Non-linear Newton Solver for a Polymer Two-phase System Using Interface-localized Trust Regions

Abstract

Models of polymer flooding account for several processes such as concentration dependent viscosity, adsorption, incomplete mixing, inaccessible pore space, and reduced permeability effects, which altogether gives strongly coupled nonlinear systems that are challenging to solve numerically. Herein, we use a sequentially implicit solution strategy that splits the equation system into a pressure and a transport part. Our objective is to improve convergence rates for the transport subproblem, which contains many of the essential nonlinearities caused by the addition of polymer. Convergence failure for the Newton solver is usually 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 saturation updates suggested by the Newton solver if these exceed a predefined limit. An improved strategy is to use trust regions to determine safe saturation updates that stay within regions having the same curvature for the numerical flux. This approach has previously been used to obtain unconditional convergence for waterflooding scenarios and multicomponent problems with realistic property curves. Herein, we extend the method to polymer flooding, and study the performance of the method for a wide range of polymer parameters and reservoir configurations.