Laboratory measurements of rocks saturated with high-viscosity fluids (such as heavy-oil, bitumen, magma, kerogen, etc.) often exhibit considerable seismic velocity dispersion, which is usually underestimated by the Biot theory. Over the years, grain-scale dispersion mechanisms such as squirt (local-flow) and shear relaxation (nonzero shear stress in the pore fluid) have been more successful in explaining the measured dispersion. We developed a new method to quantify the combined high-frequency effects of squirt and shear dispersion on the effective moduli of rocks saturated with viscous fluids. Viscous fluid at high frequencies was idealized as an elastic solid of finite shear modulus, hydraulically locked in stiff and soft pores. This method entailed performing solid substitution in stiff pores of a dry rock frame, which itself was unrelaxed due to solid-filled soft pores. The unrelaxed frame stiffness solutions required information on the pressure dependency of the rock stiffness and porosity. This method did not have any adjustable parameters, and all required inputs can be directly measured. With various laboratory and numerical examples, we noted that accounting for combined effects of squirt and shear relaxation was necessary to explain laboratory-measured velocities of rocks saturated with fluids of high viscosity. Predictions of the new method were in good agreement with the laboratory data.

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