This study discusses wave propagation in perhaps the most general model of a poroelastic medium. The medium is considered as a viscoelastic, anisotropic and porous solid frame such that its pores of anisotropic permea...This study discusses wave propagation in perhaps the most general model of a poroelastic medium. The medium is considered as a viscoelastic, anisotropic and porous solid frame such that its pores of anisotropic permeability are filled with a viscous fluid. The anisotropy considered is of general type, and the attenuating waves in the medium are treated as the inhomogeneous waves. The complex slowness vector is resolved to define the phase velocity, homogeneous attenuation, inhomogeneous attenuation, and angle of attenuation for each of the four attenuating waves in the medium. A non-dimensional parameter measures the deviation of an inhomogeneous wave from its homogeneous version. An numerical model of a North-Sea sandstone is used to analyze the effects of the propagation direction, inhomogeneity parameter, frequency regime, anisotropy symmetry, anelasticity of the frame, and viscosity of the pore-fluid on the propagation characteristics of waves in such a medium.展开更多
Boundary conditions are derived to represent the continuity requirements at the boundaries of a porous solid saturated with viscous fluid. They are derived from the physically grounded principles with a mathematical c...Boundary conditions are derived to represent the continuity requirements at the boundaries of a porous solid saturated with viscous fluid. They are derived from the physically grounded principles with a mathematical check on the conservation of energy. The poroelastic solid is a dissipative one for the presence of viscosity in the interstitial fluid. The dissipative stresses due to the viscosity of pore-fluid are well represented in the boundary conditions. The unequal particle motions of two constituents of porous aggre~ gate at a boundary between two solids are explained in terms of the drainage of pore-fluid leading to imperfect bonding. A mathematical model is derived for the partial connec- tion of surface pores at the porous-porous interface. At this interface, the loose-contact slipping and partial pore opening/connection may dissipate a part of strain energy. A numerical example shows that, at the interface between water and oil-saturated sandstone, the modified boundary conditions do affect the energies of the waves refracting into the isotropic porous medium.展开更多
文摘This study discusses wave propagation in perhaps the most general model of a poroelastic medium. The medium is considered as a viscoelastic, anisotropic and porous solid frame such that its pores of anisotropic permeability are filled with a viscous fluid. The anisotropy considered is of general type, and the attenuating waves in the medium are treated as the inhomogeneous waves. The complex slowness vector is resolved to define the phase velocity, homogeneous attenuation, inhomogeneous attenuation, and angle of attenuation for each of the four attenuating waves in the medium. A non-dimensional parameter measures the deviation of an inhomogeneous wave from its homogeneous version. An numerical model of a North-Sea sandstone is used to analyze the effects of the propagation direction, inhomogeneity parameter, frequency regime, anisotropy symmetry, anelasticity of the frame, and viscosity of the pore-fluid on the propagation characteristics of waves in such a medium.
文摘Boundary conditions are derived to represent the continuity requirements at the boundaries of a porous solid saturated with viscous fluid. They are derived from the physically grounded principles with a mathematical check on the conservation of energy. The poroelastic solid is a dissipative one for the presence of viscosity in the interstitial fluid. The dissipative stresses due to the viscosity of pore-fluid are well represented in the boundary conditions. The unequal particle motions of two constituents of porous aggre~ gate at a boundary between two solids are explained in terms of the drainage of pore-fluid leading to imperfect bonding. A mathematical model is derived for the partial connec- tion of surface pores at the porous-porous interface. At this interface, the loose-contact slipping and partial pore opening/connection may dissipate a part of strain energy. A numerical example shows that, at the interface between water and oil-saturated sandstone, the modified boundary conditions do affect the energies of the waves refracting into the isotropic porous medium.
