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

Abstract

A nitrogen concentration prediction method according to the present invention predicts the nitrogen concentration in molten steel during a vacuum degassing treatment. The method comprises a prediction step for calculating a predicted value of the nitrogen concentration in molten steel using a nitrogen concentration prediction model which is a physical model in which a gas-liquid reaction interfacial area for a nitrogen absorption reaction and a denitrification reaction is used as an input variable and the predicted value of the nitrogen concentration in molten steel S is used as an output variable. The prediction step includes an estimation step for estimating the gas-liquid reaction interfacial area by estimating at least one of a bubble reaction interfacial area, a molten steel bath surface area in the vacuum tank, and the amount of change in the gas-liquid reaction interfacial area due to generation of air bubbles from the molten steel, using a calculation formula in which vacuum degassing treatment conditions are used as variables.

Description

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

[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.

[0002] Generally, molten steel processed in a converter or the like is transported to a secondary refining process, where its nitrogen concentration is controlled by a vacuum degassing process. Since appropriate control of the nitrogen concentration in molten steel contributes to increased functionality of steel products, control as accurately as possible is required. Against this background, numerous techniques for controlling the nitrogen concentration in molten steel during vacuum degassing have been proposed. Specifically, Patent Document 1 describes a method in which, in the first half of the vacuum degassing process, the nitrogen concentration in molten steel is analyzed while the hydrogen and oxygen concentrations are maintained at or below predetermined values, and in the second half of the vacuum degassing process, processing conditions are determined based on the analyzed nitrogen concentration. In the method described in Patent Document 1, the nitrogen concentration in molten steel is predicted taking into account the nitrogen absorption and denitrification reactions at the surface of the molten steel bath and the bubble interface in a vacuum vessel, the nitrogen absorption reaction due to the intrusion of air through an immersion tube, and mixing due to the reflux of the molten steel.

[0003] Patent No. 5836187

[0004] T. Kuwabara, K. Umezawa, K. Mori, and H. Watanabe: Trans. Iron Steel Inst. Jpn., 28 (1988), 305. 19th Committee of the Japan Society for the Promotion of Science (ed.): Recommended Equilibrium Values ​​for Steelmaking Reactions, Revised and Supplemented: 1984. T. Kitamura, K. Miyamoto, R. Tsujino, S. Mizoguchi, and K. Kato: 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.

[0005] In the method described in Patent Document 1, the reaction interface area of ​​the nitrogen absorption and denitrification reactions in the vacuum degassing process is calculated on the assumption that the surface area of ​​the molten steel bath in the vacuum vessel is proportional to the 2 / 3 power of the reflux rate, and the bubble interface area is proportional to the 2 / 3 power of the reflux gas flow rate. However, the actual reaction interface area does not change according to such a simple proportional formula, but changes in a complex manner depending on the reflux gas flow rate, the degree of vacuum, the equipment configuration, the nitrogen concentration in the molten steel, etc. For this reason, the method described in Patent Document 1 cannot accurately predict the nitrogen concentration, and as a result, it is difficult to accurately control the nitrogen concentration in the molten steel in the vacuum degassing process.

[0006] The present invention has been made in view of the above-mentioned problems, and an object of the present invention is to provide a nitrogen concentration prediction method and a nitrogen concentration prediction device that can accurately predict the nitrogen concentration in molten steel during vacuum degassing. Another object of the present invention is to provide a nitrogen concentration control method and a nitrogen concentration control device that can accurately control the nitrogen concentration in molten steel during vacuum degassing.

[0007] The nitrogen concentration prediction method of the present invention predicts the nitrogen concentration in molten steel in vacuum degassing treatment, and includes a prediction step of calculating a predicted value of the nitrogen concentration in molten steel using a nitrogen concentration prediction model, which is a physical model that has gas-liquid reaction interface areas of the nitriding reaction and the denitriding reaction as input variables and a predicted value of the nitrogen concentration in molten steel S as an output variable, and the prediction step includes an estimation step of estimating the gas-liquid reaction interface area by estimating at least one of the gas 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 that has variables of the vacuum degassing treatment conditions.

[0008] The estimation step may include a step of estimating the reaction interface area of ​​bubbles of the reflux gas injected into the molten steel by using a function for calculating the surface area of ​​the bubbles, the function having the volume or diameter of the bubbles as a variable.

[0009] The estimation step may include a step of calculating the volume of the bubbles by multiplying the volume of the bubbles near the inlet of the vacuum degassing device by the rate of change in the volume of the bubbles in response to changes in static pressure around the bubbles and the rate of change in the volume of the bubbles in response to changes in the amount of gas in the bubbles due to absorption and release of gas components by the bubbles.

[0010] The estimation step may estimate the volume of bubbles generated from the blowing port using the physical properties of the liquid phase, the diameter of the blowing port, and the blowing conditions of the reflux gas, and may estimate the volume of bubbles near the blowing port of the vacuum degassing device, assuming that multiple bubbles merge together immediately after generation.

[0011] The estimation step is performed by determining the flow rate V of the reflux gas. ｇ , the degree of vacuum P in the vacuum chamber of the vacuum degassing device ｖ , and the volume V of bubbles on the surface of the molten steel bath in the vacuum vessel Ｂ，Ｓ The surface area A of the static molten steel bath in the vacuum vessel is a variable. Ｓ，０ Increase in molten steel bath surface area ΔA ｓ The surface area A of the molten steel bath in the vacuum vessel is calculated using the following formula (1) including a function indicating Ｓ The method may include a step of estimating

[0012]

[0013] The estimation step preferably includes a step of determining bubble precipitation conditions using the equilibrium partial pressure values ​​of gas components in the molten steel and the static pressure at a predetermined depth of the molten steel, and estimating the amount of change in the bubble reaction interface area due to the generation of gas components as bubbles from the molten steel being processed in a reduced pressure atmosphere using the equilibrium partial pressure values, the increase in the bubble reaction interface area due to bubbles generated that satisfy the bubble precipitation conditions, and the increase in the bath surface area in the vacuum tank.

