Review of the use of Peclet numbers to determine the relative importance of advection and diffusion in low permeability environments

In low permeability environments, transport by advection is often neglected based on a Peclet number criterion. Such a criterion usually states that if the Peclet number (Pe) is much smaller than 1, diffusion dominates over advection and transport may be modeled considering diffusion only. Unfortunately, up to 10 different Peclet number definitions exist and for a particular case these different definitions lead to very diverse Peclet number values, differing several orders of magnitude from each other. In this paper, the different Peclet number definitions are therefore evaluated on their ability to determine the relative importance of transport by advection and by diffusion in low permeability environments. This is done by comparing the results of the analytical solution for pure diffusion with the analytical solution for diffusion, advection and dispersion for a large number of different input parameter values. The relation between the different Peclet numbers and the difference between the calculated concentration considering diffusion only and the calculated concentration considering both diffusion and advection is studied. These calculations show that some Peclet number definitions are not well suited to decide whether advection may be neglected in low permeability media.