Robust modeling of hysteretic capillary pressure and relative permeability for two phase flow in porous media

•Numerical simulation of hysteretic capillary pressure and relative permeability.•Application of plasticity theory to hysteresis in reservoir simulation.•Mathematical stability analysis of the proposed numerical approach.•Numerical investigation for cyclic imbibition-drainage processes. We investigate a robust and systematic modeling approach for hysteretic capillary pressure and relative permeability in porous media by using the theory of plasticity, considering that plasticity and hysteresis exhibit both irreversible physical processes. Focusing on the immiscible two-phase flow, we investigate stability analysis and find that the method based on the plasticity can yield well posedness (contractivity) and algorithmic stability (B-stability). This modeling approach can track and compute history-dependent flow properties such as residual saturation. In numerical simulation, we apply the algorithm of the 1D isotropic/kinematic hardening plasticity to reservoir simulation of gas-water flow. For weak and strong capillarity, the modeling yields strong numerical stability even for several drainage-imbibition processes. We also identify differences between with and without hysteresis, showing the importance of hysteretic capillary pressure and relative permeability. Thus, the hysteresis modeling based on the theory of plasticity is promising for robust numerical simulation of strong hysteresis.