A parametric model is developed to describe relative permeability‐saturation‐fluid pressure functional relationships in two‐ or three‐fluid phase porous media systems subject to monotonic saturation paths. All functions are obtained as simple closed‐form expressions convenient for implementation in numerical multiphase flow models. Model calibration requires only relatively simple determinations of saturation‐pressure relations in two‐phase systems. A scaling procedure is employed to simplify the description of two‐phase saturation‐capillary head relations for arbitrary fluid pairs and experimental results for two porous media are presented to demonstrate its applicability. Extension of two‐phase relations to three‐ phase systems is obtained under the assumption that fluid wettability follows the sequence water > nonaqueous phase liquid > air. Expressions for fluid relative permeabilities are derived from the scaled saturation‐capillary head function using a flow channel distribution model to estimate effective mean fluid‐conducting pore dimensions. Constraints on model application are discussed.

In these companion papers, a general theoretical model is presented for the description of functional relationships between relative permeability k, fluid saturation S, and pressure P in two‐or three‐phase (e.g., air‐water or air‐oil‐water) porous media systems subject to arbitrary saturation paths. A parametric description of hysteretic S‐P relations is developed in paper 1 which includes effects of air and oil phase occlusion or “entrapment” during imbibition. Entrapped nonwetting fluid saturations at a given point along a saturation path are linearly interpolated between endpoints of primary imbibition scanning curves using maximum trapped saturations estimated by extension of the method of Land (1968). Arbitrary order scanning curves are predicted using an empirical interpolation scheme coupled with a scaling procedure which simplifies computations and minimizes the parametric complexity of the model. All model parameters are defined in terms of measurements which may be obtained from two‐phase systems (air‐water, air‐oil, oil‐water). Extension to three‐phase systems is based on the assumption that fluid entrapment processes in three phase systems are similar to those in two‐phase systems and that wettability decreases in the order: water to oil to air.

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 realtive permeabilities are presented which extend the nonhysteretic relative permeability model of Parker et al. (1987) to accomodate 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 of paper 1 (Parker and Lenhard, this issue) 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. 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 in paper 1 (Parker and Lenhard, this issue). 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.

This paper provides a simple way to convert Brooks‐Corey (BC) parameters to van Genuchten (vG) parameters and vice versa, for use primarily in situations where saturated conditions are likely to be encountered. Essential in this conversion is the preservation of the maximum value of a physical characteristic, the “effective capillary drive” HcM [Morel‐Seytoux and Khanji, 1974], defined with a good approximation for a soil water and air system as HcM = ∫0∞ krw dhc, where krw is relative permeability (or conductivity) to water and hc is capillary pressure (head), a positive quantity. With this conversion, infiltration calculations are essentially insensitive to the model used to represent the soil hydraulic properties. It is strictly a matter of convenience for the user which expression is used. On the other hand, the paper shows that other equivalences may lead to great variations in predictions of infiltration capacity. Consequently, the choice of the proper equivalence to use in calculations for rainfall‐runoff modeling or for low‐level radioactive waste disposal design is a serious matter.

Under the assumption of local vertical equilibrium, fluid pressure distributions specified from well fluid levels in monitoring wells may be used to predict water and hydrocarbon saturation profiles given expressions for air‐water‐hydrocarbon saturation‐pressure relations. Vertical integration of the oil‐saturation profile yields the actual oil volume in porous media per unit area adjacent to the well. Three‐phase fluid distributions are predicted using a scaling procedure which requires knowledge of two‐phase air‐water saturation‐pressure relations, hydrocarbon density, and hydrocarbon surface tension. Air‐water saturation‐pressure relations are parameterized by either the Brooks‐Corey or van Genuchten expressions. Parameters in the models are estimated from grain‐size distribution data for two hypothetical soils. Results reveal that whereas the distance above an oil‐water table at which oil saturations become zero may be independent of soil type, estimated light nonaqueous phase liquid (LNAPL) volumes per unit area may differ substantially. Hence, estimates of LNAPL volume cannot be inferred directly from soil LNAPL thickness or well LNAPL thickness data without consideration of effects of soil properties. Furthermore, it is demonstrated that no simple linear conversion scheme can be employed to relate the height of LNAPL in a monitoring well to the LNAPL volume in porous media. Effects of grain‐size distribution and well LNAPL thickness on the ratio of actual LNAPL thickness in the aquifer to well LNAPL thickness are shown.