Calculation method for thickness of inner oxide layer of martensitic heat-resistant steel in steam environment

Abstract

The present application discloses a calculation method for thickness of inner oxide layer of a martensitic heat-resistant steel in steam environment. The calculation method takes into account the steam temperature, the steam pressure and the operation time, which are the three factors that have significant effects on the thickness of the oxide layer, and with the help of a metal oxidation kinetic model, the formula is mathematically modified by combining a large number of actual operation and laboratory simulation experimental data of the power plant. A calculation method for thickness of inner oxide layer of 9% Cr martensitic heat-resistant steel in steam environment is obtained by using linear fitting and curve fitting, etc.

Claims

1. A non-destructive method for enhancing a structural management of a martensitic heat-resistant steel component in a steam environment, wherein the martensitic heat-resistant steel component is 9% Cr martensitic heat-resistant steel component, and the method comprising: obtaining operation parameters of the 9% Cr martensitic heat-resistant steel component, wherein the operation parameters comprises a steam temperature T, a steam pressure p, and an operation time t; calculating a thickness Y of an inner oxide layer on a wall surface of the 9% Cr martensitic heat-resistant steel component, wherein the thickness Y of the inner oxide layer directly indicates a consumed metal thickness of a component wall, and using a coupled functional model that accounts for a combined influence of the steam temperature and the steam pressure:
Y=*Y.sub.T+(1)*Y.sub.p wherein Y is the thickness of the inner oxide layer in the steam environment (m), Y.sub.T is a relationship between the steam temperature and the thickness of the inner oxide layer in the steam environment (m), Y.sub.p is a relationship between the steam pressure and the thickness of the inner oxide layer in the steam environment (m), is a weight coefficient representing a relative contribution of the steam temperature and the steam pressure to an inner oxide layer growth, T is the steam temperature (K), p is the steam pressure (MPa), t is time (h); and determining an effective remaining wall thickness of the 9% Cr martensitic heat-resistant steel component by subtracting the calculated thickness Y from an initial wall thickness, and evaluating a risk of pipe failure based on the effective remaining wall thickness, thereby providing an improved basis for preventing pipe burst accidents without requiring destructive physical inspection.

2. The method according to claim 1, wherein Y.sub.T and Y.sub.p are calculated by: $Y_{T} = k \exp (\frac{- Q}{RT}) t^{n}$ $Y_{p} = a + bt + cp + {dt}^{2} + hpt + {ip}^{2}$ wherein k, a, b, c, d, h, i are fitting coefficients, Q is an activation energy (J.Math.mol.sup.1), R is a gas constant; and the steam temperature is from 550 to 650 C. and the steam pressure is from 5.0 to 25.0 MPa.

3. The method according to claim 1, wherein the time t is from 1,000 to 150,000 h.

4. The method according to claim 1, wherein in the formula for calculating the Y, in response to that the steam temperature T is less than 600 C., is 0.16820.1136; in response to that the steam temperature T is not less than 600 C., is 0.68910.2269.

5. The method according to claim 1, wherein in the formula for calculating the Y.sub.T, n is equal to 0.25.

6. The method according to claim 2, wherein a mathematical relationship between the fitting coefficient k and the steam temperature T in the formula for calculating the Y.sub.T is
k=1.0110.sup.42T.sup.14.68.

7. The method according to claim 2, wherein an activation energy (Q) is a variable that changes with time; and wherein a mathematical relationship between the activation energy Q and the time t in the formula for calculating Y.sub.T is
Q=106661.335570.36498t+3.0791510.sup.6t.sup.2.

8. The method according to claim 2, wherein in the formula for calculating Y.sub.p, the fitting coefficient a is 22.21, the fitting coefficient b is 0.0009334, the fitting coefficient c is 0.8198, the fitting coefficient d is 7.65510.sup.10, the fitting coefficient h is 1.7910.sup.5, and the fitting coefficient i is 0.1152.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) FIG. 1a-e is a fitted curve diagram of the thickness of the inner oxide layer YT and Z according to an embodiment of the present application.

(2) FIG. 2 is a relationship diagram of the thickness of the inner oxide layer Yp and the selected pressure p and time t according to an embodiment of the present application.

(3) FIG. 3 is a three-time replicate fitted verification diagram of the actual data of the thickness of the inner oxide layer Yp and the selected pressure p and time t according to an embodiment of the present application.

DETAILED DESCRIPTION OF THE EMBODIMENTS

(4) The technical solutions of the present application are further explained and illustrated by specific embodiments below.

