Corrosion Science 51 (2009) 1022–1029

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Corrosion Science

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Prediction of oxide scale growth in superheater and reheater tubes

J. Purbolaksono a,*, A. Khinani a, A.Z. Rashid a, A.A. Ali a, N.F. Nordin b

a Department of Mechanical Engineering, Universiti Tenaga Nasional, Km 7 Jalan Kajang-Puchong, Kajang 43009, Selangor, Malaysiab TNB Research Sdn Bhd, No. 1 Lorong Air Hitam, Kajang 43000, Selangor, Malaysia

a r t i c l e i n f o

Article history:Received 20 August 2008Accepted 24 February 2009Available online 6 March 2009

Keywords:A. SteelA. SteamB. Modeling studiesB. Heat transferC. Oxidation

0010-938X/$ - see front matter � 2009 Elsevier Ltd. Adoi:10.1016/j.corsci.2009.02.025

* Corresponding author. Tel.: +60 3 89212213; fax:E-mail addresses: judha@uniten.edu.my,

(J. Purbolaksono).

a b s t r a c t

In this paper a procedure on how to estimate the oxide scale growth in superheater and reheater tubeutilizing the empirical formulae and the finite element modeling is proposed. An iterative procedure con-sisting of empirical formulae and numerical simulation is used to determine scale thickness as both tem-perature and time increase. Results of the scale thickness over period of time for two different designtemperatures of the steam and different heat transfer parameters are presented. The procedures may pro-vide better estimation on the oxide scale growth, provided that all the heat transfer parameters are wellspecified.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

Failures resulting from long-term overheating occur in steam-cooled tubes such as superheaters and reheaters. As reported byPort and Herro [1], almost 90% of failures caused by long-termoverheating occur in superheaters, reheaters and wall tubes. Tubesthat are especially subjected to overheating often contain signifi-cant deposits. The deposits will reduce coolant flow, and the tubesexperience excessive fire-side heat input. They also described thatheat transfer is markedly influenced by a thin gas film that nor-mally exists on external surfaces. A temperature drop commonlyoccurs across this film. Scales and other materials on external sur-faces will slightly reduce metals temperatures. The thermal resis-tance of the tube wall may cause a very slight drop intemperature across the wall. When heat transfer through thesteam-side surface is considered, the effect of deposits is reversed.Steam layers and scales insulate the metal from the cooling effectsof the steam, resulting in reduced heat transfer into the steam andincreased metal temperatures.

When the tube metal is in contact with the steam over period oftime, the oxidation process may begin to form a layer of magnetite(Fe3O4) scale. In the prolonged exposure this phenomenon willworsen situation that leads to potential creep rupture problems.Scales inside the superheater and reheater steam tubes have alsobeen found to be one of the major contributors to the tube failure.Heat transfer rate across the tube also decreases due to the accu-mulated scales inside the tube.

ll rights reserved.

+60 3 89212116.j.purbolaksono@gmail.com

A further effect of growing scales is that the tube will have high-er temperatures than those as originally specified. Such exposuremay cause degradation of the tube alloy, and this eventually willlead to tube rupture. It is estimated that 10% of all power-plantbreakdowns are caused by creep fractures of boiler tubes due tothe scales formation [2].

Clark et al. [3], who were working for Aptech Engineering Ser-vices Inc., provided a validated procedure in the form of computercode for predicting the remaining useful life of SA213-T22 super-heater and reheater tubes. One of the important tasks they per-formed is acquisition and compilation of oxide growthinformation for 2.25%Cr-1Mo steel. The procedure was to be basedon steam-side oxide scale measurements by ultrasonic technique,tube geometry measurements and other readily available operat-ing parameters.

Viswanathan et al. [4,5] reported a methodology developed byElectric Power Research Institute (EPRI) and its contractors to helputilities make more informed run/replace decisions for tubes byjudiciously combining calculation, nondestructive, and destructiveevaluations. In the methodology, the tubes/tube assemblies at riskare identified by ultrasonically measuring the thickest steam-sideoxide scale and thinnest wall thickness in the tubes. The researchhas further refined the methodology by validating the ultrasonictechnique for scale measurement, identifying the appropriatestress formula and oxide growth laws.

