Pore-Scale Mixing and Transverse Dispersivity of Randomly Packed Monodisperse Spheres

Abstract

We show that transverse dispersion in flow through randomly packed monodisperse spheres (sphere diameter d) is a velocity-dependent superposition of three separable random processes-diffusion with coefficient D(r), intrinsic mechanical dispersion with dispersivity l(m)=d/33 caused by advection on streamlines, and a newly identified coupled mechanical dispersion with dispersivity l(c)=d/11, which arises by coupled advection and transverse diffusion at the pore scale. The velocity dependence of the transverse dispersivity is derived from first principles. Our analysis is insensitive to details of the pore geometry and is verified by pulsed field gradient NMR experiments which covered 4.5 orders of magnitude in reduced velocity.