Adaptive Nonlinear Elimination Preconditioning for Transport in Fractured Porous Media

Abstract

Sequential implicit (SI) formulations are gaining increasing interest due to their ability to decouple reservoir simulation problems into distinct flow and transport subproblems, allowing for the use of specialized solvers tailored to each. This separation often improves solver efficiency and flexibility, especially in weakly coupled systems. However, for fractured reservoirs, even the decoupled subproblems may generate nonlinearly stiff systems. This is specifically evident in the transport subproblem, where fracture-induced non-linearity imbalances often lead to poor Newton convergence, including failed iterations and frequent timestep cuts. To address this challenge, we propose and investigate an adaptive Nonlinear Elimination (NE) preconditioned exact Newton algorithm specifically tailored to transport subproblems that arise from the sequential splitting of two-phase flow in fractured porous media. The proposed method is evaluated through a series of waterflooding test cases involving discrete fracture networks. The adaptive NE-preconditioned algorithm consistently demonstrates improved convergence behavior and computational efficiency compared to standard Newton.