On the modelling of miscible displacements in porous media with stagnant fluid

Equations of miscible fluids displacement in porous media presenting a capacitance effect, i.e., porous media with a mobile fraction and a stagnant fraction, are derived by means of a volume or a surface averaging technique in the case of high Peclet numbers. The models thus obtained are constituted by two coupled equations. The first is a convective-dispersive equation related to the transfer in mobile fraction; the second is a first-order rate expression describing mass transfer between the mobile and immobile regions. These derivations justify the equations which can be obtained by means of an heuristic approach and specify their conditions of validity.These models are compared to the models in which the second equation is a diffusion equation; the latter are shown to be erroneous.