Study on Mass Transfer of Phosphorus Based on New Hot-Metal Dephosphorization Kinetic Model

Abstract

To investigate mass transfer of phosphorus in hot-metal dephosphorization process, it is necessary to reduce the deviation of traditional dephosphorization models in fitting accuracy. According to the change in hot-metal phosphorus content during dephosphorization, a new dephosphorization model was established by introducing the concept of “dynamic relative area”. With the help of literature data and comparative analysis of the new and old models, the rationality of the new model was verified. On this basis, in order to reveal the effects of CaO and its derivatives on mass transfer of phosphorus, based on the dephosphorization effect of Fe_tO–CaO–SiO₂–CaCl₂ slags on high-phosphorus hot metal at 1673 K (1400 °C), the mass transfer process of phosphorus was investigated by calculating, analyzing, and discussing the overall mass transfer coefficients of phosphorus using CaO, Ca(OH)₂, and CaCO₃ with equal molar amount as fixatives (slag formers) in dephosphorizer respectively. The results show that the overall mass transfer coefficients of phosphorus under the action of Ca(OH)₂ and CaCO₃ are 0.0216 cm/s and 0.0363 cm/s, respectively, which are significantly lower than 0.0840 cm/s under the action of CaO.

1. Introduction

In industrial production, CaO is often used as a fixative in slag. However, because it is often exposed to the air or drenched by rain during storage or transportation, some CaO will inevitably produce Ca(OH)₂ [1]. Meanwhile, CaO is mostly made by calcining CaCO₃. When CaCO₃ particles are too large to burn through, some of them also inevitably remain in the CaO. So far, although the physicochemical properties, decomposition thermodynamics, and kinetics of Ca(OH)₂ and CaCO₃ have been fully researched [2,3,4,5], their effects on hot-metal dephosphorization have not been investigated yet. Therefore, it is valuable to reveal the effects of Ca(OH)₂ and CaCO₃ on mass transfer of phosphorus.

At present, many achievements have been made in research on mass transfer of phosphorus in hot metal, slag, or both phases [6,7,8,9,10,11]. Although these achievements have played an important role in research on dephosphorization kinetics, they still have defects in practical application. Among them, the deviation between the model curve and experimental data is a prominent problem. Most models can only ensure that the fitting curve is consistent with a few experimental data.

It was unusual that when the product of the interface area (A) and the overall mass transfer coefficient (k_O) was taken as the mass transfer parameter (A·k_O), it was found that A·k_O would gradually decrease as dephosphorization reaction proceeded. In the explanation of this phenomenon, Manning et al. [12] proved that emulsification can increase the slag-iron interface area (A) through the existence of metal droplets in the slag. However, because the number of droplets entering the slag was small and it was not clear whether they could return to the hot metal, their effect on the mass transfer parameter remains to be determined. Meanwhile, Diao [13,14] and Ji [15] proposed that flux (fluxing agent) can increase A·k_O in the early stage of dephosphorization by improving the fluidity of the initial slag, but this does not explain the difference of A·k_O in the early and late stages. In addition, according to Wang et al. [16], the increase in P₂O₅ content and the decrease in Fe_tO content in slag can reduce k_O by increasing slag viscosity, but their effect at high temperatures is not significant, so it is difficult to cause a sharp decrease in A·k_O. It is worth mentioning that although Gu et al. [17] believe that CO generated in hot metal is easy to increase A and k_O through the stirring of bubbles. However, the oxidation sequence of carbon and phosphorus in hot metal is different in different dephosphorization processes, so it is not discussed at present.

In conclusion, these researchers did not explain the reasons for the deviation in data fitting. Although some explanations for the decrease in mass transfer parameter are reasonable to a certain extent, they have not been confirmed by establishing models. In view of this situation, according to the change in phosphorus content in hot metal during dephosphorization, a concept of “dynamic relative area” is proposed to establish a new dephosphorization kinetic model. Then, with the help of literature data, the rationality of the new model will be verified from the fitting accuracy and the characteristics of the mass transfer parameter. Finally, combined with a brief analysis, the new model will be applied to research the mass transfer of phosphorus under the action of CaO and its derivatives.

