Scale generation amount estimation method

Abstract

To estimate the amount of scale formation in piping where high-temperature materials come into contact discontinuously. [Solution] A method for estimating the amount of scale 4 generated in a pipe 1 that is in discontinuous contact with a high-temperature object 3, comprising: performing transient calculations that switch between heat transfer conditions when in contact with the high-temperature object 3 and when not in contact to calculate the temperature history of the surface of the pipe 1; and calculating the amount of scale generated from that temperature history.

Description

[Technical Field]

[0001] The present invention relates to a method for estimating the amount of scale formation in piping where high-temperature materials come into discontinuous contact. [Background technology]

[0002] Oxide scale forms on the surface of piping used in an oxidizing atmosphere, and this oxide scale peels off, causing thinning of the pipe wall. In high-temperature environments, this thinning caused by oxide scale formation is particularly pronounced, and therefore the lifespan of the piping is determined by the amount of oxide scale formed.

[0003] Therefore, if the amount of oxide scale generated can be estimated, it becomes possible to predict the lifespan of the piping. As a result, repairs can be carried out at the appropriate time, preventing accidents caused by piping damage and reducing repair costs.

[0004] Therefore, methods for estimating the amount of oxide scale generated in piping are being investigated.

[0005] For example, Patent Document 1 proposes a method for estimating the thickness of oxide scale in piping such as boiler superheater tubes. [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2015-230119 [Overview of the project] [Problems that the invention aims to solve]

[0007] However, piping is used in a variety of environments, and in some cases, high-temperature materials may come into discontinuous contact with the surface of the piping. In such cases, the temperature of the piping surface changes moment by moment.

[0008] In prior art such as Patent Document 1, the above-mentioned environmental fluctuations were not taken into consideration, making it impossible to accurately estimate the amount of oxide scale generated.

[0009] This invention has been made in view of the above circumstances, and aims to accurately estimate the amount of oxide scale generated. [Means for solving the problem]

[0010] The present invention aims to solve the above-mentioned problems, and its gist is as follows.

[0011] 1. A method for estimating the amount of scale formation in piping where high-temperature materials come into discontinuous contact, The temperature history of the piping surface is calculated by performing transient calculations that switch between heat transfer conditions when in contact with the high-temperature object and when not in contact with it. A method for estimating scale generation amount, which calculates the scale generation amount from the aforementioned temperature history.

[0012] 2. Calculation of the scale generation amount from the temperature history, From the temperature at each time in the aforementioned temperature history, the oxidation rate constant at that time is determined. The amount of scale generated at that time is determined using the oxidation rate constant. This is done by integrating the aforementioned scale generation amount. The method for estimating the scale generation amount described in item 1 above.

[0013] 3. The method for estimating the amount of scale formation according to 1 or 2 above, further comprising determining the amount of wall thinning of the piping from the estimated amount of scale formation.

[0014] 4. The method for estimating the amount of scale formation described in 3 above, further, for estimating the lifespan of the piping from the amount of wall thinning. [Effects of the Invention]

[0015] According to the present invention, the amount of oxide scale formation can be accurately estimated. Further, the amount of metal removal can be determined from the estimated amount of oxide scale formation. Furthermore, the life of the pipe can be estimated from the determined amount of metal removal.

Brief Description of the Drawings

[0016] [Figure 1] It is a schematic diagram showing an example of the influence of contact with a high-temperature object. [Figure 2] It is a schematic diagram showing an example of a heat transfer calculation model used for calculating the temperature history. [Figure 3] It is a schematic diagram showing an example of a heat transfer calculation model used for calculating the temperature history. [Figure 4] It is the temperature history actually measured in the embodiment. [Figure 5] It is the temperature history calculated by the method of the present invention.

Mode for Carrying Out the Invention

[0017] Hereinafter, the present invention will be specifically described. The following description is about an example of a preferred embodiment of the present invention, and the present invention is not limited to the embodiments described below.

[0018] In the present invention, in order to estimate the amount of scale formation in a pipe where a high-temperature object contacts discontinuously, first, the temperature history of the pipe surface is calculated, and the amount of scale formation is calculated from the obtained temperature history.

[0019] [Pipe] The pipe is not particularly limited, and any pipe can be targeted as long as a high-temperature object contacts it discontinuously. Here, the fact that a high-temperature object contacts discontinuously means that the state where the high-temperature object is in contact and the state where it is not in contact are alternately repeated. In other words, it is a pipe where a high-temperature object contacts intermittently.

[0020] The position where the high-temperature object contacts is not particularly limited, and it may be either one or both of the outer surface and the inner surface of the pipe.

