NUMERICAL ANALYSIS OF VISCOUS FINGERING INSTABILITY DUE TO MISCIBLE DISPLACEMENT
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MERICAL ANALYSIS OF VISCOUS FINGERING INSTABILITY DUE TO MISCIBLE DISPLACEMENT A. Nemati, H. Saffari∗ , B. Z. Vamerzani,
UDC 532.5
R. Azizi, S. M. Hosseinalipoor, and H. Miri
Abstract: In this study, miscible viscous fingering instability is examined numerically by using the two-phase Darcy’s law and transport equations. The effects of the viscosity ratio, anisotropic permeability, and porosity on instabilities are investigated. The finger patterns and their splitting and spreading in the domain are discussed. An image processing algorithm is applied to concentration contours to quantify instability parameters, such as the breakthrough time, efficiency, and fractal dimension. It is revealed that more complex fingers are obtained as the viscosity ratio increases, while the efficiency and the breakthrough time decrease. It is demonstrated that high permeability perpendicular to the flow direction leads to instability intensification and to an increase in the fractal dimension, whereas changing the porosity does not have any considerable impact on viscous fingering instability. Keywords: viscous fingering instability, two-phase Darcy’s law, porous media, miscible flow displacement. DOI: 10.1134/S0021894420040069 INTRODUCTION The instability occurring at the interface of two fluids when the fluid of lower viscosity displaces a more viscous fluid in a porous medium is called the viscous fingering instability or the Saffman–Taylor instability [1]. This phenomenon can appear in various processes, such as filtration, hydrology, enhanced oil recovery, and chromatography. Viscous fingering instability can be seen in both miscible and immiscible fluids. Miscible displacement in which viscosity strongly depends on the concentration of the solute has been an interesting subject to study for the past decades due to its numerous applications [2, 3]. Hill [4] studied viscous fingering instability in miscible fluids for the first time, based on a force due to the pressure difference and turbulence at the interface of two fluids. Peaceman and Rachford [5] described miscible displacement by a system of partial differential equations, taking into account the effects of gravity, permeability, diffusion, and viscosity. The results of the numerical simulation of Zimmerman and Homsy [6] on nonlinear viscous fingering miscible displacements in a 2D medium demonstrated that interactions between fingers are independent of the concentration field and are influenced by the pressure field. Waggoner et al. [7] performed a numerical simulation of displacements with unit mobility and demonstrated the relation between the mobility and flow patterns in a heterogeneous permeable porous medium.
School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran; [email protected], ∗ saff[email protected]; b [email protected]; [email protected]; [email protected]; [email protected]. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 61, No. 4, pp. 46–53, July–August, 2020. Original article submitted September 20, 2019; revision s
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