This work presents an extension of the Operator-Based Linearization (OBL) framework to model irreversible thermodynamic behavior in geological carbon storage (CCS). Traditional OBL employs adaptive parameterization over primary state variables (pressure, temperature, and composition) but lacks the ability to represent hysteresis phenomena critical to CO2–brine systems. To address this, we introduce an additional state parameter—the historical maximum gas saturation into the OBL operator space, enabling accurate modeling of hysteresis in relative permeability and capillary pressure.

The extended framework is validated through a series of numerical tests. A single-cell simulation demonstrates how Land–Killough hysteresis formulations capture saturation-path-dependent permeability behavior. A 2D aquifer model further illustrates improved CO2 trapping and sharper plume fronts due to hysteresis effects. Finally, we apply the model to the heterogeneous SPE11 benchmark, showing enhanced capillary trapping and reduced dissolution under realistic subsurface conditions.

This approach allows for the rigorous integration of irreversible physics into adaptive interpolation without altering the solver structure. Future work includes incorporating capillary pressure hysteresis, validating against field-scale simulators, and extending to fully implicit formulations.

In supercritical CO2 pipeline transport, the operation of pumps and valves often causes the pipeline to enter a transient state. Accurately describing the dynamic response in this state is crucial for making safety control decisions. This paper proposes a nonisothermal one-dimensional transient flow model for supercritical CO2 pipelines based on one-dimensional transient flow equations and equipment characteristic equations. By comparison with experimental data, the GERG-2008 equation, known for its high accuracy, is chosen to calculate the physical property parameters of CO2. By comparing with several sets of literature data, the results show that the errors are all within the acceptable range, which verifies the high accuracy of the model. The study investigates the hydraulic and thermal changes in the pipeline under transient operating conditions, including valve closure, slow startup, and sudden shutdown of the centrifugal pump. The results showed that the water-strike intensity of a supercritical CO2 pipeline is one-third that of a water pipeline but 12 times that of a methane pipeline, which requires sufficient attention. The effect of impurity composition on water strike is significant, particularly when the N2 content reaches 5%, at which point the maximum pressure decreases by 15.1%. In addition, the timing and method of valve shutoff significantly impact water strikes. It is recommended to prioritize the calculation of piping cycles, determine the maximum valve closing time in conjunction with industry standards, and use a linear valve closing method to reduce the water strike pressure. Studies have shown that the startup or sudden shutdown of centrifugal pumps at the inlet can cause sharp fluctuations in the pressure and flow rate, but the new equilibrium state will be established quickly. In addition, doping reduces the magnitude and rate of pressure changes in the pipeline. This study provides an essential foundation for the safe and stable operation of supercritical CO2 pipelines.