Transient Thermal Modelling of Heat Recovery Steam Generators in Combined Cycle Power Plants

INTERNATIONAL INTERNATIONAL JOURNAL OF ENERGY RESEARCH Int. J. Energy Res. 2007; 31:1047–1063 Published Published online 22 January 2007 in Wiley InterScience InterScience (www.interscience.wiley.com) DOI: 10.1002/er.1297

Transient thermal modelling of heat recovery steam generators in combined cycle power plants Sepehr Sanaye*,y and Moein Rezazadeh Energy Systems Improvement Laboratory, Mechanical Engineering Department, Iran University of Science and Technology (IUST), Narmak, Tehran 16844, Islamic Republic of Iran

SUMMARY Heat recovery steam generator (HRSG) is a major component of a combined cycle power plant (CCPP). This equipment equipment is particula particularly rly subject subject to severe severe thermal thermal stress stress especiall especially y during during cold start-up start-up period. period. Hence, it is important to predict the operational parameters of HRSGs such as temperature of steam, water, hot gas and tube metal of heating elements as well as pressure change in drums during transient and steady-s steady-state tate operation operation.. These These paramete parameters rs may be used for estimating estimating thermal thermal and mechanica mechanicall stresses stresses which are important in HRSG design and operation. In this paper, the results of a developed thermal model for predicting the working conditions of HRSG elements elements during transient transient and steady-state steady-state operations operations are reported. reported. The model is capable capable of analysing analysing arbitr arbitrary ary numbe numberr of pressu pressure re levels levels and any number number of eleme elements nts such such as superh superheat eater er,, evapor evaporato ator, r, economizer, deaerator, desuperheater, reheater, as well as duct burners. To assess the correct performance of the developed model two kinds of data verification were performed. In the first kind of data verification, the program output was compared with the measured data collected from from a cold cold startstart-up up of an HRSG HRSG at Tehra Tehran n CCPP CCPP.. The variatio variations ns of gas gas,, water water/st /steam eam and metal metal temperatures at various sections of HRSG, and pressure in drums were among the studied parameters. Mean differences of about 3.8% for temperature and about 9.2% for pressure were observed in this data comparison. In the second kind of data verification, the steady-state numerical output of the model was checked with the output of the well-known commercial software. An average difference of about 1.5% was found between the two latter groups of data. Copyright # 2007 John Wiley & Sons, Ltd. KEY WORDS:

heat recover recovery y steam generator generator (HRSG); (HRSG); thermal analysis; analysis; transient transient modelling modelling

1. INTRODUCTIO INTRODUCTION N The higher efficiency of combined cycle power plants (CCPPs) in comparison with Brayton or Rankine cycle has made this form of power generation quite attractive. Since damage from

*Correspondence to: Sepehr Sanaye, Energy Systems Improvement Laboratory, Mechanical Engineering Department, Iran University of Science and Technology, Narmak, Tehran 16844, Islamic Republic of Iran. y E-mail: [email protected]

Copyright # 2007 John Wiley & Sons, Ltd.

Received 22 May 2006 Revised 22 November 2006 Accepted 29 November 2006

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S. SANAYE AND M. REZAZADEH

cycling occurs mainly during start-up and shutdown intervals, it is very important to follow the correct correct start-up and shutdown shutdown procedures. procedures. Correct Correct procedure proceduress reduce reduce the magnitude of the temperat temperature ure and pressure pressure gradients gradients in heat recovery steam generator generator (HRSG) component components, s, avoiding high thermal stress. Therefore, a correct operation program extends the useful life of HRSG. The HRSG HRSG transi transient ent analys analysis is allows allows design designers ers and manufa manufactu cturer rerss to better better predic predictt the impact of intended plant operational scenarios on the longer life cycle of the heating elements and to develop the best operational scenarios of HRSG. For the life cycle analysis, the steam, gas and metal metal temper temperatu atures res during during transi transient ent operat operation ion are used used to determ determine ine temper temperatu ature re gradients in the HRSG components which are most susceptible to thermal and mechanical cycling-related damage. High-pressure parts of HRSG and heating elements which are exposed to high high temper temperatu ature re gas are consid considere ered d as the critic critical al parts parts in design design and manufa manufactu cturin ring, g, therefore, the rate of temperature increase in high-pressure superheaters and evaporator which causes thermal stress is the most important parameter in design, operating and HRSG life cycle. The results of the transient analysis may also be used as input data in finite element models to determine the impact of various transient plant operational scenarios on the potential of fatigue damage to boiler heating elements. For a modern combined-cycle power plant, typically three different start-up scenarios are defined: * * *

Cold start}more than 48 h since the gas turbine turbine was last synchronized. synchronized. Warm start}between between 8 and 48 h since the gas turbine was last synchronize synchronized. d. Hot Start }less than 8 h since the gas turbine turbine was last synchronized. synchronized.