(5) (1) The Relationship Between the Thickness of the Inner Oxide Layer YT and the Temperature T.

(6) To explore the effect of temperature T and time t on the oxide layer of high temperature heating surface of the power plant boiler, the thickness of the inner oxide layer YT and temperature T in high temperature conditions conforms to the following exponential function law:

(7) $\begin{matrix} Y_{T} = k \exp (\frac{- Q}{RT}) t^{n} & (1) \end{matrix}$ where k is the coefficient, Q is the activation energy (J.Math.mol-1), R is a gas constant, T is the temperature (K), and t is the time (h).

(8) A large amount of data from the actual power plant and the simulation experiments in the laboratory is collected in the embodiment of the present application, including the thickness of the inner oxide layer of 9% Cr heat-resistant steel such as T/P91 and T/P92 at the temperature from 550 C. to 650 C. and at the steam pressure from 5.0 to 25.0 MPa for the oxidation time from 1,000 to 150,000 h; the parameters n, Q, and k in the formula (1) are calculated by using the above data. The calculation method is shown below:

(9) Step 1: calculating n.

(10) When a specific temperature T is taken, kexp

(11) $\frac{- Q}{(RT)}$
is a constant. When the pressure is certain, the experimental data at each temperature is substituted into the formula for fitting, and the fitting results of two different sets of data as follows.

(12) The first set: When T=550 C., then YT=5.33070.36426t0.257450.00604. When T=575 C., then YT=3.86950.25881t0.327590.00588. When T=600 C., then YT=7.42950.57287t0.297280.00675. When T=625 C., then YT=16.09281.29516t0.249910.0071. When T=650 C., then YT=31.47841.91864t0.210770.0054.

(13) The second set: When T=550 C., then YT=5.15230.76277t0.262990.01301. When T=575 C., then YT=3.93820.52155t0.334340.01156. When T=600 C., then YT=5.664280.63578t0.332180.00987. When T=625 C., then YT=5.526650.39467t0.365690.00628. When T=650 C., then YT=2.475270.14564t0.376880.00511.

(14) It can be found that n is from about 0.21 to 0.35 and fluctuates around 0.25, indicating that the oxidation kinetics of 9% Cr heat-resistant steel basically obey the cubic law, so n is taken as 0.25, and then the formula (1) is modified as follows

(15) $\begin{matrix} Y_{T} = k \exp (\frac{- Q}{RT}) t^{0.25} & (2) \end{matrix}$

(16) Step 2: calculating the activation energy Q.

(17) Making logarithmic transformation on both sides of formula (2) to obtain

(18) $\ln Y_{T} = \ln ({kt}^{0.25}) - \frac{Q}{RT} .$

(19) When a specific time t is taken, then ln(kt.sup.0.25) is a constant and is noted as G. The above formula is simplified to

(20) $\begin{matrix} \ln Y_{T} = G - \frac{Q}{RT} . & (3) \end{matrix}$

(21) When t is equal to 1,000 h, 10,000 h, 50,000 h, 100,000 h, 150,000 h, the experimental data are substituted into the fitting formula obtained in step 1, and the values lnY are calculated for T equal to 550 C., 575 C., 600 C., 625 C., 650 C., respectively, and then substituted back to the formula (3) to calculate the activation energy Q for different times t as shown in Table 1.

(22) TABLE-US-00001 TABLE 1 Activation energy at different times t/h Q/J .Math. mol.sup.1 1000 106391.7023 10000 103465.6272 50000 95473.5117 100000 101548.8781 150000 121001.0501

(23) From Table 1, it can be seen that the Q differs at different times, indicating that the activation energy of the oxidation reaction varies at different times. It is found that the oxidation reaction of 9% Cr heat-resistant steel is a complex and dynamic process. The composition and structure of the oxidation products and oxidation mechanism vary at different stages of the reaction. Therefore, the present application uses a mathematical model to fit the variation of the activation energy with time and obtains that the activation energy Q with time t is highly consistent with the following mathematical model, the formula is:
Q=106661.335570.36498t+3.0791510.sup.6t.sup.2(4).

(24) Substituting the formula (4) back into the formula (2), the corrected thickness formula is:

(25) $\begin{matrix} Y_{T} = k \exp (\frac{- (106661.33557 - 0.36498 t + 3.07915 10^{- 6} t^{2})}{RT}) t^{0.25} . & (5) \end{matrix}$

(26) Step 3, calculating the coefficient k.

