Unconditionally Convergent Nonlinear Solver for Multiphase Flow in Porous Media under Viscous Force, Buoyancy, and Capillarity

Numerical simulations of multiphase flow in porous media often face convergence difficulties in the nonlinear Newton solver, including erratic time stepping, large number of (Newton) iterations, and timestep cuts. Such convergence problems can lead to unacceptably large computational time and are often the main impediment to performing simulation studies of large scale problems, such as oil/gas recovery, groundwater remediation, and CO2 geological sequestration. We analyze the nonlinearity of the discrete transport (mass conservation) equation for immiscible, two-phase flow in porous media in the presence of viscous, buoyancy, and capillary forces. The critical features that cause oscillations and divergence of the Newton iterations are identified and located. Based on the analysis, we develop a nonlinear solver that guides Newton iterations safely and efficiently, such that convergence is achieved for arbitrary timestep sizes.