Three-Phase Relative Permeability Correlations

Abstract

Several correlations have been proposed for prediction of three-phase relative permeability from two-phase data or from saturation/capillary-pressure relationships. These include the models of Stone, Hirasaki, Corey et al., Naar and Wygal, Land, Aleman, and Parker et al. This paper compares predictions of these models with predictions of two additional models (saturation-weighted interpolation and true-linear interpolation). The comparison is made using all the published three-phase experimental relative permeability data complete enough for application of the models.

The comparison shows that the models are often not very good predictors of the experimental data. This points out a need for better relative permeability models in cases where three-phase flow may have a significant effect. In most cases, straight-line interpolation or saturation-weighted interpolation between the permeabilities at the two-phase boundaries of the three-phase flow region provided a better fit of the experimental data than did the theoretically-based models.

The paper also demonstrates the utility of comparing the effects of different relative permeability models before using them in a reservoir simulation. Sometimes the result of a simulation can be heavily biased by the choice of relative permeability model used.

Introduction

Three-phase relative permeability measurements and correlation methods have been reported in the literature since 1941. This paper lists the sources of published three-phase relative permeability data and compares the simple correlation methods which have been proposed for prediction of three-phase relative permeability. Two additional interpolation methods are proposed and compared to the published methods.

Discussion

Data Sources for Three-Phase Relative Permeability

Three-phase (gas/oil/water) relative permeability data for water-wet sandpacks have been reported by Leverett and Lewis, Reid, Hosain, Snell and Ivanov. Three-phase data for water-wet cores have been reported by Caudle, et al. Corey, et al. Sarem, Donaldson and Dean, Saraf, Juckert; Saraf et al., van Spronsen, Holmgren and Morse, Slack and Ehrlich and Schneider and Owens. Very limited three-phase data for oil-wet cores (gas and water relative permeabilities at constant, non-flowing oil saturation) were published by Schneider and Owens. Descriptions of the test procedures and calculation methods are available in the original references. Donaldson and Kayser provide a summary of the test protocols and results for most of the data published prior to 1980.

The data for water-wet cores and for sandpacks show generally consistent behavior; isoperms (contours of constant phase relative permeability) for gas and water primarily depend on the gas or water saturation respectively, and are weak functions of the saturations of other phases present. The permeability to each phase is clearly affected by the saturation history when there is hysteresis between the inhibition and drainage curves for that phase. These data indicate that a strongly wetting phase (water) and a non-wetting phase (gas) are affected little by interactions with other phases (except for the physical obstruction caused by the presence of the other phases). An intermediate wetting phase (oil) appears to be more influenced by interactions with the other phases. The nature of the inter action is not clear, however.

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