Theoretical basis for the measurement of local transverse dispersion in isotropic porous media

Spreading of a conservative solute in potential flow in a helical porous medium is dominated by the radial velocity distribution within the domain. Higher velocities at the inside of the helix compared to the outside leads to spreading that is balanced by transverse pore-scale dispersion. The angular moments of the concentration distribution exhibit the typical behavior of Taylor-Aris dispersion in which the rate of change of the second central moment is inversely proportional to pore-scale transverse dispersion. We present numerical results for the angular moments over the entire time range and derive analytical expressions for the angular macrodispersion coefficient at the large time limit. We propose a method in which macrodispersion is measured in a helix filled with the porous material of interest in order to infer pore-scale transverse dispersivity values that are difficult to determine with existing methods.