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GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L09306, doi:10.1029/2007GL033074, 2008

Velocity-saturation relation for partially saturated rocks with fractal pore fluid distribution

T. M. Müller

Geophysikalisches Institut, Universität Karlsruhe (TH), Karlsruhe, Germany


J. Toms-Stewart

ExxonMobil Upstream Research Company, Houston, Texas, USA


F. Wenzlau

Geophysikalisches Institut, Universität Karlsruhe (TH), Karlsruhe, Germany


Abstract

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.

Received 21 December 2007; accepted 3 April 2008; published 10 May 2008.

Keywords: wave attenuation; partial saturation; fractals.

Index Terms: 5144 Physical Properties of Rocks: Wave attenuation; 5102 Physical Properties of Rocks: Acoustic properties; 5114 Physical Properties of Rocks: Permeability and porosity; 3285 Mathematical Geophysics: Wave propagation (0689, 2487, 4275, 4455, 6934); 5139 Physical Properties of Rocks: Transport properties.

Subscriber Access to Full Article (Nonsubscribers may purchase for $9.00, Includes print PDF, file size: 274071 bytes)

Citation: Müller, T. M., J. Toms-Stewart, and F. Wenzlau (2008), Velocity-saturation relation for partially saturated rocks with fractal pore fluid distribution, Geophys. Res. Lett., 35, L09306, doi:10.1029/2007GL033074.