Dispersion and Reservoir Heterogeneity

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Abstract
Summary: Macroscopic dispersion is the mixing, on the scale of several hundreds of grain diameters, at a point in a permeable medium that is free of boundary effects. Megascopic dispersion is the one-dimensional (1D) dispersion derived by averaging across an entire cross section. This work investigates how both dispersions vary with heterogeneity, aspect ratio, diffusion coefficient, and autocorrelation. The theoretical results are compared to existing field and laboratory data and to existing theories for limiting cases. The degree of autocorrelation in the medium determines whether or not megascopic dispersivity (dispersion coefficient divided by velocity) is uniquely defined. Large correlation distances (with respect to the medium dimensions) imply a dispersivity that grows with distance traveled. Small correlation distances imply a dispersivity that is eventually stabilized at some constant value. This value is related to the heterogeneity of the medium. On the field scale, diffusion is insignificant, but on a laboratory scale, it can stabilize the dispersivity even if the medium is correlated. Macroscopic dispersivity is sensitive to diffusion in both the laboratory and field scale. It is smaller than or equal to megascopic dispersivity, also in conformance with experimental data, and comparable to laboratory-measured dispersivity.