Model for Hysteretic Constitutive Relations Governing Multiphase Flow. 2. Permeability-Saturation Relations

摘要

A theoretical model is described for the prediction of relative permeability-saturation (k-S) relations in two-phase (air-water) and three phase (air-oil-water) porous media systems subject to arbitrary saturation paths. Integral expressions for air, water, and oil relative permeabilities are presented. The parametric model for saturation-pressure relations and fluid entrapment is employed in the integral equations to enable derivation of closed-form expressions for air, water, and oil relative permeabilities as functions of current fluid saturations and saturation history. Three-phase k-S relations are calculated for main drainage and imbibition paths for a hypothetical soil to illustrate usage of the model and to evaluate the magnitude of fluid entrapment effects on relative permeabilities. Water permeability-saturation relations are predicted to exhibit mild hysteretic effects except at high saturations, while hysteresis in air permeability-saturation relations is much more pronounced. Predictions of k-S-P relations for a hypothetical NAPL contamination scenario are presented using model parameters determined for a sandy soil by two methods. The results indicate that hysteresis and nonwetting fluid entrapment effects on k-S-P relations may be substantial. Sensitivity to calibration method is found to be small. (Copyright (c) American Geophysical Union, 1987.)