Non-linear Evolution of P-waves in Viscous–Elastic Granular Saturated Media

Abstract

The Frenkel-Biot P-wave of the first type is a seismic longitudinal wave observed in rocks fully saturated with oil, water or high-pressure gas. The P-wave of the second type is observed in unsaturated soils and other porous media saturated with gas of low pressure. Their models include properties of the skeleton, that is, its elastic modules and its own viscosity. If the non-linear terms are accounted for, the asymptotic analysis, usual for weak non-linear waves, might be applied to get the wave spectrum evolution. The wetness of grains contacts in soils and such components of oil as tars or bitumen, which attached to the skeleton, can be described by generalized viscous-elastic stress-strain connections. The latter are nominated in such a way that creates the narrow frequency interval of wave of negative dissipation where the non-linear terms begin to play the main role besides the neutral stability for waves of zero wave number. The corresponding case, relevant to single continuum model, was analyzed in the literature. Here it is shown that the interpenetrating continua with interaction of the Darcy type provide the dissipation sink in the wave evolution equation. This generalization, (Tribelsky, M.I.: Phys. Rev. Lett. (2007, submitted)), can stabilize the asymptotic solution of the evolution equation, where the dispersion terms are omitted. The asymptotic solution of the equation is invariant to initial conditions and it means a transformation of initial wave spectra to unique one while wave is spreading in the viscous-elastic medium under consideration. This explains the phenomenon, observed in wave tests at marine beach, when any dynamics action (impact, explosion, and ultrasound action) created at some distance a wave of a single frequency (∼25 Hz).

Recent Advance and Prospect of Enhanced Oil Recovery Mechanisms in Reservoir Sandstone

“…The relative permeability curve is critical to reservoir oil production because it reveals the oil saturation threshold Sor below which the oil is immobile. Nikolaevsky [136] determined that seismic waves can raise the relative permeability of the oil phase, hence increasing the oil phase's movement ability lower than Sor. By altering the flow direction of the oil or water phase regularly, Vibro-energy can produce quasi-or periodic motions.…”

The Effect of Rheology with Gas Bubbles on Linear Elastic Waves in Fluid-Saturated Granular Media

“…Following the approach of Nikolaevskiy [10], we consider the P1-wave in porous media under full saturation. Accordingly, we assume that the mass velocities v and u have the same sign…”

“…Note that here we keep (as Nikolaevskiy did in [10]) higher powers of ε to represent small corrections to the leading terms. These corrections will eventually translate into small corrections in the Nikolaevskiy equation derived further in this paper; they will be the object of our study.…”

“…Experimental evidence indicated that the existence of gas bubbles in the saturated porous medium changes the characteristics of this medium [11]- [13], acoustic properties and the velocity of the wave. As Nikolaevskiy pointed out [10], in rocks saturated with fluids, the P1-wave is the only observable wave. However, the presence of gas, even in small proportion can affect the wave type [14], so that P2-wave may be visible.…”

“…(1.1) account for the effects of non-linearity, dissipation and dispersion. Based on [9] Nikolaevskiy extended [10] the evolution Eq. (1.1) to include the global dissipation…”