Prediction of pressure gradient and hold-up in horizontal liquid-liquid pipe flow

This paper aims to propose correlations to predict pressure gradient, friction factor and fluid phase hold-up in liquid-liquid horizontal pipe flow. To develop the correlations, experiments are conducted using high viscous oils (202 mPa⋅s and 630 mPa⋅s) in a steel pipe of length 11.25 m and length-to-diameter ratio of 708. In addition, the experimental data from the literature comprising wide range of flow and fluid properties is analyzed. For the analysis, the liquid-liquid pipe flow data is categorized into two as: stratified and dispersed. The existing friction factor correlations are modified to incorporate the effects of viscosity of the oil phase, interfacial curvature (contact/wetting angle-in lieu of material of the pipe) and fluid phase fraction. In the two-fluid model of stratified flow, the wall stress and interfacial stress correlations are substituted with superficial velocities of fluids and superficial Reynolds numbers of fluid phases replacing fluid phase velocities and fluid Reynolds numbers. Similarly, for dispersed flow, an effective Reynolds number is described as the sum of superficial Reynolds number of oil and water phases. Substituting the generally employed mean or mixture Reynolds number with the effective Reynolds number into the existing single-phase turbulent flow friction factor correlation, an effective friction factor for oil-water flow is proposed. Employing the proposed correlations, the pressure gradient across the oil-water flow and hold-up volume fraction are predicted with significant reduction in error compared with that of conventionally employed correlations. The average error and standard deviation values of −7.06%, 20.72% and 0.31%, 18.79% are found for stratified flow and dispersed flow respectively.