Abstract
The effect of fluid density and viscosity on dispersion in miscible displacements in porous media is examined. Miscible displacement experiments with fluid pairs having density and viscosity differences are carried out in a Plexiglas column containing a homogeneous and isotropic sand pack. Tracer tests and tests of both stable and unstable miscible displacement are conducted using NaCl and glycerine solutions. Concentration breakthrough curves are measured through an electrical monitoring technique. Following the conventional convection–dispersion formulation, the dispersion coefficient is determined by performing a least squares fit to the measured concentration breakthrough curves. It is found that for stable displacements dispersion coefficients drop continually when density differences increase or when viscosity ratios of the displaced and displacing fluid decrease. In the unstable case the dispersion coefficients increase with both density and viscosity differences.
Similar content being viewed by others
References
Asif, M. and Narayan, K. A.: 1990, Stability of miscible fluid displacement in a porous medium, Ing. Arch. 60, 345–349.
Bachmat, Y. and Elrick, D. E.: 1970, Hydrodynamic instability of miscible fluids in a vertical porous column, Water Resour. Res. 6, 156–170.
Bacri, J.-C., Rakotomalala, N. and Salin, D.: 1987, Stable and unstable miscible flows through porous media, In: J. R. Banavar (ed.), Physics and Chemistry of Porous Media, American Institute of Physics, New York, pp. 116–128.
Bacri, J.-C., Hoyos, M., Rakotomalala, N., Salin, D., Bourlion, M., Daccord, G., Lenormand, R. and Soucemarianadin, S.: 1991, Ultrasonic diagnostic in porous media and suspensions, J. Phys. III France 1, 1455–1466.
Bacri, J.-C., Rakotomalala, N., Salin, D. and Woumeni, R.: 1992, Miscible viscous fingering: experiments versus continuum approach, Phys. Fluids A Fluid 4, 1611–1619.
Bear, J.: 1972, Dynamics of Fluids in Porous Media, Elsevier, New York.
Boggs, J. M., Young, S. C., Beard, L. M., Gelhar, L. W., Rehfeldt, K. R. and Adams, E. E.: 1992, Field study of dispersion in a heterogeneous aquifer, 1. Overview and site description, Water Resour. Res. 28, 3281–3291.
Bouhroum, A.: 1985, Beitrag zur Verdrängung mischbarer Flüssigkeiten in porösen Medien unter Berücksichtigung der Dichte-und Viskositäts-Unterschiede, PhD Thesis, Fakultät für Bergbau, Hüttenwesen und Maschinenwesen der Technischen Universität Clausthal.
Bues, M. A. and Aachib, M.: 1991, Influence of the heterogeneity of the parameters of miscible displacement in a saturated porous medium, Exp. Fluids 11, 25–32.
Chang, S.-H. and Slattery, J. C.: 1986, A linear stability analysis formiscible displacement, Transport Porous Med. 1, 179–199.
Chang, S.-H. and Slattery, J. C.: 1988a, Stability of vertical miscible displacements with developing density and viscosity gradients, Transport Porous Med. 3, 277–297.
Chang, S.-H. and Slattery, J. C.: 1988b, A new description for dispersion, Transport Porous Med. 3, 515–527.
Chang, S.-H. and Slattery, J. C.: 1989, The effect of dispersion model on the linear stability of miscible displacement in porous media, Transport Porous Med. 4, 85–96.
Christie, M. A., Jones, A. D. W. and Muggeridge, A. H.: 1990, Comparison between laboratory experiments and detailed simulations of unstable miscible displacement influenced by gravity, in: J. Kleppe (ed), North Sea Oil and Gas Reservoirs-II, The Norwegian Institute of Technology, Graham and Trotman, pp. 245–250.
Dane, J. H., Güven, O., Oostrom, M. and Hayworth, J. S.: 1991, Stability and mixing of dense aqueous phase plumes in porous media, EOS Trans. Am. Geophys. Union 72, 126.
Freeze, R. A. and Cherry, J. A.: 1979, Groundwater, Preintice-Hall, Englewood Cliffs, NJ, pp. 315–389.
Freyberg, D. L.: 1986, A natural gradient experiment on solute transport in a sand aquifer. 2. Spatial moments and the advection and dispersion of nonreactive tracers, Water Resour. Res. 22, 2031–2046.
