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Properties of low‐frequency trapped mode in viscous‐fluid waveguides
Author(s) -
Nikitin Anatoly A.,
Plyushchenkov Boris D.,
Segal Arkady Yu.
Publication year - 2016
Publication title -
geophysical prospecting
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.735
H-Index - 79
eISSN - 1365-2478
pISSN - 0016-8025
DOI - 10.1111/1365-2478.12306
Subject(s) - attenuation , biot number , poromechanics , dispersion relation , mechanics , newtonian fluid , elasticity (physics) , viscosity , physics , viscous liquid , wavenumber , porous medium , optics , porosity , geology , thermodynamics , geotechnical engineering
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 10 3 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.