Journal of Mechanical Science and Technology

  • 제16권7호
  • /
  • Pages.959-965
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  • 2002
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  • 1738-494X(pISSN)
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  • 1976-3824(eISSN)
대한기계학회 (The Korean Society of Mechanical Engineers)
권호 표지

A Study on the Effective Hydraulic Conductivity of an Anisotropic Porous Medium

  • Seong, Kwanjae (Associate Professor, Dept. of Mechanical Engineering Dong Guk University)
  • 발행 : 2002.07.01
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초록

Effective hydraulic conductivity of a statistically anisotropic heterogeneous medium is obtained for steady two-dimensional flows employing stochastic analysis. Flow equations are solved up to second order and the effective conductivity is obtained in a semi-analytic form depending only on the spatial correlation function and the anisotropy ratio of the hydraulic conductivity field, hence becoming a true intrinsic property independent of the flow field. Results are obtained using a statistically anisotropic Gaussian correlation function where the anisotropy is defined as the ratio of integral scales normal and parallel to the mean flow direction. Second order results indicate that the effective conductivity of an anisotropic medium is greater than that of an isotropic one when the anisotropy ratio is less than one and vice versa. It is also found that the effective conductivity has upper and lower bounds of the arithmetic and the harmonic mean conductivities.

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참고문헌

  1. Dagan, G., 1987, 'Theory of Solute Transport in Groundwater,' Ann. Rev. Fluid Mech, Vol. 19, pp. 187-215
  2. Dagan, G., 1987, Flow and Transport in Porous Formations, p. 465, Springer-Verlag
  3. Deng, F. W. and Cushman, J. H., 1998, 'Higher-order Corrections to the Flow Velocity Covariance Tensor, Revisited,' Water Resour. Res., Vol. 34, pp. 103-106 https://doi.org/10.1029/97WR02610
  4. Freeze, R. A., 1975, 'A Stochastic Conceptual Analysis of One-dimensional Groundwater Flow in Nonuniform Homogeneous Media,' Water Resour. Res., Vol. 11, pp. 725-741 https://doi.org/10.1029/WR011i005p00725
  5. Friedman, S. P. and Seaton, N. A., 1996, 'On the Transport Properties of Anisotropic Network of Capillaries,' Water Resour. Res., Vol. 23, pp. 339-437 https://doi.org/10.1029/95WR02830
  6. Gelhar, L. W., 1993, Stochastic subsurface hydrology, p. 385, Prentice Hall.
  7. Gelhar, L. W. and Axness, C. L., 1983, 'Three-dimensional Stochastic Analysis of Macrodispersion in Aquifers,' Water Resour. Res., Vol. 19, pp. 161-180 https://doi.org/10.1029/WR019i001p00161
  8. Hoeksema, R. J. and Kitanidis, P. K., 1984, 'An Application of the Geostatistical Approach to the Inverse Problem in Two-dimensional Groundwater Modeling,' Water Resour. Res., Vol. 20, pp. 1021-1029 https://doi.org/10.1029/WR020i007p01021
  9. Joo, Y., Fontinich, A. and Dhir, V. K., 1998, 'Remediation of Contaminated Soil with Diesel by Soil Venting Technique,' KSME Int. J., Vol. 12, pp. 1174-1183 https://doi.org/10.1007/BF02942591
  10. Lumley, J. L. and Panofsky, H. A., 1964, The Structure of Atmospheric Turbulence, p. 239, John Wiley
  11. Naff, R. L., 1978, 'A Continuum Approach to the Study and Determination of Field Longitudinal Dispersion Coefficients,' Ph.D. dissertation, N. M. Inst. of Mining and Tech., p. 176, Socorro
  12. Rubin, Y. and Dagan, G., 1988, 'Stochastic Analysis of Boundary Effects on Head Spatial Variability in Heterogeneous Aquifers, 1. Constant Head Boundaries,' Water Resour. Res., Vol. 24, pp. 1689-1697 https://doi.org/10.1029/WR024i010p01689
  13. Salandin, P. and Rinaldo, A., 1990, 'Numerical Experiment on Dispersion in Heterogeneous Porous Media,' Computational Methods in Subsurface Hydrology (ed. G. Gambolati et al.) p. 575, Springer-Verlag