Развитие поросетевого подхода для моделирования переноса модифицирующих добавок в процессе нефтевытеснения

Развитие поросетевого подхода для моделирования переноса модифицирующих добавок в процессе нефтевытеснения

Филимонов С. А., Минаков А. В.
Сибирский журнал индустриальной математики, 28, 3(103), 104–116 (2025)
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УДК 532.5 
DOI: 10.33048/SIBJIM.2025.28.307

Аннотация:

Представлены результаты разработки оригинальной математической модели и программного модуля для поросетевого моделирования переноса модифицирующих добавок (растворы ПАВ и наночастиц) в процессе вторичного заводнения нефтеносных пластов. В рамках двухфазного поросетевого подхода реализовано моделирование конвективнодиффузионного механизма переноса модифицирующей добавки в пределах водной фазы с учётом влияния локальной концентрации добавки на вязкость, межфазное натяжение и краевой угол смачивания. За счёт применения оригинального подхода добавления фиктивных узлов на ветви удалось существенно уменьшить влияние численной диффузии, характерной для моделей конвективно-диффузионного переноса в сетевых задачах. В результате тестирования на решении одномерной конвективно-диффузионной задачи с аналитическим решением показана удовлетворительная разрешающая способность предложенного расчётного алгоритма.

Литература:
  1. Cancela B. R. et al. Rheological study of polymeric fluids based on hpam and fillers for application in EOR // Fuel 2022. V. 330. P. 125647.
     
  2. Vik B. et al. Viscous oil recovery by polymer injection; impact of in-situ polymer rheology on water front stabilization// SPE Europec featured at EAGE Conference and Exhibition. SPE, 2018.
     
  3. Sepehri M. et al. Experimental study and numerical modeling for enhancing oil recovery from carbonate reservoirs by nanoparticle flooding // Oil Gas Sci. Technol. – Rev. d’IFP Energies Nouv. 2019. V. 74. P. 5.
     
  4. Wei B. et al. Pore scale simulation of surfactant flooding by lattice boltzmann method // Day 3 Wed, December 12, 2018. SPE, 2018.
     
  5. Zhao J., Wen D. Pore-scale simulation of wettability and interfacial tension effects on flooding process for enhanced oil recovery // RSC Adv. 2017. V. 7, N 66. P. 41391–41398.
     
  6. Minakov A. V. et al. Numerical study of the mechanisms of enhanced oil recovery using nanosuspensions // Theor. Comput. Fluid Dyn. 2021. V. 35, N 4. P. 477–493.
     
  7. Yang Y. et al. Pore-scale simulation of remaining oil distribution in 3D porous media affected by wettability and capillarity based on volume of fluid method // Inter. J. Multiph. Flow. 2021. V. 143. P. 103746.
     
  8. Singh M. Dynamic modeling of drainage through three-dimensional porous materials // Chem. Eng. Sci. 2003. V. 58, N 1. P. 1–18.
     
  9. Regaieg M. et al. Finger thickening during extra-heavy oil waterflooding: simulation and interpretation using pore-scale modelling // PLoS One / ed. Coles J.A. 2017. V. 12, N 1. P. e0169727.
     
  10. Aghaei A., Piri M. Direct pore-to-core up-scaling of displacement processes: Dynamic pore network modeling and experimentation // J. Hydrol. 2015. V. 522. P. 488–509.
     
  11. Gang S. G., Ryou J. E., Jung J. Increase in injection efficiency using surfactant for the geological carbon sequestration // Smart Geotechnics for Smart Societies. CRC Press, 2023. P. 2191–2196.
     
  12. Salmo I. C. et al. Use of dynamic pore network modeling to improve our understanding of experimental observations in viscous oil displacement by polymers // Day 2 Tue, September 01, 2020. SPE, 2020.
     
  13. Li J., McDougall S. R., Sorbie K. S. Fragmentation // Rev. Fluid Mech. 2007. V. 39.
     
  14. Filimonov S. A. et al. Development and testing of a mathematical model for dynamic network simulation of the oil displacement process // Fluids. 2022. V. 7, N 9. P. 311.
     
  15. Филимонов С. А. и др. Моделирование сопряжённого теплообмена в системе микроканалов при помощи гибридного алгоритма //Сиб. журн. индустр. математики. 2015. Т. 18 № 3. С. 86–97.
     
  16. Patankar S. Numerical heat transfer and fluid flow // Series in coputational methods in mechanics and thermal sciences. 1980.
     
  17. Pryazhnikov M. et al. Microfluidic study of enhanced oil recovery during flooding with polyacrylamide polymer solutions // Micromachines. 2023. V. 14, N 6. P. 1137.
     
  18. Minakov A. V., Rudyak V. Y., Pryazhnikov M. I. Systematic experimental study of the viscosity of nanofluids // Heat Transf. Eng. 2021. V. 42, N 12. P. 1024–1040.
     
  19. Minakov A. V., et al. An experimental study of the effect of the addition of silicon oxide nanoparticles on the wettability characteristics of rocks with respect to oil // Tech. Phys. Letters. 2020. V. 46, N 12. P. 1238–1240.
     
  20. Pryazhnikov M. I. et al. Spontaneous imbibition experiments for enhanced oil recovery with silica nanosols // Capillarity. 2024. V. 10, N 3. P. 73–86.

Работа выполнена при финансовой поддержке Российского научного фонда (проект 23-79- 30022, https://rscf.ru/project/23-79-30022/). Других источников финансирования проведения или руководства данным конкретным исследованием не было.

