Nitrogen concentration prediction method, nitrogen concentration control method, nitrogen concentration prediction device, and nitrogen concentration control device

Abstract

A nitrogen concentration prediction method related to the present invention is a nitrogen concentration prediction method for predicting the nitrogen concentration in molten steel during vacuum degassing treatment, comprising a prediction step for calculating the predicted value of the nitrogen concentration in molten steel using a nitrogen concentration prediction model which is a physical model having the gas-liquid reaction interface area of ​​the adsorption reaction and the denitrification reaction as input variables and the predicted value of the nitrogen concentration in molten steel (S) as an output variable, wherein the prediction step comprises an estimation step for estimating the gas-liquid reaction interface area by estimating at least one of the bubble reaction interface area, the surface area of ​​the molten steel bath in the vacuum tank, and the amount of change in the gas-liquid reaction interface area due to the generation of bubbles from the molten steel using a calculation formula having the conditions of vacuum degassing treatment as variables.

Description

Technology Field

[0001] The present invention relates to a nitrogen concentration prediction method, a nitrogen concentration control method, a nitrogen concentration prediction device, and a nitrogen concentration control device. Background Technology

[0002] Generally, molten steel processed in a converter or similar facility is returned to a secondary refining process, and its nitrogen concentration is controlled by vacuum degassing. Since properly controlling the nitrogen concentration in molten steel contributes to increasing the functionality of steel products, control with the highest possible precision is required. Against this backdrop, many technologies for controlling the nitrogen concentration in molten steel during vacuum degassing have been proposed. Specifically, Patent Document 1 describes a method in which, during the first half of the vacuum degassing process, the nitrogen concentration in the molten steel is analyzed while the treatment is performed so that the hydrogen concentration and oxygen concentration are below a predetermined value, and during the second half of the vacuum degassing process, the treatment conditions are determined based on the analyzed value of the nitrogen concentration. In the method described in Patent Document 1, the nitrogen concentration in the molten steel is predicted by considering the adsorption and denitrification reactions at the surface of the molten steel bath and the bubble interface within the vacuum tank, the adsorption reaction caused by the intrusion of atmosphere from the immersion tube, and mixing due to the reflux of the molten steel. Prior art literature

[0003] Japanese Patent Publication No. 5836187

[0004] T. Kuwabara, K. Umezawa, K. Mori, and H. Watanabe: Trans. Iron Steel Inst. Jpn., 28 (1988), 305 Japan Society for the Promotion of Science, 19th Committee, ed.: Recommended Equilibrium Values ​​for Steelmaking Reactions, Revised and Expanded: 1984 T. Kitamura, K. Miyamoto, R. Tsujino, S. Mizoguchi, and K. Katao: ISIJ International, 36 (1996), 395 K. Harashima, S. Mizoguchi, H. Kajioka, and M. Sakakura: Tetsu-to-Hagane, 73 (1987), 1559 M. Sano, K. Mori, and T. Sato: Tetsu-to-Hagane, 63 (1977), 2308 The problem to be solved

[0005] In the method described in Patent Document 1, the surface area of ​​the molten steel bath in the vacuum tank is proportional to the power of 2 / 3 of the reflux rate, and the bubble interface area is proportional to the power of 2 / 3 of the reflux gas flow rate, thereby calculating the reaction interface area for the adsorption and denitrification reactions in vacuum degassing treatment. However, the actual reaction interface area does not change according to such a simple proportional equation, but rather changes in a complex manner depending on the reflux gas flow rate, vacuum level, equipment shape, nitrogen concentration in the molten steel, etc. For this reason, according to the method described in Patent Document 1, the nitrogen concentration cannot be predicted with high precision, and consequently, it becomes difficult to control the nitrogen concentration in the molten steel with high precision during vacuum degassing treatment.

[0006] The present invention has been made in consideration of the above-mentioned problem, and its purpose is to provide a nitrogen concentration prediction method and a nitrogen concentration prediction device capable of predicting the nitrogen concentration in molten steel during vacuum degassing with high precision. Furthermore, another purpose of the present invention is to provide a nitrogen concentration control method and a nitrogen concentration control device capable of controlling the nitrogen concentration in molten steel during vacuum degassing with high precision. means of solving the problem

[0007] A nitrogen concentration prediction method for predicting the nitrogen concentration in molten steel in a vacuum degassing process related to the present invention comprises a prediction step for calculating the predicted value of the nitrogen concentration in molten steel using a nitrogen concentration prediction model, which is a physical model having the gas-liquid reaction interface area of ​​the adsorption reaction and the denitrification reaction as input variables and the predicted value of the nitrogen concentration in molten steel (S) as an output variable, wherein the prediction step comprises an estimation step for estimating the gas-liquid reaction interface area by estimating at least one of the bubble reaction interface area, the surface area of ​​the molten steel bath in the vacuum tank, and the amount of change in the gas-liquid reaction interface area due to the generation of bubbles from the molten steel using a calculation formula having the conditions of the vacuum degassing process as variables.

[0008] The above estimation step may include a step of estimating the bubble reaction interface area by estimating the reaction interface area of ​​the bubbles of the reflux gas blown into the molten steel using a function that calculates the surface area of ​​the bubbles with the volume or diameter of the bubbles as a variable.

[0009] The above estimation step may include a step of calculating the volume of a bubble by multiplying the volume of a bubble near the blower port of a vacuum degassing device by the rate of change of the volume of the bubble due to a change in the static pressure around the bubble and the rate of change of the volume of the bubble due to a change in the amount of gas inside the bubble caused by the absorption and release of gas components of the bubble.

[0010] The above estimation step involves estimating the volume of bubbles generated from the inlet using the physical properties of the liquid phase, the diameter of the inlet, and the injection conditions of the reflux gas, and estimating the volume of bubbles near the inlet of the vacuum degassing device by assuming that the bubbles combine in multiples immediately after generation.

[0011] The above estimation step is the flow rate of the reflux gas (V g ) , vacuum level (P) inside the vacuum chamber of the vacuum degassing device v ), and the volume of bubbles (V) on the surface of the molten steel bath in the vacuum chamber. B,S Surface area of ​​the stationary molten steel bath in the vacuum chamber with ) as a variable (A S,0 Increase in molten steel bath surface area from ) (ΔA s Using the following formula (1) which includes a function representing ) the surface area (A) of the molten steel bath in the vacuum tank S You just need to include a step to estimate ).

