CN116486950A - Calculation method for inner layer thickness of pearlite heat-resistant steel oxide layer in steam environment - Google Patents
Calculation method for inner layer thickness of pearlite heat-resistant steel oxide layer in steam environment Download PDFInfo
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Abstract
The invention discloses a calculation method of the thickness of an inner layer of a pearlite heat-resistant steel oxide layer in a steam environment. The method comprehensively considers three factors of steam temperature, steam pressure and operation time, which have the greatest influence on the thickness of the oxide layer, and by means of a metal oxidation dynamics model and combining a large amount of actual operation of a power plant and laboratory simulation experiment data, mathematical correction is carried out on a formula, and the method for calculating the thickness of the inner layer of the oxide layer of the T22 pearlite heat-resistant steel under the steam environment is obtained by using linear fitting, curve fitting and other methods. According to the invention, the thickness of the inner layer of the oxide layer of the T22 pearlite heat-resistant steel in the steam environment can be conveniently and rapidly calculated according to the steam temperature, the steam pressure and the running time, and the pipe cutting is not needed for measurement, so that the cost is saved, the thickness of the inner layer of the oxide layer of the pipe is estimated under the condition that the running is not influenced, the oxidation corrosion thinning degree of the inner wall of the pipe is reflected, the reference is provided for evaluating the residual service life of a part, and the safe running of a unit is ensured.
Description
Technical Field
The invention relates to the technical field of pearlite heat-resistant steel oxidation, in particular to a calculation method of the thickness of an inner layer of a pearlite heat-resistant steel oxidation layer in a steam environment.
Background
T22 pearlite heat-resistant steel has excellent high-temperature creep strength, good thermal conductivity and low linear expansion coefficient, and is widely applied to manufacturing important high-temperature parts such as main steam pipes, headers, superheaters, reheaters and the like of subcritical and supercritical (super) critical units. With the increase of the working steam pressure of the unit, the steam oxidation resistance of the pearlite heat-resistant steel becomes one of key factors affecting the service life of high-temperature parts. In the long-term operation process of the high-temperature component, the effective wall thickness of the pipe wall is reduced due to the increase of the thickness of the oxide layer, and the stress of the pipe wall is correspondingly increased; meanwhile, the heat conduction performance of the pipe wall is deteriorated due to the oxide skin, so that the average running temperature of the pipe wall is improved, the pipe wall is in an over-temperature service state for a long time, and when the pipe wall is developed to a certain degree, the pipe explosion accident finally occurs. Therefore, the service life of the part is estimated, early warning is achieved, and in order to reduce accidents, it is very necessary to predict the thickness of the oxide layer of the part serving under steam, such as a superheater, a reheater and the like.
The thickness of the inner layer of the oxide film is calculated by means of an oxidation kinetic model of heat-resistant steel in a steam environment. The current dynamic model of pearlite heat-resistant steel steam oxidation at home and abroad generally only considers the influence of steam temperature, rarely considers the influence of steam pressure change, and especially does not consider the comprehensive influence under the coupling effect of the two. In practice, the steam temperature and steam pressure parameters in the various components of the unit vary widely, e.g., the high temperature reheater steam temperature is higher than the superheater, but the steam pressure is significantly lower than the superheater. Therefore, only the comprehensive influence of the steam temperature and the steam pressure is considered, the thickness of the oxide layer of different parts can be accurately predicted, and the residual life of the oxide layer can be further predicted. In addition, most of the current pearlite heat-resistant steel steam oxidation kinetic models are obtained based on experimental results of an oxidation weight increasing method, and the thickness of an oxide layer cannot be directly calculated. While there are few documents reporting a high temperature steam oxidation kinetic model of pearlitic heat-resistant steel based on the increase in oxide layer thickness, the oxide layer includes an inner layer and an outer layer, and these documents do not distinguish between the outer layer thickness and the inner layer thickness. However, the applicant's research shows that only the increase in the thickness of the inner layer of the oxide layer results in a reduction in the wall thickness of the tube, affecting the life of the tube, and therefore it is more practical to predict the thickness of the inner layer of the oxide layer.