A cold start-up usually takes place after gas turbine inspection/overhaul, which normally happens once a year. During the cold start-up due to the change in gas turbine load, hot gas mass flow rate and temperature flowing into HRSG, hot gas temperature distribution in HRSG elements and the pressure in drums change with time. This is a dynamic situation for an HRSG which is analysed in this paper. There are various authors such as Walter and Linzer (2004) who studied the flow stability in natural circulation HRSGs as well as Schmidt and Arnold (2002) who described the necessary measu measurem rement ent points points for proper proper HRSG HRSG testin testing. g. Decha Dechamps mps (1995) (1995) propos proposed ed a model model for predicting the transient operation of HRSG focusing on transient thermal modelling of the entire HRSG as a whole system. In his model, various elements of a vertical flow HRSG were replac replaced ed by equiva equivalent lent heat heat exchan exchanger gers. s. An equiva equivalen lentt heat heat exchan exchanger ger had the same same heat heat transfer surface area and the same mass of tube metal as of the real HRSG elements. This heat exchanger was then divided into a number of differential elements for applying the mass and energy conservation equations. The set of simultaneous equations were finally solved to provide the trans transien ientt temper temperatu ature re distri distribut bution ion in HRSG. HRSG. Pas Pasha ha (1992) (1992) and Jolly Jolly et al . (1994) (1994) also explained the HRSG start-up effects and constraints in HRSG thermal modelling, as well as Kim et al . (2000) who used transient mass and energy conservation equations for high-pressure superheater or evaporator in a horizontal flow HRSG to get the variation of parameters of interest during cold start-up. Thermal modelling of HRSG in transient operation mode was also performed by Sanaye and Moradi (2001, 2002, 2003), and Sanaye and Razazadeh (2006). The numerical output of the final developed version of their model is presented here. In this paper, the transient gas, water/steam and tube metal temperature variations of heating elements in an HRSG, as well as the pressure change in drums are studied. To validate the Copyright # 2007 John Wiley & Sons, Ltd.

Int. J. Energy Res. Res . 2007; 31:1047–1063 DOI: 10.1002/er

TRANSIENT TRANSIENT THERMAL THERMAL MODELLING MODELLING OF HEAT RECOVERY RECOVERY STEAM GENERATORS GENERATORS

1049

numeric numerical al result resultss of the develo developed ped model, model, the data data were were compar compared ed with with the corres correspon ponding ding numerical values of the actual measurements collected at Tehran CCPP during the cold start-up (transient operation mode), as well as with the output of a commercial software (Thermoflow Inc., 2002) in steady-state operation mode. Acceptable closeness was found in the above data comparisons. As a summary, the followings are the contribution of this paper in the field: *

*

*

*

*

*

*

Provid Providing ing the relati relations ons,, var variab iables les,, the typical typical val values ues of parame parameter terss and approp appropria riate te explanations for a special method of HRSG transient thermal modelling. The mathematical mathematical and physical physical explanation explanation of the method method for solving the specific specific form of transient conservation equations using appropriate steady state-steady flow (SSSF) and uniform state-uniform flow (USUF) control volumes. Also explaining the initial condition and many other complicated points in HRSG, cold start-up. Presenting the numerical output of the explained transient model for the shown HRSG and comput computing ing change change in gas gas,, water/ water/ste steam am temper temperatu ature, re, pressu pressure re and flow in all HRSG HRSG elements. Comparing the numerical output of the model with the actual measurements at a real power plant. Also comparing the steady-state numerical results of the presented model with the corresponding data obtained from commercial software. Providing an analytical method of finding the numerical values of time steps in performing computations. Also comparing the step size values obtained from analytical and numerical results for the presented model. Performing error analysis and predicting the run time by choosing the various step size values for the presented model. Reporting the capabilities of the in-house developed software.

2. ASSUMPTIONS ASSUMPTIONS AND GOVERNING GOVERNING EQUATIONS EQUATIONS

’ g after passing an HRSG component is expressed as The flue gas energy reduction rate Q follows:

ð Þ

’g Q

¼ m’ ðh À h Þð1 À K Þ ð1Þ indicates the flue gas mass flow rate and ( h Àh ) is the gas enthalpy reduction. It was g

g1

g2

loss loss

where m ’g g1 g2 assumed that a part of hot gas energy was lost through HRSG casing (about 2% as the typical value for K loss loss). Also gas energy reduction rate is equal to heat transfer between gas and an HRSG element

’g Q

¼ U A ðT % À T % Þ o

o

g

m

ð2Þ

where U o represents the gas side heat transfer coefficient (including convection and radiation effects) and Ao is the outer heat transfer surface area. ’ g is absorbed by the tube wall ( Q ’ m ; Equation (4)), fins ( Q ’ f ; Equation (5)) as well as steam in Q superheaters, water in economizers and the mixture of steam and water in evaporator tubes ’ sw ; Equation (7)) as is shown in the following equation: (Q

’g Q Copyright # 2007 John Wiley & Sons, Ltd.

