Generalization of the Biot’s Equations for Account of Fluid Shear Relaxation

Properties of heavy-oil reservoirs show rheological behavior and their correct description in porous medium is important for optimization of recovery methods. Account of viscosity relaxation is usually introduced through generalization of the Biot’s operator for dissipation function. But this approach is not completely consistent because it doesn't take into account additional degree of freedom dealt with shear motion of viscous fluid which is omitted in the variational principle being the initial basis of Biot’s theory . Based on the generalized variational principle Maximov (2006a, 2006b) the system of the generalized Biot’s equations is derived for consistent account of fluid shear relaxation. Account of shear viscosity relaxation leads to existence of a couple shear propagation modes additionally to a couple of longitudinal modes as in the Biot’s approach. At this the one shear mode is an acoustical one, while the other shear mode has diffusive behavior at low frequencies. Phase velocity and attenuation factor for the second shear mode linearly depend on frequency in the low frequency limit that is different from analogous behavior of diffusive longitudinal mode with the root frequency behavior of analogous values.