Modeling of irreversible thermodynamics relevant to CCS using parameterization approach

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.