CN116486952A - Method for calculating thickness of inner layer of bainite heat-resistant steel oxide layer in steam environment - Google Patents
Method for calculating thickness of inner layer of bainite heat-resistant steel oxide layer in steam environment Download PDFInfo
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- 229910000831 Steel Inorganic materials 0.000 title claims abstract description 40
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Abstract
The invention discloses a method for calculating the thickness of an inner layer of a bainite 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 number 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 T23 bainite 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 oxidation layer of the T23 bainite heat-resistant steel under steam can be conveniently and rapidly calculated according to the steam temperature, the steam pressure and the running time, and the measurement is not needed by cutting a pipe, so that the cost is saved, the thickness of the inner layer of the oxidation 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 can be reflected, the residual service life of a part is estimated, and the safe running of a unit is ensured.
Description
Technical Field
The invention belongs to the technical field of oxidation of bainite heat-resistant steel, and particularly relates to a calculation method of the thickness of an inner layer of an oxidation layer of bainite heat-resistant steel in a steam environment.
Background
T23 bainite heat-resistant steel has excellent high-temperature creep strength, good heat 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 super (super) critical units. With the increase of the working steam pressure of the unit, the steam oxidation resistance of the bainite heat-resistant steel becomes one of key factors influencing the service life of high-temperature components. 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 domestic and foreign steam oxidation dynamics model of the bainite heat-resistant steel 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 bainite 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 bainitic heat resistant steel high temperature steam oxidation kinetics model based on oxide layer thickness growth, 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. Applicant's studies have shown that only an 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 method for calculating the thickness of the inner layer of the bainite heat-resistant steel oxide layer in the steam environment, which can conveniently and rapidly calculate the thickness of the inner layer of the oxide layer of the T23 bainite heat-resistant steel pipe 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 present invention adopts the following technical scheme:
the method for calculating the thickness of the inner layer of the oxide layer of the bainite heat-resistant steel in the steam environment is provided, wherein the bainite heat-resistant steel is T23 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 ＝322.2-0.003013t-44.85p+1.451×10 -8 t 2 +1.985×10 -4 tp+1.696p 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 a gas constant, T is a temperature, and the unit is K; p isSteam 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=146473.45114+0.08095t+3.26684×10 -7 t 2 ；
The fitting coefficient k and the temperature T conform to the formula: k=1.251×10 -71 T 24.22 。
According to the scheme, the high-temperature steam temperature range is 550-650 ℃, and the steam pressure range is 0.1-25.0 MPa.
According to the scheme, the time t ranges from 100 to 150,000 hours.
According to the scheme, in the formula of the thickness Y of the inner layer of the bainite heat-resistant steel steam oxidation layer, the value of omega is 0.9251 +/-0.055.
There is provided the use of the above calculation method for assessing the life of bainitic heat resistant steel parts operating under steam in a power plant.
The invention has the beneficial effects that:
1. the method has the advantages that the thickness of the inner layer of the oxide layer of the bainite heat-resistant steel in the supercritical (super) steam environment is researched, the thickness of the inner layer of the steam oxide layer of the T23 bainite heat-resistant steel is calculated conveniently and rapidly by integrating three factors of steam temperature, steam pressure and operation time, the prediction accuracy is greatly improved, the error can be controlled within 4%, the thickness of the inner layer of the oxide layer can be measured without cutting a pipe in the actual power plant operation, 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 oxidation layer of the T23 bainite 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 T23 bainite heat-resistant steel pipe can be fully reflected, the method is used for evaluating the residual life of a part, the safe operation of a unit is ensured, and the method has important industrial application value.
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 schematic illustration of an oxide layer inner layer in accordance with an embodiment of the present inventionThickness Y p And a plot of selected pressure p versus time t.
FIG. 3 shows the thickness Y of the inner layer of the oxide layer in an embodiment of the 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 research shows that the thickness Y of the oxide layer 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 T23 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 is Y T ＝3.6559±0.1725t 0.30288±0.00412 ；
T=575 ℃): y is Y T ＝0.6389±0.0402t 0.50795±0.00544 ；
T=600℃: y is Y T ＝0.1194±0.0142t 0.70865±0.01027 ；
T=625℃: y is Y T ＝0.2098±0.0199t 0.71778±0.00822 ；
T=650℃: y is Y T ＝13.5633±0.7699t 0.40058±0.00498 ；
It can be found that the value of n fluctuates in the range of 0.3 to 0.7, and taking n as 0.45 reasonably, the formula (1) is modified as follows:
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 0.45 ) 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 T23 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＝146473.45114+0.08095t+3.26684×10 -7 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 ＝(0.703±0.007)*Z；
When t=575 ℃, Y T ＝(1.305±0.007)*Z；
When t=600 ℃, Y T ＝(2.006±0.479)*Z；
When t=625 ℃, Y T ＝(3.871±0.867)*Z；
When t=650 ℃, Y T ＝(8.098±0.049)*Z。
The relationship between k and temperature T is obtained as follows:
k＝1.251×10 -71 T 24.22 (6)
