End Points and Hysteresis

Relative Permeability Remembers Its History

Relative permeability is not a single curve. As gas saturation rises along the drainage path and then water or oil flows back in (imbibition), some gas is cut off into disconnected bubbles and can no longer move. Which curve applies depends on whether the saturation is increasing or decreasing.

The Trapped Gas Endpoint

On the way back the gas relative permeability follows a lower scanning curve and falls to zero not at zero saturation but at a trapped gas saturation $S_{gt}$ well above zero. The higher the gas saturation reached before the reversal, the more gas is left behind immobile.

Why It Matters

This trapping drives water-alternating-gas floods and geological gas storage: the same hysteresis that strands gas during a waterflood is exactly what holds injected CO2 securely underground.