Premium
Kozeny‐Carman relation for a medium with tapered cracks
Author(s) -
Dvorkin Jack,
Gvirtzman Haim,
Nur Amos
Publication year - 1991
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/91gl01069
Subject(s) - permeability (electromagnetism) , porosity , materials science , geology , geometry , mechanics , composite material , mathematics , physics , chemistry , biochemistry , membrane
We examine the permeability of a medium with thin tapered cracks to a single‐phase fluid flow in the presence of immobile matter which is accumulated in the tips of cracks. The original Kozeny‐Carman relation shows an increase in permeability of such a material relative to the case when tips are free of accumulated matter. To resolve this paradox we introduce a corrected version of the Kozeny‐Carman relation for the case when the shape of a crack cross‐section can be described by a power law. This class of crack shapes includes the important cases of triangular cracks and space between two contacting circular grains. The revised relation includes the original porosity Φ and specific surface area S of the material without accumulated matter as well as the degree of filling a crack space by accumulated matter Z . The permeability is proportional to Φ 3 and S −2 , and decreases with increasing Z .