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Kinetics of reduction of MnO in powder mixtures with carbon

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Abstract

Experimental data on the kinetics of the reaction between MnO and graphite in a mixture of fine powders, obtained earlier by one of the authors, were reassessed. The principal motive was to test on this system a new kinetic model, the “intrinsic transport” model, published previously by th present authors. In this model, the reaction-rate-limiting step is assumed to be transport of a gaseous intermediate by pore diffusion between reaction sites on the surfaces of the reactant particles. Various other model formalisms potentially applicable to this reaction also were tested. It is shown that the intrinsic transport of CO2 gave good to excellent fits to the experimental data over a wide range of reaction conditions. Other models gave poor agreement. It is shown, furthermore, that for the case where the CO2 pore-diffusion path lengths were made small (fine MnO and coarse graphite particle size), thus speeding up rapid intrinsic transport, the graphite-surface reaction became rate controlling.

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Abbreviations

C O :

initial concentration of graphite in the mixture (mol m−3)

D CO2 :

diffusivity of CO2 in CO-CO2-Ar gas mixtures (m2 s−1)

\(D_{CO_2 }^{eff} \) :

effective diffusivity of CO2 in CO-CO2 within the pores of the reaction mixture (m2 s−1)

k :

reaction rate constant

k 1 :

intrinsic-transport reaction rate constant, first stage (mol s−1 m−1)

k 2 :

intrinsic-transport reaction rate constant, second stage (s−1/2)

k s :

first-order, surface reaction rate constant (kg m−2 s−1 kPa−1)

K :

equilibrium constant (—)

L :

reaction-bed depth (m)

L 0 :

total Reaction-bed depth (at bottom of crucible) (m)

m :

generation rate of CO (mol m−3 s−1)

n c :

moles of carbon reacted (mol)

N :

initial molar ratio of carbon to MnO in the reaction mixture (—)

\(P_{CO_2 } \) :

equilibrium partial pressure of CO2 (atm)

P [3] :

CO pressure in equilibrium with Reaction [3] (atm)

P CO :

equilibrium partial pressure of CO (atm)

\(P_{_{CO_2 } }^ * \) and \(P_{_{CO_2 } }^{ * * } \) :

CO2 pressures in a diffusion gradient, at the MnO/gas and C/gas interfaces, respectively (atm)

P 0CO and P wCO :

CO pressures in the pore space of the reaction mixture, at the bottom and surface of the reaction bed, respectively (atm)

r t c ,r r MnO :

initial radius of MnO and C particles, respectively (m)

R:

gas constant (8.206 × 10−5 m3 atm K−1 mol−1)

t :

time of reaction (s)

t i :

time for initiation of the reaction (s)

T :

temperature (K)

V MnO :

initial volume of MnO in the reaction mixture (m3)

V T :

initial total volume (including porosity) of the reaction mixture (m3)

X C :

fractional reaction of carbon (—)

X MnO :

fractional reaction of MnO (—)

Z :

volumetric reaction mixture parameter defined by Eq. [10] (—)

β :

parameter in Eq. [12], defined by Eq. [13] (—)

ε :

initial void fraction in the reaction mixture (—)

η :

effectiveness factor, defined by Eq. [14]

ρ C :

density of graphite (kg m−3)

τ :

tortuosity factor for the reaction mixture (—)

ϕ L :

auxiliary parameter, Eq. [15]

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Author notes

  1. W. J. Rankin (Director, Market Development Manager) & J. R. Wynnyckyj (Professor Emeritus)

    Present address: G.K. Williams Cooperative Research Centre for Extractive Metallurgy, Department of Chemical Engineering, The University of Melbourne, 3052, Parkville, Victoria, Australia

Authors and Affiliations

  1. CSIRO Minerals, 3052, Clayton, Victoria, Australia

    W. J. Rankin (Director, Market Development Manager)

  2. Department of Chemical Engineering, University of Waterloo, N2L 3G1, Waterloo, ON, Canada

    J. R. Wynnyckyj (Professor Emeritus)

Authors
  1. W. J. Rankin
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Rankin, W.J., Wynnyckyj, J.R. Kinetics of reduction of MnO in powder mixtures with carbon. Metall Mater Trans B 28, 307–319 (1997). https://doi.org/10.1007/s11663-997-0097-0

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  • DOI: https://doi.org/10.1007/s11663-997-0097-0

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