6.6 Dimensionless numbers

Péclet number (Pe) is often used to describe the relative importance of advection and dispersion/diffusion in terms of their respective time scales $\tau_{a} \text { and } \tau_{d}$:

where L is the length of the domain of interest (m), u is the average Darcy flow velocity in the direction of interest (m/s), $D_{h}$ is the dynamic dispersion coefficient (m²/s). There are also some mathematical equations to define the time scales of these processes with similar concepts, mostly depending on the selected characteristic length [Elkhoury et al., 2013; Huysmans and Dassargues, 2005; Steefel and Maher, 2009; Szymczak and Ladd, 2009]. For example, L can also be the grid spacing (m) or correlation length (m) [Huysmans and Dassargues, 2005]. As shown in Figure 3, increasing Pe values indicate increasing dominance of advective transport and sharper front in breakthrough curves.

Figure 3. Effects of Pe on the shape of concentration profiles at steady state. Large Pe indicates that the dominant advective transport compared to dispersion or diffusion.

Steefel et al., 2005