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Research on Remaining Life Evaluation Method of T92 Steel for Superheater Tube Based on Oxide Layer Growth

  • Jiansan Li
  • Haitong WeiEmail author
  • Zhou Yuan
Technical Article---Peer-Reviewed
  • 13 Downloads

Abstract

T92 steel is widely used in high-temperature superheater of supercritical power station boiler, and the researches on its remaining life have always been the hot spot of scholars around the world. In this paper, based on the analysis of high-temperature creep rupture strength data, the optimum C value of Larson–Miller parameter formula for T92 steel is obtained by using isothermal extrapolation method. On this basis, combining the relationship between the thickness of the oxide layer and the operating time, the relationship between the thickness of the oxide layer and the temperature of the tube wall and the relationship between the thickness of the oxide layer and the stress of the tube wall, a new remaining life evaluation formula is deduced. Finally, based on the cumulative creep damage life evaluation method, the service life of superheater tube is divided into three stages, which provides a new reference for the service life evaluation of superheater tube of ultra-supercritical boiler.

Keywords

Larson–Miller parameter Superheater Oxide layer growth Remaining life evaluation Cumulative creep damage 

Introduction

Due to the large heat transfer resistance of the oxide layer, the heat exchange between the steam medium and the wall metal is blocked, which leads to the increase in the temperature of the wall metal. Relevant calculations show that for every 0.025 mm oxide increase, the superheater wall temperature increases by about 1.67 °C. At the same time, exfoliated oxide skin will block the steam flow and cause superheater tube over-temperature explosion. This has become the second major cause of boiler tube failure in the world [1]. T92 steel is widely used in high-temperature superheater of supercritical power station boiler. Therefore, it is of great significance to evaluate the remaining life of T92 steel for superheater tubes. Rolf Sandström et al. [2] combined the precipitation hardening model to derive the life assessment model for ductile fracture of austenitic heat-resistant steel. Purbolaksono et al. [3] found that the major contributor which results in the failure of the tube was interaction between the excessive scale formation on the inner surface and outer wall thinning due to coal-ash corrosion. Kapayeva et al. [4] presented the method that considers a combined effect of overheating and wall thinning. They used LMP method for creep evaluation, while adding the effect of wall thinning. The actual data for the thickness of tube wall and thickness of internal oxide layer were taken from measurements using nondestructive testing methods. Ilman et al. [5] found the cause of failure was overheating due to deposit buildup inside the superheater tube. In this paper, based on the LMP formula, considering the relationship between the thickness of the oxide layer and the operating time and the relationship between the thickness of the oxide layer and the temperature and stress of the tube wall, a new remaining life evaluation formula is derived to evaluate the use of the ultra-supercritical boiler superheater tube life.

Establishment of Remaining Life Assessment Method Under Ideal Conditions

In order to simplify the analysis, the derivation of the remaining life assessment method under ideal conditions mainly considers the following aspects and makes relevant assumptions:
  1. 1.

    Considering the formula for the growth rule of the oxide layer with the boiler operating time.

     
  2. 2.

    Considering the effect of oxide layer thickness on tube temperature and the relationship between them.

     
  3. 3.

    Considering the effect of oxide layer thickness on tube stress and the relationship between them.

     
  4. 4.

    It is assumed that the oxide layer is structurally continuous and isotropic and will not fall off during the growth process.

     
Considering the influence of tube operating temperature, high-temperature corrosion and operating stress state on the remaining life of the superheater tube, the LMP formula with temperature and stress as the parameter variables is selected as the basic formula for evaluating the remaining life of superheater tube. By studying the influence and law of the oxide layer generated by the high-temperature corrosion of the superheater tube on the temperature and stress of the tube, the relationship between each influencing factor and the operation time is derived and the life prediction formula is obtained by combining the LMP formula. Then, using the cumulative creep damage life assessment method from the perspective of safe operation of the tube, the formula is transformed again to obtain a new remaining life assessment method. Finally, the derived formula is synthesized to evaluate the remaining life of the superheater tube. The specific derivation process of the remaining life assessment method is shown in Fig. 1.
Fig. 1

