Nonlinear Simulation of Viscoelastic Fingering Instability in Miscible Displacement through Homogeneous and Heterogeneous Porous Media
Publication: Journal of Engineering Mechanics
Volume 145, Issue 12
Abstract
The miscible displacement of a Newtonian fluid pushed by a nonlinear viscoelastic fluid (viscous fingering instability) has been investigated via a pseudospectral method and Hartley transform. The results of the present study could be useful for enhanced oil recovery (EOR) using chemical flooding technique. Here, the Giesekus model is applied as the constitutive equation of viscoelastic fluid. In addition to the homogeneous media, the simulations are performed for a horizontal layered heterogeneous medium and the results are presented as concentration contours, transversely averaged concentration profiles, mixing length, and sweep efficiency. It is concluded that the heterogeneity of the medium has a great effect on the flow structure. The channeling regime is observed in these media. Higher layers in the heterogeneous medium reduces the intensity of instability while permeability variance acts on the contrary. This is the first attempt in simulation of the viscoelastic-Newtonian displacement (polymer flooding) in heterogeneous media.
Get full access to this article
View all available purchase options and get full access to this article.
References
Azaiez, J., and A. Mohamad. 2004. “Fingering instabilities in miscible displacement flows of non-Newtonian fluids.” J. Porous Media 7 (1): 29–40. https://doi.org/10.1615/JPorMedia.v7.i1.40.
Azaiez, J., and B. Singh. 2002. “Stability of miscible displacements of shear thinning fluids in a Hele-Shaw cell.” Phys. Fluids 14 (5): 1557–1571. https://doi.org/10.1063/1.1462030.
Bird, R. B., R. C. Armstrong, O. Hassager, and C. F. Curtiss. 1977. Dynamics of polymeric liquids. New York: Wiley.
Chang, J., and K. B. Nakshatrala. 2017. “Variational inequality approach to enforcing the non-negative constraint for advection-diffusion equations.” Comput. Methods Appl. Mech. Eng. 320 (Jun): 287–334. https://doi.org/10.1016/j.cma.2017.03.022.
Daccord, G., J. Nittmann, and H. E. Stanley. 1986. “Radial viscous fingers and diffusion-limited aggregation: Fractal dimension and growth sites.” Phys. Rev. Lett. 56 (4): 336–339. https://doi.org/10.1103/PhysRevLett.56.336.
De Wit, A., and G. Homsy. 1997a. “Viscous fingering in periodically heterogeneous porous media. I. Formulation and linear instability.” J. Chem. Phys. 107 (22): 9609–9618. https://doi.org/10.1063/1.475258.
De Wit, A., and G. Homsy. 1997b. “Viscous fingering in periodically heterogeneous porous media. II. Numerical simulations.” J. Chem. Phys. 107 (22): 9619–9628. https://doi.org/10.1063/1.475259.
Ghesmat, K., and J. Azaiez. 2008. “Viscous fingering instability in porous media: Effect of anisotropic velocity-dependent dispersion tensor.” Transp. Porous Med. 73 (3): 297–318. https://doi.org/10.1007/s11242-007-9171-y.
Govindarajan, R., and K. C. Sahu. 2014. “Instabilities in viscosity-stratified flow.” Annu. Rev. Fluid Mech. 46 (1): 331–353. https://doi.org/10.1146/annurev-fluid-010313-141351.
Hill, S. 1952. “Channeling in packed columns.” Chem. Eng. Sci. 1 (6): 247–253. https://doi.org/10.1016/0009-2509(52)87017-4.
Homsy, G. M. 1987. “Viscous fingering in porous media.” Annu. Rev. Fluid Mech. 19 (1): 271–311. https://doi.org/10.1146/annurev.fl.19.010187.001415.
Joodat, S. H. S., K. B. Nakshatrala, and R. Ballarini. 2018. “Modeling flow in porous media with double porosity/permeability: A stabilized mixed formulation, error analysis, and numerical solutions.” Comput. Methods Appl. Mech. Eng. 337 (Aug): 632–676. https://doi.org/10.1016/j.cma.2018.04.004.
Joshaghani, M., S. Joodat, and K. Nakshatrala. 2018. “A stabilized mixed discontinuous Galerkin formulation for double porosity/permeability model.” Comput. Methods Appl. Mech. Eng. 352 (Aug): 508–560. https://doi.org/10.1016/j.cma.2019.04.010.
Kim, M. C., and C. K. Choi. 2011. “Linear analysis on the stability of miscible dispersion of shear-thinning fluids in porous media.” J. Non-Newtonian Fluid Mech. 166 (21): 1211–1220. https://doi.org/10.1016/j.jnnfm.2011.07.008.
Li, H., B. Maini, and J. Azaiez. 2006. “Experimental and numerical analysis of the viscous fingering instability of shear-thinning fluids.” Can. J. Chem. Eng. 84 (1): 52–62. https://doi.org/10.1002/cjce.5450840109.
Manickam, O., and G. Homsy. 1993. “Stability of miscible displacements in porous media with nonmonotonic viscosity profiles.” Phys. Fluids A- Fluid Dyn. 5 (6): 1356–1367. https://doi.org/10.1063/1.858571.
