Homogenisation of advective–diffusive transport in poroelastic media

Advective–diffusive solute transport in a poroelastic medium is usually modelled at the macroscopic scale by considering a poroelastic formulation associated with the classical advective–diffusive solute transport equation. The purpose of the present work is to rigorously determine the macroscopic model by starting with the pore-scale equations that describe transient advective/diffusive solute transport in a saturated deformable elastic porous medium. The macroscopic model is derived by using an homogenisation method. It includes Biot’s model of consolidation and a transport equation of advective–diffusive type. This latter contains a coupling term which reveals a mechanically-induced solute transport mechanism.