Mathematical analysis of reactions in metal oxide/carbon mixtures
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THE
reduction of metal oxides, in particular iron oxides, by carbon has been studied to varying deg r e e s of completeness by numerous investigators. References to e a r l i e r investigations are given in pap e r s , for example, by Yun1 and by Rao.2 More recently, Fruehan3 made a further study of the reduction of iron oxides by carbon, and Kor4 studied the reduction of Mn304 t o MnO by carbon. The concensus is that when a mixture of a m e t a l oxide and carbon is heated, the consecutive reduction and oxidation reactions o c c u r via the intermediate gaseous reaction products CO and CO2, thus M O + C O = M +CO2
[1]
COs + C = 2CO.
[2]
The e x c e s s gas generated diffuses out of the s y s tem through the interparticle pores, where the COz/ CO ratio can vary over a wide r a n g e , depending on the type of m e t a l oxide and carbon in the mixture. For example, in the reduction of higher oxides of iron 3 and manganese4 to t h e i r lower oxides and of lead oxide S to lead by carbon, the reaction product is essentially pure CO2. For the wustite + carbon mixtures 1'3 the C O J C O r a t i o in the gas evolved is initially c l o s e to the value for the iron-wustite equilibrium, but decreases with the progress of reduction. Howe v e r , indications are that in all the systems studied the overall rate of reduction of the oxide is controlled primarily by the rate of oxidation of carbon in the CO2-CO mixture that prevails within the interparticle pores. In a mathematical analysis of this problem Sohn and Szekely6 derived a rate expression on the assumption that the overall isothermal rate is controlled simultaneously by the reduction of metal oxide with CO and oxidation of carbon with CO2 and that the gas composition is uniform throughout the pellet. T h e i r analysis is applicable under the limiting conditions of negligible interaction between the g a s e s in the interparticle pores and the ambient atmosphere, as defined in their article. When t h e r e is a substantial interaction between the two, as is the case for the R. H. TIEN is Associate Research Consultant and E. T. TURKDOGAN is Senior Research Consultant, U. S. Steel Corporation, Research Laboratory, Monroeville, Pa. 15146. Manuscript submitted November 5, 1976.
METALLURGICAL TRANSACTIONS B
system described below, the effect of this interaction should be included in the analysis. Another approach to the mathematical modelling was that by Rao,~ who assumed that the rate is controlled simultaneously by the oxidation of carbon with CO2 and the forced viscous flow of gas t o the furnace atmosphere from the pores of the pellet. From the equations he derived, coupled with his reduction data for iron oxide-carbon mixtures, s Rao concluded that the buildup of CO2 pressure at 2 cm below the surface of the powder mixture was more than 20 atm at the 20 pct reduction stage, and about 6 atm at the 40 pct reduction stage. Such enormous e x c e s s pressures cannot be sustained in relatively shallow powder mixtures. Obviously the mathematical formulation of Rao do
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