A Robust Asymptotically Based Modeling Approach for Two-Phase Flow in Porous Media

Abstract

A simple semitheoretical method for calculating the two-phase frictional pressure gradient in porous media using asymptotic analysis is presented. The two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for liquid and gas flowing alone. In the present model, the two-phase frictional pressure gradient for x≅0 is nearly identical to the single-phase liquid frictional pressure gradient. Also, the two-phase frictional pressure gradient for x≅1 is nearly identical to the single-phase gas frictional pressure gradient. The proposed model can be transformed into either a two-phase frictional multiplier for liquid flowing alone (ϕl2) or a two-phase frictional multiplier for gas flowing alone (ϕg2) as a function of the Lockhart–Martinelli parameter X. The advantage of the new model is that it has only one fitting parameter (p), while the other existing correlations, such as the correlation of Larkins et al., Sato et al., and Goto and Gaspillo, have three constants. Therefore, calibration of the new model to the experimental data is greatly simplified. The new model is able to model the existing multiparameter correlations by fitting the single parameter p. Specifically, p=1/3.25 for the correlation of Midoux et al., p=1/3.25 for the correlation of Rao et al., p=1/3.5 for the Tosun correlation, p=1/3.25 for the correlation of Larkins et al., p=1/3.75 for the correlation of Sato et al., and p=1/3.5 for the Goto and Gaspillo correlation.