Publication Details
On breakdown of macroscopic models of mixing-controlled heterogeneous reactions in porous media
Citation
Battiato I, DM Tartakovsky, AM Tartakovsky, and TD Scheibe. 2009. "On breakdown of macroscopic models of mixing-controlled heterogeneous reactions in porous media." Advances in Water Resources 32(11):1664-1673.
Journal Article
Abstract
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 that occur on liquid-solid interfaces. We establish 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 Damkohler 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 to describe such phenomena, we upscaled the pore-scale RDEs to the continuum (macroscopic) scale and used pore-scale numerical simulations to verify various upscaling assumptions.
