CPR-Based Multilevel Preconditioning for Efficient Solution of Two-Phase Flow in Highly Heterogeneous Petroleum Reservoirs

Resumo

Simulating multiphase flow in heterogeneous petroleum reservoirs presents significant computational challenges due to ill-conditioned discrete systems of equations with a huge number of unknowns that result from the numerical discretization of these problems. Industry applications require multiple scenario analyses, including optimization and uncertainty quantification, requiring efficient numerical methods for the decision-making process. This work presents the Nom-Uniform Algebraic Dynamic Multilevel (NU-ADM) method, combining the Algebraic Multi-Scale (AMS) and the Two-Point Flux Approximation (TPFA) finite volume formulations for fully implicit two-phase flow simulation. The pressure system is obtained via the Constrained Pressure Residual (CPR) method, with multiscale operators serving as preconditioners for an iterative solver. We compare our NU-ADM against standard industrial preconditioners (ILU, AMG) for the CPR pressure system. Our preliminary results show the advantages of the NU-ADM in heterogeneous cases, where traditional methods struggle with slow convergence, and presents itself as a promising alternative in terms of computational cost. The method maintains accuracy while improving computational efficiency through dynamic resolution adaptation. Current investigations aim to explore the use of multi-stage preconditioning (MSP) to further improve performance. This approach combines multiple preconditioning steps, potentially improving robustness for complex cases. Future work will extend our current approach to more complex physical processes and further optimize preconditioning strategies.