Localized Nonlinear Solution Strategies for Efficient Simulation of Unconventional Reservoirs (2008.01539v2)

Abstract: Accurate and efficient numerical simulation of unconventional reservoirs is challenging. Long periods of transient flow and steep potential gradients occur due to the extreme conductivity contrast between matrix and fracture. Detailed near-well/near-fracture models are necessary to provide sufficient resolution, but they are computationally impractical for field cases with multiple fracture stages. Previous works in the literature of unconventional simulations mainly focus on gridding level that adapts to wells and fractures. Limited research has been conducted on nonlinear strategies that exploit locality across timesteps and nonlinear iterations. To perform localized computations, an a-priori strategy is essential to first determine the active subset of simulation cells for the subsequent iteration. The active set flags the cells that will be updated, and then the corresponding localized linear system is solved. This work develops localization methods that are readily applicable to complex fracture networks and flow physics in unconventional reservoirs. By utilizing the diffusive nature of pressure updates, an adaptive algorithm is proposed to make adequate estimates for the active domains. In addition, we develop a localized solver based on nonlinear domain decomposition (DD). Comparing to a standard DD method, domain partitions are dynamically constructed. The new solver provides effective partitioning that adapts to flow dynamics and Newton updates. We evaluate the developed methods using several complex problems with discrete fracture networks. The results show that large degrees of solution locality present across timesteps and iterations. Comparing to a standard Newton solver, the new solvers enable superior computational performance. Moreover, Newton convergence behavior is preserved, without any impact on solution accuracy.