Babcock & Wilcox Company, USA, has designed and built theportable, ultrasonic Nondestructive Oxide Thickness InspectionSystem (NOTIS�) for measuring oxide scale on the inner surfaceof tubes [6]. The application of NOTIS� makes it possible to non-destructively assess a large number of tubes within asuperheater.

Initial tube thickness

Hot gases

Steam Oxide Scale

100 mm

X Remaining metal thicknessHollow Radius

Steel

Fig. 1. Model of the superheater and reheater tubes with scale on the inner surface.

Table 1Geometries of the tubes.

Tube Inner radius (m) Outer radius (m)

1 0.0219 0.02542 0.0219 0.02743 0.0199 0.0254

Table 2Properties of steam and solid materials.

Temperature, 540 �C Temperature, 605 �C

Inlet steam properties [11]Thermal conductivity 0.0604 W/m C 0.0662 W/m CSpecific heat 2161 J/kg C 2205 J/kg CDensity 0.2697 kg/m3 0.2489 kg/m3

Dynamic viscosity 2.834 e�05 N s/m2 3.071 e�05 N s/m2

Water wall properties [7]Tube material SA213-T22Thermal conductivity 34.606 W/m C

Fe3O4 iron oxide (magnetite) [7]Thermal conductivity 0.592 W/m C

J. Purbolaksono et al. / Corrosion Science 51 (2009) 1022–1029 1023

An accurate prediction of the scale growth on the inner surfacesof the superheater and reheater tubes will aid the power plantinspectors or engineers in order to evaluate the remaining life ofthe boiler tubes. French [7] described the procedures to estimatethe growth of scale thickness on the inner surface of the tubesusing empirical formula correlating scale thickness with Larsen-Miller parameter [8] and approximated formulae of the tempera-ture increase for limited cases.

Ennis and Quadakkers [9] discussed the significance of the for-mation of thick oxide scales during exposure of Cr steels in steam-containing environments on the service life of components. Thequantitative effects of the loss of load-bearing cross-section onthe creep rupture life are presented. Potentially much more dam-aging is, however, the thermal insulation effect of the porous, thickoxide scales, which leads to overheating of heat transfer tubes. Thehigher metal temperatures will then lead to early failure by creep.The scale present after 10,000 h exposure in steam may be suffi-cient to cause a temperature increase which will reduce the rup-ture time for a constant stress. They also reported severalconsequences of the formation of thick oxide scales for the servicebehaviour of components.

Starr et al. [10] proposed an expert system for identifying theroot causes of the failures in superheater tubing made of the P91and P92 martensitic alloys. The system may encapsulate currentknowledge about superheater problems in the form of ‘‘If-Then”rules. Root causes of creep failures include furnace design andoperation, overestimation of alloy creep properties, inadequateheat treatment and a non-optimum content of strengthening ele-ments. A characteristic of the P91 and P92 martensitic alloys is thatoxidation on the steam side of the tubing can induce prematurefailures due to the insulating effect of the oxide scales raising tubetemperatures. In addition, scale spallation could also increase tubetemperatures, as spallation debris may collect in the bottom oftubes, blocking steam flow. Attention is drawn to a potential ‘‘run-away affect” in which the tube temperature and rate of oxidationincrease with time as the oxide builds up. The root cause of thiscould either be excessive rates of heat transfer or could be due toinadequate oxidation resistance caused by low levels of protectiveelements.

