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Journal of Porous Media
IF: 1.752 5-Year IF: 1.487 SJR: 0.43 SNIP: 0.762 CiteScore™: 2.3

ISSN Print: 1091-028X
ISSN Online: 1934-0508

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Journal of Porous Media

DOI: 10.1615/JPorMedia.v17.i8.70
pages 731-740

RESISTANCE TO CREEPING FLOW AND PERMEABILITY OF STACKED SPHERES

Ryszard Blazejewski
Dept. of Hydraulic and Sanitary Engineering, University of Life Sciences, Piatkowska St. 94a, 60-649 Poznan, Poland
S. Murat-Blazejewska
Dept. of Land Reclamation and Env. Eng., University of Life Sciences, Piatkowska St. 94a, 60-649 Poznan, Poland

ABSTRACT

Six regularly packed beds (simple cubic, orthorhombic I and II, tetragonal sphenoidal, and rhombohedral I and II), treated as unit cells made of monosized spheres, were analyzed. A formula to calculate permeability of such beds at creeping flow conditions was proposed. It is based on similar assumptions as the Kozeny−Carman equation, but instead of mean porosity and tortuosity, their local values were taken into account. Two different values of the pore shape factors, regarding triangular and square pores, according to Boussinesq, were applied. The new formula, in its integral form, agrees better with experiments than those given by Slichter, Kozeny and Carman, Martin et al. as well as Franzen; it underestimates the analyzed packings' permeabilities by less than 22%, on average by 13%.


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