georesГеоресурсыGeoresources1608-50431608-5078Georesursy LLC10.18599/grs.2026.1.5geores-649Research ArticleСТАТЬИRESEARCH ARTICLESВлияние фильтрационно-емкостных свойств природных терригенных пород-коллекторов на эффективность нефтевытеснения при различной минерализации пластовой водыImpact of Filtration-Capacity Properties of Natural Terrigenous Reservoir Rocks on Oil Displacement Efficiency at Various Formation Water SalinitiesЗакировТ. Р.ZakirovT. R.

Тимур Рустамович Закиров – кандидат физ.-мат. наук, зав. кафедрой математических методов в геологии Института геологии и нефтегазовых технологий

420111, Казань, ул. Кремлевская, д 4/5 

Timur R. Zakirov – Cand. Sci. (Physics and Mathematics), Head of the Department of Mathematical Methods in Geology, Institute of Geology and Petroleum Technologies

4/5 Kremlevskaya st., Kazan, 420111

tirzakirov@kpfu.ruХаюзкинА. С.KhayuzkinA. S.

Алексей Сергеевич Хаюзкин – ассистент, Институт геологии и нефтегазовых технологий

420111, Казань, ул. Кремлевская, д 4/5 

Alexey S. Khayuzkin – Assistant, Institute of Geology and Petroleum Technologies

4/5 Kremlevskaya st., Kazan, 420111

alexeykhaiuzkin@mail.ruМаннаповаЛ. М.MannapovaL. M.

Ляйсан Минисовна Маннапова – инженер, Институт геологии и нефтегазовых технологий

420111, Казань, ул. Кремлевская, д 4/5 

Leysan M. Mannapova – Engineer, Institute of Geology and Petroleum Technologies

4/5 Kremlevskaya st., Kazan, 420111

liaisan.mannapova@yandex.ruЕлизаровА. М.ElizarovA. M.

Александр Михайлович Елизаров – доктор физ.-мат. наук, профессор Института информационных технологий и интеллектуальных систем

420008, Казань, ул. Кремлевская, д. 35 

Alexander M. Elizarov – Dr. Sci. (Physics and Mathematics), Professor at the Institute of Information Technology and Intelligent Systems

4/5 Kremlevskaya st., Kazan, 420111

Moscow

 

amelizarov@gmail.comКазанский (Приволжский) федеральный университетРоссияKazan (Volga Region) Federal UniversityRussian FederationКазанский (Приволжский) федеральный университет; НИЦ «Курчатовский институт»РоссияKazan (Volga Region) Federal University; National Research Center “Kurchatov Institute”Russian Federation20262703202628154–64Copyright © Закиров Т.Р., Хаюзкин А.С., Маннапова Л.М., Елизаров А.М., 20262026Закиров Т.Р., Хаюзкин А.С., Маннапова Л.М., Елизаров А.М.Zakirov T.R., Khayuzkin A.S., Mannapova L.M., Elizarov A.M.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.geors.ru/jour/article/view/649

Работа посвящена исследованию влияния минерализации пластовой воды, определяющей краевые условия смачивания, на коэффициент извлечения нефти в природных терригенных породах-коллекторах с различными фильтрационно-емкостными свойствами. В качестве объектов исследования рассматриваются песчаники, отобранные на Ашальчинском, Восточно-Бирлинском и Зюзеевском месторождениях республики Татарстан и ульяновской области. Инструментом исследования является математическое моделирование на цифровых моделях песчаников, полученных при помощи метода рентгеновской микротомографии. установлено, что прирост коэффициента извлечения нефти в результате гидрофилизации породы за счет варьирования минерализации воды существенно зависит от фильтрационных свойств образца. увеличение проницаемости приводит к усилению положительного эффекта от изменения условий смачивания. Выявлена прямо пропорциональная зависимость между приростом коэффициента извлечения нефти и коэффициентом проницаемости.

