Determining three-phase permeability—saturation—pressure relations from two-phase system measurements

Abstract

A mathematical model is outlined for fluid flow in porous media containing up to three fluid phases: air, water and nonaqueous phase liquid (NAPL). Nonhysteretic saturation-pressure relations are described using a scaled parametric function, assumed to be unique to the porous medium and fluid-pair dependent scaling coefficients which scale S w( h ow) and S t(( h ao) in three fluid-phase systems or S w( h aw) in two fluid-phase systems, where S w and S t are water and total liquid saturation and h ow, h ao and h aw are NPL-water, air-NAPL and air-water capillary pressures, respectively Expressions for fluid relative permeabilities are derived from the saturation-pressure functions using a generalized Kozeny-Carman-type analysis. Three methods are considered for calibration of the constitutive model from two-phase system measurements: (1) direct measurement of saturation-pressure relations in air-water, air-NAPL and NAPL-water systems, (2) direct measurement of saturation-pressure relations in a single two-phase system with scaling coefficients estimated from interfacial tension data and (3) numerical inversion of transient two-phase displacement experiments using a nonlinear optimization procedure. The three methods are evaluated for two porous media systems with p-cymene and trichloroethylene as the nonaqueous fluids.