(27) A specific temperature T and the operation time t are selected, then

(28) $k \exp (\frac{- (106661.33557 - 0.36498 t + 3.07915 10^{- 6} t^{2})}{RT}) t^{0.25}$
is a constant value and is recorded as Z, then the above formula is changed to YT=k*Z. The experimental data at each temperature is substituted into the formula (5) in turn and fitted to obtain the coefficient k. It is found that the k varies at different temperatures, the fitted curve is shown in the FIG. 1a-e, and the results are: When T=550 C.; then YT=(6.370.109)*Z. When T=575 C.; then YT=(11.020.17)*Z. When T=600 C., then YT=(15.390.23)*Z. When T=625 C., then YT=(21.980.25)*Z. When T=650 C., then YT=(35.580.42)*Z.

(29) The relationship between the k and temperature T is obtained as:
k=1.011042T14.68(6).

(30) It can be seen that as the temperature increases, the k becomes larger. This indicates that the higher the temperature, the greater the influence of temperature on the thickness of the inner oxide layer. Therefore, finally, the fitting formula for the thickness of the inner oxide layer YT and the temperature T is

(31) $\begin{matrix} Y_{T} = 1.01 10_{- 42} T^{14.68} \exp (\frac{- (106661.33557 - 0.36498 t + 3.07915 10^{- 6} t^{2})}{RT}) t^{0.25} & (7) \end{matrix}$

(32) In the above formula, the unit of the temperature T is K, the unit of the time t is h, and the unit of the calculated thickness of the inner oxide layer YT is m.

(33) (2) The Relationship Between the Thickness of the Inner Oxide Layer Yp and the Steam Pressure p.

(34) To investigate the influence of the pressure p and the time t on the formation of the oxide layer on the high temperature heating surface of the power plant boiler, the experimental data about the thickness of the inner oxide layer of 9% Cr martensitic heat-resistant steel at different time t and different pressure p is filtrated and processed, the results are shown in Table 2:

(35) TABLE-US-00002 TABLE 2 The thickness of the inner oxide layer of 9%Cr martensitic heat- resistant steel at different times and different steam pressures: Steam pressure thickness of the inner Time t/h p/Mpa oxide layer Y.sub.p/m 1169.916 5.0 35.422 1466.175 15.0 48.916 1767.934 20.0 69.157 1228.343 25.0 107.108 10018.521 5.0 42.169 10031.581 15.0 58.193 10048.766 20.0 79.277 10084.509 25.0 123.133 50267.199 5.0 75.060 50004.621 15.0 102.892 50034.178 20.0 139.157 50081.607 25.0 197.349 100222.328 5.0 117.229 100264.946 15.0 169.518 100308.250 20.0 222.651 100064.232 25.0 273.253 150177.458 5.0 159.398 150242.071 15.0 238.675 150270.941 20.0 274.096 122611.575 25.0 287.590

(36) The above data is drawn to obtain a relationship diagram of the thickness of the inner oxide layer Yp and the selected pressure p and the time t shown in the FIG. 2.

(37) It can be found that there is a binary quadratic relationship between the thickness of the inner oxide layer Yp and the pressure p and time t. The following formula is obtained by three-dimensional nonlinear surface fitting:
Yp=a+bt+cp+dt2+hpt+ip2(8).

(38) Step 1: Determining the coefficients i, h, c with the p term.

(39) When a specific time t is selected, the term containing t is fixed and the formula (8) is transformed into a parabolic formula about p. The coefficients i, h, c with the p term can be obtained by fitting the data after substitution. i=0.11520.03315 h=1.791054.74106 c=0.81981.0842.

(40) Step 2: Determining the coefficients d, b with the t term.

(41) Similarly, when a specific pressure p is selected, the term containing p is fixed and formula (8) is transformed into a parabolic formula about t. The coefficient d, b with the t term can be obtained by fitting the data after substitution. d=7.65510107.77351010 b=0.00093340.0001543.

(42) Step 3: Determining the coefficient after the five coefficients are determined. The coefficients already obtained above are substituted into the formula (8), and then substituting all data for three-dimensional nonlinear surface fitting, to obtain the coefficient a=22.219.65, thus the formula (8) is changed to:
Yp=22.21+0.0009334t+(0.8198p)+(7.65510.sup.10t.sup.2)+1.7910.sup.5tp+0.1152p.sup.2(9).