¼ Q’ þ Q’ þ Q’ m

f

sw

ð 3Þ Int. J. Energy Res. Res . 2007; 31:1047–1063 DOI: 10.1002/er

1050


At the beginning of the start-up during which there is no steam production, the numerical value ’ sw is zero in superheaters since only tube walls and fins are energy absorbers. for Q ’ m is expressed as The rate of energy absorbed by the metal of HRSG heating element Q e M m cm T m Dt

ð Þ

i m

ð À T Þ

’m Q

ð 4Þ

¼ ’ Þ is Also the rate of energy absorbed by fins ðQ ’ ¼ M c ðT À T Þ Q Dt f

e f

f f f

f

i f

ð 5Þ

where M and M and c in Equations (4) and (5) represent mass and specific heat, respectively. Equation (6) predicts an average value for the fin temperature. T f f

¼ T þ 0:3ðT À T Þ sw sw

g

ð6Þ

sw sw

where T g, T f f and T sw sw are the gas, fin and steam/water temperatures, respectively. ’ sw can be estimated by the following equations: The absorbed energy by steam or water Q

’ sw Q

¼ ðQ’

out

ð Þ À Q’ Þ þ Q’ in

accum

À Q’

ð 7Þ

bd

’ out and Q ’ in are the rate of energy flowing in and out of an HRSG heating element as where Q explained below ’ out Q

¼ m’

’ in Q

¼ m’

sw;out hsw;out

ð 8Þ

sw;in hsw;in

ð 9Þ

where m ’ sw denotes the mass flow rate of steam or water while hsw;out and hsw;in refer to the enthalpy of outlet and inlet flows. ’ accum is the energy accumulation inside a heating element which is produced by the change in Q temperature and mass of steam/water with time and is computed by relation (10)

’ accum Q

e e st st

i i st st

e e wt uwt

¼ ðM u DÀt M u Þ þ ðM

i i wt uwt

À M

Dt

Þ

ð10Þ

where u stands stands for internal energy and Dt represents the time step. Superscripts e and i refer to the end and the beginning of a time step. During the transient operation of an HRSG, due to slow energy variation during a time interval in a heating element which is a control volume, SSSF process dE cv 0 was applied cv =dt for the gas flow, as well as the water or steam flow in economizers and superheaters. However, due to large mass of water/steam mixture in evaporator and drum, and the high rate of energy variat var iation ion due to boiling boiling,, USUF USUF proces processs was considere considered d in the mass and energy energy analys analysis. is. ’ Subsequently Qaccum in Equation (10) was set equal to zero for single phase flow (including gas/ water/ste water/steam am flows). flows). However, However, for analysing two-phase two-phase flow in evaporato evaporators rs and drums, the ’ numerical value of Qaccum was computed from Equation (10). ’ bd describes the amount of energy loss in drum due to blow down to keep the water inside Q the drum chemically balanced. The blow down mass flow rate was considered to be about 1% of water mass flow rate entering the drum and was evaluated by

ð

’ bd Q

¼ m’

bd hwt;bd

¼ Þ

ð11Þ

where hwt,bd denotes the enthalpy of saturated water in the drum. Copyright # 2007 John Wiley & Sons, Ltd.



1051

To estimate the heat transfer rate between tube walls and steam/water, Equation (12) was used

’ sw Q

¼ U A ðT % À T % Þ i

i

m

ð12Þ

sw sw

where U i is the overal overalll heat heat transf transfer er coeffici coefficient ent comput computed ed based based on the inner inner heat heat transf transfer er surface area (A ( Ai). The equations for estimating the overall heat transfer coefficients ( U ) U ) and radiation heat transfer are available in the mentioned references (ESDU, 1968, 1986; Collier and Thome, 1994; Kreith, 1998). For pressure drop relations, ESDU Item 84016 (1984) was referred to. The mass conservation relation inside the drum and evaporator is d M wt M st wt st dt

ð

þ

Þ ¼ m’

wt;in

À m’ ;

ð13Þ

st out

where M wt ’ wt;in indicates wt and M st st are the water and steam mass in evaporator, respectively. m the water mass flow rate entering the evaporator and is estimated by Equations (14) and (15) and m ’ st;out is the mass flow rate of the steam flowing out of the drum and is computed by Equation (16). de t m K d 14 ’ wt;in;tþDt m ’ wt;t K p e t dt

¼

et

þ

ð Þþ

ð Þ ¼ WL À WLðtÞ pre

ðÞ

ð Þ ð15Þ

In Equation (14), K p and K d are related to the HP and IP drum water level control system. The numerical values of these parameters were obtained from the plant technical documents, equal to 180kgmÀ1 sÀ1 and and 9200kg 9200kg mÀ1, respectively. In Equation (15), WL pre is the appropriate water level specified by the manufacturer for HP and IP drums. In Tehran CCPP, WL pre is zero for HP and IP drums. Zero for water level corresponds to the drum centre line. Water level for DA drum is set to 560 mm above the centre line due to its duty for feeding other elements. elements. Equation (16) was applied based on the assumption of considering the steam exit passage as a nozzle (Bartlett, 1958)

þ

m ’ st;out

¼ K p ffiT Pffi ffi ffi st st

sw

sw sw

ð16Þ

where T sw ’ st;out is the sw and Psw are the saturation temperature and pressure in the drum and m steam mass flow rate out of drum at the steady-state operation. K st st was estimated 0.101 and 0.303 0.3 03 for HP and IP drums, drums, respec respectiv tively. ely. During During steam steam produc productio tion, n, an empiri empirical cal diagra diagram m (Lokshin et al ., ., 1988) was used to correlate the water level in drums, with the amount of increase in volume of steam bubbles inside water. The mentioned governing governing equations equations constructed constructed a set of nonlinear nonlinear equations which were solved by forward finite difference method to get temperature of gas, tube wall and water/steam at the end of each time interval. To simplify solving the governing equations, the following points were considered: 1. In each time interval, enthalpy and thermo-physical properties of gas and steam/water were computed based on the average temperature in a time step. 2. There was no heat heat accumu accumulati lation on in HRSG HRSG duct, duct, econom economize izers rs and superh superheat eaters ers (as a ’ control control volume) during during a time interval, interval, therefore therefore Qaccum was set equal to zero in Equation (7). Copyright # 2007 John Wiley & Sons, Ltd.