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

[0015] The nitrogen concentration prediction device according to the present invention is a nitrogen concentration prediction device that predicts the nitrogen concentration in molten steel during vacuum degassing treatment, and includes a prediction means that calculates a predicted value of the nitrogen concentration in molten steel using a nitrogen concentration prediction model, which is a physical model that has gas-liquid reaction interface areas of the nitriding reaction and the denitriding reaction as input variables and a 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 gas 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 that has variables of the vacuum degassing treatment conditions.

[0016] The nitrogen concentration control device according to the present invention includes control means for controlling the conditions of the vacuum degassing process in accordance with the nitrogen concentration in the molten steel predicted by the nitrogen concentration prediction device according to the present invention.

[0017] The nitrogen concentration prediction method and nitrogen concentration prediction device according to the present invention can accurately predict the nitrogen concentration in molten steel during vacuum degassing treatment, and the nitrogen concentration control method and nitrogen concentration control device according to the present invention can accurately control the nitrogen concentration in molten steel during vacuum degassing treatment.

[0018] FIG. 1 is a schematic diagram showing the configuration of a vacuum degassing apparatus according to one embodiment of the present invention. FIG. 2 is a diagram showing an example of the relationship between bubble volume and the value of the variable β. FIG. 3 is a diagram for explaining the change in bubble volume due to a pressure difference. FIG. 4 is a diagram for explaining the change in bubble volume due to the reaction of bubble gas components. FIG. 5 is a diagram showing the coalescence of bubbles near the injection port. FIG. 6 is a diagram showing the generation of gas components in molten steel as bubbles under reduced pressure. FIG. 7 is a flowchart showing the flow of a nitrogen concentration prediction process according to one embodiment of the present invention. FIG. 8 is a diagram showing the gas-liquid reaction interface area in an example. FIG. 9 is a diagram showing the nitrogen concentration in molten steel predicted using the gas-liquid reaction interface area shown in FIG. 8.

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

[0020] [Vacuum Degassing Apparatus] First, with reference to FIG. 1, the configuration of a vacuum degassing apparatus according to one embodiment of the present invention will be described.

[0021] Fig. 1 is a schematic diagram showing the configuration of a vacuum degassing apparatus according to one embodiment of the present invention. As shown in Fig. 1, the vacuum degassing apparatus 1 according to one embodiment of the present invention includes a ladle 2 for accommodating molten steel S and a vacuum vessel 3 whose interior can be controlled to a vacuum state. Two immersion pipes 4 are provided at the bottom of the vacuum vessel 3 and communicate with the interior of the vacuum vessel 3. One of the immersion pipes 4 is formed with an inlet 5 for injecting a reflux gas G into the vacuum vessel 3. An exhaust port 6 is formed at the top of the vacuum vessel 3 for discharging gas generated by the vacuum degassing process to the outside.

[0022] When performing vacuum degassing using such a vacuum degassing apparatus, first, the lower ends of the two immersion tubes 4 are immersed in the molten steel S contained in the ladle 2. Next, the vacuum vessel 3 is depressurized while a reflux gas G, such as argon gas or nitrogen gas, is blown in through the blowing port 5, thereby circulating the molten steel S between the ladle 2 and the vacuum vessel 3, thereby performing the degassing treatment. During this process, the molten steel S in the vacuum vessel 3 is exposed to a reduced-pressure atmosphere, and degassing reactions actively occur, primarily resulting in decarburization, denitrification, dehydrogenation, and the like. The gases generated by the degassing reactions are discharged to the outside through the exhaust port 6. Additionally, alloys, auxiliary materials, and the like are added to the molten steel S to adjust the composition of the molten steel S.

[0023] 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 the operating conditions, such as switching the type of reflux gas G, adjusting the flow rate of the reflux gas G, and adjusting the degree of vacuum in the vacuum vessel 3. For example, using nitrogen gas as the reflux gas G increases the nitrogen absorption rate. Also, increasing the degree of vacuum in the vacuum vessel 3 and lowering the pressure in the vacuum vessel 3 increases the denitrification rate in the vacuum vessel 3. The nitrogen concentration in the molten steel S can be controlled by such operations.

[0024] The control of the operating conditions of the vacuum degassing apparatus 1 is executed 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 apparatus 1 based on information indicating the operating state of the vacuum degassing apparatus 1 obtained from sensors and the like provided in the vacuum degassing apparatus 1. In this embodiment, the control device 10 is equipped with a nitrogen concentration prediction model M, which is a physical model that uses the gas-liquid reaction interface areas of the nitriding reaction and the denitriding reaction as input variables and the predicted value of the nitrogen concentration in the molten steel S as an output variable. The control device 10 predicts the nitrogen concentration in the molten steel S using this nitrogen concentration prediction model M, and controls the nitrogen concentration in the molten steel S by controlling the operating conditions of the vacuum degassing apparatus 1 based on the predicted nitrogen concentration. Details of the nitrogen concentration prediction model M will be described later.

[0025] [Nitrogen Concentration Prediction Model] Next, the nitrogen concentration prediction model M will be described.

[0026] Rate of change d [N] of nitrogen concentration in molten steel S in ladle 2 and vacuum vessel 3 Ｌ / dt, d[N] Ｖ Assuming complete mixing of the molten steel S, / dt can be expressed by the following formulas (2) and (3): where t is time (sec) [N] Ｖ is the nitrogen concentration (mass%) in the molten steel S in the vacuum vessel 3, V Ｖ is the volume of molten steel S in the vacuum vessel 3 (m ３ ), Q is the amount of molten steel S circulating (m ３ / sec), [N] Ｌ is the nitrogen concentration (mass%) in the molten steel S in the ladle 2, V Ｌ is the volume of molten steel S in the ladle 2 (m ３ ) is shown.

