Heavy oils are defined as having high densities and extremely high viscosities. Due to their viscoelastic behaviour the traditional rock physics based on Gassmann theory becomes inapplicable. In this paper, we use effective-medium approach known as coherent potential approximation (CPA) as an alternative fluid substitution scheme for rocks saturated with viscoelastic fluids. Such rocks are modelled as solids with elliptical fluid inclusions when fluid concentration is small and as suspensions of solid particles in fluid when solid concentration is small. This approach is consistent with concepts of percolation and critical porosity, and allows one to model sandstones and unconsolidated sands. We test the approach against known solutions. First, we apply CPA to fluid-solid mixtures and compare obtained estimates with Gassmann results. Second, we compare CPA predictions for solid-solid mixtures with numerical simulations. Good match between the results confirms the applicability of the CPA scheme. We extend the scheme to predict effective frequency- and temperature-dependent properties of heavy oil rocks. CPA scheme reproduces frequency-dependent attenuation and dispersion which are qualitatively consistent with laboratory measurements and numerical simulations. This confirms that the proposed scheme provides realistic estimates of the properties of rocks saturated with heavy oil.


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