This study examines the impact of formation water mineralization – a key determinant of wettability boundary conditions – on oil recovery efficiency in natural terrigenous reservoir rocks exhibiting diverse filtration and storage properties. The investigation focuses on sandstone samples obtained from three hydrocarbon fields (Ashalchinskoye, Vostochno-Birlinskoye, and Zuyevskoye) located in the Republic of Tatarstan and Ulyanovsk region, employing advanced digital rock physics techniques through X-ray microtomography-based reconstruction of porescale models. The research establishes that the incremental oil recovery achieved through rock hydrophilization via controlled water salinity modification demonstrates strong dependence on the sample’s filtration characteristics, with enhanced permeability correlating directly with more pronounced positive effects from wettability alteration. A distinct linear relationship emerges between the magnitude of oil recovery improvement and the permeability coefficient, revealing that reservoirs with superior flow capacity exhibit greater responsiveness to salinity-engineered wettability modification. These findings provide critical quantitative insights for optimizing waterflooding performance in terrigenous reservoirs through strategic manipulation of injection water chemistry, particularly for the studied fields in the Volga-Urals petroleum province, while establishing a fundamental relationship between petrophysical properties and recovery enhancement potential through salinity-controlled wettability alteration.

минерализация пластовой водыкраевой угол смачиваниятерригенные породыматематическое моделированиецифровой кернformation water salinitycontact angleterrigenous rocksmathematical modelingdigital coreРабота выполнена за счет гранта Академии наук Республики Татарстан, предоставленного молодым кандидатам наук (постдокторантам) с целью защиты докторской диссертации, выполнения научно-исследовательских работ, а также выполнения трудовых функций в научных и образовательных организациях Республики Татарстан в рамках Государственной программы Республики Татарстан «Научно-технологическое развитие Республики Татарстан».This work was supported by a grant from the Academy of Sciences of the Republic of Tatarstan.ReferencesГерке К.М., Корост Д.В., Карсанина М.В., Корост с.р., Васильев р.В., Лаврухин е.В., Гафурова Д.р. (2021). Изучение и анализ современных подходов к построению цифровых моделей керна и методов моделирования многофазной фильтрации в масштабах порового пространства. Георесурсы, 23(2), с. 197–213. doi: 10.18599/grs.2021.2.20Akai T., Bijeljic B., Blunt M.J. (2018). Wetting boundary condition for the color-gradient lattice Boltzmann method: validation with analytical and experimental data. Advances in Water Resources, 116, pp. 56–66. doi: 10.1016/j.advwatres.2018.03.014Закиров Т.р., Храмченков М.Г. (2022). Влияние краевых эффектов смачивания на двухфазные течения жидкостей в цифровой модели неоднородного керна при динамических режимах вытеснения. Георесурсы, 24(1), с. 16–26. doi: 10.18599/grs.2022.1.2Bakhshian S., Hosseini S.A., Shokri N. (2019). Pore-scale characteristics of multiphase flow in heterogeneous porous media using the lattice Boltzmann method. Scientific Reports, 9(1), 3377. doi: 10.1038/s41598-019-39741-xЗлобин А.А., Юшков И.р. (2014). о механизме гидрофобизации поверхности пород-коллекторов нефти и газа. Вестник Пермского университета. Геология, 3. doi: 10.17072/psu.geol.24.68Balashov V., Savenkov E., Khlyupin A., Gerke K. M. (2025). Twophase regularized phase-field density gradient Navier–Stokes based flow model: Tuning for microfluidic and digital core applications. Journal of Computational Physics, 521, 113554. doi: 10.1016/j.jcp.2024.113554Пономарев А.А., Заватский М.Д., Нуруллина Т.с., Кадыров М.А., Галинский К.А., Тугушев о.А. (2021). Применение рентгеновской микротомографии керна в нефтепромысловой геологии. Георесурсы, 23(4), с. 34–43. doi: 10.18599/grs.2021.4.4Chen S., Doolen G. (1998). Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 30, pp. 329–364. doi: 10.1146/annurev.fluid.30.1.329Саптарова З.р., Мамонов А.А., усманов с.А., Лутфуллин А.А., судаков В.А., Шипаева М.с., Шакиров А.А. (2022). Потенциал повышения эффективности заводнения на залежах нефти в терригенных отложениях на месторождениях республики Татарстан на основе низкоминерализованной воды. Георесурсы, 24(4), с. 82–90. doi: 10.18599/grs.2022.4.7Evstigneev N. M., Ryabkov O. I., Gerke K. M. (2023). Stationary Stokes solver for single-phase flow in porous media: A blastingly fast solution based on Algebraic Multigrid Method using GPU. Advances in Water Resources, 171, 104340. doi: 10.1016/j.advwatres.2023.104340Akai T., Bijeljic B., Blunt M.J. (2018). Wetting boundary condition for the color-gradient lattice Boltzmann method: validation with analytical and experimental data. Advances in Water Resources, 116, pp. 56–66. doi: 10.1016/j.advwatres.2018.03.014Gerke 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.2021.2.20Bakhshian S., Hosseini S.A., Shokri N. (2019). Pore-scale characteristics of multiphase flow in heterogeneous porous media using the lattice Boltzmann method. Scientific Reports, 9(1), 3377. doi: 10.1038/s41598-019-39741-xGuo Z., Zheng C., Shi B. (2002). Discrete lattice effects on the forcing term in the lattice Boltzmann method. Physical Review E, 65, 046308. https://doi.org/10.1103/PhysRevE.65.046308Balashov V., Savenkov E., Khlyupin A., Gerke K. M. (2025). Twophase regularized phase-field density gradient Navier–Stokes based flow model: Tuning for microfluidic and digital core applications. Journal of Computational Physics, 521, 113554. doi: 10.1016/j.jcp.2024.113554Guo Z., Zheng C., Shi B. (2008). Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow. Physical Review E, 77, 036707. doi: 10.1103/PhysRevE.77.036707Chen S., Doolen G. (1998). Lattice Boltzmann method for fluid flows. Annual Review of Fluid Mechanics, 30, pp. 329–364. doi: 10.1146/annurev.fluid.30.1.329Holtzman R. (2016). Effects of pore-scale disorder on fluid displacement in partially wettable porous media. Scientific Reports, 6, 36221. doi: 10.1038/srep36221Evstigneev N. M., Ryabkov O. I., Gerke K. M. (2023). Stationary Stokes solver for single-phase flow in porous media: A blastingly fast solution based on Algebraic Multigrid Method using GPU. Advances in Water Resources, 171, 104340. doi: 10.1016/j.advwatres.2023.104340Holtzman R., Segre E. (2015). Wettability stabilizes fluid invasion into porous media via nonlocal, cooperative pore filling. Physical Review Letters, 115(6), 164501. doi: 10.1103/PhysRevLett.115.164501Guo Z., Zheng C., Shi B. (2002). Discrete lattice effects on the forcing term in the lattice Boltzmann method. Physical Review E, 65, 046308. https://doi.org/10.1103/PhysRevE.65.046308Hu R., Lan T., Wei G.-J., Chen Y.-F. (2019). Phase diagram of quasistatic immiscible displacement in disordered porous media. Journal of Fluid Mechanics, 875, pp. 448–475. doi: 10.1017/jfm.2019.504Guo Z., Zheng C., Shi B. (2008). Lattice Boltzmann equation with multiple effective relaxation times for gaseous microscale flow. Physical Review E, 77, 036707. doi: 10.1103/PhysRevE.77.036707Huang H., Huang J.-J., Lu X.-Y. (2014). Study of immiscible displacements in porous media using a color-gradient-based multiphase lattice Boltzmann method. Computers & Fluids, 93, pp. 164–172. doi: 10.1016/j.compfluid.2014.01.025Holtzman R. (2016). Effects of pore-scale disorder on fluid displacement in partially wettable porous media. Scientific Reports, 6, 36221. doi: 10.1038/srep36221Jung M., Brinkmann M., Seemann R., Hiller T., de la Lama M.S., Herminghaus S. (2016). Wettability controls slow immiscible displacement through local interfacial instabilities. Physical Review Fluids, 1, 074202. doi: 10.1103/PhysRevFluids.1.074202Holtzman R., Segre E. (2015). Wettability stabilizes fluid invasion into porous media via nonlocal, cooperative pore filling. Physical Review Letters, 115(6), 164501. doi: 10.1103/PhysRevLett.115.164501Jing W., Fu S., Zhang L., Li A., Ren X., Xu C., Gao Z. (2021). Pore scale experimental and numerical study of surfactant flooding for enhanced oil recovery. Journal of Petroleum Science and Engineering, 196, 107999. doi: 10.1016/j.petrol.2020.107999Hu R., Lan T., Wei G.