Experimental study of finger behavior due to miscible viscous and gravity contrast in a porous model

References

• Buka, A., and L. Kramer. 2012. Pattern formation in liquid crystals. New York, NY: Springer Science & Business Media.
   Google Scholar
• Chandrasekhar, S. 1961. Hydrodynamics and hydrodynamic stability. Oxford: Clarendon.
   Google Scholar
• Chatenever, A., and J. C. Calhoun. 1952. Visual examinations of fluid behavior in porous. Journal of Petroleum Technology 4 (06):149–56. doi:10.2118/135-G.
   Google Scholar
• Chen, Y. F., S. Fang, D. S. Wu, and R. Hu. 2017. Visualizing and quantifying the crossover from capillary fingering to viscous fingering in a rough fracture. Water Resources Research 53 (9):7756–72. doi:10.1002/2017WR021051.
   Web of Science ®Google Scholar
• Christie, M. A., A. D. W. Jones, and A. H. Muggeridge. 1990. Comparison between laboratory experiments and detailed simulations of unstable miscible displacement influenced by gravity. In North Sea Oil and Gas Reservoirs—II, edited by A. T. Buller, E. Berg, O. Hjelmeland, J. Kleppe, O. Torsæter and J. O. Aasen, 245–50. doi:10.1007/978-94-009-0791-1_20
   Google Scholar
• Enjamoori, S., J. Azaiez, and B. Maini. 2010. Viscous fingering instability in the displacements of oil in water emulsions. HEFAT 2010.
   Google Scholar
• Farzaneh, S. A., R. Kharrat, and M. H. Ghazanfari. 2008. Experimental investigation of factors affecting miscible two-phase flow in fractured and non-fractured micromodels. ASME Sixth International Conference on Nanochannels, Microchannels and Minichannels, Darmstadt, Germany, June 23–25.
   Google Scholar
• Ferer, M., C. Ji, G. S. Bromhal, J. Cook, G. Ahmadi, and D. H. Smith. 2004. Crossover from capillary fingering to viscous fingering for immiscible unstable flow: Experiment and modeling. Physical Review E 70 (1):016303. doi:10.1103/PhysRevE.70.016303.
   Web of Science ®Google Scholar
• Gharbi, R. B. C., F. Qasem, and E. J. Peters. 2001. A relationship between the fractal dimension and scaling groups of unstable miscible displacements. Experiments in Fluids 31 (4):357–66. doi:10.1007/s003480100278.
   Web of Science ®Google Scholar
• Gopalakrishnan, S. S., J. Carballido-Landeira, A. De Wit, and B. Knaepen. 2017. Relative role of convective and diffusive mixing in the miscible Rayleigh-Taylor instability in porous media. Physical Review Fluids 2 (1):012501. doi:10.1103/PhysRevFluids.2.012501.
   Web of Science ®Google Scholar
• Goyal, N., and E. Meiburg. 2004. Unstable density stratification of miscible fluids in a vertical Hele-Shaw cell: Influence of variable viscosity on the linear stability. Journal of Fluid Mechanics 516:211–38. doi:10.1017/S002211200400068.
   Web of Science ®Google Scholar
• Homsy, G. M. 1987. Viscous fingering in porous media. Annual Review of Fluid Mechanics 19 (1):271–311. doi:10.1146/annurev.fl.19.010187.001415.
   Google Scholar
• Islam, T., and P. S. Gandhi. 2017. Viscous fingering in multiport Hele Shaw cell for controlled shaping of fluids. Scientific Reports 7 (1):16602. doi:10.1038/s41598-017-16830-3.
   PubMedGoogle Scholar
• Jiao, C., and T. Maxworthy. 2008. An experimental study of miscible displacement with gravity-override and viscosity-contrast in a Hele Shaw cell. Experiments in Fluids 44 (5):781–94. doi:10.1007/s00348-007-0434-8.
   Web of Science ®Google Scholar
• Kawaguchi, M., M. Makino, and T. Kato. 1997. Viscous fingering patterns in polymer solutions. Physica D: Nonlinear Phenomena 109 (3–4):325–32. doi:10.1016/S0167-2789(97)00069-9.
   Google Scholar
• Kopf‐Sill, A. R., and G. Homsy. 1988. Nonlinear unstable viscous fingers in Hele–Shaw flows. I. Experiments. The Physics of Fluids. 31 (2):242–49. doi:10.1063/1.866854.
   Web of Science ®Google Scholar
• Lajeunesse, E., J. Martin, N. Rakotomalala, D. Salin, and Y. Yortsos. 1999. Miscible displacement in a Hele-Shaw cell at high rates. Journal of Fluid Mechanics 398:299–319. doi:10.1017/S0022112099006357.
   Web of Science ®Google Scholar
• Lewis, D. 1950. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. II. Proceedings of the Royal Society of London A: Mathematical and Physical Sciences 202 (1068):81–96. doi:10.1098/rspa.1950.0086.
   Google Scholar
• Li, H., B. Maini, and J. Azaiez. 2006. Experimental and numerical analysis of the viscous fingering instability of Shear‐thinning fluids. The Canadian Journal of Chemical Engineering 84 (1):52–62. doi:10.1002/cjce.5450840109.
   Web of Science ®Google Scholar
• Liu, J. Z., L. D. Zhang, and G. H. Yue. 2003. Fractal dimension in human cerebellum measured by magnetic resonance imaging. Biophysical Journal 85 (6):4041–46. doi:10.1016/S0006-3495(03)74817-6.
