3-D wave propagation in fluid-filled irregular boreholes in elastic formations

Abstract

Different seismic testing techniques rely on the propagation of acoustic waves in¯uid-®lled boreholes from sources placed within the borehole and in the solid media. The interpretation of the signals recorded relies on understanding how waves propagate in the borehole and its immediate vicinity. It is known that very complex wave patterns can arise, depending on the distance between the source and the receiver, and their placement and orientation relative to the axis of a circular borehole. The problem becomes more complex if the cross-section is not circular, conditions for which analytical solutions are not known. In this work, the Boundary Element Method (BEM) is used to evaluate the three-dimensional wave ®eld elicited by monopole sources in the vicinity of a¯uid-®lled borehole. This model is used to assess the effects of the receiver position on the propagation of both axisymmetric and non-axisymmetric wave modes when different borehole cross-sections are used. Both frequency vs. axial-wave number responses and time-domain responses are calculated. q

Wave motion between two fluid-filled boreholes in an elastic medium

“…The time plots con®rm this phenomenon by attributing a slightly delayed arrival to the Stoneley pulses. This effect agrees with the tendency found by Randall [19] when calculating the dispersion curves for modes of noncircular¯uid-®lled boreholes for low frequencies, and later con®rmed by the authors Tadeu et al [39] in the calculation of time series for oval¯uid-®lled boreholes. In addition, as we move from the circular to the oval, our results indicate that the amplitude of the Stoneley pulses increases.…”

“…The effect of the irregular boreholes on the response has also been studied by Randall [38] and Tadeu et al [39]. These effects result from the mechanical action of the drill string in vertically deviated wells, rock failure adjacent to a drilled borehole, plastic deformation and washing out of the borehole in soft or poorly consolidated rocks, as reported by Bell et al [40] and by Zheng et al [41].…”

Assessing the effect of a barrier between two rooms subjected to low frequency sound using the boundary element method

“…The BEM has been used to simulate wave propagation between two fluid-filled boreholes, where the source and receivers are placed in different boreholes [30]. The technique thus reproduced is cross-hole surveying, a seismic prospecting technique that is often used to find the properties of an elastic medium separating two boreholes.…”

“…Randall [33] and Tadeu et al [30] simulated irregularities that might be caused by the mechanical action of the drill string in vertically inclined wells, or by rock collapse next to a borehole, plastic deformation, or washing a borehole drilled in soft or crumbling rocks, Bell et al [34] and Zheng et al [35].…”

3D seismic response of a limited valley via BEM using 2.5D analytical Green's functions for an infinite free-rigid layer

“…Santos et al [36] computed the 3D scattering field obtained when a 2D smooth topographical deformation is subjected to a dilatational point load placed at some point in the medium, using the BEM to discretize the free surface. Tadeu and Santos [37] used the BEM to evaluate the 3D wave field elicited by monopole sources in the vicinity of a fluid-filled borehole. Pei and Papageorgiou [38] simulated the propagation of surface waves in the Santa Clara valley, CA using a hybrid numerical technique, which combines the boundary integral equation method with the finite element method.…”