Application of Toroidal Coils to Obtain Electrical Resistivity of Core Samples: Mathematical Modeling
https://doi.org/10.18599/grs.2024.3.16
Abstract
We consider the capability of evaluating the specific electrical resistivity of a cylindrical core by means of a transmitter-receiver system with toroidal coils placed around it. An algorithm for two-dimensional finite-difference modeling of electrical and magnetic signals from an external circular magnetic harmonic current equivalent to a toroidal coil has been developed and verified. We perform twodimensional numerical modeling of the real (in-phase) and imaginary (quadrature) part of the vertical component of the electric field and the tangential component of the magnetic field for a practically-significant range of core resistivities, the sample being located within an insulating or highly conductive tube with toroidal coils. Following the results of numerical simulation, the optimal length of the measuring system is selected, as well as the operating frequency and type of measured signals. The transformation of the latter into the apparent resistivity values of vertically inhomogeneous samples is proposed. Moreover, criteria have been established for the correspondence of the measured signals in thinlayered and equivalent electrically macroanisotropic samples when changing the resistivity contrast and thickness of the interlayers.
Keywords
toroidal coil,
core material,
specific electrical resistivity,
mathematical modeling,
finite difference method,
two-dimensional model,
signal transformation
Supporting agencies: The research was carried out with the financial support of the Russian federal research project No. FWZZ-2022- 0026 “Innovative aspects of electrodynamics in problems of exploration and oilfield geophysics”.
About the Authors
M. I. Epov
Trofimuk Institute of Petroleum Geology and Geophysics of the Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Mikhail I. Epov – Dr. Sci. (Engineering), Professor, RAS Academician, Chief Researcher
3 Ac. Koptyug av., Novosibirsk, 630090
V. G. Mamyashev
Industrial University of Tyumen
Russian Federation
Russian Federation
Vener G. Mamyashev – Cand. Sci. (Geology and Mineralogy), Associate Professor
38 Volodarskogo st., Tyumen, 625000
I. V. Mikhaylov
Trofimuk Institute of Petroleum Geology and Geophysics of the Siberian Branch of the Russian Academy of Sciences; Novosibirsk State University
Russian Federation
Russian Federation
Igor V. Mikhaylov – Cand. Sci. (Engineering), Senior Researcher; Associate Professor
3 Ac. Koptyug av., Novosibirsk, 630090
1 Pirogova st., Novosibirsk, 630090
I. V. Surodina
Trofimuk Institute of Petroleum Geology and Geophysics of the Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Irina V. Surodina – Cand. Sci. (Physics and Mathematics), Senior Researcher
3 Ac. Koptyug av., Novosibirsk, 630090
M. N. Nikitenko
Trofimuk Institute of Petroleum Geology and Geophysics of the Siberian Branch of the Russian Academy of Sciences
Russian Federation
Russian Federation
Marina N. Nikitenko – Dr. Sci. (Engineering), Lead Researcher
3 Ac. Koptyug av., Novosibirsk, 630090
References
1. Ahmed H.M., Ahmed H.A.M., Adewuyi S.O. (2021). Characterization of Microschist Rocks under High Temperature at Najran Area of Saudi Arabia. Energies, 14(22), 7612. https://doi.org/10.3390/en14227612
2. Ashrafi J., Faramarzi L., Darbor M., Sharifzadeh M., Ferdosi B. (2020). The effects of temperature on mechanical properties of rocks. International Journal of Mining and Geo-Engineering, 54(2), pp. 147–152. https://doi.org/10.22059/ijmge.2019.271982.594771