Disclosure of Invention
The invention aims to solve the problems in the prior art, and provides a calculation method for the thickness of the inner layer of the oxide layer of the pearlite heat-resistant steel in the steam environment, which can conveniently and rapidly calculate the thickness of the inner layer of the oxide layer of the T22 heat-resistant steel in the steam according to the steam temperature, the steam pressure and the running time, has high calculation accuracy, can realize the evaluation of the residual life of a high-temperature part without pipe cutting in the actual power plant running, ensures the safe running of a unit, reduces the cost and has important industrial application value.
In order to achieve the above purpose, the technical scheme provided by the invention is as follows:
the method for calculating the thickness of the inner layer of the oxide layer of the pearlite heat-resistant steel in the steam environment is provided, wherein the pearlite heat-resistant steel is T22 heat-resistant steel, and the calculation formula of the thickness of the inner layer of the oxide layer in the steam environment is as follows:
Y＝ω*Y T +(1-ω)*Y p
wherein, the liquid crystal display device comprises a liquid crystal display device,
Y p ＝369.1-0.002736t-68.56p+1.643×10 -8 t 2 +2.302×10 -4 tp+3.214p 2
wherein: y is the thickness of the inner layer of the oxide layer in the steam environment, Y T Is the relation between the temperature and the thickness of the inner layer of the oxide layer in the steam environment, Y p The unit is mu m, which is the relation between the pressure and the thickness of the inner layer of the oxide layer in the steam environment; omega is a weight coefficient, and k is a fitting coefficient; q is activation energy, and the unit is J.mol -1 The method comprises the steps of carrying out a first treatment on the surface of the R is gas constant, T is steamSteam temperature, the unit is K; p is steam pressure in MPa; t is time, and the unit is h;
Y T in the calculation formula of (a):
the activation energy Q and the time t conform to the formula: q= 156908.32387-0.7554t+4.0662×10 -6 t 2 ；
The fitting coefficient k and the temperature T conform to the formula: k= 1.932 ×10 -68 T 23.16 。
According to the scheme, the high-temperature steam temperature ranges from 550 ℃ to 650 ℃ and the steam pressure ranges from 5.0MPa to 25.0MPa.
According to the above scheme, the time t ranges from 1,000 to 150,000 hours.
According to the scheme, when T is less than 600 ℃, the value of omega is 0.2217 +/-0.1317; when T is more than or equal to 600 ℃, the value of omega is 0.7943 +/-0.2049.
There is provided the use of the above calculation method for assessing the life of a pearlitic heat-resistant steel part operating under steam in a power plant.
The invention has the beneficial effects that:
1. the thickness of the inner layer of the steam oxidation layer of the T22 pearlite heat-resistant steel is calculated by combining three factors of steam temperature, steam pressure and operation time, the result is accurate, the error can be controlled within 7%, and the thickness of the inner layer of the oxidation layer can be measured without cutting a pipe in actual power plant operation, so that the cost is reduced, the working efficiency is improved, and the method has more practical value.
2. The thickness of the inner layer of the oxide layer of the T22 pearlite heat-resistant steel in the supercritical (super) steam environment is calculated with high accuracy, the oxidation corrosion thinning degree of the inner wall of the reaction tube can be fully reacted, the residual service life of the part is estimated, the safe operation of the unit is ensured, and the method has important industrial application value.
3. According to the method, different weights of the influence of the temperature on the thickness of the oxide layer in different temperature ranges are determined, and the calculation accuracy is further improved.
Drawings
FIG. 1 shows the thickness Y of the inner layer of the oxide layer in an embodiment of the invention T Fitting graph to Z.
FIG. 2 is a graph showing the relationship between the thickness Yp and the selected pressure p and time t in the embodiment of the present invention
FIG. 3 shows the thickness Y in an embodiment of the present invention p The prediction map is fitted to three repetitions of the actual data for the selected pressure p and time t.
Detailed Description
The technical scheme of the invention is further explained by the specific examples.
