Vol. 7 pp. 550-570

F.I. Mavrikidi, S.A. Khorkov

 

AN APPROACH TO MODELING THE UNIQUENESS AND INTEGRITY OF AN OIL AND GAS BEARING RESERVOIR

Annotation. The article is devoted to the development of a mathematical model of an oil-and-gas reservoir taking into account its macrogeometry and multiphysics. The macrogeometry of reservoir systems became available with the development of 3D models, which provided an opportunity to apply mathematical methods of fractal geometry to describe the global distribution of geological and physical local properties and to introduce the general geometry of the reservoir as an independent parameter. The mathematical content of the proposed approach is based on numerical asymmetry, which is a formal analog of fractal geometry of matter. This approach allows one to unite the theory of linear transport with the percolation theory of filtration processes. Moreover, inheriting the universality of fractals in natural science, the method can be extended to the processes of surface physico-chemical and nano phenomena. In general, the potency of the proposed approach contains the description of the productive formation as a holistic, interdisciplinary object of oil and gas production. The integrity is displayed in the method by system numerical characteristics - hologram and multifractality of properties, which synthesize scientific description languages. Computational asymmetry - as a numerical method of embodiment of the proposed method - is described. It consists in the interaction of smooth and discrete methods of numerical analysis. This, in turn, for the first time allows one to develop modeling of reservoirs taking into account their uniqueness, which makes mathematical description a reliable basis for the development of oil and gas recovery technologies.

Keywords: fractals, numerical asymmetry, oil and gas reservoir, filtration, percolation, macrogeometry, interdisciplinarity, mathematical modeling, systems theory.

For citation: Mavrikidi F.I., Khorkov S.A. [Аn approach to modeling the uniqueness and integrity of an oil and gas bearing reservoir]. Upravlenie tekhnosferoi, 2024, vol. 7, issue 4. (In Russ.). Available at: https://technosphere-ing.ru/ рр. 550–570.

REFERENCES

 

