METHOD FOR DETERMINING QUANTITY OF CALCIUM LINE FED INTO MOLTEN STEEL BASED ON MINIMUM GIBBS FREE ENERGY PRINCIPLE

Abstract

Provided is a method for determining a quantity of a calcium line fed into molten steel based on a minimum Gibbs free energy principle, which relates to an calcium treatment process of molten steel refining for iron and steel metallurgy. The method includes: establishing a connection with a database to read composition information and a temperature of the molten steel in an actual production process; calculating contents of inclusions in the molten steel according to the read composition information; calculating a required quantity of calcium of the molten steel to control the inclusions in a target area under a current condition; and calculating a length of the fed calcium line according to parameter information of the calcium treatment process and the required quantity of calcium of the molten steel. With the method, a scientific and reasonable guidance is provided for the calcium treatment process in the actual production process.

Claims

1. A method for determining a quantity of a calcium line fed into molten steel based on a minimum Gibbs free energy principle, comprising: S1, obtaining, from a factory database, composition information of the molten steel before a calcium treatment process and parameter information of the calcium treatment process; S2, performing thermodynamic calculation on the composition information of the molten steel based on the minimum Gibbs free energy principle to obtain contents of inclusions in the molten steel and a required quantity of calcium of the molten steel, specifically comprising: S21, calculating a minimum Gibbs free energy of the molten steel based on the minimum Gibbs free energy principle using a formula (1) expressed as follows: $\begin{array}{cc}\min .G_s=\underset{i=1}{\overset{c}{.Math.}}{n}_i{G}_i=\underset{i=1}{\overset{c}{.Math.}}{n}_i\left(G_{m,i}^{\Theta }+\mathrm{RT}\ln a_i\right)=n_m\left[G_m^{\Theta }+\mathrm{RT}\ln \left(a_m\right)\right]+n_{slag}\left[G_{\mathrm{slag}}^{\Theta }+\mathrm{RT}\ln \left(a_{\mathrm{slag}}\right)\right]+n_{solid}\times G_{solid}^{\Theta }& \left(1\right)\end{array}$ where min.G.sub.s represents the minimum Gibbs free energy of the molten steel, G.sub.i.sup.Θ represents a standard molar Gibbs free energy of a composition i of the molten steel, a.sub.i represents an activity value of the composition i, the composition i comprises a solid-phase inclusion, a liquid-phase inclusion and a liquid-phase steel, m represents elements of the liquid-phase steel, n represents a number of moles, R represents a gas constant, T represents a temperature of the molten steel, slag represents the liquid-phase inclusion of the molten steel, solid is the solid-phase inclusion of the molten steel, and c represents the number of compositions of the molten steel; and S22, calculating Gibbs free energies of the solid-phase inclusion, the liquid-phase inclusion, and the liquid-phase steel, where the Gibbs free energy of the solid-phase inclusion is calculated based on a formula (2) expressed as follows:
min.G.sub.Solid=n.sub.SolidG.sub.Solid.sup.Θ=n.sub.Al.sub.2.sub.O.sub.3G.sub.Al.sub.2.sub.O.sub.3.sup.Θ+n.sub.CaO.Math.6Al.sub.2.sub.O.sub.3G.sub.CaO.Math.6Al.sub.2.sub.O.sub.3.sup.Θ+n.sub.CaO.Math.2Al.sub.2.sub.O.sub.3G.sub.CaO.Math.2Al.sub.2.sub.O.sub.3.sup.Θ+n.sub.CaOG.sub.CaO.sup.Θ+n.sub.CaSG.sub.CaS.sup.Θ  (2) where the Gibbs free energy of the liquid-phase inclusion is calculated based on a formula (3) expressed as follows:
min.G.sub.slag=n.sub.Al.sub.2.sub.O.sub.3[G.sub.Al.sub.2.sub.O.sub.3+RT ln(a.sub.Al.sub.2.sub.O.sub.3)]n.sub.CaO[G.sub.CaO.sup.73 +RT ln(a.sub.CaO)]  (3) where the Gibbs free energy of the liquid-phase steel is calculated based on a formula (4) expressed as follows: $\begin{array}{cc}\min .G_{Fe}=\underset{i=1}{\overset{C}{.Math.}}{n}_i{G}_i=\underset{i=1}{\overset{C}{.Math.}}{n}_i\left(G_{m,i}^{\Theta }+\mathrm{RT}\ln a_i\right)=n_{Al}\left[G_{Al}^{\Theta }+\mathrm{RT}\ln \left(x_{Al}{\gamma }_{Al}\right)\right]+n_{\mathrm{Ca}}\left[G_{\mathrm{Ca}}^{\Theta }+\mathrm{RT}\ln \left(x_{\mathrm{Ca}}{\gamma }_{\mathrm{Ca}}\right)\right]+n_O\left[G_O^{\Theta }+\mathrm{RT}\ln \left(x_O{\gamma }_O\right)\right]+n_S\left[G_S^{\Theta }+\mathrm{RT}\ln \left(x_S{\gamma }_S\right)\right].& \left(4\right)\end{array}$ where C represents the number of the elements of the liquid-phase steel, x represents a molar fraction of the elements in the liquid-phase steel, and γ represents an activity coefficient of the elements in the liquid-phase steel; S23, calculating activity values of compositions of the solid-phase inclusion and activity values of compositions of the liquid-phase inclusion, wherein each of the activity values of the compositions of the solid-phase inclusion is 1, and the activity values of the compositions of the liquid-phase inclusion is calculated based on formulas (5) and (6) expressed as follows:
a.sub.Al.sub.2.sub.O.sub.3=(−3.9367*m.sub.Al.sub.2.sub.O.sub.3.sup.4+8.1721*m.sub.Al.sub.2.sub.O.sub.3.sup.3−3.7817*m.sub.Al.sub.2.sub.O.sub.3.sup.2+0.57821*m.sub.Al.sub.2.sub.O.sub.3−0.0145   (5)
a.sub.CaO=(−6.4181*m.sub.Al.sub.2.sub.O.sub.3.sup.4+13.8441*m.sub.Al.sub.2.sub.O.sub.3.sup.3−8.1761*m.sub.Al.sub.2.sub.O.sub.3.sup.2+0.2823*m.sub.Al.sub.2.sub.O.sub.3+1.0129   (6) where a.sub.Al.sub.2.sub.O.sub.3 represents an activity value of a composition Al.sub.2O.sub.3 of the liquid-phase inclusion, a.sub.CaO represents an activity value of a composition CaO of the liquid-phase inclusion, m.sub.Al.sub.2.sub.O.sub.3 represents a mass fraction of the composition Al.sub.2O.sub.3 of the liquid-phase inclusion; and S24, determining the contents of the inclusions in the molten steel, by substituting the formulas (2) to (6) into the formula (1), adding a constraint condition, in which an input variable is the composition information of the molten steel when the contents of the inclusions in the molten steel are calculated, and solving the substituted formula (1); and determining the required quantity of the calcium of the molten steel on a condition that the inclusions in the molten steel are controlled in a liquid phase region; S3, predicting a yield rate of the calcium during the calcium treatment process; and S4, determining a length of the fed calcium line according to the required quantity of calcium of the molten steel, the yield rate of the calcium, and the parameter information of the calcium treatment process, wherein the length of the fed calcium line is calculated based on a formula (7) expressed as follows: $\begin{array}{cc}L=\frac{W\times \left({n\left[\mathrm{Ca}\right]}_T-{n\left[\mathrm{Ca}\right]}_O\right)\times M_{Ca}}{\eta \times \beta \times \mu \times M_{Fe}}& \left(7\right)\end{array}$ where L represents the length of the fed calcium line with a unit of meter; W represents a weight of the molten steel with a unit of ton; n[Ca].sub.T represents the required quantity of calcium of the molten steel with a unit of %; n[Ca].sub.0 represents a calcium content of the molten steel before the calcium treatment process with a unit of %; M.sub.ca represents a molar mass of calcium with a unit of gram per mole (g/mol); M.sub.Fe is represents a molar mass of iron with a unit of g/mol; η represents the yield rate of the calcium with a unit of %; β represents a content of calcium of the calcium line with a unit of %; and μ represents a weight per meter of the calcium line with a unit of gram per meter (g/m).

