A Novel Nonlinear Acceleration Algorithm for Two-Phase Massively Parallel Reservoir Simulation

Abstract Numerical reservoir simulation is a physics-based, high-fidelity approach, and it’s critical for optimizing subsurface flow in complex engineering applications such as hydrocarbon recovery, unconventional reservoir development, and CO2 sequestration, etc. Realistic full-field models often pose numerical challenges due to nonlinearities, phase transitions, and highly heterogeneous media. This work presents a novel nonlinear acceleration method that improves robustness and efficiency of Newton-based solvers by addressing convergence issues arising from derivative discontinuities in the solution space. The proposed approach uses linear system solutions to guide mass updates and restricts updates along convergent directions, effectively managing multiphase transitions and saturated/undersaturated states. Extensive testing on full-field models in production—including those with billions of cells, fine-scale heterogeneity, and diverse rock types—demonstrates that this method consistently achieves 2X–9X speedups over conventional approaches. By directly targeting the root causes of nonlinear solver failure, the method advances the reliability and performance of large-scale reservoir simulations and has reached a level of maturity necessary for routine practical use.