Properties of low-frequency trapped mode in viscous-fluid waveguides
2016
We derived the 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 a poroelastic or a purely elastic rock. The dispersion relation corresponding to
a linearized Navier–Stokes equation in a fracture coupling to either Biot or elasticity
equations in the rock via proper boundary conditions was rigorously derived. A
cubic equation for wavenumber was found that provides a rather precise analytical
approximation of the full dispersion relation, in the frequency range of 10−3 Hz to
103 Hz and for layer width of less than 10 cm and fluid viscosity below 0.1 Pa·s
[100 cP]. We compared our results to earlier results addressing viscous fluid in either
porous rocks with a rigid matrix or in a purely elastic rock, and our formulae are
found to better match the numerical solution, especially regarding attenuation. The
computed attenuation was used to demonstrate detectability of fracture tip reflections
at wellbore, for a range of fracture lengths and apertures, pulse frequencies, and fluid
viscosity.
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