2. The method for determining the quantity of the calcium line fed into molten steel based on the minimum Gibbs free energy principle according to claim 1, wherein the constraint condition is expressed by formulas (8)-(11) as follows:
Σn.sub.Ca=n.sub.[Ca]+n.sub.CaO+n.sub.CaS+n.sub.CA.sub.2+n.sub.CA6   (8)
Σn.sub.Al=n.sub.[Al]+2n.sub.Al.sub.2.sub.O.sub.3+4n.sub.CA.sub.2+12n.sub.CA6   (9)
Σn.sub.O=n.sub.[O]+3n.sub.Al.sub.2.sub.O.sub.3+7n.sub.CA.sub.2+19n.sub.CA6+n.sub.CaO   (10)
Σn.sub.S=n.sub.[S]+n.sub.CaS   (11) where Σn.sub.Ca represents a total number of moles of calcium in the molten steel, n.sub.[Ca] represents a number of moles of dissolved calcium in the liquid-phase steel, n.sub.[Al] represents a number of moles of dissolved aluminum in the liquid-phase steel, n.sub.[O] represents a number of moles of dissolved oxygen in the liquid-phase steel, n.sub.[S] represents a number of moles of dissolved sulfur in the liquid-phase steel, n.sub.CaO represents a number of moles of CaO in the inclusions, n.sub.CaS represents a number of moles of CaS in the inclusions, n.sub.Al.sub.2.sub.O.sub.3 represents a number of moles of Al.sub.2O.sub.3 in the inclusions, n.sub.CA.sub.6 represents a number of moles of CaO.Math.6Al.sub.2O.sub.3 in the inclusions, and n.sub.CA2 represents the number of moles of CaO.Math.2Al.sub.2O.sub.3 in the inclusions.

3. The method for determining the quantity of the calcium line fed into molten steel based on the minimum Gibbs free energy principle according to claim 1, wherein the parameter information of the calcium treatment process comprises: a content of Carbon (C) of the molten steel, a content of Silicon (Si) of the molten steel, a content of Manganese (Mn) of the molten steel, a content of Phosphorus (P) of the molten steel, a content of Sulphur (S) of the molten steel, a content of Calcium (Ca) of the molten steel, a content of Aluminum (Al) of the molten steel, a total content of dissolved oxygen in the molten steel, a content of dissolved oxygen in the liquid-phase steel, the temperature of the molten steel, the weight per meter of the calcium line, the content of calcium of the calcium line, and the weight of the molten steel.

