kaz29Вестник Казахстанско-Британского технического университетаHerald of the Kazakh-British Technical University1998-66882959-8109Казахстанско-Британский Технический Университет10.55452/1998-6688-2021-18-2-6-11kaz29-75Research ArticleНЕФТЕГАЗОВАЯ ИНЖЕНЕРИЯ И ГЕОЛОГИЯOIL AND GAS ENGINEERING, GEOLOGYПОРОМАСШТАБНОЕ МОДЕЛИРОВАНИЕ ПОТОКА ЖИДКОСТИ В ПРОНИЦАЕМЫХ СФЕРАХ С ИСПОЛЬЗОВАНИЕМ ПРОЕКЦИОННОГО МЕТОДА ДЛЯ НЕСЖИМАЕМЫХ УРАВНЕНИЙ НАВЬЕ-СТОКСАPORE-SCALE MODELLING OF FLUID FLOW IN PENETRABLE SPHERES USING THE PROJECTION METHOD FOR INCOMPRESSIBLE NAVIER-STOKES EQUATIONShttps://orcid.org/0000-0001-7668-8911АкашеваЖ. К.AkashevaZh. K.

050000, Алматы

Akasheva Zhibek Kairatovna - Deputy Head of the Research Laboratory «Computational Modeling and Information Technologies»

050000, Almaty

zhibek_akasheva@mail.ruhttps://orcid.org/0000-0002-4389-4097КудайкуловА. А.KudaikulovA. A.

050000, Алматы

Kudaikulov Aziz Anarbayevich - PhD, Professor

050000, Almaty

aziz.kudaikulov@gmail.comhttps://orcid.org/0000-0002-0368-0131АсылбековБ. К.AssilbekovB. K.

050000, Алматы

Assilbekov Bakytzhan Kalzhanovich – PhD, Head of the Research Laboratory «Computational Modeling and Information Technologies»

050000, Almaty

assilbekov@mail.ruhttps://orcid.org/0000-0001-8936-3921БолысбекД. А.BolysbekD. A.

050000, Алматы

Bolysbek Darezhat Abilseyituly - Researcher at the Research Laboratory «Computational Modeling and Information Technologies»

050000, Almaty

bolysbek.darezhat@gmail.comКазахский Национальный исследовательский технический университет имени К. И. СатпаеваКазахстанSatbayev UniversityKazakhstanКазахский Национальный исследовательский технический университет имени К. И. Сатпаева; Казахский Национальный университет имени аль-ФарабиКазахстанSatbayev University; Al-Farabi Kazakh National UniversityKazakhstan202104112021182611Copyright © Акашева Ж.К., Кудайкулов А.А., Асылбеков Б.К., Болысбек Д.А., 20212021Акашева Ж.К., Кудайкулов А.А., Асылбеков Б.К., Болысбек Д.А.Akasheva Z.K., Kudaikulov A.A., Assilbekov B.K., Bolysbek D.A.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://vestnik.kbtu.edu.kz/jour/article/view/75

Прямое численное моделирование (DNS) - эффективный и полезный инструмент для изучения двухфазного течения жидкости. В данной статье применяется проекционный метод с использованием шахматной сетки для решения уравнений Навье-Стокса для несжимаемой жидкости в нерегулярных областях на поромасштабном уровне (нерегулярная граница представлена функцией установки уровня). Проницаемость пористой среды, которая была построена путем случайного расположения проницаемых сфер равного радиуса, была рассчитана численно и подтверждена путем сравнения с теоретическими оценками проницаемости, основанными на численном решении уравнения решетки-Больцмана в нерегулярных областях в предыдущих работах. Все численные расчеты проводились с использованием симулятора PARIS.

The direct numerical simulation (DNS) is an effective and useful tool in the two-phase fluid flow studying. The projection method on the staggered grid was applied in this paper to solve the incompressible Navier-Stokes equations in irregular domains at the pore-scale level (irregular boundary is presented by its level-set function). The permeability of porous medium which was constructed by the random positioning of penetrable spheres of equal radii were numerically calculated and validated by comparing with theoretical estimations of permeability based on the numerical solution of the lattice-Boltzmann equation in irregular domains in previous works. All numerical calculations were performed using PARIS simulator.

уравнения Навье-Стоксапроекционный методпористая средапроницаемостьпористостьNavier-Stokes equationsprojection methodporous mediumpermeabilityporosityThis research is funded by the Science Committee of the Ministry of Education and Science of the Republic of Kazakhstan (Grant No. AP08052055), which is gratefully acknowledged by the authors.ReferencesJ. Koplik. Creeping flow in two-dimensional networks. J. Fluid Mech., 1982, vol. 119, pp. 219-247.J. Koplik. Creeping flow in two-dimensional networks. J. Fluid Mech., 1982, vol. 119, pp. 219-247.H. J. Vogel, J. Tolke, V.P. Schulz, M. Krafczyk and K. Roth. Comparison of a Lattice-Boltzmann Model, a Full-Morphology Model, and a Pore Network Model for Determining Capillary Pressure-Saturation Relationships. Vadose Zone J., 2005, vol. 4, pp. 380-388.H. J. Vogel, J. Tolke, V.P. Schulz, M. Krafczyk and K. Roth. 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The authors declare that there are no conflicts of interest present.