[0027]

[0028]

[0029] In equation (2), the terms on the right side, starting from the first term, represent the mixing of the molten steel S between the vacuum vessel 3 and the ladle 2 due to the reflux, the rate of change in the nitrogen concentration at the surface of the molten steel bath in the vacuum vessel 3, and the rate of change in the nitrogen concentration at the bubble interface of the reflux gas G. Furthermore, equation (3) takes into account the mixing of the molten steel S between the vacuum vessel 3 and the ladle 2 due to the reflux.

[0030] The amount of molten steel S returned, Q, in the formulas (2) and (3) can be calculated using the formula (4) shown below, with reference to the description in Non-Patent Document 1. In the formula (4), Q ｇ is the reflux gas flow rate (NM ３ / min), D is the immersion pipe diameter (m), P Ｖ indicates the pressure (atm) inside the vacuum chamber 3.

[0031]

[0032] In this embodiment, the rate of change in the nitrogen concentration at each reaction site of the nitrogen absorption and denitrification reactions is assumed to be controlled by a mixture of mass transfer on the molten steel side and chemical reaction at the gas-liquid interface, as shown in the following formula (5). By rearranging formula (5), the following formula (6) is obtained, which shows the reaction rate of nitrogen in the molten steel S in the vacuum vessel 3. Therefore, 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 formula (6) shown below. In formulas (5) and (6), A is the gas-liquid reaction interface area (m ２ ), k ｍ is the mass transfer coefficient of nitrogen on the molten steel side (m / sec), k ｒ is the chemical reaction rate constant of nitrogen (m / sec mass%), [N] ｉ is the nitrogen concentration (mass%) on the molten steel side of the gas-liquid interface, [N] ｅｑ indicates the nitrogen concentration in molten steel in equilibrium with nitrogen gas in the gas phase (equilibrium nitrogen concentration) (mass %).

[0033]

[0034]

[0035] The reaction sites for calculating the rate of change of the nitrogen concentration using equation (6) are the surface of the molten steel bath in the vacuum vessel 3 and the bubble interface. The difference between these is the gas-liquid reaction interface area A and the equilibrium nitrogen concentration [N]. ｅｑ Among these, the equilibrium nitrogen concentration [N] ｅｑ can be calculated using the following formula (7) with reference to the description in Non-Patent Document 2. In formula (7), f Ｎ is the activity coefficient of nitrogen, P Ｎ２ is the nitrogen partial pressure, R is the gas constant (J / K·mol), and T is the temperature of the molten steel S (K).

[0036]

[0037] The nitrogen activity coefficient f in formula (7) Ｎ Regarding the above, the influence of the main components C, Si, Mn, and O is taken into consideration. Specifically, the activity coefficient of nitrogen f is calculated by the following formula (8) using the values ​​shown in Table 1 below as the first-order interaction coefficients between these components and nitrogen described in Non-Patent Document 2. Ｎ In the formula (8), e Ｎ ｊ , and the coefficient of first-order interaction with nitrogen (j=C, Si, Mn, O). However, the above-mentioned components are only examples, and it goes without saying that the number of components to be considered will increase or decrease depending on the component system of the steel type to be processed.

[0038]

[0039]

[0040] In addition, the nitrogen mass transfer coefficient k ｍ can be calculated using the following formulas (9) to (13) with reference to the description in Non-Patent Document 3. In formulas (9) to (13), the molten steel side mass transfer coefficient k of nitrogen is calculated by taking into account the time it takes for the molten steel S around the bubbles to be replaced. ｍ In the formulas (9) to (13), θ is the contact time (min) between the molten steel S and the bubbles, D Ｎ is the diffusion coefficient of nitrogen (m ２ / min), d Ｂ is the bubble diameter (m), U Ｂ is the bubble rising speed (m / min), UＬ is the rising speed of the molten steel (m / min), g is the gravitational acceleration (m ２ / s), and L indicates the bath surface height (m) in the vacuum chamber 3 from the position where the reflux gas is blown in.

[0041]

[0042]

[0043]

[0044]

[0045]

[0046] In addition, the chemical reaction rate constant k of nitrogen in the formula (6) ｒ can be calculated using the following formula (14) 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.

[0047]

[0048] Furthermore, the reaction that occurs at the interface of the nitrogen bubbles when nitrogen gas is injected will be either a nitriding reaction or a denitriding reaction, depending on the magnitude of the nitrogen concentration in equilibrium between the nitrogen concentration in the molten steel S and the nitrogen partial pressure in the nitrogen bubbles. Furthermore, as the injected nitrogen bubbles rise in the molten steel, the static pressure from the molten steel changes, causing the nitrogen partial pressure in the nitrogen bubbles to decrease. As a result, the reaction speed and reaction direction of the rising nitrogen bubbles are not constant, and the nitrogen concentration prediction model M takes this into account and calculates the rate of change in the nitrogen concentration at the interface of the nitrogen bubbles using the following formula (15). [N] in formula (15) ｅｑ (x) is the equilibrium nitrogen concentration (mass %) in the nitrogen bubbles at the floating distance x from the position where the reflux gas is injected, and can be calculated using the above-mentioned formula (7).

[0049]

[0050] [Method for Estimating Gas-Liquid Reaction Interface Area] Next, a method for estimating the gas-liquid reaction interface area A (gas bubble interface area and molten steel bath surface area in the vacuum vessel), which is an input variable of the nitrogen concentration prediction model M, will be described.

[0051] [Method for Estimating Bubble Interface Area] First, a method for estimating the bubble interface area will be described. The bubble interface area can be calculated using the following formula (16). In formula (16), A Ｂ is the bubble interfacial area (m ２ ), N Ｂ is the number of bubbles remaining in the molten steel S, and S Ｂ is the surface area per bubble (m ２ ) is shown.

