TY - JOUR

T1 - Velocity of viscous fingers in miscible displacement: Intermediate concentration

AU - Bakharev, F.

AU - Enin, A.

AU - Matveenko, S.

AU - Pavlov, D.

AU - Petrova, Y.

AU - Rastegaev, N.

AU - Tikhomirov, S.

N1 - Export Date: 19 October 2024 Адрес для корреспонденции: Tikhomirov, S.; Pontifícia Universidade Católica do Rio de Janeiro, 225, Rio de Janeiro, RJ, Brazil; эл. почта: sergey.tikhomirov@gmail.com Сведения о финансировании: Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, CAPES Сведения о финансировании: E-26/210.702/2024 Сведения о финансировании: Ministry of Education and Science of the Russian Federation, Minobrnauka, 075-15-2022-287 Сведения о финансировании: Conselho Nacional de Desenvolvimento Científico e Tecnológico, CNPq, E-26/210.700/2024, 295287, 406460/2023-0, 404123/2023-6, APQ1 E-26/210.700/2024 Сведения о финансировании: Fundação Carlos Chagas Filho de Amparo à Pesquisa do Estado do Rio de Janeiro, FAPERJ, APQ1 E-26/210.702/2024, 295291 Текст о финансировании 1: The authors are extremely grateful to anonymous reviewers for their constructive suggestions and comments, which allowed to improve exposition of the manuscript. The research of Fedor Bakharev, Aleksandr Enin, Sergey Matveenko, Nikita Rastegaev, and Dmitry Pavlov was performed at the Saint-Petersburg Leonhard Euler International Mathematical Institute and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-287). The research of Sergey Matveenko and Dmitry Pavlov was supported by \u201CNative towns\u201D, a social investment program of PJSC \u201CGazprom Neft\u201D. The research of Sergey Tikhomirov and Yulia Petrova were supported by Projeto Paz and Coordena\u00E7\u00E3o de Aperfei\u00E7oamento de Pessoal de N\u00EDvel Superior - Brasil (CAPES) - Finance Code 001. Sergey Tikhomirov is additionally supported by FAPERJ APQ1, Brazil E-26/210.702/2024 (295291) and CNPq, Brazil grant 404123/2023-6. Yulia Petrova is additionally supported by FAPERJ APQ1, Brazil E-26/210.700/2024 (295287) and CNPq, Brazil grant 406460/2023-0. Figs. 1, 3, 6, 7, 8 were obtained with Paraview [39], an open-source data visualization tool. Figs. 2, 5, 9, 11, 12 were obtained with Seaborn [40], an open-source data visualization tool. Текст о финансировании 2: The research of Fedor Bakharev, Aleksandr Enin, Sergey Matveenko, Nikita Rastegaev, and Dmitry Pavlov was performed at the Saint-Petersburg Leonhard Euler International Mathematical Institute and supported by the Ministry of Science and Higher Education of the Russian Federation (agreement no. 075-15-2022-287 ). Текст о финансировании 3: The research of Sergey Tikhomirov and Yulia Petrova were supported by Projeto Paz and Coordena\u00E7\u00E3o de Aperfei\u00E7oamento de Pessoal de N\u00EDvel Superior - Brasil (CAPES) - Finance Code 001. Sergey Tikhomirov is additionally supported by FAPERJ APQ1 E-26/210.702/2024 (295291) and CNPq grant 404123/2023-6 . Yulia Petrova is additionally supported by FAPERJ APQ1 E-26/210.700/2024 (295287) and CNPq grant 406460/2023-0 .

PY - 2024/12/1

Y1 - 2024/12/1

N2 - We investigate one-phase flow in porous medium corresponding to a miscible displacement process in which the viscosity of the injected fluid is smaller than the viscosity in the reservoir fluid, which frequently leads to the formation of a mixing zone characterized by thin fingers. The mixing zone grows in time due to the difference in speed between its leading and trailing edges. The transverse flow equilibrium (TFE) model provides estimates of these speeds. We propose an enhancement for the TFE estimates, and provide its theoretical justification. It is based on the assumption that an intermediate concentration exists near the tip of the finger, which allows to reduce the integration interval in the speed estimate. Numerical simulations were conducted that corroborate the new estimates within the computational fluid dynamics model. The refined estimates offer greater accuracy than those provided by the original TFE model. © 2024 Elsevier B.V.

AB - We investigate one-phase flow in porous medium corresponding to a miscible displacement process in which the viscosity of the injected fluid is smaller than the viscosity in the reservoir fluid, which frequently leads to the formation of a mixing zone characterized by thin fingers. The mixing zone grows in time due to the difference in speed between its leading and trailing edges. The transverse flow equilibrium (TFE) model provides estimates of these speeds. We propose an enhancement for the TFE estimates, and provide its theoretical justification. It is based on the assumption that an intermediate concentration exists near the tip of the finger, which allows to reduce the integration interval in the speed estimate. Numerical simulations were conducted that corroborate the new estimates within the computational fluid dynamics model. The refined estimates offer greater accuracy than those provided by the original TFE model. © 2024 Elsevier B.V.

KW - Miscible displacement

KW - Porous media

KW - Transverse flow equilibrium

KW - Viscous fingers

KW - Computational fluid dynamics

KW - Mixing

KW - Two phase flow

KW - Viscosity

KW - Displacement process

KW - Equilibrium modelling

KW - Flows in porous media

KW - Mixing zones

KW - Phase flow

KW - Porous medium

KW - Transverse flow

KW - Porous materials

UR - https://www.mendeley.com/catalogue/a83d73a0-6a57-309a-9f20-3c7f97470f2e/

U2 - 10.1016/j.cam.2024.116107

DO - 10.1016/j.cam.2024.116107

M3 - статья

VL - 451

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

ER -