With the respect to the concerns stated in the previous works[1–7,9,10], the present study confined the analysis in the absenceof oxide scale developed on the external surface of the boiler tubes.The procedure on how to estimate oxide scale growth in reheaterand superheater tubes utilizing the empirical formula correlatingscale thickness with Larsen-Miller parameter [8] and the finite ele-ment modeling is proposed in this paper. Finite element models forheat transfer analyses, that involve forced convections on the innersurface due to the turbulent flow of steam and on the outer surfacedue to cross flow of the hot flue gas over bare tubes, are carried outin order to obtain temperature distribution in the tube. An iterativeprocedure is used to determine scale thickness as both tempera-ture and time increase. The scale thickness over period of timefor two different design temperatures for steam and different heattransfer parameters is presented. The finite element analysis is car-ried out using software package of ANSYS.

2. Numerical models

In modeling of the steady state heat transfer for the problemusing ANSYS, the area of the model is divided into two regions,i.e. scale region and tube region (see Fig. 1). The steam region is ta-ken into account in determining the convection coefficient ofsteam film for fully developed turbulent flow in circular tube. Mod-el of the tube section used is 100 mm in length. Three differentgeometries of the tube as shown in Table 1 are used. Steam flowsthrough the internal of tube with two different inlet temperatures

of 540 and 605 �C, and the detailed other heat transfer parametersare tabulated in Tables 2–4. Heat transfer along the external sur-face between the flue gas and the tube wall is considered as forcedconvection heat transfer due to cross flow of the hot flue gas overbare tubes. The material of the seamless ferritic low-alloy steeltube used in this work is SA213-T22 (see Table 2 for its thermalconductivity). The chemical composition of the material is listedin Table 5. Ferritic low-alloy material such as SA213-T22 generallycannot withstand highly oxidizing environment for a long period oftime. The use of the material is usually limited to locations wherethe temperatures are relatively lower.

The steam-side scale is usually reported to be duplex (inner spi-nel layer and outer magnetite layer) or triplex (inner spinel layer,middle magnetite layer and outer hematite layer). In this studymaterial of the scale is treated to be all magnetite.

Phenomenon of heat transfer inside the boiler tube is consid-ered as forced convection with turbulent flow. Correlation for fullydeveloped turbulent flow in tube is expressed as [11]:

Nus ¼ 0:023ðResÞ0:8ðPrsÞ0:4 ð1Þ

where Res is Reynolds number that may be expressed as

Res ¼4 ms

o

pDlsð2Þ

Table 3Combinations of the studied models.

Model Steamtemperature(�C)

Mass flowrate (kg/h)

Steampressure(MPa)

Flue gastemperature(�C)

Tube

1 540 3600 4 800 12 540 720 4 800 13 540 3600 4 900 14 540 3600 4 1000 15 540 3600 4 900 26 540 3600 4 900 37 605 3600 4 800 1

Table 4Properties of the flue gas and convection coefficients at different temperatures [11].

Temperature (�C) 800 900 1000

Dynamics viscosity lg (N s/m2) 0.0418 0.0442 0.0465Specific heat Cpg (J/kg �C) 3158 3220 3277Thermal conductivity kg (W/m �C) 0.0410 0.0440 0.0469

Table 5Chemical composition of SA213-T22 [12].

Code C Si Mn P(max)

S(max)

Cr Mo

SA213-T22

0.05–0.15

0.5 0.3–0.6

0.025 0.025 1.90–2.60

0.87–1.13

Table 7Parameters used to determine gas mass velocity G.

1024 J. Purbolaksono et al. / Corrosion Science 51 (2009) 1022–1029

in which mso

is mass flow rate of the steam; D is the inner diameterof the tube; ls is steam viscosity, and Prs is its Prandtl number thatis defined as

Prs ¼lsCps

ksð3Þ

in which Cps and ks are specific heat and thermal conductivity of thesteam, respectively.

Eq. (1) must comply with the following conditions:

– Fluid properties are evaluated at the mean bulk temperature.– Res > 10;000.– 0:7 < Prs < 100.– L/D P 10; L is the length of the tube.

Convection coefficient of steam film for fully developed turbu-lent flow in circular tube is expressed as [11]:

hs ¼ 0:023ks

DðResÞ0:8ðPrsÞ0:4 ð4Þ

where ks is steam conductivity. The convection coefficients hs on theinternal surface of the boiler tube are obtained from Eq. (4) usingparameters given in Tables 2 and 3. The coefficient values are pre-sented in Table 6.

