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  • A linear dynamic model for a saturated porous medium

    Author(s)
    Lu, Jian-Fei
    Hanyga, Andrzej
    Jeng, Dong-sheng
    Griffith University Author(s)
    Jeng, Dong-Sheng
    Year published
    2007
    Metadata
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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. ...
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    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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    Journal Title
    Transport in Porous Media
    Volume
    68
    DOI
    https://doi.org/10.1007/s11242-006-9051-x
    Subject
    Civil Geotechnical Engineering
    Applied Mathematics
    Chemical Engineering
    Civil Engineering
    Publication URI
    http://hdl.handle.net/10072/63984
    Collection
    • Journal articles

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