Derivation process of remaining life assessment method

Establishment of the Basic Model of the Life Assessment Method

The life evaluation formula model of T92 steel has been widely concerned at home and abroad. The Larson–Miller parameter method based on creep damage life evaluation is a time–temperature parameter (TTP) method. The method comprehensively considers the stress and temperature during the operation of the boiler superheater tube. And after a lot of verification, the C value in the formula is constantly revised [3], which has played a good guiding role in the life evaluation of the superheater tube of the power station boiler for many years [6].

The Larson–Miller parameter model is as follows:
$$ P(\sigma ) = T(C + \lg t_{\text{r}} ) $$
(1)
or
$$ \lg t_{\text{r}} = \frac{P(\sigma )}{T} - C $$
(2)
where tr is the fracture time; T is the absolute temperature (K); C is the material constant; P(σ) is a stress function, when the stress is determined and the corresponding P(σ) is also determined.
In the TTP model, the parameter P(σ) is generally taken as the cubic function of lgσ:
$$ P(\sigma ) = a + b\lg \sigma + c(\lg \sigma )^{2} + d(\lg \sigma )^{3} $$
(3)
For convenience, Eq (3) can be deformed as follows:
$$ \lg \sigma = a + bP(\sigma ) + cP(\sigma )^{2} + dP(\sigma )^{3} $$
(4)
where a, b, c, d are constants.
Based on LMP model, this paper calculated the C value of LMP formula of T92 steel under different stress conditions by isotherm extrapolation method according to the data of high-temperature creep persistent strength of T92 steel published by Japan National Institute of Materials in 2012, as given in Table 1.
Table 1

Linear fitting results of lgtr and temperature 1/T under different stress values

σ/Mpa

T/°C

Fitting equation

C value

80

625–650–675

y = − 20.92 + 23159.23x

C1 = 20.92

90

625–650–675

y = − 24.89 + 26614.63x

C2 = 24.89

100

625–650–675

y = − 27.29 + 28551.98x

C3 = 27.29

110

625–650–675

y = − 32.30 + 32905.4x

C4 = 32.30

130

600–625–650

y = − 29.41 + 29714.09x

C5 = 29.41

140

600–625–650

y = − 26.76 + 27209.87x

C6 = 26.76

160

600–625–650

y = − 24.98 + 25100.97x

C7 = 24.98

180

550–575–600

y = − 35.29 + 33641.73x

C8 = 35.29

190

550–575–600

y = − 33.96 + 32126.39x

C9 = 33.96

210

550–575–600

y = − 38.91 + 35803.57x

C10 = 38.91

Average value \( \bar{C} \) = 29.47

Table 1 shows the calculation results of C values under 10 stress values and the average values under 10 conditions, a total of 11 C values, and fit equation of lgσ and P(σ). The degree of fit between lgσ and P(σ) is determined by the coefficient of determination (COD) R2 and the adjustable decision coefficient Adj. R2. The closer to 1, the better the degree of fit. The fitting results are given in Table 2.
Table 2