2. Experimental

2.1. Materials

The pig iron powder (melting point < 1400 °C) used in the experiments was obtained by mixing pure iron, ferrosilicon, ferrophosphorus, and graphite according to their respective composition and content. The dephosphorizer was based on Fe_tO–CaO–SiO₂–CaCl₂ slags and prepared with Fe₂O₃, CaO, CaCl₂, Ca(OH)₂, CaCO₃ powders (Note: SiO₂ was obtained by oxidizing silicon in the hot metal, CaCl₂ is better than CaF₂ in dephosphorization of medium-phosphorus hot metal [18]). All raw materials of the dephosphorizer were analytically pure, and the particle size of CaO, Ca(OH)₂, and CaCO₃ powders was 0.106 to 0.088 mm. The chemical compositions of the pig iron powder and the dephosphorizers are shown in

Table 1. Chemical composition of the pig iron powder (wt.%).

Composition	C	Si	Mn	P	S
Content	3.0	0.50	0.45	0.30	0.045

and

Table 2. Chemical composition of the dephosphorizer (wt.%).

No.	Composition
	Fe2O3	CaO	CaCl2	Ca(OH)2	CaCO3
A	31.3	49.1	19.6	—	—
B	27.1	—	17.0	56.0	—
C	22.6	—	14.1	—	63.3

, respectively.

2.2. Methods

In order to investigate the mass transfer of phosphorus when dephosphorizer only uses CaO, Ca(OH)₂, or CaCO₃ as its fixative, the numbers of dephosphorizers used in the experiment were A, B, and C, respectively, and dephosphorizer number was also used as experiment number.

The experiment process is as follows. At room temperature, an Al₂O₃ crucible (55 mm I.D. × 120 mm) was put into the T-1700VCB crucible furnace and kept warm when the furnace was heated to 1400 ± 20 °C, and then the paper-coated pig iron powder (600 g) was added to the crucible with an equal diameter glass tube. When the pig iron powder was completely melted, the paper-wrapped dephosphorizer (A 62.0 g, B 71.8 g, or C 86.2 g) was added to the hot metal, and the hot-metal sample was collected by using a glass tub (6 mm I.D.) at different times. Finally, the surface of the cooled metal sample was polished, and a small amount of the metal filings was drilled, which was analyzed by the ICP-AES after acid leaching. Meanwhile, the slag sample was analyzed by the XRF after being ground into powder.

In the initial components, n(Fe₂O₃) = 0.67n[Si] + 0.83n[P], n_A(CaO) = n_B(Ca(OH)₂) = n_C(CaCO₃) = 2.68n[Si] + 12.68n[P], where n represents the molar amount of substance, ( ) and [] indicate that the substance is in the slag and hot metal, respectively. Subscripts A, B and C are dephosphorizer numbers.

3. Theoretical Analysis and Model Establishment

Generally, the dephosphorization process includes:

• [P] diffuses from the hot-metal interior to the slag-metal interface;
• [O] diffuses from the hot-metal or slag interior to the slag-metal interface;
• (O²⁻) diffuses from the slag interior to the slag-metal interface;
• [P], [O], and (O²⁻) react and form (PO₄³⁻);
• (PO₄³⁻) diffuses from the slag-metal interface to the slag interior.

In the above process, the ion reaction of phosphorus transferred from hot metal to slag is as follows:

$$\left[\mathrm{P}\right]+\frac{5}{2}\left[\mathrm{O}\right]+\frac{3}{2}\left({\mathrm{O}}^{2-}\right)=\left(\mathrm{P}{\mathrm{O}}_4^{3-}\right)$$

(1)

Obviously, in this reaction, the mass transfer of phosphorus includes the transfer of [P] in the hot metal and (PO₄³⁻) in the slag. Normally, in the two-film theory in liquid-liquid reaction, the slag-metal contact area A is mostly taken as a constant. However, in the actual reaction, the contact area between phosphorus and oxygen at the interface is not fixed.

