Anozie Ebigbo

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.

Flow through rock fractures is frequently represented using models that correct the cubic law to account for the effects of roughness and contact area. However, the scope of such models is often restricted to relatively smooth aperture fields under small confining stresses. This work studies the link between fracture permeability and fracture geometry under normal loads. Numerical experiments are performed to deform synthesized aperture fields of various correlation lengths and roughness values under normal stress. The results demonstrate that aperture roughness can more than triple for applied stresses up to 50 MPa – exceeding the valid range for roughness in most previously published models. Investigating the relationship between permeability and contact area indicates that the increase in flow obstructions due to the development of new contact points strongly depends on the correlation length of the unloaded aperture field. This study eliminates these dependencies by employing a parameter known as the No‐Flow Fraction (NFF) to capture the effect of flow stagnation zones. With this concept, a new Cubic‐law‐based permeability model is proposed that significantly improves the accuracy of permeability estimations, compared to previous models. For cases, where the NFF is difficult to obtain, we introduce an empirical relationship to estimate the parameter from the aperture roughness. The new models yield permeability estimates accurate to within a factor of 2 of the simulated permeability in over three‐quarters of the 3,000 deformed fractures studied. This compares with typical deviations of at least one order of magnitude for previously published permeability models.