On breakdown of macroscopic models of mixing-controlled heterogeneous reactions in porous media

Reactive transport in porous media is a complex nonlinear phenomenon that involves both homogeneous (bio-)chemical reactions between species dissolved in a fluid and heterogeneous reactions occurring on liquid-solid interfaces. We establish sufficient conditions under which macroscopic reaction-diffusion equations (RDEs) provide an adequate averaged description of pore-scale processes. These conditions are represented by a phase diagram in a two-dimensional space, which is spanned by Damköhler number and a scale-separation parameter. This phase diagram shows that highly localized phenomena in porous media, including precipitation on (and/or dissolution of) a porous matrix, do not lend themselves to macroscopic (upscaled) descriptions. To compute the predictive errors resulting from the use of macroscopic RDEs, we upscaled the pore-scale RDEs to the continuum (macroscopic) scale and used pore-scale numerical simulations to verify various upscaling assumptions.