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Geosciences 2018, 8(6), 225; https://doi.org/10.3390/geosciences8060225

A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements

1
Basque Center for Applied Mathematics (BCAM), Mazarredo 14, E48009 Bilbao, Spain
2
Applied Geology, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, WA 6845, Australia
3
University of the Basque Country (UPV/EHU), Barrio Sarriena, s/n, 48940 Lejona, Spain
4
Ikerbasque (Basque Foundation for Sciences), Maria Diaz de Haro 3, 6 solairua, 48013 Bilbao, Spain
5
Department of Mathematics, Assiut University, Assiut 71515, Egypt
6
Mineral Resources, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kensington, WA 6152, Australia
7
Curtin Institute for Computation, Curtin University, Perth, WA 6845, Australia
8
Instituto de Matemáticas, Pontificia Universidad Católica de Chile, Valparaíso 2350026, Chile
*
Author to whom correspondence should be addressed.
Received: 15 May 2018 / Revised: 9 June 2018 / Accepted: 14 June 2018 / Published: 20 June 2018
(This article belongs to the Special Issue Petroleum Engineering Applications: Borehole Simulations)

Abstract

In some geological formations, borehole resistivity measurements can be simulated using a sequence of 1D models. By considering a 1D layered media, we can reduce the dimensionality of the problem from 3D to 1.5D via a Hankel transform. The resulting formulation is often solved via a semi-analytic method, mainly due to its high performance. However, semi-analytic methods have important limitations such as, for example, their inability to model piecewise linear variations on the resistivity. Herein, we develop a multi-scale finite element method (FEM) to solve the secondary field formulation. This numerical scheme overcomes the limitations of semi-analytic methods while still delivering high performance. We illustrate the performance of the method with numerical synthetic examples based on two symmetric logging-while-drilling (LWD) induction devices operating at 2 MHz and 500 KHz, respectively. View Full-Text
Keywords: logging-while-drilling (LWD); resistivity measurements; finite element method; Hankel transform; multi-scale method; secondary field logging-while-drilling (LWD); resistivity measurements; finite element method; Hankel transform; multi-scale method; secondary field
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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Shahriari, M.; Rojas, S.; Pardo, D.; Rodríguez-Rozas, A.; Bakr, S.A.; Calo, V.M.; Muga, I. A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements. Geosciences 2018, 8, 225.

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