longitudinal dispersion in nonuniform isotropic porous media

porous medium and an unconsolidated one 1S important in the
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determination of structure at the grain scale.
The transport and dispersion of solutes are dependent on the type
of medium involved. Simple advection-diffusion (equation (1.6)) is
found to be valid for homogeneous, isotropic porous media, subject to
the limitations described in Section 1.2. Although the mechanisms of
dispersion are the same, nonuniformity and heterogeneity provide
greater variations in solute speed and tortuosity. The result of this
is increased dispersion, as indicated by the data of Orlob (1958) for
nonuniform material. For heterogeneous, isotropic porous media, a
generalization of equation (1.6) is possible (Bear, 1972) if the
spatial variations of all the macroscopic properties are known. The
effects of anisotropy on miscible mass transport are not completely
understood.
Heterogeneous porous media are often modeled as homogeneous media
with an overall (super-macroscopic) mean flow direction and super­
macroscopic dispersion coefficient, since data on the exact nature of
the heterogeneities are usually not available. At this level, the
heterogeneity in permeability creates significant dispersive effects.
Extremely high dispersion coefficients are found when an advection­
diffusion modeling approach is used at this scale (Bredehoeft and
Pinder (1973)). Viewing the effects of heterogeneous permeability as a
dispersive phenomenon may create a nondiffusive dispersion in which
transport cannot be satisfactorily modeled using the advection-
diffusion equation. Nondiffusive dispersion is expected when