The flow of two immiscible liquids such as oil and water is very important in the petroleum industry like oil recovery processes. For example, the injection of water into the oil flowing in the pipeline reduces the resistance to flow and the pressure gradient. Thus, there is no need for large pumping units. In the present study, a simple semi-theoretical method for calculating the two-phase frictional pressure gradient for liquid-liquid flow in pipes using asymptotic analysis is presented. The two-phase frictional pressure gradient is expressed in terms of the asymptotic single-phase frictional pressure gradients for the more viscous liquid and the less viscous liquid flowing alone. The proposed model can be transformed into either a two-phase frictional multiplier for the more viscous liquid flowing alone (φ12) or two-phase frictional multiplier for the less viscous liquid flowing alone (φ22) as a function of the Lockhart-Martinelli parameter, X. The advantage of the new model is that it has only one fitting parameter (p). Therefore, calibration of the new model to experimental data is greatly simplified. The new model is able to model the existing multi parameters correlations by fitting the single parameter p. Comparison with experimental data for two-phase frictional multiplier versus the Lockhart-Martinelli parameter (X) is presented.

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