Table 6The convection coefficients hs on internal surface of the boiler tube.

Model hs (W/m2 �C)

1 2053.652 566.703 2053.654 2053.655 2053.656 2440.007 2118.21

Heat transfer outside the boiler tube is considered as forcedconvection due to cross flow of the hot flue gas over bare tubes.A conservative estimated convection coefficient of flue gas hg onouter surface of bare tube in inline and staggered arrangements(see Fig. 4) is given by [13]

hg ¼ 0:3312kg

d0ðRegÞ0:6ðPrgÞ0:33 ð5Þ

where kg is flue gas conductivity; d0 is outer diameter of the tube;Prg is defined as

Prg ¼lgCpg

kgð6Þ

in which Cpg and kg are specific heat and thermal conductivity of theflue gas, respectively. The corresponding Reynolds number Reg maybe expressed as

Reg ¼Gd0

12lgð7Þ

where G is gas mass velocity and may be defined as

G ¼ 12Wg

NwLðSt � d0Þð8Þ

in which Wg is gas flow; Nw is number of tube wide; St is transversepitch (see Fig. 4), and L is the tube length. In this study parametersused to determine gas mass velocity are given in Table 7. Composi-tions of flue gas at 15% excess air as shown in Table 8 is used in thisstudy. The convection coefficients hg on external surface of the boi-ler tube are obtained from Eq. (5) using parameters given in Tables4 and 7. The coefficient values are presented in Table 9.

Superheater and reheater tubes operate at a continuallyincreasing temperature, and a prediction must be made of scalethickness as a function of time and temperature. In this work in or-der to perform a scale growth prediction, steam-side scale forma-tion for ferritic steel of 1–3% chromium correlated with theLarsen-Miller parameter as reported by Rehn et al. [8] is utilized(see Fig. 2). The data of Fig. 2 may be approximated as

logX

0:0254

� �¼ 0:00022P � 7:25 ð9Þ

where X is scale thickness in mm.In the Larsen-Miller method, time and temperature are related

by the following equation:

95

T þ 492� �

ðC þ log tÞ ¼ P ð10Þ

where P is the Larsen-Miller parameter; T is the temperature in de-gree Celsius; t is the service time in hours; C is a constant equal to 20.

The increasing of metal temperature DT for the reheater orsuperheater tube (SA213-T22) may be obtained from the

Table 8Compositions of flue gas at 15% excess air [13].

Nitrogen (mole %) 71.08Oxygen (mole %) 2.46Carbon dioxide (mole %) 8.29Water (mole %) 18.17

Gas flow (kg/h) 400,000Number of tube wide 32Transverse pitch (m) 0.1016Tube length (m) 10

Table 9The convection coefficients hg on external surface of the boiler tube.

Temperature (�C) 800 900 1000

Outer diameter of tube (m)0.0508 0.0508 0.0548 0.0508

Convection coefficient hg (W/m2 �C) 126.01 130.96 133.47 135.62

Laboratory data

Y 621 C/ 2500 hr

Z 649 C/ 2500 hr

X 538 C/ 2500 hr0

0

0

Parameter 34,000 36,000 38,000 40,000 42,000

P = (9/5 T + 492) (20 + log t)

25

50

100

150

250

500

Scal

e th

ickn

ess,

µm

538 C - 1 yr 0

538 C - 5 yr 0

538 C - 100,000 hr 0

621 C - 5 yr 0

Field observations year’s exposure

Scal

e thic

knes

s

Pene

tratio

n

Fig. 2. Steam-side scale formation for ferritic steels of 1–3% chromium correlatedwith the Larsen-Miller parameter [8].