-J., Chen Y.-F. (2019). Phase diagram of quasistatic immiscible displacement in disordered porous media. Journal of Fluid Mechanics, 875, pp. 448–475. doi: 10.1017/jfm.2019.504Kuznik F., Obrecht C., Rusaouen G., Roux J.-J. (2010). LBM based flow simulation using GPU computing processor. Computers and Mathematics with Applications, 59, pp. 2380–2392. doi: 10.1016/j.camwa.2009.08.052Huang H., Huang J.-J., Lu X.-Y. (2014). Study of immiscible displacements in porous media using a color-gradient-based multiphase lattice Boltzmann method. Computers & Fluids, 93, pp. 164–172. doi: 10.1016/j.compfluid.2014.01.025Lan T., Hu R., Yang Z., Wu D.-S., Chen Y.-F. (2020). Transitions of fluid invasion patterns in porous media. Geophysical Research Letters, 47, e2020GL089682. doi: 10.1029/2020GL089682Jung M., Brinkmann M., Seemann R., Hiller T., de la Lama M.S., Herminghaus S. (2016). Wettability controls slow immiscible displacement through local interfacial instabilities. Physical Review Fluids, 1, 074202. doi: 10.1103/PhysRevFluids.1.074202Leclaire S., Parmigiani A., Malaspinas O., Chopard B., Latt J. (2017). Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media. Physical Review E, 95, 033306. doi: 10.1103/PhysRevE.95.033306Jing W., Fu S., Zhang L., Li A., Ren X., Xu C., Gao Z. (2021). Pore scale experimental and numerical study of surfactant flooding for enhanced oil recovery. Journal of Petroleum Science and Engineering, 196, 107999. doi: 10.1016/j.petrol.2020.107999Liu H., Valocchi A.J., Werth C., Kang Q., Oostrom M. (2014). Pore-scale simulation of liquid CO2 displacement of water using a two-phase lattice Boltzmann model. Advances in Water Resources, 73, pp. 144–158. doi: 10.1016/j.advwatres.2014.07.010Kuznik F., Obrecht C., Rusaouen G., Roux J.-J. (2010). LBM based flow simulation using GPU computing processor. Computers and Mathematics with Applications, 59, pp. 2380–2392. doi: 10.1016/j.camwa.2009.08.052Mahani, H., Berg, S., Ilic, D., Bartels, W.-B., and V. Joekar-Niasar. (2013). Kinetics of the Low Salinity Waterflooding Effect Studied in a Model System (SPE 165255). doi: 10.2118/165255-MSLan T., Hu R., Yang Z., Wu D.-S., Chen Y.-F. (2020). Transitions of fluid invasion patterns in porous media. Geophysical Research Letters, 47, e2020GL089682. doi: 10.1029/2020GL089682Mostaghimi P., Blunt M., Bijeljic B. (2012). Computations of absolute permeability on micro-CT images. Mathematical Geosciences, 45. doi: 10.1007/s11004-012-9431-4Leclaire S., Parmigiani A., Malaspinas O., Chopard B., Latt J. (2017). Generalized three-dimensional lattice Boltzmann color-gradient method for immiscible two-phase pore-scale imbibition and drainage in porous media. Physical Review E, 95, 033306. doi: 10.1103/PhysRevE.95.033306Pan C., Luo L.S., Miller C.T. (2006). An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Computers and Fluids, 35, pp. 898–909. doi: 10.1016/j.compfluid.2005.03.008Liu H., Valocchi A.J., Werth C., Kang Q., Oostrom M. (2014). Pore-scale simulation of liquid CO2 displacement of water using a two-phase lattice Boltzmann model. Advances in Water Resources, 73, pp. 144–158. doi: 10.1016/j.advwatres.2014.07.010Park H., Park Y., Lee Y., Sung W. (2018). Efficiency of enhanced oil recovery by injection of low-salinity water in barium-containing carbonate reservoirs. Petroleum Science, 15, pp. 772–782. doi: 10.1007/s12182-018-0244-zMahani, H., Berg, S., Ilic, D., Bartels, W.