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’ accum was negligi Numeri Numerical cal evalua evaluation tion of terms terms in Equati Equation on (10) (10) showed showed that that Q negligible ble in ’ out and Q ’ in in Equation (7) during a time step (SSSF process). However, comparison with Q due to large mass of water/steam mixture in evaporator and drum and the high rate of energy variation due to boiling, the numerical values of heat accumulation computed from Equation (10) were comparable with the corresponding numerical values of other terms in Equation (7) during a time step (USUF process). Two following initial conditions were also applied: (a) At the beginning beginning of the start-up start-up period period during which the temperatu temperature re of fluid inside the evaporator was less than saturation temperature, there was no vapour production, so the evaporator tube walls as well as water, absorbed the energy of the hot gas. Furthermore, due to no vapour production in drums at the beginning of start-up period, there was no water flow in economizers. Hence, internal energy ( u) was used in Equations (8) and (9) instead of enthalpy (h ( h), considering economizers as a control mass, instead of a control volume. (b) (b) In the the cold cold star startt-up up anal analys ysis is,, the the tube tube wall wall init initia iall temp temper erat atur uree was was the the ambie ambient nt temperature. The enthal enthalpy py and thermo thermo-ph -physi ysical cal proper propertie tiess of hot gas mixtur mixturee enteri entering ng HRSG HRSG were were obtained obtained from in-house developed developed software. software. Steam and water thermodynamic thermodynamic properties properties in superheat, saturated and subcooled regions as well as transport properties (thermal conductivity and viscosity) at various sections of HRSG were obtained from in-built database (International Formulation Committee (IFC), 1986).

3. RESULTS RESULTS AND DISCUSSIONS DISCUSSIONS To ass assess ess the perfor performan mance ce of the develo developed ped trans transien ientt therma thermall model, model, two kinds kinds of data data verification were performed. Regarding the first kind of data verification, model numerical output was compared with the corresponding actual measured values obtained for the cold start-up of an HRSG at Tehran CCPP (Tehran CCPP, 2004). The measured data were collected during the HRSG start-up using the own Tehran CCPP instruments. The data were recorded for 53 chosen points of HRSG in each each 3 min. min. The geometric specifications of this HRSG are given in Table I. The diameter, thickness, length and pitch of tubes, also the geometry and weight of fins and drums are included in the given data. data. This power plant has four four 100 MW gas turbine turbine at site condition condition (90 kPa and 303 K ambient pressure and temperature). It has also four HRSGs consisting of HP drum, IP drum and deaerator deaerator which their pressure were 60, 6 and 2 bar, respectively respectively.. The arrangement of HRSG heating elements at Tehran CCPP is shown in Figure 1 and Table Table II. The high-p high-pres ressur suree part part of HRSG HRSG includ includes es high high temper temperatu ature re and low temper temperatu ature re superheaters and two economizers. Figure 2 shows the variation of gas mass flow rate entering HRSG with time. During the cold start-up, the gas turbine load was increasing (gas turbine was in the load increasing mode). Thus, the gas turbine exit mass flow rate and temperature were increasing during the HRSG Copyright # 2007 John Wiley & Sons, Ltd.



r to . a A ro p Da v E re .l iz e d P m o I o n m o c d e E p re lo e z v e I i d I m e P o n th H o c E to t r u o p t n a i r o e P I p th a v s a E P r P te C a e C P n I rh e a r p h u e S T t r e a iz I m ts n e P o Hn m o lee c E G r S to R r H P a o f H p o a v a t E a d r c te rti a e e T L h m P re o e Hp g u S d n r a te t h T a e g ie H h r P e W Hp u I. S el b a T

