Reactor models for a series of continuous stirred tank reactors with a gas-liquid-solid leaching system: Part II. Gas-tr
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I.
INTRODUCTION
IN Part I, m the case of solid spherical particles reacting according to the surface reaction control-shrinking core model (SRC-SCM) in a cascade of continuous reactors was considered. First, the mass and heat balance equations, which have to be solved simultaneously to allow for the computation of conversion (.ft) and temperature (T~) in each reactor stage, were derived (Eqs. [9] and [11] in Part I). Subsequently, appropriate equations were developed for the first time to describe the size distribution of partially reacted particles under isothermal or nonisothermal operating conditions. However, in g-l-s leaching systems, the process kinetics might be controlled by the rate by which the gaseous reactant is transferred into the liquid phase rather than the intrinsic rate of the leaching reaction itself. In other words, in the following two-step reaction scheme: A (g) --~ A (aq)
[1 ]
A (aq) + bB (s) --~ c C (aq) + d D (aq)
[2]
the rate of the mass-transfer step 1 might be the controlling step. Work that was done in the past in the direction of formulating models for three-phase reaction systems [2'3'4}did not address the case of pure gas-transfer control for multisize particles. It is the object of this article to develop model equations suitable for the calculation of conversion and exit V.G. PAPANGELAKIS, Assistant Professor, is with the Department of Chemical Engineering and Applied Chemistry, University of Toronto, Toronto, ON M5S 1A4, Canada. G.P. DEMOPOULOS, Associate Professor, is with the Department of Metallurgical Engineering, McGill University, Montreal, PQ H3A 2A7, Canada. Manuscript submitted August 2, 1991. METALLURGICAL TRANSACTIONS B
size distribution of multisize feeds reacting in a continuous stirred tank reactor (CSTR) under pure gas-transfer control. For the development of these model equations, two different routes are followed. The basis for both approaches is the coupling of the maximum gas-transfer reactor capacity with the particle dissolution kinetics. In the first one (model version 1), the steps followed are: (1) the formulation of an SCM equation for particles reacting under gas-transfer control ( G T C - S C M ) by assuming that A (aq), which is formed via Reaction [1], is distributed equally among all particles; (2) the derivation of a mass-PSD for the reacting solids using the G T C - S C M and the population balance model (PBM); [5'61 and (3) the use of the segregated flow model tl] to calculate the conversions at each stage. In the second route (model version 2), the steps followed are: (1) the formulation of an equation describing the rate of particle size change by assuming that A (aq) is distributed among particles in proportion to their individual surface area; (2) the derivation of equations describing the total specific surface area (g) and size distribution of reacting solids using the PBM; and (3) the calculation of the conversion using the PBM. The equations are first developed for a single heterogeneous reaction and then are extended to several para
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