[0052]

[0053] The number of bubbles N in equation (16) Ｂ is the bubble residence time t Ｂ and the number of bubbles blown in per unit time. Ｂ is the bubble residence time (sec), h is the depth of the molten steel S (m), v Ｂ is the bubble rising speed (m / sec), f Ｂ is the bubble generation frequency (sec －１ ), v Ｂ，０ is the initial bubble volume (m ３ ) is shown.

[0054]

[0055]

[0056]

[0057] The bubble rising velocity v in Equation (17) Ｂ The following formula (20) can be used as an example of the calculation formula for d Ｂ is the bubble diameter (m), g is the gravitational acceleration (m ２ / s). The first term on the right side of equation (20) represents the terminal velocity due to buoyancy, and the second term represents the ascent velocity due to the circulating current.

[0058]

[0059] The surface area S per bubble in formula (16) ＢIt is thought that the Weber number W increases as the bubble volume increases. However, since the actual floating bubbles undergo deformation, it is difficult to express this in a simple mathematical formula. This bubble deformation is expressed by the Weber number W, which is expressed by the following mathematical formula (21): ｅ In equation (21), σ is the surface tension (N / m), ρ is the liquid density (kg / m ３ ), L indicates a characteristic length (m), and U indicates a characteristic velocity (m / s).

[0060]

[0061] Weber number W ｅ is a dimensionless number related to the deformation of a submerged bubble, and the Weber number W ｅ If the characteristic length L is the same, the bubble shape can be considered to be similar. The characteristic length L can be treated as the diameter of the bubble. The characteristic velocity U is calculated by the bubble rising velocity v Ｂ As shown in equation (20), the bubble diameter d Ｂ Considering these together, the Weber number W ｅ can be approximately expressed by the bubble diameter or bubble volume, so the effect of bubble deformation on the bubble surface area can be organized in terms of the bubble diameter or bubble volume. From this study, in the nitrogen concentration prediction model M, the function for calculating the bubble surface area uses the bubble volume as a variable. An example of a formula for calculating the bubble surface area is the following formula (22). In formula (22), β is a variable representing the degree of bubble deformation, V Ｂ is the volume per bubble (m ３ ) is shown.

[0062]

[0063] The variable β increases as the degree of bubble deformation increases, corresponding to an increase in the bubble surface area per volume. The value of variable β can be determined using bubble volume as a variable. Figure 2 shows the value of variable β versus bubble volume obtained in a simulation experiment using a water model. As shown in Figure 2, when the bubble volume is small, there is variation in the value of variable β, but when the bubble volume is larger than a certain level, it can be confirmed that there is a region where the variable β has a certain tendency. The results of the simulation experiment using the water model and the Weber number Wｅ It was confirmed by a similarity study using the above that bubbles exist in the molten steel mainly in a region where the variable β has a certain tendency. From this, it is possible to estimate the surface area per bubble by making the variable β a function of the bubble volume.

[0064] The above-mentioned function for calculating the surface area of ​​a bubble is merely an example, and it is expected that an even better function will be obtained through more precise experiments and detailed analysis. On the other hand, when considering the deformation behavior of the bubbles under investigation, it is important to consider the effects of the bubble diameter and bubble volume, as in the above study, so it is desirable to use these as the main variables.

[0065] As explained above, bubble volume is important when calculating the bubble surface area using Equation (22). However, the volume of bubbles rising to the surface in molten steel changes from moment to moment. This change is due to factors such as the change in bubble volume caused by a pressure difference as shown in Fig. 3 and the change in bubble volume caused by the reaction of bubble gas components as shown in Fig. 4. In Figs. 3 and 4, symbols B1 to B4 indicate bubbles. Fig. 3 shows how the bubble volume increases as the pressure decreases, and Fig. 4 shows how the bubble volume increases as the bubble gas components react with nitrogen in the molten steel.

[0066] The change in volume due to the pressure difference occurs because the static pressure on the bubbles changes as the depth of the molten steel changes when the injected bubbles rise. In the vacuum degassing process, which reduces the pressure inside the vacuum vessel, the pressure difference between the injection port and the surface of the molten steel bath is large, which has a large effect on the change in the volume of the bubbles. If this is taken as the expansion coefficient, the expansion coefficient can be expressed as shown in the following formula (23). In formula (23), R Ｖ，Ｐｒｅｓｓｕｒｅ is the rate of change in bubble volume (expansion rate) due to the change in static pressure around the bubble, P ｖ is the pressure in the vacuum vessel (atm), ρ is the density of the molten steel (kg / m ３ ), g is the gravitational acceleration (m ２ / s), h １ is the depth of the molten steel before bubble expansion (m), h ２ indicates the depth (m) of the molten steel after bubble expansion.

[0067]

[0068] The above formula (23) is a formula assuming that the volume of the bubbles changes ideally simply depending on the pressure ratio. Under reduced pressure, the pressure P ｖ As a result, the effect is relatively greater than under normal pressure. For example, the pressure P ｖ 0.01 (atm), molten steel depth h １ 1.0 m, molten steel depth h ２ is set to 0.2 m, the bubble volume expands by 4.7 times, and it can be said that the expansion rate is an important factor in estimating the bubble interfacial area.

[0069] Although the above equation (23) takes into account changes in static pressure, the pressure that bubbles actually experience is also affected by the rate at which the bubbles rise. Therefore, it is possible to express bubble expansion due to pressure changes in a way other than equation (23).

[0070] Regarding the reaction of the bubble gas components, a nitrification reaction or denitrification reaction occurs due to the reflux gas blown in. At this time, the gas components in the bubbles increase or decrease due to the reaction, causing the bubble volume to change. 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 in the following equation (24). In equation (24), R Ｖ，Ｒｅａｃｔｉｏｎ is the rate of change in bubble volume due to absorption and release of gas components, M Ｂ is the number of moles of gas component per bubble before reaction, ΔM Ｂ indicates the number of moles of gas component per bubble that changes due to the reaction.

