Abstract
Abstract Time-step selection in fully implicit reservoir simulations is typically guided by the magnitude of changes in solution variables and the number of nonlinear iterations required to converge the previous steps. However, for complex reservoir models, these criteria often fail to accurately predict the need for reduced time steps. Strong nonlinearities in the flow equations can lead to scenarios where even minor saturation changes in a few cells cause significant variations in flow rates, capillary pressures, or injectivity—particularly near wells operating under tight pressure constraints. Similarly, changes in active well controls, such as the onset of gas injection or a drop in reservoir pressure below the bubble point, can necessitate abrupt reductions in step size. Failure to adequately adjust the time step in these situations often results in convergence issues and wasted computational effort. Consequently, an optimal simulation setup, from a runtime efficiency perspective, requires long stable time steps interspersed with short steps during dynamic transitions. In practice, shortcomings in automatic time-step controllers are frequently addressed manually by fine-tuning step-size controls and numerical tolerances to balance accuracy, time-step length, and overall runtime. We introduce a data-driven approach to reduce the need for manual intervention in time-step selection, implemented within an open-source reservoir simulator. The method leverages readily available observables—including well controls, phase conditions, pressures, compositions, and saturations—along with the current time-step length, as inputs to a "cost function" that predicts the computational cost of a given time step. The relationship between these observables and the cost function is modeled using a generalized linear model (GLM). This cost function is then optimized to determine time-step lengths or other numerical hyperparameters (e.g., linear solver preconditioners, numerical tolerances) that maximize computational efficiency. The GLM is computationally lightweight, enabling in-situ training during simulations so that the simulator learns to select optimal time steps tailored to the specific model being simulated. Additionally, the trained GLM can be saved for reuse, for example, in parameter optimization studies or for running ensembles of model realizations with similar dynamic behavior. We demonstrate the effectiveness of this approach on various synthetic and real-world models, identifying the observables that most significantly influence time-step length. To the best of our knowledge, our new self-learning time-step selector is the first to be based on a statistical approach.