J. Purbolaksono et al. / Corrosion Science 51 (2009) 1022–1029 1025

numerical simulation corresponding to the given running hoursand scale thickness. In this work, the simulations performed forthe predictions are made up to the maximum of 160,000 h withan increment of time as shown in Table 10. The iterative proce-dures used to determine scale thickness as a function of time andtemperature are as follows:

Step 1. The design temperature for the steam is set to Ts at theinlet of reheater or superheater tube. From the numerical simula-tion in the absence of scale (X0), the average temperature of Tave1

is the temperature on the inner surface of the tube. Eqs. (9) and

Table 10Total time after the steps of time used in the iterative procedure.

Step h

1 2502 5003 10004 25005 50006 10,0007 20,0008 40,0009 60,000

10 80,00011 100,00012 120,00013 140,00014 160,000

(10) are used to calculate the scale thickness of X1a for the servicehours of 1 h and the scale thickness of for the service hours of250 h (see Table 10) using the average temperature of Tave1. Next,by subtracting one from the other, the scale increase ofDX1(= X1b � X1a) is determined and a new scale thickness ofX1(= X0 + DX1) is obtained.

Step 2. The average temperature of Tave2 is then determinedfrom the numerical modeling with the new scale thickness onthe inner surface. The average temperature of Tave2 obtainedfrom the average of the inner surface and the scale/metal inter-face temperatures is then used to calculate the incremental scalethickness from 250 to 500 h using Eqs. (9) and (10). For servicehours of 500 h, P is calculated using Eq. (10) and X2b is foundfrom Eq. (9). For service hours of 250 h, P is calculated usingEq. (10) and X2a is found from Eq. (9). Subtracting one fromthe other (X2b � X2a) produces the incremental scale formationfrom 250 to 500 h, which is added to X1 to give a new scalethickness of X2. Repeat Step 2 for further predictions up to themaximum of 160,000 h with the steps of time shown inTable 10.

Since the initial increment of time determines the furtherestimation results, it is proposed to use the steps of time asshown in Table 10. A smaller increment of time might providea better estimation, whereas a bigger increment of time for ini-tial iteration may be resulting in inaccuracy estimation or lessconservative prediction. For estimations starting from the servicehours of 20,000 h, an increment of time may be proposed to betaken at every 20,000 h. There is general agreement that thegrowth of thick scales on iron follows a parabolic-rate law [7]and [14]. However, in the extreme conditions with very highsteam and flue gas temperatures the scale growth will initiallyfollow a parabolic-rate and then tends to follow an exponen-tial-rate [3].

Finite element models are generated according to the geome-try of the tube, the scale thickness and heat transfer parametersgoverning the problem. It is important to note that all the geo-metrical units used for modeling are in m. Hence, the meshingsize control of 0.0001 is used to generate the 2D solid triangularelements in order to allow the model having appropriate size ofelements. The properties of the elements are then defined as 2D-axisymmetric solid elements. As stated in Step 1, the finite ele-ment model is produced in the absence of oxide scale. The bulktemperature and convection coefficient hg of the flue gas are ap-plied on the right edge of the model (see Fig. 1). Next, the bulktemperature and convection coefficient hs of the steam are ap-plied on the left edge of the model. In the presence of the oxidescale as stated in Step 2 the model will have two domain areas,i.e. scale and tube metal. In order to make connectivity of thedomain areas at scale/metal interface, a merge-size control of0.00001 is used. The merge-size control should considerably besmaller than the meshing size control. The bulk temperatureand convection coefficient hg of the flue gas are applied on theright edge of the tube metal region and the bulk temperatureand convection coefficient hs of the steam are applied on the leftedge of the oxide scale region. Fig. 3 shows the isometric view ofthe 3=4 expansion model from 2D-axisymmetric model and theestimated temperature distribution in Tube 1 with the steamtemperature of 540 �C and the flue temperature of 900 �C forthe service hours of 60,000 h.

