Correlations for Prediction of Pressure Gradient of Liquid Liquid Flow Through a Circular Horizontal Pipe

Abstract

We report a detailed investigation on the measurement and prediction of pressure gradient characteristics of moderately viscous lubricating oilwater flow through a horizontal pipe of 0.025 m internal diameter. Experiments are carried out over a wide range of phase velocities of both oil (USO = 0.015–1.25 m/s) and water (USW  =  0.1–1.1 m/s). Experimental pressure gradients yield significant errors when fitted to the existing correlations, which are largely used for gasliquid flow. To predict pressure gradient characteristics for liquidliquid flow, the existing correlations need to be modified. We propose two correlations, based on the Lockhart–Martinelli's approach (by modifying the correlation between the Lockhart–Martinelli parameter and a twophase multiplier suitable for the present system) and dimensionless analysis, following the Buckingham's Pitheorem. We observe significant improvement in the prediction of pressure gradient. The correlation based on the dimensionless analysis predicts better with an average absolute error of 17.9%, in comparison with the modified Lockhart–Martinelli correlation, which yields an average error of 22%, covering all the flow patterns. The present analysis shows better prediction as compared to twofluid model Zhang et al. (2012, “Modeling HighViscosity Oil/Water Concurrent Flow in Horizontal and Vertical Pipes,â€‌ SPE J., 17(1), pp. 243–250) and AlWahaibi (2012, “Pressure Gradient Correlation for OilWater Separated Flow in Horizontal Pipes,â€‌ Exp. Therm. Fluid Sci., 42, pp. 196–203) work.