[0012]

[0013] The above estimation step may include a step of determining bubble precipitation conditions using the equilibrium partial pressure of the gas component in the molten steel and the static pressure at a predetermined molten steel depth, and estimating the change in the bubble reaction interface area caused by the generation of the gas component as a bubble from the molten steel being processed under a reduced pressure atmosphere by using the increase in the bubble reaction interface area caused by the bubble generated satisfying the equilibrium partial pressure and the bubble precipitation conditions and the increase in the bath surface area in the vacuum bath.

[0014] A nitrogen concentration control method related to the present invention includes a step of controlling the conditions of vacuum degassing treatment according to the nitrogen concentration in molten steel predicted by the nitrogen concentration prediction method related to the present invention.

[0015] A nitrogen concentration prediction device related to the present invention is a nitrogen concentration prediction device for predicting the nitrogen concentration in molten steel during vacuum degassing treatment, and comprises a prediction means for calculating the predicted value of the nitrogen concentration in molten steel by using a nitrogen concentration prediction model, which is a physical model that takes the gas-liquid reaction interface area of ​​the adsorption reaction and the denitrification reaction as input variables and the predicted value of the nitrogen concentration in molten steel (S) as an output variable, and the prediction means estimates the gas-liquid reaction interface area by estimating at least one of the bubble reaction interface area, the surface area of ​​the molten steel bath in the vacuum tank, and the amount of change in the gas-liquid reaction interface area due to the generation of bubbles from the molten steel by using a calculation formula that takes the conditions of the vacuum degassing treatment as variables.

[0016] The nitrogen concentration control device related to the present invention comprises a control means for controlling the conditions of vacuum degassing treatment according to the nitrogen concentration in the molten steel predicted by the nitrogen concentration prediction device related to the present invention. Effects of the invention

[0017] According to the nitrogen concentration prediction method and nitrogen concentration prediction device related to the present invention, the nitrogen concentration in molten steel during vacuum degassing can be predicted with high precision. Furthermore, according to the nitrogen concentration control method and nitrogen concentration control device related to the present invention, the nitrogen concentration in molten steel during vacuum degassing can be controlled with high precision. Brief explanation of the drawing

[0018] FIG. 1 is a schematic diagram showing the configuration of a vacuum degassing device, which is an embodiment of the present invention. Figure 2 is a diagram showing an example of the relationship between the volume of a bubble and the value of the variable (β). Figure 3 is a diagram illustrating the change in the volume of bubbles due to a pressure difference. Figure 4 is a diagram illustrating the change in volume of bubbles due to the reaction of bubble gas components. Figure 5 is a diagram showing the merging of bubbles near the intake port. Figure 6 is a diagram showing how gas components in molten steel are generated as bubbles under reduced pressure. FIG. 7 is a flowchart showing the flow of nitrogen concentration prediction processing, which is an embodiment of the present invention. Figure 8 is a diagram showing the gas-liquid reaction interface area in the example. Figure 9 is a diagram showing the nitrogen concentration in molten steel predicted using the gas-liquid reaction interface area shown in Figure 8. Specific details for implementing the invention

[0019] Hereinafter, with reference to the drawings, a nitrogen concentration prediction method, a nitrogen concentration control method, a nitrogen concentration prediction device, and a nitrogen concentration control device, which are embodiments of the present invention, will be described in detail.

[0020] [Vacuum Degassing Device]

[0021] First, with reference to FIG. 1, the configuration of a vacuum degassing device, which is an embodiment of the present invention, will be described.

[0022] FIG. 1 is a schematic diagram showing the configuration of a vacuum degassing device according to one embodiment of the present invention. As shown in FIG. 1, a vacuum degassing device (1) according to one embodiment of the present invention is equipped with a ladle (2) in which molten steel (S) is received and a vacuum tank (3) capable of controlling the interior to a vacuum state. In addition, two immersion pipes (4) communicating with the interior of the vacuum tank (3) are formed at the bottom of the vacuum tank (3), and an inlet port (5) for blowing reflux gas (G) into the vacuum tank (3) is formed in one of the immersion pipes (4). In addition, an exhaust port (6) for discharging gas generated by vacuum degassing treatment to the outside is formed at the top of the vacuum tank (3).

[0023] When performing vacuum degassing using such a vacuum degassing device, first, the lower ends of two immersion tubes (4) are immersed in the molten steel (S) contained in the ladle (2). Next, while blowing in a reflux gas (G), such as argon gas or nitrogen gas, from the blower port (5), the inside of the vacuum tank (3) is depressurized, thereby circulating the molten steel (S) between the ladle (2) and the vacuum tank (3) to perform degassing. At this time, since the molten steel (S) inside the vacuum tank (3) is exposed to a depressurized atmosphere, the degassing reaction occurs actively, and mainly decarburization, denitrification, and dehydrogenation treatments are performed. The gas generated by the degassing reaction is discharged to the outside through the exhaust port (6). At the same time, the composition of the molten steel (S) is adjusted by adding alloys or auxiliary materials to the molten steel (S).

[0024] When it is required to control the nitrogen concentration in the molten steel (S), the nitrogen concentration in the molten steel (S) is controlled by changing operating conditions, such as switching the type of reflux gas (G), adjusting the flow rate of the reflux gas (G), and adjusting the vacuum level in the vacuum tank (3). For example, if nitrogen gas is used as the reflux gas (G), the nitrogen absorption rate increases. Also, by increasing the vacuum level in the vacuum tank (3) and lowering the pressure inside the vacuum tank (3), the denitrification rate inside the vacuum tank (3) increases. The nitrogen concentration in the molten steel (S) can be controlled by such operations.

[0025] Control of the operating conditions of such a vacuum degassing device (1) is performed by a control device (10) configured by an information processing device such as a computer. The control device (10) controls the operating conditions of the vacuum degassing device (1) based on information indicating the operating state of the vacuum degassing device (1) obtained from sensors formed in the vacuum degassing device (1). In addition, in this embodiment, the control device (10) is equipped with a nitrogen concentration prediction model (M), which is a physical model that takes the gas-liquid reaction interface area of ​​the nitrogen adsorption reaction and the denitrification reaction as input variables and the predicted value of the nitrogen concentration in the molten steel (S) as output variables. The control device (10) uses this nitrogen concentration prediction model (M) to predict the nitrogen concentration in the molten steel (S) and controls the nitrogen concentration in the molten steel (S) by controlling the operating conditions of the vacuum degassing device (1) based on the predicted nitrogen concentration. Details of the nitrogen concentration prediction model (M) will be described later.