Fitting results of LMP principal curve equation of T92 steel

C value

lgσ = a+b × P+c × P2 + d×P3

R 2

Adj. R2

a

b

c

d

C1 = 20.92

−14.97876

0.00216

−8.23746E−8

8.9505E−13

0.97927

0.97739

C2 = 24.89

−6.81824

8.6542E−4

−2.09939E−8

2.80638E−14

0.99065

0.9898

C3 = 27.29

0.85624

−4.96756E−5

1.36089E−8

−3.6646E−13

0.99317

0.99255

C4 = 32.30

20.10741

−0.00187

6.81892E−8

−8.4807E−13

0.99235

0.99165

C5 = 29.41

8.64311

−8.5289E−4

3.97613E−8

−6.2093E−13

0.99362

0.99304

C6 = 26.76

−0.95225

1.53245E−4

6.42646E−9

−2.8983E−13

0.99283

0.99217

C7 = 24.98

−6.58054

8.37503E−4

−1.9729E−8

1.25266E−14

0.99078

0.98994

C8 = 35.29

32.40352

−0.00281

8.96105E−8

−9.7377E−13

0.98949

0.98853

C9 = 33.96

26.91026

−0.00241

8.09986E−8

−9.9158E−13

0.99092

0.99009

C10 = 38.91

47.11671

−0.00375

1.06526E−7

−1.0262E−12

0.98474

0.98335

\( \bar{C} \) = 29.47

8.8808

−8.75846E−4

4.0458E−8

−6.2715E−13

0.99361

0.99303

As given in Table 2, when C = 29.40979, the coefficient of determination (COD) R2 is higher than when other C values are taken and when C = 20.91966, the coefficient of determination (COD) R2 is lower than when other C values are taken. These two C values are selected and substituted into the actual equation to make the relation diagram of fracture time and stress, and the results were compared with the experimental test data of creep fracture of T92 steel, as shown in Fig. 2. It can be found that the LMP equation with parameter C = 29.40979 is very close to the measured data in the range of 550–675 °C. It coincides basically with the measured data and has a high degree of fitting. However, the LMP equation under parameter C = 20.91966 is far from the measured data, which basically does not coincide with each other. Therefore, when C = 29.40979, the equation is closest to the experimental data point, and the agreement degree is the highest.
Fig. 2

Comparison of the stress–endurance life prediction curve of T92 steel under different LMP constants C with experimental data

So the LMP model of T92 steel is as follows:
$$ \begin{aligned} & \lg \sigma = 8.64311 - 8.5289 \times 10^{ - 4} P \\ & \quad + 3.97613 \times 10^{ - 8} P^{2} + 6.2093 \times 10^{ - 13} P^{3} \\ \end{aligned} $$
(5)
$$ P = T(29.40979 + \lg t_{\text{r}} ) $$
(6)
where σ is stress; T is temperature (K); and tr is fracture time
Figure 3 shows a comparison between the life prediction results of the T92 steel LMP model and the data published by the European Creep Collaborative Committee (ECCC) database [7]. It can be seen from the figure that the life prediction equation derived from the LMP method when the parameter C = 29.40979 is selected is relatively accurate for the life prediction of T92 steel.
Fig. 3

Prediction results of the LMP model of T92 steel and results of ECCC database

Relationship Between Growth Thickness of Oxide Layer and Operation Time of Boiler

The oxide layer on the inner wall of the ultra-supercritical boiler superheater tube is formed by chemical reaction between the inner wall of the high-temperature tube and the high-temperature and high-pressure steam. In the high-temperature and high-pressure steam environment, the formation of oxide layer in the tube is a natural process. The thickness and growth rate of oxide layer are the result of multiple factors. According to the study of Wright and Pint of oak ridge national laboratory (ORNL), the thickness growth of the oxide layer is as follows [8]:
$$ \varepsilon = A \cdot e^{ - Q/RT} \cdot t^{1/n} $$
(7)
where ε is the thickness of oxide layer; A is the Arrhenius constant; Q is the process rate control activation energy; R is the gas constant; T is absolute temperature (K); and t is operation hours.

In general, the index n is related to the actual working condition, and the value ranges from 1 to 2. When the reaction kinetics curve shows linear oxidation, the index n = 1; when the reaction kinetic curve shows parabolic oxidation, the index n = 2. According to the experimental study of high-temperature steam of T92 steel, the reaction kinetic curve of steam oxidation of T92 steel is parabolic oxidation [9], so the index n in the formula is 2.

The Arrhenius constant A is related to the composition of the metal alloy material. When the Cr content in the alloy is 0–2%, A = 3.70; when the Cr content in the alloy is 9–12%, A = 230.5, so A of T92 material is 230.5 [10].

The process rate control activation energy Q is related to the metal material and operating conditions. In the 9–12% Cr alloy, when the temperature is between 290 and 700 °C, Q is about 146 kJ/mol.

