Taylor dispersion in a packed tube

Presented in this paper is a theoretical analysis for longitudinal scalar spread of mean concentration under a fully developed flow in a tube packed with porous media. A general form of momentum equation for superficial flow in porous media is introduced as a combination of the Navier–Stokes equation and Darcy’s law plus a superficial dispersion term due to phase discontinuity between the fluid flow and solid frame. The analytical solution presented for the fully developed superficial flow includes that for the Poiseulle flow in an evacuated tube as a limiting case. As an extension of Taylor’s classical work on dispersion of soluble matter in solvent flowing slowly through an evacuated tube, a one-dimensional dispersion equation valid for overall environmental assessment of contaminant is rigorously derived by cross-sectionally averaging the superficial mass equation and introducing a closure relation for a new unknown out of the averaging procedure, and corresponding Taylor dispersivity determined is shown to be a generalization of Taylor’s well-known result for the Poiseulle flow.