| Summary: | 碩士 === 國立成功大學 === 水利及海洋工程學系碩博士班 === 95 === A lot of attention has been paid for acoustic wave propagation through porous media containing muti-phase fluids on the application of poroelasticity in recent years. We considered the coupling of inertial drag and viscous drag in this discussion. To apply Lo et al. model (2005), it is explicative to the behaviors of elastic waves in an elastic porous medium permeated by two immiscible, compressible and viscous fluids. The characteristics of dilatational waves for a homogeneous porous medium analysed through linear Stress-Strain relation and a general set of coupled partial differential equations derived from continuum mechanics of mixtures to describe these phenomena. The existence of three different motive modes of dilatational wave was solved to explain by the dispersion equations in a matrix form. These wave modes were called by P1, P2 and P3 in the magnitude of wave speed order, so as to talk about them.
Nowadays, it has been known from previous issues concerning wave propagation for an two-fluid system in unconsolidated porous media that P1 mode, which results from in-phase motions of the solid framework and the two fluids, moves with a speed equal to the square root of the ratio of an effective bulk modulus to an effective density of the fluid-containing porous medium, regardless of excitation frequency. The nature of the pore-fluids saturation and excitation frequency exert different measurable influence on the attenuation of the P1 wave and the speed and attenuation of the two diffusive modes (P2 and P3). The P2 wave results from out-of-phase motions of the solid framework and the fluids. After that, the lowest velocity of three dilatational waves propagating is P3 which arise from the presence of a second fluid in the pore space. The speed and attenuation of the two diffusive modes (P2 and P3) were associated with an effective dynamic shear viscosity of the pore fluids. In three dilatational waves there are different from the others on complex physical mechanisms, which probably concealed certain of the coupling relations, such as inertial and viscous forces.
Following this research of three waves, we took material parameter for Columbia Fine Sandy Loam Saturated with either an air-water or oil-water mixtures. The behaviors of dilatation wave were examined by the relative change of fluid saturation and wave excitation frequencies (50 and 200 Hz). The numerical simulations were accessible to assess the effects of inertial coupling and viscous coupling on account of the speed and attenuation of three waves. An assessment of inertial coupling in this fixed condition controlled was closely associated with tortuosity factor as compared with Lo et al. model (2005), besides it depended on volume fraction and material density of two phases. In conclusion, inertial coupling is neglected for low range of excitation frequencies. On the other hand, the suppression of viscous coupling involve generalized relative permeabilites or mobilities due to transport equations as a result of stretching Darcy’s law. Recently transport equations developed for two-phase flow through porous media have another term that has been included to account properly for interfacial coupling between the two flowing phases. Fluids have not only different material viscosity but also different material permeability. The porous media is saturated by fluids according to a relative proportion. Therefore, viscous coupling parameters were associated with relative saturation of fluid phase and generalized relative permeabilites and material viscosities of the fluid. We use generalized relative permeabilites to correct relative permeabilites of the wetting and nonwetting fluids in the theoretical pore size distridution model of Mualem (1976) by The interfacial coupling parameter. The interfacial coupling parameter controls the amount of viscous coupling. The effect of viscous coupling was not involved in the speed of P1 wave, but took part in the attenuation of P1 wave. The result showed different effect of viscous relations was dissimilar greatly in the speed and attenuation of P2 or P3 wave. Furthermore, our numerical results demonstrated that the viscous coupling effects for immiscible phase flowing in porous media are not implicated to ignore practically.
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