A phosphorus distribution prediction model for CaO–SiO 2 –MgO–FeO–Fe 2 O 3 –Al 2 O 3

Abstract

A thermodynamic model for predicting the phosphorus distribution ratio L _P of CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags was developed by considering the mass action concentration of ion couples or structural units in slags based on the ion-molecule coexistence theory (IMCT) and is referred to as the IMCT-L _P model. Compared with the equilibrium mole number or mass percentage of the slag components, the mass action concentration for structural units of CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags used in HIsmelt smelting reduction ironmaking can characterize the reaction ability of the components. The mass action concentration of the iron oxides may characterize the oxidizing ability of the slag. The dephosphorization reactions in the HIsmelt smelting reduction vessel are jointly controlled by basic oxides and the oxidizing ability of the slag. The IMCT model can not only accurately predict the total phosphorus distribution ratio of metallurgical slags but also forecast the respective phosphorus distribution ratio of basic oxides in the slag, i.e. the dephosphorization contribution rates of 3CaO·P₂O₅, 4CaO·P₂O₅ and 2CaO·P₂O₅ were 99.7%, 0.227% and 0.033%, respectively. Moreover, to more conveniently predict the phosphorus distribution ratio, the empirical formulas of the phosphorus distribution ratio considering slag composition and temperature were determined by mathematical regression.

Introduction

For most steel products, phosphorus is a harmful element that negatively affects the quality of the steel. However, it cannot be readily removed during blast furnace ironmaking so that dephosphorization is an important task in the steelmaking process. HIsmelt is a direct smelting process that utilizes fine iron ore and non-coking coals for the production of molten pig iron. The HIsmelt ironmaking process may provide favourable dephosphorization conditions, such as high basicity, high FeO content, high slag content and low temperature. Therefore, HIsmelt has a higher dephosphorization capacity than the blast furnace process, which is not effective at dephosphorization [1–3].

There has been much research into phosphorus equilibrium in the steelmaking process. However, the majority of the research has focused on high FeO slag, low-carbon iron and relatively high temperature characteristic of the basic oxygen furnace (BOF) process. Few researchers have studied the dephosphorization process of HIsmelt in detail [4]. Moreover, researchers have studied the dephosphorization ability of molten iron and established a few models for the phosphorus distribution ratio based on experience or mathematical regression based on the measured data. In these studies, the relationship between the phosphorus distribution ratio and the composition and temperature of slag was discussed. However, phosphorous distribution ratio models are not sufficient and scarce from the perspective of dephosphorization reactions based on metallurgical physicochemistry.

The ion-molecule coexistence theory (IMCT) [5–9] is based on the mass action concentration law, which characterizes the physicochemical properties of metallurgical slags. The IMCT assumes that simple ions, simple molecules and complex molecules all exist in metallurgical slag. The reaction capacity or activity of the component in the slag is characterized by the mass action concentration of the component. Duan et Al. [10,11] and Yang et al. [12–14] established a number of models for predicting the distribution ratio of Mn, P and S in different slag systems based on the IMCT. The results show that the predicted results based on the IMCT have a good correspondence with the measured data in the slags. Furthermore, the prediction model based on the IMCT was proven to be more effective than previous empirical formulas or mathematical regression models.

Yang et al. [15] developed a thermodynamic model for calculating the phosphorus distribution ratio between top–bottom combined blown converter steelmaking slags and molten steel by coupling with a developed thermodynamic model for calculating mass action concentrations of structural units in CaO–SiO₂–MgO–FeO–Fe₂O₃–MnO–Al₂O₃–P₂O₅ slags based on the IMCT. In this study, the dephosphorization characteristics of HIsmelt slags were studied with reference to the method developed by Yang. From the perspective of mass action concentration law, the IMCT explains why slags with a high basicity and high oxidation ability could substantially promote dephosphorization. The IMCT model can not only accurately predict the total phosphorus distribution ratio of metallurgical slags but also forecast the respective phosphorus distribution ratio of basic oxides FeO, CaO and MgO in the slags.

Phosphorus distribution prediction model for CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags based on the IMCT

Establishment of L _P prediction model based on slag oxidization ability

In this study, the data for CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags were provided by HIsmelt industrial trials. The normalized chemical compositions of both slags and metal for 18 runs are listed in Table 1.

Table 1.

Chemical composition of CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and hot metal during HIsmelt ironmaking process.

