Model for hysteretic constitutive relations governing multiphase flow. 2. Permeability-saturation relations

Journal Article · Tue Dec 01 04:00:00 EST 1987 · Water Resour. Res.; (United States)

DOI:https://doi.org/10.1029/WR023i012p02197· OSTI ID:5451324

Lenhard, R J; Parker, J C

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 which extend the nonhysteretic relative permeability model of Parket et al. to accommodate effects of pore blockage by air trapped in water and oil phases and oil trapped in the water phase. The parametric model for saturation-pressure (S-P) relations and fluid entrapment is employed in the integral equations to enable derivation of close-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. Predicted hysteresis in oil permeability is low at low water saturations but becomes quite marked as water saturation increases. 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 quite substantial. Sensitivity to calibration method is found to be rather small.

• Research Organization: Virginia Polytechnic Institute and State Univ., Blacksburg
• OSTI ID: 5451324
• Journal Information: Water Resour. Res.; (United States), Journal Name: Water Resour. Res.; (United States) Vol. 23:12; ISSN WRERA
• Country of Publication: United States
• Language: English

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54 ENVIRONMENTAL SCIENCES
AIR-WATER INTERACTIONS
ENERGY SOURCES
ENVIRONMENTAL TRANSPORT
FLUID FLOW
FOSSIL FUELS
FUELS
GROUND WATER
HYDROGEN COMPOUNDS
MASS TRANSFER
MATERIALS
MATHEMATICAL MODELS
OXYGEN COMPOUNDS
PERMEABILITY
PETROLEUM
POROUS MATERIALS
SOILS
WATER