fact that for agiven TOT, using 3P allows reaching higher pressures than in thecases of 2P and 1P.

Unlike the boilers where a reheat can produce higher temper-atures and therefore high pressures, in the case of HRSG the reheatof steam is constrained by TOT that leads to lower reheat temper-atures (Fig. 6), and this is why the optimum pressures at inlet of HPsteam turbine are relatively lower when using lower TOT values.

Fig. 7 shows that the pinch point tends to its minimal value of10K whatever the value of TOT which is in accordance with thatgiven by Mohagheghi and Shayegan [11], who optimized severalmodels of HRSG for TOT equal 550 �C and showed that the pinchpoint takes the lowest value.

Fig. 5. Optimum pressure at inlet of HP turbine 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) HRSGconfigurations for a range of exhaust gas temperatures, Energy (2015), http://dx.doi.org/10.1016/j.energy.2015.04.023

Fig. 9. Steam temperature at inlet HP turbine: a) HRSG 1P, b) HRSG 2P, c) HRSG 3P.

Fig. 10. Steam cycle specific work versus TOT.


The superheater effectiveness keeps its maximum value, butmarks a drop for TOT higher than 600 �C due to constraint ofmaximal steam temperature of 580 �C (Fig. 8). This result is arguedby Fig. 9 which compares between the cases with and withoutimposed constraint on the maximal steam cycle temperature. Forthe three types of HRSG and values of TOT less or equal 600 �C, thecurves are practically the same, this means that the temperature atoutlet of superheater is at its maximal value, and the superheatereffectiveness takes its maximal value of 0.85. According to Fig. 9when the constraint of maximal steam cycle temperature isignored, the limit of 580 �C is exceeded from TOT¼ 600 �C, and thisis why above this temperature, the effectiveness must have a lowvalue to keep the steam temperature of highest level under itsrequired limit.

Fig. 10 shows a comparison of obtained specific work for threeHRSG configurations. As seen, for all TOT values, HRSG 3P leads to ahigher value of specific work than HRSG 2P and 1P, respectively.Adding a pressure level is always interesting whatever the TOTvalues. These curves also reveal that the steam cycle is stronglyinfluenced by TOT, and there is a considerable increase in the spe-cific work with it. For TOT equal 600 �C, which is representative ofmodern gas turbines, the addition of a pressure level (2P) seems toincrease the specific work of about 17 kJ/kg, which represents abenefit of about 10% for the steamcycle. For the same temperature, a


third level of pressure (3P) adds about 8 kJ/kg which corresponds toa benefit of 4% in the steam cycle specific work, and in overall thereis an increase of 25 kJ/kg which is equivalent to 14% and it is a sig-nificant percentage. For example, a CC in which the gas cycle


Fig. 11. Optimal total steam fractions versus TOT.Fig. 13. Destroyed exergy rate of steam cycle.


participates with 65% in the produced power, an increase of about14% in the steam cycle corresponds to about 5% of specific workincrease in the entire CC. If the gas cycle has a thermal efficiency of36%, when TOT is equal to 600 �C, the combined cycle with 1P mayhave an overall efficiency of 55% and subsequently an increase of25 kJ/kg in steam cycle specific work corresponds to a 3% ofimprovement in the overall thermal efficiency reaching a value of58%.

The total optimal steam fractions produced by the three types ofHRSG are given by Fig.11. HRSG 3P allows to producemore steam ascompared with HRSG 2Pand HRSG 1P, and this applies to all thevalues of TOT. This result supports the one presented by Fig. 10which comes to the conclusion that the specific work achieved by3P 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% and16.4% for 1P, 2P and 3P respectively, but, an additional steamquantity usually leads to a higher HRSG size and this wouldconsequently impact the economic aspect.

Fig. 12 shows, for HRSG 2P and 3P, the repartition of steamfractions on their different pressure levels. For HP level, the steamfractions seem to be much higher than IP (Intermediate pressure)and LP levels, particularly when considering high TOT values. Forinstance, for 600 �C, the fractions of the 1st and 2nd level represent

Fig. 12. Steam fractions of different


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 levelrepresents about 1/5 in relation to the total fraction of 2P.

The evolution of destroyed exergy with TOT is illustrated byFig. 13. It is clear that for HRSG with the highest pressure level, thedestroyed exergy is the lowest. For all TOT values, steam cycle withthree pressure levels destroys less exergy as compared with 2P and1P. Steam cycle with one pressure level destroys more exergynamely for low TOT, where for example for values less than 450 �Cit destroys more than 40% of the exergy supplied at the HRSG. Also,this figure shows that the destroyed exergy rate decreases whenTOT is increased.

To summarize, the pinch point tends to the lowest possiblevalue and the superheater effectiveness tends to the highestpossible value, but they are limited by the heat exchange area. Thisresult has already been shown by other studies considering a singleTOT value. However, the present study has shown that for TOThigher than 600 �C, superheater effectiveness is also constrained bythe maximal steam cycle temperature. Adding another pressurelevel allows achieving higher pressure, producing more steamquantities, destroying less exergy and finally producing more spe-cific work.

levels: a) HRSG 2P, b) HRSG 3P.



5. Conclusion

A thermodynamic optimization has been undertaken fordifferent HRSG configuration 1P, 2P and 3Pwith reheat, consideringseveral values of exhaust gas temperature and several constraintsthat represent the state of art of combined cycles. The results showthat adding another level of pressure leads to improving the steamcycle performance independently of TOT. Concerning the optimi-zation method, PSO algorithm was used successfully in HRSGoptimization, moreover, this method is easy to implementcomparing with the other methods. Concerning the design pa-rameters, the following conclusions can also be drawn:

� Adding a pressure level, allows reaching higher optimal pres-sures and producing higher steam fractions for all consideredTOTs.

� Steam fractions at LP and IP levels are lower than those of HPlevel.

� Optimal superheater effectiveness tends to a maximum, but it isconstrained by the limit of temperature.

� Pinch point tends to its lowest value, but it is constrained by theexchange area.

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Nomenclature

cp: Specific heat capacity [kJ/kg K]E: Effectiveness of exchangerEx: Exergy [kJ]ex: Specific exergy [kJ/kg]f: Fitness functionGbest: Global best solutionh: Steam or water specific enthalpy [kJ/kg]N: Number of particles in populationPbest: Best solution for each particleQ: Heat supplied [kJ/kg]T: Temperature [K]p: Pressure [bar]Pop: PopulationV: speed of particle vectorW: Inertia weightW: Specific work [kJ/kg]x: Vapor fraction at turbine exitX: Optimization variables vectorDTP: Pinch point [K]h: Efficiencyu: Steam to gas ratio

Subscripts

d: Destroyeddr: Destroyed ratee: ExitEC: EconomizerEV: Evaporatorg: GasHP: High pressurei: Inletj: Thermal exchange frontier with the outside environment


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IP: Intermediate pressureK: ParticleLP: Low pressuremax: MaximalN: NetRH: ReheaterS: SteamSC: Steam cycleSH: SuperheaterT: Iteration or generationth: Thermal1P: First level2P: Second level3P: Third level


0: reference environment condition1e11: Gas station at different heat exchangers

Abbreviations

CC: Combined cycleGT: Gas turbineHRSG: Heat recovery steam generatorIAPWS: International Association for the Properties of Water and SteamTOT: Turbine outlet temperature1P: Reheat one pressure level HSRG2P: Reheat two pressures level HSRG3P: Reheat three pressures level HSRG


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