Dynamic poroelasticity: A unified model with the squirt and the Biot mechanisms

Abstract

The velocities and attenuation of seismic and acoustic waves in rocks with fluids are affected by the two most important modes of fluid/solid interaction: (1) the Biot mechanism where the fluid is forced to participate in the solid’s motion by viscous friction and inertial coupling, and (2) the squirt‐flow mechanism where the fluid is squeezed out of thin pores deformed by a passing wave. Traditionally, both modes have been modeled separately, with the Biot mechanism treated in a macroscopic framework, and the squirt flow examined at the individual pore level. We offer a model which treats both mechanisms as coupled processes and relates P‐velocity and attenuation to macroscopic parameters: the Biot poroelastic constants, porosity, permeability, fluid compressibility and viscosity, and a newly introduced microscale parameter—a characteristic squirt‐flow length. The latter is referred to as a fundamental rock property that can be determined experimentally. We show that the squirt‐flow mechanism dominates the Biot mechanism and is responsible for measured large velocity dispersion and attenuation values. The model directly relates P‐velocity and attenuation to measurable rock and fluid properties. Therefore, it allows one to realistically interpret velocity dispersion and/or attenuation in terms of fluid properties changes [e.g., viscosity during thermal enhanced oil recovery (EOR)], or to link seismic measurements to reservoir properties. As an example of the latter transformation, we relate permeability to attenuation and achieve good qualitative correlation with experimental data.