As shown in Figure 1, with the oxidation and transfer (to the slag) of phosphorus at the slag-metal interface, the content of phosphorus in the hot metal continues to decrease, so the phosphorus diffused from the hot-metal interior to the slag-metal interface will be less and less, which will directly reduce the P–O contact area at the interface. In traditional dephosphorization models, the reaction area is directly replaced by the slag-metal contact area, which is difficult to reflect the effect of the decrease in hot-metal phosphorus content on P–O contact area. Therefore, according to the restrictive conditions of the reaction, it is more reasonable to use a “dynamic relative area” which is based on the slag-metal contact area and can reflect the change in P–O contact area relative to the initial value.

Since the content of oxygen (O²⁻) in slag during dephosphorization is much higher than that of phosphorus in hot metal, the restrictive condition at this time is the phosphorus content in hot metal. Therefore, the use of “dynamic relative area” $\frac{\left[\%\mathrm{P}\right]}{{[\%\mathrm{P}]}^0}A$ ([%P]⁰ is the initial hot-metal phosphorus content during the selected dephosphorization period) can well reflect the relative decrease in P–O contact area in hot metal. At this time, the mass transfer flux equations of phosphorus in the hot metal and slag can be expressed as:

$$\frac{\mathrm{d}\left[\%\mathrm{P}\right]}{\mathrm{d}t}=-\frac{\left[\%\mathrm{P}\right]}{{[\%\mathrm{P}]}^0}\frac{A}{W_{\mathrm{m}}}{\rho }_{\mathrm{m}}{k}_{\mathrm{m}}\{\left[\%\mathrm{P}\right]-{[\%\mathrm{P}]}^{*}\}$$

(2)

$$\frac{\mathrm{d}\left(\%\mathrm{P}\right)}{\mathrm{d}t}=-\frac{\left[\%\mathrm{P}\right]}{{[\%\mathrm{P}]}^0}\frac{A}{W_{\mathrm{s}}}{\rho }_{\mathrm{s}}{k}_{\mathrm{s}}\{\left(\%\mathrm{P}\right)-{(\%\mathrm{P})}^{*}\}$$

(3)

where [%P] and (%P) represent phosphorus content in the hot metal and slag, respectively, [%P]* and (%P)* represent phosphorus content in the hot metal and slag at the slag-metal interface. k_m and k_s are mass transfer coefficients in the hot metal and slag, respectively. ρ_m and ρ_s are the density of hot metal and slag, respectively. W_m and W_s are the mass of the hot metal and slag, respectively, and A is the slag-metal contact area.

Meanwhile, the mass balance equation of phosphorus in the dephosphorization process is as follows:

$$\frac{\mathrm{d}\left(\%\mathrm{P}\right)}{\mathrm{d}t}{W}_{\mathrm{s}}=-\frac{d\left[\%\mathrm{P}\right]}{\mathrm{d}t}{W}_{\mathrm{m}}$$

(4)

Based on the above equations, the dephosphorization rate can be expressed as:

$$\frac{\mathrm{d}\left[\%\mathrm{P}\right]}{\mathrm{d}t}=-\frac{A{\rho }_{\mathrm{m}}}{{[\%\mathrm{P}]}^0{W}_{\mathrm{m}}}\frac{1}{\frac{{\rho }_{\mathrm{m}}}{{\rho }_{\mathrm{s}}{k}_{\mathrm{s}}{L}_{\mathrm{P}}}+\frac{1}{k_{\mathrm{m}}}}\{{[\%\mathrm{P}]}^2-\left[\%\mathrm{P}\right]\frac{\left(\%\mathrm{P}\right)}{L_{\mathrm{P}}}\}$$

