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Universal scaling of the formation factor in porous media derived by combining percolation and effective medium theories
Author(s) -
Ghanbarian Behzad,
Hunt Allen G.,
Ewing Robert P.,
Skinner Thomas E.
Publication year - 2014
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 - 10.1002/2014gl060180
Subject(s) - porous medium , scaling , percolation (cognitive psychology) , statistical physics , percolation theory , physics , geology , theoretical physics , porosity , mathematics , geotechnical engineering , geometry , conductivity , quantum mechanics , psychology , neuroscience
The porosity dependence of the formation factor for geologic media is examined from the perspective of universal scaling laws from percolation and effective medium theories. Over much of the range of observed porosity, the expected percolation scaling is observed, but the values of the numerical prefactor do not conform to the simple predictions from percolation theory. Combining effective medium and percolation theories produces a numerical prefactor whose value depends on both the threshold porosity and the porosity above which the formation factor crosses from percolation to effective medium scaling. This change allows extraction of a numerical value of the prefactor, which is reasonably close to experimental values. Subsequent evaluation of the porosity dependence of the formation factor shows that difficulties in prior comparisons of theory and experiment are largely removed when percolation scaling is allowed to transition to effective medium scaling far above the percolation threshold.