Application of a nonisothermal thermogravimetric method to the kinetic study of the reduction of metallic oxides: Part I
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I.
INTRODUCTION
Trm application of a nonisothermal gravimetric method in the determination of the activation energies of solidgas reactions and the advantages of such a method have been introduced in an earlier publication, ill This was also exemplified in the case of the reduction of the oxides of molybdenum by hydrogen. The present work forms the second part of the study aiming at developing a nonisothermal method to evaluate the activation energy of a solid-gas reaction in a powder bed, where the reaction proceeds by a reaction front moving mechanism. As in the case of the earlier study, the present treatment deals with the reaction at a microscopic level between the reactant gas and single particles of the solid reactant. The reliability of this method is examined by applying the same to the reduction of WO3 in a powder bed. II.
THEORETICAL CONSIDERATIONS OF NONISOTHERMAL R E D U C T I O N
A typical reaction between a powder bed of loosely packed reactant B and gas A can be represented as follows: A (g) + bB (s) = e E (g) + f F
(s)
[1]
The powder bed is assumed to be porous and shallow, as shown in Figure 1. The reaction can be considered to proceed by the reaction front moving from the surface of the bed to the bottom. This would imply that the small particles of B in a thin reaction layer of Ay at the surface of the bed must have reacted completely with gas A before the particles in the next lower Ay layer have the J.A. BUSTNES, Research Assistant, DU SICHEN, Research Associate, and S. SEETHARAMAN, Professor, are with the Department of Theoretical Metallurgy, Royal Institute of Technology,
chance to react. Reaction [1] will continue successively layer by layer down to the bottom of the bed. We assume that the reactant gas A obtains access to all of the small particles within the very thin reaction layer and the product gas F can leave the reaction site without any hindrance. This would mean that at a constant temperature, the partial pressures of gas A and E are constant at the reaction front all the way from the surface of the bed to the bottom during the course of the reaction. Under these conditions, the "shrinking-core model ''12j can be applied to the individual particle in the reaction layer. If the resistance of the product layer of the small particle to the diffusion of A (g) and E (g) is also negligible, the reaction rate can be considered to be controlled by the chemical reaction at the interface between the unreacted core and product layer of the small particles. Smith t3j has derived the time, t~, required for complete reaction of a single particle based on the assumption that the reaction is controlled by surface chemical reaction. Reaction [ 1] is to be of first order with respect to A and irreversible. The temperature would be uniform throughout the heterogeneous region. The time required for complete reaction of a single particle, ty, is expressed as pr ts =
-
-
b lcd~4nC a
[2j
where P and r are the density and radius of the particle respectively, Me is the molecular weight of B,
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