Decarburization of Iron Carbon Droplets with Oxidizing Slag: An Experimental Study to Understand the Effect of Ionic and Electronic Conductivity on Decarburization Kinetics

Abstract

An experimental study was performed to investigate the effect of ionic and electronic conductivity of oxidizing slags on the kinetics of decarburization of liquid metal droplets. An approach based on Wagner’s oxidation theory was developed to analyze the reaction kinetics with the variation of the slag conductivity. Despite the sufficiency of reactants, a sudden shutdown of decarburization reaction was observed for lower conductivity slag, whereas the reaction reached near thermodynamic equilibrium where the conductivity was higher. Based on this observation, a mechanism of accumulation of charge at the slag–metal interface has been proposed as the cause of premature shutdown of the reaction. While increasing basicity was also found to accelerate reaction kinetics and to eliminate or mitigate against premature shutdown of the reaction, it made no difference for slags of high electronic conductivity. This observation suggests that the desired rate of decarburization can be attained at lower basicity if the electronic conductivity of the slag is high.

Appendix A

The slag oxygen potential is a function of Fe³⁺/Fe²⁺ ratio and can be expressed as follows:

$$\text{ln}{p}_{{\rm O}_{2}}={A}_{1}\times ln\frac{\text{Fe}^{3+}}{\text{Fe}^{2+}}\; \text{where}\; {A}_{1}\; \text{is\; a \;constant}$$

(A.1)

$$\text{d\;ln}{p}_{{\rm O}_{2}}={A}_{1}\times \text{d\;ln}\frac{\text{Fe}^{3+}}{\text{Fe}^{2+}}={A}_{1}\times \text{d\;ln}\frac{\frac{\text{Fe}^{3+}}{\text{Fe}_{t}}}{\frac{\text{Fe}^{2+}}{\text{Fe}_{t}}}={A}_{1}\times \text{d\;ln}\frac{y}{1-y}$$

(A.2)

The slag conductivities can be expressed as a function of ferric fraction (y)

• 1. Ionic conductivity

  $${\sigma }_{\rm ion}={\sigma }_{0}-ay$$

  (A.3)

• 2. Electronic conductivity

  $${\sigma }_{\rm e1}=b\left[\text{Fe}^{2+}\right]\left[\text{Fe}^{3+}\right]=by\left(1-y\right)$$

  (A.4)

  where the constants ${\sigma }_{0},\;a$ and b are functions of slag composition. From the Nernst–Einstein equation for ionic conductivity,

  $${\sigma }_{0}=\frac{4{F}^{2}}{RT}\times ({C}_{\text{Ca}^{2+}}{D}_{\text{Ca}^{2+}}+{C}_{\rm Fe}{D}_{\text{Fe}^{2+}})$$

  (A.5)
  $$a=\frac{4{F}^{2}}{RT}{C}_{\rm Fe}{D}_{\text{Fe}^{2+}}$$

  (A.6)

From the diffusion-assisted charge hopping model for electronic conductivity,

$$b=4\pi {N}_{\rm a}\times \frac{{r}^{0}{r}^{\ast}}{{r}^{0}-{r}^{\ast}}\times \frac{{D}_{\text{Fe}^{2+}}{F}^{2}}{RT}\times {C}_{\rm Fe}^{2}$$

(A.7)

Applying these to Eq. [3] and integrating from the slag–metal interface to bulk

$$\frac{\text{d}{n}_{\rm FeO}}{\text{d}t}=\frac{RT}{8{F}^{2}}\times \left(\frac{{A}_{1}}{\Delta x}\right){\int }_{\rm int}^{\rm bulk}\frac{{(\sigma }_{0}-ay)by(1-y)}{{\sigma }_{0}-ay+by\left(1-y\right)}\text{d\;ln}\frac{y}{1-y}$$

(A.8)

$$=\frac{RT}{8{F}^{2}}\times \left(\frac{{A}_{1}}{\Delta x}\right){\int }_{i}^{b}\left[\frac{b{(\sigma }_{0}-ay)(1-y)}{{\sigma }_{0}-ay+by\left(1-y\right)}\text{d}y+\frac{{(\sigma }_{0}-ay)by}{{\sigma }_{0}-ay+by\left(1-y\right)}\text{d}y\right]$$

(A.9)

$$=\frac{RT}{8{F}^{2}}\times \left(\frac{{A}_{1}}{\Delta x}\right){\int }_{i}^{b}\left[\frac{b{(\sigma }_{0}-ay)}{{\sigma }_{0}-ay+by\left(1-y\right)}\text{d}y\right]$$

(A.10)

$$=\frac{RT}{16{F}^{2}}\times \left(\frac{{A}_{1}a}{\Delta x}\right){\int }_{\rm int}^{\rm bulk}\left[\frac{-2by+\left(b-a\right)}{{\sigma }_{0}-ay+by\left(1-y\right)}\text{d}y+\frac{\frac{2b{\sigma }_{0}}{a}-\left(b-a\right)}{{\sigma }_{0}-ay+by\left(1-y\right)}\text{d}y\right]$$

(A.11)

$$=\frac{RT}{16{F}^{2}}\times \left(\frac{{A}_{1}a}{\Delta x}\right)[\text{ln}\left({\sigma }_{\rm tot}\right)+{\int }_{\rm int}^{\rm bulk}\left\{\frac{2b{\sigma }_{0}-a\left(b-a\right)}{-ab}\right\}\frac{\text{d}y}{{\left(y+\frac{a-b}{2b}\right)}^{2}-\left\{{\left(\frac{a-b}{2b}\right)}^{2}+\frac{{\sigma }_{0}}{b}\right\}}]$$

(A.12)

We know from integration, $\int \frac{\text{d}x}{{x}^{2}-{a}^{2}}=\frac{1}{2a}\text{ln}\frac{x-a}{x+a}+constant$

$$=\frac{RT}{16{F}^{2}}\times \left(\frac{{A}_{1}a}{\Delta x}\right){\left[\text{ln}\left({\sigma }_{\rm tot}\right)+\frac{2b{\sigma }_{0}-a\left(b-a\right)}{-ab}\times \frac{1}{2\sqrt{{\left(\frac{a-b}{2b}\right)}^{2}+\frac{{\sigma }_{0}}{b}}}\text{ln}\frac{y+\frac{a-b}{2b}-\sqrt{{\left(\frac{a-b}{2b}\right)}^{2}+\frac{{\sigma }_{0}}{b}}}{y+\frac{a-b}{2b}-\sqrt{{\left(\frac{a-b}{2b}\right)}^{2}+\frac{{\sigma }_{0}}{b}}}\right]}_{\rm int}^{\rm bulk}$$

(A.13)

$$\frac{\text{d}{n}_{\rm FeO}}{\text{d}t}\left(\frac{\text{mol}}{{\text{m}}^{2}-\text{s}}\right)=\frac{RT}{16{F}^{2}}\times \left(\frac{{A}_{1}a}{\Delta x}\right){\left[\text{ln}\left({\sigma }_{\rm tot}\right)-\frac{a\left(a-b\right)+2b{\sigma }_{0}}{a\sqrt{{\left(a-b\right)}^{2}+4b{\sigma }_{0}}}\text{ln}\frac{2by+\left(a-b\right)-\sqrt{{\left(a-b\right)}^{2}+4b{\sigma }_{0}}}{2by+\left(a-b\right)+\sqrt{{\left(a-b\right)}^{2}+4b{\sigma }_{0}}}\right]}_{\rm int}^{\rm bulk}$$

(A.14)