Two-dimensional power series solution for non-axisymmetrical transport in a radially convergent tracer test with scale-dependent dispersion

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Abstract

It has been known for many years that dispersivity increases with solute travel distance in a subsurface environment. The increase of dispersivity with solute travel distance results from the significant variation of hydraulic properties of heterogeneous media and was identified in the literature as scale-dependent dispersion. This study presents an analytical solution for describing two-dimensional non-axisymmetrical solute transport in a radially convergent flow tracer test with scale-dependent dispersion. The power series technique coupling with the Laplace and finite Fourier cosine transform has been applied to yield the analytical solution to the two-dimensional, scale-dependent advection-dispersion equation in cylindrical coordinates with variable-dependent coefficients. Comparison between the breakthrough curves of the power series solution and the numerical solutions shows excellent agreement at different observation points and for various ranges of scale-related transport parameters of interest. The developed power series solution facilitates fast prediction of the breakthrough curves at any observation point.

Original languageEnglish
Pages (from-to)430-438
Number of pages9
JournalAdvances in Water Resources
Volume30
Issue number3
DOIs
StatePublished - Mar 2007

Keywords

  • Convergent flow field
  • Power series solution
  • Scale-dependent dispersion

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