  1. Ter-Sarkisov R.M., Maksimov V.M., Basniev K.S. [i dr.]. Geologicheskoe i gidrotermodinamicheskoe modelirovanie mestorozhdenii nefti i gaza [Geological and hydrothermodynamic modeling of oil and gas fields] In M. Maksimova i prof. R.M. Ter-Sarkisova (eds.). Moscow: Izhevsk: Institut komp'yuternykh issledovanii, 2015, 452 p. (In Russ.).
  2. Hyde S. et.al. The Language of Shape. Elsevier, 1997. 383 p., ch.1.
  3. Izotov A.D., Mavrikidi F.I., Khor'kov S.A. Matematicheskii bazis innovatsionnykh tekhnologii neftegazovoi promyshlennosti [Mathematical basis of innovative technologies in the oil and gas industry]. Upravlenie tekhnosferoi: elektron. zhurnal. 2019, vol. 2, Issue 4. URL: f-ing.udsu.ru/technosphere (In Russ.).
  4. Wei Peng et.al. Hyperbolic Deep Neural Networks: A Survey, arXiv:2101.04562v3 [cs.LG] 17 Feb 2021
  5. Krioukov D. [et.al]. Hyperbilic geometry of complex networks, Phys. Rev., 2010, E 82, 036106
  6. Zhen (Leo) Lui Multiphysics in Porous Materials. Springer, 2018. 431 p.
  7. Khor'kov S.A., Mavrikidi F.I. Tsenozy, sistemy i ikh modeli: monografiya [Cenoses, systems and their models: monograph]. Izhevsk: Publ."Udmurt University", 2021, 92 p. (In Russ.).
  8. Surguchev, M.L., Zheltov Yu. V., Simkin E. M. Fiziko-khimicheskie mikroprotsessy v neftegazonosnykh plastakh [Physicochemical microprocesses in oil and gas formations]. Moscow: Nedra, 1984, 215 p. (In Russ.).
  9. Grzybowski B.A. Chemistry in Motion. Reaction-Diffusion Systems for Micro- and NanoTechnology. Wiley, 2009, 288 p.
  10. .Adamatzky A. [et.al]. Reaction-Diffusion Computers. Elsevier, 2005, 349p.
  11. Gibou F., Fedkiw R., Osher S. A Review of Level-Set Methods and Some Recent Applications, J. Comput. Physics, 2018, vol. 3, pp. 82 – 109.
  12. Zakrevskii K.E. Geologicheskoe 3D modelirovanie [Geological 3D Modeling]. Moscow: Maska, 2009, 376 p. (In Russ.).
  13. Sukhonos S.I. Masshtabnaya garmoniya Vselennoi. [Large-scale harmony of the Universe]. Moscow: Publ. New Center, 2002, 253 p. (In Russ.).
  14. Panfilov M. Physicochemical Fluid Dynamics in Porous Media. Wiley, 2019. 396 p.
  15. Cai J. Et.al. (eds.) Modelling of Flow and Transport in Fractal Porous Media. Elsevier, 2021. 272 p., Ch.3-5.
  16. Si Suo et.al. Fingering Patterns in Hierarchical Porous Media, Phys. Rev., 2020, Fluids 5, 034301.
  17. Galteland O, Bedeaux D, Hafskjold B., Kjelstrup S. Pressures Inside a Nano-Porous Medium. The Case of a Single Phase Fluid, Front. Phys, 2019, 7:60. doi: 10.3389/fphy.2019.00060
  18. Chopard B., Droz M. Cellular Automata Modeling of Physical Systems. Cambridge U.P., 1998, 340 p.
  19. Succi S. The Lattice Boltzmann Equation for Complex States of Flowing Matter. Elsevier, 2018, 288 p., Ch.19.
  20. Izotov, A.D., Mavrikidi F.I. Fraktaly. Delimost' veshchestva kak stepen' svobody v materialovedenii [Divisibility of Matter as a Degree of Freedom in Materials Science]. Samara, SGAU, 2011, 128 p. (In Russ.).
  21. Yaglom I. M. Buleva struktura i ee modeli. [Boolean Structure and Its Models]. Moscow: Sov. Radio, 1980, 192 p. (In Russ.).
  22. Toffoli T., Margolus N. Mashiny kletochnykh avtomatov [Cellular Automata Machines]. In Toffoli T., Margolus N. (eds). Moscow: Mir, 1991, 280 p. (In Russ.).
  23. Khor'kov S. A., Mavrikidi F. I. Prichinnost' tsenozov i sistem [Causality of cenoses and systems]. Fedorovskie chteniya. 2023: LIII Vseros. nauch.-praktich. konf. s mezhdunar. uchastiem (s elementami nauch. shk. dlya molodezhi) [Fedorov readings – 2023: LIII All-Russian scientific-practical. conf. with international. participation (with elements of scientific school for youth)]. (Moscow, November 15-17, 2023). Moscow: Publ. MPEI, 2023, pp. 442–450. (In Russ.).
  24. Bennethum LS, Weinstein T. Three pressures in porous media, Transp Porous Media, 2004, 54:1–34. doi: 10.1023/A:1025701922798
  25. Galteland O, Bedeaux D, Hafskjold B, Kjelstrup S. Pressures Inside a Nano-Porous Medium. The Case of a Single Phase Fluid., Front. Phys, 2019, 7:60. doi: 10.3389/fphy.2019.00060
  26. Nikiel S. Iterated Function Systems for Real-Time Image Synthesis. Springer, 2007. 152 p.
  27. Aja-Fernandez S. et.al. Tensors in Image Processing and Computer Vision. Springer, 2009 – 466 p.
  28. Valavanides M.S., Payatakes A.C. True-to-mechanism model of steady-state two-phase flow in porous media, using decomposition into prototype flows, Advances in Water Recourses 24, 2001, pp. 385 – 407.
  29. Dyubua D., Prad A. Teoriya vozmozhnostei. Prilozheniya k predstavleniyam znanii v informatike [Possibility theory. Applications to knowledge representations in computer science]. Prad A. (eds). Moscow: Radio and Communications, 1990, 288 p. (In Russ.).
  30. Khor'kov S.A. Teoriya vozmozhnosti pri raschete elektropotrebleniya mnogonomenklaturnogo tsekha promyshlennogo predpriyatiya [Possibility theory in calculating the power consumption of a multi-product workshop of an industrial enterprise]. Fedorovskie chteniya-2019: materialy XLIX Mezhdunarodnoi nauchno-prakticheskoi konferentsii s elementami nauchnoi shkoly (Moskva 20 – 22 noyabrya 2019) [Fedorovskie Readings-2019: Proceedings of the XLIX International Scientific and Practical Conference with Elements of a Scientific School (Moscow, November 20 – 22, 2019)]. In B.I. Kudrina, Yu.V. Matyuninoi (ed). Moscow: Publ. MPEI, 2019, pp. 90 – 94. (In Russ.).
  31. Krzhizhanovskaya V.V. Sun S. Simulation of Multiphysics multiscale systems: Introduction to the ICCS’2007 workshop., In: International conference on computational science. Springer, Berlin/Heidelberg, (2007), pp 755–761.
  32. Meagher D. Geometric Modelling Using Octree Encoding, COMPUTER GRAPHICS AND IMAGE PROCESSING, 1982, 19, 129 – 147.
  33. Khavkin A. Ya. Nanoyavleniya i nanotekhnologii v dobyche nefti i gaza [Nanophenomena and nanotechnologies in oil and gas production]. Moscow–Izhevsk: NITs Institut komp'yuternykh issledovanii, 2010, 692 p. (In Russ.).
  34. Nurgatin R.I., Lysov B.A. Primenenie 3D modelirovaniya v neftegazovoi otrasli [Application of 3D modeling in the oil and gas industry]. Izvestiya Sibirskogo otdeleniya Sektsii nauk o Zemle RAEN. [Bulletin of the Siberian Branch of the Earth Sciences Section of the Russian Academy of Natural Sciences]. 2014, no. 1(44), pp. 66–73. (In Russ.).
  35. Mirzadzhanzade A.Kh., Khasanov M.M., Bakhtizin R.N. Modelirovanie protsessov neftegazodobychi. Nelineinost', neravnovesnost', neopredelennost'. [Modeling of oil and gas production processes. Nonlinearity, nonequilibrium, uncertainty]. Moscow: Izhevsk: Institut komp'yuternykh issledovanii, 2004, 368 p. (In Russ.).

 

About the Authors

Mavrikidi Fyodor Ivanovich

Candidate of Technical Sciences, senior researcher,  Institute of oil and gas problems of the Russian Academy of Sciences, Moscow, Russia.

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Khorkov Sergey Alekseevich

Associate Professor of the Department of Thermal Power Engineering, Institute of Oil and Gas named after M.S. Gutseriev, Federal State Budgetary Educational Institution of Higher Education "Udmurt State University", 426034, University st., 1, Izhevsk, Russia.

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