Skip to main content
SpringerLink
Log in

Reversible and Irreversible Tracer Dispersion in an Oscillating Flow Inside a Model Rough Fracture

  • Published:
Transport in Porous Media Aims and scope Submit manuscript

Abstract

We study the mixing dynamics of a dyed and a clear miscible fluid by an oscillating flow inside an Hele-Shaw cell with randomly distributed circular obstacles. A transparent setup allows us to analyze the distribution of the two fluids and the reversible and irreversible mixing components. At the lower Péclet numbers Pe (based on the averaged absolute fluid velocity), geometrical dispersion due to the disordered flow field between the obstacles is dominant: the corresponding dispersivity is constant with Pe and, at constant Pe, increases with the amplitude of the oscillations and is negligible at small ones. Compared to echo dispersion with only one injection–suction cycle, oscillating flows are shown to provide additional information when the number of oscillations and, as a result, the distance of transverse mixing are varied. Geometrical dispersion is dominant up to a limiting Pe increasing with the amplitude. At higher \({\textit{Pe}}'{\textit{s}}\), the results are similar to those of Taylor dispersion in cells with smooth walls.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Aris, R.: On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. Lond. A 235, 67–77 (1956)

    Article  Google Scholar 

  • Ashorynejad, H.R., Javaherdeh, K., Van den Akker, H.E.A.: The effect of pulsating pressure on the performance of a PEM fuel cell with a wavy cathode surface. Int. J. Hydrogen Energy 41, 14239–14251 (2016)

    Article  Google Scholar 

  • Bear, J.: Dynamics of Fluids in Porous Media. Dover Publications, New-York (1972)

    Google Scholar 

  • Boschan, A., Auradou, H., Chertcoff, R., Ippolito, I., Hulin, J.P.: Miscible displacement fronts of shear thinning fluids inside rough fractures. Water Resour. Res. 43, W03438 (2007)

    Article  Google Scholar 

  • Boschan, A., Ippolito, I., Chertcoff, R., Auradou, H., Hulin, J.P.: Geometrical and Taylor dispersion in a fracture with random obstacles: an experimental study with fluids of different rheologies. Water Resour. Res. 44, W06420 (2008)

    Article  Google Scholar 

  • Charette, V.J., Evangelista, E., Chertcoff, R., Auradou, H., Hulin, J.P., Ippolito, I.: Influence of the disorder on solute dispersion in a flow channel. Eur. Phys. J. Appl. Phys. 39, 267–274 (2007)

    Article  Google Scholar 

  • Cirkel, D.G., van der Zee, S., Meeussen, J.C.L.: Front spreading with nonlinear sorption for oscillating flow. Water Resour. Res. 51, 2986–2993 (2015)

    Article  Google Scholar 

  • de Anna, P., Dentz, M., Tartakovsky, A., Le Borgne, T.: The filamentary structure of mixing fronts and its control on reaction kinetics in porous media flows. Geophys. Res. Lett. 41, 4586–4593 (2014)

    Article  Google Scholar 

  • Dey, B., Raja, G.P.: Sekhar “Mass transfer and species separation due to oscillatory flow in a Brinkman medium”. Int. J. Eng. Sci. 74, 35–54 (2014)

    Article  Google Scholar 

  • Fried, J.J., Combarnous, M.A.: Dispersion in Porous Media. In: Ven Te Chow (ed.) Advances in Hydroscience, pp. 1 69–282. Academic Press, New York (1971)

  • Horobin, R.W., Kiernan, J.A.: Conn’s Biological Stains: A Handbook of Dyes, Stains and Fluorochromes for Use in Biology and Medicine. Taylor and Francis, Philadelphia (2002)

    Google Scholar 

  • Hulin, J.P., Plona, T.J.: Echo tracer dispersion in porous media. Phys. Fluids A 1, 1341–1347 (1989)

    Article  Google Scholar 

  • Ippolito, I., Daccord, G., Hinch, E.J., Hulin, J.P.: Echo tracer dispersion in model fractures with a rectangular geometry. J. Contam. Hydrol. 16, 87–108 (1994)

    Article  Google Scholar 

  • Jha, R.K., Bryant, S.L., Lake, L.W., John, A.: Investigation of pore-scale (local) mixing. In: Paper SPE 99782 presented at the SPE Improved Oil Recovery Symposium, Tulsa (2006)

  • Jha, R.K., John, A., Bryant, S.L., Lake, L.W.: Flow reversal and mixing. SPE J. 14, 41–49 (2009)

    Article  Google Scholar 

  • Le Borgne, T., Dentz, M., Villermaux, E.: Stretching, coalescence, and mixing in porous media. Phys. Rev. Lett. 110, 204501 (2013)

    Article  Google Scholar 

  • Le Borgne, T., Dentz, M., Villermaux, E.: The lamellar description of mixing in porous media. J. Fluid Mech. 770, 458–498 (2015)

