Mining of Mineral Deposits

ISSN 2415-3443 (Online)

ISSN 2415-3435 (Print)

Flag Counter

Application of the Radial Basis Function interpolation method in selected reservoirs of the Croatian part of the Pannonian Basin System

Josip Ivšinović1, Tomislav Malvić2

1INA-Industry of Oil Plc., Zagreb, 10000, Croatia

22University of Zagreb, Zagreb, 10000, Croatia


Min. miner. depos. 2020, 14(3):37-42


https://doi.org/10.33271/mining14.03.037

Full text (PDF)


      ABSTRACT

      Purpose. The use of interpolation methods of mapping Radial Basis Function (RBF) on reservoir data from one field in Croatian part of Pannonian Basin System (CPBS).

      Methods. The RBF method (with five single basic mathematical functions) was applied to small datasets. Application of the Radial Basis Function (RBF) method and comparison with previous application of the Inverse Distance Weighting (IDW) method applied in the CPBS area. The IDW and RBF methods were compared by cross-validation value and visual inspection of interpolated maps.

      Findings. The RBF method was tested on a small data sample. The RBF method can be used independently when using the Inverse Multiquadric Function (RBF-IM) mathematical function, while the remaining analyzed mathematical multilog function (RBF-M) and “multiquadric function” (RBF-M2) can be used as additional sources of information when mapping.

      Originality.. For the first time RBF is applied as a method in the CPBS area for small input data sets.

      Practical implications. For small sample the RBF method cannot be applied independently. According to the cross-validation value and visual inspection of interpolated maps, the method that can be used with the IDW method when mapping a small sample is RBF-IM. It could be primary or additional method for a small sample, while for a large sample it offers additional information.

      Keywords: Pannonian Basin System, Radial Basis Function (RBF), Inverse Distance Weighting (IDW), geostatistics, small dataset