1) Thickness of inner layer of oxide layer Y T Relation to temperature T
The influence of the temperature T and the time T on the oxide layer of the high-temperature heating surface of the power station boiler is explored, and the thickness Y of the oxide layer is measured under the high-temperature working condition T Meets the following exponential model rules:
wherein k is a coefficient, Q is metal oxidation activation energy, R is a gas constant, T is temperature, and T is time.
The invention collects a large amount of actual operation and laboratory simulation experiment data of the power plant, including the thickness data of the inner layer of the T22 heat-resistant steel oxide layer under the temperature of 550-650 ℃, the steam pressure of 5.0-25.0 MPa and the oxidation time of 1,000-150,000 h; parameters n, Q, and k in the expression (1) are calculated using the above data. The calculation method is as follows:
step 1: n is calculated
When a specific temperature T is taken, thenIs constant. When the pressure is fixed, substituting experimental data at each temperature T into the equation to perform linear fitting, and obtaining a fitting formula as follows:
t=550℃: y= 0.02859 ± 0.00391t 0.45745±0.01178 ；
T=575 ℃): y= 0.18864 ± 0.00955t 0.47783±0.00437 ；
T=600℃: y= 1.8599 ± 0.10151t 0.51248±0.00475 ；
T=625℃: y= 2.3737 ± 0.10522t 0.6972±0.02447 ；
T=650℃: y= 3.7645 ± 0.21904t 0.14476±0.00209 ；
It can be found that the n value fluctuates around 0.5, which indicates that the oxidation kinetics of the T22 pearlite heat resistant steel substantially conforms to the parabolic law, so taking n to be 0.5, then the formula (1) is modified as:
step 2: find activation energy Q
Taking logarithms from two sides of the (2), and obtaining the following steps:
when a specific time t is taken, ln (kt 0.5 ) The constant, denoted as G, is reduced to:
when t=1,000 h, 10,000h, 50,000h, 100,000h, 150,000h, experimental data are substituted into the fitting formula obtained in step 1, lnY values at t=550 ℃, 575 ℃, 600 ℃, 625 ℃, 650 ℃ are calculated respectively, and then the values are replaced to the formula (3), and the activation energy Q values at different times T are calculated as shown in table 1.
TABLE 1 activation energies at different times
From Table 1, it can be seen that the Q values at different times are different, indicating that the activation energy of the oxidation reaction at different time periods is different. It was found that the oxidation reaction of T22 heat resistant steel is a complex, dynamically changing process, and the reaction mechanism, the products formed, and the composition and structure of the oxides change at different stages of oxidation. Therefore, the invention adopts a mathematical model to fit the change of the activation energy along with time, and the obtained activation energy Q and time t highly conform to the following mathematical model, and the formula is as follows:
Q＝156908.32387-0.7554t+4.0662×10 -6 t 2 (4)
substituting the formula (4) back to the formula (2), and obtaining a corrected thickness formula as follows:
step 3, calculating coefficient k
Selecting a specific temperature T value and a specific running time T, thenIs a fixed value, marked as Z, and the above formula is changed into Y T =k×z. Substituting the data at each temperature into the formula (5) in sequence, and fitting to obtain a coefficient k, wherein the k values at different temperatures are found to be different, the fitting curve is shown in the attached figure 1, and the result is that:
when t=550 ℃, Y T ＝(1.242±0.040)*Z；
When t=575 ℃, Y T ＝(1.861±0.029)*Z；
When t=600 ℃, Y T ＝(2.229±0.031)*Z；
When t=625 ℃, Y T ＝(4.071±0.250)*Z；
When t=650 ℃, Y T ＝(9.124±0.349)*Z。
The relationship between k and temperature T is obtained as follows:
k＝1.932×10 -68 T 23.16 (6)
it can be seen that as the temperature increases, the k value increases, meaning that the higher the temperature, the greater the effect of temperature on the thickness of the oxide layer inner layer. Thus finally obtainingThickness of oxide layer Y T The fitting formula with temperature T is:
in the above formula, the unit of temperature T is K, the unit of time T is h, and the thickness Y of the inner layer of the obtained oxide layer is calculated T In μm.