    Article  Google Scholar 

  • Leong, K.C., Jin, L.W.: Characteristics of oscillating flow through a channel filled with open-cell metal foam. Int. J. Heat Fluid Flow 27, 144–153 (2006)

    Article  Google Scholar 

  • Leroy, C., Hulin, J.P., Lenormand, R.: Tracer dispersion in stratified porous media: influence of transverse dispersion and gravity. J. Contam. Hydrol. 11, 51–68 (1992)

    Article  Google Scholar 

  • Nowamooz, A., Radilla, G., Fourar, M., Berkowitz, B.: Non-Fickian transport in transparent replicas of rough-walled rock fractures. Transp. Porous Med. 98, 651–682 (2013)

    Article  Google Scholar 

  • Raats, P.A.C.: Effect of a finite response time upon propagation of sinusoidal oscillations of fluids in porous media. Z. Angew. Math. Phys. 20, 936–946 (1969)

    Article  Google Scholar 

  • Rigord, P., Calvo, A., Hulin, J.P.: Transition to irreversibility for the dispersion of a tracer in porous media. Phys. Fluids A 2, 681–687 (1990)

    Article  Google Scholar 

  • Roht, Y.L., Auradou, H., Hulin, J.-P., Salin, D., Chertcoff, R., Ippolito, I.: Time dependence and local structure of tracer dispersion in oscillating liquid Hele-Shaw flows. Phys. Fluids 27, 103602 (2015)

    Article  Google Scholar 

  • Roux, S., Plouraboué, F., Hulin, J.P.: Tracer dispersion in rough open cracks. Transport Porous Med. 32, 97–116 (1998)

    Article  Google Scholar 

  • Russel, W.B., Saville, D.A., Schowalter, W.R.: Colloidal Dispersions. Cambridge University Press, Cambridge (1995)

    Google Scholar 

  • Saffman, P.G.: A theory of dispersion in porous media. J. Fluid Mech 6, 321–349 (1959)

    Article  Google Scholar 

  • Sanz-Prat, A., Lu, C., Finkel, M., Cirpka, O.A.: Using travel times to simulate multi-dimensional bioreactive transport in time-periodic flows. J. Cont. Hydro. 187, 1–17 (2016)

    Article  Google Scholar 

  • Scotter, D.R., Raats, P.A.C.: Dispersion in porous mediums due to oscillating flow. Water Resour. Res. 4, 1201–1206 (1968)

    Article  Google Scholar 

  • Scotter, D.R., Thurtell, G.W., Raats, P.A.C.: Dispersion resulting from sinusoidal gas flow in porous materials. Soil Sci. 104, 306–308 (1967)

    Article  Google Scholar 

  • Taylor, G.I.: Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. Lond. A 219, 186–203 (1953)

    Article  Google Scholar 

  • Wang, P., Chen, G.Q.: Environmental dispersion in a tidal wetland with sorption by vegetation. Commun. Nonlinear Sci. Numer. Simulat. 22, 348–366 (2015)

    Article  Google Scholar 

  • Watson, E.J.: Diffusion in oscillatory pipe flow. J. Fluid. Mech. 133, 233–244 (1983)

    Article  Google Scholar 

Download references

Acknowledgements

We acknowledge support by “Investissements d’Avenir” LabEx PALM (ANR-10-LABX-0039-PALM), by the LIA PMF-FMF (Franco-Argentinian International Associated Laboratory in the Physics and Mechanics of Fluids) and from UBACyT 20020130100570BA. The thesis of Y. L. Roht has been supported by a fellowship from the Peruilh foundation of the Faculty of Engineering of the Buenos-Aires University, by a Bec.Ar fellowship and by an Eiffel fellowship. The authors wish to thank A. Aubertin, L. Auffray and R. Pidoux for their help in the design and realization of the experimental setup.

Author information

Authors and Affiliations

  1. Universidad de Buenos Aires, Facultad de Ingeniería, Grupo de Medios Porosos, Paseo Colón 850, 1063, Buenos Aires, Argentina

    Yanina Lucrecia Roht, Ricardo Chertcoff & Irene Ippolito

  2. Lab. FAST, CNRS, Univ. Paris-Sud, Bât. 502, Campus Univ, 91405, Orsay, France

    Jean-Pierre Hulin & Harold Auradou

Authors
  1. Yanina Lucrecia Roht
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ricardo Chertcoff
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jean-Pierre Hulin
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Harold Auradou
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Irene Ippolito
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jean-Pierre Hulin.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Roht, Y.L., Chertcoff, R., Hulin, JP. et al. Reversible and Irreversible Tracer Dispersion in an Oscillating Flow Inside a Model Rough Fracture. Transp Porous Med 122, 421–436 (2018). https://doi.org/10.1007/s11242-018-1014-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11242-018-1014-5

Keywords

Search

Navigation