Modeling Hysteresis of Water–NAPL–Air Suction–Saturation Relationship in Porous Media

We propose a novel approach to capture the hysteresis of suction–degree of saturation (s–S), relationship of three–phase fluids in porous media. We defined effective suction, s', that incorporates the delay in the variation of saturation due to hysteresis, with its movement in a closed domain in suction space. This domain defines a possible range of effective suction in which matric suction s always locates at the center of locus, and the incremental change in matric suction determines the movement in the effective suction space. This effective suction is incorporated in a unique s–S relationship defined by the van Genuchten’s equation to obtain a delayed variation in the degrees of saturation caused due to hysteresis during wetting and drying scanning paths. Through the incorporation of entire effective suction space in the van Genuchten’s s–S relationship, we proposed a direct and modest approach to represent the saturation of air, NAPL, and water through a single point in a triangular model along with their possible respective hysteretic variation in both, 2–phase and 3–phase systems. Vertical profiles of realistic soil behavior are also simulated to understand the effect of hysteresis by incorporating the proposed model in a 3–phase system.