Mineral dissolution is a dominant control on atmospheric CO<sub>2</sub> levels, water chemistry, contaminant reactive transport, and global element cycles. Although existing literature has documented the dependence of mineral dissolution on time and spatial scales in natural systems, a general upscaled rate law in heterogeneous media across scales still remains elusive. Here we fill this gap by answering three questions: 1) How does the relative importance of transport (advection and diffusion) and reactions change across scales? 2) How and to what extent does the effects of spatial heterogeneity change as scales change? 3) What is the form of an upscaled rate law in heterogeneous media that integrate the effects of time and spatial scales? With data constraints from experimental work, we carried out 640 Monte-Carlo numerical experiments of magnesite dissolution within quartz matrix with spatial distributions characterized by permeability variance and correlation length under a wide range of flow velocity and domain length. We found that the relative strength between reaction, advection, and diffusion/dispersion in the magnesite zones controls the significance of spatial heterogeneity on dissolution rates. Long residence times at small flow velocities and long domain lengths promotes the importance of diffusive-dispersive transport that homogenizes the spatial profiles of solute concentration, therefore leading to less heterogeneous impacts. An upscaled rate law was developed to quantify effective dissolution rates across scales based on kinetic rate constant measured under well-mixed conditions, and timescales of transport through reactive zones and the whole domain. This work provides a potential approach to predict the effects of spatial heterogeneity on mineral dissolution and water chemistry affected by water-rock interactions in natural subsurface systems.

Upscaled rate law for mineral dissolution rates across scales in heterogeneous porous media

254th National Meeting (2017)

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