3. Ben Aoun N., Kouki A., Aouina N., Haj Amara A.B. (2018). Radial Electrical Resistivity Measurements of Rocks on Laboratory Core Samples Using an Electromagnetic Sensor: Macro and Micro Eddy Currents. Journal of Sensors, 2018, 6435070. https://doi.org/10.1155/2018/6435070
4. Elsayed M., Isah A., Hiba M., Hassan A., Al-Garadi K., Mahmoud M., El‑Husseiny A., Radwan A.E. (2022). A review on the applications of nuclear magnetic resonance (NMR) in the oil and gas industry: laboratory and field‑scale measurements. Journal of Petroleum Exploration and Production Technology, 12, pp. 2747–2784. https://doi.org/10.1007/s13202-022-01476-3
5. Epov M.I., Nikitenko M.N., Glinskikh V.N. (2018). Mathematical substantiation of a new electromagnetic tool with toroidal coils for high-resolution logging of oil and gas wells. Vestnik NSU. Series: Information Technologies, 16(1), pp. 113–129. (In Russ.) https://doi.org/10.25205/1818-7900-2018-16-1-113-129
6. Epov M.I., Shurina E.P., Dobrolyubova D.V., Kutishcheva A.Yu., Markov S.I., Shtabel N.V., Shtanko E.I. (2023). Determination of the Effective Electrical Conductivity of a Fluid-Saturated Core from Computed Tomography Data. Izvestiya, Physics of the Solid Earth, 59(5), pp. 672–681. http://dx.doi.org/10.31857/S0002333723050046
7. Fadeeva I.I., Duchkov A.A., Manakov A.Y., Aunov D.E. (2020). Quantification of СО 2 hydrate in laboratory samples using a two-needle probe. Geofizicheskie issledovanija = Geophysical Research, 21(2), pp. 61–77. (In Russ.) http://dx.doi.org/10.21455/gr2020.2-5
8. Gerke K.M., Korost D.V., Karsanina M.V., Korost S.R., Vasiliev R.V., Lavrukhin E.V., Gafurova D.R. (2021). Modern approaches to pore space scale digital modeling of core structure and multiphase flow. Georesursy = Georesources, 23(2), pp. 197–213. (In Russ.) https://doi.org/10.18599/grs.2021.2.20
9. Gu B., Wan Z., Zhang Y., Ma Y., Xu X.B. (2020). Influence of Real-Time Heating on Mechanical Behaviours of Rocks. Advances in Civil Engineering, 2020, 8879922. https://doi.org/10.1155/2020/8879922
10. Karinskiy A.D. (2018). Electromagnetic field in electrically anisotropic medium models. Мoscow: GEOS, 184 p. (In Russ.)
11. Kästner F., Klaeschen D., Berndt C., Pierdominici S., Hedin P. (2022). Anisotropic velocity models for (3-D) seismic imaging of the Lower Seve Nappe in Jämtland, Sweden. Geophysical Journal International, 228(1), pp. 66–77. https://doi.org/10.1093/gji/ggab339
12. Kästner F., Pierdominici S., Elger J., Zappone A., Kück J., Berndt C. (2020). Correlation of core and downhole seismic velocities in high-pressure metamorphic rocks: A case study for the COSC-1 borehole, Sweden. Solid Earth, 11(2), pp. 607–626. https://doi.org/10.5194/se-11-607-2020
13. Khachkova T.S., Lisitsa V.V., Reshetova G.V., Tcheverda V.A. (2020). Numerical estimation of electrical resistivity in digital rocks using GPUs. Vychislitel’nye metody i programmirovanie = Numerical Methods and Programming, 21(3), pp. 306–318. (In Russ.) https://doi.org/10.26089/NumMet.v21r326
14. Khachkova T.S., Lisitsa V.V., Sotnikov O.S., Islamov I.A., Ganiev D.I. (2023). A new technique for numerical estimation of the absolute permeability of rocks from their microtomographic images. Geofizika = Geophysics, 1, pp. 34–40. (In Russ.) https://doi.org/10.34926/geo.2023.46.58.005
