Frequency-domain simulation of logging-while-drilling borehole sonic waveforms

SummaryIn goal-oriented adaptivity, the error in the quantity of interest is represented using the error functions of the direct and adjoint problems. This error representation is subsequently bounded above by element-wise error indicators that are used to drive optimal refinements. In this work, we propose to replace, in the error representation, the adjoint problem by an alternative operator. The main advantage of the proposed approach is that, when judiciously selecting such alternative operator, the corresponding upper bound of the error representation becomes sharper, leading to a more efficient goal-oriented adaptivity.While the method can be applied to a variety of problems, we focus here on two-and three-dimensional (2-D and 3-D) Helmholtz problems. We show via extensive numerical experimentation that the upper bounds provided by the alternative error representations are sharper than the classical ones and lead to a more robust p-adaptive process. We also provide guidelines for finding operators delivering sharp error representation upper bounds. We further extend the results to a convection-dominated diffusion problem as well as to problems with discontinuous material coefficients. Finally, we consider a sonic logging-while-drilling problem to illustrate the applicability of the proposed method.

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“…[63][64][65] To simplify the implementation, we focus only on a purely acoustic media (without elasticity).…”

Section: Appendix C: Geophysical Borehole Application: Frequency Domamentioning

confidence: 99%

“…In this appendix, we apply our adaptive strategy to the simulation of sonic LWD measurements, as described in Pardo et al, Matuszyk et al, and Matuszyk and Torres-Verdín. [63][64][65] To simplify the implementation, we focus only on a purely acoustic media (without elasticity).…”

Section: Appendix C: Geophysical Borehole Application: Frequency Domamentioning

confidence: 99%

Goal‐oriented adaptivity using unconventional error representations for the multidimensional Helmholtz equation

Darrigrand

Rodríguez-Rozas

Muga

et al. 2017

Numerical Meth Engineering

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“…Pardo et al [18,19] obtained the waveforms and the dispersion curves of the propagating modes in wireline and logging-while-drilling techniques with an eccentred tool. Matuszyk, Torres-Verdín and Pardo [20] and Matuszyk and Torres-Verdín [21] numerically studied different and complex geometric conĄgurations in logging-while-drilling and wireline situations: the presence of the tool (with and without grooves), fractures, and layering. They explored the axial symmetry of the system and implemented a 2D model in which formation nonuniformities in the radial and axial directions are easily tailored.…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…Therefore, we solve equation 2.1.17 in the 2D plane and a full rotation around the axis of symmetry is performed afterwards. This approach has been successfully employed by Matuszyk et al [20,21] in sonic logging simulations using FEM. The general solution for the solid displacement and Ćuid acoustic pressure associated to the other guided modes could be obtained using the following transformation…”

Section: Time Domain Analysismentioning

confidence: 99%

Computational analysis of dispersive acoustic waves in fluid-filled boreholes

Canhassi¹

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Agradeço aos meus pais e irmãos por todo apoio e compreensão ao longo da gradução e do mestrado.A TODOS os meus amigos que contribuiram de forma direta ou indireta para conclusão deste trabalho. Também ao pessoal do GPO e do GFNMN pelos cafés e conversas jogadas fora.Ao Prof. Dr. Pablo Diniz Batista e ao Prof. Dr. Tobias Heimfarth pelos códigos cedidos e pelas frutíferas discussões ao longo do projeto.

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