The gas constant R is the ratio of the product of the absolute pressure p of the ideal gas and the specific volume v to the thermodynamic temperature T, and R is 8.314 J/(mol*K).

The maximum temperature T of tube operation is 953 K according to the T92 steel manual.

Therefore, the growth formula of the oxide layer inside the superheater tube of ultra-supercritical boiler (T92 steel) is as follows:
$$ \varepsilon = 2.29094t^{0.5} $$
(8)

The Formula of Remaining Life is Obtained by Combining L–M Formula

Through the analysis of the operating stress of superheater tube, the initial stress value of tube wall is about 47 MPa. The initial stress value is taken into Eq 5 to obtain P(σ) = 32215.8 and bring P(σ) into the LMP formula to get the remaining life of T92 steel as follows:
$$ t_{\text{r}} = 10^{{\left( {\frac{32215.8}{T} - 29.40979} \right)}} $$
(9)
The equation between the thickness of oxide layer and the maximum wall temperature (outside wall temperature) is obtained by numerical simulation as follows:
$$ T = 917.78 + 0.072\varepsilon $$
(10)
where T is the highest wall temperature of the tube (K) and ε is thickness of oxide layer.
Substituting Eq 10 into Eq 9 yields:
$$ t_{\text{r}} = 10^{{\left( {\frac{32215.8}{917.78 + 0.072\varepsilon } - 29.40979} \right)}} $$
(11)
And substituting Eq 8 into Eq 11 yields:
$$ t_{\text{r}} = 10^{{^{{\left( {\frac{32215.8}{{917.78 + 0.16494768t^{0.5} }} - 29.40979} \right)}} }} $$
(12)
where tr is fracture time an t is operation hours.
Thus, the relationship between the remaining life of superheater tube of ultra-supercritical boiler and the operating time of the unit can be obtained. According to Eq 12, the relation diagram of remaining life of tube with unit operation time is made, as shown in Fig. 4. As the unit’s operating time increases, the remaining life of the superheater tube decreases gradually and approaches zero. Since the growth of the oxide layer exhibits a parabolic law, the remaining life of the tube in the initial stage of service declines drastically, and the rate of decline is large. As the formation of the oxide layer is stable, the rate of decline tends to moderate, but, at this time, the remaining life of the superheater tube has been greatly reduced, and the safety risk of the unit operation has intensified.
Fig. 4

Relationship between residual life and running time of random group of superheater tube in a power plant

Remaining Life Assessment Method Based on Cumulative Creep Damage

The life assessment method for cumulative creep damage is to consider the problem from a dynamic perspective. During the operation of the unit, the temperature and stress of the tube are varied. In order to adapt to this change, Robinson’s life fraction rule [11] proposed a cumulative creep damage life assessment method. For the calculation of cumulative creep damage, each damage unit is calculated according to each temperature and stress level. When the sum of these damages reaches 1, it can be deemed as the failure of the pressure tube. The cumulative creep damage formula is as follows:
$$ D_{1} = \sum\limits_{i = 1}^{n} {\frac{{t_{\text{i}} }}{{t_{\text{ri}} }}} \le 1 $$
(13)
where ti is the operating time of the pressurized tube under ith stress and temperature and tri is the creep rupture time of pressure tube under ith stress and temperature.
From Eq 12, it is known that the remaining life of the superheater tube is different under different operating times, that is, the remaining life of the tube is time-varying under different temperatures and stresses. So Eq 13 can be expanded as shown in Eq 14. Since the operating conditions are constantly changing, the corresponding t1, t2tn are consecutive infinitesimal instantaneous time periods, and these instantaneous times can be represented by ∆t. Equation 14 can be transformed into Eq 15. Since tr is a function of the unit operating time t and is continuous, 1/tr can be regarded as a function of the unit operating time t, denoted as f(t). Then, Eq 16 can be regarded as the definite integral of the integrand function f(t), so that Eq 17 can be obtained.
$$ \sum\limits_{i = 1}^{n} {\frac{{t_{i} }}{{t_{\text{ri}} }}} = \frac{{t_{1} }}{{t_{{{\text{r}}1}} }} + \frac{{t_{2} }}{{t_{{{\text{r}}2}} }} + \frac{{t_{3} }}{{t_{{{\text{r}}3}} }} + \cdots + \frac{{t_{\text{n}} }}{{t_{\text{rn}} }} $$
(14)
$$ \sum\limits_{i = 1}^{n} {\frac{{t_{\text{i}} }}{{t_{\text{ri}} }}} = \mathop {\lim }\limits_{\Delta t \to 0} \sum\limits_{i = 1}^{n} {\frac{1}{{t_{\text{ri}} }}} \Delta t $$
(15)
$$ \mathop {\lim }\limits_{\Delta t \to 0} \sum\limits_{i = 1}^{n} {\frac{1}{{t_{\text{ri}} }}} \Delta t = \int_{0}^{t} {f(t){\text{d}}t} $$
(16)
$$ D_{1} = \int_{0}^{t} {f(t){\text{d}}t} $$
(17)

