A linear dynamic model for a saturated porous medium |
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Authors: | Jian-Fei Lu Andrzej Hanyga Dong-sheng Jeng |
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Institution: | (1) Mathematics and Physics College of Jiangsu University, Zhenjiang, Jiangsu, 212013, P.R. China;(2) Department of Earth Science, University of Bergen, Allegaten 41, N5007 Bergen, Norway;(3) School of Civil Engineering, The University of Sydney, Sydney, NSW, 2006, Australia |
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Abstract: | A linear isothermal dynamic model for a porous medium saturated by a Newtonian fluid is developed in the paper. In contrast
to the mixture theory, the assumption of phase separation is avoided by introducing a single constitutive energy function
for the porous medium. An important advantage of the proposed model is it can account for the couplings between the solid
skeleton and the pore fluid. The mass and momentum balance equations are obtained according to the generalized mixture theory.
Constitutive relations for the stress, the pore pressure are derived from the total free energy accounting for inter-phase
interaction. In order to describe the momentum interaction between the fluid and the solid, a frequency independent Biot-type
drag force model is introduced. A temporal variable porosity model with relaxation accounting for additional attenuation is
introduced for the first time. The details of parameter estimation are discussed in the paper. It is demonstrated that all
the material parameters in our model can be estimated from directly measurable phenomenological parameters. In terms of the
equations of motion in the frequency domain, the wave velocities and the attenuations for the two P waves and one S wave are
calculated. The influences of the porosity relaxation coefficient on the velocities and attenuation coefficients of the three
waves of the porous medium are discussed in a numerical example. |
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Keywords: | Porous media Porosity Dynamic model Attenuation Entropy inequality |
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