No.	Chemical composition of slags (mass pct)							Chemical composition of hot metal (mass pct)
No.	CaO	SiO₂	MgO	FeO	Fe₂O₃	Al₂O₃	P₂O₅	[C]	[Si]	[P]	[S]
1	39.54	32.40	6.97	2.66	0.88	17.28	0.27	4.18	0.143	0.072	0.124
2	38.98	31.90	6.78	3.75	1.24	16.99	0.37	3.97	0.144	0.044	0.163
3	38.59	31.98	6.75	4.05	1.35	16.92	0.35	3.90	0.141	0.029	0.165
4	38.63	32.88	6.86	2.60	0.87	18.01	0.15	4.26	0.063	0.064	0.117
5	37.82	32.47	6.78	2.95	0.98	17.87	1.12	4.63	0.024	0.137	0.084
6	38.65	33.41	6.97	1.64	0.54	18.74	0.04	4.60	0.024	0.180	0.084
7	39.57	30.17	9.11	4.90	1.36	13.64	1.25	3.70	0.001	0.015	0.050
8	37.91	31.88	7.33	2.34	0.78	19.59	0.17	4.11	0.119	0.122	0.152
9	38.66	31.38	7.62	2.61	0.87	18.65	0.20	3.98	0.143	0.099	0.164
10	39.34	31.24	8.01	2.01	0.67	18.49	0.25	3.95	0.189	0.179	0.170
11	38.82	31.01	8.43	2.85	0.95	17.70	0.22	4.18	0.147	0.050	0.159
12	38.36	30.98	8.59	2.82	0.94	17.99	0.31	4.51	0.095	0.075	0.147
13	37.66	31.21	8.61	2.82	0.94	18.35	0.40	3.84	0.060	0.103	0.137
14	39.68	32.02	7.28	3.06	1.02	16.25	0.69	4.02	0.038	0.078	0.148
15	40.35	31.82	7.24	3.03	1.01	16.23	0.31	3.91	0.047	0.041	0.059
16	39.97	31.44	6.91	3.78	1.26	16.50	0.15	3.96	0.015	0.025	0.053
17	40.55	31.89	6.81	3.83	1.28	15.41	0.23	4.20	0.015	0.024	0.056
18	38.98	31.58	7.08	4.72	1.57	15.50	0.56	4.05	0.002	0.022	0.044

Based on the IMCT [5–9], is the mass action concentration of each structural unit, and is the total equilibrium mole number of all structural units, which is calculated by solving the algebraic equation groups. The basic meaning of the defined from the IMCT is the equilibrium mole fraction of structural unit i, and the physicochemical meaning of is nearly consistent with the traditionally applied activity of component i in slags, in which pure solid or liquid matter is chosen as the standard state and the mole fraction is selected as the concentration unit. Numerous studies proved that of structural units or ion couples in various slags has good agreement with the reported of the related components.

There are seven components, namely CaO, SiO₂, MgO, FeO, Fe₂O₃, Al₂O₃ and P₂O₅, in CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags, and they could interact to form approximately 31 kinds of complex molecules, such as , , , and , in slags at 1773 K. The extracted phosphorus from liquid iron gradually enters into the slags as P₂O₅, 3FeO·P₂O₅, 3FeO·P₂O₅, 2CaO·P₂O₅, 3CaO·P₂O₅, 4CaO·P₂O₅, 2MgO·P₂O₅ and 3MgO·P₂O₅ as the dephosphorization reactions proceed until the dephosphorization reactions reach equilibrium or quasi-equilibrium in terms of classic metallurgical physicochemistry. However, the IMCT suggests that the extracted phosphorus from molten steel into the slags can be bonded with ion couples (Fe²⁺+O²⁻), (Ca²⁺+O²⁻) and (Mg²⁺+O²⁻) to form structural units, such as P₂O₅, 3FeO·P₂O₅, 3FeO·P₂O₅, 2CaO·P₂O₅, 3CaO·P₂O₅, 4CaO·P₂O₅, 2MgO·P₂O₅ and 3MgO·P₂O₅, in oxidizing slags containing Fe _t O.

