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

We report a detailed investigation on the measurement and prediction of pressure gradient characteristics of moderately viscous lubricating oil-water 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 gas-liquid flow. To predict pressure gradient characteristics for liquid-liquid 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 two-phase multiplier suitable for the present system) and dimensionless analysis, following the Buckingham's Pi-theorem. 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 two-fluid model Zhang et al. (2012, “Modeling High-Viscosity Oil/Water Concurrent Flow in Horizontal and Vertical Pipes,” SPE J., 17(1), pp. 243–250) and Al-Wahaibi (2012, “Pressure Gradient Correlation for Oil-Water Separated Flow in Horizontal Pipes,” Exp. Therm. Fluid Sci., 42, pp. 196–203) work.