Wave propagation through elastic porous media containing two immiscible fluids

Abstract

Acoustic wave phenomena in porous media containing multiphase fluids have received considerable attention in recent years because of an increasing scientific awareness of poroelastic behavior in groundwater aquifers. To improve quantitative understanding of these phenomena, a general set of coupled partial differential equations was derived to describe dilatational wave propagation through an elastic porous medium permeated by two immiscible fluids. These equations, from which previous models of dilatational wave propagation can be recovered as special cases, incorporate both inertial coupling and viscous drag in an Eulerian frame of reference. Two important poroelasticity concepts, the linearized increment of fluid content and the closure relation for porosity change, originally defined for an elastic porous medium containing a single fluid, also are generalized for a two‐fluid system. To examine the impact of relative fluid saturation and wave excitation frequency (50, 100, 150, and 200 Hz) on free dilatational wave behavior in unconsolidated porous media, numerical simulations of the three possible modes of wave motion were conducted for Columbia fine sandy loam containing either an air‐water or oil‐water mixture. The results showed that the propagating (P1) mode, which results from in‐phase motions of the solid framework and the two pore fluids, moves with a speed equal to the square root of the ratio of an effective bulk modulus to an effective density of the fluid‐containing porous medium, regardless of fluid saturation and for both fluid mixtures. The nature of the pore fluids exerts a significant influence on the attenuation of the P1 wave. In the air‐water system, attenuation was controlled by material density differences and the relative mobilities of the pore fluids, whereas in the oil‐water system an effective kinematic shear viscosity of the pore fluids was the controlling parameter. On the other hand, the speed and attenuation of the two diffusive modes (P2, resulting from out‐of‐phase motions of the solid framework and the fluids, and P3, the result of capillary pressure fluctuations) were closely associated with an effective dynamic shear viscosity of the pore fluids. The P2 and P3 waves also had the same constant value of the quality factor, and by comparison of our results with previous research on these two dilatational wave modes in sandstones, both were found to be sensitive to the state of consolidation of the porous medium.