Mora, S., and M. Manna. 2012. “From viscous fingering to elastic instabilities.” J. Non-Newtonian Fluid Mech. 173 (Apr): 30–39. https://doi.org/10.1016/j.jnnfm.2012.01.010.
Nittmann, J., G. Daccord, and H. E. Stanley. 1985. “Fractal growth of viscous fingers: Quantitative characterization of a fluid instability phenomenon.” Nature 314 (6007): 141–144. https://doi.org/10.1038/314141a0.
Norouzi, M., and M. Shoghi. 2014. “A numerical study on miscible viscous fingering instability in anisotropic porous media.” Phys. Fluids 26 (8): 084102. https://doi.org/10.1063/1.4891228.
Pascal, H. 1983. “Nonsteady flow of non-Newtonian fluids through a porous medium.” Int. J. Eng. Sci. 21 (3): 199–210. https://doi.org/10.1016/0020-7225(83)90021-6.
Pascal, H. 1986. “Stability of a moving interface in porous medium for non-Newtonian displacing fluids and its applications in oil displacement mechanism.” Acta Mech. 58 (1): 81–91. https://doi.org/10.1007/BF01177108.
Pramanik, S., and M. Mishra. 2015. “Effect of Péclet number on miscible rectilinear displacement in a Hele-Shaw cell.” Phys. Rev. E 91 (3): 033006. https://doi.org/10.1103/PhysRevE.91.033006.
Pye, D. J. 1964. “Improved secondary recovery by control of water mobility.” J. Pet. Technol. 16 (8): 911–916. https://doi.org/10.2118/845-PA.
Sader, J. E., D. Y. Chan, and B. D. Hughes. 1994. “Non-Newtonian effects on immiscible viscous fingering in a radial Hele-Shaw cell.” Phys. Rev. E 49 (1): 420–432. https://doi.org/10.1103/PhysRevE.49.420.
Sajjadi, M., and J. Azaiez. 2013. “Scaling and unified characterization of flow instabilities in layered heterogeneous porous media.” Phy. Rev. E 88 (3): 033017. https://doi.org/10.1103/PhysRevE.88.033017.
Sandiford, B. 1964. “Laboratory and field studies of water floods using polymer solutions to increase oil recoveries.” J. Pet. Technol. 16 (8): 917–922. https://doi.org/10.2118/844-PA.
Shoghi, M. R., and M. Norouzi. 2015. “Linear stability analysis and nonlinear simulation of non-Newtonian viscous fingering instability in heterogeneous porous media.” Rheol. Acta 54 (11–12): 973–991. https://doi.org/10.1007/s00397-015-0887-2.
Shokri, H., M. Kayhani, and M. Norouzi. 2017. “Nonlinear simulation and linear stability analysis of viscous fingering instability of viscoelastic liquids.” Phys. Fluids 29 (3): 033101. https://doi.org/10.1063/1.4977443.
Shokri, H., M. Kayhani, and M. Norouzi. 2018. “Saffman-Taylor instability of viscoelastic fluids in anisotropic porous media.” Int. J. Mech. Sci. 135 (1): 1–13. https://doi.org/10.1016/j.ijmecsci.2017.11.008.
Singh, B. K., and J. Azaiez. 2001. “Numerical simulation of viscous fingering of shear-thinning fluids.” Can. J. Chem. Eng. 79 (6): 961–967. https://doi.org/10.1002/cjce.5450790614.
Tan, C., and G. Homsy. 1986. “Stability of miscible displacements in porous media: Rectilinear flow.” Phys. Fluids 29 (11): 3549–3556. https://doi.org/10.1063/1.865832.
Tan, C., and G. Homsy. 1988. “Simulation of nonlinear viscous fingering in miscible displacement.” Phys. Fluids 31 (6): 1330–1338. https://doi.org/10.1063/1.866726.
Tan, C., and G. Homsy. 1992. “Viscous fingering with permeability heterogeneity.” Phys. Fluids A: Fluid Dyn. 4 (6): 1099–1101. https://doi.org/10.1063/1.858227.
Wilson, S. 1990. “The Taylor-Saffman problem for a non-Newtonian liquid.” J. Fluid Mech. 220 (Nov): 413–425. https://doi.org/10.1017/S0022112090003329.
Zimmerman, W., and G. Homsy. 1991. “Nonlinear viscous fingering in miscible displacement with anisotropic dispersion.” Phys. Fluids A: Fluid Dyn. 3 (8): 1859–1872. https://doi.org/10.1063/1.857916.
Zimmerman, W., and G. Homsy. 1992. “Three-dimensional viscous fingering: A numerical study.” Phys. Fluids A: Fluid Dyn. 4 (9): 1901–1914. https://doi.org/10.1063/1.858361.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 145 • Issue 12 • December 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Dec 26, 2018
Accepted: Apr 24, 2019
Published online: Sep 26, 2019
Published in print: Dec 1, 2019
Discussion open until: Feb 26, 2020
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.