[0026] [Nitrogen Concentration Prediction Model]

[0027] Next, the above nitrogen concentration prediction model (M) is described.

[0028] Rate of change of nitrogen concentration d[N] in molten steel (S) in ladle (2) and vacuum tank (3) L / dt, d[N] V / dt can be expressed by the following formulas (2) and (3), assuming complete mixing of the molten steel (S). Here, in formulas (2) and (3), t is time (sec), [N] V is the nitrogen concentration (mass%) in the molten steel (S) in the vacuum tank (3), V V ε is the volume (㎥) of molten steel (S) in the vacuum tank (3), Q is the reflux rate (㎥ / sec) of molten steel (S), [N] L Nitrogen concentration (mass%) in molten steel (S) in ladle (2), V Lrepresents the volume (m³) of molten steel (S) in the ladle (2).

[0029]

[0030]

[0031] In Equation (2), each term on the right side represents, in order from the first term, the mixing of molten steel (S) between the vacuum tank (3) and the ladle (2) by reflux, the rate of change of nitrogen concentration at the surface of the molten steel bath in the vacuum tank (3), and the rate of change of nitrogen concentration at the bubble interface of the reflux gas (G). Also, Equation (3) takes into account the mixing of molten steel (S) between the vacuum tank (3) and the ladle (2) by reflux.

[0032] In addition, the reflux amount Q of the molten steel (S) in formulas (2) and (3) can be calculated using formula (4) shown below with reference to the description in Non-Patent Literature 1. In formula (4), Q g ε is the reflux gas flow rate (N㎥ / min), D is the immersion tube diameter (m), P V represents the pressure (atm) inside the vacuum tank (3).

[0033]

[0034] In this embodiment, regarding the rate of change of nitrogen concentration at each reaction site of the adsorption and denitrification reactions, the mixing rate of the chemical reaction and the mass transfer to the molten steel side at the gas-liquid interface are assumed as shown in the following equation (5). Thus, by rearranging equation (5), the following equation (6) is obtained as an equation representing the reaction rate of nitrogen in the molten steel (S) in the vacuum tank (3). Accordingly, the nitrogen concentration prediction model (M) calculates the predicted value of the nitrogen concentration in the molten steel (S) by inputting the necessary values ​​into the following equation (6). In equations (5) and (6), A is the gas-liquid reaction interface area (m²), k mε is the mass transfer coefficient of nitrogen to the molten steel side (m / sec), k r [N] is the chemical reaction rate constant of nitrogen (m / sec·mass%). i is the nitrogen concentration (mass%) on the molten steel side of the gas-liquid interface, [N] eq represents the nitrogen concentration in molten steel in equilibrium with nitrogen gas in the gas phase (equilibrium nitrogen concentration) (mass%).

[0035]

[0036]

[0037] Additionally, the reaction sites for calculating the rate of change in nitrogen concentration using Equation (6) are the molten steel bath surface and the bubble interface within the vacuum tank (3), and the difference between them is the gas-liquid reaction interface area A and the equilibrium nitrogen concentration [N] eq is. Among these, equilibrium nitrogen concentration [N] eq It can be calculated using the formula (7) shown below with reference to the description in Non-Patent Document 2. In formula (7), f N is the activity coefficient of nitrogen, P N2 ε₀ represents the partial pressure of nitrogen, R₀ represents the gas constant (J / K·mol), and T₀ represents the temperature (K) of the molten steel (S).

[0038]

[0039] Nitrogen activity coefficient (f) in formula (7) N Regarding ), the influence of C, Si, Mn, and O as major components is considered. Specifically, using the values ​​shown in Table 1 below as the first-order interaction coefficients between these components and nitrogen described in Non-Patent Literature 2, the nitrogen activity coefficient (f) is calculated by the following formula (8). N Calculates ). In formula (8), e N j, and the coefficient of first-order interaction with nitrogen (j=C, Si, Mn, O). However, the components listed above are examples, and it goes without saying that in reality, the components to be considered may increase or decrease depending on the compositional system of the steel grade to be treated.

[0040]

[0041]

[0042] Also, the mass transfer coefficient of nitrogen to the molten steel side (k) in formula (6) m ) can be calculated using the following formulas (9) to (13) with reference to the description in Non-Patent Literature 3. In formulas (9) to (13), the mass transfer coefficient (k) of nitrogen to the molten steel side is taken into account the time during which the molten steel (S) around the bubbles is replaced. m ) determines. In formulas (9) to (13), θ is the contact time (min) between the molten steel (S) and the bubbles, D N ε is the diffusion coefficient of nitrogen (m² / min), d B is the blown bubble diameter (m), U B is the bubble rising speed (m / min), U L represents the molten steel rising speed (m / min), g represents the acceleration due to gravity (m² / s), and L represents the height of the bath surface (m) in the vacuum tank (3) from the position where the reflux gas is blown.

[0043]

[0044]

[0045]

[0046]

[0047]

[0048] Also, the chemical reaction rate constant of nitrogen (k) in formula (6) r) can be calculated using the formula (14) shown below with reference to the description in non-patent document 4. In formula (14), [O] represents the oxygen concentration (mass%) in the molten steel (S), and [S] represents the sulfur concentration (mass%) in the molten steel (S).

[0049]

[0050] Furthermore, when nitrogen gas is blown in, the reaction occurring at the nitrogen bubble interface is either an adsorption reaction or a denitrification reaction, depending on the magnitude of the nitrogen concentration in equilibrium with the nitrogen partial pressure within the nitrogen bubble and the nitrogen concentration in the molten steel (S). Also, since the blown-in nitrogen bubble rises within the molten steel, the nitrogen partial pressure within the nitrogen bubble decreases as the static pressure from the molten steel changes. Consequently, because the reaction rate and reaction direction of the rising nitrogen bubble are not constant, the nitrogen concentration prediction model (M) calculates the rate of change of nitrogen concentration at the nitrogen bubble interface by the following equation (15) which takes this into account. [N] in equation (15) eq (x) is the equilibrium nitrogen concentration (mass%) in the nitrogen bubble at a floating distance x from the reflux gas injection position, and can be calculated using the formula (7) described above.