   PubMed Web of Science ®Google Scholar
• Maes, R., G. Rousseaux, B. Scheid, M. Mishra, P. Colinet, and A. D. Wit. 2010. Experimental study of dispersion and miscible viscous fingering of initially circular samples in Hele-Shaw cells. Physics of Fluids 22 (12):123104. doi:10.1063/1.3528039.
   Web of Science ®Google Scholar
• Mandelbrot, B. B. 1983. The fractal geometry of nature, 495. New York: WH freeman and Co.
   Google Scholar
• Maxworthy, T. 1987. The nonlinear growth of a gravitationally unstable interface in a Hele-Shaw cell. Journal of Fluid Mechanics 177:207–32. doi:10.1017/S0022112087000922.
   Web of Science ®Google Scholar
• McKellar, M., and N. Wardlaw. 1982. A method of making two-dimensional glass micromodels of pore systems. Journal of Canadian Petroleum Technology 21:04. doi:10.2118/82-04-03.
   Google Scholar
• Mohammadi, S., A. Maghzi, M. H. Ghazanfari, M. Masihi, A. Mohebbi, and R. Kharrat. 2013. On the control of glass micro-model characteristics developed by laser technology. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 35 (3):193–201. doi:10.1080/15567036.2010.516325.
   Web of Science ®Google Scholar
• Nittmann, J., G. Daccord, and H. E. Stanley. 1985. Fractal growth viscous fingers: Quantitative characterization of a fluid instability phenomenon. Nature 314 (6007):141–44. doi:10.1038/314141a0.
   Web of Science ®Google Scholar
• Ruith, M., and E. Meiburg. 2000. Miscible rectilinear displacements with gravity override. Part 1. Homogeneous porous medium. Journal of Fluid Mechanics 420:225–57. doi:10.1017/S0022112000001543.
   Web of Science ®Google Scholar
• Saffman, P. G., and G. I. Taylor. 1958. The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid. Proceedings of the Royal Society of London A: Mathematical, and Physical Sciences 245 (1242):312–29. doi:10.1098/rspa.1958.0085.
   Web of Science ®Google Scholar
• Saidian, M., M. H. Ghazanfari, M. Masihi, and R. Kharrat. 2013. Monitoring the role of fracture geometrical characteristics on fingering initiation/development during heavy oil miscible displacements in fractured porous media. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 35 (12):1129–39. doi:10.1080/15567036.2010.516321.
   Web of Science ®Google Scholar
• Saidian, M., M. Masihi, M. H. Ghazanfari, R. Kharrat, and S. Mohammadi. 2014. An experimental study of the matrix-fracture interaction during miscible displacement in fractured porous media: A micromodel study. Energy Sources, Part A: Recovery, Utilization, and Environmental Effects 36 (3):259–66. doi:10.1080/15567036.2010.536828.
   Web of Science ®Google Scholar
• Shaw, H. H. 1898. On the motion of a viscous fluid between two parallel plates. Nature 58:34–36.
   Google Scholar
• Sobel, I. 1990. An isotropic 3 × 3 image gradient operator. In Machine Vision for Three-Dimensional Scenes, 376–79. New York, NY: Academic Press.
   Google Scholar
• Suekane, T., J. Ono, A. Hyodo, and Y. Nagatsu. 2017. Three-dimensional viscous fingering of miscible fluids in porous media. Physical Review Fluids 2 (10):103902. doi:10.1103/PhysRevFluids.2.103902.
   Web of Science ®Google Scholar
• Tan, C., and G. Homsy. 1988. Simulation of nonlinear viscous fingering in miscible displacement. The Physics of Fluids 31 (6):1330–38. doi:10.1063/1.866726.
   Web of Science ®Google Scholar
• Taylor, G. 1950. The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proceedings of the Royal Society of London A: Mathematical and Physical Sciences 201 (1065):192–96. doi:10.1098/rspa.1950.0052.
   Google Scholar
• Wang, L., S. Cai, and T. Suekane. 2018. gravitational fingering due to density increase by mixing at a vertical displacing front in porous media. Energy & Fuels 32 (1):658–69. doi:10.1021/acs.energyfuels.7b02819.
   Web of Science ®Google Scholar
• Wooding, R. A. 1969. Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell. Journal of Fluid Mechanics 39 (3):477–95. doi:10.1017/S002211206900228X.
   Google Scholar
• Yu, L., and N. C. Wardlaw. 1986. Mechanisms of nonwetting phase trapping during imbibition at slow rates. Journal of Colloid and Interface Science 109 (2):473–86. doi:10.1016/0021-9797(86)90325-5.
   Web of Science ®Google Scholar
• Zhang, H., T. S. Ramakrishnan, A. Nikolov, and D. Wasan. 2018. Enhanced oil displacement by nanofluid’s structural disjoining pressure in model fractured porous media. Journal of Colloid and Interface Science 511:48–56. doi:10.1016/j.jcis.2017.09.067.
   PubMed Web of Science ®Google Scholar
• Zimmerman, W., and G. Homsy. 1991. Nonlinear viscous fingering in miscible displacement with anisotropic dispersion. Physics of Fluids A: Fluid Dynamics 3 (8):1859–72. doi:10.1063/1.857916.
   Web of Science ®Google Scholar