4. The method for determining the quantity of the calcium line fed into molten steel based on the minimum Gibbs free energy principle according to claim 1, wherein the predicting the yield rate of the calcium during the calcium treatment process comprises: predicting the yield rate of the calcium according to one of a neural network model and a content of oxygen in the liquid-phase steel; wherein predicting the yield rate of the calcium according to the content of dissolved oxygen in the liquid-phase steel is expressed as a formula (12) as follows:
y=50000*x.sub.o+10   (12) where x.sub.o represents the content of dissolved oxygen in the liquid-phase steel, and y represents the yield rate of the calcium predicted according to the content of dissolved oxygen in the liquid-phase steel.

5. The method for determining the quantity of the calcium line fed into molten steel based on the minimum Gibbs free energy principle according to claim 4, wherein the neural network model is one of a shallow neural network model and a deep neural network model.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0024] FIG. 1 illustrates an overall flow diagram of the present disclosure.

[0025] FIG. 2 illustrates a schematic flow chart of a method for determining feed quantity of a calcium line into molten steel based on a minimum Gibbs free energy principle according to an embodiment of the present disclosure.

[0026] FIG. 3 illustrates a schematic flow chart for calculating a composition of inclusions in steel using a minimum Gibbs free energy principle according to an embodiment of the present disclosure.

[0027] FIG. 4 illustrates a schematic view of the influence of a calcium content in steel on inclusions calculated based on the minimum Gibbs free energy principle according to an embodiment of the present disclosure.

DETAILED DESCRIPTION OF EMBODIMENTS

[0028] Exemplary embodiments, features and aspects of the present disclosure will be described in detail below combined with accompanying drawings. The same reference numerals in the accompanying drawings indicate elements with the same or similar functions. Although various aspects of the embodiments are shown in the accompanying drawings, the accompanying drawings are not necessarily drawn to scale unless otherwise specified.

[0029] An embodiment of the present disclosure provides a method for determining a quantity of a calcium line fed into molten steel based on a minimum Gibbs free energy principle, which includes:

[0030] S1, obtaining, from a factory database, composition information of the molten steel before a calcium treatment process and parameter information of the calcium treatment process;

[0031] S2, performing thermodynamic calculation on the composition information of the molten steel based on the minimum Gibbs free energy principle to obtain contents of inclusions in the molten steel and a required quantity of calcium of the molten steel, specifically including:

[0032] S21, calculating a minimum Gibbs free energy of the molten steel based on the minimum Gibbs free energy principle using a formula (1) expressed as follows:

[00004]$\begin{array}{cc}\begin{array}{c}\min .G_s=\underset{i=1}{\overset{c}{.Math.}}{n}_i{G}_i=\underset{i=1}{\overset{c}{.Math.}}{n}_i\left(G_{m,i}^{\Theta }+\mathrm{RT}\ln a_i\right)\\ =n_m\left[G_m^{\Theta }+\mathrm{RT}\ln \left(a_m\right)\right]+n_{slag}\left[G_{\mathrm{slag}}^{\Theta }+\mathrm{RT}\ln \left(a_{\mathrm{slag}}\right)\right]+n_{solid}\times G_{solid}^{\Theta }\end{array}& \left(1\right)\end{array}$

where min.G.sub.s represents the minimum Gibbs free energy of the molten steel, G.sub.i.sup.Θ represents a standard molar Gibbs free energy of a composition i of the molten steel, a.sub.i represents an activity value of the composition i, the composition i includes a solid-phase inclusion, a liquid-phase inclusion and a liquid-phase steel, m represents elements of the liquid-phase steel, n represents a number of moles, R represents a gas constant, T represents a temperature of the molten steel, slag represents the liquid-phase inclusion of the molten steel, solid is the solid-phase inclusion of the molten steel, and c represents the number of compositions of the molten steel; and

[0033] S22, calculating Gibbs free energies of the solid-phase inclusion, the liquid-phase inclusion and the liquid-phase steel, [0034] where the Gibbs free energy of the solid-phase inclusion is calculated based on a formula (2) expressed as follows:

min.G.sub.Solid=n.sub.SolidG.sub.Solid.sup.Θ=n.sub.Al.sub.2.sub.O.sub.3G.sub.Al.sub.2.sub.O.sub.3.sup.Θ+n.sub.CaO.Math.6Al.sub.2.sub.O.sub.3G.sub.CaO.Math.6Al.sub.2.sub.O.sub.3.sup.Θ+n.sub.CaO.Math.2Al.sub.2.sub.O.sub.3G.sub.CaO.Math.2Al.sub.2.sub.O.sub.3.sup.Θ+n.sub.CaOG.sub.CaO.sup.Θ+n.sub.CaSG.sub.CaS.sup.Θ  (2)

where the Gibbs free energy of the liquid-phase inclusion is calculated based on a formula (3) expressed as follows:

min.G.sub.slag=n.sub.Al.sub.2.sub.O.sub.3[G.sub.Al.sub.2.sub.O.sub.3.sup.Θ+RT ln(a.sub.Al.sub.2.sub.O.sub.3)]n.sub.CaO[G.sub.CaO.sup.73 +RT ln(a.sub.CaO)]  (3)

where the Gibbs free energy of the liquid-phase steel is calculated based on a formula (4) expressed as follows:

