A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements
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 me...
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| Format: | Article |
| Language: | English |
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MDPI AG
2018-06-01
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| Series: | Geosciences |
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| Online Access: | http://www.mdpi.com/2076-3263/8/6/225 |
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| author | Mostafa Shahriari Sergio Rojas David Pardo Angel Rodríguez-Rozas Shaaban A. Bakr Victor M. Calo Ignacio Muga |
| author_facet | Mostafa Shahriari Sergio Rojas David Pardo Angel Rodríguez-Rozas Shaaban A. Bakr Victor M. Calo Ignacio Muga |
| author_sort | Mostafa Shahriari |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-12T21:30:11Z |
| format | Article |
| id | doaj.art-7df173d5843d47d4bed5380ffa3a3ca1 |
| institution | Directory Open Access Journal |
| issn | 2076-3263 |
| language | English |
| last_indexed | 2024-04-12T21:30:11Z |
| publishDate | 2018-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Geosciences |
| spelling | doaj.art-7df173d5843d47d4bed5380ffa3a3ca12022-12-22T03:16:03ZengMDPI AGGeosciences2076-32632018-06-018622510.3390/geosciences8060225geosciences8060225A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity MeasurementsMostafa Shahriari0Sergio Rojas1David Pardo2Angel Rodríguez-Rozas3Shaaban A. Bakr4Victor M. Calo5Ignacio Muga6Basque Center for Applied Mathematics (BCAM), Mazarredo 14, E48009 Bilbao, SpainApplied Geology, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, WA 6845, AustraliaBasque Center for Applied Mathematics (BCAM), Mazarredo 14, E48009 Bilbao, SpainBasque Center for Applied Mathematics (BCAM), Mazarredo 14, E48009 Bilbao, SpainBasque Center for Applied Mathematics (BCAM), Mazarredo 14, E48009 Bilbao, SpainApplied Geology, Western Australian School of Mines, Faculty of Science and Engineering, Curtin University, Perth, WA 6845, AustraliaInstituto de Matemáticas, Pontificia Universidad Católica de Chile, Valparaíso 2350026, ChileIn 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.http://www.mdpi.com/2076-3263/8/6/225logging-while-drilling (LWD)resistivity measurementsfinite element methodHankel transformmulti-scale methodsecondary field |
| spellingShingle | Mostafa Shahriari Sergio Rojas David Pardo Angel Rodríguez-Rozas Shaaban A. Bakr Victor M. Calo Ignacio Muga A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements Geosciences logging-while-drilling (LWD) resistivity measurements finite element method Hankel transform multi-scale method secondary field |
| title | A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements |
| title_full | A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements |
| title_fullStr | A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements |
| title_full_unstemmed | A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements |
| title_short | A Numerical 1.5D Method for the Rapid Simulation of Geophysical Resistivity Measurements |
| title_sort | numerical 1 5d method for the rapid simulation of geophysical resistivity measurements |
| topic | logging-while-drilling (LWD) resistivity measurements finite element method Hankel transform multi-scale method secondary field |
| url | http://www.mdpi.com/2076-3263/8/6/225 |
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