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A model for hysteretic relations governing multiphase flow; Refinements and numerical simulations
Water Resources Research
  • R. J. Lenhard
  • J. C. Parker
  • J. J. Kaluarachchi, Utah State University
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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.

Citation Information
R. J. Lenhard, J. C. Parker and J. J. Kaluarachchi. "A model for hysteretic relations governing multiphase flow; Refinements and numerical simulations" Water Resources Research Vol. 25 Iss. 7 (1989) p. 1727 - 1736
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