Fried, J. J. and Combarnous, M. A.: 1971, Dispersion in porous media, Adv. Hydrosci. 7, 169–282.
Guillot, G., Kassab, G., Hulin, J. P. and Rigord, P.: 1991, Monitoring of tracer dispersion in porous media by NMR imaging, J. Phys. D Appl. Phys. 24, 763–773.
Hayworth, J. S., Güven, O., Dane, J. H. and Oostrom, M.: 1991, Experimental studies of dense solute plumes in porous media, EOS Trans. Am. Geophys. Union 72, 130.
Heller, J. P.: 1965, Onset of instability patterns between miscible fluids in porous media, J. Appl. Phys. 37, 1566–1579.
Hickernell, F. J. and Yortsos, Y. C.: 1986, Linear stability of miscible displacement processes in porous media in the absence of dispersion, Stud. Appl. Math. 74, 93–115.
Hill, S.: 1952, Channelling in packed columns, Chem. Eng. Sci. 1, 247–253.
Holm, L. W.: 1986, Miscibility and miscible displacement, J. Petrol. Technol. 8, 817–818.
Homsy, G. M.: 1987, Viscous fingering in porous-media, Annu. Rev. Fluid Mech. 19, 271–311.
Homsy, G. M. and Sherwood, A. E.: 1976, Convective instabilities in porous media with through flow, AICHE J. 22, 168–174.
Istok, J. D. and Humphrey, M. D.: 1995, Laboratory investigation of buoyancy-induced flow (plume sinking) during two-well tracer tests, Ground Water 33, 597–604.
Jiao, C.: 2002, Miscible displacements in porous media with variation of fluid density and viscosity, Schriftenreihe Angewandte Geologie Karlsruhe 66, 147.
Kimmel, A. E. and Braids, O. C.: 1980, Leachate plumes in ground water from Babylon and Islip Landfill, Long Island, New York, U.S. Geol. Surv. Prof. Paper 1085.
Koch, M. and Zhang, G.: 1992, Numerical simulation of the effects of variable density in a contaminant plume, Ground Water 30, 731–742.
Krupp, H. K. and Elrick, D. E.: 1969, Miscible displacement in an unsaturated glass bead medium, Water Resour. Res. 4, 809–815.
LeBlanc, D. R., Garabedian, S. P., Hess, K. M., Gelhar, L. W., Quadri, R. D., Stollenwer, K. G. and Wood, W. W.: 1991, Large-scale natural gradient tracer test in sand and gravel, Cape Cod, Massachusetts, 1. Experimental design and observed tracer movement, Water Resour. Res. 27, 895–910.
Leroy, C., Hulin, J. P. and Lenormand, R.: 1992, Tracer dispersion in stratified porous media: influence of transverse dispersion and gravity, J. Contam. Hydrol. 11, 51–68.
Loggia, D., Rakotomalala, N., Salin, D. and Yortsos, Y. C.: 1995, Evidence of new instability thresholds in miscible displacements in porous media, Europhys. Lett. 32, 633–638.
MacFarlane, D. S., Cherry, J. A., Gillham, R.W. and Sudicky, E. A.: 1983, Migration of contaminants in groundwater at a landfill: a case study, 1. Groundwater flow and plume delineation, J. Hydrol. 63, 1–29.
Manickam, O. and Homsy, G. M.: 1993, Stability of miscible displacements in porous media with nonmonotonic viscosity profiles, Phys. Fluids A Fluid 5, 1356–1367.
Manickam, O. and Homsy, G. M.: 1994, Simulation of viscous fingering in miscible displacements with nonmonotonic viscosity profiles, Phys. Fluids 6, 95–107.
Manickam, O. and Homsy, G. M.: 1995, Fingering instabilities in vertical miscible displacement flows in porous media, J. Fluid Mech. 288, 75–102.
Mannhardt, K. and Hisham, A. N.: 1994, A review of one-dimensional convection-dispersion models and their applications to miscible displacement in porous media, In Situ 18, 277–345.
Moser, H.: 1995, Einfluss der Salzkonzentration auf die hydrodynamische dispersion im poroesen medium, PhD Thesis, Bauingenieurwesen und angewandte Geowissenschaften der Technischen Universitaet Berlin, Berlin.
