Modares Mechanical Engineering

Modares Mechanical Engineering

Numerical Investigation of Miscible Viscous Fingering Instability in Darcian and Non-Darcian Porous Media

Document Type : Original Research

Authors
H. Miri 1
B. Zare vamarzani 2
H. Saffari 1
S.M. Hosseinalipoor 1
arash nemati 1
1 School of Mechanical Engineering Iran University of Science and Technology, Tehran, Iran
2 School of Mechanical Engineering,Iran University of Science and Technology, Tehran, Iran
Abstract
In this paper, miscible viscous fingering instability in a Darcy and non-Darcy porous media was studied through numerical solution and the formation and growth of finger patterns were discussed. According to the porosity coefficient, the media can be divided into Darcy and non-Darcy categories. Also, flow velocity and fluid used (Newtonian or non-Newtonian) are the factors that limit the use of Darcy’s relation. In this simulation, against most previous studies which had been used the two-phase Darcy’s structural equation to approximate examination of instabilities, a two-dimensional model was used. This model was based on coupling flow equations in porous media (Darcy or Brinkman) and transport of diluted species. The effects of increasing injection rates and viscosity changes were investigated based on Peclet non-dimensional number and viscous ratio on instabilities. Besides, a comparison was done between the results of Darcy’s and Brinkman’s solution at different porosity coefficient and viscosity ratio. Image processing techniques were performed to measure the break through time, perimeter of the interface, fractal dimension and sweep efficiency. With increasing viscosity in Darcy and Brinkman solution, the perimeter of the interface and fractal dimension were increased and more complex fingers generated. As a result, the sweep efficiency of the porous media reduces. In addition, the growth of the media porosity led to sweep efficiency. Finally, it was observed that with increasing injection velocity in Brinkman’s solution, the fingers complexity and perimeter of the interface increased and sweep efficiency decreased.
Keywords
Viscous fingering
Brinkman Equation
Darcy Low
Miscible
Numerical solution

