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Borehole resistivity simulations of oil-water transition zones with a 1.5D numerical solver

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Abstract

When simulating borehole resistivity measurements in a reservoir, it is common to consider an oil-water contact (OWC) planar interface. However, this consideration can lead to an unrealistic model since in the presence of capillary actions, the mix of two immiscible fluids (oil and water) often appears as an oil-water transition (OWT) zone. These transition zones may be significant in the vertical direction (20 m or above), and in context of geosteering, an efficient method to simulate the OWT zone can maximize the production of an oil reservoir. Herein, we propose an efficient one and a half-dimensional (1.5D) numerical solver to accurately simulate the OWT zone in an oil reservoir. Using this method, we can easily consider arbitrary resistivity distributions in the vertical direction, as it occurs in an OWT zone. Numerical results on synthetic examples demonstrate significant differences between the results recorded by a geosteering device when considering a realistic OWT zone vs an OWC sharp interface.

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References

  1. Bakr, S.A., Pardo, D., Mannseth, T.: Domain decomposition Fourier FE method for the simulation of 3D marine CSEM measurements. J. Comput. Phys. 255, 456–470 (2013)

    Article  Google Scholar 

  2. Streich, R., Becken, M.: Sensitivity of controlled-source electromagnetic fields in planarly layered media. Geophys. J. Int. 187, 705–728 (2011)

    Article  Google Scholar 

  3. Constable, S., Srnka, L.J.: An introduction to marine controlled-source electromagnetic methods for hydrocarbon exploration. Geophysics 72(2), WA3–WA12 (2007)

    Article  Google Scholar 

  4. Pardo, D., Nam, M.J., Torres-Verdin, C., Hoversten, M.G., Garay, I.: Simulation of marine controlled source electromagnetic measurements using a parallel Fourier hp-finite element method. Comput. Geosci. 15, 53–67 (2011)

    Article  Google Scholar 

  5. Key, K.: 1D inversion of multicomponent, multifrequency marine CSEM data: methodology and synthetic studies for resolving thin resistive layers. Geophysics 74(2), F9–F20 (2009)

    Article  Google Scholar 

  6. Martí, A.: The role of electrical anisotropy in magnetotelluric responses: from modelling and dimensionality analysis to inversion and interpretation. Surv. Geophys. 35, 179–218 (2014)

    Article  Google Scholar 

  7. Alvarez-Aramberri, J., Pardo, D.: Dimensionally adaptive hp-finite element simulation and inversion of 2D magnetotelluric measurements. J. Comput. Sci. 18, 95–105 (2017)

    Article  Google Scholar 

  8. Pardo, D., Torres-Verdin, C.: Fast 1D inversion of logging-while-drilling resistivity measurements for the improved estimation of formation resistivity in high-angle and horizontal wells. Geophysics 80(2), E111–E124 (2014)

    Article  Google Scholar 

  9. Davydycheva, S., Wang, T.: A fast modelling method to solve Maxwell’s equations in 1D layered biaxial anisotropic medium. Geophysics 76(5), F293–F302 (2011)

    Article  Google Scholar 

  10. Wang, G.L., Barber, T., Wu, P., Allen, D., Abubakar, A.: Triaxial induction tool response in dipping and crossbedded formations. Soc. Explor. Geophys., 585–590 (2014)

  11. Ijasana, O., Torres-Verdín, C., Preeg, W.E.: Inversion-based petrophysical interpretation of logging-while-drilling nuclear and resistivity measurements. Geophysics 78(6), D473–D489 (2013)

    Article  Google Scholar 

  12. Davydycheva, S., Homan, D., Minerbo, G.: Triaxial induction tool with electrode sleeve: FD modeling in 3D geometries. J. Appl. Geophys. 67, 98–108 (2004)

    Article  Google Scholar 

  13. Seydoux, J., Legendre, E., Mirto, E., Dupuis, C., Denichou, J.M., Bennett, N., Kutiev, G., Kuchenbecker, M., Morriss, C., Yang, L.: Full 3D deep directional resistivity measurements optimize well placement and provide reservoir-scale imaging while drilling. Soc. Petrophys. Well-Log Analysts, 1–14 (2014)

  14. Bell, C., Hampson, J., Eadsforth, P., Chemali, R., Helgesen, T., Meyer, H., Peveto, C., Poppitt, A., Randall, R., Signorelli, J., Wang, T.: Navigating and imaging in complex geology with azimuthal propagation resistivity while drilling. Soc. Petrophys. Well-Log Analysts, 1–14 (2006)

  15. Bittar, M., Klein, J., Beste, R., Hu, G., Wu, M., Pitcher, J., Golla, C., Althoff, G., Sitka, M., Minosyam, V., Paulk, M.: A new azimuthal deep-reading resistivity tool for geosteering and advanced formation evaluation. Soc. Petrophysicists Well-Log Analysts, 1–10 (2009)

  16. Chemali, R., Bittar, M., Hveding, F., Wu, M., Dautel, M.: Improved geosteering by integrating in real time images from multiple depths of investigation and inversion of azimuthal resistivity signals. Soc. Petrophysicists Well-Log Analysts, 1–7 (2010)

  17. Davydycheva, S.: Separation of azimuthal effects for new-generation resistivity logging tools — part 1. Geophysics 75(1), E31–E40 (2010)

    Article  Google Scholar 

  18. Davydycheva, S.: Separation of azimuthal effects for new-generation resistivity logging tools — part 2. Geophysics 76(3), F185–F202 (2011)

    Article  Google Scholar 

  19. 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 8(6), 1–28 (2018)

    Article  Google Scholar 

  20. Omeragic, D., Habashy, T., Chen, Y.H., Polyakov, V., Kuo, C., Altman, R., Hupp, D., Maeso, C.: Reservoir characterization and well placement in complex scenarios using LWD directional EM measurements. Petrophysics 50, 396–415 (2009)

