Adaptive Nonlinear Elimination Preconditioning for Transport in Fractured Porous Media

TL;DR

This work addresses slow Newton convergence in the transport subproblem of sequential implicit simulations for fractured reservoirs. It introduces an adaptive Nonlinear Elimination (NE) preconditioned exact Newton method that treats the fracture subsystem as a targeted preconditioner, activated by a physics-informed flux-change criterion. Implemented on EDFM within MRST, the approach yields consistent reductions in total nonlinear iterations (up to 25%) and CPU time (up to 17%) across three waterflood test cases, with adaptive activation limiting overhead. The method offers a practical pathway to more efficient transport solves in highly fractured media, with potential extensions to more nonlinear regimes such as three-phase and compositional flow.

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.

Figures (22)

• Figure 1: Schematic of the Sequential Implicit (SI) solution strategy.
• Figure 2: Fracture network and location of wells.
• Figure 3: Saturation profile at $t = 0.15T$.
• Figure 4: Saturation profile at $t = 0.5T$.
• Figure 5: Saturation profile at $t = T$.