The dephosphorization reactions between CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and liquid iron can be represented by all basic ion couples, such as (Fe²⁺+O²⁻), (Ca²⁺+O²⁻) and (Mg²⁺+O²⁻), in oxidizing slags, which can be described by Fe _t O, to form eight dephosphorization products or molecules, including P₂O₅, 3FeO·P₂O₅, 3FeO·P₂O₅, 2CaO·P₂O₅, 3CaO·P₂O₅, 4CaO·P₂O₅, 2MgO·P₂O₅ and 3MgO·P₂O₅, according to the IMCT as follows: (1a) (1b) (1c) (1d) (1e) (1f) (1g) (1h)

is the equilibrium constant of each chemical reaction in Equation (1), which can be expressed as follows: (2a) (2b) (2c) (2d) (2e) (2f) (2g) (2h)

According to Equation (2), the respective phosphorous distribution ratio of the basic components can be determined as follows: (3a) (3b) (3c) (3d) (3e) (3f) (3g) (3h)

where is the molecular weight of and is the activity coefficient of [P] in hot metal that can be calculated by Wagner’s equation. The reaction equilibrium constant of the dephosphorization reactions mentioned above is referred to the paper of Yang [15]. The oxidizing ability of the slag is expressed by the mass action concentration of in the slag, which is defined as follows: (4)

According to , , and , the total phosphorus distribution ratio of the slag and respective phosphorus distribution ratio of the basic components can be calculated. The total phosphorus distribution ratio between CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and hot metal can be expressed by Equation (5): (5)

The comparison of and

of the prediction model based on the IMCT is compared with , as shown in Figure 1. Figure 1 shows that and have a 1:1 reliable linear relationship with the industrial trials that consisted of 18 runs. It can be concluded from Figure 1 that the developed IMCT model can be applied to reliably predict the phosphorus of the slags. Therefore, the calculated values of the phosphorus distribution ratio by the IMCT model are applied as a basis for further discussion in the following sections.

The comparison of calculated by different models and different data

The

prediction models of oxidizing slag are widely accepted by global investigators, as listed in Table 2. All these models consider the co-effect of the temperature and slag composition on

, such as CaO, MgO, MnO, SiO₂, Fe _t O, TFe and FeO. Some of these models are empirical thermodynamic models that are derived from the mathematical regression of experimental data. The models in Table 2 can be summarized as follows. (1) Increasing the content of basic components (CaO, MgO and MnO) can improve dephosphorization ability according to, for instance, the model by Healy [16], all of the models by Suito [17,18], the model by Sommerville [19,20], the model by Balajiva [21] and the model by Lee [4]. The contribution of CaO to dephosphorization is more than that of MgO and MnO in all models by Suito, the model by Sommerville and the model by Balajiva. (2) The increase in the content of other substances can also promote dephosphorization, such as the content of Fe _t O in the No. 1 and No. 2 models by Suito and the model by Balajiva; the content of TFe in the model by Healy and the No. 3 model by Suito; and the content of FeO in the model by Sommerville and the model by Lee. The contribution ratio of iron oxides (Fe _t O, TFe, FeO) is less than that of basic oxides (CaO, MgO, MnO) with the same mass percentage. (3) The content of SiO₂ has nearly no effect on the dephosphorization ability of the slag. (4) Except for the No. 3 model by Suito, other models indicate that P₂O₅ can reduce the dephosphorization ability of the slag. (5) The model by Lee considers the effect of [C] in the hot metal.

Table 2.

The comparison of the phosphorus distribution ratio prediction model for metal–slag.

L _P model	Slags	Ref.
The model by Healy	Multi-slag system	[16]
The No.1 model by Suito	Multi-slag system	[17,18]
The No.2 model by Suito	Multi-slag system	[17,18]
The No.3 model by Suito	Multi-slag system	[17,18]
The model by Sommerville	Multi-slag system	[19,20]
The model by Balajiva	Multi-slag system	[21]
The model by Lee	Multi-slag system	[4]

A comparison between the in the HIsmelt smelting reduction vessel and the calculated of different prediction models is shown in Figure 2(a). It can be clearly concluded from Figure 2(a) that , , , and all have a reliable corresponding relationship with . Therefore, the IMCT model and the models by Healy, Sommerville, Balajiva and Lee can accurately predict the phosphorus distribution ratio between CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and hot metals.

Based on the IMCT, the phosphorus distribution ratios of different slags from various studies [4,15,17,18,22] were calculated. In these publications, Lee studied the HIsmelt slag, and others studied BOF or similar slags. These slags differed greatly in basicity and FeO content. The data for in the study by Lee and in the present work were concentrated in the range of 1–3, while that of others were in the range of 3–7. The comparison between the and the in logarithmic form by the various data is shown in Figure 2(b). The results show that the IMCT model can also accurately predict the phosphorus distribution ratios of various slags, which further proves the accuracy and universality of the model based on the IMCT.

