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https://hdl.handle.net/2142/72142
Description
Title
Acoustic Propagation in Poroelastic Media
Author(s)
Chapman, Andrew Michael
Issue Date
1993
Doctoral Committee Chair(s)
Higdon, J.J.L.
Department of Study
Chemical Engineering
Discipline
Chemical Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Geophysics
Physics, Fluid and Plasma
Physics, Acoustics
Abstract
The propagation of acoustic waves in porous media is of interest in a variety of areas, including oil well logging, the seepage of contaminants into ground water supplies, and the flow of fluids in packed beds. The aim of this work is to solve the equations of motion for the fluid and solid domains of a porous media, for the propagation of acoustic or small amplitude waves through the media. Porous media are modeled as periodic cubic arrays of spheres, with solid concentration ranging from dilute, through touching, to fully consolidated. Applications of the work are to determining macroscopic properties of porous media, like permeability, from in-situ measurements of wave speed and attenuation.
At a more technical level, an acoustic wave in a porous medium can be thought of as a stress disturbance. The disturbance propagates due to a balance between inertia and restoring force, where restoring force in the fluid domain is due to compressibility, and in the solid domain is due to elasticity. The linearized Navier-Stokes equations are used to describe the motion in the fluid domain of a porous medium. The linear equations of elasticity are used for the solid domain. Boundary conditions at the fluid solid interface are no slip, and the continuity of stress and strain. The equations are simplified by a two space asymptotic analysis, in which it is assumed that wavelength is orders of magnitude greater than pore size. The asymptotic analysis separates behavior at the length scale of pore size (microscopic scale), from behavior at the length scale wavelength (macroscopic scale). Macroscopic scale equations describe wave propagation, and its attributes like wave speed, phase lag, and attenuation rate. They contain four constitutive parameters which can be calculated by solving equations at the microscopic scale. Microscopic scale equations decouple. For the fluid domain, they are the equations of oscillatory incompressible Stokes flow in a rigid porous medium, and for the solid domain, the effective equations of elasticity for a drained porous medium. The equations are solved on a Cray Y-MP, using series solutions and the least squares collocation method. One of the parameters is related to dynamic permeability, and it is calculated from solutions to the fluid domain equations. The other three parameters are contained in an effective elasticity tensor, and they are calculated from solid domain solutions.
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