Abstract
Practical field-scale simulations often face efficiency challenges due to convergence issues in the nonlinear Newton solver, stemming from imbalances in nonlinearities across time and space. Factors such as saturation changes near displacement fronts, coupled well-reservoir equations, abrupt well control variations, and non-smooth rock-fluid properties contribute to these challenges, especially on non-orthogonal grids with high aspect ratios and strong petrophysical property heterogeneities. Standard upstream discretization introduces flux discontinuities, and distant initial guesses further hinder convergence.
The runtime of simulations depends heavily on the number of global Newton iterations. While various methods exist to enhance robustness, such as line search, relaxation, time-step cuts, and limiting changes in pressures/saturations, they are often applied universally, even when needed for a single time-step. Local-global domain-decomposition strategies may also improve robustness but come with a potentially unjustified computational cost.
This study explores a straightforward heuristic approach for assessing convergence within a standard Newton iteration and terminating the process if the progress toward convergence is deemed unsatisfactory. This strategy is computationally inexpensive and relies on quantities readily available in most simulators. Despite its simplicity, it has proved highly efficient, as demonstrated herein for two open test cases and one real asset model.
The runtime of simulations depends heavily on the number of global Newton iterations. While various methods exist to enhance robustness, such as line search, relaxation, time-step cuts, and limiting changes in pressures/saturations, they are often applied universally, even when needed for a single time-step. Local-global domain-decomposition strategies may also improve robustness but come with a potentially unjustified computational cost.
This study explores a straightforward heuristic approach for assessing convergence within a standard Newton iteration and terminating the process if the progress toward convergence is deemed unsatisfactory. This strategy is computationally inexpensive and relies on quantities readily available in most simulators. Despite its simplicity, it has proved highly efficient, as demonstrated herein for two open test cases and one real asset model.
