Although properties of bulk heavy oil can be approximated by an appropriate viscoelastic model, only a few attempts to model properties of rocks saturated with heavy oil have been reported. Rock-physics models used for rocks saturated with conventional fluids are inapplicable to those saturated with heavy oil because its viscoelastic rheology invalidates the main assumptions of the Gassmann and Biot theories. We estimate viscoelastic properties of mixtures of rock and heavy oil by considering (1) a system of layers of a solid and a viscoelastic medium and (2) by computing Hashin-Shtrikman (HS) bounds for this system. These two methods give approximate bounds for the frequency- and temperature-dependent velocities and attenuation coefficients in rocks saturated with heavy oil. We also propose a method to compute a realistic estimate of these properties that lie between those bounds. This estimate is based on a self-consistent equivalent-medium approach known as coherent-potential approximation. In a more general form, this approximation can be used for approximate fluid substitution for heavy oil. This approach gives frequency-dependent velocities and attenuation values that are qualitatively consistent with experimental observations.

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