Robust nonlinear Newton solver with adaptive interface-localized trust regions

Abstract

The interplay of multiphase flow effects and PVT behavior encountered in reservoir simulations often gives strongly coupled nonlinear systems that are challenging to solve numerically. In a sequentially implicit method, many of the essential nonlinearities are associated with the transport equation, and convergence failure for the Newton solver is often caused by steps that pass inflection points and discontinuities in the fractional flow functions. The industry-standard approach is to heuristically chop time steps and/or dampen updates suggested by the Newton solver if these exceed a predefined limit. Alternatively, one can use trust regions to determine safe updates that stay within regions having the same curvature for the numerical flux. This approach has previously been shown to give unconditional convergence for polymer- and waterflooding problems, also when property curves have kinks or near-discontinuous behavior. While unconditionally convergent, this method tends to be overly restrictive. Herein, we show how detection of oscillations in the Newton updates can be used to adaptively switch on and off trust regions, resulting in a less restrictive method better suited for realistic reservoir simulations. We demonstrate the performance of the method for a series of challenging test cases ranging from conceptual 2D setups to realistic (and publicly available) geomodels like the Norne field and the recent Olympus model from the ISAPP optimization challenge