Analytical decoupling of poroelasticity equations for acoustic-wave propagation and attenuation in a porous medium containing two immiscible fluids |
| |
Authors: | Wei-Cheng Lo Garrison Sposito Ernest Majer |
| |
Affiliation: | (1) Department of Hydraulic and Ocean Engineering, National Cheng Kung University, Tainan, 701, Taiwan, ROC;(2) Department of Civil and Environmental Engineering, University of California, Berkeley, CA 94720-1710, USA;(3) Department of Geophysics, Earth Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA |
| |
Abstract: | Poroelasticity theory has become an effective and accurate approach to analyzing the intricate mechanical behavior of a porous
medium containing two immiscible fluids, a system encountered in many subsurface engineering applications. However, the resulting
partial differential equations in the theory intrinsically take on a coupled form in the terms pertinent to inertial drag,
viscous damping, and applied stress, making it difficult to obtain closed-form, steady-state analytical solutions to boundary-value
problems except in special cases. In the present paper, we demonstrate that, for dilatational wave excitations, these partial
differential equations can be decoupled analytically into three Helmholtz equations featuring complex-valued, frequency-dependent
normal coordinates that correspond physically to three independent modes of dilatational wave motion. The normal coordinates
in turn can be expressed in the frequency domain as three different linear combinations of the solid dilatation and the linearized
increment of fluid content for each pore fluid, or equivalently, as three different linear combinations of total dilatational
stress and two pore fluid pressures. These representations are applicable to strain-controlled and stress-prescribed boundary
conditions, respectively. Numerical calculations confirm that the phase speed and attenuation coefficient of the three dilatational
waves represented by the Helmholtz equations are exactly identical to those obtained previously by numerical solution of the
dispersion relations for dilatational wave excitation of a porous medium containing two immiscible fluids. Thus, dilatational
wave motions in unsaturated porous media subject to suitable boundary conditions can now be accurately modeled analytically. |
| |
Keywords: | Decoupling Dilatational wave motions Poroelasticity |
本文献已被 SpringerLink 等数据库收录! |
|