m tIe

d ree g g ta S

8 . 0 5

2 . 3

3 . 5 1

1 0 1

4 1 1

4 8 5

7 9 1

9 1

0 1 5 8 1

4 3 4 5 . 0

0 5

9 . 1 4

d ree g g ta S

8 . 0 5

2 . 3

3 . 5 1

1 0 1

4 1 1

1 8 5

7 9 1

6 0 9 5 1 . 8 1 2 4 1 8 7 6

4 3 4 5 . 0

0 5

}}

8 . 0 5

7 . 4

3 . 5 1

1 0 1

4 1 1

4 8 5

7 9 1

9 1

5 2 . 1

3 4 5 1 3

4 0 6 5 2

4 3 4 5 . 0

0 5

}}

8 . 0 5

9 . 2

3 . 5 1

1 0 1

4 1 1

2 8 1 5

7 9 1

9 1

5 2 . 1

0 3 7 5 9

0 1 6 5 6

4 3 4 5 . 0

0 5

1 . 5 1

8 . 0 5

9 . 2

3 . 5 1

1 0 1

4 1 1

2 8 5

. A . N

. . . 2 0 A . A . A . 8 NNN2 1

4 3 4 5 . 0

0 5

}}

8 . 0 5

7 . 4

3 . 5 1

1 0 1

4 1 1

2 8 1 5

7 9 1

9 1

5 2 . 1

0 3 6 4 9

2 1 8 6 7

4 3 4 5 . 0

0 5

}}

8 . 0 5

9 . 2

3 . 5 1

1 0 1

4 1 1

8 8 1 5

7 9 1

9 1

5 2 . 1

5 4 9 1 4 1

5 1 4 8 9

4 3 4 5 . 0

0 5

4 . 2 2

8 . 0 5

2 . 4

3 . 5 1

1 0 1

4 1 1

4 8 5

7 9 1

7 4 7 0 5 5 2 6 . 1 1 4 3 5 2 2

8 7 4 . 0

6 8 . 6 3

}}

8 . 0 5

2 . 4

3 . 5 1

1 0 1

4 1 1

2 8 5

7 9 1

5 1

8 7 4 . 0

6 8 . 6 3

}}

s n fi f o r re te b e mm u re Np

) ) g ) m k ( m ) m( s g s (m se n (k fi t n f f . h k o o tc g ie ic t t e h h s, h th g ie g ie e b in in F F W W tu

d ree g g ta S d ree g g ta S d ree g g ta S d ree g g ta S d ree g g ta S d ree g g ta S d ree g g ta S

se b u T

t n e m e g n a rr a

e b u T

) m (m r tee m a i d

e b u T

) m (m ss e n k ic th

e b u T


e ) b m u ( t . th g g n n o le L

) m (m h tic p

e b u t s. n a r T

s w ro ) f m ro e (m b h m tic u p N

se b tu f o re w b o m rr u e Np

5 2 . 1

5 2 . 1

3 4 5 1 3

9 3 7 1 1

2 0 8 2 1

1053

6 7 3 6 1

7 3 5 5

2 3 2 5 4

) ) g (m (k e t ) 1) m 1 h À À ie lu g Ko p K v w c 1 k1 – l g l À a a m te k te m m J ru ru M (k M (W D D 3


1054


Figure Figure 1. The arrangemen arrangementt of HRSG elements elements at Tehran Tehran CCPP.

Table II. II. Tehran CCPP HRSG elements. Tehran CCPP HRSG elements HPHT SH. HPLT SH. HP Eva. HP Eco.1 IP SH. IP Eva. HP Eco.2 IP Eco. DA. Eva. DA Eco.

High pressure high temperature superheater High pressure low temperature superheater High pressure evaporator High pressure economizer (1) Intermediate pressure superheater Intermediate pressure evaporator High pressure economizer (2) Intermediate pressure economizer Deaerator evaporator Deaerator economizer

start-up start-up transient transient mode of operation, operation, as they were shown in Figures Figures 2 and 3. Only about 80 min after start-up, the gas turbine was allowed to reach the full load. The mass flow rate of hot gas during start-up period was controlled by a diverter damper at the HRSG entrance to avoid damages resulting from high thermal stress acting on the elements. Based on the procedure explained in start-up operation manual of Tehran CCPP, only 30% of the turbine exhaust gas flowed flowed into into the HRSG at first first until until the HP drum drum pressu pressure re reached reached 10 bar. bar. At this moment moment,, diverter damper let 60% of turbine exhaust gas mass flow rate pass through HRSG. After HP drum pressure increased to 25 bar, diverter damper allowed 80% of the turbine exhaust gas mass flow rate to enter the HRSG. When HP drum pressure reached about 45 bar, diverter damper opened completely and all the gas turbine exhaust flowed over HRSG heat transfer elements. Figure 3 shows the variation of HRSG inlet gas temperature with time which was recorded at Tehran CCPP. Figures 4–6 show the variation of the computed values of hot gas temperature with the corresponding measured ones at various sections in HRSG at Tehran power plant. Copyright # 2007 John Wiley & Sons, Ltd.



1055

450

) /s 400 g k ( 350 e t ra 300 w o lf 250 s s a 200 m s a 150 G

m.gas (kg/s) (kg/s)

100 0

20

40

60

80

100

120

140

Time (min.)

Figure 2. Variation of hot gas mass flow rate entering entering HRSG with opening the diverter diverter damper and time.

800

700

) K ( 600 . p m e T 500 400

Meas. 300 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 3. Variation Variation of hot gas temperatur temperaturee entering HRSG (T g1 g1) with time.

Figure 3 also shows increase in the hot gas temperature entering HRSG with time. The same rate of increase in gas temperature was also observed in gas temperature variations at the exit of heating elements in the front of HRSG (HPHT SH. and HPLT SH.) as is shown in Figures 3 and 4. This behaviour occurred due to the fact that at initial time steps, there was no steam flow inside tubes and tube wall was the only energy absorber that resulted in high rate of hot gas temperature increase at initial time steps. However, when the hot gas passed over the evaporator there was a considerable amount of energy absorption by water-filled tubes, which caused the gas temperature temperature rise after about 20 min delay (Figure 5). When the steam pressure pressure in HP drum reached about 45 bar, the saturated saturated steam was allowed allowed to enter the steam turbine. Due to the steam flow out of HP drum, the pressure in this drum became approximately constant for a while (Figure 12). Furthermore, HP drum steam outlet and economizer water mass flow rate increased in this period. Increase in economizer water mass flow rate decreased decreased the gas temperature temperature leaving HP Eco.1 (Figure 6). After After about 80 min when the HP drum pressure pressure reached about 45 bar, the diverter damper was completely completely open with the maximum amount of hot gas mass flow rate passing over the tube bundles (Figure 2). Copyright # 2007 John Wiley & Sons, Ltd.


