Upscaling solute transport in porous media in the presence of an irreversible bimolecular reaction

We present a volume-averaging based theoretical analysis of upscaling of reactive transport processes involving fast bimolecular homogeneous irreversible reactions occurring within a porous medium. We start from the formulation driving the system dynamics at the pore scale and derive the governing equations at observation scales associated with laboratory-scale scenarios involving advection-dominated transport of two reactants and the resulting product in the presence of different relative strengths of Dahmköhler (Da) and Péclet (Pe) numbers, i.e., Da ≫ Pe and O(Da) ≈ O(Pe). We provide an original theoretical formulation describing the space–time propagation of advection-dominated conservative components. This formulation includes time dependent dispersive terms, consistently with previous experimental and numerical works. The (upscaled) system of reactive transport equations includes non-Fickian and time dependent dispersive terms which embed a direct link between pore scale dynamics and the chemistry of the problem. We then discuss the appropriateness of adopting effective reaction parameters of the type proposed in previous literature studies for the conditions analyzed. Our results provide a theoretical support to observations according to which (a) dispersion coefficients calibrated under conservative transport scenarios and (b) kinetic parameters measured in a batch reactor might not be appropriate to model the distribution of reactive species in the presence of fast homogeneous irreversible reactions without a proper scaling.