[00005]$\begin{array}{cc}\min .G_{Fe}=\underset{i=1}{\overset{C}{.Math.}}{n}_i{G}_i=\underset{i=1}{\overset{C}{.Math.}}{n}_i\left(G_{m,i}^{\Theta }+\mathrm{RT}\ln a_i\right)=n_{Al}\left[G_{Al}^{\Theta }+\mathrm{RT}\ln \left(x_{Al}{\gamma }_{Al}\right)\right]+n_{\mathrm{Ca}}\left[G_{\mathrm{Ca}}^{\Theta }+\mathrm{RT}\ln \left(x_{\mathrm{Ca}}{\gamma }_{\mathrm{Ca}}\right)\right]+n_O\left[G_O^{\Theta }+\mathrm{RT}\ln \left(x_O{\gamma }_O\right)\right]+n_S\left[G_S^{\Theta }+\mathrm{RT}\ln \left(x_S{\gamma }_S\right)\right]& \left(4\right)\end{array}$

where C represents the number of the elements of the liquid-phase steel, x represents a molar fraction of the elements in the liquid-phase steel, and γ represents an activity coefficient of the elements in the liquid-phase steel;

[0035] S23, calculating activity values of compositions of the solid-phase inclusion and activity values of compositions of the liquid-phase inclusion, where each of the activity values of the compositions of the solid-phase inclusion is 1, and the activity values of the compositions of the liquid-phase inclusion is calculated based on formulas (5) and (6) expressed as follows:

a.sub.Al.sub.2.sub.O.sub.3=(−3.9367*m.sub.Al.sub.2.sub.O.sub.3.sup.4+8.1721*m.sub.Al.sub.2.sub.O.sub.3.sup.3−3.7817*m.sub.Al.sub.2.sub.O.sub.3.sup.2+0.57821*m.sub.Al.sub.2.sub.O.sub.3−0.0145   (5)

a.sub.CaO=(−6.4181*m.sub.Al.sub.2.sub.O.sub.3.sup.4+13.8441*m.sub.Al.sub.2.sub.O.sub.3.sup.3−8.1761*m.sub.Al.sub.2.sub.O.sub.3.sup.2+0.2823*m.sub.Al.sub.2.sub.O.sub.3+1.0129   (6)

where a.sub.Al.sub.2.sub.O.sub.3 represents an activity value of a composition Al.sub.2O.sub.3 of the liquid-phase inclusion, a.sub.CaO represents an activity value of a composition CaO of the liquid-phase inclusion, m.sub.Al.sub.2.sub.O.sub.3 represents a mass fraction of the composition Al.sub.2O.sub.3 of the liquid-phase inclusion; and

[0036] S24, determining the contents of the inclusions in the molten steel, by substituting the formulas (2) to (6) into the formula (1), adding a constraint condition, in which an input variable is the composition information of the molten steel when the contents of the inclusions in the molten steel are calculated, and solving the substituted formula (1); and determining the required quantity of the calcium of the molten steel on a condition that the inclusions in the molten steel are controlled in a liquid phase region;

[0037] S3, predicting a yield rate of the calcium during the calcium treatment process; and

[0038] S4, determining a length of the fed calcium line according to the required quantity of calcium of the molten steel, the yield rate of the calcium, and the parameter information of the calcium treatment process, [0039] where the length of the fed calcium line is calculated based on a formula (7) expressed as follows:

[00006]$\begin{array}{cc}L=\frac{W\times \left({n\left[\mathrm{Ca}\right]}_T-{n\left[\mathrm{Ca}\right]}_O\right)\times M_{Ca}}{\eta \times \beta \times \mu \times M_{Fe}}& \left(7\right)\end{array}$

where L represents the length of the fed calcium line with a unit of meter; W represents a weight of the molten steel with a unit of ton; n[Ca].sub.T represents the required quantity of calcium of the molten steel with a unit of %; n[Ca].sub.0 represents a calcium content of the molten steel before the calcium treatment process with a unit of %; M.sub.Ca represents a molar mass of calcium with a unit of gram per mole (g/mol); M.sub.Fe is represents a molar mass of iron with a unit of g/mol; η represents the yield rate of the calcium with a unit of %; β represents a content of calcium of the calcium line with a unit of %; and μ represents a weight per meter of the calcium line with a unit of gram per meter (g/m).

[0040] In an illustrated embodiment, the constraint condition is expressed by formulas (8)-(11) as follows:

Σn.sub.Ca=n.sub.[Ca]+n.sub.CaO+n.sub.CaS+n.sub.CA.sub.2+n.sub.CA6   (8)

Σn.sub.Al=n.sub.[Al]+2n.sub.Al.sub.2.sub.O.sub.3+4n.sub.CA.sub.2+12n.sub.CA6   (9)

Σn.sub.O=n.sub.[O]+3n.sub.Al.sub.2.sub.O.sub.3+7n.sub.CA.sub.2+19n.sub.CA6+n.sub.CaO   (10)

Σn.sub.S=n.sub.[S]+n.sub.CaS   (11)

where Σn.sub.Ca represents a total number of moles of calcium in the molten steel, n.sub.[Ca] represents a number of moles of dissolved calcium in the liquid-phase steel, n.sub.[Al] represents a number of moles of dissolved aluminum in the liquid-phase steel, n.sub.[O] represents a number of moles of dissolved oxygen in the liquid-phase steel, n.sub.[S] represents a number of moles of dissolved sulfur in the liquid-phase steel, n.sub.CaO represents a number of moles of CaO in the inclusions, n.sub.CaS represents a number of moles of CaS in the inclusions, n.sub.Al.sub.2.sub.O.sub.3 represents a number of moles of Al.sub.2O.sub.3 in the inclusions, n.sub.CA.sub.6 represents a number of moles of CaO.Math.6Al.sub.2O.sub.3 in the inclusions, and n.sub.CA2 represents the number of moles of CaO.Math.2Al.sub.2O.sub.3 in the inclusions.

