Schlumberger

Technical Paper: Theoretical Estimate of Tube-Wave Modulus in Arbitrarily Anisotropic Media: Comparisons Between Semi-Analytical, FEM, and Approximate Solutions

Society: SEG
Paper Number: 2012-392
Presentation Date: 2012
 

Abstract

We revisit an exact, quasi-static, semi-analytical solution for the effective tube-wave modulus for any borehole orientation relative to an anisotropic medium of arbitrary symmetry and strength. Next, we show that this exact solution agrees very well with the one computed from a finite element model (FEM). Then, we compare the exact solution with several analytical approximations (Norris and Sinha, 1993; Rice, 1987; Chi and Tang, 2003) for well deviations from vertical to horizontal and for different transversely isotropic media. For elliptic media, we show that the Rice and Chi-Tang approximations are in accordance with the exact solution as they depend only on the horizontal and vertical shear wave velocity. For anelliptic media, we show that the maximum difference between the exact solution and the Norris-Sinha perturbation approximation becomes increasingly significant with increasing degree of anellipticity and shear wave anisotropy with a maximum error of 5 %, 10 % and 18 % for Thomsen parameters less than 0.25, 0.4 and 0.6 respectively.

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