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700

) 600 K ( . p m500 e T 400

Cal. Meas. 300 0

20

40

60

80

100

1 20

140

Time (min.)

Figure Figure 4. Variation Variation of hot gas temperat temperature ure at the exit of HPLT SH. (3) with time.

600

550

) 500 K ( . p 450 m e T 400

Cal.

350

Meas. 300 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 5. Variation Variation of hot gas temperatu temperature re at the exit of HP Eva. (4) with time.

At that time the gas turbine exhaust temperature was increasing (Figure 3). These conditions caused gas temperature increase in HPLT SH. and HP Eva. with time (Figures 4 and 5). Variation of metal temperature of elements in HRSG is shown in Figure 7. In this figure metal temperature tends to stabilize at the middle time of start-up. But as is shown in Figure 3, the inlet hot gas temperature was increasing at the minute of about 90. This effect increases the superheater metal temperature sharply. Figures 8–11 illustrate the variation of water/steam temperature with time. Steam did not enter superheaters until specified pressures were reached in drums. These specific pressure values were 3 and 10 bar for IP and HP drums, drums, respectively. respectively. However, However, sensors sensors showed some numerical numerical values as tube inside temperature when there was no steam flow in superheaters illustrated in Figures 8 and 10. In these figures some parts of computed results are missing due to the fact that comput computing ing steam steam temper temperatu ature re at superh superheat eaters ers outlet outlet start started ed just just after after flowing flowing steam steam into into superheaters. Copyright # 2007 John Wiley & Sons, Ltd.



1057

550

500

) K ( 450 . p m e 400 T 350

Cal. Meas.

300 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 6. Variation Variation of hot gas temperature temperature at the exit of HP Eco.1 Eco.1 (5) with time.

800

700

) K ( 600 . p m e T 500 400

Cal. Meas .

300 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 7. Variation Variation of metal temperatur temperaturee at the HPHT SH. with time.

750 700 650 600

) K ( . 550 p m500 e T 450 400

Cal.

350

Meas .

300 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 8. Variation Variation of steam temperature temperature at the HPHT SH. outlet with time. Copyright # 2007 John Wiley & Sons, Ltd.


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600 550

) 500 K ( . p450 m e T 400

Cal.

350

Meas . 300 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 9. Variation Variation of steam temperature temperature at the HP Eva. outlet outlet with time.

530

480

) K ( 430 . p m e T 380 330

Cal. Meas

280 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 10. Variation Variation of steam temperature temperature at the IP SH. outlet outlet with time.

450

) 400 K ( . p m e T 350

Cal. Meas . 300 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 11. Variation Variation of water temperatur temperaturee at the IP Drum inlet with time. Copyright # 2007 John Wiley & Sons, Ltd.



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The mean difference values between numerical output and experimental data were found to be 3.8% for temperature and 9.2% for pressure during the start-up period. The maximum amount of difference between numerical and experimental values of gas temperature (in transient mode) was about 15%. The difference values were smaller at starting and ending periods (steady-state mode) mode) in compar comparison ison with ones ones obtain obtained ed in the middle time interv intervals als.. The main main reason reason of existing existing difference between between two groups of data was the rapid change of parameter parameter values in the middle time intervals. The size of HRSG is big and the number of installed sensors in one section of this device was just one (and in some special cases two). Therefore, detecting the mean value val ue of parame parameter terss during during transie transient nt mode mode was accomp accompanie anied d with with larger larger errors errors.. Als Also o the sensors’ time lag in detecting the rapid temperature or pressure change was another main reason of the bigger difference between numerical and experimental results in the middle time intervals. The latter error decreased as the steady-state condition approached. It should be added that the slope of temperature and pressure variation with time which is related to the imposing thermal stress was approximately the same for both numerical and experimental results. The variations of HP and IP drum pressures were also illustrated in Figures 12 and 13. The drum pressure is an important parameter in estimating stress and strain during cold start-up. At about 85 min after start-up, the IP drum pressure increased increased slightly (Figure 13). The reason was, incr increa ease se in gas gas mass mass flow flow rate rate (Fig (Figur uree 2) and and temp temper erat atur uree (Fig (Figur uree 3) ente enteri ring ng HRSG HRSG as explained explained before. This behaviour behaviour reduced the gas temperat temperature ure leaving IP Eva. and therefore therefore IP drum pressure (Figure 13). Regard Regarding ing the second second group group of data data verifica verificatio tion, n, the numeric numerical al output output in steady steady-st -state ate condit condition ion was compar compared ed with with the result resultss of well-k well-know nown n commer commercia ciall softwa software. re. That That is a computer program for designing, modelling, and analysis of steam, gas and CCPPs in steadystate mode using mass and energy conservation equations. Steady Steady-st -state ate conditio condition n occurs occurs when there there is no change change in gas turbine turbine load load and HRSG operating parameters. This situation occurs at the end of the HRSG cold start-up. Table III shows that there was a good agreement between two groups of results. An average difference of about 1.5% was found.

