Augmented operator-based linearization for modeling of history-dependent behavior with applications to CO2 sequestration

Abstract

Accurate simulation of CO2 sequestration in deep saline aquifers requires consistent treatment of history-dependent processes. Operator-Based Linearization (OBL) provides an efficient and robust framework for compositional flow simulation. However, it was originally designed for reversible physical processes, since the operator evaluation depends solely on the instantaneous thermodynamic state. In this work, we extend the OBL approach by introducing history-dependent variables into the operator parameter space while keeping them outside the Newton unknown vector, thereby augmenting OBL with history dependency while preserving the dimension of the Jacobian matrix. To apply the augmented OBL framework to hysteresis modeling, a new hysteresis algorithm is proposed, in which the maximum gas saturation is used as the history coordinate; the flow equations are solved fully implicitly with respect to the primary variables, while this history variable is held fixed during Newton iterations and updated locally after timestep convergence to capture drainage–imbibition transitions and CO2 dissolution feedback. The augmented OBL approach is validated against the academic DARSim simulator and the commercial CMG simulator, demonstrating close agreement with conventional hysteresis modeling approaches. A sensitivity analysis of the operator parameterization shows that the resolution of the parameter space governs both accuracy and computational cost within the OBL framework. Numerical experiments in one-dimensional homogeneous and two-dimensional heterogeneous models further demonstrate that the proposed approach provides a practical and accurate means of incorporating history-dependent physics into reservoir-scale compositional simulations of CO2 sequestration.