Miscible flows in heterogeneous porous media are studied by using a simple analytical model based on convective flow in a bundle of streamtubes. The results are analysed through the concept of fractional flow and compared to existing models. For tracer flow in a permeability field with short range correlations, the fractional flow can be written as a function of the dispersivity of the medium. The dispersivity is related to the statistical properties of the permeability field. For miscible displacement, a general formula is derived for the fractional flow which accounts for the viscosity ratio, the gravity number, and the heterogeneity. The model describes the continuous cross-over between macrodispersion and viscous fingering. It also accounts for the stabilising effects due either to viscosity or density differences. Although some adjustments must be done for the mixing laws, the model agrees with laboratory experiments.


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