Kinetics of the zinc slag-Fuming Process: part II. mathematical model
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I.
INTRODUCTION
H A V I N G conducted industrial trials which revealed important kinetics phenomena in the slag-fuming process, described in Part I ~'Industrial Measurements', the next logical step was to describe the phenomena in a mathematical model of the process. In this way a quantitative description of the process, including, for example, the quantity of coal entrained in the slag, could be developed much more easily than by direct experiment alone. Moreover, a properly formulated model could predict the effect of process variables, e . g . , coal/air ratio and coal reactivity, on the timedependent composition and temperature of the slag bath. But more importantly, rate limiting steps could be identified and, based on these, methods determined for increasing the fuming rate. Development of the mathematical model is described in this paper. The model has been formulated in terms of heat and mass balances on the slag, coupled with reaction kinetics in the reduction and oxidation zones of the furnace. The formulation has involved consideration of the reaction of entrained coal particles to form 'secondary' gas bubbles, and the subsequent reaction of these char particle-gas bubble systems with the slag during their residence time in the bath. The model has also been extended to include heat losses through the slag chill on the furnace walls. In the third and final part of this paper the model is applied to study the effect of particular process variables and to determine the rate controlling steps in the process. II.
PREVIOUS MATHEMATICAL MODELS
As mentioned earlier, thermodynamic models of slag fuming have been developed in the past by Bell et al.,2 Kellogg, 3 and Grant and Barnett. 4 The early model of Bell G. G, RICHARDS. formerly Graduate Student, now Assistant Professor, and J. K BRIMACOMBE, Stelco Professor of Process Metallurgy, are with The Centre for Metallurgical Process Engineering, Department of Metallurgical Engineering, The University of Brlush ColurnbLa, Vancouver, BC V6T 1W5, Canada Manuscript submated July 11, 1984.
METALLURGICAL TRANSACTIONS B
et al. was based on the assumption of equilibrium for the
CO reduction of ZnO and for the water gas reaction; and mass balances were performed on carbon, hydrogen, oxygen, and nitrogen. The partial pressures of CO, CO2, H2, H20, N2, and Zn in the gas discharging from the slag bath were calculated with the model. Kellogg extended this firstgeneration model by including the thermodynamics of the FeO-Fe304 couple and PbO reduction as well as the behavior of dissolved sulfur. He also incorporated a heat balance which accounted for the sensible heat in the input slag, the build-up of frozen slag on the water jackets, and the reactions above the bath. This more comprehensive process model was able to predict the change with time of slag temperature and the concentrations of iron (FeO/Fe304), sulfur, lead, and zinc in the bath. Some empirical adjustments were made to heat-transfer coefficients and activity coefficients to fit model predictions to industria
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