[0071]

[0072] Equation (24) calculates the volume change rate as the ratio of the number of moles in the bubbles before and after the change. There are several possible methods for calculating the number of moles of a gas component that changes. For example, there is a method that calculates based on the rate of change of the nitrogen concentration at the bubble interface obtained by model calculation. This method has the advantage of being able to perform calculations taking mass balance into account, but the disadvantage of making the calculations more complicated. Another method is to assume that the reaction rate of the bubbles is constant over a certain length, which has the advantage of simplifying the calculations. The calculation method that should be selected is thought to vary depending on the required accuracy and equipment constraints.

[0073] In order to apply the above-described changes in bubble volume, it is necessary to estimate the original bubble volume. The volume of bubbles generated from the blowing port 5 is thought to change depending on the liquid phase physical properties such as the density and viscosity of the liquid, and on the blowing conditions such as the diameter of the blowing port 5 and the reflux gas flow rate. As for the conditions that can be changed, it is thought that the smaller the diameter of the blowing port 5, the smaller the bubble volume, and the larger the reflux gas flow rate, the larger the bubble volume. It is desirable to estimate the volume of bubbles generated from the blowing port 5 taking these effects into consideration.

[0074] Furthermore, when observing bubbles immediately after injection in a water model simulation, it was confirmed that the bubbles immediately coalesced near the injection port, as shown in Figure 5. From this, it is reasonable to assume that the original volume of the bubbles actually rising in the molten steel is the volume of the bubbles after coalescence. In observations of the water model simulation, the most frequent coalescence was a total of two bubbles. Depending on the conditions, coalescence of three or four bubbles was also observed, so it is important to set the appropriate number of coalescing bubbles depending on the conditions.

[0075] As an estimation formula for the above-mentioned bubble volume, the following formulas (25) and (26) can be given with reference to the description in Non-Patent Document 5. In formulas (25) and (26), d Ｂ，ｎ is the diameter (m) of one of the bubbles generated immediately after the introduction of reflux gas, and d ｎ is the equivalent diameter of the blowing port (m), K ｎ is the fitting parameter for each bubble, V ｇ is the reflux gas flow rate (m３ / sec), V Ｂ，０ is the initial bubble volume (m ３ ), n indicates the ordinal number of bubbles that coalesce immediately after the introduction of reflux gas. Ｂ，０ is the bubble volume when multiple bubbles coalesce as described above.

[0076]

[0077]

[0078] 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 the blowing conditions. ｎ In addition, since the conditions for the bubble coalescence phenomenon described above are different between the bubbles injected first and the bubbles injected later, this difference can be corrected by using the fitting parameter K ｎ The fitting parameter K obtained from the experimental results can be corrected by ｎ An example of the value of the fitting parameter K ｎ The value of was in the range of 0.588 to 0.667. As an example of calculation, when every two bubbles are injected, the fitting parameter K ｎ Then, the bubble diameter is calculated using the fitting parameter K determined for the case of n = 2. ｎ The bubble diameter is calculated using the formula (26), and the bubble volume is calculated using the obtained bubble diameter value.

[0079] [Surface Area of ​​Molten Steel Bath in Vacuum Tank] Next, a method for estimating the bath surface area in a vacuum tank will be described. The surface area of ​​the molten steel bath increases from a static state due to two possible mechanisms: surface deformation caused by circulating molten steel from the immersion tube 4 and disturbance of the bath surface due to injected bubbles. Based on this, we investigated factors affecting the surface area of ​​the molten steel bath in a vacuum tank and found that the reflux gas flow rate, degree of vacuum (pressure in the vacuum tank), and volume of bubbles on the surface of the molten steel bath have a significant influence. Specifically, the reflux gas flow rate affects the reflux rate and the number and volume of injected bubbles, and the higher the reflux gas flow rate, the greater the bath surface area in the vacuum tank. Furthermore, the degree of vacuum is closely related to the expansion of bubbles near the surface of the molten steel bath, and the greater the vacuum level, the greater the surface area of ​​the molten steel bath in the vacuum tank. Furthermore, the volume of bubbles on the surface of the molten steel bath is related to the bubble velocity at the surface of the molten steel bath, and therefore to the degree of disturbance of the molten steel bath surface by bubbles. From these considerations, it was determined that the recirculation gas flow rate, the degree of vacuum, and the bubble volume on the surface of the molten steel bath are important variables for estimating the increase in the surface area of ​​the molten steel bath in a vacuum vessel, and that these variables should be incorporated into the estimation formula. That is, as shown in the following formula (27), it was determined that the surface area of ​​the molten steel bath in a vacuum vessel is estimated from a function having at least two variables selected from the recirculation gas flow rate, the degree of vacuum, and the bubble volume on the surface of the molten steel bath. In formula (27), A Ｓ is the surface area of ​​the molten steel bath in the vacuum vessel (m ２ ), A Ｓ，０ is the surface area of ​​the stationary molten steel bath in the vacuum vessel (m ２ ), ΔA Ｓ () is a function (m ２ ), V ｇ is the reflux gas flow rate (m ３ / sec), P ｖ is the degree of vacuum (atm), V Ｂ，Ｓ is the bubble volume (m ３ ) is shown.

[0080]

[0081] As a specific example, a numerical analysis simulating vacuum degassing was performed to evaluate the influence of the reflux gas flow rate and the bubble volume on the surface of the molten steel bath in the vacuum vessel on the surface area of ​​the molten steel bath. As a result, the increase in the surface area of ​​the molten steel bath in the vacuum vessel due to the reflux of molten steel, ΔAＳ，ｃ can be expressed by the following formula (28), and the increase in the surface area of ​​the molten steel bath due to bubbles is ΔA Ｓ，Ｂ can be expressed as the following formula (29). In formulas (28) and (29), C １ , C ２ , D １ , D ２ , D ３ , D ４ is a coefficient that varies depending on the facility, N Ｂ is the number of bubbles, V Ｂ，Ｓ indicates the bubble volume at the surface of the molten steel bath.

