Dephosphorization Kinetics between Bloated Metal Droplets and Slag Containing FeO: The Influence of CO Bubbles on the Mass Transfer of Phosphorus in the Metal

Abstract

Dephosphorization kinetics of bloated metal droplets was investigated in the temperature range from 1813 K to 1913 K (1540 °C to 1640 °C). The experimental results showed that the overall mass transfer coefficient, ${k_{\text{o}}}$, decreased with increasing temperature because of decreasing phosphorus partition ratio, ${L_{\text{P}}}$. It was also found that the mass transfer coefficient for phosphorus in the metal, ${k_{\text{m}}}$, had the highest value at the lowest temperature [i.e., 1813 K (1540 °C)] because the formation of smaller CO bubbles increased the rate of surface renewal, leading to faster mass transport. Meanwhile, metal droplets without carbon were also employed to study the effect of decarburization on dephosphorization. The results show that although decarburization lowers the driving force significantly, ${k_{\text{m}}}$ (6.2 × 10⁻² cm/s) for a carbon containing droplet is two orders of magnitude higher than that for carbon free droplets (5.3 × 10⁻⁴ cm/s) because of the stirring effect provided by CO bubbles. This stirring offers a faster surface renewal rate, which surpasses the loss of driving force and then leads to a faster dephosphorization rate.

APPENDIX

In the authors’ previous study,[14] it was shown that by balancing the oxygen supply from reducible oxides in the slag and oxygen consumption by carbon in the metal, the ${{\text{P}}_{{{\text{O}}_2}}}$at the interface between slag and liquid metal can be determined via Eq. [A1].

$$ {k_{\text{FeO}}}\left( {C_{\text{FeO}}^{\text{b}} - C_{\text{FeO}}^i} \right) = \frac{1}{A}\frac{{{\text{d}}{n_{\text{CO}}}}}{{{\text{d}}t}} $$

(A1)

Here, $\frac{{{\text{d}}{n_{\text{CO}}}}}{{{\text{d}}t}}$ is the CO generation rate (mole/s), ${C_{\text{FeO}}}$ is the concentration of FeO, $A$ is the surface area of the droplet, ${k_{\text{FeO}}}$ describes oxygen transport in the slag conceptually defined as the mass transfer coefficient for FeO. $C_{\text{FeO}}^i$ may be expressed in terms of activity of oxygen at the interface and $C_{\text{FeO}}^{\text{b}}$ expressed as a function of the initial concentration of FeO modified by the amount reduced (${\text{d}}{n_{\text{FeO}}}$). If one makes these substitutions, and further recognizes that ${\text{d}}{n_{\text{FeO}}}$ is equivalent to the amount of CO generated (${\text{d}}{n_{\text{CO}}}$), one may rearrange Eq. [A1] to obtain Eqs. [A2] and [A3].

$$ {\text{P}}_{{{\text{O}}_{2} }}^i = \left[ {\frac{{\gamma_{\text{FeO}} K_{\text{Fe}} }}{{C_{\text{s}} *a_{\text{Fe}}^i *K_{\text{O}} }}\left( {C_{\text{FeO}}^{\text{b}} - \frac{1}{A}\frac{1}{{k_{\text{FeO}} }}\frac{{{\text{d}}n_{\text{CO}} }}{{{\text{d}}t}}} \right)} \right]^{2} $$

(A2)

$$ {\text{P}}_{{{\text{O}}_2}}^i = {\left[ {\frac{{{\gamma_{\text{FeO}}}{K_{\text{Fe}}}}}{{{C_{\text{s}}}*a_{\text{Fe}}^{\text{i}}*{K_{\text{O}}}}}\left( {C_{\text{FeO}}^{\text{o}} - \frac{1}{{{V_{\text{s}}}}}\mathop \smallint \limits_{{n_{\text{C}}}, t = {\text{initial}}}^{{n_{\text{C}}}, t = t} {\text{d}}{n_{\text{CO}}} - \frac{1}{A}\frac{1}{{{k_{\text{FeO}}}}}\frac{{{\text{d}}{n_{\text{CO}}}}}{{{\text{d}}t}}} \right)} \right]^2} $$

(A3)

where ${K_{\text{Fe}}}$ and ${K_{\text{O}}}$are the equilibrium constants for FeO dissociation and oxygen dissolution in iron; ${\gamma_{\text{FeO}}}$ is the activity coefficient for FeO in the slag, ${C_{\text{s}}}$ is the overall molar density of the slag, and ${V_{\text{S}}}$ is the volume of slag. The term, $C_{\text{FeO}}^{\text{o}} - \frac{1}{{{V_{\text{s}}}}}\mathop \smallint \limits_{{n_{\text{C}}}, t = {\text{initial}}}^{{n_C}, t = t} {\text{d}}{n_{\text{C}}}$, represents the FeO content of the slag at time t. It is important to note that ${V_{\text{s}}}$ must be defined as either the volume of dense slag or the foamy slag depending on the location of the droplet.

The middle term, $\frac{1}{{{V_{\text{s}}}}}\mathop \smallint \limits_{{n_{\text{C}}}, t = {\text{initial}}}^{{n_{\text{C}}}, t = t} {\text{d}}{n_{\text{C}}}$, in Eq. [A3] describes the amount of carbon oxidized, which is taken from experimental measurements. To use this equation for a specific reaction time, one will be required to calculate the concentration of FeO. This instantaneous FeO concentration can be calculated from the initial concentration of FeO and the amount of carbon oxidized between time zero and time t. Using the X-ray videos, one can calculate the volume of foamy slag and dense slag at any given time, thereby determining the amount of liquid slag in each phase. Assuming no mixing between the two after the droplet is in the foamy slag, one can calculate the change in FeO for the foamy slag.