Abstract

Due to spatial scaling effects, there is a discrepancy in mineral dissolution rates in porous media measured at different spatial scales. Many reasons for this spatial scaling effect can be given. We investigate one such reason, i.e. how pore-scale spatial heterogeneity in porous media affects overall mineral dissolution rates. Using the bundle-of-tubes model as an analogy for porous media, we show that the Darcy-scale reaction order increases as the statistical similarity between the pore sizes and the effective-surface-area ratio of the porous sample decreases. The analytical results quantify mineral spatial heterogeneity using the Darcy-scale reaction order and give a mechanistic explanation to the usage of reaction order in Darcy-scale modeling. The relation is used as a constitutive relation of reactive transport at the Darcy scale. We test the constitutive relation by simulating flow-through experiments. The proposed constitutive relation is able to model the solute breakthrough curve of the simulations. In addition, our results imply that we can infer mineral spatial heterogeneity of a porous medium using measured solute concentration over time in a flow-through dissolution experiment.