15. Kim J.-W., Hong C.-H., Kim J.-S., Chong S.-H. (2021). Theoretical and Numerical Study on Electrical Resistivity Measurement of Cylindrical Rock Core Samples Using Perimeter Electrodes. Energies, 14(14), 4382. https:// doi.org/10.3390/en14144382
16. Li J., Ke S., Yin C., Kang Z., Jia J., Ma X. (2019). A laboratory study of complex resistivity spectra for predictions of reservoir properties in clear sands and shaly sands. Journal of Petroleum Science and Engineering, 177, pp. 983–994. https://doi.org/10.1016/j.petrol.2019.01.061
17. Liu H.Q., Tian J., Youming D., Chunning Q. (2016). Study of the lowfrequency dispersion of permittivity and resistivity in tight rocks. International Journal of Petrochemical Science & Engineering, 1(3), pp. 55‒61. https:// doi.org/10.15406/ipcse.2016.01.00011
18. Luc Leroy M.N., Marius F.W., François N. (2021). Experimental and Theoretical Investigations of Hard Rocks at High Temperature: Applications in Civil Engineering. Advances in Civil Engineering, 2021, 8893944. https:// doi.org/10.1155/2021/8893944
19. Mezin A.A., Shumskayte M.Y., Glinskikh V.N., Golikov N.A., Chernova E.S. (2020). Reservoir properties of drill cutting by the nuclear magnetic resonance relaxometry and dielectric spectroscopy data. Earth Sciences and Subsoil Use, 43(3), pp. 364–374. (In Russ.) http://dx.doi.org/10.21285/2686-9993-2020-43-3-364-374
20. Morte M., Hascakir B. (2019). Characterization of complex permittivity for consolidated core samples by utilization of mixing rules. Journal of Petroleum Science and Engineering, 181, 106178. https://doi.org/10.1016/j.petrol.2019.06.042
21. Ponomarev A.A., Kadyrov М.А., Tugushev O.A., Drugov D.A., Vaganov Y.V., Leontiev D.S., Zavatsky M.D. (2024). Digital core reconstruction research: challenges and prospects. Geology, Ecology, and Landscapes, 8(1), pp. 49–56. https://doi.org/10.1080/24749508.2022.2086201
22. Reshetova G.V., Anchugov A.V. (2021). Digital Core: Time Reversal Modeling of Acoustic Emission Events. Russian Geology and Geophysics, 62(4), pp. 486–494. http://dx.doi.org/10.2113/RGG20194152
23. Samarskii A.A., Nikolaev E.S. (1978). Methods for Solving Grid Equations. Мoscow: Nauka, 592 p. (In Russ.)
24. Sharifi J., Nooraiepour M., Amiri M., Mondol N.H. (2023). Developing a relationship between static Young’s modulus and seismic parameters. Journal of Petroleum Exploration and Production Technology, 13, pp. 203–218. https://doi.org/10.1007/s13202-022-01546-6
25. Shumskayte M., Mezin A., Chernova E., Burukhina A., Golikov N., Melkozerova S. (2022). Estimating Water Content in Water–Oil Mixtures and Porous MEDIA They Saturate: Joint Interpretation of NMR Relaxometry and Dielectric Spectroscopy. Geosciences, 12(4), 179. https://doi.org/10.3390/geosciences12040179
26. Shumskayte M.Y., Yan P.A., Golikov N.A. (2022). Relaxation characteristics of core samples on the example of parametric well: database of formation properties by NMR-data. Russian Journal of Geophysical Technologies, 1, pp. 88–98. (In Russ.) https://doi.org/10.18303/2619-1563-2022-1-88
27. Svetov B.S. (1984). Electrodynamic foundations of quasi-stationary geoelectrics. Moscow: IZMIRAN, 183 p. (In Russ.)
Review
For citations:
Epov M.I., Mamyashev V.G., Mikhaylov I.V., Surodina I.V., Nikitenko M.N. Application of Toroidal Coils to Obtain Electrical Resistivity of Core Samples: Mathematical Modeling. Georesursy = Georesources. 2024;26(3):151-161. (In Russ.) https://doi.org/10.18599/grs.2024.3.16
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