Pore transport-controlled shrinking-core systems involving diffusion, migration, and homogeneous reactions: Part II. App
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2 2 CO22 3 (aq) 1 H2O (l) s HCO3 (aq) 1 OH (aq) [2]
I. INTRODUCTION
IN Part I of this article, a comprehensive model for the conversion of PbSO4 to lead carbonate in sodium carbonate solutions was formulated.[1] Guided by the experimental study of Gong et al.,[2] we envisage the reaction to proceed according to a shrinking-core model controlled by transport of aqueous species through the pores in the hydrocerrusite product layer. The model represents a further extension of previous efforts[3–11] to generalize the applicability of the pore transport–controlled shrinking-core model by allowing for diffusion, migration, and homogeneous reactions within the product layer in addition to the heterogeneous reaction at the shrinking-core interface. The model is composed of a complete set of transport equations for all of the aqueous species likely to exist in the system (eight species have been considered in this particular case). From these equations, the rate law expressing the variation of the conversion (a) of PbSO4 with time can be derived. One heterogeneous reaction and three homogeneous reactions are incorporated in the model. The heterogeneous reaction occurring at the shrinking-core interface involves the conversion of PbSO4 to hydrocerrusite (Pb3(CO3)2(OH)2), which can be written as follows: 2 3 PbSO4 (s) 1 2 CO22 3 (aq) 1 2 OH (aq)
s Pb3(CO3)2(OH)2 (s) 1 3 SO22 4 (aq)
[1]
This is coupled with homogeneous reactions involving carbonate species and water dissociation, which occur throughout the product layer and bulk solution:
MARK PRITZKER, Associate Professor, is with the Department of Chemical Engineering, University of Waterloo, Waterloo, ON, Canada N2L 3G1. Manuscript submitted August 12, 1999. METALLURGICAL AND MATERIALS TRANSACTIONS B
HCO32 (aq) s CO2 (aq) 1 OH2 (aq) H2O (l) s H+ (aq) 1 OH2 (aq)
[3] [4]
An important result of Part I was the finding that the rate expression for the PbSO4 conversion is predicted by the model to have the familiar form 12
2 2G a 2 (1 2 a)2/3 5 t 3 rPbSO4 r 20
[5]
where G is a constant. It should be noted that the transport equations themselves must be solved by numerical methods. The form of the rate expression is in agreement with the empirical findings of Gong et al.[2] Furthermore, it was shown that this result is not specific to this system and applies to others, provided the heterogeneous and homogeneous reactions are fast in comparison to the pore transport. The objective of Part II of this article is to directly apply the model to the experimental results of Gong et al.[2] The model will first be fit to some of these data using leastsquares analysis and values for the effective diffusion coefficients of the various species determined. Once this has been done, comparisons of the model predictions to other experimental data not used in the fitting procedure will be made, in order to further assess the validity of the model, to gain more insight into the reaction system, and, in some cases, to reanalyze experimental data. Among the aspects to be considered include
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