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Differential effective medium modeling of rock elastic moduli with critical porosity constraints
Author(s) -
Mukerji Tapan,
Berryman Jim,
Mavko Gary,
Berge Patricia
Publication year - 1995
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 - 10.1029/95gl00164
Subject(s) - porosity , percolation threshold , percolation (cognitive psychology) , percolation theory , moduli , geotechnical engineering , porous medium , geology , elastic modulus , materials science , mechanics , physics , composite material , electrical resistivity and conductivity , conductivity , quantum mechanics , neuroscience , biology
Rocks generally have a percolation porosity at which they lose rigidity and fall apart. Percolation behavior is a purely geometrical property, independent of any physical properties, and is a powerful constraint on any valid velocity‐porosity relation. We show how the conventional Differential Effective Medium (DEM) theory can be modified to incorporate percolation of elastic moduli in rocks by taking the material at the critical porosity as one of the constituents of a two‐phase composite. Any desired percolation porosity can be specified as an input. In contrast, the conventional DEM model always predicts percolation at a porosity of either 0 or 100 percent. Most sedimentary rocks however have intermediate percolation porosities and are therefore not well represented by the conventional theory. The modified DEM model incorporates percolation behavior, and at the same time is always consistent with the Hashin‐Shtrikman bounds. The predictions compare favorably with laboratory sandstone data.