(43) Step 4: Repeating the fit for FIG. 2 and verifying the error rate of each coefficient in formula (9). A curved graph is drawn based on the formula (9), and then all data are substituted into the graph. If the data points basically fall on the curved graph, the prediction results of formula (9) are basically in line with the actual results. Since each coefficient fluctuates in a certain range, three fittings are performed to improve the accuracy and reduce the error. Finally, a three-time replicate fitted verification diagram of the actual data shown in FIG. 3 is obtained. It can be found that the data points in different working conditions basically fall on three predicted curved surfaces (boundaries) with an average error rate of 5%, indicating that the relationship between the thickness of the inner oxide layer Yp, the pressure p and the time tin the actual working conditions basically conforms to the function law described in the formula (9), then the coefficients are determined as a=22.21 b=0.0009334 c=0.8198 d=7.6551010 h=1.79105 i=0.1152.

(44) The fitting formula for the thickness of the inner oxide layer Yp and the steam pressure p is finally obtained as follows:
Yp=22.21+0.0009334t+(0.8198p)+(7.655100.sup.10t.sup.2)1.7910.sup.5tp+0.1152p.sup.2(10)

(45) In the above formula, the unit of the time t is h, the unit of the steam pressure p is MPa, and the unit of the thickness of the inner oxide layer Yp is m.

(46) (3) A Relationship Between the Total Thickness of the Inner Oxide Layer Y and the Steam Temperature T and the Steam Pressure p.

(47) In the process of fitting the experimental data, it is found that if the T and p are imported and fitted simultaneously, the results are not in line with the reality, and the error rate is high. The reason is that if temperature and pressure are simultaneously imported into a system, the two physical quantities themselves will interplay to be changed, and the system will have a closed-loop repeatability error, resulting in a large gap between the fitted results and the reality. The relationship between the thickness of the inner oxide layer and the steam temperature T or the steam pressure p has been obtained from the previous text. Next, we study the weight coefficients of the two on the thickness and determine a formula for calculating the total thickness of the inner oxide layer containing T and p.

(48) Step 1: Determining the total thickness of the inner oxide layer by the formula:
Y=*YT+(1)*Yp(11).

(49) From the above, it can be seen that

(50) 0 $Y_{T} = 1.01 10_{- 42} T^{14.68} \exp (\frac{- (106661.33557 - 0.36498 t + 3.07915 10^{- 6} t^{2})}{RT}) t^{0.25}$ $Yp = 22.21 + 0.0009334 t + (- 0.8198 p) + (- 7.655 10^{- 10} t^{2}) + 1.79 10^{- 5} tp + 0.1152 p^{2} .$

(51) where is the weight coefficient, YT is the relationship between the temperature and the thickness of the inner oxide layer in steam environment, and Yp is the relationship between the pressure and the thickness of the inner oxide layer in steam environment. The data at different temperatures and different pressures are substituted into the formulas to obtain calculated values and the calculated values are fitted against the actual values.

(52) Step 2: After substituting the measured data of the thickness of the inner oxide layer at T=550 C., 575 C., 600 C., 625 C. and 650 C. for fitting, it is found that when the temperature is lower (T=550 C., 575 C.), w will fluctuate within 0.10.2, indicating that the effect of the temperature on the thickness of the inner oxide layer is not as great as that of pressure when the temperature is lower, and finally the measured data is substituted for fitting to obtain the value of the weight coefficient w of the temperature T as 0.16820.1136, and then the formula (11) is changed to Y=(0.16820.1136)*YT+(0.83180.1136)*Yp (12).

(53) When the temperature is higher (T=600 C., 625 C., 650 C.), w will fluctuate within 0.60.8, indicating that when the temperature is higher, the effect of the temperature on the thickness of the inner oxide layer is greater than that of the pressure, and finally the measured data is substituted for fitting to obtain the value of the weight coefficient w of the temperature T as 0.68910.2269, and then the formula (11) is changed to
Y=(0.68910.2269)*YT+(0.31090.2269)*Yp(13).

(54) From the above steps, it can be seen that the weight coefficient w will become larger as the temperature increases, which is basically consistent with the variation law of the relationship between the temperature and the thickness of the inner oxide layer YT. In summary, the calculation formula for the thickness of the inner oxide layer Y and the temperature T and the pressure p is as follows: When T is less than 600 C., Y=(0.16820.1136)*YT+(0.83180.1136)*Yp When T is not less than 600 C., Y=(0.68910.2269)*YT+(0.31090.2269)*Yp

(55) $Y_{T} = 1.01 10_{- 42} T^{14.68} \exp (\frac{- (106661.33557 - 0.36498 t + 3.07915 10^{- 6} t^{2})}{RT}) t^{0.25}$ $Yp = 22.21 + 0.0009334 t + (- 0.8198 p) + (- 7.655 10^{- 10} t^{2}) + 1.79 10^{- 5} tp + 0.1152 p^{2} .$

(56) 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 thickness of the inner oxide layer Y is m.