The effect of slag components on the phosphorus distribution ratio

The relationship between mass action concentration of slag components and or

The relationship between the mass action concentration of slag components and or is shown in Figure 3. Figure 3(a) and (c) show that increases with increasing or content, but the correlation is not remarkable. It can be observed in Figure 3(b) and (f) that or values decrease with an increase in or . The effect of the mass action concentration of iron oxides, namely , , and , on the phosphorus distribution ratio is represented in Figure 3(d), (e), (g) and (h), respectively, where it can be noted that the phosphorus distribution ratio increases with the increase in the mass action concentration of the iron oxides and shows a good linear relationship.

The relationship between mass percentage of slag components and or

Figure 4(a)–(f) shows the relationship between the mass percentage of the slag components and or . It can be concluded from Figure 4(b) and (f) that increasing the mass percentage of SiO₂ and Al₂O₃ can cause a decrease in the values of or . Meanwhile, Figure 4(d) and (e) found that a significant increase in the or can be caused by increasing the mass percentage of FeO or Fe₂O₃.

A comparison between Figure 3 and Figure 4 indicates that the mass action concentration and mass percentage of iron oxides FeO, Fe₂O₃, Fe₃O₄ and Fe _t O may play an important role in the oxidation ability of the slags and the dephosphorization reaction at the metal–slag interface.

However, the relationship between slag components, such as CaO, MgO, SiO₂ and phosphorus distribution ratio seems to be divergent. This is because the mass action concentration defined by the IMCT is the effective equilibrium concentration of the slag component, which refers to the activity in the traditional physicochemical approach. When studying the interaction between slag and liquid iron, the chemical reactions between slag components must be considered. The basic oxides, such as CaO and MgO, form a large number of complex molecules in slags, such as , , , and , which affect their activities at the equilibrium conditions and then affected the phosphorus distribution ratio. The calculation of the formation of these complex molecules is the core of the IMCT model.

Similarly, the higher the content of Al₂O₃ in the slag is, the more complex molecules, such as and , are formed, which consumes the basic components in the slag and reduces the phosphorus distribution ratio. Another possible reason is that slag with a higher Al₂O₃ content has higher viscosity, which affects the dephosphorization efficiency.

Therefore, the effect of the slag basicity on the phosphorus distribution ratio should also be considered, as shown in Section 3.3.

The relationship between the slag basicity of and or

The relationship between the slag basicity of and or is shown in Figure 5. The phosphorus distribution ratio increases with an increase in the slag basicity whether it was a binary basicity , ternary basicity or complex basicity . Moreover, compared with the single slag component, the effect of slag basicity on the phosphorus distribution ratio presents a clearer rule; thus the co-effect of slag components plays an important role in the phosphorus distribution ratio.

The influence of basic oxides on dephosphorization ability

Phosphorus in a hot metal is oxidized by Fe _t O in the slag and oxygen in the hot metal to form dephosphorization product P₂O₅. Other complex molecules are reaction products of the basic components in the slag, such as MgO, CaO, FeO and P₂O₅, as follows: 2MgO·P₂O₅, 3MgO·P₂O₅, 2CaO·P₂O₅, 3CaO·P₂O₅, 4CaO·P₂O₅, 3FeO·P₂O₅ and 4FeO·P₂O₅. Based on the oxidizing ability of the slag, different basic oxides have different effects on the total dephosphorization ability.

Regressed results between and of the simple P₂O₅ molecule and complex molecules are shown in Figure 6. The average contribution ratio of eight structural units for is listed in Table 3. It can be concluded from Figure 6 and Table 3 that a signiﬁcant difference in the dephosphorization contribution ratio for 3CaO·P₂O₅, 4CaO·P₂O₅ and 2CaO·P₂O₅ was determined to be approximately 99.7%, 0.227% and 0.033%, respectively. The dephosphorization contribution ratios for P₂O₅, 3FeO·P₂O₅, 4FeO·P₂O₅, 2MgO·P₂O₅ and 3MgO·P₂O₅ are too low to be considered.

Table 3.

Regressed results between and of eight structural units and average contribution ratio of eight structural units on .