Ogata, A.: 1970, Theory of dispersion in a granular medium, Geol. Surv. Prof. Paper 411-I.
Oostrom, M., Hayworth, J. S., Dane, J. H. and Güven, O.: 1992a, Behavior of dense aqueous phase leachate plumes in homogeneous porous media, Water Resour. Res. 28, 2123–2134.
Oostrom, M., Dane, J. H., Güven, O. and Hayworth, J. S.: 1992b, Experimental investigation of dense solute plumes in an unconfined aquifer model, Water Resour. Res. 28, 2315–2326.
Ophori, D. U.: 1998, The significance of viscosity in density dependent flow of groundwater, J. Hydrol. 204, 261–270.
Quintard, M., Bertin, H. and Prouvost, L.: 1987, Criteria for the stability of miscible displacement through porous columns, Chem.-Ing.-Tech. 59, 354–355.
Rogerson, A. and Meiburg, E.: 1993a, Shear stabilization of miscible displacement processes in porous media, Phys. Fluids A Fluid 5, 1344–1355.
Rogerson, A. and Meiburg, E.: 1993b, Numerical simulation of miscible displacement processes in porous media flow under gravity, Phys. Fluids A Fluid 5, 2644–2660.
Rose, D. A. and Passioura, J. B.: 1971, Gravity segregation during miscible displacement experiments, Soil Sci. 111, 258–265.
Saffman, P. G. and Taylor, G. I.: 1958, The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid, P. Roy. Soc. Lond. A24, 312–329.
Schincariol, R. A. and Schwartz, F.W.: 1990, An experimental investigation of variable density flow and mixing in homogeneous and heterogeneous media, Water Resour. Res. 26, 2317–2329.
Schowalter, W. R.: 1965, Stability criterion for miscible displacement of fluids from a porous medium, AICHE J. 11, 99–105.
Sudicky, E. A., Cherry, J. A. and Frind, E. O.: 1983, Migration of contaminants in groundwater at a landfill: a case study, 4. A natural-gradient dispersion test, J. Hydrol. 63, 81–108.
Tan, C. T. and Homsy, G. M.: 1986, Stability of miscible displacements in porous media: rectilinear flow, Phys. Fluids 29, 3549–3556.
Tan, C. T. and Homsy, G. M.: 1988, Simulation of nonlinear viscous fingering in miscible displacement, Phys. Fluids 31, 1330–1338.
Tchelepi, H. A., Orr Jr., F. M., Rakotomalala, N., Salin, D. and Woumeni, R.: 1993, Dispersion, permeability heterogeneity, and viscous fingering: acoustic experimental observations and particle-tracking simulations, Phys. Fluids A Fluid 5, 1558–1574.
Weast, R. C.: 1989, CRC Handbook of Chemistry and Physics, 68th edn, Chemical Rubber Company Press, Boca Raton, FL.
Welty, C. and Gelhar, L. W.: 1991, Stochastic analysis of the effects of fluid density and viscosity variability on macrodispersion in heterogeneous porous media, Water Resour. Res. 27, 2061–2075.
Wooding, R. A.: 1962, Free convection of fluid in a vertical tube filled with porous material, Fluids Mech. 13, 129–144.
Wooding, R. A.: 1969, Growth of fingers at an unstable diffusing interface in a porous medium or Hele-Shaw cell, J. Fluid Mech. 39, 477–495.
Yortsos, Y. C.: 1987, Stability of a certain class of miscible displacement processes in porous media, IMA J. Appl. Math. 38, 167–179.
Yortsos, Y. C.: 1990, Instabilities in displacement processes in porous media, J. Phys. Condens. Mat. 2, SA 443.
Zimmerman, W. B. and Homsy, G. M.: 1991, Nonlinear viscous fingering in miscible displacement with anisotropic dispersion, Phys. Fluids A Fluid 3, 1859–1872.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Jiao, CY., Hötzl, H. An Experimental Study of Miscible Displacements in Porous Media with Variation of Fluid Density and Viscosity. Transport in Porous Media 54, 125–144 (2004). https://doi.org/10.1023/A:1026383019300
Issue Date:
DOI: https://doi.org/10.1023/A:1026383019300