[0021] The material of the piping is not particularly limited and can be any material on which scale can form. Typically, it may be steel. In other words, in one embodiment of the present invention, it is possible to estimate the amount of scale formed in a steel pipe that is in discontinuous contact with a high-temperature object.

[0022] [High-temperature objects] The aforementioned high-temperature object is not particularly limited and may be any high-temperature object. Here, "high temperature" merely indicates that the temperature of the object is high enough to generate scale in the piping; it is not intended to limit the temperature of the object to a specific numerical range.

[0023] While this invention focuses on the effect of high-temperature substances adhering to pipes on the pipe temperature, other factors that affect the pipe temperature may also exist. Examples of factors that affect the pipe temperature include heat sources in contact with the pipe, heat sources located at a distance (non-contact) from the pipe, and cooling media located at a distance from the pipe. Heat sources in contact with the pipe cause the pipe temperature to rise through heat conduction. Heat sources located at a distance from the pipe cause the pipe temperature to rise through radiation. Furthermore, cooling media located at a distance from the pipe (e.g., cooling water) cause the pipe temperature to fall through heat conduction. When these factors exist, their effects can be incorporated into the boundary conditions when calculating the temperature history, as described later.

[0024] [Temperature history] In calculating the temperature history, transient calculations are performed that switch between heat transfer conditions when in contact with a high-temperature object and when not in contact. The specific calculation method is not particularly limited, but usually, a heat transfer calculation model of the piping is created and heat transfer calculations are performed within the material of the piping. The method of the heat transfer calculation is not particularly limited, and any numerical method that can solve the heat conduction equation can be used. Representative numerical methods include the finite difference method, finite element method, and boundary element method, but the finite difference method is preferred.

[0025] In general, the temperature history should be the surface temperature history (time change) of the piping. For example, if a high-temperature object is in contact with the outer surface of the piping, the temperature history of the outer surface should be used, and if a high-temperature object is in contact with the inner surface of the piping, the temperature history of the inner surface should be used.

[0026] [Scale generation amount] Next, the scale generation amount is calculated from the obtained temperature history. Since the scale generation rate is determined by temperature, if the temperature history is known, the scale generation amount at each time point can be estimated. Then, by accumulating the scale generation amounts at each time point, the total scale generation amount can be estimated.

[0027] Furthermore, when calculating the amount of scale formation, it is preferable to determine the oxidation rate constant at each time point from the temperature in the temperature history, as described later, and then use the oxidation rate constant to determine the amount of scale formation at that time point.

[0028] Furthermore, the amount of wall thinning in the piping can also be determined from the estimated amount of scale generation.

[0029] Furthermore, the lifespan of the pipe can be estimated from the difference between the amount of wall thinning and the initial wall thickness of the pipe.

[0030] [Specific example] Next, an example of a preferred embodiment of the present invention will be described based on a specific example. Here, an example of a method for estimating the amount of scale formation will be described using the case where there is a high-temperature heat source near a pipe through which cooling water flows, and high-temperature material is intermittently (discontinuously) ejected from the heat source onto the outer surface of the pipe as an example. An example of a pipe used under such conditions is a water-cooled pipe for a shutter installed in front of a converter in a steel mill or the like. The water-cooled pipe is exposed to radiant heat from the furnace, and high-temperature molten material is intermittently ejected from the furnace opening of the converter and adheres to the surface of the pipe.

[0031] Figure 1 is a schematic diagram illustrating the effect of contact with high-temperature objects in the above-mentioned piping. Pipe 1 is a steel pipe with a circular cross-section, and cooling water 2 flows continuously inside pipe 1. On the other hand, the outside of pipe 1 is an atmospheric environment, but high-temperature objects 3 intermittently fly in and adhere to the outer surface of pipe 1. As a result, the temperature of the part in contact with the high-temperature objects 1 rises, and oxide scale 4 is formed on the surface of pipe 1. The formed oxide scale detaches from the surface of pipe 1 when subjected to impact or vibration, resulting in thinning of pipe 1.

[0032] When high-temperature material 3 adheres to the surface of pipe 1, the temperature of the outer surface of pipe 1 rises, and that heat is transferred to the inside of pipe 1. Also, as mentioned above, there is a high-temperature heat source (not shown) near pipe 1, so when no high-temperature material 3 is attached, pipe 1 receives radiant heat from the heat source. On the other hand, the inner surface of pipe 1 is cooled by cooling water 2. As a result, a temperature gradient is formed in the wall thickness direction of pipe 1. As a result of this heat input and cooling, the surface temperature of pipe 1 changes moment by moment.