Structural unit of the slag	Regressed relationship of and	Average contribution ratio on




		0.997

The empirical formulas for phosphorus distribution ratio

On the basis of Section 3.1–3.3, it is known that L _P has a certain correlation with the mass action concentration (or mass fraction) of the components in the slag. Therefore, it is possible to develop a reasonably good empirical correlation formula based on these data, as Suito et al. did. Theoretically, L _P is a function of all the components of the slag, but some variables with weak correlation can be eliminated by multiple regression fitting. Previous studies indicate that the reciprocal of temperature is proportional to lgL _P, and the coefficient varies from 11,000 to 23,000. For example, Suito and Inoue [17] reported a value of 11,570, Healy [16] reported a value of 22,350 and a value of 22,810 was given by Balajiva [21]. A value of 20,000 was chosen in this work to be reasonable over a limited temperature range. In the HIsmelt process, the slag temperature can always be maintained within a certain range. In the IMCT model, temperature affects the equilibrium constants of chemical reactions between structural units in slags. Suito et al. [17,18] performed a large amount of research on the relationship between slag temperature and phosphorus distribution ratio, so the discussion of temperature is not involved in this study. After determining the value of 20,000, the correction of the fitting result was completed by the constant term in the expression. In fact, this did not affect the validity of fitting, considering that the essence of fitting is based on the IMCT calculation.

Using this temperature dependence and the existing data, the empirical formulas for lgL _P vs. the mass action concentration N_i and lgL _P vs. the mass fraction are given. In Figure 7, the measured data for lg L _P are compared with those predicted by Equation (4): (4a) (4b)

The physicochemical meaning of N_i is nearly consistent with the traditionally applied activity a_i of component i in slags, so there is a clear correlation between mass action concentration and mass percentage concentration [5–9,12–15]. The IMCT has important advantages in the accuracy of phosphorus distribution ratio prediction, but its calculation process is very complicated, which is not conducive to practical application. Therefore, a relatively simple form of fitting expression is given, which is unified with other studies in form. It should be noted that these two fitting methods are based on the calculation of the IMCT, and it is hoped that the fitting expressions can provide application convenience. Using the provided formulas, the phosphorus distribution ratio can be predicted more easily based on the known composition of the slag. More importantly, we can learn how to create a more favourable condition to promote dephosphorization.

Conclusion

Thermodynamic models for predicting the phosphorus distribution ratio of CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags were developed based on the IMCT and are referred to as IMCT-L _P models. The developed IMCT-L _P models were tested with industrial trials of 18 runs. The main conclusions can be summarized as follows:

The developed IMCT model for predicting the phosphorus distribution ratio can be successfully applied to not only phosphorus equilibrium experiments but also industrial production processes in HIsmelt smelting reduction vessels at metallurgic temperatures.

The calculated mass action concentrations of structural units or ion couples based on the IMCT can be applied to reliably represent the reaction abilities of components in CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags.

Compared with a single slag component, the effect of slag basicity on the phosphorus distribution ratio presented a clearer rule; thus the co-effect of slag components plays an important role in the phosphorus distribution ratio.

A signiﬁcant difference in the dephosphorization contribution ratio among 3CaO·P₂O₅, 4CaO·P₂O₅ and 2CaO·P₂O₅ was found to be approximately 99.7%, 0.227% and 0.033%, respectively.

The empirical formulas for lgL _P vs. the mass action concentration N_i and lgL _P vs. mass fraction were given.

Dephosphorization cannot be commonly accomplished in a blast furnace; however, the oxidation atmosphere can promote dephosphorization reactions in the smelting reduction vessel used for the HIsmelt ironmaking process. In this sense, the HIsmelt ironmaking process has feasible applications in the Chinese steel industry.

Footnotes

Disclosure statement

No potential conflict of interest was reported by the authors.

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A phosphorus distribution prediction model for CaO–SiO 2 –MgO–FeO–Fe 2 O 3 –Al 2 O 3 –P 2 O 5 slags based on the IMCT

Abstract

Introduction

Phosphorus distribution prediction model for CaO–SiO2–MgO–FeO–Fe2O3–Al2O3–P2O5 slags based on the IMCT

Establishment of L P prediction model based on slag oxidization ability

Chemical composition of CaO–SiO2–MgO–FeO–Fe2O3–Al2O3–P2O5 slags and hot metal during HIsmelt ironmaking process.

The comparison of and

The comparison of calculated by different models and different data

The comparison of the phosphorus distribution ratio prediction model for metal–slag.

The effect of slag components on the phosphorus distribution ratio

The relationship between mass action concentration of slag components and or

The relationship between mass percentage of slag components and or

The relationship between the slag basicity of and or

The influence of basic oxides on dephosphorization ability

Regressed results between and of eight structural units and average contribution ratio of eight structural units on .

The empirical formulas for phosphorus distribution ratio

Conclusion

Footnotes

Disclosure statement

References

Phosphorus distribution prediction model for CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags based on the IMCT

Establishment of L _P prediction model based on slag oxidization ability

Chemical composition of CaO–SiO₂–MgO–FeO–Fe₂O₃–Al₂O₃–P₂O₅ slags and hot metal during HIsmelt ironmaking process.