Dispersion of inert solutes in spatially periodic, two-dimensional model porous media

D. A. Edwards*, M. Shapiro, H. Brenner, M. Shapira

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

115 Scopus citations


Taylor dispersion of a passive solute within a fluid flowing through a porous medium is characterized by an effective or Darcy scale, transversely isotropic dispersitivity {Mathematical expression}, which depends upon the geometrical microstructure, mean fluid velocity, and physicochemical properties of the system. The longitudinal, {Mathematical expression} and lateral, {Mathematical expression} dispersivity components for two-dimensional, spatially periodic arrays of circular cylinders are here calculated by finite element techniques. The effects of bed voidage, packing arrangement, and microscale Péclet and Reynolds numbers upon these dispersivities are systematically investigated. The longitudinal dispersivity component is found to increase with the microscale Péclet number at a rate less than Pe2. This accords with previous calculations by Eidsath et al. (1983), although the latter calculations were found to yield significantly lower longitudinal dispersivities than those obtained with the present numerical scheme. With increasing Péclet number, a Pe2 dependence is, however, approached asymptotically, particularly for square cylindrical arrays - owing to the creation of a linear streamline zone between cylinders. Increasing tortuosity of the intercellular flow pattern reduces the longitudinal dispersivity component and enhances the lateral component. Longitudinal dispersivities for square and hexagonal arrays are found to be quite similar at high porosities; yet they diverge dramatically from one another with decreasing porosity. The longitudinal dispersivity is found to increase markedly with increasing Reynolds number. Comparison of this longitudinal dispersivity with available experimental results shows that {Mathematical expression} experimentally measured for three-dimensional arrays of spheres may be correlated by the present two-dimensional model by an appropriate choice of the array's packing arrangement. In general, the calculated dispersivities were found to be sensitive to the bed packing arrangement and apparently no rationale exists for choosing any one particular geometric microstructure over another for a comparison with existing experimental data. It is thus concluded that existing experimental data pertaining to three-dimensional beds of spherical particles cannot rationally provide a basis for verification of two-dimensional, circular cylindrical dispersion models. The finite-element scheme employed in this work was tested in the purely diffusive, nonflow limit by calculating the composite diffusivities of square cylindrical arrays for different volume fractions and various dispersed solid-continuous phase diffusivity ratios, subsequently comparing these with existing analytical results. An additional test was provided by comparing calculated with analytical axial dispersivities for transport of a dissolved solute in a Poiseuille flow between two parallel plates.

Original languageEnglish
Pages (from-to)337-358
Number of pages22
JournalTransport in Porous Media
Issue number4
StatePublished - Aug 1991
Externally publishedYes


  • Convective dispersion
  • arrays of cylinders
  • coarse-scale transport
  • coefficients
  • finite-element solution
  • solute diffusivity


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