[0051]

[0052] [Method for Estimating Gas-Liquid Reaction Interfacial Area]

[0053] Next, we will explain the method for estimating the gas-liquid reaction interface area A (bubble interface area and molten steel bath surface area in the vacuum tank), which is an input variable of the nitrogen concentration prediction model (M).

[0054] [Method for Estimating Bubble Interface Area]

[0055] First, a method for estimating the bubble interface area is explained. The bubble interface area can be calculated using the formula (16) shown below. In formula (16), A B is the bubble interface area (m²), N B is bubble water remaining in the molten steel (S), S B represents the surface area (m²) per bubble.

[0056]

[0057] Number of bubbles (N) in formula (16) B ) is the bubble residence time (t) as shown in the following formulas (17) to (19). B It can be calculated from ) and the number of bubbles injected per unit time. In formulas (17) to (19), t B ε is the bubble residence time (sec), h is the depth of the molten steel (S) (m), v B is the bubble rise rate (m / sec), f B is the bubble generation frequency (sec -1 ), v B,0 represents the initial bubble volume (㎥).

[0058]

[0059]

[0060]

[0061] Bubble rise rate (v) in formula (17) B As a calculation formula for ), the formula (20) shown below can be exemplified. In formula (20), d B θ represents the bubble diameter (m), and g represents the acceleration due to gravity (m² / s). The first term on the right side of Equation (20) represents the terminal velocity due to buoyancy, and the second term represents the buoyancy velocity due to reflux.

[0062]

[0063] Surface area per bubble (S) in formula (16) B ) is thought to increase with the increase in bubble volume. However, since deformation of the bubble occurs in actual floating bubbles, it is difficult to express it with a simple formula. Regarding this bubble deformation, the Weber number (W) is expressed by the formula (21) shown below. e It can be summarized as follows. In Equation (21), σ represents surface tension (N / m), ρ represents liquid density (kg / m³), L represents representative length (m), and U represents representative velocity (m / s).

[0064]

[0065] Webers (W e ) is a dimensionless number relating to the deformation of bubbles in a liquid, and the Weber number (W e If ) is the same, the bubble shapes can be considered to form similar shapes. The representative length (L) can be regarded as the diameter of the bubble. The representative velocity (U) is the bubble rising velocity (v B If considered as such, it can be thought of as a function of bubble diameter (dB) as shown in Equation (20). When considering these together, since the Weber number (We) can be approximately expressed in terms of bubble diameter or bubble volume, the influence of bubble deformation on the bubble surface area can be summarized by the bubble diameter or bubble volume. Based on this consideration, in the nitrogen concentration prediction model (M), the function for calculating the bubble surface area takes bubble volume as a variable. As an example of a formula for calculating the bubble surface area, Equation (22) shown below can be used. In Equation (22), β is a variable representing the degree of bubble deformation, V B represents the volume (㎥) per bubble.

[0066]

[0067] The variable (β) increases as the degree of bubble deformation increases, corresponding to an increase in the surface area of ​​the bubble per unit volume. The value of the variable (β) can be determined using the bubble volume as a variable. Figure 2 shows the value of the variable (β) for the bubble volume obtained from a simulation using a water model. As shown in Figure 2, there is a deviation in the value of the variable (β) when the bubble volume is small, but it can be confirmed that there is a region where a constant trend exists in the variable (β) when the bubble volume is larger than a certain level. Through the results of the simulation using a water model and an examination of similarity using the Weber number (We), it was confirmed that in molten steel, bubbles mainly exist in a region where a constant trend exists in the variable (β). In this regard, the surface area per bubble can be estimated by making the variable (β) a function of the bubble volume.

[0068] The function for calculating the surface area of ​​a bubble described above is merely an example, and it is expected that a better function will be obtained through more precise experiments or detailed analysis. Meanwhile, regarding the deformation behavior of the bubble under investigation, since it is important to consider the influence of bubble diameter or bubble volume as discussed above, it is desirable to use these as the primary variables.

[0069] Although it has been explained that bubble volume is important when calculating the bubble surface area using Equation (22), the volume of bubbles rising in the molten steel changes from moment to moment. Factors contributing to this include changes in bubble volume due to pressure differences as shown in Fig. 3, and changes in bubble volume due to reactions of bubble gas components as shown in Fig. 4. In Figs. 3 and 4, symbols B1 to B4 represent bubbles, Fig. 3 shows the bubble volume increasing as pressure decreases, and Fig. 4 shows the bubble volume increasing as bubble gas components react with nitrogen in the molten steel.

[0070] The change in volume due to the pressure difference occurs because the static pressure on the bubbles changes due to the change in the depth of the molten steel when the blown bubbles rise. In vacuum degassing treatment in which the pressure inside the vacuum tank is reduced, the pressure difference between the blower port and the surface of the molten steel bath is large, and the influence on the change in the volume of the bubbles is large. If this is expressed as the expansion rate, the expansion rate can be expressed as shown in the following formula (23). In formula (23), R V,Pressure ε is the rate of change in bubble volume (expansion rate) due to the change in static pressure around the bubble, P v ε₀ is the pressure in the vacuum chamber (atm), ρ₀ is the density of the molten steel (kg / m³), g₀ is the acceleration due to gravity (m² / s), h1 is the depth of the molten steel before bubble expansion (m), and h2 is the depth of the molten steel after bubble expansion (m).

[0071]

[0072] The above equation (23) is an equation based on the assumption that the volume of the bubbles changes ideally according to the ratio of pressures, and under reduced pressure, the pressure (P inside the vacuum chamber in equation (23) v Because ) becomes very small, the effect is relatively greater than under atmospheric pressure. For example, the pressure (P inside the vacuum chamber) v When the value is 0.01 (atm), the molten steel depth (h1) is 1.0 m, and the molten steel depth (h2) is 0.2 m, it can be seen that the bubble volume expands 4.7 times, so the expansion rate can be considered an important factor in estimating the bubble interface area.

[0073] Although the above formula (23) takes into account changes in static pressure, in reality, the pressure received by the bubble is also affected by the rising speed of the bubble, so it is thought that it is possible to represent bubble expansion due to pressure changes in a form different from that of formula (23).

[0074] Regarding the reaction of the bubble gas components, an adsorption or denitrification reaction occurs due to the blown-in reflux gas. At this time, the gas components within the bubble increase or decrease due to the reaction, causing a change in the bubble volume. This effect cannot be ignored when the reaction rate is high or the bubble volume is small. The rate of change in bubble volume due to the bubble interface reaction can be expressed as shown in Equation (24) below. In Equation (24), R V,Reaction M is the rate of change in bubble volume due to the absorption and release of gas components. B ε is the number of moles of gas component per bubble before the reaction, ΔM B represents the number of moles of gas component per bubble that changes due to the reaction.