7000 6000

) 5000 a P k ( 4000 re u s 3000 s re P 2000

Cal.

1000

Meas . 0 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 12. Variation Variation of pressure pressure in the HP drum with time. Copyright # 2007 John Wiley & Sons, Ltd.


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800 700 600

) a P 500 k ( re 400 u s s 300 re P 200

Cal.

100

Meas. 0 0

20

40

60

80

100

120

140

Time (min.)

Figure Figure 13. Variation Variation of pressure pressure in the IP drum with time.

Table III. Comparison of the model output with the commercial commercial software results in steady-state condition. condition. Present work Gas temperature after HPHT SH., K Gas temperature after HPLT SH., K Gas temperature after HP Eva., K Gas temperature after HP Eco.1, K Gas temperature after IP SH., K Gas temperature after IP Eva., K Gas temperature after HP Eco.2, K Gas temperature after IP Eco., K Gas temperature after DA. Eva., K Steam temperature at HPHT SH. Outlet, K Steam temperature at HPLT SH. Outlet, K Steam temperature at IP SH. Outlet, K Water temperature at HP Drum Inlet, K Water temperature at IP Drum Inlet, K HP drum pressure, bar IP drum pressure, bar

732 699 545 483 481 431 419 417 404 691 648 464 542 410 58.05 5.99

GT MASTER 728 698 555 498 496 439 426 424 409 700 652 461 548 413 60.02 5.97

Diffe ifference (%) 0.6 0.2 1.7 2.9 2.9 1.8 1.6 1.6 1.1 1.2 0 .5 0.6 1 .0 0.5 3.2 0.2

4. CONSIDERATI CONSIDERATIONS ONS IN NUMERICAL NUMERICAL SOLUTION SOLUTION For For obta obtain ining ing the the abov abovee resu result lts, s, the the deve develo lope ped d soft softwa ware re was was run run for for 140 140 min min of HRSG HRSG operat operation ion (about (about 40 min of softwa software re run time), time), while while the time step step for computat computation ion was considered considered to be 1 s. Increase Increase in time step from from 0.1 to 1 s decreased decreased the run time considerab considerably ly as is shown in Figure Figure 14. For time steps bigger bigger than 2 s, no noticeable noticeable change was observed observed in the runn running ing time time.. The The nume numeri rica call valu values es of 1–1. 1–1.5 5 s for for time time step step was was foun found d to be the the most most appropriate, in achieving both the reasonable run time as well as guarantee for convergence of results. According to the fact that every transient phenomenon should be characterized by a time scale, one should estimate an appropriate order of magnitude for the time step to resolve the fastest disturbances. Following the discussion by Deechamps (1995), and by applying the Copyright # 2007 John Wiley & Sons, Ltd.



14000

9

12000

8.5

.) 10000 c e s ( e 8000 im t 6000 n u R

8

7.5

1061

) % ( r o rr E

7

4000 Run Time 2000

6.5

Error 6

0 0

2

4

6

8

10

Time step (sec.)

Figure Figure 14. Decreasin Decreasing g the run time and increasin increasing g the relative relative error error with increasing increasing the time step.

conservation of energy law, as well as considering the flue gas as an ideal gas, then

 L u

Á ðm’ Á c Þ

p g

@T @t

$ h Á A Á DT o

Therefore, the system time constant is L=u m ’ cp g = ho A ; where m ’ ; cp and ho are the flue gas mass flow rate, specific heat and gas side heat transfer coefficient, respectively. L, u and A are also also the length length scale scale repres represent enting ing the heat heat exchan exchanger ger dimens dimension ion,, flue gas velocit velocity y and heat heat transf transfer er surfac surfacee area. area. Substi Substitut tuting ing the follow following ing val values ues for the order order of magni magnitud tudee of the À À 1 1 À À À 1 2 mentioned parameters, m 100 1000 kgs ; cp 1000 1000 J kg K ; ho 1 0 0 W m K 1 ; A 10 0 ’ 00 m2 ; L 10 m; u 1 0 m sÀ1 ; the appropriate order of magnitude of the time step ( Dt) is 1s, which is the value mentioned above and obtained from the numerical computations. In the range of 1–1.5 s for time step, 1–3% change in mean value of output paramete parameters rs was found. The convergence criterion or relative error (the sum of difference of gas, steam and metal temperature in two consecutive iterations) for obtaining the above results was assumed to be 0.1. The numerical values of 0.01–0.1 were the suitable range for this parameter. Decrease in relative error with time step is shown in Figure 14.

ð Þð Á Þ ð Á Þ

$

$

$

$

$

$

5. SUMMARY SUMMARY AND CONCLUSION CONCLUSION A model model for trans transien ientt therma thermall analys analysis is of HRSG HRSG was develope developed. d. The model model output output was compared with actual data obtained from Tehran CCPP in transient start-up mode. Acceptable closeness was found in this comparison. The model output at the end of transient operation (durin (during g which which there there was no change change in param paramete eterr val values ues and HRSG HRSG was approxim approximate ately ly in steady-state mode of operation) was also compared with the numerical output of well-known commercial software. The agreement between these two groups of data was good. In the latter case the detailed thermal and geometrical data (arrangement and number of elements, tubes and fins geometry) of Tehran power plant HRSG (Figure 1 and Table I), were used as the input values to the commercial software. Copyright # 2007 John Wiley & Sons, Ltd.