2) Thickness of inner layer of oxide layer Y p Relationship with vapor pressure p
In order to explore the influence of pressure p and time T on the formation of the high-temperature heating surface oxide layer of the power station boiler, experimental data of the thickness of the inner layer of the T22 heat-resistant steel oxide layer under different times T and different pressures p are subjected to screening treatment, and the results are shown in Table 2:
TABLE 2 inner layer thickness of T22 pearlitic heat-resistant steel oxide at different times and different steam pressures
The data are plotted to obtain the thickness Y of the inner layer of the oxide layer shown in figure 2 p And a plot of selected pressure p versus time t.
It can be seen that the thickness Y p And a binary quadratic function relation exists between the pressure p and the time t, and the following formula is obtained through three-dimensional nonlinear surface fitting:
Y p ＝ a + bt + cp + dt 2 + hpt+ip 2 (8)
step 1: solving coefficients i, h and c containing p terms
When a specific time t is selected, the term containing t is a constant value, the equation (8) is converted into a parabolic equation about p, and the coefficients i, h and c containing p terms can be obtained by fitting after substituting data.
i＝3.214±0.311
h＝2.302×10 -4 ±3.75×10 -5
c＝-68.56±9.51
Step 2: solving for coefficients d, b containing t terms
Similarly, when a specific pressure p is selected, the term containing p is a constant value, the equation (8) is converted into a parabolic equation about t, and the coefficient d, b containing the term t can be obtained by fitting after substituting the data.
d＝1.643×10 -8 ±6.69×10 -9
b＝-0.002736±1.221×10 -3
Step 3: after 5 coefficients are determined, the coefficient a is finally determined. Substituting the obtained coefficient into formula (8), and substituting all data into the formula to perform three-dimensional nonlinear surface fitting to obtain the coefficient a=369.1±77.1. Therefore, formula (8) is rewritten as:
Y p ＝369.1-0.002736t-68.56p+1.643×10 -8 t 2 +2.302×10 -4 tp+3.214p 2 (9)
step 4: the fitting was repeated for fig. 2, and the error rate of each coefficient in equation (9) was verified. The expression of the formula (9) is plotted as a curved surface, and then all data are substituted into the graph, and if the data points basically fall on the curved surface, the predicted result of the formula (9) basically accords with the actual result. As each coefficient value has a certain fluctuation range, 3 times of fitting are performed, so that the accuracy is improved, and the error is reduced. Finally, a three-time repeated fitting prediction graph of the actual data shown in fig. 3 is obtained. It can be found that the data points under different working conditions basically fall on 3 predicted curved surfaces (boundaries), the average error rate is 5%, and the thickness Y under the actual working conditions is explained p The relation between the pressure p and the time t basically accords with the function change rule described by the formula (9), and then each coefficient is determined as follows:
a＝369.1
b＝-0.002736
c＝-68.56
d＝1.643×10 -8
h＝2.302×10 -4
i＝3.214
finally obtaining the thickness Y of the inner layer of the oxide layer p The fitting formula to the vapor pressure p is as follows:
Y p ＝369.1-0.002736t-68.56p+1.643×10 -8 t 2 +2.302×10 -4 tp+3.214p 2 (10)
in the above formula, the unit of time t is h, the unit of steam pressure p is MPa, and the thickness Y of the inner layer of the oxide layer p In μm.
3) Relation between oxide scale inner layer thickness Y and steam temperature T and steam pressure p
In the fitting process of experimental data, if T and p data are simultaneously imported and fitting processing is carried out, the results are not practical, and the error reporting rate is high. The analytical reasons may be: if temperature and pressure are simultaneously introduced into a system, the two physical quantities of temperature and pressure are mutually influenced and changed, the system can generate closed loop repeatability errors, the fitting result is greatly different from the actual situation, the relation between the thickness of the inner layer of the oxide layer and the temperature T or the pressure p of steam is obtained, the weight coefficient of the temperature and the pressure to the thickness is studied, and a calculation formula of the total thickness of the inner layer of the oxide layer containing T and p is determined.