it can be seen that the k value increases with increasing temperature. This means that the higher the temperature, the greater the effect of temperature on the thickness of the oxide layer inner layer. Thus finallyThickness Y of the inner layer of the oxide layer obtained 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 high-temperature heating surface oxide layer of the power station boiler, experimental data of the thickness of the inner layer of the T23 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 2T 23 bainitic heat resistant Steel oxide layer inner layer thickness 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＝1.696±0.181
h＝1.985×10 -4 ±2.28×10 -5
c＝-44.85±5.68
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＝1.451×10 -8 ±4.07×10 -9
b＝-0.003013±7.65×10 -4
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=322.2±47.8. Therefore, formula (8) is rewritten as:
Y p ＝322.2-0.003013t-44.85p+1.451×10 -8 t 2 +1.985×10 -4 tp+1.696p 2 (9)
step 4: repeated fitting is performed on the graph of fig. 2, and error rates of the coefficients in equation (9) are 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＝322.2
b＝-0.003013
c＝-44.85
d＝1.451×10 -8
h＝1.985×10 -4
i＝1.696
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 ＝322.2-0.003013t-44.85p+1.451×10 -8 t 2 +1.985×10 -4 tp+1.696p 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 thickness Y of oxide scale inner layer, 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)
as can be seen from the foregoing, the present invention,
Y p ＝322.2-0.003013t-44.85p+1.451×10 -8 t 2 +1.985×10 -4 tp+1.696p 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: substituting data of T=550 ℃, 575 ℃, 600 ℃, 625 ℃, 650 ℃ into fitting finds that the value of omega fluctuates within the range of 0.8-0.95, which proves that the influence of temperature on the thickness of the oxide scale is great, the influence of pressure is small, and finally substituting the data into fitting to obtain the value of the weight coefficient omega of the temperature T as 0.9251 +/-0.055, the formula (11) is changed into:
Y＝(0.9251±0.055)* Y T +(0.0749±0.055)* Y p (12)
the weight coefficient omega value of the temperature T changes along with the temperature, which is basically consistent with the change rule of the relation between the previous temperature and the thickness, and the weight coefficient omega is larger and larger along with the temperature rise. In summary, the fitting formula of the oxide skin inner layer thickness Y, the temperature T and the vapor pressure p is:
Y＝(0.9251±0.055)*Y T +(0.0749±0.055)*Y p
Y p ＝322.2-0.003013t-44.85p+1.451×10 -8 t 2 +1.985×10 -4 tp+1.696p 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
The calculation method related by the invention is compared with the oxidation experimental result of the T23 steel.
Fry et al measured that the thickness of the inner layer of the oxidation layer is about 40 mu m after the T23 steel is oxidized for about 500 hours at the steam temperature of 600 ℃ and the steam pressure of 0.1MPa, and the operating parameters are substituted into the formula (12) provided by the embodiment of the invention to calculate the thickness of the inner layer of the oxidation layer to be about 41.4788 mu m, and the error is 3.6%.
Example 2
The calculation method related by the invention is compared with the oxidation experimental result of the T23 steel.
Fry et al measured that the thickness of the inner layer of the oxide layer is about 170 mu m after T23 steel is oxidized for about 1000 hours at the steam temperature of 650 ℃ and the steam pressure of 5MPa, and the operating parameters 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 166.7994 mu m, and the error is 1.8%.
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 555 ℃, the steam pressure is about 19.2MPa, the T23 steel is adopted for a pipeline, and after the boiler runs for about 47,640 hours, the thickness of an inner layer of an oxide layer in the pipeline is about 115 mu m.
Substituting the steam temperature in the operation parameters into Y T (equation 7) the thickness of the inner layer of the 47,640h oxide layer was 109.5317 μm with an error percentage of 4.7%. Substituting the steam pressure in the operation parameters into Y p (equation 10) the thickness of the inner layer of the 47,640h oxide layer was 124.0139 μm with a percent error of 7.8%. 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 110.9799 mu m, and the error is 3.5%.
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 steam temperature of a boiler of a supercritical power plant is about 555 ℃, the steam pressure is about 19.2MPa, a pipeline is made of T23 steel, after the boiler runs for about 78,640 hours, the thickness of an inner layer of an oxide layer in the pipeline is measured to be about 140 mu m,
substituting the steam temperature in the operation parameters into Y T (equation 7) the thickness of the inner layer of the oxidized layer was 132.5317 μm and the error percentage was 5.3% at 78,640 h. Substituting the steam pressure in the operation parameters into Y p (equation 10) the thickness of the inner layer of the oxidized layer was 150.0139 μm and the error percentage was 7.1% at 78,640 h. 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 134.2799 mu m, and the error is 4.1%.
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 T23 bainite steel oxide film inner layer calculated by the method of the invention is in good agreement with the actual measurement result, and the error is within 5%.
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 bainite heat-resistant steel oxide layer in a steam environment is characterized by comprising the following steps: the bainite heat-resistant steel is T23 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 ＝322.2-0.003013t-44.85p+1.451×10 -8 t 2 +1.985×10 -4 tp+1.696p 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 a gas constant, T is a 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=146473.45114+0.08095t+3.26684×10 -7 t 2 ；
The fitting coefficient k and the temperature T conform to the formula: k=1.251×10 -71 T 24.22 。
2. The computing method according to claim 1, wherein: the steam temperature ranges from 550 ℃ to 650 ℃ and the steam pressure ranges from 0.1MPa to 25.0MPa.
3. The computing method according to claim 1, wherein: the time t is in the range of 100 to 150,000 hours.
4. The computing method according to claim 1, wherein: the value of omega is 0.9251 +/-0.055 according to the formula of the thickness Y of the inner layer of the steam oxidation layer of the bainite heat-resistant steel.
5. Use of the calculation method of claim 1 for assessing the life of bainitic heat resistant steel parts operating under steam in a power plant.
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2023
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