Properties of low-frequency trapped mode in viscous-fluid waveguidesстатья
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Дата последнего поиска статьи во внешних источниках: 26 декабря 2018 г.
Аннотация:Phase velocity and attenuation of a generalized Stoneley wave being a symmetric trapped mode of a layer filled with a Newtonian fluid and embedded into either poroelastic or a purely elastic rock are derived. Dispersion relation corresponding to linearized Navier-Stokes equation in a fracture
coupling to either Biot or elasticity equations in the rock via proper boundary conditions is rigorously derived. A cubic equation for wavenumber is found that provides a rather precise analytical approximation of the full dispersion relation, in the frequency range of 10−3−103 Hz and for layer width of less than 10 cm and fluid viscosity below 1 P. Comparison to earlier results addressing viscous fluid in either porous rock with rigid matrix or in a purely elastic rock is made, and our formulae are found to better match the numerical solution, especially regarding attenuation. The computed attenuation is used to demonstrate detectability of fracture tip reflections at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid viscosities.