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A novel theoretical model for calculating the effective diffusivity of gases in a porous pellet composed of two different grains

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Abstract

Effective diffusivity of gases is an important property when modeling the physicochemical processes occurring in a pellet. Calculating effective diffusivity in a pellet composed of a mixture of particles is a difficult task. In this paper, a theoretical model is presented in order to describe the diffusion of gases in a porous pellet made up of a mixture of two kinds of solid grain. Solid grains can either be fully dense and thus non-porous or contain pores, with a grain being sub-divided into sub-grains. The results predicted by the model have been evaluated and validated by use of experimental data obtained by reduction of cuprous sulfide in the presence of lime. Finally, the effects of structural properties and operating conditions on the effective diffusivity of the gases in the pellet have been evaluated.

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Abbreviations

b :

Number of moles of solid B reacted per mole of gas A in reaction 4

c :

Stoichiometric coefficient in reaction 4

d :

Stoichiometric coefficient in reaction 5

D Ak,B, D Ak,D :

Knudsen diffusivity of gas A in solids B and D, respectively

D e :

Effective diffusivity in the porous solid

D e,c , D e,s, D e,u,:

Effective diffusivity calculated by Sohn and Won and by use of the theoretical model with and without lime sub-structural effect, respectively

\( D_{{{\text{H}}_{ 2} {\text{ - H}}_{ 2} {\text{O}}}} \) :

Molecular diffusivity of hydrogen in water vapor

D k :

Knudsen diffusivity

D k,c, D k,s, D k,u :

Knudsen diffusivity calculated by use of mercury penetration porosimetry and the theoretical model with and without lime sub-structural effect, respectively

D m,b , D m,c :

Molecular diffusivity calculated by Slattery and Bird and by use of the Chapman–Enskog formula, respectively

E :

Stoichiometric coefficient in reaction 5

F p :

Shape factor of the pellet (= 1, 2, and 3 for flat plates, long cylinders, and spheres, respectively)

F B, F D, F p :

Shape factor of grain B, sub-grain D, and pellet, respectively

M A :

Molecular weight of gaseous A

n d,B, n d,D :

Number of solid grains of B and sub-grains of D, respectively

P :

System pressure

r d,B, r d,D :

Average radius of solid grains of B and sub-grains of D, respectively

r p :

Radius or half-thickness of the pellet depending on the geometry

\( \bar{R} \) :

Universal gas constant

T :

System temperature

α B, α D :

Fractions of pellet volume occupied by solids B and D, respectively

γ :

Ratio of the molar quantities of solids B and D, defined by Eq. 11

ε :

Porosity of the pellet

ρ B, ρ D :

True molar densities of solids B and D, respectively

τ :

Tortuosity of the pellet

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Acknowledgments

The authors are thankful to Professor H. Y. Sohn for his useful comments. The authors used his experimental data related to hydrogen reduction of cuprous sulfide in this research to validate the model. The authors express their sincere gratitude to him.

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Authors and Affiliations

  1. Department of Chemical Engineering and Mineral Industries Research Center, Shahid Bahonar University of Kerman, 76175, Kerman, Iran

    Bahador Abolpour & M. Mehdi Afsahi

  2. Department of Material Science and Metallurgy, University of Cambridge, Cambridge, CB2 3QZ, UK

    R. Vasant Kumar

Authors
  1. Bahador Abolpour
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  2. M. Mehdi Afsahi
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  3. R. Vasant Kumar
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Correspondence to M. Mehdi Afsahi.

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Abolpour, B., Mehdi Afsahi, M. & Vasant Kumar, R. A novel theoretical model for calculating the effective diffusivity of gases in a porous pellet composed of two different grains. Res Chem Intermed 38, 1455–1465 (2012). https://doi.org/10.1007/s11164-011-0476-7

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