Nonlinear solver based on trust region approximation for CO₂ utilization and storage in subsurface reservoir

Simulation of CO₂ utilization and storage (CCUS) in subsurface reservoirs with complex heterogeneous structures requires a model that captures multiphase compositional flow and transport. Accurate simulation of these processes necessitates the use of stable numerical methods that are based on an implicit treatment of the flux term in the conservation equation. Due to the complicated thermodynamic phase behavior, including the appearance and disappearance of multiple phases, the discrete approximation of the governing equations is highly nonlinear. Consequently, robust and efficient techniques are needed to solve the resulting nonlinear system of algebraic equations. In this study, we present a powerful nonlinear solver based on a generalization of the trust-region technique for compositional multiphase flows. The approach is designed to embed a newly introduced Operator-Based Linearization technique and is grounded on the analysis of multi-dimensional tables related to parameterized convection operators. We split the parameter space of the nonlinear problem into a set of trust regions where the convection operators preserve the second-order behavior (i.e., they remain positive or negative definite). We approximate these trust regions in the solution process by detecting the boundary of convex regions via analysis of the directional derivative. This analysis is performed adaptively while tracking the nonlinear update trajectory in the parameter space. The proposed nonlinear solver locally constrains the update of the overall compositions across the boundaries of convex regions. We tested the performance of the proposed nonlinear solver for various scenarios. In many cases, our approach yields an improved behavior of the nonlinear solution in comparison to state-of-the-art solvers.