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Abstract: 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. [ABSTRACT FROM AUTHOR]

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 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. [Copyright &y& Elsevier]