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Non-Fickian Description of Tracer Transport Through Heterogeneous Porous Media

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Abstract

The porosity and the in situ concentration of tracer testing through different heterogeneous carbonate cores were performed using X-ray computed tomography. The results were interpreted using three approaches: the convection–diffusion equation, the arrival time moments and the stratified model. The results showed that (i) the Fickian approach led to a dispersion coefficient varying along each sample (ii) the statistical approach led to a power law of the variance of the arrival time as a function of the distance and (iii) the stratified model allowed quantification of the heterogeneity factor, which also appeared to be a power function of the distance. These data suggest that the temporal moments approach and the stratified model, but not the classical Fickian approach, are suitable for describing tracer transport through heterogeneous media at the core scale.

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References

  • Aggelopoulos C.A., Tsakiroglou C.D.: The longitudinal dispersion coefficient of soils as related to the variability of local permeability. Water Air Soil Pollut. 185, 223–237 (2007). doi:10.1007/s11270-007-9445-6

    Article  Google Scholar 

  • Barenblatt G.E., Zheltov I.P., Kochina I.N.: Basic concept of the theory of seepage of homogeneous liquids in fissured rocks. J. Appl. Math. Mech. Eng. Transl. 24, 1286–1303 (1960). doi:10.1016/0021-8928(60)90107-6

    Article  Google Scholar 

  • Bauget F., Fourar M.: Non-Fickian dispersion in a single fracture. J. Contam. Hydrol. 100, 137–148 (2008). doi:10.1016/j.jconhyd.2008.06.005

    Article  Google Scholar 

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

    Google Scholar 

  • Berkowitz B., Scher H.: The role of probalilistic approaches to transport theory in heterogeneous media. Transp. Porous Media 42, 241–263 (2001). doi:10.1023/A:1006785018970

    Article  Google Scholar 

  • Berkowitz B., Cortis A., Dentz M., Scher H.: Modeling non-Fickian transport in geological formations as a continuous time random walk. Rev. Geophys. 44, RG2003 (2006). doi:10.1029/2005RG000178

    Article  Google Scholar 

  • Carlier E.: Solute transport in dual porosity medium and scale effect of dispersivity: proposal of a probabilistic equation. J. Environ. Hydrol. 15(4), 1–8 (2007)

    Google Scholar 

  • Coasts K.H., Smith B.D.: Dead-end pore volume and dispersion in porous media. Soc. Pet. Eng. J. Trans. AIME 231(4), 73–84 (1964)

    Google Scholar 

  • Communar G.M.: A solute Transport in Stratified Media. Transp. Porous Media 31, 133–134 (1998). doi:10.1023/A:1006557032656

    Article  Google Scholar 

  • Cortis A., Gallo C., Scher H., Berkowitz B.: Numerical simulation of non-Fickian transport in geological formations with multiple-scale heterogeneities. Water Resour. Res. 40, W04209 (2004). doi:10.1029/2003WR002750

    Article  Google Scholar 

  • Dauba, C., Hamon, G., Quintard, M., Cherblanc, F.: Identification of parallel heterogeneities with miscible displacement, SCA paper 9933, Golden, USA (1999)

  • Dagan G.: Flow and Transport in Porous Formations. Springer-Verlag, New York (1989)

    Google Scholar 

  • Dagan G., Neuman P.: Subsurface Flow and Transport: A Stochastic Approach. Cambridge University Press, New York (1997)

    Google Scholar 

  • Domenico P.A., Robbins G.A.: A dispersion scale effect in model calibration and field tracer experiments. J. Hydrol. (Amst.) 70, 123–132 (1984). doi:10.1016/0022-1694(84)90117-3

    Article  Google Scholar 

  • Fourar, M., Konan, G., Fichen, C., Rosenberg, E., Egermann, P., Lenormand, R.: Tracer tests for various carbonate cores using X-ray CT, society of core analysis. Annual international symposium, Toronto, Canada, 21–25 Aug 2005

  • Fourar, M.: Characterization of heterogeneities at the core-scale using the equivalent stratified porous medium approach. In: International symposium of the society of core analysts, Trondheim, Norway, 12–16 Sept 2006

  • Gerke H.H., van Genuchten M.T.: A dual-porosity model for simulating the preferential movement of water and solutes in structured porous media. Water Resour. Res. 29(2), 305–320 (1993). doi:10.1029/92WR02339