[0082]

[0083]

[0084] The coefficients in the formulas (28) and (29) can be determined by experiments or numerical analysis. An example of the results of numerical analysis is C １ = 112, C ２ = 4.47, D １ = 0.126, D ２ = 5 / 6, D ３ = 0.0853, D ４ = 2.14 x 10 －５ This value is an example obtained by experiments and numerical analysis simulating a certain facility, and different values ​​are obtained depending on the facility and conditions. This example is a calculation example using numerical analysis for the facility investigated by the inventors, and when the facility or the method of investigation into the formulation is changed, a different calculation method can be easily obtained. Even in such a case, as described above, the reflux gas flow rate, the degree of vacuum, and the 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 vessel.

[0085] [Effect of bubbles generated in molten steel] Bubbles generated in molten steel are a factor that affects the bubble interface area and the surface area of ​​the molten steel bath in the vacuum vessel. Specifically, as shown in Fig. 6, gas components in molten steel may be generated as bubbles under reduced pressure, 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 vessel. The bubble generation conditions can be determined by the partial pressure that is in equilibrium with the gas component concentration in the molten steel, and the balance between the static pressure and surface tension that the generated bubbles experience. The following formula (30) can be used as an example of a formula that shows the bubble generation conditions. In formula (30), P Ｎ２ is the nitrogen partial pressure (Pa) that is in equilibrium with the nitrogen concentration in the molten steel, P ｖ indicates the pressure in the vacuum vessel (atm), r indicates the diameter of the bubbles generated in the molten steel (m), and h indicates the depth of the molten steel (m).

[0086]

[0087] Equation (30) is obtained by considering the balance between the bubbles generated in molten steel and static pressure. It is believed that there are other stages in the generation of bubbles in molten steel, but as a result of investigation, it can be said that Equation (30), which expresses whether bubbles can exist stably beyond the point of balance with static pressure, is the most important. Based on the results of molten steel experiments, it is appropriate that the diameter r of bubbles generated in molten steel is approximately 1 to 5 mm. Hereinafter, the increase in the bubble reaction interface area due to bubbles generated under the above conditions and the increase in the surface area of ​​the molten steel bath in the vacuum vessel can be used to estimate the change in the bubble reaction interface area due to the generation of gas components as bubbles from molten steel processed in a reduced-pressure atmosphere.

[0088] Specifically, the diameter r of the generated bubbles is a value assuming that the bubbles are spherical, so the volume of the generated bubbles can be calculated. The volume of the generated bubbles can be calculated, similarly to the bubble reaction interface area of ​​the injected bubbles, from the rate of change in bubble volume depending on the change in static pressure and the change in the amount of gas in the bubbles due to the absorption and release of gas components by the bubbles. The surface area of ​​the generated bubbles can be calculated using Equation (22). This allows for an estimate of the increase in the bubble reaction interface area due to the generated bubbles. Furthermore, this calculation also allows for the calculation of the bubble volume at the surface of the molten steel bath, which can then be used, for example, to estimate the increase in the surface area of ​​the molten steel bath. In addition to the change in reaction rate due to the change in the reaction interface area calculated as above, it is necessary to consider that, because bubbles are generated by nitrogen in the molten steel, the nitrogen concentration in the molten steel decreases by the amount of nitrogen required to generate the bubbles.

[0089] [Estimation of Gas-Liquid Reaction Interface Area] The gas-liquid reaction interface area A can be estimated by taking into account the above-mentioned phenomena and formulating and using them as described above, taking into account the complex operational conditions. Although the accuracy of prediction and control of the nitrogen concentration can be improved by taking each phenomenon into account individually, estimating the gas-liquid reaction interface area by taking into account and combining multiple behaviors enables prediction and control of the nitrogen concentration with even higher accuracy.

[0090] [Nitrogen Concentration Prediction Process] Finally, with reference to FIG. 7, the flow of the nitrogen concentration prediction process using the nitrogen concentration prediction model M will be described.

[0091] 7 is a flowchart showing the flow of the nitrogen concentration prediction process according to one embodiment of the present invention. The flowchart shown in FIG. 7 starts when initial conditions are input to the control device 10 and a command to execute the nitrogen concentration prediction process is input to the control device 10 (step S1), and the nitrogen concentration prediction process proceeds to step S2. Examples of the 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 apparatus 1, and the operating conditions (degree of vacuum, reflux gas flow rate, reflux gas type, etc.).

[0092] In the processing of step S2, the control device 10 determines parameters in the mathematical formulas used to calculate the molten steel side mass transfer coefficient of nitrogen, the chemical reaction rate constant, the activity coefficient, etc., contained in the nitrogen concentration prediction model M. The control device 10 also calculates the reflux state of the molten steel using the reflux gas flow rate, the degree of vacuum, etc. This completes the processing of step S2, and the nitrogen concentration prediction processing proceeds to the processing of step S3.

[0093] In the process of step S3, the control device 10 calculates the volume, velocity, and nitrogen partial pressure of the injected bubbles. This completes the process of step S3, and the nitrogen concentration prediction process proceeds to the processes of steps S4 and S6.

[0094] In the process of step S4, the control device 10 calculates the gas-liquid reaction interface area of ​​the bubble interface, which completes the process of step S4, and the nitrogen concentration prediction process proceeds to the process of step S5.

[0095] In the process of step S5, the control device 10 calculates the rate of change of the nitrogen concentration at the bubble interface using the nitrogen concentration prediction model M. This completes the process of step S5, and the nitrogen concentration prediction process proceeds to the process of step S8.

[0096] In the process 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 vessel. This completes the process of step S6, and the nitrogen concentration prediction process proceeds to the process of step S7.

[0097] In the process of step S7, the control device 10 calculates the rate of change of the nitrogen concentration at the surface of the molten steel bath in the vacuum tank using the nitrogen concentration prediction model M. This completes the process of step S7, and the nitrogen concentration prediction process proceeds to the process of step S8.