[0041] In an illustrated embodiment, the parameter information of the calcium treatment process includes: a content of Carbon (C) of the molten steel, a content of Silicon (Si) of the molten steel, a content of Manganese (Mn) of the molten steel, a content of Phosphorus (P) of the molten steel, a content of Sulphur (S) of the molten steel, a content of Calcium (Ca) of the molten steel, a content of Aluminum (Al) of the molten steel, a total content of oxygen in the molten steel, a content of dissolved oxygen in liquid-phase steel, the temperature of the molten steel, the weight per meter of the calcium line, the content of calcium of the calcium line, and the weight of the molten steel.

[0042] In an illustrated embodiment, the predicting the yield rate of the calcium during the calcium treatment process includes: [0043] predicting the yield rate of the calcium according to a neural network model or a content of dissolved oxygen in the liquid-phase steel; [0044] where predicting the yield rate of the calcium according to the content of dissolved oxygen in the liquid-phase steel is expressed as a formula (12) as follows:

y=50000*x.sub.o+10   (12)

where x.sub.o represents the content of dissolved oxygen in the liquid-phase steel, and y represents the yield rate of the calcium predicted according to the content of dissolved oxygen in the liquid-phase steel.

[0045] Further, the method may include feeding the calcium line with the length into the molten steel.

[0046] In the actual calculation process, the yield rate of the calcium can also be predicted and calculated by a prediction method of the yield rate of the calcium during the calcium treatment process based on a deep neural network previously applied by the applicant, which is not repeated herein.

First Embodiment

[0047] Referring to FIGS. 2 and 3, a method for determining a quantity of a calcium line fed into molten steel based on a minimum Gibbs free energy principle includes following steps S1 to S4:

[0048] S1, establishing a connection with a factory database to obtain composition information of the molten steel before a calcium treatment process and parameter information of the calcium treatment process: C=0.06%, Si=0.08%, Mn=1.4%, P=0.002%, S=0.0035%, Ca=0.0021%, Al=0.083%, T.O=0.007%, which represents a total content of oxygen in the molten steel consisting of an content of oxygen in a liquid-phase inclusion of the molten steel and an content of oxygen in dissolved liquid-phase steel, [O]=0.0003%, which represents the content of dissolved oxygen in liquid-phase steel , a temperature of the molten steel T=1873K, a weight per meter of the calcium line being 200 g/m, a content of calcium of the calcium line being 40%, and a weight of the molten steel being 100 t; [0049] S2, performing thermodynamic calculation on the composition information of the molten steel obtained in step S1 based on the minimum Gibbs free energy principle to obtain contents of inclusions in the molten steel and a required quantity of calcium of the molten steel; [0050] S3, predicting a yield rate of the calcium during the calcium treatment process; and [0051] S4, determining a length of the fed calcium line according to the required quantity of calcium of the molten steel calculated in step S2, the yield rate of the calcium obtained in step S3, and the parameter information of the calcium treatment process obtained in step S1.

[0052] Further, in the step S2, a minimum Gibbs free energy of the molten steel is calculated based on the minimum Gibbs free energy principle using a formula (1) expressed as follows:

[00007]$\begin{array}{cc}\begin{array}{c}\min .G_s=\underset{i=1}{\overset{c}{.Math.}}{n}_i{G}_i=\underset{i=1}{\overset{c}{.Math.}}{n}_i\left(G_{m,i}^{\Theta }+\mathrm{RT}\ln a_i\right)\\ =n_m\left[G_m^{\Theta }+\mathrm{RT}\ln \left(a_m\right)\right]+n_{slag}\left[G_{\mathrm{slag}}^{\Theta }+\mathrm{RT}\ln \left(a_{\mathrm{slag}}\right)\right]+n_{solid}\times G_{solid}^{\Theta }\end{array}& \left(1\right)\end{array}$

where min.G.sub.S represents the minimum Gibbs free energy of the molten steel, G.sub.i.sup.Θ represents a standard molar Gibbs free energy of a composition i of the molten steel, in which used data is shown in table 1, a.sub.i represents an activity value of the composition i, the composition i includes a solid-phase inclusion, a liquid-phase inclusion and a liquid-phase steel.

TABLE-US-00001 TABLE 1 Standard molar Gibbs free energies of the compositions of the molten steel Compositions of the molten steel G.sub.m, i.sup.Θ (J .Math. mol.sup.−1) Al −116510 O −92146 Ca −150683 S −79068 Al.sub.2O.sub.3 −1974037 CaO −799279 CaS −577916 CaO•6Al.sub.2O.sub.3 −12728232 CaO•2Al.sub.2O.sub.3 −4821505

[0053] The Gibbs free energy of the solid-phase inclusion is calculated based on a formula (2) expressed as follows:

min.G.sub.Solid=n.sub.SolidG.sub.Solid.sup.Θ=n.sub.Al.sub.2.sub.O.sub.3G.sub.Al.sub.2.sub.O.sub.3.sup.Θ+n.sub.Ca6G.sub.CA6.sup.Θ+n.sub.CA2G.sub.CA2.sup.Θ+n.sub.CaOG.sub.CaO.sup.Θ+n.sub.CaSG.sub.CaS.sup.Θ  (2)

