Re-oxidation Kinetics of Flash-Reduced Iron Particles in H₂-H₂O(g) Atmosphere Relevant to a Novel Flash Ironmaking Process

Abstract

A novel flash ironmaking process based on hydrogen-containing reduction gases is under development at the University of Utah. The goal of this work was to study the possibility of the re-oxidation of iron particles in a H₂-H₂O gas mixture in the lower part of the flash reactor from the kinetic point of view. The last stage of hydrogen reduction of iron oxide, i.e., the reduction of wustite, is limited by equilibrium. As the reaction mixture cools down, the re-oxidation of iron could take place because of the decreasing equilibrium constant and the high reactivity of the freshly reduced fine iron particles. The effects of temperature and H₂O partial pressure on the re-oxidation rate were examined in the temperature range of 823 K to 973 K (550 °C to 700 °C) and H₂O contents of 40 to 100 pct. The nucleation and growth kinetics model was shown to best describe the re-oxidation kinetics. The partial pressure dependence with respect to water vapor was determined to be of first order, and the activation energy of re-oxidation reaction was 146 kJ/mol. A complete rate equation that adequately represents the experimental data was developed.

Appendix

Evaluation of the Effect of Inter-particle Diffusion

Whether inter-particle diffusion has a significant effect on the overall rate of a gas–solid can be assessed by comparing the diffusion-controlled rate with the experimentally observed rate. In the reaction investigated in this work, water vapor diffuses through a porous layer of iron particles, as illustrated in Figure A1, and undergoes the following reaction:

Fig. A1

Illustration of water vapor diffusing through a porous layer of iron particles

$$ {\text{Fe}} + {\text{H}}_{2} {\text{O}}\left( {\text{g}} \right) = {\text{FeO}} + {\text{H}}_{2} \left( {\text{g}} \right). $$

(A1)

The relationship between conversion and time under inter-particle diffusion control in a flat geometry is given by[12]

$$ X^{2} = \frac{K}{1 + K}\left( {C_{{{\text{H}}_{2} {\text{O}}_{\text{b}} }} - \frac{{C_{{{\text{H}}_{{2{\text{b}}}} }} }}{K}} \right)\frac{{2bD_{\text{e}} }}{{\left( {1 - \in } \right)\rho_{\text{s}} }} \left( {\frac{{A_{\text{p}} }}{{F_{\text{p}} V_{\text{p}} }}} \right)^{2} t $$

(A2)

where t is the reaction time, X is the fractional conversion of the solid, K is the equilibrium constant of the reaction of interest, b is the stoichiometry coefficient of reaction (=1 for the reaction in question), $F_{\text{p}} = 1$, $D_{\text{e}}$ is the effective gas phase diffusion coefficient, $\in$ is the voidage of the particle bed, $\left( {1 - \in } \right)\rho_{\text{s}}$ is the number of moles of solid reactant per unit volume of the bed, $V_{\text{p}}$ and $A_{\text{p}}$ are, respectively, the volume and surface area of the particle layer, and $C_{{{\text{H}}_{2} {\text{O}}_{\text{b}} }}$ and $C_{{{\text{H}}_{{2{\text{b}}}} }}$ are, respectively, the bulk molar concentration of water vapor and hydrogen. The time needed to reach complete conversion is

$$ t_{X = 1} = \frac{1 + K}{K}\; \frac{{\left( {1 - \in } \right)\rho_{\text{s}} (V_{\text{p}} /A_{\text{p}} )^{2} }}{{2D_{\text{e}} \left( {C_{{{\text{H}}_{2} {\text{O}}_{\text{b}} }} - C_{{{\text{H}}_{{2{\text{b}}}} }} /K} \right)}} = \frac{1 + K}{K}\; \frac{{\left( {1 - \in } \right)\rho_{\text{s}} L_{\text{p}}^{2} }}{{2D_{\text{e}} \left( {C_{{{\text{H}}_{2} {\text{O}}_{\text{b}} }} - C_{{{\text{H}}_{{2{\text{b}}}} }} /K} \right)}} $$

(A3)

where $L_{\text{p}}$ is the thickness of the particle layer. The equilibrium constant of Reaction [A1] at 873 K (600 °C) is

$$ K = 2.88 $$

(A4)

Molar density of iron particles is

$$ \rho_{\text{s}} = 0.14\;{\text{mol/cm}}^{3} . $$

(A5)

The voidage of an iron particle bed of 100 mg with area of 9 cm² and thickness of 0.5 mm is

$$ \in = 0.97 $$

(A6)

and

$$ V_{\text{p}} /A_{\text{p}} = L_{\text{p}} . $$

(A7)

Consider in the gas mixture, $p_{{{\text{H}}_{2} {\text{O}}}} /p_{{{\text{H}}_{2} }} = 80\;{\text{pct}}/20\;{\text{pct}}$, (atmospheric pressure = 0.85 atm),

$$ C_{{{\text{H}}_{2} {\text{O}}_{\text{b}} }} - C_{{{\text{H}}_{{2{\text{b}}}} }} /K = 8.66 \times 10^{ - 6} \;{\text{mol/cm}}^{3} $$

(A8)

According to the Fuller–Schettler–Giddings[30] method, the gas phase diffusion coefficient can be obtained from the following relationship:

$$ D_{{{\text{H}}_{2} {\text{O - H}}_{2} }} = \frac{{1.00 \times 10^{ - 7} T^{1.75} \left( {\frac{1}{{M_{{{\text{H}}_{2} {\text{O}}}} }} + \frac{1}{{M_{{{\text{H}}_{2} }} }}} \right)^{1/2} }}{{P\left[ {\left( {\Upsigma \nu_{{{\text{H}}_{2} {\text{O}}}} } \right)^{\frac{1}{3}} + \left( {\Upsigma \nu_{{{\text{H}}_{2} }} } \right)^{1/3} } \right]^{2} }} $$

(A9)

$$ D_{\text{e}} = D \cdot \in^{2} $$

(A10)

where T = 873 K (600 °C), total pressure P = 0.85 atm, molecular weights $M_{{{\text{H}}_{2} {\text{O}}}}$ = 18 g/mol, $M_{{{\text{H}}_{2} }}$ = 2 g/mol, $\nu_{{{\text{H}}_{2} }} = 7.07$, and $\nu_{{{\text{H}}_{2} }} = 12.7$.

Substitute all known variables to get

$$ D_{\text{e}} = 6.4\;{\text{cm}}^{2} / {\text{s}}. $$

(A11)

Therefore,

$$ t_{X = 1} = \frac{1 + K}{K} \;\frac{{\left( {1 - \in } \right)\rho_{\text{s}} (V_{\text{p}} /A_{\text{p}} )^{2} }}{{2D_{\text{e}} \left( {C_{{{\text{H}}_{2} {\text{O}}_{\text{b}} }} - C_{{{\text{H}}_{{2{\text{b}}}} }} /K} \right)}} = \frac{1 + 2.88}{2.88}\;\frac{{(1 - 0.97) \times 0.14 (L_{\text{p}} )^{2} }}{{2 \times 6.4 \times 8.66 \times 10^{ - 6} }}. $$

(A12)

According to the above equation, if the thickness of a sample layer is 0.05 cm, the time required for the reaction to reach completion is 0.13 seconds. However, the observed rate was much slower than this calculated rate. Thus, it can be concluded that the reaction rate was not affected by the inter-particle diffusion.