According to Eq 17, the value of the integral upper limit t of f(t) can be calculated when the pressure tube is identified as cumulative creep damage failure, that is, when D1 = 1. After the calculation of Mathematica1 1.2 software, when the operating time of a power plant unit is t = 49202.1, D1 = 1. It means that the boiler superheater tube has been identified as cumulative creep damage failure after the unit has been running for 49,202.1 h. From the perspective of safe operation of the boiler, this situation requires the replacement of a new superheater tube to ensure safe operation of the units.

According to Eq 12, when the unit runs for 49,202.1 h, the remaining life tr of the superheater tube is 22,213.4 h. Combined with the boiler overhaul work, the service life of superheater tube made of T92 steel for an ultra-supercritical unit of a power plant can be divided into three stages, as shown in Fig. 5. The first stage is the normal operation phase of the superheater tube. (The unit’s operation time is about 0–50,000 h.) When the superheater tube system does not have a safety accident such as a squib, the maintenance work can be carried out normally. The second stage is the critical aging stage of the superheater tube. (The unit’s operation time is about 50,000–72,000 h.) In this stage, the operation state of the superheater tube needs to be closely monitored. The sampling density can be increased appropriately in the maintenance work, and the operation state and remaining life of the tube can be evaluated by various testing methods. The third stage is the dangerous stage of the superheater tube. (The unit’s operation time is over 72,000 h.) From the point of view of the safe operation of the unit, the condition of replacing the new tube has been reached. Even if there is no similar squib accident, the subsequent service time of the tube should be carefully considered, and the parameters of these long-serving tubes should be closely monitored.
Fig. 5

Three life stages of superheater tube made of T92 steel in an ultra-supercritical unit of a power plant

Conclusion

This paper is mainly based on the creep fracture data of superheater tube T92 steel, using the isotherm extrapolation method to complete the required data, and deduces the optimal C value of the LMP formula of T92 steel. The formula is validated using data published by the European Creep Collaborative Committee (ECCC). Then, a new method for predicting the remaining life of superheater tube is derived by combining the variation law of wall temperature and stress along the growth of oxide layer, the LMP formula and the creep damage life evaluation method. At last, the remaining life of the T92 steel used in the superheater tube of a power plant is evaluated and the operation and maintenance opinions are put forward. Conclusions can be drawn as follows:
  1. 1.

    It is deduced that the optimum C value of LMP formula based on T92 steel is 29.40979.

     
  2. 2.

    According to the remaining life assessment method derived in this paper, in the practical situation, the power plant operators detect the oxide thickness of the tubes and then substitute the measured data into Eq 8 in the text to calculate the running time. Finally, the calculated running time is substituted into Eq 12 in the text to get the remaining time.

     

Notes

References

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Copyright information

© ASM International 2019

Authors and Affiliations

  1. 1.School of Mechanical and Automotive EngineeringSouth China University of TechnologyGuangzhouPeople’s Republic of China

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