(5)

Among them, the phosphorus distribution ratio L_P is calculated by phosphorus content in the hot metal and slag when the reaction reaches equilibrium.

$$L_{\mathrm{P}}=\frac{{(\%\mathrm{P})}^{*}}{{[\%\mathrm{P}]}^{*}}$$

(6)

Because the mass transfer of phosphorus is affected by both the hot metal and slag, according to previous research, the overall mass transfer coefficient k_O is still defined as:

$$k_{\mathrm{O}}=\frac{1}{\frac{{\rho }_{\mathrm{m}}}{{\rho }_{\mathrm{s}}{k}_{\mathrm{s}}{L}_P}+\frac{1}{k_{\mathrm{m}}}}$$

(7)

At any time during dephosphorization, the mass of phosphorus in the hot metal and slag should meet the following equation:

$$W_{\mathrm{m}}\left[\%\mathrm{P}\right]=W_{\mathrm{m}}{[\%\mathrm{P}]}^0-W_{\mathrm{s}}\left(\%\mathrm{P}\right)$$

(8)

Finally, the dephosphorization kinetic model is as follows:

$$\left[\%\mathrm{P}\right]=\frac{W_{\mathrm{m}}{[\%\mathrm{P}]}^0}{W_{\mathrm{s}}{L}_{\mathrm{P}}}{(\frac{W_{\mathrm{m}}}{W_{\mathrm{s}}{L}_{\mathrm{P}}}+1-e^{-\frac{A{\rho }_{\mathrm{m}}{k}_{\mathrm{O}}}{W_{\mathrm{s}}{L}_{\mathrm{P}}}t})}^{-1}$$

(9)

Moreover, referring to the definition of traditional mass transfer parameters (A·k_O), a new expression of A·k_O can be obtained through deformation:

$$A\cdot k_{\mathrm{O}}t=-\frac{W_{\mathrm{s}}{L}_{\mathrm{P}}}{{\rho }_{\mathrm{m}}}\ln (-\frac{W_{\mathrm{m}}}{W_{\mathrm{s}}{L}_{\mathrm{P}}}\frac{{[\%\mathrm{P}]}^0}{\left[\%\mathrm{P}\right]}+\frac{W_{\mathrm{m}}}{W_{\mathrm{s}}{L}_{\mathrm{P}}}+1)$$

(10)

For the follow-up analysis, referring to the definition of previous scholars, the expression on the right side of the equal sign of Formula (10) is still represented by “RHS”.

4. Results and Discussion

4.1. Effect of “Dynamic Relative Area” on Fitting Deviation

In order to verify the rationality of the new dephosphorization model, the new and old models need to be compared and analyzed with the help of [%P]—time data in the literature. Since the dephosphorization model is based on the melting state of slag and hot metal, according to Mori’s experiment method [10], his data will be more convincing. The fitting results of the two models to Mori’s [%P]—time data are shown in Figure 2 and Figure 3.

Compared with Figure 2 and Figure 3, the new dephosphorization model (the new model) shows a higher consistency with Mori’s experimental data than the traditional dephosphorization model (the old model). After calculation, the determination coefficient R² (0.993) of the new model is also higher than that of the old model (0.973). Through further observation, it is found that the fitting curve of the old model presents a certain accuracy only after 360 s, while the fitting curve within 0 to 360 s deviates greatly from the experimental data. Comparatively speaking, the new model shows no obvious deviation during the whole dephosphorization period. Obviously, compared with the change in the phosphorus content in hot metal after 360 s, the phosphorus content within 0 to 360 s decreases faster, which means that the relative change value of P–O reaction area is larger, but the old model can not reflect this feature, so the k_O calculated by it has low credibility.

