Modelling gravitational convection and miscible flows in heterogeneous porous media with a semi-Eulerian-Lagrangian scheme: implications for deep carbon sequestration.

The non-linear interaction of supercritical CO2 with brine in confined saline aquifers is an important problem in geophysical fluid dynamics and understanding its mechanism is pivotal for the design of carbon-sequestration schemes. In principle, dissolution of CO2 into the ambient brine from a buoyant supercritical phase across the CO2-brine interphase causes the density of the mixed diffusive layer to increase, thereby triggering gravitational instability generating Rayleigh-Taylor like convection and increasing CO2 dissolution and uptake by the reservoir. These dynamics are nonlinear and must be studied numerically, with previous works commonly focusing on homogeneous domains and pure diffusion only and often assuming no background flow in the aquifer.

We discuss a large-scale numerical Monte Carlo study considering the three-way interaction of heterogeneous permeability and porosity field structure, background flow, and local-scale dispersion on CO2 uptake. For this purpose, we developed a novel combined Eulerian flow—Lagrangian transport code for simulating single-phase CO2-enriched brine movement in systems featuring a spatially varying density field controlled by dissolved CO2 concentration and a background pressure gradient. The usage of the Lagrangian approach uniquely allows us to quantify the effect of local-scale horizontal and longitudinal dispersion on the flow dynamics and capture relevant non-Fickian transport behaviors without the confounding effect of numerical dispersion and to maintain numerical stability under strongly advective conditions.

We present results characterizing the impact permeability-porosity structure, background flow, local dispersion on CO2 uptake and fingering dynamics. Quantifying these factors via appropriate dimensionless groups, we analyze their impact on onset time of convection, and on regime transition from gravitationally dominated convection to background flow dominated advection-macrodispersion regimes. The relationship between porosity-permeability structure and fingering dynamics is also outlined and quantified.