Step 1: the formula for determining the total thickness of the inner layer of the oxide layer is as follows:
Y＝ω* Y T +(1-ω)* Y p (11)
Y p ＝369.1-0.002736t-68.56p+1.643×10 -8 t 2 +2.302×10 -4 tp+3.214p 2
wherein ω is a weight coefficient, Y T Is the relation between the temperature and the thickness of the inner layer of the oxide layer in the steam environment, Y p Is the relation between the pressure in the steam environment and the thickness of the inner layer of the oxide layer. Substituting data at different temperatures and different pressures into the expression to obtain a calculated value, and performing comparison fitting with an actual value.
Step 2: after substituting the measured data of the thickness of the oxide layer at t=550 ℃, 575 ℃, 600 ℃, 625 ℃, 650 ℃ into the fitting, it is found that when the temperature is lower (t=550 ℃, 575 ℃), the value of ω fluctuates within the range of 0.1-0.35, which means that when the temperature is lower, the influence of the temperature on the thickness of the oxide layer is less than the influence of the pressure, and finally the measured data is substituted, and the value of the weight coefficient ω of the fitting obtained temperature T is 0.2217 ± 0.1317, then the formula (11) is changed into:
Y＝(0.2217±0.1317)* Y T +(0.7783±0.1317)* Y p (12)
when the temperature is higher (t=600 ℃, 625 ℃, 650 ℃), the ω value fluctuates in the range of 0.6 to 0.95, which means that when the temperature is higher, the influence of the temperature on the oxide layer thickness exceeds the pressure, and finally the actual measurement data is substituted, the value of the weight coefficient ω of the temperature T obtained by fitting is 0.7943 ± 0.2049, and then the formula (11) is changed into:
Y＝(0.7943±0.2049)* Y T +(0.2057±0.2049)* Y p (13)
as can be seen from the above steps, the weight coefficient ω becomes larger as the temperature increases, which is related to the temperature and the thickness of the oxide layer, Y T Is basically consistent with the change rule of the (c). In summary, the calculation formula of the total thickness Y of the oxide layer inner layer, the temperature T and the vapor pressure p is as follows:
when T < 600 ℃, y= (0.2217 ± 0.1317) ×y T +(0.7783±0.1317)*Y p
When T is more than or equal to 600 ℃, Y= (0.7943 +/-0.2049) Y T +(0.2057±0.2049)*Y p
Y p ＝369.1-0.002736t-68.56p+1.643×10 -8 t 2 +2.302×10 -4 tp+3.214p 2
In the above formula, the unit of the steam temperature T is K, the unit of the steam pressure p is MPa, the unit of the time T is h, and the unit of the oxide layer thickness Y is μm.
Example 1
Eberle et al measured that the thickness of the inner layer of the oxide layer is about 127 μm after T22 steel is oxidized for about 4,380 hours at the steam temperature of 592 ℃ and the steam pressure of 14.5Mpa, and the experimental conditions are substituted into the formula (12) provided by the embodiment of the invention to calculate the thickness of the inner layer of the oxide layer to be about 121.8426 μm, and the error percentage is 4.1%.
Example 2
The calculation method related by the invention is compared with the oxidation experimental result of the T22 steel.
Eberle et al measured that the thickness of the inner layer of the oxide layer was about 660 μm after the T22 steel was oxidized for about 8,742 hours at a steam temperature of 648℃and a steam pressure of 14.5MPa, and the experimental conditions were substituted into the formula (13) provided in the example of the present invention to calculate the thickness of the inner layer of the oxide layer to be about 688.4337 μm, with an error percentage of 4.3%.
Example 3
The calculation method is applied to an actual power plant environment.
The steam temperature of a boiler of a supercritical power plant is about 552 ℃, the steam pressure is about 14.6MPa, the heating surface component adopts T22 steel, and after the operation for about 100,000 hours, the thickness of the inner layer of the oxidation layer in the tube is about 322 mu m.