It should be noted that the k_O calculated by the new and old models are 0.0418 cm/s and 0.0293 cm/s, respectively. The k_O of the new model is significantly higher than that of the old model, indicating that the actual k_O should be higher after eliminating the interference of the P–O contact area change.

In short, compared with the traditional dephosphorization model, the rationality of the new dephosphorization model can be confirmed in relatively ideal experiments. Therefore, it is feasible to apply the new model to investigate the mass transfer of phosphorus.

4.2. Effect of “Dynamic Relative Area” on Mass Transfer Parameter

According to Manning’s research [12], the mass transfer parameter (A·k_O) should not change with time or composition. He believes that even if some dynamic interface phenomena may cause a distortion of the interface, the interface area will only increase temporarily without continuous and significant changes. However, the A·k_O calculated by traditional dephosphorization models usually shows an obvious downward trend, which has been confirmed by the research results of Manning, Diao, and Ji. Therefore, the rationality of the new model can be judged indirectly by investigating the effect of “dynamic relative area” on A·k_O.

First, it is based on Mori’s RHS-time data, two models are used to calculate and fit them respectively, and Figure 4 and Figure 5 were obtained. In the figures, the RHS-time fitting curves are divided into three stages (0 to 120 s, 120 to 360 s, 360 to 900 s), and the average values of A·k_O in each stage are marked.

Figure 4 and Figure 5 show the relationship between RHS and time fitted by two models, respectively. The fitting curves obtained by two models are obviously different. There is a more obvious “bulge” in Figure 4, while the curve in Figure 5 is relatively straight, that is, its slope (A·k_O) fluctuates less, indicating that as the dephosphorization reaction proceeds, the decrease in P–O contact area caused by the hot-metal phosphorus content decrease indeed affects A·k_O, and mainly in two aspects of numerical value and stability.

In terms of numerical value, the A·k_O of the new and old models in three stages are 0.486, 0.428, 0.342 cm²/s and 0.348, 0.191, 0.098 cm²/s, respectively. The A·k_O of the new model are higher than those of the old model, indicating that after considering the effect of “dynamic relative area”, real A·k_O tends to be higher, and the decrease is not obvious with the reaction going on.

In terms of stability, K is temporarily used to represent the change rate of the A·k_O between the initial and final points of the RHS-time curve, which is defined as:

$$K=\frac{{(A\cdot k_{\mathrm{O}})}_{final}-{(A\cdot k_{\mathrm{O}})}_{iniial}}{{(A\cdot k_{\mathrm{O}})}_{iniial}}$$

(11)

The smaller the K, the more stable the curve. Through the calculation, the K of the new and old models are 0.415 and 0.856, respectively, and the K of the new model curve is obviously smaller, that is, its stability is higher. It is obvious that this result, to some extent, explains the phenomenon that has perplexed some scholars about the abnormal decline of A·k_O for a long time.

However, considering that the K of the new model curve is not zero, the viewpoint of “dynamic relative area” is still not enough to explain all the phenomena.

4.3. Effects of CaO and Its Derivatives on Mass Transfer of Phosphorus

The previous discussion has proved the rationality of the new dephosphorization model from two aspects, including the effect of “dynamic relative area” on fitting deviation and mass transfer parameter. Therefore, it is feasible to investigate the mass transfer of phosphorus in CaO and its derivatives using the new model. Based on the data of experiments A, B, and C, the new model is used to draw Figure 6.

Figure 6, Figure 7 and Figure 8 demonstrate the fitting results of the new dephosphorization model to the [%P]—time data in experiments A, B, and C. Considering the interference of the dephosphorizer melting process, the new model only fits the experimental data after 300 s. As can be seen, the hot-metal phosphorus content in three experiments decreases rapidly in the first 300 s and tends to be a constant with the reaction progress, but the k_O in each experiment is significantly different. According to Figure 6, Figure 7 and Figure 8, the k_O of three experiments are 0.0840 cm/s, 0.0216 cm/s, and 0.0363 cm/s, respectively. The k_O of A is much higher than that of B and C, indicating that the existence of Ca(OH)₂ and CaCO₃ is not conducive to mass transfer of phosphorus.