3. Results and discussion

Results of scale thickness predictions over the increasing of ser-vice hours obtained using the iterative procedures with differentheat transfer parameters as specified in Tables 2–4 are plotted in

587.384

584.688

581.993

579.297

576.601

573.905

571.209

568.513

565.817

563.131

3/4 expansion 2D axisymmetric

Fig. 3. Temperature distribution in Tube 1 with the steam temperature of 540 �Cand the flue temperature of 900 �C for the service hours of 60,000 h.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Service time, h

Scal

e th

ickn

ess,

mm

Model 3, Tube 1Model 5, Tube 2Model 6, Tube 3

Fig. 5. Estimated scale thickness as a function of time with the steam temperatureof 540 �C for different tube geometries (see Table 3).

1026 J. Purbolaksono et al. / Corrosion Science 51 (2009) 1022–1029

Figs. 5–8. The corresponding temperatures at scale/metal interfaceare presented in Table 11. Some features may be deduced accord-ing to the specified parameters as follows:

– Geometries of the tubes. Three different sizes of tube asshown in Table 1 are used in this study. It can be seen fromFig. 5, the largest estimated scale thickness at every servicehours is found in Tube 2. According to the geometry of thetubes shown in Table 1, inner radius of Tube 2 is bigger thanthe radius of Tube 3; the tube thickness of Tube 2 is largerthan the thickness of Tube 1. It is clear that the geometryof tube influences the growth of oxide scale. The thinnertube has less incremental scale formation. It means that themetal temperature is also less increasing (see Table 11).However, the thinner tube causes higher operational hoopstress. Conversely, the thicker tubes have the greater growthof scale as a result of higher temperature increase. It mayresult in changes of microstructure of the tube metal andcause material degradation.

– Mass flow rate of steam. Mass flow rate is taken into accountin determining coefficient of the forced convection. Thelower mass flow rate of steam at a design temperature willincrease the growth of oxide scale on the inner surface. Itmay indicate that the poor or impaired mass flow rate ofthe steam, e.g. blocking steam flow, will cause significantincrease of the scale growth as a result of higher tempera-ture developed in scale/tube metal interface (see Table 11).

Fig. 4. Inline and staggered arra

The effect of different mass flow rate of steam on scalegrowth is shown in Fig. 6.

– Steam temperature. For design temperature of 605 �C shownin Fig. 7, the curve tends to have higher increasing of scalethickness at the same of service hours. This feature is relatedto the reduced oxidation resistance if the tube metal hashigher temperature. The increasing of scale thickness conse-quently becomes larger, and it will result in the greater tem-perature increase in the tube metal (see Table 11).

– Convection coefficient on the outer surface of tube and flue gastemperature. It can be deduced from Fig. 8, the higher con-vection coefficient and higher flue gas temperature lead toa larger increase of scale thickness. In order to estimatethe growing of scale in a certain tube, the convection coeffi-cient and flue gas temperature used in finite element model-ing may be specified according to the particular location ofthe tube, for instance, the tube situated facing directly tothe furnace section has different convection coefficient andflue gas temperature.

– Increments of time. Fig. 9 shows that a bigger incrementsresults in less conservative estimation. Initial incrementsare particularly important to be treated since they will sig-nificantly affect further estimation during the iterations.

In order to validate the reference data used shown in Fig. 2 andthe results obtained, comparison of the data for a long-term expo-sure needs to be made. However, the heat transfer parameters and

ngements of the bare tubes.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Service time, h

Sca

le t

hic

knes

s, m

m

Model 1, 3600 kg/h

Model 2, 720 kg/h

Fig. 6. Estimated scale thickness as a function of time with the steam temperatureof 540 �C for different mass flow rates of steam (see Table 3).

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Service time, h

Scal

e th

ickn

ess,

mm

Model 1, 5400CModel 7, 6050C

Fig. 7. Estimated scale thickness as a function of time for different steamtemperatures (see Table 3).

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Service time, h

Scal

e th

ickn

ess,

mm

Model 1, 8000C

Model 3, 9000C

Model 4, 10000C

Fig. 8. Estimated scale thickness as a function of time for different flue gastemperatures (see Table 3).

