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Nonlocal dispersion in porous media: Nonmechanical effects

Chemical Engineering Science
Publication Date
DOI: 10.1016/0009-2509(87)85010-8


Abstract Nonmechanical dispersion mechanisms at high Peclet number in porous media give rise to persistent transients that cannot be predicted by a local Fickian macrotransport equation. Instead, a nonlocal macrotransport equation is derived, which relates the average mass flux to a convolution integral in space and time between the average concentration gradient and a spatial- and temporal-wavelength-dependent effective diffusivity. The nonlocal diffusivity is derived from the fundamental microstructural transport processes. The transient effects arising due to stagnant and recirculating regions in the medium and due to a diffusive boundary layer near solid surfaces are shown to affect the residence-time distribution (RTD) of media whose overall length to microscale size ratio L/a is not large compared to Pe and Pe 1/3, respectively. Here, the Peclet number, Pe = Ua/D, is based on the average velocity through the medium U, the microstructural length scale a and the molecular diffusivity D in the medium. The nonlocal dispersion theory allows a calculation of the full form of the RTDs, which may be bimodal and generally exhibit long-time tails in media of short to moderate length. Experimental measurements of transient dispersion in consolidated media are shown to be in agreement with the theoretical prediction of dispersion due to the diffusive boundary layers near solid surfaces.

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