From the perspective of the dephosphorization thermodynamics, both CaCO₃ and Ca(OH)₂ will absorb heat and decompose under high-temperature conditions, thereby reducing the temperature of the hot metal and slag, which is very beneficial to dephosphorization [2,3]. Meanwhile, the decomposition heat of CaCO₃ (△_rH^θ_m (1673 K) = 146.12 kJ/mol) is obviously higher than that of Ca(OH)₂ (△_rH^θ_m (1673 K) = 21.51 kJ/mol). Therefore, the thermodynamic advantages of CaO, Ca(OH)₂, and CaCO₃ increase in turn.

However, in order to realize the oxidation of phosphorus, the movement of oxidants in slag is also very important, which is directly related to the fluidity of slag. First of all, the melting points of Ca(OH)₂, CaCO₃ and CaO increase in turn, which causes their fluidity to decrease in turn at the same temperature. Secondly, when CaCO₃ and Ca(OH)₂ are decomposed at high temperatures, the greater the decomposition heat is, the more obvious the hindrance to the heating and melting of slag is.

Specifically, the P–O reaction in experiment B had a moderate thermodynamic condition, and the slag fluidity was the highest in the three experiments. However, Ca(OH)₂ would inevitably produce excessive bubbles in the decomposition process, which caused continuous and serious foaming of the slag. Meanwhile, because the slag and hot metal were not stirred in the experiment, even if Ca(OH)₂ was completely decomposed, most of the foamed slag would be suspended above the hot metal because of its adsorption on the inner wall of the crucible, so it was difficult to contact the hot metal (this has been confirmed in the experiment, and resulted in a relatively higher final phosphorus content). As a result, the foam formed by Ca(OH)₂ expanded the mass transfer distance of O²⁻, and even hindered the reaction of some slag and hot metal, eventually resulting in a very low k_O.

Comparatively speaking, experiment C had an obvious thermodynamic advantage in reducing the P–O reaction temperature, but due to the excessive heat absorption of CaCO₃ in the decomposition process, the heat required for slag melting had to be restricted, which directly reduced the fluidity of the slag. In addition, according to Zhong et al. [5], when the temperature exceeds 850 °C, there will be an obvious sintering phenomenon in the decomposition process of CaCO₃, which is consistent with the surface hardening and cracking of slag until the end of the experiment. At this time, the conversion rate of CaO decreased, and the fluidity of slag became worse. Both cases seriously hindered the diffusion of O²⁻ and PO₄³⁻ in the slag. As a result, the k_O was only slightly higher than that in experiment B.

Finally, as a reference, experiment A had no thermodynamic advantage, and the fluidity of the slag was the lowest among the three because of the high melting point of CaO. Fortunately, compared with Ca(OH)₂ and CaCO₃, CaO did not absorb excessive heat or cause foaming slag formation during heating. Therefore, it was obvious that the diffusion resistance of O²⁻ and PO₄³⁻ in the slag was relatively small, and a high k_O was easy to obtain.

4.4. Effect of Slag Viscosity on Transfer of Phosphorus Mass

To further evaluate the reliability of the results obtained, it is necessary to understand the change in slag viscosity during dephosphorization. The chemical compositions of the final hot metal and slags are shown in

Table 3. Chemical composition of the final hot metal (wt.%).

No.	Composition
	C	Si	Mn	P	S
A	2.03	0.003	0.13	0.013	0.013
B	2.18	0.007	0.20	0.041	0.009
C	2.16	0.008	0.21	0.036	0.010

and

Table 4. Chemical composition of the final slag (wt.%).

