Pattern formation and coarsening dynamics in three-dimensional convective mixing in porous media

Abstract

Geological carbon dioxide (CO 2 ) sequestration entails capturing and injecting CO 2 into deep saline aquifers for long-term storage. The injected CO 2 partially dissolves in groundwater to form a mixture that is denser than the initial groundwater. The local increase in density triggers a gravitational instability at the boundary layer that further develops into columnar plumes of CO 2 -rich brine, a process that greatly accelerates solubility trapping of the CO 2 . Here, we investigate the pattern-formation aspects of convective mixing during geological CO 2 sequestration by means of high-resolution three-dimensional simulation. We find that the CO 2 concentration field self-organizes as a cellular network structure in the diffusive boundary layer at the top boundary. By studying the statistics of the cellular network, we identify various regimes of finger coarsening over time, the existence of a non-equilibrium stationary state, and a universal scaling of three-dimensional convective mixing.

Rock dissolution patterns and geochemical shutdown of –brine–carbonate reactions during convective mixing in porous media

“…This decoupled formulation ((1.3) and (1.4)) has been shown to be a good approximation in systems with fast (but not instantaneous) reactions (Sanchez-Vila, Dentz & Donado 2007). It has been adopted by various authors to study reactions driven by fluid mixing, including calcite dissolution in coastal carbonate aquifers (Rezaei et al 2005;Romanov & Dreybrodt 2006;De Simoni et al 2007) and numerical modelling of laboratory experiments of saltwater-freshwater mixing (Guadagnini et al 2009). In our system, the time to reach geochemical equilibrium is estimated to be of the order of tens of hours, which is indeed small compared with the time for flow and transport over the natural length scale in a typical aquifer (see appendix A).…”

“…The phenomenon of convective mixing has been studied through nonlinear simulations in two dimensions (e.g. Riaz et al 2006;Hassanzadeh, Pooladi-Darvish & Keith 2007;Hidalgo & Carrera 2009;Neufeld et al 2010;Hidalgo et al 2012;Szulczewski, Hesse & Juanes 2013;Bolster 2014;Slim 2014), three dimensions (Pau et al 2010;Fu, Cueto-Felgueroso & Juanes 2013) and experimental systems reproducing the conditions for a stationary horizontal layer (Kneafsey & Pruess 2010;Neufeld et al 2010;Backhaus, Turitsyn & Ecke 2011;Slim et al 2013) or a migrating buoyant current MacMinn & Juanes 2013). In the case of three-dimensional simulations, a striking self-organized network pattern is observed near the top boundary layer (Fu et al 2013).…”

Pattern formation in the geosciences

“…Alternatively, the approaches of Murray & Ashton [21] to coastline migration, or Da Lio et al [16] to wetland development use nonlinear feedback to make explicit testable predictions, which will be important in attempts to minimize disruption of coastal regions by changing climates. Finally, large-scale experiments on carbon capture and storage will require understanding and engineering patterns of reactive porous media flow over many cubic kilometres and inspired modelling such as that of Fu et al [23].…”

“…Similar networks can also be found in surprising places, for example in fluid mixing. Fu et al [23] present a numerical study of the dissolution of CO 2 that is expected as a result of carbon capture and storage in underground aquifers. The convective mixing initially selects a most unstable wavelength, but the pattern rapidly develops into a well-defined cellular network of columnar fingers of CO 2 -rich fluid.…”

A short review on porous media convection

“…Although an extra freedom in 3D may lead to more complicated convective patterns and affect the transport efficiency, the studies by [38,53,54] show that in 3D the flow still retains a similar columnar structure at large Ra in horizontal porous layers, and the convective flux increases linearly with Ra but with a slightly larger prefactor. Therefore, the analysis in 2D does, indeed, shed light on the real 3D system.…”