georesГеоресурсыGeoresources1608-50431608-5078Georesursy LLC10.18599/grs.2026.1.6geores-510Research ArticleСТАТЬИRESEARCH ARTICLESВычисление средней скорости потока флюида в пористой среде с помощью функционалов МинковскогоMean Velocity Calculation for Single-Phase Flow in Porous Media Based on Minkowski Functionalshttps://orcid.org/0009-0009-6996-141XЧернявскийМ. В.ChernyavskiyM. V.

Михаил Валерьевич Чернявский – аспирант, кафедра математического моделирования и информатики, физический факультет

119991, ГсП-1, Москва, Ленинские горы, д. 1, стр. 2

Mikhail V. Chernyavskiy – PhD student, Faculty of Physics

1-2 Leninskie Gory, Moscow, 119991

chernjavskiy.mv15@physics.msu.ruhttps://orcid.org/0009-0008-5916-8867ТимошенкоВ. В.TimoshenkoV. V.

Василий Витальевич Тимошенко – аспирант, кафедра физико-математических методов управления, физический факультет

119991, ГсП-1, Москва, Ленинские горы, д. 1, стр. 2

Vasilii V. Timoshenko – PhD student, Faculty of Physics

1-2 Leninskie Gory, Moscow, 119991

timoshenko.vv19@physics.msu.ruhttps://orcid.org/0000-0002-2467-5665МорковкинА. И.MorkovkinA. I.

Андрей Игоревич Морковкин – инженер, Центр науки и технологий добычи углеводородов

121205, Москва, территория Инновационного Центра «Сколково», Большой бульвар, д. 30, стр.1

Andrey I. Morkovkin – Engineer, Center for Hydrocarbon Recovery

30, bld. 1, Bolshoy Boulevard, Moscow, 121205

a.morkovkin@skoltech.ruhttps://orcid.org/0000-0003-0015-2920ГришинП. А.GrishinP. A.

Павел Андреевич Гришин – заместитель директора Центра науки и технологий добычи углеводородов

121205, Москва, территория Инновационного Центра «Сколково», Большой бульвар, д. 30, стр.1

Pavel A. Grishin – Deputy Director for laboratory facilities, Center for Hydrocarbon Recovery

30, bld. 1, Bolshoy Boulevard, Moscow, 121205

p.grishin@skoltech.ruhttps://orcid.org/0000-0002-2229-1158ФедотовА. Б.FedotovA. B.

Андрей Борисович Федотов – аспирант, кафедра математического моделирования и информатики, физический факультет

119991, ГсП-1, Москва, Ленинские горы, д. 1, стр. 2

Andrey B. Fedotov – PhD student, Faculty of Physics

1-2 Leninskie Gory, Moscow, 119991

ab.fedotov@physics.msu.ruГрачевЕ. А.GrachevE. A.

Евгений Александрович Грачев – кандидат тех. наук, доцент, кафедра математического моделирования и информатики, физический факультет

119991, ГсП-1, Москва, Ленинские горы, д. 1, стр. 2

Eugene A. Grachev – Cand. Sci. (Technology), Associate Professor, Faculty of Physics

1-2 Leninskie Gory, Moscow, 119991

grachevea@gmail.comМосковский государственный университет имени М.В. ЛомоносоваРоссияLomonosov Moscow State UniversityRussian FederationСколковский институт науки и технологийРоссияSkolkovo Institute of Science and TechnologyRussian Federation202627032026281318Copyright © Чернявский М.В., Тимошенко В.В., Морковкин А.И., Гришин П.А., Федотов А.Б., Грачев Е.А., 20262026Чернявский М.В., Тимошенко В.В., Морковкин А.И., Гришин П.А., Федотов А.Б., Грачев Е.А.Chernyavskiy M.V., Timoshenko V.V., Morkovkin A.I., Grishin P.A., Fedotov A.B., Grachev E.A.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/510

Динамика флюидов в сложных неупорядоченных средах является важным предметом изучения в таких прикладных областях, как материаловедение, почвоведение, химическая инженерия, а также разработка месторождений нефти, газа и подземных вод. Методы интегральной геометрии представляют собой полезный инструмент для исследования сложных сред. В настоящей работе показано, что для всякого заданного типа (класса) пористых сред можно оценивать средние значения скорости потока флюида в каждом слое образца с помощью геометрических параметров (функционалов Минковского) порового пространства в данном слое. Такой подход позволит избежать проведения ресурсозатратных фильтрационных экспериментов и численного моделирования потоков для осуществления первичного анализа фильтрационных свойств образцов. Представлен метод построения моделей для оценки распределения средних значений скорости однофазного потока в образцах пористых сред с помощью их геометрических параметров, вычисляемых из бинаризованных изображений. образцы из газовых резервуаров выбраны в качестве примеров пористой среды, c учетом растущей значимости данного типа резервуаров, вызванной глобальным переходом на природный газ как ключевой источник энергии. Проведено прямое сравнение результатов расчетных средних значений скоростей, полученных из моделей, со средними значениями, полученными из численного моделирования потоков в промышленных симуляторах. результаты вычислений по построенным моделям с относительно высокой точностью воспроизводят тренды распределений средних скоростей, полученных из численного моделирования, что позволяет говорить о достаточно высокой степени статистической значимости построенных моделей. Это предоставляет полезный инструмент для быстрых и устойчивых вычислений для целей первичного анализа образцов в задачах моделирования и ремасштабирования (скейлинга).

Studies of flow dynamics in complex disordered media are very important in many practical areas, such as materials science, soil science, groundwater engineering, chemical engineering, and especially petroleum and gas engineering. Integral geometry methods are a useful tool for studying complex media. In this work, it is shown that, for a given porous media class, the by-layer mean flow velocity for any sample within the same class can be characterized as a function of Minkowski functionals, allowing to avoid costly natural core flood experiments or numerical simulation for screening purposes. This paper proposes the flow characterization method based on integral geometry. This method allows for obtaining the single-phase fluid flow velocity characterization models across a wide range of porous media classes for a quick estimation of the mean by-layer velocity distribution purely by extracting the geometrical measures from binary sample images. Samples from gas reservoirs are chosen as the relevant porous media examples, with regard to the growing importance of this type of reservoir caused by the global shift towards natural gas as a key energy source. Direct comparison with numerical simulation based on Stokes equation was made with commercial class software. The results demonstrate that the proposed algorithm has a relatively high degree of statistical significance and closely captures mean velocity trends. That provides a useful tool for quick, robust modelling for screening, agile calculations, and upscaling tasks.

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