[0054] The Gibbs free energy of the liquid-phase inclusion is calculated based on a formula (3) expressed as follows:

min.G.sub.slag=n.sub.Al.sub.2.sub.O.sub.3[G.sub.Al.sub.2.sub.O.sub.3+RT ln(a.sub.Al.sub.2.sub.O.sub.3)]n.sub.CaO[G.sub.CaO.sup.73 +RT ln(a.sub.CaO)]  (3)

[0055] The Gibbs free energy of the liquid-phase steel is calculated based on a formula (4) expressed as follows:

[00008]$\begin{array}{cc}\min .G_{Fe}=\underset{i=1}{\overset{C}{.Math.}}{n}_i{G}_i=\underset{i=1}{\overset{C}{.Math.}}{n}_i\left(G_{m,i}^{\Theta }+\mathrm{RT}\ln a_i\right)=n_{Al}\left[G_{Al}^{\Theta }+\mathrm{RT}\ln \left(x_{Al}{\gamma }_{Al}\right)\right]+n_{\mathrm{Ca}}\left[G_{\mathrm{Ca}}^{\Theta }+\mathrm{RT}\ln \left(x_{\mathrm{Ca}}{\gamma }_{\mathrm{Ca}}\right)\right]+n_O\left[G_O^{\Theta }+\mathrm{RT}\ln \left(x_O{\gamma }_O\right)\right]+n_S\left[G_S^{\Theta }+\mathrm{RT}\ln \left(x_S{\gamma }_S\right)\right].& \left(4\right)\end{array}$

[0056] Further, each of the activity values of the compositions of the solid-phase inclusion is 1, and the activity values of the compositions of the liquid-phase inclusion is calculated based on formulas (5) and (6) expressed as follows:

a.sub.Al.sub.2.sub.O.sub.3=(−3.9367*m.sub.Al.sub.2.sub.O.sub.3.sup.4+8.1721*m.sub.Al.sub.2.sub.O.sub.3.sup.3−3.7817*m.sub.Al.sub.2.sub.O.sub.3.sup.2+0.57821*m.sub.Al.sub.2.sub.O.sub.3−0.0145   (5)

a.sub.CaO=(−6.4181*m.sub.Al.sub.2.sub.O.sub.3.sup.4+13.8441*m.sub.Al.sub.2.sub.O.sub.3.sup.3−8.1761*m.sub.Al.sub.2.sub.O.sub.3.sup.2+0.2823*m.sub.Al.sub.2.sub.O.sub.3+1.0129   (6)

where a.sub.Al.sub.2.sub.O.sub.3 represents an activity value of a composition Al.sub.2O.sub.3 of the liquid-phase inclusion, a.sub.CaO represents an activity value of a composition CaO of the liquid-phase inclusion, m.sub.Al.sub.2.sub.O.sub.3 represents a mass fraction of the composition Al.sub.2O.sub.3 of the liquid-phase inclusion.

[0057] In the step S2, the constraint condition is expressed by formulas (8)-(11) as follows:

Σn.sub.Ca=n.sub.[Ca]+n.sub.CaO+n.sub.CaS+n.sub.CA.sub.2+n.sub.CA6   (8)

Σn.sub.Al=n.sub.[Al]+2n.sub.Al.sub.2.sub.O.sub.3+4n.sub.CA.sub.2+12n.sub.CA6   (9)

Σn.sub.O=n.sub.[O]+3n.sub.Al.sub.2.sub.O.sub.3+7n.sub.CA.sub.2+19n.sub.CA6+n.sub.CaO   (10)

Σn.sub.S=n.sub.[S]+n.sub.CaS   (11)

where Σn.sub.Ca represents a total number of moles of calcium in the molten steel, n.sub.[Ca] represents a number of moles of dissolved calcium in the liquid-phase steel, n.sub.[Al] represents a number of moles of dissolved aluminum in the liquid-phase steel, n.sub.[O] represents a number of moles of dissolved oxygen in the liquid-phase steel, n.sub.[S] represents a number of moles of dissolved sulfur in the liquid-phase steel, n.sub.CaO represents a number of moles of CaO in the inclusions, n.sub.CaS represents a number of moles of CaS in the inclusions, n.sub.Al.sub.2.sub.O.sub.3 represents a number of moles of Al.sub.2O.sub.3 in the inclusions, n.sub.CA.sub.6 represents a number of moles of CaO.Math.6Al.sub.2O.sub.3 in the inclusions, and n.sub.CA2 represents the number of moles of CaO.Math.2Al.sub.2O.sub.3 in the inclusions.

[0058] The formulas (2) to (6) are substituted into the formula (1), and a solution of the formula (1) is found by MATLAB. It is found that the molten steel contains 0.0021% of CaO.Math.6Al.sub.2O.sub.3 and 0.0024% of CaO.Math.2Al.sub.2O.sub.3, and the required quantity of the calcium of the molten steel is in a range from 0.0018% to 0.0027% to control the inclusions in the liquid phase region.

[0059] Further, in the step S3, the predicting the yield rate of the calcium during the calcium treatment process includes: [0060] predicting the yield rate of the calcium according to a neural network model or a content of dissolved oxygen in the liquid-phase steel; [0061] where predicting the yield rate of the calcium according to the content of dissolved oxygen in the liquid-phase steel is expressed as a formula as follows:

y=50000*x.sub.o+10   (12)

where x.sub.o represents the content of dissolved oxygen in the liquid-phase steel, and y represents the yield rate η of the calcium predicted according to the content of dissolved oxygen in the liquid-phase steel.

