Transport of pollutant or of heat in porous media is governed by a combination of advection and diffusion (Chapter 6, Section 6.3.1). The advection phenomenon is related to the transport (noted as a flow f ) of any substance by a fluid flow,
described by the fluid’s velocity, f df/:
fad. = Cf (11.11)
The substance concentration, C, is generally supposed to be small enough not to influence the fluid flow. In porous media, due to the tortuosity of the pore network, and due to the friction, advection is always associated with a diffusion characterised by the diffusion-dispersion tensor, D. Therefore, the total flux of substance is:
Lad. = Cf — iD9’C <1U2>
Balance equations and storage equations may be written in a similar way to the one for diffusion problems Eqs. 11.6, 11.8 and 11.10.
Compared to the diffusion constitutive law, Eqs. 11.7 and 11.9, here an advection term appears which doesn’t depend on the concentration gradient, but directly on the concentration. This is modifying completely the nature of the equations to be solved. Problems dominated by advection are very difficult to solve numerically (Charlier & Radu, 2001). In order to evaluate the relative advection effect, it is useful to evaluate the Peclet’s number, Pe, which is the ratio between the diffusive and advective effects:
fluid j-
Pe = fdiff— (11.13)
2 Dh V ‘
where L is an element dimension and Dh is the hydrodynamic dispersion coefficient (see Chapter 6, Section 6.3.1).
