Dissolution trapping of CO2 in brine can reduce the risk of leakage of supercritical CO2 during long-term Geological Carbon Sequestration (GCS). The dissolution of overlying gaseous CO2 into brine increases the density of brine in its upper portion, which causes gravity-driven convection (GDC) and thus significantly increases the rate of CO2 dissolution. To date, most studies on GDC-driven dissolution are based on homogeneous media and only few studies exist on the effect of heterogeneity on GDC-driven dissolution. Here, we study the effect of heterogeneity on GDC-driven dissolution rate by using numerical simulations with randomly obtained permeability fields. Dissolution rates calculated by these simulations are related to properties of the permeability field by using least-squares regression. We obtained two empirical formulas for predicting the asymptotic GDC-driven dissolution rate. In the first formula the dissolution rate is almost linearly proportional to the dimensionless equivalent vertical permeability. In the second one the dissolution rate is linearly proportional to a dimensionless vertical finger-tip velocity. Both formulas show a non-linear relation between dissolution and anisotropy with higher anisotropy giving lower dissolution rates.

The presence of solute concentration fluctuations at spatial scales much below the scale of resolution is a major challenge for modeling reactive transport in porous media. Overlooking small-scale fluctuations, which is the usual procedure, often results in strong disagreements between field observations and model predictions, including, but not limited to, the overestimation of e˙ective reaction rates. Existing innovative approaches that account for local reactant segregation do not provide a general mathematical formulation for the generation, transport and decay of these fluctuations and their impact on chemical reactions. We propose a Lagrangian formulation based on the random motion of fluid particles carrying solute concentrations whose departure from the local mean is relaxed through multi-rate interaction by exchange with the mean (MRIEM). We derive and analyze the macroscopic description of the local concentration covariance that emerges from the model, showing its potential to simulate the dynamics of mixing-limited processes. The action of hydrodynamic dispersion on coarse-scale concentration gradients is responsible for the production of local concentration covariance, whereas covariance destruction stems from the local mixing process represented by the MRIEM formulation. The temporal evolution of integrated mixing metrics in two simple scenarios shows the trends that characterize fully-resolved physical systems, such as a late-time power-law decay of the relative importance of incomplete mixing with respect to the total mixing. Experimental observations of mixing-limited reactive transport are successfully reproduced by the model.

In this work we employ a reduced-order basis of conservative chemical components to model reactive transport using a Lagrangian (particle tracking) method. While this practice is well-understood in the Eulerian (grid-based) context, its adaptation to a Lagrangian context requires a novel reformulation of particle transport properties. Because the number of conservative-species particles need not change during simulation, spatial resolution stays constant in time, and there is no increase in computational expense due to increasing numbers of product particles. Additionally, this treatment simplifies the interaction between equilibrium and kinetic reactions and allows the use of species-dependent transport operators at the same time. We apply this method to model a suite of simple test problems that include equilibrium and kinetic reactions, and results exhibit excellent match with base-case Eulerian results. Finally, we apply the new method to model a 2D problem concerning the mobilisation of cadmium by a CO$_2$ leak, showing the potential applicability of the proposed methodology.

Geological Carbon Sequestration mitigates climate change by capturing and storing carbon emissions in deep geologic formations. Dissolution trapping is one mechanism by which CO2 can be trapped in a deep formation. However, heterogeneity can significantly influenced dissolution efficiency. This work addresses the injection of CO2 in perfectly stratified saline formations under uncertainty. Monte Carlo two-phase flow compositional simulations involving the dissolution of CO2 into brine and evaporation of water into the CO2-rich phase are presented. We systematically analyzed the interplay between heterogeneity and buoyant forces, which is shown to control the migration of the CO2 plume as well as the temporal evolution of dissolution efficiency. Results show that when buoyant forces are important, vertical segregation controls the overall behavior of CO2, diminishing the influence of small-scale heterogeneity on dissolution. However, when buoyant forces are relatively small compared to the degree of heterogeneity, CO2 migrates preferentially through high permeability layers and dissolution efficiency increases with heterogeneity due to the stretching of the CO2 plume that enhances mixing. As a result, in this situation, the upscaling of permeability leads to an underestimation of the dissolution efficiency. A review of field sites shows that dissolution is heterogeneity-controlled in most real systems. Knowing that most numerical models cannot afford to represent heterogeneity at an adequate scale, results indicate that dissolution efficiency can be typically underestimated by a factor close to 1.5.

Aquifer remediation with in situ soil washing techniques and enhanced oil removal typically involve the injection of liquid solutions into the geological formation to displace and mobilize non-aqueous phase liquids (NAPLs). The efficiency of these systems is oftentimes low because the displacing fluid bypasses large quantities of NAPL due to the inherent complexity of a heterogeneous natural system. Here, chaotic advection generated by a rotating periodic injection pulse is proposed as a method to enhance NAPL removal and mixing. To evaluate the method, we perform two-phase flow simulations in multiple realizations of random permeability fields with different correlation structures and connectivity between injection and extraction wells embedded in a five-spot pattern. Results show that chaotic advection can significantly improve removal efficiency and mixing depending on several controlling factors. Chaotic advection effects are more significant under unfavorable conditions, i.e., when injection and extraction wells are well-connected through preferential channels, permeabilities are highly heterogeneous, and/or the mobility ratio between the wetting and the non-wetting fluid is larger than one. Removal efficiency reaches its maximum value when the Kubo number is close to one, i.e., when the saturation front travels one range of the permeability field in an injection pulse. These effects can develop in just a few cycles. However, removal efficiency should undergo first an early stage with detrimental effects in order to maximize removal in the long term. Chaotic advection not only enhances NAPL removal and mixing, but also reduces the uncertainty, making the system more reliable and less dependent on heterogeneity.