[0075]

[0076] Formula (24) calculates the ratio of the number of moles in a bubble before and after a change in volume as the rate of change in volume. Several methods can be considered for calculating the number of moles of changing gas components. For example, there is a method based on the rate of change of nitrogen concentration at the bubble interface obtained from model calculations, which has the advantage of being able to perform calculations while considering mass balance, but the disadvantage of being cumbersome. Another method is one in which the reaction rate of the bubble is constant for a certain length, which has the advantage of simplifying calculations. It is thought that which calculation method should be selected depends on the required precision and equipment constraints.

[0077] In order to apply the above change in bubble volume, it is necessary to estimate the original bubble volume, but it is thought that the volume of bubbles generated from the blower port (5) changes depending on liquid physical properties such as the density or viscosity of the liquid, and blower conditions such as the diameter of the blower port (5) and the reflux gas flow rate. As for the changing conditions, it is thought that the bubble volume decreases as the diameter of the blower port (5) decreases, and the bubble volume increases as the reflux gas flow rate increases. It is desirable to estimate the bubble volume generated from the blower port (5) after considering these effects.

[0078] Furthermore, when observing the bubbles immediately after injection through simulations using a water model, it was confirmed that the bubbles merged immediately near the injection port, as shown in Fig. 5. In this regard, it is reasonable to consider the original volume of the bubbles actually rising within the molten steel as the volume of the bubbles after this merging. In the observations from the water model simulations, the frequency of a total of two bubbles merging was the highest. Since the merging of three to four bubbles was also observed under certain conditions, it is important to determine the appropriate number of merging bubbles according to the conditions.

[0079] As an estimation formula for the above bubble volume, formulas (25) and (26) shown below can be exemplified by referring to the description in Non-Patent Literature 5, for example. In formulas (25) and (26), d B,n is the diameter (m) of one of the multiple bubbles generated immediately after the blowing of reflux gas, d n Eun, equivalent diameter of the intake (m), K n is the fitting parameter for each bubble, V g is the reflux gas flow rate (㎥ / sec), V B,0 ε is the initial bubble volume (㎥), and n represents the ordinal number of bubbles that coalesce immediately after the blowing of reflux gas. V B,0 is the bubble volume when multiple bubbles combine as described above.

[0080]

[0081]

[0082] Equation (25) is an estimation formula for the bubble diameter when the bubble shape is assumed to be spherical, and estimates the bubble diameter based on the liquid phase properties and blowing conditions. Fitting parameter (K n Differences varying depending on the equipment or operating conditions can be corrected by ). In addition, regarding the bubble aggregation phenomenon described above, since the conditions differ between bubbles blown in first and bubbles blown in later, this difference can be corrected by the fitting parameter (Kn). The fitting parameter (K) obtained from experimental results n An example of the value of ) is the fitting parameter (K n The value of ) was within the range of 0.588 to 0.667. As an example of the calculation, when blown bubbles combine every two, first, the predetermined fitting parameter (K ​​for the case n=1) n Calculate the bubble diameter using ). Then, calculate the bubble diameter using the fitting parameter (Kn) determined for the case n=2, and calculate the bubble volume using the obtained bubble diameter value by formula (26).

[0083] [Surface area of ​​molten steel bath inside vacuum]

[0084] Next, a method for estimating the surface area of ​​the bath inside the vacuum tank will be explained. Two types of mechanisms can be considered for the increase in the surface area of ​​the molten steel bath from the state of the stationary molten steel bath: surface deformation caused by the reflux molten steel from the immersion tube (4) and disturbance of the bath surface by the blown-in bubbles. Based on this, as a result of examining the factors affecting the surface area of ​​the molten steel bath inside the vacuum tank, it was determined that the reflux gas flow rate, the vacuum level (pressure inside the vacuum tank), and the volume of bubbles on the surface of the molten steel bath have a significant influence. Specifically, the reflux gas flow rate affects the amount of reflux and the number and volume of the blown-in bubbles, and the larger the reflux gas flow rate, the larger the surface area of ​​the bath inside the vacuum tank. In addition, the vacuum level is deeply related to the expansion of bubbles near the surface of the molten steel bath, and the larger the vacuum level, the larger the surface area of ​​the molten steel bath inside the vacuum tank. Furthermore, the bubble volume on the surface of the molten steel bath is related to the degree to which the surface of the molten steel bath is disturbed by bubbles, in that it is also related to the bubble velocity on the surface of the molten steel bath. Based on this consideration, when estimating the increase in the surface area of ​​the molten steel bath within the vacuum tank, the reflux gas flow rate, the vacuum level, and the bubble volume on the surface of the molten steel bath are important and were determined to be variables that must be included in the estimation formula. That is, as shown in the following formula (27), the surface area of ​​the molten steel bath within the vacuum tank is estimated from a function that takes at least two of the reflux gas flow rate, the vacuum level, and the bubble volume on the surface of the molten steel bath as variables. In formula (27), A S is the surface area of ​​the molten steel bath in the vacuum chamber (㎡), A S,0 θ is the surface area of ​​the stationary molten steel bath in the vacuum (㎡), ΔA S () is a function (m²), V representing the increase in the surface area of ​​the molten steel bath in the vacuum chamber. g is the reflux gas flow rate (㎥ / sec), P v is the degree of vacuum (atm), V B,S represents the bubble volume (㎥) on the surface of the molten steel bath.

[0085]

[0086] As a specific example, the influence of the reflux gas flow rate and the bubble volume on the surface of the molten steel bath on the surface area of ​​the molten steel bath in the vacuum vessel was evaluated by performing a numerical analysis simulating vacuum degassing treatment. As a result, the increase in the surface area ΔA of the molten steel bath in the vacuum vessel due to molten steel reflux was S,c It can be expressed as shown in the following formula (28), and the increase in the surface area of ​​the molten steel bath due to bubbles ΔA S,B It could be expressed as shown in the following formula (29). In formulas (28) and (29), C1, C2, D1, D2, D3, and D4 are coefficients that differ depending on the equipment, N B is the number of bubbles, V B,S represents the bubble volume on the surface of the molten steel bath.

