Nonlinear Solver Based on Flux-function Trust-regions for Accurate Modeling of Co2 Plume Migration in Aquifers

We describe a Newton-based nonlinear solver for immiscible two-phase transport in the presence of significant viscous, buoyancy, and capillary forces. The evolution of CO2 plumes in heterogeneous saline aquifers, especially during the post-injection period, is an important example of this class of problem. The flux (fractional flow) function, which is strongly nonlinear function of saturation, is divided into trust regions. The delineation of the regions is dictated by the unit-flux point and inflection points in the flux function. Within each trust region, the standard Newton iterative scheme is guaranteed to converge. For problems where the dynamics are dominated by buoyancy and capillary forces, the proposed scheme allows for taking much larger time steps than existing Newton based solvers. The nonlinear solver is demonstrated using challenging problems dominated by buoyancy and capillary forces in heterogeneous domains with emphasis on the CO2 post-injection period.