-B., and V. Joekar-Niasar. (2013). Kinetics of the Low Salinity Waterflooding Effect Studied in a Model System (SPE 165255). doi: 10.2118/165255-MSPonomarev A.A., Zavatsky M.D., Nurullina T.S., Kadyrov M.A., Galinsky K.A., Tugushev O.A. (2021). Application of core X-ray microtomography in oilfield geology. Georesursy = Georesources, 23(4), pp. 34–43. (In Russ.) https://doi.org/10.18599/grs.2021.4.4Mostaghimi P., Blunt M., Bijeljic B. (2012). Computations of absolute permeability on micro-CT images. Mathematical Geosciences, 45. doi: 10.1007/s11004-012-9431-4Primkulov B.K., Pahlavan A.A., Fu X., Zhao B., MacMinn C.W., Juanes R. (2021). Wettability and Lenormand’s diagram. Journal of Fluid Mechanics, 923, A34. doi: 10.1017/jfm.2021.579Pan C., Luo L.S., Miller C.T. (2006). An evaluation of lattice Boltzmann schemes for porous medium flow simulation. Computers and Fluids, 35, pp. 898–909. doi: 10.1016/j.compfluid.2005.03.008Primkulov B.K., Pahlavan A.A., Fu X.-J., Zhao B.-Z., MacMinn C.W., Juanes R. (2019). Signatures of fluid-fluid displacement in porous media: wettability, patterns and pressures. Journal of Fluid Mechanics, 875, R4. doi: 10.1017/jfm.2019.554Park H., Park Y., Lee Y., Sung W. (2018). Efficiency of enhanced oil recovery by injection of low-salinity water in barium-containing carbonate reservoirs. Petroleum Science, 15, pp. 772–782. doi: 10.1007/s12182-018-0244-zSaptarova Z.R., Mamonov A.A., Usmanov S.A., Lutfullin A.A., Sudakov V.A., Shipaeva M.S., Shakirov A.A. (2022). Potential for improving the efficiency of terrigenous oil deposits waterflooding with the use of low salinity technology at fields of the Tatarstan Republic. Georesursy = Georesources, 24(4), pp. 82–90. (In Russ.) https://doi.org/10.18599/grs.2022.4.7Primkulov B.K., Pahlavan A.A., Fu X., Zhao B., MacMinn C.W., Juanes R. (2021). Wettability and Lenormand’s diagram. Journal of Fluid Mechanics, 923, A34. doi: 10.1017/jfm.2021.579Sedahmed M., Coelho R. C. V. (2024). Wetting and pressure gradient performance in a lattice Boltzmann color gradient model. Physics of Fluids, 36. doi: 10.1063/5.0228835Primkulov B.K., Pahlavan A.A., Fu X.-J., Zhao B.-Z., MacMinn C.W., Juanes R. (2019). Signatures of fluid-fluid displacement in porous media: wettability, patterns and pressures. Journal of Fluid Mechanics, 875, R4. doi: 10.1017/jfm.2019.554Succi S. (2001). The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, UK. https://doi.org/10.1093/oso/9780198503989.001.0001Sedahmed M., Coelho R. C. V. (2024). Wetting and pressure gradient performance in a lattice Boltzmann color gradient model. Physics of Fluids, 36. doi: 10.1063/5.0228835Suijkerbuijk B., Sorop T., Parker A.R., Masalmeh S., Chmuzh I.V., Karpan V., Volokitin Y.E., Skripkin A. (2014). Low salinity waterflooding at West Salym: laboratory experiments and field forecasts. doi: 10.2118/169691-MSSucci S. (2001). The Lattice Boltzmann Equation for Fluid Dynamics and Beyond. Oxford University Press, UK. https://doi.org/10.1093/oso/9780198503989.001.0001Trojer M., Szulczewski M.L., Juanes R. (2015). Stabilizing fluid-fluid displacements in porous media through wettability alteration. Physical Review Applied, 3(5), 054008. doi: 10.1103/PhysRevApplied.3.054008Suijkerbuijk B., Sorop T., Parker A.R., Masalmeh S., Chmuzh I.V., Karpan V., Volokitin Y.E., Skripkin A. (2014). Low salinity waterflooding at West Salym: laboratory experiments and field forecasts. doi: 10.2118/169691-MSTsuji T., Jiang F., Christensen K.T. (2016). Characterization of immiscible fluid displacement processes with various capillary numbers and viscosity ratios in 3D natural sandstone. Advances in Water Resources, 95, pp. 3–15. doi: 10.1016/j.advwatres.2016.03.005Trojer M., Szulczewski M.L., Juanes R. (2015). Stabilizing fluid-fluid displacements in porous media through wettability alteration. Physical Review Applied, 3(5), 054008. doi: 10.1103/PhysRevApplied.3.054008Semenchuk A., Kondratyuk N., Gerke K., Kopanichuk I. (2025). Towards reproducible wetting studies: Automated contact angle determination by molecular simulations. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 137586. doi: 10.1016/j.colsurfa.2025.137586Tsuji T., Jiang F., Christensen K.T. (2016). Characterization of immiscible fluid displacement processes with various capillary numbers and viscosity ratios in 3D natural sandstone. Advances in Water Resources, 95, pp. 3–15. doi: 10.1016/j.advwatres.2016.03.005Washburn E.W. (1921). The dynamics of capillary flow. Physical Review, 17(3), pp. 273–283. https://doi.org/10.1103/PhysRev.17.273Semenchuk A., Kondratyuk N., Gerke K., Kopanichuk I. (2025). Towards reproducible wetting studies: Automated contact angle determination by molecular simulations. Colloids and Surfaces A: Physicochemical and Engineering Aspects, 137586. doi: 10.1016/j.colsurfa.2025.137586Xiao L., Zhu G., Zhang L., Yao J., Sun H. (2021). Effects of pore-size disorder and wettability on forced imbibition in porous media. Journal of Petroleum Science and Engineering, 201, 108485. doi: 10.1016/j.petrol.2021.108485Washburn E.W. (1921). The dynamics of capillary flow. Physical Review, 17(3), pp. 273–283. https://doi.org/10.1103/PhysRev.17.273Xu Z., Liu H., Valocchi A.J. (2017). Lattice Boltzmann simulation of immiscible two-phase flow with capillary valve effect in porous media. Water Resources Research, 53(5), pp. 3770–3790. doi: 10.1002/2017WR020373Xiao L., Zhu G., Zhang L., Yao J., Sun H. (2021). Effects of pore-size disorder and wettability on forced imbibition in porous media. Journal of Petroleum Science and Engineering, 201, 108485. doi: 10.1016/j.petrol.2021.108485Zakirov T.R., Khayuzkin A.S., Kolchugin A.N., Malevin I.V. (2025). Phase diagram of invasion patterns in “capillary number, wetting angle, disorder” coordinates: A lattice Boltzmann study. Advances in Water Resources, 195, 104861. doi: 10.1016/j.advwatres.2024.104861Xu Z., Liu H., Valocchi A.J. (2017). Lattice Boltzmann simulation of immiscible two-phase flow with capillary valve effect in porous media. Water Resources Research, 53(5), pp. 3770–3790. doi: 10.1002/2017WR020373Zakirov T.R., Khramchenkov M.G. (2023). Representative elementary volumes for various characteristics of two-phase flows in porous media: a statistical approach. Geoenergy Science and Engineering, 229, 212104. doi: 10.1016/j.geoen.2023.212104Zakirov T.R., Khayuzkin A.S., Kolchugin A.N., Malevin I.V. (2025). Phase diagram of invasion patterns in “capillary number, wetting angle, disorder” coordinates: A lattice Boltzmann study. Advances in Water Resources, 195, 104861. doi: 10.1016/j.advwatres.2024.104861Zakirov T.R., Khramchenkov M.G. (2022). Investigation of the wetting effects on two-phase fluid flows in a heterogeneous digital core under dynamic conditions. Georesursy = Georesources, 24(1), pp. 16–26. (In Russ.) https://doi.org/10.18599/grs.2022.1.2Zakirov T.R., Khramchenkov M.G. (2023). Representative elementary volumes for various characteristics of two-phase flows in porous media: a statistical approach. Geoenergy Science and Engineering, 229, 212104. doi: 10.1016/j.geoen.2023.212104Zakirov T.R., Zhuchkova O.S., Khramchenkov M.G. (2024). Mathematical model for dynamic adsorption with immiscible multiphase flows in three-dimensional porous media. Lobachevskii Journal of Mathematics, 45, pp. 888–898. doi: 10.1134/S1995080224600134Zakirov T.R., Zhuchkova O.S., Khramchenkov M.G. (2024). Mathematical model for dynamic adsorption with immiscible multiphase flows in three-dimensional porous media. Lobachevskii Journal of Mathematics, 45, pp. 888–898. doi: 10.1134/S1995080224600134Zlobin A.A., Yushkov I.R. (2014). On the mechanism of hydrophobization of the surface of oil and gas reservoir rocks. Bulletin of Perm University, 3(24). (In Russ.) https://doi.org/10.17072/psu.geol.24.68Zou Q., He X. (1997). On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Physics of Fluids, 9, pp. 1591–1598. doi: 10.1063/1.869307Zou Q., He X. (1997). On pressure and velocity boundary conditions for the lattice Boltzmann BGK model. Physics of Fluids, 9, pp. 1591–1598. doi: 10.1063/1.869307

The authors declare that there are no conflicts of interest present.