    Article  Google Scholar 

  • Gelhar L.W., Gutjahr A.L., Naff R.L.: Stochastic analysis of macrodispersion in a stratified aquifer. Water Resour. Res. 15, 1387–1397 (1979). doi:10.1029/WR015i006p01387

    Google Scholar 

  • Gelhar L.W., Welty C., Rehfeldt K.R.: A critical review of data on field-scale dispersion in aquifers. Water Resour. Res. 28, 1955–1974 (1992). doi:10.1029/92WR00607

    Article  Google Scholar 

  • Güven O., Molz F.J., Melville J.G.: An analysis of dispersion in a stratified aquifer. Water Resour. Res. 20, 1337–1354 (1984). doi:10.1029/WR020i010p01337

    Article  Google Scholar 

  • Han N., Bhakta J., Carbonell R.G.: Longitudinal and lateral dispersion in packed beds: Effect of column length and particle size distribution. AIChE J. 31, 277–288 (1985). doi:10.1002/aic.690310215

    Article  Google Scholar 

  • Hidajat, I., Mohanty, K.K., Flaum, M., Hirasaki, G.: Study of vuggy carbonates using NMR and X-Ray CT scanning. SPE Reservoir Evaluation and Engineering, October (2004)

  • Lenormand R.: Determining flow equations from stochastic properties of a permeability field: The MHD model. SPE J. 1, 179–190 (1996)

    Google Scholar 

  • Marle C.M., Simandoux P., Pacsirszky J., Gaulier C.: Etude du déplacement de fluids miscibles en milieu poreux stratifié. Rev. Inst. Fr. Pet. 22, 272–294 (1967)

    Google Scholar 

  • Matheron G., de Marsily G.: Is transport in porous media always diffusive? A counterexample. Water Resour. Res. 16, 901–917 (1980). doi:10.1029/WR016i005p00901

    Article  Google Scholar 

  • Mercado A., de Marsily G.: The spreading pattern of injected waters in a permeability stratified aquifer. IAHS AISH Publ. 72, 23–36 (1967)

    Google Scholar 

  • Moctezuma-B, A., Fleury, M.: Permeability mapping on vuggy core sample using tracer experiments and streamline simulations. SCA paper 9919 Golden, USA (1999)

  • Naff R.L.: On the nature of the dispersive flux in saturated heterogeneous porous media. Water Resour. Res. 5, 1013–1026 (1990)

    Article  Google Scholar 

  • Olivier, P., Cantegrel, L., Laveissière, J., Guillonneau, N.: Multiphase flow behaviour in vugular carbonates using X-Ray CT, SCA paper 2004-13, Abu Dhabi, UAE (2004)

  • Rajaram H., Gelhar L.W.: Plume scale-dependent dispersion in heterogeneous aquifers, 2, Eulerian analysis and three dimensional aquifers. Water Resour. Res. 29, 3261–3276 (1993). doi:10.1029/93WR01068

    Article  Google Scholar 

  • Siddiqui, S., Funk, J., Khamees, A.: Static and dynamic measurements of resevoir heterogeneities in carbonate reservoirs, SCA paper 2000-06, Abu Dhabi, UAE (2000)

  • Srivastava R.K., Chatzis I., Dullien A.L.: A computerized technique for measuring in-situ concentrations during miscible displacements in porous media. Transp. Porous Media 7, 127–145 (1992). doi:10.1007/BF00647393

    Article  Google Scholar 

  • Sternberg S.P.K.: Dispersion measurements in highly heterogeneous laboratory scale porous media. Transp. Porous Media 54, 107–124 (2004). doi:10.1023/A:1025708313812

    Article  Google Scholar 

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  1. Ecole Nationale Supérieure des Mines de Nancy, LEMTA, Parc de Saurupt, 54042, Nancy Cedex, France

    Mostafa Fourar & Giovanni Radilla

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  1. Mostafa Fourar
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  2. Giovanni Radilla
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Correspondence to Mostafa Fourar.

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Fourar, M., Radilla, G. Non-Fickian Description of Tracer Transport Through Heterogeneous Porous Media. Transp Porous Med 80, 561–579 (2009). https://doi.org/10.1007/s11242-009-9380-7

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