### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 4pEA13. Coupling finite element and impedance element to model the
radiation of piezoelectric transducers in boreholes.

**Didace Ekeom
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**
Bertrand Dubus
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**
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*Inst. d'Electron. et de Microelectron. du Nord, UMR CNRS 9929, Dept. ISEN,
41 boulevard Vauban, 59046 Lille Cedex, France
*

*
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In the context of petroleum acoustics, it is of great interest to modelize
the radiation of the piezoelectric transducer in a borehole surrounded by an
homogeneous isotropic elastic formation of infinite extent without restrictive
assumptions on the geometry, radiation pattern, or types of waves. The finite
element method is well suited to solve such problems if the troncature of the
infinite formation is correctly treated. This troncature generates ingoing
waves which normally do not exist in infinite domain. In this paper, classical
finite elements (atila code) are used to model in steady state the transducer,
the fluid-filled borehole, and part of the formation inside a spherical
boundary. On this exterior boundary, impedance elements are used to take into
account the infinite character of the formation. These elements are obtained by
discretizing the mechanical impedance of outgoing spherical P and S waves. The
method is validated by studying two configurations having analytical solutions:
the pulsating sphere and the oscillating point. Results include displacement
fields and radiation patterns for P or/and S waves. Finally, the radiation of a
cylindrical piezoelectric transducer in an oil-filled borehole [S. Kostek et
al., J. Acoust. Soc. Am. 95, 109 (1994)] is analyzed. P and S components of the
displacement field, electrical admittance of the transducer, directivity
patterns, and distribution of radiated energy are displayed.