[0087]

[0088]

[0089] The coefficients in formulas (28) and (29) can be determined by experiment or numerical analysis, and as an example of the results of numerical analysis, C1=112, C2=4.47, D1=0.126, D2=5 / 6, D3=0.0853, D4=2.14×10 -5 This value was obtained as follows. This value is an example obtained through experiments and numerical analysis simulating a certain facility, and different values ​​are obtained depending on the facility or conditions. This example is a calculation example where numerical analysis was used for the facility that the inventors examined, and other calculation methods can be easily obtained when the facility or the examination method of formulation is changed. Even in that case, as described above, the reflux gas flow rate, vacuum level, and bubble volume on the surface of the molten steel bath remain important factors in estimating the change in the surface area of ​​the molten steel bath in the vacuum tank.

[0090] [Influence of bubbles generated from molten steel]

[0091] As a factor affecting the bubble interface area and the surface area of ​​the molten steel bath in the vacuum tank described above, there are bubbles generated from the molten steel. Specifically, as shown in FIG. 6, under reduced pressure, gas components in the molten steel may be generated as bubbles, and if the concentration of gas components in the molten steel is high, many bubbles are generated, contributing to an increase in the bubble interface area and the surface area of ​​the molten steel bath in the vacuum tank. The conditions for bubble generation can be determined by the partial pressure in equilibrium with the concentration of gas components in the molten steel and the balance between the static pressure and surface tension received by the generated bubbles. As a formula representing the conditions for bubble generation, the following formula (30) can be exemplified. In formula (30), P N2 ε is the partial pressure of nitrogen (Pa) in equilibrium with the nitrogen concentration in the molten steel, P v ε₀ represents the pressure in the vacuum chamber (atm), r represents the diameter of the bubbles generated from the molten steel (m), and h represents the depth of the molten steel (m).

[0092]

[0093] Formula (30) is a formula obtained by considering the balance between the bubbles generated from the molten steel and the static pressure. Although it is thought that there are other stages of bubble generation from the molten steel, as a result of the review, Formula (30), which indicates whether it can exist stably beyond the balance point with the static pressure, can be considered the most important. The diameter (r) of the bubbles generated from the molten steel is approximately 1 to 5 mm based on the results of the molten steel experiment. Subsequently, by using the increase in the bubble reaction interface area caused by the bubbles generated under the above conditions and the increase in the surface area of ​​the molten steel bath in the vacuum tank, the change in the bubble reaction interface area caused by the generation of gas components as bubbles from the molten steel processed under a reduced pressure atmosphere can be estimated.

[0094] Specifically, since the diameter (r) of the generated bubble is a value assuming the bubble is spherical, the volume of the generated bubble can be calculated. The volume of the generated bubble can be calculated from the rate of change in the volume of the bubble due to changes in static pressure and changes in the amount of gas inside the bubble caused by the absorption and release of gas components of the bubble, just like the bubble reaction interface area of ​​the blown bubble. Also, the surface area of ​​the generated bubble is calculated by Equation (22). Thus, the increase in the bubble reaction interface area caused by the generated bubble can be estimated. Also, by this calculation, the volume of the bubble on the surface of the molten steel bath can be calculated, and thus, the increase in the surface area of ​​the molten steel bath can be estimated by using Equation (29) as an example. In addition, in addition to the change in reaction rate due to the change in the reaction interface area obtained as above, it is necessary to consider that the nitrogen concentration in the molten steel decreases by the amount of nitrogen required for bubble formation, given that bubbles are generated by nitrogen in the molten steel.

[0095] [Estimation of Gas-Liquid Reaction Interface Area]

[0096] The gas-liquid reaction interface area A can be estimated by considering the phenomena described above and formulating them as described above, thereby taking into account complex operating conditions. Furthermore, while it is possible to expect improvements in the prediction and control precision of nitrogen concentration by considering each phenomenon individually, it becomes possible to predict and control nitrogen concentration with higher precision by performing a gas-liquid reaction interface area estimation that combines multiple behaviors.

[0097] [Nitrogen Concentration Prediction Processing]

[0098] Finally, with reference to Fig. 7, the flow of nitrogen concentration prediction processing using a nitrogen concentration prediction model (M) is described.

[0099] FIG. 7 is a flowchart illustrating the flow of a nitrogen concentration prediction process, which is an embodiment of the present invention. The flowchart shown in FIG. 7 is initiated at a timing (step S1) when initial conditions are input to the control device (10) and an execution command for the nitrogen concentration prediction process is input to the control device (10), and the nitrogen concentration prediction process proceeds to the processing of step S2. Examples of initial conditions input to the control device (10) include the amount of molten steel, the initial composition of the molten steel, the shape of the vacuum degassing device (1), and operating conditions (vacuum degree, reflux gas flow rate, reflux gas type, etc.).

[0100] In the processing of Step S2, the control device (10) determines the parameters in the formula used in the calculation of the nitrogen-to-molten steel mass transfer coefficient, chemical reaction rate constant, activity coefficient, etc., included in the nitrogen concentration prediction model (M). In addition, the control device (10) calculates the reflux state of the molten steel using the reflux gas flow rate, vacuum level, etc. Thus, the processing of Step S2 is completed, and the nitrogen concentration prediction process proceeds to the processing of Step S3.

[0101] In the processing of step S3, the control device (10) calculates the volume, velocity, and partial pressure of the injected bubbles. With this, the processing of step S3 is completed, and the nitrogen concentration prediction process proceeds to the processing of steps S4 and S6.

[0102] In the processing of step S4, the control device (10) calculates the gas-liquid reaction interface area of ​​the bubble interface. With this, the processing of step S4 is completed, and the nitrogen concentration prediction processing proceeds to the processing of step S5.

[0103] In the processing of step S5, the control device (10) calculates the rate of change of nitrogen concentration at the bubble interface using a nitrogen concentration prediction model (M). With this, the processing of step S5 is completed, and the nitrogen concentration prediction processing proceeds to the processing of step S8.

[0104] In the processing of step S6, the control device (10) calculates the gas-liquid reaction interface area on the surface of the molten steel bath in the vacuum tank. With this, the processing of step S6 is completed, and the nitrogen concentration prediction process proceeds to the processing of step S7.

[0105] In the processing of Step S7, the control device (10) calculates the rate of change of nitrogen concentration on the surface of the molten steel bath in the vacuum bath using a nitrogen concentration prediction model (M). With this, the processing of Step S7 is completed, and the nitrogen concentration prediction process proceeds to the processing of Step S8.

