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Velocity‐saturation relation for partially saturated rocks with fractal pore fluid distribution
Author(s) -
Müller T. M.,
TomsStewart J.,
Wenzlau F.
Publication year - 2008
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 - 10.1029/2007gl033074
Subject(s) - saturation (graph theory) , fractal , mesoscopic physics , fractal dimension , attenuation , porosity , geology , mineralogy , porous medium , fluid dynamics , materials science , mechanics , geotechnical engineering , physics , optics , mathematics , condensed matter physics , mathematical analysis , combinatorics
Reservoir rocks saturated with two immiscible fluids may exhibit considerable wave attenuation and dispersion due to wave‐induced fluid flow. Attenuation‐ and velocity‐saturation relations of P ‐waves are developed for partially saturated porous media in which the fluid patches form random fractals on the mesoscopic scale. Depending on the fractal dimension of the pore fluid distribution the velocity‐saturation relation can vary between the exact Gassmann‐Wood and Gassmann‐Hill bounds. The results indicate that the fractal dimension is an additional measure that should be accounted for to consistently model effective acoustic properties of partially saturated rocks.