[0033] As will be explained later, the rate of oxide scale formation depends on temperature, so in order to estimate the amount of oxide scale formed, it is necessary to determine the temperature history of the pipe surface, which changes moment by moment.

[0034] Therefore, we perform heat transfer calculations to determine the temperature history of the pipe surface. Here, we will explain the method of solving the heat conduction equation using the finite difference method as an example.

[0035] Figures 2 and 3 are schematic diagrams showing an example of a heat transfer calculation model used to calculate the temperature history. Figure 2 shows the model when the high-temperature object 3 is in contact, and Figure 3 shows the model when it is not in contact. As shown in Figures 2 and 3, the pipe 1 is divided into n+1 points in the thickness direction, and the thickness direction division length, which is the distance between adjacent points, is represented by x. For example, the thickness direction division length between the 1st and 2nd points is x1, and the thickness direction division length between the nth and (n+1)th points is x n This is represented by the following: Here, the first point represents the outer surface of pipe 1, and the (n+1)th point represents the inner surface.

[0036] When the heat conduction equation is discretized based on the above model, it can be expressed by equation (1) below.

[0037]

number

[0038] The meaning of each symbol in the formula is as follows: ρ: Density (kg / m 3 ) C p Specific heat (J / kg·K) λ: Thermal conductivity (W / m K) h: Heat transfer coefficient (W / m) 2 ·K) q r :Radiant heat flux (W / m 2 ) x: Length of division in the thickness direction (m) T: Temperature (℃)

[0039] Furthermore, the meanings of the subscripts for each symbol are as follows: i: Time division number j: Thickness direction division number s: High temperature p:Cooling water w:Water a: atmosphere

[0040] As mentioned above, the generated scale detaches from the surface of the pipe, causing gradual thinning of the pipe's wall thickness. However, since the amount of thinning in typical environments is small compared to the original pipe thickness, the pipe thickness can be considered constant in the heat transfer calculations described above.

[0041] The boundary conditions are expressed by equations (2) to (4) below. Here, equation (2) is the boundary condition on the surface of the pipe when a high-temperature object is in contact (Figure 2), equation (3) is the boundary condition on the surface of the pipe when a high-temperature object is not in contact (Figure 3), and equation (4) is the boundary condition on the inner surface of the pipe. Note that equation (3) takes into account heat conduction between the outer surface of the pipe and the atmosphere, and heat input due to radiation from the heat source.

[0042]

number

[0043]

number

[0044]

number

[0045] In this invention, when performing calculations based on the above model, it is important to perform transient calculations that switch between heat transfer conditions (i.e., boundary conditions) when in contact with a high-temperature object and when not in contact. In this example, the temperature history can be calculated by switching between equations (2) and (3) above as boundary conditions on the outer surface in contact with the high-temperature object. Regarding the temperature of the high-temperature object, if the actual temperature of the high-temperature object is known, that temperature can be used; otherwise, an approximate temperature can be used. In heat transfer calculations, the temperature of the high-temperature object can be treated as a fixed value. On the other hand, equation (4) above can always be used as the boundary condition on the inner surface.

[0046] The timing for switching boundary conditions should be set appropriately according to the environment in which you want to estimate the amount of scale generated. In other words, the switching should be done according to the frequency of contact with high-temperature objects and the duration of contact (contact time).

[0047] If high-temperature objects come into contact at regular intervals, the boundary conditions can be switched at those intervals. In addition, in environments such as the water-cooling piping of the converter furnace shutter described above, high-temperature objects fly in irregularly. In such cases, it is preferable to measure, for example, the interval (frequency) at which high-temperature objects fly in and the time they are in contact in the actual environment, and use the average value to set the timing for switching the boundary conditions.

[0048] In this way, the temperature history of the pipe surface can be calculated.

[0049] Next, the scale generation rate is calculated from the obtained temperature history. First, it is known that the scale generation rate depends on temperature, and can be specifically expressed by equation (5) below.

[0050]

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[0051] Therefore, the oxidation rate constant k at each time point can be determined from the temperature T in the aforementioned temperature history.

[0052] Then, the following relationship (6) holds between the thickness of the generated scale, the rate constant k, and time t, and by discretizing equation (6), we obtain equation (7) below.

[0053]

number

[0054]

number

[0055] Therefore, by using the oxidation rate constant k to determine the thickness (amount produced) of the oxide scale that grows during a small time interval Δt, and then accumulating these values, the total amount of oxide scale produced can be calculated.