No.	Composition
	CaO	SiO2	FeO	MnO	MgO	Al2O3	P2O5	CaCl2
A	35.32	17.21	3.03	3.97	1.65	11.88	6.74	16.23
B	39.07	11.54	5.11	3.14	0.704	13.87	6.07	15.07
C	39.97	9.55	5.12	3.04	0.586	13.52	6.02	15.82

, respectively.

It can be seen from Table 3 and Table 4 that other elements besides P in hot metal were also partially oxidized and entered the slag. Among them, Si and Mn have a relatively greater effect on the mass transfer of phosphorus. Generally, the viscosity of slag is two orders of magnitude higher than that of hot metal, so its effect on mass transfer of phosphorus is much greater than that of hot metal. In view of this, the following mainly investigates the effect of Si and Mn on slag viscosity.

As we all know, the viscosity of basic steelmaking slag is relatively small in homogeneous state and decreases with increasing FeO content. Because both the basicity of slag (>2) and FeO content (>10 wt.%) are high, the Si–O complexions in it mostly exist in the smallest structural unit SiO₄⁴⁻, and the melting point of this slag is also relatively low [19].

However, with the progress of dephosphorization reaction, the FeO content will decrease, while the contents of SiO₂ and MnO will increase in the slag. Among them, the slag viscosity can increase with the increase in SiO₂ content and decrease with the increase in MnO content. Considering the reduction in FeO content and the changes in other components in the slag, their final effect is often difficult to determine.

Nevertheless, it is feasible to use empirical Formula (12) [19] to roughly judge the viscosity of the initial and final slag.

$$\ln \eta =\frac{1}{0.15-0.44\Lambda }-\frac{1.77+2.88\Lambda }{T}$$

(12)

where, η represents the viscosity of the slag, Λ represents the optical basicity of the slag, and T represents the temperature.

For the convenience of analysis, the effect of flux in the experiment is not considered temporarily, and it is assumed that all slag components were completely dissolved at 1400 °C and the temperature remained constant. Through calculation, the viscosity of the initial slag is 0.0073 Pa·s, and viscosities of final slag A, B, and C are 0.0011, 0.0019 and 0.0023 Pa·s, respectively. It is not difficult to find that the dephosphorization process reduced the slag viscosity, and the final slag viscosity in experiment A was significantly lower than that in experiments B and C, which explains the reason for the larger k_O obtained in experiment A to a certain extent.

In addition, the basicity of the final slags (R = w(CaO)/(w(SiO₂) + w(P₂O₅)) is 1.47, 2.22, and 2.57, respectively. They all have a certain deviation from the set ideal value, but considering the heterogeneous slag composition and sampling error, this is still acceptable. Obviously, the lower basicity in experiment A is due to its higher dephosphorization efficiency than experiments B and C.

5. Conclusions

The main results are as follows:

(1) According to the change in hot-metal phosphorus content during dephosphorization, a new dephosphorization kinetic model has been established by introducing a new concept “dynamic relative area”. The test of [%P]—time data in the related literature shows that the consistency of the new model is higher than that of the traditional model.

(2) The research on the mass transfer parameter shows that neglecting the decrease in P–O contact area at the slag-metal interface during the reaction is an important reason for the fluctuation in the A·k_O calculated by traditional dephosphorization models.

(3) In the research on CaO and its derivatives, the k_O values affected by CaO, Ca(OH)₂, and CaCO₃ are 0.0840, 0.0216, and 0.0363 cm/s, respectively.

(4) The dephosphorization reaction can reduce the viscosity of the slags and has a greater effect on the viscosity of CaO-based slag, which explains the reason for its larger k_O to a certain extent.

(5) The establishment of the new dephosphorization kinetic model can provide feasibility for the research on the mass transfer mechanism of phosphorus under the action of CaO and its derivatives. The results have shown that the existence of Ca(OH)₂ and CaCO₃ is extremely disadvantageous to mass transfer of phosphorus in slag, which needs to be avoided as much as possible.