[0098] In the process of step S8, the control device 10 calculates the change amount Δ[N] of the nitrogen concentration in the molten steel in the vacuum vessel and the ladle, using the change rate of the nitrogen concentration at the bubble interface calculated in the process of step S5 and the change rate of the nitrogen concentration at the surface of the molten steel bath in the vacuum vessel calculated in the process of step S7. This completes the process of step 8, and the nitrogen concentration prediction process proceeds to the process of step S9.

[0099] In the process of step S9, the control device 10 calculates the nitrogen concentration [N] of the molten steel in the vacuum vessel and the ladle using the change amount Δ[N] of the nitrogen concentration in the molten steel in the vacuum vessel and the ladle calculated in the process of step S8. Ｖ , [N] Ｌ This completes the process of step S9, and the nitrogen concentration prediction process proceeds to step S10.

[0100] In step S10, the control device 10 determines whether the calculated vacuum degassing process time exceeds the set process time. If the calculated vacuum degassing process time does not exceed the set process time (step S10: No), the control device 10 advances the vacuum degassing process time by a predetermined amount and returns the nitrogen concentration prediction process to step S2. On the other hand, if the calculated vacuum degassing process time exceeds the set process time (step S10: Yes), the control device 10 terminates the nitrogen concentration prediction process. Thereafter, the operator compares the predicted nitrogen concentration value with the target value and modifies the process conditions for adjusting the nitrogen concentration based on the comparison results. Examples of process conditions include the recirculation gas type, recirculation gas flow rate, vacuum degassing process time, and vacuum level.

[0101] In this example, nitrogen concentration control was performed on multiple steel grades. The molten steel composition before vacuum degassing was in the range of [C] < 0.1%, [P] < 0.01%, [S] < 0.01%, [Mn] = 0.02-1.2%, [Si] = 0.1-4.0%, and [Al] < 0.1%. The target nitrogen concentration was 20-120 ppm, the molten steel temperature was 1480-1630°C, and the processed molten steel volume was 180-240 tons. Nitrogen gas or argon gas was used as the reflux gas, the reflux gas flow rate was 1000-3000 (NL / min), the degree of vacuum during stable processing was 0.001-0.1 (atm), and the reflux processing time was approximately 30 minutes. Multiple samplings were taken during processing to analyze the nitrogen concentration, and the actual values ​​were recorded.

[0102] As a control method, initial conditions were input at the start of processing to determine the processing conditions. Nitrogen concentration was predicted based on these processing conditions, and if the predicted nitrogen concentration at the end of processing differed from the target value by more than a certain value, the processing conditions were modified to control the nitrogen concentration. When actual values ​​were obtained by nitrogen concentration analysis during processing, the nitrogen concentration was predicted again from the actual values, and if necessary, the processing conditions were similarly modified. The difference between the predicted value and the target value, which is used as the basis for modifying the processing conditions, should be appropriately determined based on the behavior of change in nitrogen concentration, which differs depending on the equipment, molten steel composition, and molten steel conditions, and the accuracy of the nitrogen concentration prediction model; in the example, it was set to 2 ppm.

[0103] The estimation of the gas-liquid reaction interface area and nitrogen concentration described above will be explained using values ​​from one example of the working examples. The processing conditions for the working example are shown in Table 2, and the target nitrogen concentration for this steel grade is 65 ppm. In this example, the injection port diameter was 4 mm and the number of injection ports was 16. Therefore, calculations for bubbles were performed for one injection port, and it was necessary to treat the number of bubbles as 16 times that number. Figure 8 shows the gas-liquid reaction interface area calculated based on the above processing conditions. The model considers the reaction rate at the molten steel bath surface and the reaction rate at the bubble interface separately, so the molten steel bath surface area and bubble interface area were calculated separately. As shown in Figure 8, the behavior of the change in the gas-liquid reaction interface area due to changes in operating conditions was successfully reproduced.

[0104]

[0105] As shown in Figure 8, the gas-liquid reaction area decreased as the gas flow rate decreased from 2500 (NL / min) to 1600 (NL / min) at the 9-minute mark. Furthermore, the gas-liquid reaction area increased as the degree of vacuum increased, i.e., the pressure inside the vacuum chamber decreased. The effect of changing the reflux gas type was also reflected. For example, when switching from nitrogen gas to argon gas, the bubble reaction shifted from a nitrogen absorption reaction to a denitrification reaction, which increased the bubble volume. This resulted in an increase in the gas-liquid reaction area at the same gas flow rate and vacuum. Figure 9 shows the results of predicting the nitrogen concentration in molten steel using the estimated gas-liquid reaction area. In actual operation, the target nitrogen concentration was achieved by taking corrective action, starting at the 24-minute mark, to change the reflux gas type to nitrogen gas for a predetermined time based on this prediction. In the example discussed, control was performed by changing the reflux gas type. However, as mentioned above, control is also possible by changing the reflux gas flow rate, the degree of vacuum, and the treatment time. Models using this technology can accurately reflect the effects of such changes in processing conditions, making it possible to implement a wide range of control methods.

[0106] The above-described control was performed on multiple charges, and the control accuracy of the present invention was evaluated based on the results. The method for estimating the gas-liquid reaction interface area was divided into bubble interface area estimation, molten steel bath surface area estimation, and consideration of bubble generation phenomena. The influence of each element on control accuracy was evaluated by switching whether or not to use each of these elements in the model calculation. Furthermore, when the present invention was not used, calculations were performed assuming that the molten steel bath surface area is proportional to the 2 / 3 power of the reflux flow rate, and the bubble interface area is proportional to the 2 / 3 power of the reflux gas flow rate, as in the prior art. The results of the control accuracy evaluation are shown in Table 3. Approximately 100 charges were evaluated for each example, and the evaluation methods were the standard deviation σ of the difference between the target value and the actual value at the end of treatment, and the percentage of deviations from the target nitrogen concentration range of ±5 ppm.