[0056] Furthermore, the amount of pipe wall thinning can be determined from the amount of scale generated. For example, if the pipe is made of a pipe mainly composed of Fe (such as a steel pipe) and the scale generated is FeO, the amount of scale generated can be converted to the amount of pipe wall thinning using equation (8) below. Here, the coefficient 0.582 in equation (8) below is a value determined by the volume ratio of FeO to Fe.

[0057]

number

[0058] In addition, the meanings of the symbols in the above formulas (5) to (7) are as follows. δ FeO : Scale thickness (m) k: Oxidation rate constant (m 2 / sec) k0: Standard rate constant (m 2 / sec) Q: Activation energy (kJ / mol) R: Gas constant (J / K·mol) T: Temperature (K) δ Fe : Subway wall thickness reduction (m)

[0059] And the life of the pipe can be estimated from the wall thickness reduction amount. The method for estimating the life is not particularly limited. For example, the time when the wall thickness reduction amount reaches a specific thickness (critical wall thickness reduction) can be regarded as the life of the pipe. The critical wall thickness reduction may be determined from the perspective of equipment maintenance of the target pipe. For example, the wall thickness reduction amount that is judged to require repair can be predetermined as the critical wall thickness reduction, and the life can be estimated based on this.

Example

[0060] Next, the present invention will be further specifically described based on examples. The following examples show examples of preferred embodiments of the present invention, and the present invention is not limited by these examples. The embodiments of the present invention can be appropriately changed within the scope conforming to the gist of the present invention, and all of them are included in the technical scope of the present invention.

[0061] Using the above-described heat transfer calculation model and boundary conditions, the scale generation amount of the water-cooled pipe for the shutter installed in front of the converter was estimated. FIG. 4 is the temperature history of the surface temperature actually measured using a thermocouple, and FIG. 5 is the surface temperature history calculated by the method of the present invention. In the actual environment, the interval between the flying of high-temperature objects is not constant, and the operation pitch also changes. Therefore, although the shape of the temperature history is not exactly the same, the maximum temperature and the tendency of temperature change could be reproduced.

[0062] In practice, it is difficult to measure the surface temperature of the water-cooled piping directly. Therefore, the surface temperature of a cast iron plate placed in an environment almost identical to that of the water-cooled piping was measured at three points, A, B, and C, and is shown in Figure 4. One side of the cast iron plate is in an environment where high-temperature substances adhere, similar to the water-cooled piping, while the other side is water-cooled. Therefore, it can be considered to be under conditions roughly the same as those of the water-cooled piping.

[0063] Furthermore, the amount of wall thinning in water-cooled piping that had been used for five years in the above environment was measured. Specifically, the inner surface of the piping was divided into 16 points at equal intervals in the circumferential direction, and the amount of wall thinning at each point was measured. The maximum amount of wall thinning was found to be 2.32 mm.

[0064] On the other hand, when the amount of thinning is calculated from the temperature history calculated by the method of the present invention, the amount of thinning per converter treatment is 5.3 × 10⁻⁶. -5 The result was mm. In this calculation, k0 = 8.33 × 10 -4 (m 2 The values ​​were set as follows: ( / s), Q = 169.54 (kJ / mol), and R = 8.31 (J / (K·mol)).

[0065] Based on the amount of material loss per processing cycle described above, the amount of material loss over 5 years was calculated to be 2.41 mm using the converter's operating conditions, namely, 50 processing cycles per day and a DRP ratio of 0.5. This value was in close agreement with the measured value of 2.32 mm.

[0066] Thus, according to the method of the present invention, it is possible to estimate the amount of scale formation in piping where high-temperature materials come into contact discontinuously. [Explanation of Symbols]

[0067] 1 Piping 2 Cooling water 3 High-temperature objects 4. Oxide scale

Claims

1. A method for estimating the amount of scale formation in piping where high-temperature materials come into discontinuous contact, The temperature history of the piping surface is calculated by performing transient calculations that switch between heat transfer conditions when in contact with the high-temperature object and when not in contact with it. A method for estimating scale generation amount, which calculates the scale generation amount from the aforementioned temperature history.

2. The calculation of the scale generation amount from the aforementioned temperature history is performed as follows: From the temperature at each time in the aforementioned temperature history, the oxidation rate constant at that time is determined. The amount of scale generated at that time is determined using the oxidation rate constant. This is done by integrating the aforementioned scale generation amount. A method for estimating the amount of scale generated according to claim 1.

3. Furthermore, the method for estimating the amount of scale formation according to claim 1 or 2, wherein the amount of wall thinning of the piping is determined from the estimated amount of scale formation.

4. Furthermore, the method for estimating the amount of scale formation according to claim 3, wherein the lifespan of the piping is estimated from the amount of wall thinning.

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