Kinetic model for the chemical dissolution of multiparticle systems
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I.
INTRODUCTION
IN previous
studies the authors have presented several modified kinetic models that take account of the effect of individual particle shape on dissolution. 1.2 Practically all the solid systems used in extractive metallurgy, as grind solids or flotation concentrates, are multiparticle systems. J.A. Herbst 3 has discussed the relevant aspects of the behavior of multiparticle systems. He states that for batch leaching with a solid sample consisting of single-size spherical particles in a dilute suspension, a plot of 1 (1 - x) ~'3, where x is the fraction reacted, vs time. should yield a straight line with a slope inversely proportional to particle size. The same author discusses another sample of chalcopyrite having a "wide distribution of particle sizes". Even though the kinetics of the reaction is controlled by the surface reaction rate, the plot of the integrated rate expression [1 (l - x) 1'3] against time does not follow a straight line, and the overall rate for a given multiparticle system is a compound rate. To process the kinetic data from chemical leaching of a multiparticle sample, particles must be characterized in terms of both size and shape distribution. For individual isometric particles the following holds: 12
K'ore~[1 - (1 - x) 1'3] = 6kC, t
[1]
where t is the time of reaction, k the chemical constant, C, the product of the activities of the reagents raised to their respective orders, V the molar volume of the solid, reo the radius of a sphere of equal volume as the initial volume of the particle, and Ks the shape factor defined as (S/V) 9 de, i.e., the product of the body's surface area multiplied by the diameter of a sphere whose volume is equal to that of the body divided by the volume, s If tO is the sphericity factor:
K,O = 6 C NUNEZ, Head of the Metallurgy Department and Full Professor in Materials Scxence and Engineenng Metallurgy, and F ESPIELL. Professor of Metallurgy, Department of Metallurgy. are with Barcelona Umvers W, Barcelona 08028, Spain. Manuscript submitted April 30, 1984. METALLURGICAL TRANSACTIONS B
Expression [ 1 ] is satisfied similarly for multiparticle systems, bearing in mind that: 1. The plot of fraction reacted against time gives the same curve for all particles whose reo/Kr value is the same, independently of the specific values of re0 and Kr. Here Kr denotes the shape factor of an irregular particle. 2. The time, (r), necessary for complete reaction (x = 1) of a particle is the same for all the individual particles of the concentrate with the same ratio re,,/K, From Eq. [11, when x = 1, t = r, and:
1 6 reo r~oto --=-kC, V K< VkC,
r =---~--
12]
Thus, it seems more reasonable to take the distribution of the reo/K~o ratio to describe a concentrate rather than only the distribution of reo as calculated directly from the sieying data. The shape factor remains constant throughout the reaction only when the solid particle is isometric and has fiat sides. The term isometric refers here to all bodies that may contain an inscribed sphere tangent to all
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