Reply to ‘ ‘ Comment on upscaling geochemical reaction rates using pore - scale network modeling ’ ’ by Peter C . Lichtner and Qinjun Kang

Our paper ‘‘Upscaling geochemical reaction rates using pore-scale network modeling’’ [1] presents a novel application of pore-scale network modeling to upscale mineral dissolution and precipitation reaction rates from the pore scale to the continuum scale, and demonstrates the methodology by analyzing the scaling behavior of anorthite and kaolinite reaction kinetics under conditions related to CO2 sequestration. We conclude that under highly acidic conditions relevant to CO2 sequestration, the traditional continuum-based methodology may not capture the spatial variation in concentrations from pore to pore, and scaling tools may be important in correctly modeling reactive transport processes in such systems. This work addresses the important but difficult question of scaling mineral dissolution and precipitation reaction kinetics, which is often ignored in fields such as geochemistry, water resources, and contaminant hydrology. Although scaling of physical processes has been studied for almost three decades [2–5], very few studies have examined the scaling issues related to chemical processes [6–8], despite their importance in governing the transport and fate of contaminants in subsurface systems. Lichtner and Kang correctly point out that under conditions of relatively slow reaction rates and fast diffusion, the continuum approach should apply. However, they failed to note that in our model, such ‘‘benign’’ conditions only apply at the single pore level. The relative importance of reaction and diffusion rates is determined by the spatial scale. At the network scale, the larger spatial length requires longer times for the diffusion process to homogenize the concentration field, while reaction rates are faster