J. Purbolaksono et al. / Corrosion Science 51 (2009) 1022–1029 1027

geometry of the specimens for the reference data (Fig. 2) are notgiven. It might give the comparison to be compromised. Scalethickness for service time of 100,000 h at 538 �C is used for com-parison with the estimated results obtained using the proposedtechnique.

Table 11Temperatures (�C) at the scale/metal interface of the tubes.

Service time (h) Model 1 Model 2 Model 3

0 557.06 592.73 564.47250 558.58 595.06 567.01500 559.05 595.80 567.81

1000 560.21 596.73 568.812500 560.68 598.35 570.545000 561.68 599.95 572.27

10,000 562.95 601.98 574.4620,000 564.53 604.52 577.2340,000 566.52 607.73 580.7660,000 567.92 609.98 583.2780,000 569.04 611.78 585.31

100,000 570.00 613.30 587.04120,000 570.82 614.62 588.57140,000 571.57 615.80 589.95160,000 572.24 616.88 591.21

The corresponding Larsen-Miller parameter P for service time of100,000 h at 538 �C is 36,500. It can be obtained from Fig. 2 that thecorresponding scale thickness is around 140–200 lm (0.14–0.2 mm). It can be seen from Figs. 5–8 that the estimated resultsfor the models with steam temperature of 540� and mass flow rateof 3600 kg/h are ranging from 0.25 to 0.47 mm and showing higherthan those shown in Fig. 2. The differences might be due to differ-ent parameters used. According to Figs. 5–8, parameters governingthe problem such as higher mass flow rate of steam, lower steamand flue gas temperature and smaller inner diameter and thicknessof the tube may reduce the scale growth rate.

Further, it is important to compare the estimated values withthe actual data of the available reports [15] and [16] which wereobtained from dimensional measurements for the scale thicknessof the as-received reheater tube samples taken from Kapar PowerStation Malaysia. Two different cases with different tube diametersfrom two different locations are used. The detailed samples usedare shown in Table 12. Sample for Case 1 was located at the firstrow facing to the burner while the sample for Case 2 was locateda relatively further from the burner. Operating steam temperatureof both tubes is 576 �C. The flue gas temperatures were reportedranging from 800–900 �C. Parameters used to determine gas massvelocity G and the estimated convection coefficients hs and hg forthe internal and external surfaces are shown in Tables 13 and 14,respectively. The estimated scale thickness and the actual dataare plotted in Fig. 10. It can be seen that the scale thickness forthe actual data of Case 1 is relatively close to the estimated scale

Model 4 Model 5 Model 6 Model 7

572.28 566.49 562.89 617.43576.22 569.35 565.30 621.39577.47 570.24 566.13 622.68579.06 571.37 567.20 624.33581.83 573.32 569.04 627.19584.61 575.27 570.87 630.05588.17 577.74 573.18 633.66592.74 580.88 576.13 638.21598.65 584.88 579.85 643.92602.96 587.74 582.52 647.96606.50 590.05 584.68 651.17609.55 592.04 586.53 653.88612.27 593.78 588.15 656.25614.75 595.35 589.61 658.35617.04 596.79 590.95 660.26

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 20000 40000 60000 80000 100000 120000 140000 160000 180000

Service time, h

Scal

e th

ickn

ess,

mm

Model 1 with steps of time as specified in Table 10

Model1 with increment of time at every 20,000 h

Fig. 9. Estimated scale thickness as a function of time for different increment oftime.

Table 12Oxide scale thickness and geometry of the as-received tubes.

Case Inner radius(m)

Tube thickness(mm)

Servicetime (h)

Year offailure

Scalethickness, mm

1 0.0225 4 92,525 2001 0.682 0.0219 3.5 117,522 2003 0.58

Table 13Parameters used to determine gas mass velocity G for validation of actual data.

Gas flow (kg/h) 500,000Number of tube wide 50Transverse pitch (m) 0.1016Tube length (m) 8

Table 14The estimated convection coefficients hs and hg for internal and external surfaces,respectively.

