In this paper, we introduce a physics-based nonlinear preconditioned Inexact Newton Method (INB) for the multi-physical simulation of fractured reservoirs. Instead of solving the partial differential equations (PDE) exactly, Inexact Newton method finds a direction for the iteration and solves the equations inexactly with fewer iterations. However, when the equations are not smooth enough, especially when local discontinuities exits, and when proper preconditioning operations are not adopted, the Inexact Newton method may be slow or even stagnant.
As pointed out by Keyes et al. [1], multi-physical numerical simulation faces several challenges, one of which is the local-scale nonlinearity and discontinuity. In this work, we have proposed and studied a nonlinear preconditioner to improve the performance of Inexact Newton Method. The nonlinear preconditioner is essentially a physics-based strategy to adaptively identify and eliminate the highly nonlinear zones.
The proposed algorithm has been implemented into our fully coupled, fully implicit THM reservoir simulator (Wang et al. [2, 3]) to study the effects of cold water injection on fractured petroleum reservoirs. The results of this work show that after the implementation of this nonlinear preconditioner, the iterative solver has become significantly more robust and efficient.