Hostname: page-component-55f67697df-gmt7q Total loading time: 0 Render date: 2025-05-12T03:21:37.756Z Has data issue: false hasContentIssue false
  • English
  • Français

Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media

Published online by Cambridge University Press:  06 October 2015

Satyajit Pramanik ,
A. De Wit  and
Manoranjan Mishra
Satyajit Pramanik*
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, India
A. De Wit
Affiliation:
Université libre de Bruxelles (ULB), Nonlinear Physical Chemistry Unit, CP231, 1050 Brussels, Belgium
Manoranjan Mishra
Affiliation:
Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140001, India
*
†Email address for correspondence: satyajit.math16@gmail.com
Get access Rights & Permissions [Opens in a new window]

Abstract

The deformation of an initially circular miscible blob in a rectilinear displacement is investigated numerically for porous media when the blob is more viscous than the displacing fluid. We find in the parameter space spanned by the Péclet number and log-mobility ratio the existence of a new lump-shaped instability zone between two distinct regimes of comet and viscous fingering (VF) deformations. The more viscous circular blob is destabilized by VF only over a finite window of log-mobility ratio, contrary to the displacement of a more viscous finite slice with planar interfaces. This difference is attributed to the initial curvature of the miscible blob.

JFM classification

Interfacial Flows (free surface): Fingering instability Mixing: Mixing Low-Reynolds-number flows: Porous media
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 782 , 10 November 2015 , R2
Check for updates
Copyright
© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Bacri, J.-C., Salin, D. & Wouméni, R. 1991 Three dimensional miscible viscous fingering in porous media. Phys. Rev. Lett. 67, 2005–2008.CrossRefGoogle ScholarPubMed
Chen, C.-Y., Wang, L. & Meiburg, E. 2001 Miscible droplet in a porous medium and the effects of Korteweg stresses. Phys. Fluids 13 (9), 2447–2456.CrossRefGoogle Scholar
Chen, C.-Y. & Wang, S.-W. 2001 Miscible displacement of a layer with finite width in porous media. Intl J. Numer. Meth. Heat Fluid Flow 11, 761–778.CrossRefGoogle Scholar
Dentz, M., Le Borgne, T., Englert, A. & Bijeljic, B. 2011 Mixing, spreading and reaction in heterogeneous media: a brief review. J. Contam. Hydrol. 120–121, 1–21.CrossRefGoogle ScholarPubMed
De Wit, A. & Homsy, G. M. 1999 Viscous fingering in reaction–diffusion systems. J. Chem. Phys. 110, 8663–8675.CrossRefGoogle Scholar
De Wit, A., Bertho, Y. & Martin, M. 2005 Viscous fingering of miscible slices. Phys. Fluids 17, 054114.CrossRefGoogle Scholar
Homsy, G. M. 1987 Viscous fingering in porous media. Annu. Rev. Fluid Mech. 19, 271–311.CrossRefGoogle Scholar
Huppert, H. E. & Neufeld, J. A. 2014 The fluid mechanics of carbon dioxide sequestration. Annu. Rev. Fluid Mech. 46, 255–272.CrossRefGoogle Scholar
Jha, B., Cueto-Felgueroso, L. & Juanes, R. 2011a Fluid mixing from viscous fingering. Phys. Rev. Lett. 106, 194502.CrossRefGoogle ScholarPubMed
Jha, B., Cueto-Felgueroso, L. & Juanes, R. 2011b Quantifying mixing in viscously unstable porous media flows. Phys. Rev. E 84, 066312.CrossRefGoogle ScholarPubMed
Jha, B., Cueto-Felgueroso, L. & Juanes, R. 2013 Synergetic fluid mixing from viscous fingering and alternating injection. Phys. Rev. Lett. 111, 144501.CrossRefGoogle ScholarPubMed
Lagneau, V., Pipart, A. & Catalette, H. 2005 Reactive transport modelling of CO $_{2}$ sequestration in deep saline aquifers. Oil Gas Sci. Technol. 60 (2), 231–247.CrossRefGoogle Scholar
Maes, R., Rousseaux, G., Scheid, B., Mishra, M., Colinet, P. & De Wit, A. 2010 Experimental study of dispersion and miscible viscous fingering of initially circular samples in Hele-Shaw cells. Phys. Fluids 22, 123104.CrossRefGoogle Scholar
Mainhagu, J., Golfier, F., Oltéan, C. & Buès, M. A. 2012 Gravity-driven fingers in fractures: experimental study and dispersion analysis by moment method for a point-source injection. J. Contam. Hydrol. 132, 12–27.CrossRefGoogle ScholarPubMed
Mishra, M., Martin, M. & De Wit, A. 2008 Differences in miscible viscous fingering of finite width slices with positive or negative log mobility ratio. Phys. Rev. E 78, 066306.CrossRefGoogle ScholarPubMed
Mishra, M., Trevelyan, P. M. J., Almarcha, C. & De Wit, A. 2010 Influence of double diffusive effects on miscible viscous fingering. Phys. Rev. Lett. 105, 204501.CrossRefGoogle ScholarPubMed
Nicolaides, C., Jha, B., Cueto-Felgueroso, L. & Juanes, R. 2015 Impact of viscous fingering and permeability heterogeneity on fluid mixing in porous media. Water Resour. Res. 51, 2634–2647.CrossRefGoogle Scholar
Ott, H., Berg, S. & Oedai, S. 2012 Displacement and mass transfer of CO $_{2}$ /brine in sandstone. Energy Procedia 23, 512–520.CrossRefGoogle Scholar
Pramanik, S. & Mishra, M. 2013 Linear stability analysis of Korteweg stresses effect on miscible viscous fingering in porous media. Phys. Fluids 25, 0741404.CrossRefGoogle Scholar
Pramanik, S. & Mishra, M. 2015 Effect of Péclet number on miscible rectilinear displacement in a Hele-Shaw cell. Phys. Rev. E 91, 033006.CrossRefGoogle Scholar
Ruyer-Quil, C. 2001 Inertial corrections to the Darcy law in a Hele-Shaw cell. C. R. Acad. Sci. IIb Mech. 329, 337–342.Google Scholar
Sauzade, M. & Cubaud, T. 2013 Initial microfluidic dissolution regime of CO $_{2}$ bubbles in viscous oils. Phys. Rev. E 88, 051001(R).CrossRefGoogle ScholarPubMed
Talon, L., Goyal, N. & Meiburg, E. 2013 Variable density and viscosity, miscible displacements in Hele-Shaw cells. Part 1. Linear stability analysis. J. Fluid Mech. 721, 268–294.CrossRefGoogle Scholar
Tan, C. T. & Homsy, G. M. 1988 Simulation of non-linear viscous fingering in miscible displacement. Phys. Fluids 31, 1330.CrossRefGoogle Scholar
Welty, C., Kane, A. C. III & Kauffman, L. J. 2003 Stochastic analysis of transverse dispersion in density-coupled transport in aquifers. Water Resour. Res. 39, 1150.CrossRefGoogle Scholar

Pramanik supplementary movie

Comet deformation of the blob for R = 3, r = 0.5, Pe = 1000

Download Pramanik supplementary movie(Video)
Video 61.5 KB

Pramanik supplementary movie

Lump-shaped instability of a circular blob for R = 1.25, r = 0.5, Pe = 900

Download Pramanik supplementary movie(Video)
Video 59.1 KB

Pramanik supplementary movie

Viscous fingering instability of a circular blob for R = 1.25, r = 0.5, Pe = 1000

Download Pramanik supplementary movie(Video)
Video 66.3 KB