Embodiment 1

(57) Comparison of the calculation method involved in the present application with the experimental results of oxidation of T91 steel.

(58) Nishimura et al. measures that at the steam temperature of 555568 C. and the steam pressure of 25 MPa, the thickness of the inner oxide layer of T91 steel is about 71 m after oxidation for about 1,451 hours. The experimental conditions are substituted into the formula (12) proposed in the embodiment of the present application to calculate the thickness of the inner oxide layer to be about 70.8602 with an error 0.19%.

Embodiment 2

(59) Comparison of the calculation method involved in the present application with the experimental results of oxidation of T92 steel.

(60) Muraki et al. measures that at the steam temperature of 555568 C. and the steam pressure of 25 MPa, the thickness of the inner oxide layer of T92 steel is about 149 m after oxidation for about 29,920 hours. The experimental conditions are substituted into the formula (12) proposed in the embodiment of the present application to calculate the thickness of the inner oxide layer to be about 140.2092 with an error 5.9%.

Embodiment 3

(61) An application of the calculation method involved in the present application in an actual power plant.

(62) The material for the connecting pipe of the high re-collector of unit #6 in a power plant is T92 steel, the steam temperature is 615 C. and the steam pressure 5 MPa. After 15,479 hours and 19,037 hours of operation, the thickness of the inner oxide layer is measured to be 98 m and 112 m, respectively.

(63) The steam temperature in the above operation parameters is substituted into YT (formula 7) to obtain the thickness of the inner oxide layer for 15,479 hours to be 105.8385 m, with an error 7.9%. The steam pressure in the above operation parameters is substituted into Yp (formula 10) to obtain the thickness of the inner oxide layer for 15,479 hours to be 90.6411 m, with an error 7.5%. The above two operation parameters are substituted into the formula (13) proposed in the embodiment of the present application to obtain the thickness of the inner oxide layer for 15,479 hours to be 100.9753 m, with an error 3.0%.

(64) The steam temperature in the above operation parameters is substituted into YT (formula 7) to obtain the thickness of the inner oxide layer for 19,037 hours to be 120.1865 m, with an error 7.3%. The steam pressure in the above operation parameters is substituted into Yp (formula 10) to obtain the thickness of the inner oxide layer for 19,037 hours to be 103.4091 m, with an error 7.7%. The above two operation parameters are substituted into the formula (13) proposed in the embodiment of the present application to obtain the thickness of the inner oxide layer for 19,037 hours to be 114.8177 m, with an error 2.5%.

(65) This shows that the error is smaller and the prediction result is more accurate after considering the temperature and the pressure together.

Embodiment 4

(66) An application of the calculation method involved in the present application in an actual power plant.

(67) The steam temperature of a supercritical power plant boiler is about 571 C., the steam pressure is about 25.4 MPa, and the pipe is made of T91 steel. After operation for about 12,956 hours, the thickness of the inner oxide layer is measured to be about 101 m.

(68) The steam temperature in the above operation parameters is substituted into YT (formula 7) to obtain the thickness of the inner oxide layer for 12,956 hours to be 108.4956 m, with an error 7.4%. The steam pressure in the above operation parameters is substituted into Yp (formula 9) to obtain the thickness of the inner oxide layer for 12,956 hours to be 91.4774 m, with an error 9.4%. The above two operation parameters are substituted into the formula (12) proposed in the embodiment of the present application to obtain the thickness of the inner oxide layer for 12,956 hours to be 102.8971 m, with an error 1.8%.

(69) This shows that the error is smaller and the prediction result is more accurate after considering the temperature and the pressure together.

(70) All of the above embodiments show that the thickness of the inner oxide layer of 9% Cr martensitic steel calculated by the calculation method is in good agreement with the actual measurement results, and the error is within 6%.

(71) The technical solutions of the present application are not limited to the above embodiments, and any technical solution obtained by using equivalent substitution falls within the scope of the present application.

Calculation method for thickness of inner oxide layer of martensitic heat-resistant steel in steam environment

Inventors

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B01J2219/0281

PERFORMING OPERATIONS; TRANSPORTING

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G01B21/08

PHYSICS

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B01J2219/024

PERFORMING OPERATIONS; TRANSPORTING

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B01J19/02

PERFORMING OPERATIONS; TRANSPORTING

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B01J2219/0286

PERFORMING OPERATIONS; TRANSPORTING

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G01B21/08

PHYSICS

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B01J19/02

PERFORMING OPERATIONS; TRANSPORTING

Abstract

Claims

Description