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The developed and proposed transient model is an important tool to check the temporal temperature and pressure variation in heating elements in an HRSG to evaluate the system performance as well as to control the thermal and mechanical stresses in various elements.

NOMENCLATURE A c e h K d K loss loss K p K st st L M m ’ P ’ Q T u U WL Dt

=heat transfer surface area (m 2) =specific =specific heat (J kgÀ1 K)À1 =deviation of water level from the set point value (mm) =enthalpy =enthalpy (J kgÀ1) =derivativ =derivativee gain of the water level control control logic (kg m À1) =heat loss coefficient (dimensionless) =proporti =proportional onal gain of the water level control control logic (kg m À1 sÀ1) =mass =mass flow parameter parameter (kg K 0.5 sÀ1kPaÀ1) =length scale (m) =mass (kg) =mass =mass flow rate rate (kg s À1) =pressure (kPa) =rate of heat transfer (W) =temperature (K) =flue =flue gas velocit velocity y (m s À1) =overall =overall heat transfer coefficient coefficient (W m À2 KÀ1) =water level (mm) =time step (s)

Subscripts 1,2,. . . accu accum m bd ec ev f g i in m o out pre sw

=sections at HRSG elements =acc =a ccum umul ulat ated ed =blow down =economizer =evaporator =fins =flue gases =inside =inlet =metal =outside =outlet =prescribed =steam or water

Superscripts e i

=value at the end of the time step =value at the beginn inning ing of the time step




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REFERENCES Bartlett RL. 1958. Steam Turbine Performance and Economics . McGraw-Hill Book Company: New York. Collier JH, Thome JR. 1994. Convective Boiling and Condensation (3rd edn). Oxford University Press: London. Dechamps PJ. 1995. Modelling the transient behaviour of heat recovery steam generators. Journal of Power and Energy 209:265–273. Engineering Engineering Sciences Data Unit (ESDU). (ESDU). 1968. ESDU Items 68006, 68007 . ESDU International Ltd: London. Engineering Engineering Sciences Data Unit (ESDU). (ESDU). 1984. ESDU Item 84016. 84016. ESDU International Ltd: London. Engineering Engineering Sciences Data Unit (ESDU). (ESDU). 1986. ESDU Item 86022. 86022. ESDU International Ltd: London. Internation International al Formulation Formulation Committee Committee (IFC). 1986. Thermodynamic Properties of Water and Steam . Edward Arnold: London. Jolly S, Gurevich A, Pasha A. 1994. Modelling of start-up behaviour of combined cycle HRSG. 94-GT-370, 94-GT-370, International Gas Turbine and Aero-engine Congress, Congress , ASME, The Netherlands. Kim TS, Lee DK, Ro ST. 2000. Dynamic Dynamic behavi behaviour our analysis analysis of a heat heat recove recovery ry steam steam genera generator tor during start-up. start-up. International Journal of Energy Research 24(2):137–149. Kreith F. 1998. The CRC Handbook of Mechanical Engineering . CRC Press: Florida. Lokshi Lokshin n VA, Peterso Peterson n DF, Schwar Schwarzz AL. 198 1988. 8. Standard Standard Methods of Hydraulic Hydraulic Design for Power Power Boilers Boilers.. Energia Energia Publishing House: Moscow. Pasha A. 1992. Combined cycle power plant start-up effects and constraints of the HRSG. 92-GT–376, 92-GT–376, International Gas Turbine and Aero-engine Congress , ASME, Germany. Sanaye S, Moradi A. 2001. Dynamic modelling of horizontal flow heat recovery steam generators. 16th International Power System Conference, Conference , Iran. Sanaye S, Moradi A. 2002. Development of a new simulation program for combined cycle systems. Proceedings of ASME TURBO EXPO 2002, 2002 , The Netherlands. Sanaye S, Moradi A. 2002. Steady and transient analysis of heat recovery steam generators. 17th International Power System Conference, Conference, Iran. Sanaye S, Moradi A. 2003. Performance assessment of a transient model for HRSGs in combined cycle power plants. Proceedings of ASME TURBO EXPO 2003 , U.S.A. Sanaye Sanaye S, Rezazadeh M. 2006. Thermal modelling modelling of HRSG transient behaviour behaviour in combined combined cycle power plants. Proceedings of ASME TURBO EXPO 2006 , Spain. Schmidt D, Arnold M. 2002. The model steam turbine: more details about the heat recovery steam generator evaluating method in a combined cycle plant. Proceedings of ASME TURBO EXPO 2002 , The Netherlands. Tehran CCPP Power Plant Historical Trend Graph Display, 29 November, 2004. Thermo-flow Inc. 2002. GT PRO > MASTER Ver. 10.9. Walter H, Linzer W. 2004. Flow stability of heat recovery steam generators. Proceedings of ASME TURBO EXPO 2004 , Austria.



Transient Thermal Modelling of Heat Recovery Steam Generators in Combined Cycle Power Plants

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