Case hs (W/m2 �C) hg (W/m2 �C)

1 1990.59 125.312 2053.65 126.01

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0 20000 40000 60000 80000 100000 120000 140000

Service time, h

Scal

e th

ickn

ess,

mm

Actual Case 1 [15]

Actual Case 2 [16]

Estimated Case 1, 8000C

Estimated Case 1, 9000C

Estimated Case 2, 8000C

Estimated Case 2, 9000C

Fig. 10. The estimated scale thickness and the actual data.

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0 20000 40000 60000 80000 100000 120000 140000 160000 180000Service time, h

Scal

e th

ickn

ess,

mm

Model 1 B = 0.5B = 1.0B = 2.0

Fig. 11. The oxide scale growths for different constants B for the approximatedincreases of temperature.

1028 J. Purbolaksono et al. / Corrosion Science 51 (2009) 1022–1029

thickness for the flue gas temperature of 900 �C. It is apparentlyshown to be in good agreement with data with respect to the loca-tion of the tube since the higher temperature of the flue gas willaccelerate scale growth over period of time. Bigger inner diameterand thickness of the tube may also accelerate scale growth. Thescale thickness for Case 2 also fairly agrees with the estimatedscale thickness for the flue gas temperature of 800 �C. It is essentialto make appropriate monitoring of the heat transfer parameterswhich may govern the problem from time to time.

In order to show that the growth of thick scales on iron gener-ally follows a parabolic-rate law as stated by French [7] and Uhlig[14], a temperature increase DT as a function of a scale thicknessincrease DX over a period of time may be used as

DT ¼ B DX ð11Þ

where B is a constant. DT in Eq. (11) may be introduced by adding itwith the temperature on the inner surface stated in Step 1 to re-place the average temperature in Step 2. Model 1 is used to examinethis procedure. It can be seen from Fig. 11 that the oxide scale

growths for different B tend to follow parabolic-rate law. For in-stance, if B is set on trial to be 1 for Model 1, the estimations forthe scale thickness using the given DT over period of time areshown to be in very good agreement with those obtained using pro-cedures given in Steps 1 and 2. It means that the approximated va-lue for B can be well determined for future predictions afterestimations of scale thickness over period of time for the corre-sponding condition using Steps 1 and 2 have been made.

The oxide scale thickness developed on the inner surface ofreheater and superheater tubes over period of time can be esti-mated by utilizing the empirical formula correlating scale thick-ness with Larsen-Miller parameter and the finite elementmodeling. In the finite element simulations, the data for tubegeometries and all the heat transfer parameters that might governthe problem are taken into account in order to determine the tem-perature distribution in tube metal. The temperature increase is animportant influence on the scale growth rates. Data for heat trans-fer parameters according to variations in the operating conditionsin the system may be introduced into the iteration procedure. Bet-ter estimation of the scale growth could be obtained, provided thatall the heat transfer parameters used are well specified.

J. Purbolaksono et al. / Corrosion Science 51 (2009) 1022–1029 1029

4. Conclusions

Estimation on the oxide scale growth in superheater andreheater tube utilizing the empirical formulae and the finite ele-ment modeling was proposed. An iterative procedure was usedto determine scale thickness as both temperature and time in-crease. The scale thickness and the corresponding temperaturesat scale/metal interface over period of time for two different designtemperatures for steam and different heat transfer parameterswere presented. The scale growths were influenced by the tubegeometry and heat transfer parameters such as steam tempera-tures, mass flow rates of steam, flue gas temperatures and convec-tion coefficients on the outer surface of tube. The procedures mayprovide better estimation on the oxide scale growth, provided thatall the heat transfer parameters are well specified.

Acknowledgements

This work is supported by the Ministry of Science Technologyand Innovation, Malaysia through the research projects of IRPA09-99-03-0033 EA001 and Sciencefund 04-02-03-SF0003. Theauthors wish to thank Universiti Tenaga Nasional, Kapar EnergyVentures Sdn Bhd and TNB Research Sdn. Bhd Malaysia for permis-sion of utilizing all the facilities and resources during this study.

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