The law of additive reaction times applied to the hydrogen reduction of porous nickel-oxide pellets
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The Law of Additive Reaction Times Applied to the Hydrogen Reduction of Porous Nickel-Oxide Pellets
[ - I n ( 1 - x)] ~'" = bkNCabt
Until recently, the models for the reaction of a porous solid with a fluid have, for conceptual simplicity, generally assumed the solid to be made up of grains with a welldefined, basic geometry, namely that of a flat plate, a long cylinder, or a sphere. Furthermore, the grains have been assumed to react according to the shrinking-core model. J,2 Sohn 3'4 extended this grain model to incorporate other types of kinetics for the solid. This study showed that the following approximate solution obtained for the earlier idealized version of the grain model 5'6 is very likely to remain valid regardless of the type of rate dependence on the amount of solid reactant remaining unreacted: Time Time required to Time required to attain required attain the same the same conversion to attain --- conversion if + if the reaction of a certain the intrapellet individual grains conversion diffusion were were infinitely fast infinitely fast (rate control by productlayer diffusion)
[1] This relationship is valid for an isothermal fluid-solid reaction in which a coherent layer of solid product is formed and the effective diffusivity remains unchanged. The reactions of many finely-sized solid particles follow the nucleation and growth kinetics characterized by H.Y. SOHN is Professor in the Department of Metallurgy and Metallurgical Engineering, University of Utah, Salt Lake City, UT 84112-1 ! 83. DAESOO KIM, formerly Graduate Student in the Department of Metallurgy and Metallurgical Engineering, University of Utah, is now Section Chief, Pyrometallurgy Laboratory, Korea Institute of Energy and Resources, Guro P.O. Box 98, Seoul 150-06, Korea. Manuscript submitted August 29, 1983.
[2]
Incorporating this kinetics expression, Eq. [1] can be written as 3
t* - [-ln(1 - x) TM + 6"2 " p~(x)
[3]
t* =- bkuCAbt
[4]
Vp ~ ~pksctBpB &N = ~ V 2De
[5]
where
It is the purpose of this communication to present the results of applying Eq. [3] to the experimental data of the hydrogen reduction of porous nickel-oxide pellets reported previously. ~0The reaction can be expressed as H2(g) + NiO (s) = H20 (g) + Ni (s)
H.Y. SOHN and DAESOO KIM
METALLURGICALTRANSACTIONS B
S-shaped conversion-vs-time relationships. 7'8'9 The experimental data for the hydrogen reduction of nickel oxide exhibit this characteristic. ~0,H,12 A simplified form of the nucleation and growth kinetics attributed to Erofeev7 is as follows:
[6]
The data reported therein are most suitable for the stated purpose because experiments were carried out to obtain separately information on intrinsic kinetics and on effective diffusivity, as required for the application of Eq. [1]. Data were also taken in the intermediate regime. In the original paper, the intrinsic kinetics of the reaction of the grains were interpreted based on the shrinking-core scheme for a long cylinder. Since the shrinking-core model does not yield an S-shaped conversion curve, the
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