    Google Scholar 

  21. Al-Musharfi, N.M., Bansal, R., Ahmed, M.S., Kanj, M.Y., Morys, M., Conrad, C., Parker, T.J.: Real time reservoir characterization and geosteering using advanced high-resolution LWD resistivity imaging. Soc. Petroleum Eng., 1–11 (2010)

  22. Beer, R., Dias, L.C.T., da Cunha, A.M.V., Coutinho, M.R., Schmitt, G.H., Seydoux, J., Guedes, A.B.F.: Geosteering and/or reservoir characterization the prowess of new-generation LWD tools. Soc. Petrophys. Well-Log Analysts, 1–14 (2010)

  23. Zhang, C., Wu, Q., Wang, X., Lu, N.: Application of rotary geosteering drilling in deep and thin reservoirs of tarim basin, NW China. Pet. Explor. Dev. 40(6), 801–805 (2013)

    Article  Google Scholar 

  24. Kok, J.C.L., DeJarnett, J., Geary, D., Vauter, E.: Successful geosteering in low resistivity contrast reservoirs of the permian basin. Soc. Petrol. Eng., 1–4 (2011)

  25. Loseth, L.O., Ursin, B.: Electromagnetic fields in planarly layered anisotropic media. Geophys. J. Int. 170, 44–F80 (2007)

    Article  Google Scholar 

  26. Rojas, S., Muga, I., Pardo, D.: A quadrature-free method for simulation and inversion of 1.5D direct current (DC) borehole measurements. Comput. Geosci. 20(6), 1301–1318 (2016)

    Article  Google Scholar 

  27. Lian, P., Tan, X.Q., Ma, C.Y., Feng, R.Q., Gao, H.M.: Saturation modeling in a carbonate reservoir using capillary pressure based saturation height function: a case study of the svk reservoir in the y field. J. Petroleum Explor. Prod. Technol. 6(1), 73–84 (2016)

    Article  Google Scholar 

  28. Ghasemi, M., Yang, Y., Gildin, E., Efendiev, Y., Calo, V.M.: Fast multiscale reservoir simulations using pod-deim model reduction. Soc. Petrol. Eng., 1–18 (2015)

  29. Malekzadeh, F.A., Dusseault, M.B.: A solution for the transition zone isosats in two-phase primary drainage in the presence of gravity. Comput. Geosci. 17(5), 757–771 (2013)

    Article  Google Scholar 

  30. Bhattacharya, S., Byrnes, A., Gerlach, P.: Cost-effective integration of geologic and petrophysical characterization with material balance and decline curve analysis to develop a 3D reservoir model for pc-based reservoir simulation to design a waterflood in a mature Mississippian carbonate field with limited log data. Tech. Rep. no. 2003-31, Kansas Geological Survey, Open-file Report (2003)

  31. Glover, P.W.J.: Archie’s law – a reappraisal. Solid Earth 7(4), 1157–1169 (2016)

    Article  Google Scholar 

  32. Nédélec, J.C.: Acoustic and Electromagnetic Equations, Applied Mathematical Sciences, vol. 144. Springer, New York (2001). Integral representations for harmonic problems

    Book  Google Scholar 

  33. Habashy, T., Anderson, B.: Reconciling differences in depth of investigation between 2-MHz phase shift and attenuation resistivity measurements. Paper E presented at the 1991 SPWLA Annual Logging Symposium, Midland, Texas 16–19 June (1991)

  34. Desbrandes, R., Clayton, R.: Chapter 9 measurement while drilling. Dev. Pet. Sci. 38, 251–279 (1994)

    Google Scholar 

  35. Seifert, D.J., Dossary, S.A., Chemali, R.E., Bittar, M.S., Lotfy, A.A., Pitcher, J.L., Bayrakdar, M.A.: Deep electrical images, geosignal, and real-time inversion help guide steering decisions. Soc. Petroleum Eng., 1–9 (2009)

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Funding

Mostafa Shahriari has been financially supported by the Austrian Ministry for Transport, Innovation and Technology, the Federal Ministry for Digital and Economic Affairs, and the Province of Upper Austria in the frame of the COMET center SCCH.

David Pardo has received funding from the European Union’s Horizon 2020 research and innovation program under the Marie Sklodowska-Curie grant agreement no. 777778 (MATHROCKS), the POCTEFA H2020 Project PIXIL (EFA362/19), the Project of the Spanish Ministry of Economy and Competitiveness with reference MTM2016-76329-R (AEI/FEDER, EU), the BCAM “Severo Ochoa” accreditation of excellence (SEV-2017-0718), and the Basque Government through the BERC 2018-2021 program, the two Elkartek projects ArgIA (KK-2019-00068) and MATHEO (KK-2019-00085), and the Consolidated Research Group MATHMODE (IT1294-19) given by the Department of Education.

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Authors and Affiliations

  1. Software Competence Center Hagenberg (SCCH), Softwarepark 21, 4232, Hagenberg, im Mühlkreis, Austria

    M. Shahriari

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

    D. Pardo

  3. Basque Center for Applied Mathematics, (BCAM), Bilbao, Spain

    D. Pardo

  4. Ikerbasque (Basque Foundation for Sciences), Bilbao, Spain

    D. Pardo

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  1. M. Shahriari
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Correspondence to M. Shahriari.

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Shahriari, M., Pardo, D. Borehole resistivity simulations of oil-water transition zones with a 1.5D numerical solver. Comput Geosci 24, 1285–1299 (2020). https://doi.org/10.1007/s10596-020-09946-5

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  • DOI: https://doi.org/10.1007/s10596-020-09946-5

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