A modified local error method for adapting time step-size in coupled flow-geomechanics problems

Abstract

Coupled flow-geomechanics model is needed for investigating the stress change, rock-compaction behavior, and stress-dependent properties in many practical reservoir scenarios. However, the coupled model of large-scale simulation problems usually encounters large matrix system and high computational expenses, where the time stepping is a crucial factor for numerical stability and computational efficiency. Here, we report an adaptive time stepping with the modified local error method to reduce iteration time and improve the computational efficiency for the coupled flow-geomechanics modeling. Firstly, the iterative coupling approach with the fixed-stress method is introduced, where the flow and geomechanics equations are sequentially solved at each time step. Secondly, since updating geomechanics module consumes most of the computing time of the coupled system, the modified local error method is mainly used for geomechanics module to adapt the time step size based on the change of displacement. Finally, a synthetic two-dimensional coupled problem is established to apply the proposed adaptive time stepping approach, where the numerical results including the computational efficiency are compared with the results from regular iteratively coupled method and the fully coupled model. The sensitivity about the local error tolerance on the numerical results is also investigated. The geomechanical responses regarding mechanical loading is validated by comparing with the analytical solution of Terzaghi's consolidation problem. The numerical results of the two-dimensional coupled model show the modified local error method not only yields a higher-order solution for better accuracy, but also significantly reduces the iteration number and computational time.