[0106] In the processing of Step S8, the control device (10) calculates the change in nitrogen concentration Δ[N] in the molten steel in the vacuum tank and the ladle by using the rate of change in nitrogen concentration at the bubble interface calculated by the processing of Step S5 and the rate of change in nitrogen concentration at the surface of the molten steel bath in the vacuum tank calculated by the processing of Step S7. With this, the processing of Step 8 is completed, and the nitrogen concentration prediction processing proceeds to the processing of Step S9.

[0107] In the processing of Step S9, the control device (10) uses the change in nitrogen concentration Δ[N] in the molten steel in the vacuum tank and ladle calculated by the processing of Step S8 to [N] the nitrogen concentration in the molten steel in the vacuum tank and ladle. V , [N] L Calculate. With this, the processing of step S9 is completed, and the nitrogen concentration prediction processing proceeds to the processing of step S10.

[0108] In the processing of Step S10, the control device (10) determines whether the calculated vacuum degassing time has exceeded the set processing time. If, as a result of the determination, the calculated vacuum degassing time has not exceeded the set processing time (Step S10: No), the control device (10) proceeds with the vacuum degassing time for a predetermined time and then returns the nitrogen concentration prediction processing to the processing of Step S2. On the other hand, if the calculated vacuum degassing time has exceeded the set processing time (Step S10: Yes), the control device (10) terminates the series of nitrogen concentration prediction processing. Afterward, the operator compares the predicted value of the nitrogen concentration with the target value and modifies the processing conditions for adjusting the nitrogen concentration based on the comparison result. Examples of processing conditions may include the type of reflux gas, the flow rate of the reflux gas, the vacuum degassing time, and the degree of vacuum.

[0109] [Example]

[0110] In this embodiment, nitrogen concentration control was performed for a plurality of steel grades. Before vacuum degassing, the molten steel composition was in the range of [C] < 0.1%, [P] < 0.01%, [S] < 0.01%, [Mn] = 0.02 to 1.2%, [Si] = 0.1 to 4.0%, and [Al] < 0.1%; the target nitrogen concentration was 20 to 120 ppm, the molten steel temperature was 1480 to 1630 ℃, and the amount of molten steel treated was 180 to 240 ton. Nitrogen gas or argon gas was used as the reflux gas, the reflux gas flow rate was 1000 to 3000 (NL / min), the vacuum level during treatment stabilization was 0.001 to 0.1 (atm), and the reflux treatment time was generally about 30 minutes. During the treatment, multiple samplings were performed to analyze nitrogen concentration, and the results were recorded.

[0111] As a control method, initial conditions were input at the start of processing, and processing conditions were determined. Based on these processing conditions, nitrogen concentration was predicted; however, if the predicted nitrogen concentration at the end of processing differed from the target value by more than a certain amount, nitrogen concentration control was performed by modifying the processing conditions. When actual values ​​were obtained through nitrogen concentration analysis during processing, nitrogen concentration was predicted again based on those actual values, and if necessary, processing conditions were modified in the same manner. The difference between the predicted value and the target value used as the criterion for modifying processing conditions must be appropriately determined based on the change behavior of nitrogen concentration, which varies depending on the equipment, molten steel components, and molten steel conditions, as well as the precision of the nitrogen concentration prediction model; in the example, this difference was set to 2 ppm.

[0112] Regarding the estimation of the gas-liquid reaction interface area and nitrogen concentration described above, the values ​​in one of the examples are explained as a specific example. The processing conditions of the example described are shown in Table 2, and the target nitrogen concentration for this steel grade is 65 ppm. In this example, since the diameter of the blower port was 4 mm and the number of blower ports was 16, the calculation regarding bubbles was performed for one blower port, and it must be assumed that 16 times that number of bubbles exist. Figure 8 shows the gas-liquid reaction interface area calculated based on the above processing conditions. Since the model considers the reaction rate at the surface of the molten steel bath and the reaction rate at the bubble interface separately, the molten steel bath surface area and the bubble interface area were calculated separately. As shown in Figure 8, it was possible to reproduce the behavior in which the gas-liquid reaction interface area changes as the operating conditions change.

[0113]

[0114] As shown in Fig. 8, the gas-liquid reaction interface area decreased as the gas flow rate decreased from 2500 (NL / min) to 1600 (NL / min) at the 9-minute mark. Additionally, as the vacuum level increases—in other words, as the pressure inside the vacuum chamber decreases—the gas-liquid reaction interface area increases. The influence of changing the reflux gas type is also reflected; for example, when switching from nitrogen gas to argon gas, the reaction in the bubbles changes from an adsorption reaction to a denitrification reaction, causing the bubble volume to increase. Consequently, the gas-liquid reaction interface area increases at the same gas flow rate and vacuum level. Fig. 9 shows the results of predicting the nitrogen concentration in the molten steel using the gas-liquid reaction interface area estimated in this way. In actual operation, based on these prediction results, the target nitrogen concentration was achieved by implementing a modification action to change the reflux gas type to nitrogen gas for a predetermined time starting from the 24-minute mark. In the example embodiment, control was performed by changing the type of reflux gas, but as previously mentioned, control is also possible by changing the reflux gas flow rate, vacuum level, or processing time. Since the model using this technology can accurately reflect the effects of such changes in processing conditions, it was possible to implement various control methods.

[0115] The control described above was performed on multiple charges, and the control precision of the present invention was evaluated based on the results. At that time, regarding the method for estimating the gas-liquid reaction interface area, the bubble interface area estimation, the molten steel bath surface area estimation, and the consideration of bubble generation phenomena were classified, and the influence of each element on the control precision was evaluated by switching whether to use each of these elements in the model calculation. In addition, in the case where the present invention is not used, calculations were performed by assuming that the molten steel bath surface area is proportional to the 2 / 3 power of the reflux amount and the bubble interface area is proportional to the 2 / 3 power of the reflux gas flow rate, which is the conventional technology. The results of the control precision evaluation are shown in Table 3. The evaluation was performed on approximately 100 charges for each example, and the evaluation method was defined as the standard deviation σ of the difference between the target value and the actual value at the end of treatment, and the ratio of deviation from the target nitrogen concentration range of ±5 ppm.