[0062] The content of dissolved oxygen in the liquid-phase steel is 0.0003%, and the yield rate of the calcium predicted according to the content of dissolved oxygen in the liquid-phase steel is 25%.

[0063] Further, in the step S2, the calculated required quantity of the calcium of the molten steel is in a range from 0.0018% to 0.0027%, and the length of the fed calcium line is calculated based on a formula (7) expressed as follows:

[00009]$\begin{array}{cc}L=\frac{W\times \left({n\left[\mathrm{Ca}\right]}_T-{n\left[\mathrm{Ca}\right]}_O\right)\times M_{Ca}}{\eta \times \beta \times \mu \times M_{Fe}}& \left(7\right)\end{array}$

where L represents the length of the fed calcium line with a unit of meter; W represents a weight of the molten steel with a unit of ton; n[Ca].sub.T represents the required quantity of calcium of the molten steel with a unit of %; n[Ca].sub.0 represents a calcium content of the molten steel before the calcium treatment process with a unit of %; M.sub.Ca represents a molar mass of calcium with a unit of gram per mole (g/mol); M.sub.Fe is represents a molar mass of iron with a unit of g/mol; η represents the yield rate of the calcium with a unit of %; β represents a content of calcium of the calcium line with a unit of %; and μ represents a weight per meter of the calcium line with a unit of gram per meter (g/m).

[0064] According to the formula (1), the calculated length of the fed calcium line is in a range from 40 m to 70 m.

Second Embodiment

[0065] Referring to FIG. 2, a method for determining a quantity of a calcium line fed into molten steel based on a minimum Gibbs free energy principle includes following steps S1 to S4:

[0066] S1, establishing a connection with a factory database to obtain composition information of the molten steel before a calcium treatment process and parameter information of the calcium treatment process: C=0.06%, Si=0.08%, Mn=1.4%, P=0.002%, S=0.0035%, Ca=0.0020%, Al=0.083%, T.O=0.007%, which represents a total content of oxygen in the molten steel consisting of an content of dissolved oxygen in a liquid-phase inclusion of the molten steel and an content of oxygen in liquid-phase steel, [O]=0.0003%, which represents the content of dissolved oxygen in liquid-phase steel, a temperature of the molten steel T=1873K, a weight per meter of the calcium line being 200 g/m, a content of calcium of the calcium line being 40%, and a weight of the molten steel being 100 t;

[0067] S2, performing thermodynamic calculation on the composition information of the molten steel obtained in step S1 based on the minimum Gibbs free energy principle to obtain contents of an inclusions in the molten steel and a required quantity of calcium of the molten steel;

[0068] S3, predicting a yield rate of the calcium during the calcium treatment process; and

[0069] S4, determining a length of the fed calcium line according to the required quantity of calcium of the molten steel calculated in step S2, the yield rate of the calcium obtained in step S3, and the parameter information of the calcium treatment process obtained in step S1.

[0070] Further, in the step S2, a minimum Gibbs free energy of the molten steel is calculated based on the minimum Gibbs free energy principle using a formula (1) expressed as follows

[00010]$\begin{array}{cc}\min .G_s=\underset{i=1}{\overset{c}{.Math.}}{n}_i{G}_i=\underset{i=1}{\overset{c}{.Math.}}{n}_i\left(G_{m,i}^{\Theta }+\mathrm{RT}\ln a_i\right)=n_m\left[G_{\mathrm{metal}}^{\Theta }+\mathrm{RT}\ln \left(a_m\right)\right]+n_{\mathrm{slag}}\left[G_{\mathrm{slag}}^{\Theta }+RT\ln \left(a_{\mathrm{slag}}\right)\right]+n_{\mathrm{solid}}\times G_{\mathrm{solid}}^{\Theta }& \left(1\right)\end{array}$

where min.G.sub.s represents the minimum Gibbs free energy of the molten steel, G.sub.i.sup.Θ represents a standard molar Gibbs free energy of a composition i of the molten steel, in which used data is shown in table 1, a.sub.i represents an activity value of the composition i, the composition i includes a solid-phase inclusion, a liquid-phase inclusion and a liquid-phase steel.

TABLE-US-00002 TABLE 2 Standard molar Gibbs free energies of the compositions of the molten steel Compositions of the molten steel G.sub.m, i.sup.Θ (J .Math. mol.sup.−1) Al −116510 O −92146 Ca −150683 S −79068 Al.sub.2O.sub.3 −1974037 CaO −799279 CaS −577916 CaO•6Al.sub.2O.sub.3 −12728232 CaO•2Al.sub.2O.sub.3 −4821505

[0071] The Gibbs free energy of the solid-phase inclusion is calculated based on a formula (2) expressed as follows:

min.G.sub.Solid=n.sub.SolidG.sub.Solid.sup.Θ=n.sub.Al.sub.2.sub.O.sub.3G.sub.Al.sub.2.sub.O.sub.3.sup.Θ+n.sub.Ca6G.sub.Ca6.sup.Θ+n.sub.CA2G.sub.CA2.sup.Θ+n.sub.CaOG.sub.CaO.sup.Θ+n.sub.CaSG.sub.CaS.sup.Θ  (2)

[0072] The Gibbs free energy of the liquid-phase inclusion is calculated based on a formula (3) expressed as follows:

min.G.sub.slag=n.sub.Al.sub.2.sub.O.sub.3[G.sub.Al.sub.2.sub.O.sub.3+RT ln(a.sub.Al.sub.2.sub.O.sub.3)]n.sub.CaO[G.sub.CaO.sup.73 +RT ln(a.sub.CaO)]  (3)