Subjects

Malhotra S, Sharma MM, Lehman ER. Experimental study of the growth of mixing zone in miscible viscous fingering. Physics of Fluids. 2015;27(1):014105. [Link] [DOI:10.1063/1.4905581]
Peaceman DW, Rachford Jr HH. Numerical calculation of multidimensional miscible displacement. Society of Petroleum Engineers Journal. 1962;2(4):327-339. [Link] [DOI:10.2118/471-PA]
Vishnudas R, Chaudhuri A. A comprehensive numerical study of immiscible and miscible viscous fingers during chemical enhanced oil recovery. Fuel. 2017;194:480-490. [Link] [DOI:10.1016/j.fuel.2017.01.014]
Cueto‐Felgueroso L, Juanes R. A phase field model of unsaturated flow. Water Resources Research. 2009;45(10): [Link] [DOI:10.1029/2009WR007945]
Dicarlo D, Blunt MJ. Determination of finger shape using the dynamic capillary pressure. Water Resources Research. 2000;36(9):2781-2785. [Link] [DOI:10.1029/2000WR900184]
Mishra M, Martin M, De Wit A. Miscible viscous fingering with linear adsorption on the porous matrix. Physics of Fluids. 2007;19(7):073101. [Link] [DOI:10.1063/1.2743610]
Riaz A, Pankiewitz C, Meiburg E. Linear stability of radial displacements in porous media: influence of velocity-induced dispersion and concentration-dependent diffusion. Physics of Fluids. 2004;16(10):3592-3598. [Link] [DOI:10.1063/1.1775431]
Waggoner JR, Castillo JL, Lake LW. Simulation of EOR processes in stochastically generated permeable media. SPE Formation Evaluation. 1992;7(2):173-180. [Link] [DOI:10.2118/21237-PA]
Zimmerman WB, Homsy GM. Three‐dimensional viscous fingering: A numerical study. Physics of Fluids A: Fluid Dynamics. 1992;4(9):1901-1914. [Link] [DOI:10.1063/1.858361]
Moissis DE, Miller CA, Wheeler MF. A parametric study of viscous fingering in miscible displacement by numerical simulation. Numerical Simulation in Oil Recovery. 1988;11:227-247. [Link] [DOI:10.1007/978-1-4684-6352-1_15]
Babchin AJ, Brailovsky I, Gordon P, Sivashinsky G. Fingering instability in immiscible displacement. Physical Review E. 2008;77(2):026301. [Link] [DOI:10.1103/PhysRevE.77.026301]
Norouzi M, Shoghi MR. A numerical study on miscible viscous fingering instability in anisotropic porous media. Physics of Fluids. 2014;26(8):084102. [Link] [DOI:10.1063/1.4891228]
Nield DA, Bejan A. Convection in porous media. New York: Springer; 2006. [Link]
Durlofsky L, Brady JF. Analysis of the Brinkman equation as a model for flow in porous media. The Physics of Fluids. 1987;30(11):3329-3341. [Link] [DOI:10.1063/1.866465]
Kanschat G, Lazarov R, Mao Y. Geometric multigrid for darcy and brinkman models of flows in highly heterogeneous porous media: A numerical study. Journal of Computational and Applied Mathematics. 2017;310:174-185. [Link] [DOI:10.1016/j.cam.2016.05.016]
Booth R. Miscible flow through porous media [dissertation]. Oxford: University of Oxford; 2008. [Link]
Hill RJ, Koch DL. Moderate-Reynolds-number flow in a wall-bounded porous medium. Journal of Fluid Mechanics. 2002;453:315-344. [Link] [DOI:10.1017/S002211200100684X]
Joseph DD, Nield DA, Papanicolaou G. Nonlinear equation governing flow in a saturated porous medium. Water Resources Research. 1982;18(4):1049-1052. [Link] [DOI:10.1029/WR018i004p01049]
Guo P, Weinstein A, Weinbaum S. A hydrodynamic mechanosensory hypothesis for brush border microvilli. American Journal of Physiology-Renal Physiology. 2000;279(4):698-712. [Link] [DOI:10.1152/ajprenal.2000.279.4.F698]
Feng J, Weinbaum S. Lubrication theory in highly compressible porous media: The mechanics of skiing, from red cells to humans. Journal of Fluid Mechanics. 2000;422:281-317. [Link] [DOI:10.1017/S0022112000001725]
Tan CT, Homsy GM. Stability of miscible displacements in porous media: Rectilinear flow. The Physics of Fluids. 1986;29(11):3549-3556. [Link] [DOI:10.1063/1.865832]
De Wit A, Bertho Y, Martin M. Viscous fingering of miscible slices. Physics of Fluids. 2005;17(5):054114. [Link] [DOI:10.1063/1.1909188]
Homsy GM. Viscous fingering in porous media. Annual Review of Fluid Mechanics. 2003;19(1):271-311. [Link] [DOI:10.1146/annurev.fl.19.010187.001415]
Pramanik S, Mishra M. Nonlinear simulations of miscible viscous fingering with gradient stresses in porous media. Chemical Engineering Science. 2015;122:523-532. [Link] [DOI:10.1016/j.ces.2014.10.019]
Goyal N, Meiburg E. Miscible displacements in hele-shaw cells: Two-dimensional base states and their linear stability. Journal of Fluid Mechanics. 2006;558:329-355. [Link] [DOI:10.1017/S0022112006009992]
Wolf AV. Aqueous solutions and body fluids. New York: Hoeber Medical Division, Harper & Row; 1966. [Link]
Hosseinalipoor SM, Nemati A, Zare Vamerzani B, Saffari H. Experimental study of finger behavior due to miscible viscous and gravity contrast in a porous model. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects. 2019;42(19):2434-2447. [Link] [DOI:10.1080/15567036.2019.1607943]
Chen Z. Reservoir simulation: Mathematical techniques in oil recovery. Philadelphia: Society for Industrial and Applied Mathematics; 2007. [Link] [DOI:10.1137/1.9780898717075]
Modares Mechanical Engineering
Volume 20, Issue 10
October 2020
Pages 2471-2482