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Open AccessArticle

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

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Basque Center for Applied Mathematics (BCAM), Mazarredo 14, E48009 Bilbao, Spain
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Applied Geology, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, WA 6845, Australia
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University of the Basque Country (UPV/EHU), Barrio Sarriena, s/n, 48940 Lejona, Spain
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Ikerbasque (Basque Foundation for Sciences), Maria Diaz de Haro 3, 6 solairua, 48013 Bilbao, Spain
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Department of Mathematics, Assiut University, Assiut 71515, Egypt
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Mineral Resources, Commonwealth Scientific and Industrial Research Organisation (CSIRO), Kensington, WA 6152, Australia
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Curtin Institute for Computation, Curtin University, Perth, WA 6845, Australia
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Instituto de Matemáticas, Pontificia Universidad Católica de Chile, Valparaíso 2350026, Chile
*
Author to whom correspondence should be addressed.
Geosciences 2018, 8(6), 225; https://doi.org/10.3390/geosciences8060225
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)
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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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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