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Finite element simulations of logging-while-drilling and extra-deep azimuthal resistivity measurements using non-fitting grids

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Abstract

We propose a discretization technique using non-fitting grids to simulate magnetic field-based resistivity logging measurements. Non-fitting grids are convenient because they are simpler to generate and handle than fitting grids when the geometry is complex. On the other side, fitting grids have been historically preferred because they offer additional accuracy for a fixed problem size in the general case. In this work, we analyse the use of non-fitting grids to simulate the response of logging instruments that are based on magnetic field resistivity measurements using 2.5D Maxwell’s equations. We provide various examples demonstrating that, for these applications, if the finite element matrix coefficients are properly integrated, the accuracy loss due to the use of non-fitting grids is negligible compared to the case where fitting grids are employed.

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Funding

The authors have received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 644602, the Projects of the Spanish Ministry of Economy and Competitiveness with reference MTM2016-76329-R (AEI/FEDER, EU), and MTM2016-81697-ERC/AEI, the BCAM “Severo Ochoa” accreditation of excellence SEV-2013-0323, and the Basque Government through the BERC 2014-2017 programme, and the Consolidated Research Group Grant IT649-13 on “Mathematical Modeling, Simulation, and Industrial Applications (M2SI)”.

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Authors and Affiliations

  1. Basque Center for Applied Mathematics, Bilbao, Spain

    T. Chaumont-Frelet, D. Pardo & Á. Rodríguez-Rozas

  2. University of the Basque Country (UPV/EHU), Leioa, Spain

    D. Pardo

  3. Ikerbasque, Bilbao, Spain

    D. Pardo

Authors
  1. T. Chaumont-Frelet
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  2. D. Pardo
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  3. Á. Rodríguez-Rozas
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Correspondence to T. Chaumont-Frelet.

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Chaumont-Frelet, T., Pardo, D. & Rodríguez-Rozas, Á. Finite element simulations of logging-while-drilling and extra-deep azimuthal resistivity measurements using non-fitting grids. Comput Geosci 22, 1161–1174 (2018). https://doi.org/10.1007/s10596-018-9744-6

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  • DOI: https://doi.org/10.1007/s10596-018-9744-6

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