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. To account for viscoelastic properties of heavy oils we have proposed an approximate fluid substitution scheme based on self-consistent method mixing method known as Coherent Potential Approximation (CPA). This approach is consistent with the concepts of percolation and critical porosity, and allows one to model both sandstones and unconsolidated sand. To test the approach against the known solutions, first, we apply CPA to a rock with fluid pore fill and compare the obtained estimates with Gassmann results. Second, we compare CPA predictions for solid-solid mixtures with numerical simulations. Good match between the results confirms the usefulness of the proposed fluid substitution scheme. We extend the CPA scheme to predict the effective frequency- and temperature-dependent properties of heavy oil rock. We also use viscoelastic extension of Hashin-Shtrikman (H-S) bounds to obtain alternative estimates. The proposed fluid substitution scheme provides realistic estimates of the properties of a rock saturated with heavy oil which lie between H-S bounds.


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