Abstract
The coefficient of dispersion, D ij , and the dispersivity, a ijkl , appear in the expression for the flux of a solute in saturated flow through porous media. We present a detailed analysis of these tensors in an axially symmetric porous medium, e.g., a stratified porous medium, with alternating layers, and show that in such a medium, the dispersivity is governed by six independent moduli. We present also the constraints that have to be satisfied by these moduli. We also show that at least two independent experiments are required in order to obtain the values of these coefficients for any three-dimensional porous medium domain.
Similar content being viewed by others
References
Batchelor G.K.: The theory of axisymmetric turbulence. J. Proc. R. Soc. Lond. A Math. Phys. Sci. 186(1007), 480–502 (1946)
Bear J.: On the tensor form of dispersion. J. Geophys. Res. 66, 1185–1197 (1961)
Bear J.: Dynamics of Fluids in Porous Media, pp. 764.. American Elsevier, New York (1972)
Burnett R.D., Frind E.O.: Simulation of contaminant transport in three dimensions, 2, dimensionality effects. Water Resour. Res. 23, 695–705. (1987)
De Groot S.R., Mazur P.: Non-Equilibtium Thermodynamics, pp. 510. North-Holland Publ. Com, Amsterdam (1962)
de Marsily G.: Quantitative Hydrology. Groundwater Hydrology for Engineers. Academis Press, NY (1986)
Garabedian S.P., LeBlanc D.R.L.W., Gelhar L.W., Celia M.A.: Large-scale natural gradient tracer test in sand and gravel, analysis of spatial moments for a non-reactive tracer. Water Resour. Res. 27(5), 911–942 (1991)
Gelhar L.W., Welty C., Rehfeldt K.R.: A critical review of data on field-scale dispersion in aquifers. Water Resour. Res. 28(7), 1955–1974 (1992)
Jahn H.A.: Acta Cryst 2, 33 (1949)
Jensen K.H., Bitsch K., Bjerg P.L.: Large-scale dispersion experiments in a sandy aquifer in Denmark. Water Resour. Res. 29, 673–696 (1993)
Landau L.D., Lifshitz E.M.: Theory of Elasticity. Pergamon, Oxford (1986)
Lichtner P.C., Kelkar C., Robinson B.: New form of dispersion tensor for axisymmetric porous media with implementation in particle tracking. Water Resour. Res. 38, # 8 (2002)
Nikolaevskii V.N.: Convective diffusion in porous media. PMM 23, 1042–1050 (1959)
Poreh M.: The dispersivity tensor in isotropic and axisymmetric mediums. J. Geophys. Res. 76(16), 3909–3913 (1965)
Robertson H.P.: The invariant theory of isotropic turbulence. Proc. Phil. Soc. 36, 209–223 (1940)
Robson, S.G.: Application of Digital Profile Modeling Techniques to Groundwater Solute Transport at Barstow. US Geol. Surv. Water Supply Pap. # 2050, 28 pp. (1978)
Scheidegger A.E.: General theory of dispersion in porous media. J. Geophys. Res. 66, 3273–3278 (1961)
Sirotine, Y., Chaskolskaya, M.: Fondaments de la Physique des Crystaux, 680 pp. Edition Mir, Moscow (1984) (Russian Ed., 1975)
Zheng C., Bennett C.D.: Applied contaminant transport modeling, theory and practice, pp. 440. Van Nostrand Reinhold, NY (1995)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Fel, L., Bear, J. Dispersion and Dispersivity Tensors in Saturated Porous Media with Uniaxial Symmetry. Transp Porous Med 85, 259–268 (2010). https://doi.org/10.1007/s11242-010-9558-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11242-010-9558-z