С. А. Филимонов
  1. Сибирский федеральный университет, 
    просп. Свободный, 79, г. Красноярск 660041, Россия
  2. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Акад. Лаврентьева, 1, г. Новосибирск 630090, Россия

E-mail: sfilimonov@sfu-kras.ru

А. В. Минаков
  1. Сибирский федеральный университет, 
    просп. Свободный, 79, г. Красноярск 660041, Россия
  2. Институт теплофизики им. С. С. Кутателадзе СО РАН, 
    просп. Акад. Лаврентьева, 1, г. Новосибирск 630090, Россия

E-mail: aminakov@sfu-kras.ru

Статья поступила 10.06.2024 г.
После доработки — 10.07.2025 г.
Принята к публикации 17.09.2025 г.

Abstract:

The paper presents the results of the development of an original mathematical model and a software module for pore-network modeling of the transfer of modifying additives (solutions of surfactants and nanoparticles) in the process of secondary flooding of oil-bearing formations. Within the framework of the two-phase pore-network approach, modeling of the convective-diffusion mechanism of the transport of the modifying additive within the water phase is implemented, taking into account the influence of the local concentration of the additive on viscosity, interfacial tension and the wetting edge angle. By applying the original approach of adding fictitious nodes to branches, it was possible to significantly reduce the effect of numerical diffusion, which is characteristic of convective diffusion transport models in network problems. As a result of testing on solving a one-dimensional convective-diffusion problem with an analytical solution, the satisfactory resolution of the proposed computational algorithm is shown.

References:
  1. Cancela B. R. et al. Rheological study of polymeric fluids based on HPAM and fillers for application in EOR. Fuel, 2022, Vol. 330, pp. 125647.
     
  2. Vik B. et al. Viscous oil recovery by polymer injection; impact of in-situ polymer rheology on water front stabilization. SPE Europec Featured at EAGE Conference and Exhibition, SPE, 2018.
     
  3. Sepehri M. et al. Experimental study and numerical modeling for enhancing oil recovery from carbonate reservoirs by nanoparticle flooding. Oil Gas Sci. Technol. – Rev. d’IFP Energies Nouv, 2019, Vol. 74, pp. 5.
     
  4. Wei B. et al. Pore scale simulation of surfactant flooding by lattice boltzmann method. Day 3 Wed, December 12, 2018, SPE, 2018.
     
  5. Zhao J., Wen D. Pore-scale simulation of wettability and interfacial tension effects on flooding process for enhanced oil recovery. RSC Adv., 2017, Vol. 7, No. 66, pp. 41391–41398.
     
  6. Minakov A. V. et al. Numerical study of the mechanisms of enhanced oil recovery using nanosuspensions. Theor. Comput. Fluid Dyn., 2021, Vol. 35, No. 4, pp. 477–493.
     
  7. Yang Y. et al. Pore-scale simulation of remaining oil distribution in 3D porous media affected by wettability and capillarity based on volume of fluid method. Inter. J. Multiph. Flow, 2021, Vol. 143, pp. 103746.
     
  8. Singh M. Dynamic modeling of drainage through three-dimensional porous materials // Chem. Eng. Sci. 2003. Vol. 58, No. 1, pp. 1–18.
     
  9. Regaieg M. et al. Finger thickening during extra-heavy oil waterflooding: simulation and interpretation using pore-scale modelling. PLoS One, 2017, V. 12, No. 1, pp. e0169727.
     
  10. Aghaei A., Piri M. Direct pore-to-core up-scaling of displacement processes: Dynamic pore network modeling and experimentation. J. Hydrol., 2015, Vol. 522, pp. 488–509.
     
  11. Gang S. G., Ryou J. E., Jung J. Increase in injection efficiency using surfactant for the geological carbon sequestration. Smart Geotechnics for Smart Societies, CRC Press, 2023, pp. 2191–2196.
     
  12. Salmo I. C. et al. Use of dynamic pore network modeling to improve our understanding of experimental observations in viscous oil displacement by polymers. Day 2 Tue, September 01, 2020, SPE, 2020.
     
  13. Li J., McDougall S. R., Sorbie K. S. Fragmentation. Rev. Fluid Mech., 2007, Vol. 39.
     
  14. Filimonov S.A. et al. Development and testing of a mathematical model for dynamic network simulation of the oil displacement process. Fluids, 2022, Vol. 7, No. 9, pp. 311.
     
  15. Filimonov, S. A., and others Modelirovanie soprjazhjonnogo teploobmena v sisteme mikrokanalov pri pomoshhi gibridnogo algoritma [Modeling of coupled heat transfer in a microchannel system using a hybrid algorithm]. Sib. Zhurn. Indust. Matematiki, 2015, Vol. 18, No. 3, pp. 86–97 (in Russian).
     
  16. Patankar S. Numerical heat transfer and fluid flow. Series in Coputational Methods in Mechanics and Thermal Sciences, 1980.
     
  17. Pryazhnikov M. et al. Microfluidic study of enhanced oil recovery during flooding with polyacrylamide polymer solutions. Micromachines, 2023, Vol. 14, No. 6, pp. 1137.
     
  18. Minakov A. V., Rudyak V. Y., Pryazhnikov M. I. Systematic experimental study of the viscosity of nanofluids. Heat Transf. Eng., 2021, Vol. 42, No. 12, pp. 1024–1040.
     
  19. Minakov A. V., et al. An experimental study of the effect of the addition of silicon oxide nanoparticles on the wettability characteristics of rocks with respect to oil. Tech. Phys. Letters, 2020, Vol. 46, No. 12, pp. 1238–1240. 
     
  20. Pryazhnikov M. I. et al. Spontaneous imbibition experiments for enhanced oil recovery with silica nanosols. Capillarity, 2024, Vol. 10, No. 3, pp. 73–86.