Quasi-asymptotic Dispersion

The experimental characterization of voidspaces in porous media generally includes measurements of volume averaged scalar properties such as porosity, dispersivity, or the hydrodynamic radius r(h) = V/S, where V and S are the volume and surface area of the pore space respectively. Displacement encoding NMR experiments have made significant contributions to this characterization. It is clear, however, that NMR derived dispersivities in packed beds - the one random porous system for which there exist canonical but incompatible theoretical predictions with few or no adjustable parameters - can be affected by the same experimental complications which have substantially contributed to the puzzling scatter in published dispersion results based on elution experiments. Notable among these are macroscopic flow heterogeneities near walls, and inhomogeneous flow injection. Using the first three cumulants we delineate a transition from a pre-asymptotic to a quasi-asymptotic dispersion regime and determine the true dispersivity of the random pack of spheres.