[0116]

[0117] As shown in Table 3, in Examples 1 to 4, in which all or part of the gas-liquid reaction interface area estimation method of the present invention was applied, an improvement in control precision was confirmed compared to Comparative Example 1 of the conventional method. Examples 2 to 4 were cases in which only the estimation of the bubble interface area, only the estimation of the molten steel bath surface area, and only the estimation of bubble generation were applied, respectively; however, compared to these, Example 1, in which all gas-liquid reaction interface areas were estimated by the method of the present invention, showed the best control precision.

[0118] Although embodiments applying the invention made by the inventors have been described above, the present invention is not limited by the above description and drawings, which constitute part of the disclosure of the present invention according to the present embodiment. For example, a machine learning correction model may be created in which the conditions of vacuum degassing treatment are explanatory variables and the prediction error, which is the difference between the predicted value and the actual value of the nitrogen concentration in molten steel calculated using a nitrogen concentration prediction model (M) for said conditions, is the objective variable, and the predicted value of the nitrogen concentration in molten steel calculated using the nitrogen concentration prediction model (M) may be corrected using the created machine learning correction model. By doing so, the nitrogen concentration in molten steel can be predicted with higher precision by considering the influence due to differences in composition and temperature for each molten steel undergoing vacuum degassing treatment, the influence of added auxiliary materials on composition or degassing, and the influence of disturbances from other processing processes or conveying other than vacuum degassing treatment. In addition, in this case, the number of times the vacuum degassing device equipment is used may be included in the explanatory variables. Furthermore, the correction of the predicted value may be performed at the timing when the actual value of the nitrogen concentration in the molten steel is obtained. As such, other embodiments, examples, and operational techniques, etc., carried out by those skilled in the art based on this embodiment are all included within the scope of the present invention.

[0119] Industrial applicability

[0120] According to the present invention, a nitrogen concentration prediction method and a nitrogen concentration prediction device capable of predicting the nitrogen concentration in molten steel with high precision during air degassing treatment can be provided. Furthermore, according to the present invention, a nitrogen concentration control method and a nitrogen concentration control device capable of controlling the nitrogen concentration in molten steel with high precision during vacuum degassing treatment can be provided. Explanation of the symbols

[0121] 1 : Vacuum degassing device 2 : Radle 3 : Vacuum chamber 4 : Immersion tube 5: Intake port 6 : Exhaust port 10: Control unit G: Reflux gas S : Molten steel

Claims

Claim 1 A nitrogen concentration prediction method for predicting the nitrogen concentration in molten steel during vacuum degassing treatment, comprising a prediction step for calculating the predicted value of the nitrogen concentration in molten steel using a nitrogen concentration prediction model which is a physical model having the gas-liquid reaction interface area of ​​the adsorption reaction and the denitrification reaction as input variables and the predicted value of the nitrogen concentration in molten steel (S) as an output variable, wherein the prediction step comprises an estimation step for estimating the gas-liquid reaction interface area by estimating at least one of the bubble reaction interface area, the surface area of ​​the molten steel bath in the vacuum tank, and the amount of change in the gas-liquid reaction interface area due to the generation of bubbles from the molten steel using a calculation formula having the conditions of the vacuum degassing treatment as variables. Claim 2 A nitrogen concentration prediction method according to claim 1, wherein the estimation step includes a step of estimating the bubble reaction interface area by estimating the reaction interface area of ​​the bubbles of the reflux gas blown into the molten steel using a function that calculates the surface area of ​​the bubbles with the volume or diameter of the bubbles as a variable. Claim 3 A method for predicting nitrogen concentration according to claim 2, wherein the estimation step comprises a step of calculating the volume of a bubble by multiplying the volume of a bubble near the blower port of a vacuum degassing device by the rate of change of the volume of a bubble due to a change in static pressure around the bubble and the rate of change of the volume of a bubble due to a change in the amount of gas inside the bubble caused by the absorption and release of gas components of the bubble. Claim 4 A method for predicting nitrogen concentration according to claim 3, wherein the estimation step includes a step of estimating the volume of bubbles generated from the injection port using the physical properties of the liquid phase, the diameter of the injection port, and the injection conditions of the reflux gas, and estimating the volume of bubbles near the injection port of the vacuum degassing device by assuming that the bubbles combine in multiple numbers immediately after generation. Claim 5 In any one of claims 1 to 4, the estimation step is the flow rate of the reflux gas (V g ) , vacuum level (P) inside the vacuum chamber of the vacuum degassing device v ), and the volume of bubbles (V) on the surface of the molten steel bath in the vacuum chamber. B,S Surface area of ​​the stationary molten steel bath in the vacuum chamber with ) as a variable (A S,0 Increase in molten steel bath surface area from ) (ΔA s Using the following formula (1) which includes a function representing ) the surface area (A) of the molten steel bath in the vacuum tank S A nitrogen concentration prediction method including a step for estimating ). Claim 6 A method for predicting nitrogen concentration according to any one of claims 1 to 5, wherein the estimation step comprises determining a bubble precipitation condition using an equilibrium partial pressure value of a gas component in molten steel and a static pressure at a predetermined molten steel depth, and estimating the amount of change in the bubble reaction interface area caused by the generation of a gas component as a bubble from molten steel treated under a reduced pressure atmosphere by using the increase in the bubble reaction interface area caused by the generated bubble satisfying the equilibrium partial pressure value and the bubble precipitation condition and the increase in the bath surface area in the vacuum bath. Claim 7 A nitrogen concentration control method comprising a step of controlling the conditions of vacuum degassing treatment according to the nitrogen concentration in molten steel predicted by the nitrogen concentration prediction method described in any one of claims 1 to 6. Claim 8 A nitrogen concentration prediction device for predicting the nitrogen concentration in molten steel during vacuum degassing treatment, comprising a nitrogen concentration prediction model which is a physical model with the gas-liquid reaction interface area of ​​the adsorption reaction and denitrification reaction as input variables and the predicted value of the nitrogen concentration in molten steel (S) as output variables, and a prediction means for calculating the predicted value of the nitrogen concentration in molten steel, wherein the prediction means estimates the gas-liquid reaction interface area by using a calculation formula in which the conditions of the vacuum degassing treatment are variables, and by estimating at least one of the bubble reaction interface area, the surface area of ​​the molten steel bath in the vacuum tank, and the amount of change in the gas-liquid reaction interface area due to the generation of bubbles from the molten steel. Claim 9 A nitrogen concentration control device having a control means for controlling the conditions of vacuum degassing treatment according to the nitrogen concentration in molten steel predicted by the nitrogen concentration prediction device described in claim 8.

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