[0107]

[0108] 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, improvement in control accuracy was confirmed compared to Comparative Example 1, which was a conventional method. Examples 2 to 4 were cases in which only estimation of the bubble interface area, only estimation of the molten steel bath surface area, and only estimation of bubble generation were applied, respectively, but compared to these, Example 1, in which all gas-liquid reaction interface areas were estimated by the method of the present invention, had the best control accuracy.

[0109] Although the present invention has been described above as an embodiment, the present invention is not limited by the description and drawings that form a part of the disclosure of the present invention. For example, a machine learning correction model may be created, which is a machine learning model that uses vacuum degassing treatment conditions as explanatory variables and a prediction error, which is the difference between the predicted value of the nitrogen concentration in molten steel calculated using the nitrogen concentration prediction model M for those conditions, as the objective variable. The predicted value of the nitrogen concentration in molten steel calculated using the nitrogen concentration prediction model M may then be corrected using the created machine learning correction model. This allows for more accurate prediction of the nitrogen concentration in molten steel, taking into account the effects of differences in the components and temperature of each molten steel subjected to vacuum degassing treatment, the effects of added auxiliary materials on the components or degassing, and disturbances from other processing steps and transportation processes outside of the vacuum degassing treatment. In this case, the explanatory variables may include the number of times the vacuum degassing equipment has been used. Furthermore, the correction of the predicted value may be performed when the actual value of the nitrogen concentration in molten steel is obtained. Thus, all other embodiments, examples, and operational techniques made by those skilled in the art based on this embodiment are included in the scope of the present invention.

[0110] According to the present invention, it is possible to provide a nitrogen concentration prediction method and a nitrogen concentration prediction device that can accurately predict the nitrogen concentration in molten steel during air degassing treatment. Also, according to the present invention, it is possible to provide a nitrogen concentration control method and a nitrogen concentration control device that can accurately control the nitrogen concentration in molten steel during vacuum degassing treatment.

[0111] REFERENCE SIGNS LIST 1 Vacuum degassing device 2 Ladle 3 Vacuum tank 4 Immersion tube 5 Inlet 6 Exhaust port 10 Control device G Circulation gas S Molten steel

Claims

1. A nitrogen concentration prediction method for predicting the nitrogen concentration in molten steel during vacuum degassing treatment, comprising a prediction step of calculating a predicted value of the nitrogen concentration in molten steel using a nitrogen concentration prediction model, which is a physical model whose input variables are the gas-liquid reaction interface areas of the nitriding reaction and the denitriding reaction, and whose output variable is the predicted value of the nitrogen concentration in molten steel S, wherein the prediction step includes an estimation step of estimating the gas-liquid reaction interface area by estimating at least one of the gas 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 gas bubbles from the molten steel, using a calculation formula whose variables are the conditions of the vacuum degassing treatment.

2. The 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 injected into the molten steel using a function for calculating the surface area of ​​the bubbles, the function having the volume or diameter of the bubbles as a variable.

3. A nitrogen concentration prediction method as described in claim 2, wherein the estimation step includes a step of calculating the volume of the bubbles by multiplying the volume of the bubbles near the injection port of the vacuum degassing device by the rate of change in the volume of the bubbles in response to changes in the static pressure around the bubbles, and by the rate of change in the volume of the bubbles in response to changes in the amount of gas in the bubbles due to absorption and release of gas components by the bubbles.

4. A nitrogen concentration prediction method as described in claim 3, wherein the estimation step includes a step of estimating the volume of bubbles generated from the blowing port using the physical properties of the liquid phase, the diameter of the blowing port, and the blowing conditions of the reflux gas, and estimating the volume of bubbles near the blowing port of the vacuum degassing device, assuming that multiple bubbles merge immediately after generation.

5. The estimation step is performed by calculating the flow rate V of the reflux gas. ｇ , the degree of vacuum P in the vacuum chamber of the vacuum degassing device ｖ , and the volume V of bubbles on the surface of the molten steel bath in the vacuum vessel Ｂ，Ｓ The surface area A of the static molten steel bath in the vacuum vessel is a variable. Ｓ，０ Increase in molten steel bath surface area ΔA ｓ The surface area A of the molten steel bath in the vacuum vessel is calculated using the following formula (1) including a function indicating Ｓ The nitrogen concentration prediction method according to any one of claims 1 to 4, further comprising the step of estimating 6. A nitrogen concentration prediction method according to any one of claims 1 to 5, wherein the estimation step includes a step of determining bubble precipitation conditions using the equilibrium partial pressure value of the gas component in the molten steel and the static pressure at a predetermined depth of the molten steel, and estimating the amount of change in the bubble reaction interface area due to the generation of gas components as bubbles from the molten steel being processed in a reduced pressure atmosphere using the equilibrium partial pressure value and the increase in the bubble reaction interface area due to bubbles generated that satisfy the bubble precipitation conditions and the increase in the bath surface area in the vacuum tank.

7. A nitrogen concentration control method comprising the step of controlling the conditions of a vacuum degassing process in accordance with the nitrogen concentration in molten steel predicted by the nitrogen concentration prediction method according to any one of claims 1 to 6.

8. A nitrogen concentration prediction device for predicting the nitrogen concentration in molten steel during vacuum degassing treatment, comprising: a prediction means for calculating a predicted value of the nitrogen concentration in molten steel using a nitrogen concentration prediction model, which is a physical model with gas-liquid reaction interface areas of the nitriding reaction and the denitriding reaction as input variables and a predicted value of the nitrogen concentration in molten steel S as an output variable; wherein the prediction means estimates the gas-liquid reaction interface area by estimating at least one of the gas 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 within the molten steel, using a calculation formula with variables being the conditions of the vacuum degassing treatment.

9. A nitrogen concentration control device comprising control means for controlling the conditions of vacuum degassing treatment in accordance with the nitrogen concentration in molten steel predicted by the nitrogen concentration prediction device according to claim 8.

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