A numerical extension of White's theory of P-wave attenuation to non-isothermal poroelastic media.

Mesoscopic P-wave attenuation in layered, partially saturated thermo-poroelastic media is analyzed by combining the theories of Biot poroelasticity and Lord-Shulman thermoelasticity (BLS). The attenuation is quantified by estimating the quality factor Q. The mesoscopic attenuation effect, commonly referred to as wave-induced fluid flow (WIFF), is the process that converts fast compressional and shear waves into slow diffusive Biot waves at mesoscopic heterogeneities larger than the pore scale, but much smaller than the dominant wavelengths. This effect was first modeled in White's isothermal theory by quantifying the seismic response of a periodic sequence of planar porous layers that are alternately saturated with gas or water. This work presents a numerical extension of White's theory for the non-isothermal case in this type of sequence. For this purpose, an initial-boundary-value problem (IBVP) for the BLS wave propagation equations is solved using the finite element method, where the particle velocity field is recorded at uniformly distributed receivers. The quality factor is estimated using spectral-ratio and frequency-shift methods. The Q-estimates show that thermal effects influence the attenuation of the P-wave and the velocity dispersion compared to the isothermal case.

A model for wave propagation in a porous solid saturated by a three-phase fluid.

This paper presents a model to describe the propagation of waves in a poroelastic medium saturated by a three-phase viscous, compressible fluid. Two capillary relations between the three fluid phases are included in the model by introducing Lagrange multipliers in the principle of virtual complementary work. This approach generalizes that of Biot for single-phase fluids and allows to determine the strain energy density, identify the generalized strains and stresses, and derive the constitutive relations of the system. The kinetic and dissipative energy density functions are obtained assuming that the relative flow within the pore space is of laminar type and obeys Darcy's law for three-phase flow in porous media. After deriving the equations of motion, a plane wave analysis predicts the existence of four compressional waves, denoted as type I, II, III, and IV waves, and one shear wave. Numerical examples showing the behavior of all waves as function of saturation and frequency are presented.

A parametric analysis of waves propagating in a porous solid saturated by a three-phase fluid.

This paper presents an analysis of a model for the propagation of waves in a poroelastic solid saturated by a three-phase viscous, compressible fluid. The constitutive relations and the equations of motion are stated first. Then a plane wave analysis determines the phase velocities and attenuation coefficients of the four compressional waves and one shear wave that propagate in this type of medium. A procedure to compute the elastic constants in the constitutive relations is defined next. Assuming the knowledge of the shear modulus of the dry matrix, the other elastic constants in the stress-strain relations are determined by employing ideal gedanken experiments generalizing those of Biot's theory for single-phase fluids. These experiments yield expressions for the elastic constants in terms of the properties of the individual solid and fluids phases. Finally the phase velocities and attenuation coefficients of all waves are computed for a sample of Berea sandstone saturated by oil, gas, and water.