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The typical temporal resolution used in modern simulations significantlyexceeds characteristic time scales at which the system is driven. This isespecially so when systems are simulated over time-scales that are much longerthan the typical temporal scales of forcing factors. We investigate the impactof space-time upscaling on reactive transport in porous media driven bytime-dependent boundary conditions whose characteristic time scale is muchsmaller than that at which transport is studied or observed at the macroscopiclevel. The focus is on transport of a reactive solute undergoing diffusion,advection and heterogeneous reaction on the solid grain boundaries. We firstintroduce the concept of spatiotemporal upscaling in the context ofhomogenization by multiple-scale expansions, and demonstrate the impact oftime-dependent forcings and boundary conditions on macroscopic reactivetransport. We then derive the macroscopic equation as well as the correspondingapplicability conditions based on the order of magnitude of the P\'{e}clet andDamk\"{o}hler dimensionless numbers. Finally, we demonstrate that the dynamicsat the continuum scale is strongly influenced by the interplay between signalfrequency at the boundary and transport processes at the pore level.

Effects of Spatiotemporal Upscaling on Predictions of Reactive Transport in Porous Media