Applicability regimes for macroscopic models of reactive transport in porous media.
We consider transport of a solute that undergoes a nonlinear heterogeneous reaction: after reaching a threshold concentration value, it precipitates on the solid matrix to form a crystalline solid. The relative importance of three key pore-scale transport mechanisms (advection, molecular diffusion, and reaction) is quantified by the Péclet (Pe) and Damköhler (Da) numbers. We use multiple-scale expansions to upscale a pore-scale advection-diffusion equation with reactions entering through a boundary condition on the fluid-solid interface, and to establish sufficient conditions under which macroscopic advection-dispersion-reaction equations provide an accurate description of the pore-scale processes. These conditions are summarized by a phase diagram in the (Pe, Da)-space, parameterized with a scale-separation parameter that is defined as the ratio of characteristic lengths associated with the pore- and macro-scales.
Battiato
I
I
Department of Mechanical and Aerospace Engineering, University of California, San Diego, La Jolla, CA 92093, USA.
Tartakovsky
D M
DM
D055598:Chemical Phenomena; D004058:Diffusion; D004784:Environmental Monitoring / Q000379:methods*; D008962:Models, Theoretical; D016062:Porosity; D012989:Soil Pollutants / Q000737:chemistry*; D012996:Solutions; D014872:Water Movements; D014873:Water Pollutants / Q000737:chemistry*
D012989:Soil Pollutants; D012996:Solutions; D014873:Water Pollutants