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Lattice Boltzmann Simulations of the Interface Dynamics During Two-Phase Flow in Porous Media

  • Zakirov, T. R.1, 2
  • Khramchenkov, M. G.1, 3
  • Galeev, A. A.1
  • 1 Institute of Geology and Petroleum Technologies, Kazan Federal University, Kazan, 420008, Russia , Kazan (Russia)
  • 2 Institute of Mechanics and Engineering, FRC Kazan Scientific Center, Russian Academy of Sciences, Kazan, 420111, Russia , Kazan (Russia)
  • 3 Kazan Branch of Joint Supercomputer Center, Scientific Research Institute of System Analysis, Russian Academy of Sciences, Kazan, 420111, Russia , Kazan (Russia)
Published Article
Lobachevskii Journal of Mathematics
Pleiades Publishing
Publication Date
Jan 01, 2021
DOI: 10.1134/S1995080221010297
Springer Nature


AbstractThis paper systematically investigates the impact of porous media disorder and its coupling with flow rates, favorable and unfavorable viscosity ratios, as well as surface tensions on the dynamics of interfaces development during two-phase drainage flow. A special attention is paid to establishing relationship between the dynamics of fluid–fluid and fluid–solid interfacial lengths, the pore selectivity and the displacement efficiency using imaging of fluids distribution in porous media. As samples of study, we used artificially generated models of porous media with different disorder parameters and with two-types of pore-channels systems "— hexagonal and square. In our methodology, the disorder defines the range of grain size distribution and is applied to control the pore size range. For two-phase flow simulation, the lattice Boltzmann equations and the color-gradient model are applied. It was established the linear relationships between fluid–fluid and fluid–solid interfacial length and saturation of the invaded fluid. During numerical simulations at different disorders, the lack of disorder effect on the fluid–fluid interface dynamics and negative disorder impact on the fluid–solid interface dynamics was found. When varying the flow parameters, it was identified that the increase in the fluid–fluid interface dynamics is accompanied by a decrease in the fluid–solid interface dynamics. For all displacement mechanisms considered in this paper, except capillary fingering, an inverse relationship between pore selectivity and pore number, involved in displacement, was detected. We found a shift of pore selectivity towards higher values with increasing disorder which negatively impacts on the displacement efficiency. In capillary fingering regime, a strong tendency to minimize fluid–fluid interfacial length with surface tension explains the lack of relationship between pore selectivity and pore number which leads to bad predictable displacement efficiency in this regime.

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