Simulation of wireline sonic logging measurements acquired with Borehole-Eccentered tools using a high-order adaptive finite-element method

Authors:
David Pardo;Pawel Matuszyk;Ignacio Muga;Carlos Torres-Verdín;Angel Mora;Victor M. Calo
Affiliations:
Department of Applied Mathematics, Statistics and Operational Research, University of the Basque Country (UPV/EHU) and IKERBASQUE (Basque Foundation for Sciences), Bilbao, Spain;Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin TX, USA;Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin TX, USA and Pontificia Universidad Católica de Valparaíso, Chile;Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin TX, USA;King Abdullah University of Science and Technology (KAUST), Saudi Arabia;King Abdullah University of Science and Technology (KAUST), Saudi Arabia
Venue:
Journal of Computational Physics
Year:
2011

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Abstract

The paper introduces a high-order, adaptive finite-element method for simulation of sonic measurements acquired with borehole-eccentered logging instruments. The resulting frequency-domain based algorithm combines a Fourier series expansion in one spatial dimension with a two-dimensional high-order adaptive finite-element method (FEM), and incorporates a perfectly matched layer (PML) for truncation of the computational domain. The simulation method was verified for various model problems, including a comparison to a semi-analytical solution developed specifically for this purpose. Numerical results indicate that for a wireline sonic tool operating in a fast formation, the main propagation modes are insensitive to the distance from the center of the tool to the center of the borehole (eccentricity distance). However, new flexural modes arise with an increase in eccentricity distance. In soft formations, we identify a new dipole tool mode which arises as a result of tool eccentricity.