Substituting the steam temperature in the operation parameters into Y T (equation 7) the thickness of the inner layer of the oxide layer was 343.7852 μm at 100,000h and the error percentage was 6.8%. Substituting the steam pressure in the operation parameters into Y p (equation 10) the thickness of the inner layer of the oxide layer was 294.7941 μm at 100,000h and the error percentage was 8.6%. The two operating parameters are substituted into a formula (12) provided by the embodiment of the invention to calculate that the thickness of the inner layer of the oxide layer is about 304.5923 mu m, and the error is 5.4%.
Therefore, the error is smaller after the temperature and the pressure are comprehensively considered, and the prediction result is more accurate.
Example 4
The calculation method is applied to an actual power plant environment.
The supercritical unit used in a certain power plant has steam temperature of about 566 ℃, steam pressure of 14.6MPa, heating surface component of T22 steel, and thickness of inner layer of oxide layer in tube of about 561 μm after running for about 150,000h.
Substituting the steam temperature in the operation parameters into Y T (equation 7) the 150,000h oxide inner layer thickness was 606.8819 μm with an error percentage of 8.2%. Substituting the steam pressure in the operation parameters into Y p (equation 10) the 150,000h oxide inner layer thickness was 522.6473 μm with an error percentage of 6.8%. The two operating parameters are substituted into a formula (12) provided by the embodiment of the invention to calculate that the thickness of the inner layer of the oxide layer is about 539.4942 mu m, and the error is 3.8%.
Therefore, the error is smaller after the temperature and the pressure are comprehensively considered, and the prediction result is more accurate.
The above examples all show that the thickness of the inner layer of the T22 pearlitic steel oxide film calculated by the method of the invention is in good agreement with the actual measurement result, and the error is within 6%.
The technical scheme of the invention is not limited to the embodiments, and all technical schemes obtained by adopting equivalent substitution modes fall within the scope of the invention.
Claims (5)
1. A calculation method for the thickness of an inner layer of a pearlite heat-resistant steel oxide layer in a steam environment is characterized by comprising the following steps: the pearlite heat-resistant steel is T22 heat-resistant steel, and the calculation formula of the thickness of the inner layer of the oxide layer in the steam environment is as follows:
Y＝ω*Y T +(1-ω)*Y p
wherein, the liquid crystal display device comprises a liquid crystal display device,
Y p ＝369.1-0.002736t-68.56p+1.643×10 -8 t 2 +2.302×10 -4 tp+3.214p 2
wherein: y is the thickness of the inner layer of the oxide layer in the steam environment, Y T Is the relation between the temperature and the thickness of the inner layer of the oxide layer in the steam environment, Y p The unit is mu m, which is the relation between the pressure and the thickness of the inner layer of the oxide layer in the steam environment; omega is the weightThe coefficient, k, is the fitting coefficient; q is activation energy, and the unit is J.mol -1 The method comprises the steps of carrying out a first treatment on the surface of the R is a gas constant, T is a steam temperature, and the unit is K; p is steam pressure in MPa; t is time, and the unit is h;
Y T in the calculation formula of (a):
the activation energy Q and the time t conform to the formula: q= 156908.32387-0.7554t+4.0662×10 -6 t 2 ；
The fitting coefficient k and the temperature T conform to the formula: k= 1.932 ×10 -68 T 23.16 。
2. The computing method according to claim 1, wherein: the steam temperature ranges from 550 ℃ to 650 ℃ and the steam pressure ranges from 5.0MPa to 25.0MPa.
3. The computing method according to claim 1, wherein: the operating time t of the pearlite heat-resistant steel in a steam environment ranges from 1,000 to 150,000 hours.
4. The computing method according to claim 1, wherein:
when T is less than 600 ℃, the value of omega is 0.2217 +/-0.1317;
when T is more than or equal to 600 ℃, the value of omega is 0.7943 +/-0.2049.
5. Use of the calculation method of claim 1 for assessing the life of a pearlitic heat-resistant steel part operating under steam in a power plant.
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2023
- 2023-04-20 CN CN202310431341.3A patent/CN116486950A/en active Pending
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