[0073] The Gibbs free energy of the liquid-phase steel is calculated based on a formula (4) expressed as follows:

[00011]$\begin{array}{cc}\min .G_{Fe}=\underset{i=1}{\overset{C}{.Math.}}{n}_i{G}_i=\underset{i=1}{\overset{C}{.Math.}}{n}_i\left(G_{m,i}^{\Theta }+\mathrm{RT}\ln a_i\right)=n_{Al}\left[G_{Al}^{\Theta }+\mathrm{RT}\ln \left(x_{Al}{\gamma }_{Al}\right)\right]+n_{\mathrm{Ca}}\left[G_{\mathrm{Ca}}^{\Theta }+\mathrm{RT}\ln \left(x_{\mathrm{Ca}}{\gamma }_{\mathrm{Ca}}\right)\right]+n_O\left[G_O^{\Theta }+\mathrm{RT}\ln \left(x_O{\gamma }_O\right)\right]+n_S\left[G_S^{\Theta }+\mathrm{RT}\ln \left(x_S{\gamma }_S\right)\right].& \left(4\right)\end{array}$

[0074] Further, each of the activity values of the compositions of the solid-phase inclusion is 1, and the activity values of the compositions of the liquid-phase inclusion is calculated based on formulas (5) and (6) expressed as follows:

a.sub.Al.sub.2.sub.O.sub.3=(−3.9367*m.sub.Al.sub.2.sub.O.sub.3.sup.4+8.1721*m.sub.Al.sub.2.sub.O.sub.3.sup.3−3.7817*m.sub.Al.sub.2.sub.O.sub.3.sup.2+0.57821*m.sub.Al.sub.2.sub.O.sub.3−0.0145   (5)

a.sub.CaO=(−6.4181*m.sub.Al.sub.2.sub.O.sub.3.sup.4+13.8441*m.sub.Al.sub.2.sub.O.sub.3.sup.3−8.1761*m.sub.Al.sub.2.sub.O.sub.3.sup.2+0.2823*m.sub.Al.sub.2.sub.O.sub.3+1.0129   (6)

where a.sub.Al.sub.2.sub.O.sub.3 represents an activity value of a composition Al.sub.2O.sub.3 of the liquid-phase inclusion, a.sub.CaO represents an activity value of a composition CaO of the liquid-phase inclusion, m.sub.A.sub.2.sub.O.sub.3 represents a mass fraction of the composition Al.sub.2O.sub.3 of the liquid-phase inclusion.

[0075] In the step S2, the constraint condition is expressed by formulas (8)-(11) as follows:

Σn.sub.Ca=n.sub.[Ca]+n.sub.CaO+n.sub.CaS+n.sub.CA.sub.2+n.sub.CA6   (8)

Σn.sub.Al=n.sub.[Al]+2n.sub.Al.sub.2.sub.O.sub.3+4n.sub.CA.sub.2+12n.sub.CA6   (9)

Σn.sub.O=n.sub.[O]+3n.sub.Al.sub.2.sub.O.sub.3+7n.sub.CA.sub.2+19n.sub.CA6+n.sub.CaO   (10)

Σn.sub.S=n.sub.[S]+n.sub.CaS   (11)

where Σn.sub.Ca represents a total number of moles of calcium in the molten steel, n.sub.[Ca] represents a number of moles of dissolved calcium in the liquid-phase steel, n.sub.[Al] represents a number of moles of dissolved aluminum in the liquid-phase steel, n.sub.[O] represents a number of moles of dissolved oxygen in the liquid-phase steel, n.sub.[S] represents a number of moles of dissolved sulfur in the liquid-phase steel, n.sub.CaO represents a number of moles of CaO in the inclusions, n.sub.CaS represents a number of moles of CaS in the inclusions, n.sub.Al.sub.2.sub.O.sub.3 represents a number of moles of Al.sub.2O.sub.3 in the inclusions, n.sub.CA.sub.6 represents a number of moles of CaO.Math.6Al.sub.2O.sub.3 in the inclusions, and n.sub.CA2 represents the number of moles of CaO.Math.2Al.sub.2O.sub.3 in the inclusions.

[0076] The formulas (2) to (6) are substituted into the formula (1), and a solution of the formula (1) is found by MATLAB. All the inclusions in the molten steel are liquid calcium aluminate, and the inclusions are controlled in a target area by the constraint condition. The required quantity of the calcium of the molten steel is in a range from 0.0018% to 0.0027%. FIG. 4 illustrates an influence of a content of calcium of the molten steel on the inclusions calculated according to the minimum Gibbs free energy principle.

[0077] Further, according to the calculation method of a content of calcium in the first embodiment, it is calculated that the content of calcium in the molten steel before the calcium treatment process is 0.002%, which is in a range from 0.0018% to 0.0027%, so the molten steel does not need to be fed with calcium, and a suitable length of a fed calcium line is 0 m.

[0078] Finally, it should be explained that the above-mentioned embodiments are only used to illustrate the technical solutions of the present disclosure, but not to limit thereto. Although the present disclosure has been described in detail with reference to the foregoing embodiments, it should be understood by those skilled in the art that the technical solutions described in the foregoing embodiments can still be modified, or some or all of the technical features of the foregoing embodiments can be replaced by equivalents thereof, and these modifications or substitutions do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the forgoing embodiments of the present disclosure.