Modified predominance diagrams for gas-solid reactions
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I. INTRODUCTION
THE predominance phase diagram introduced by Kellogg and Basu[1] is a graphical representation of the thermodynamic equilibrium between a solid system and its surrounding atmosphere. The theory and creation of predominance phase diagrams can be found in metallurgical thermodynamic textbooks[2] and will not be discussed here. The predominance phase diagram is frequently used to predict the outcome of reversible chemical reactions or to define the process operating conditions to obtain a desired reaction product. However, these diagrams do not take account of any kinetic information related to the process. Because most metallurgical processes are heterogeneous, mass transfer and other kinetic limitations can lead to conditions where the predominance diagram does not correctly predict the reactions occurring in the process. It is well known that mass transfer can affect reaction rates of multiphase reactions. Mass transfer resistances can also cause non-negligible differences in gas composition between the reaction interface and the bulk gas phase. The effect of mass transfer limitations on the reaction paths predicted by thermodynamics is not reflected in conventional predominance diagrams. In this article, the effect of mass transfer on the reaction path is considered. Equations predicting the gas composition at the reaction interface are derived from transport phenomena and reaction kinetics in order to modify predominance phase diagrams. It is shown that under certain conditions, mass transfer can have a significant influence on the reaction path, even when mass transfer is not rate-limiting.
J.P. CONSTANTINEAU, formerly Graduate Student, Metals and Materials Engineering Department, is Graduate Student, Chemical and Biological Engineering Department, The University of British Columbia, Vancouver, BC, Canada V6T 1Z4. Manuscript submitted December 3, 1999.
METALLURGICAL AND MATERIALS TRANSACTIONS B
II. EFFECT OF MASS TRANSFER ON REACTION RATES A. Reaction Rate Equations A brief discussion of the effect of mass transfer on reaction rates is necessary before considering its effects on the reaction path. This section briefly presents the development of the overall reaction rate equation considering only two resistances: chemical kinetics and mass transport through the gas phase. For simplicity, other resistances, such as adsorption or product layer diffusion are not included, but their inclusion would be straightforward in most cases. Product layer diffusion can be included in the system very similarly as mass transport through the gas phase. The equations can be applied to any heterogeneous system where a solid reacts with a gas. In the present case, we consider, as an example, the oxidation of a metallic sulfide: 1MS (s) 1 mO2 (g) → products (s) 1 nSO2 (g)
[1]
where the solid products could be a metal (M), an oxide (MO), a sulfate (MSO4), another solid compound, or a mixture of solid compounds. The actual solid reaction product composition is not important in this discussion. The rate of MS cons
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