A model for hysteretic relations governing multiphase flow; Refinements and numerical simulations
Refinements are proposed to a constitutive model for hysteretic three-phase permeability-saturation-pressure relations which we have described in papers 1 and 2 of this series. The modifications involve distinguishing between various mechanisms of air entrapment in water and oil phases required to ensure consistency in mass balance calculations. Analytical saturation-pressure derivatives for the three-phase hysteretic k-S-P model are derived which provide exact representations of fluid pair capacities needed for implicit numerical solution of the governing equations for three-phase flow. The hysteretic constitutive model was incorporated into a finite element multiphase flow code to enable simulation of transient three-phase flow under conditions of arbitrary saturation path history. Simulations were conducted for a scenario involving the injection of an oil slug into a vertical soil profile subjected to a fluctuating groundwater table. In addition to simulations with the full hysteresis model, runs were performed with a model which considers hysteresis due to nonwetting fluid entrapment effects only and to a model which disregards hysteresis entirely. Full hysteresis and trapped fluid only analyses yielded very similar results. The hysteretic models predicted about two-thirds of the 7.5 cm of injected oil would become trapped by a 50-cm increase in water table elevation. Ignoring fluid entrapment thus may lead to large errors in predicted fluid distributions during periods of rising water tables.