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Localized Linear Systems For Fully-Implicit Simulation Of Multiphase Multicomponent Flow In Porous Media
- Publisher: European Association of Geoscientists & Engineers
- Source: Conference Proceedings, ECMOR XVI - 16th European Conference on the Mathematics of Oil Recovery, Sep 2018, Volume 2018, p.1 - 21
Abstract
During the solution of fully-implicit reservoir simulation time-steps, it is often observed that the computed Newton updates may be very sparse, considering computer precision. This sparsity can be as high as 95% and can vary largely from one iteration to the next.
In recent work, a mathematically sound framework was developed to predict the sparsity pattern before the full linear system is solved. The theory is restricted to general, scalar nonlinear advection-diffusion-reaction problems in multidimensional and heterogeneous settings. This theory had been applied to reduce the size of the linear systems that were computed during sequential implicit timesteps for two-phase flow. The results confirmed that the linearization computations and the linear solution processes may be localized by as much as 95% while retaining the exact Newton convergence behavior and final solution. Inspired by the great success of that methodology, this work develops algorithmic extensions in order to devise localization algorithms for fully-implicit coupled multicomponent problems.
We propose, apply, and test a novel algorithm to resolve a system of hyperbolic equations obtained from an Equation of State (EOS) based compositional simulator. When applied to various fully-implicit flow and multicomponent transport simulations, involving six thermodynamic species, on the full SPE 10 geological model, the observed reduction in computational effort ranges between six to forty-nine fold depending on the level of locality present in the system. We apply this algorithm to several injection and depletion scenarios with and without gravity and capillarity in order to investigate the adaptivity and robustness of the proposed method to the underlying heterogeneity and complexity. We demonstrate that the algorithm enables efficient and robust full-resolution fully implicit simulation without the errors introduced by adaptive discretization methods or the stability concerns of semi-implicit approaches.