      REFERENCES

  1. Balić, D., Velić, J., & Malvić, T. (2008). Selection of the most appropriate interpolation method for sandstone reservoirs in the Kloštar oil and gas field. Geologia Croatica, 61(1), 27-35.
  2. Ivšinović, J. (2018). Deep mapping of hydrocarbon reservoirs in the case of a small number of data on the example of the Lower Pontian reservoirs of the western part of Sava Depression. In Proceedings of the 2nd Croatian congress on geomathematics and geological terminology, 59-65.
  3. Malvić, T., Ivšinović, J., Velić, J., & Rajić, R. (2019). Interpolation of small datasets in the sandstone hydrocarbon reservoirs, case study of the Sava Depression, Croatia. Geosciences, 9(5), 201.https://doi.org/10.3390/geosciences9010036
  4. Balić, D., Velić, J., & Malvić, T. (2008). Selection of the most appropriate interpolation method for sandstone reservoirs in the Kloštar oil and gas field. Geologia Croatica, 61(1), 27-35.
  5. Ivšinović, J. (2018). The relationship between sandstone depositional environment and water injection system, a case study from the Upper Miocene hydrocarbon reservoir in northern Croatia. In Proceedings of the 2nd Croatian Scientific Congress from Geomathematics and Terminology in Geology, 65-75.
  6. Husanović, E., & Malvić, T. (2014). Review of deterministic geostatistical mapping methods in Croatian hydrocarbon reservoirs and advantages of such approach. Nafta, (65), 57-63.
  7. De Boer, A., van der Schoot, M.S., & Bijl, H. (2007). Mesh deformation based on radial basis function interpolation. Computers & Structures, 85(11-14), 784-795.https://doi.org/10.1016/j.compstruc.2007.01.013
  8. Jakobsson, S., Andersson, B., & Edelvik, F. (2009). Rational radial basis function interpolation with applications to antenna design. Journal of Computational and Applied Mathematics, 233(4), 889-904.https://doi.org/10.1016/j.cam.2009.08.058
  9. Nourani, V., & Babakhani, A. (2013). Integration of artificial neural networks with radial basis function interpolation in earthfill dam seepage modeling. Journal of Computing in Civil Engineering, 27(2), 183-195.https://doi.org/10.1061/(asce)cp.1943-5487.0000200
  10. Zou, Y.-L., Hu, F.-L., Zhou, C.-C., Li, C.-L., & Dunn, K.-J. (2013). Analysis of radial basis function interpolation approach. Applied Geophysics, 10(4), 397-410.https://doi.org/10.1007/s11770-013-0407-z
  11. Royden, L.H. (1988). Late Cenozoic tectonics of the Pannonian Basin System. American Association of Petroleum Geologists Memoir, (45), 27-48.
  12. Ivšinović, J. (2019). Selection and geomathematical calculation of variables for sets with less than 50 data regarding the creation of an improved subsurface model, case study from the western part of the Sava Depression. PhD. Zagreb, Croatia: University of Zagreb.
  13. Velić, J. (2007). Geology of oil and gas. Zagreb, Croatia: University of Zagreb.
  14. Malvić, T., Ivšinović, J., Velić, J., Sremac, J., & Barudžija, U. (2020). Application of the modified Shepard’s method (MSM): a case study with the interpolation of Neogene reservoir variables in Northern Croatia. Stats, (3), 68-83. https://doi.org/10.3390/stats3010007
  15. Ivšinović, J. (2018). The cost analysis of the separation of produced formation water from the hydrocarbon reservoir using the example of the upper Miocene sandstone deposits of the Sava depression. Rudarsko-Geološko-Naftni Zbornik, 33(1), 35-43.https://doi.org/10.17794/rgn.2018.1.5
  16. Ivšinović, J., Pleteš, V., & Marinić, M. (2018). Production of hydrocarbons from weakly consolidated sandstone reservoirs in the croatian part of the Pannonian basin system. Mining of Mineral Deposits, 12(2), 116-121.https://doi.org/10.15407/mining12.02.116
  17. Setianto, A., & Triandini, T. (2013). Comparison of kriging and inverse distance weighted (IDW) interpolation methods in lineament extraction and analysis. Journal of Applied Geology, 5(1), 21-29.https://doi.org/10.22146/jag.7204
  18. Li, L., Losser, T., Yorke, C., & Piltner, R. (2014). Fast inverse distance weighting-based spatiotemporal interpolation: a web-based application of interpolating daily fine particulate matter PM2.5 in the contiguous U.S. using parallel programming and k-d tree. International Journal of Environmental Research and Public Health, (11), 9101-9141.https://doi.org/10.3390/ijerph110909101
  19. Stachelek, J., & Madden, C.J. (2015). Application of inverse path distance weighting for high-density spatial mapping of coastal water quality patterns. International Journal of Geographical Information Science, 29(7), 1240-1250.https://doi.org/10.1080/13658816.2015.1018833
  20. Rodrıguez, J.D., Perez, A., & Lozano, J.A. (2010). Sensitivity analysis of k-fold cross validation in prediction error estimation. IEEE transactions on pattern analysis and machine intelligence, 3(32), 569-575.https://doi.org/10.1109/TPAMI.2009.187
  21. Arlot, S., & Lerasle, M. (2016). Choice of V for V-fold cross-validation in least-squares density estimation. Journal of Machine Learning Research, (17), 1-50.
  22. Malvić, T., Ivšinović, J., Velić, J., & Rajić, R. (2019). Kriging with a small number of data points supported by jack-knifing, a case study in the Sava Depression (Northern Croatia). Geosciences, 9(36).https://doi.org/10.3390/geosciences9010036
  23. Malvić, T., Ivšinović, J., Velić, J., Sremac, J., & Barudžija, U. (2020). Increasing efficiency of field water re-injection during water-flooding in mature hydrocarbon reservoirs: a case study from the Sava Depression, Northern Croatia. Sustainability, 12(786).https://doi.org/10.20944/preprints201912.0350.v1

    24. Лицензия Creative Commons

Copyright © 2024 Dnipro University of Technology

Underground Mining Department

All Rights Reserved.

Journal homepage Authors