Convection describes the movement of a species, such as a pollutant, with the bulk fluid velocity. The velocity field u corresponds to a superficial volume average over a unit volume of the porous medium, including both pores and matrix. This velocity is sometimes called Darcy velocity, and defined as volume flow rates per unit cross section of the medium. This definition makes the velocity field continuous across the boundaries between porous regions and regions with free flow.

The average linear fluid velocities ua, provides an estimate of the fluid velocity within the pores:

where εp is the porosity and θ = sεp the liquid volume fraction, and s the saturation, a dimensionless number between 0 and 1.

The Transport of Diluted Species in Porous Media interface includes two formulations of the convective term. The conservative formulation of the species equations in Equation 5-11 is written as:

If the conservative formulation is expanded using the chain rule, then one of the terms from the convection part, ci∇·u, would equal zero for an incompressible fluid and would result in the non-conservative formulation described in Equation 5-11.

When using the non-conservative formulation, which is the default, the fluid is assumed incompressible and divergence free: ∇ ⋅ u = 0. The non-conservative formulation improves the stability of systems coupled to a momentum equation (fluid flow equation).