Development of New Wall Friction Factor and Interfacial Friction Factor Correlations for Gas-Liquid Stratified Flow in Wells and Pipelines
Authors: Ouyang Liang-Biao , Aziz Khalid 
Published: December 2007

Abstract
Stratified flow is one of the most basic flow pattern in the analysis of gas-liquid two-phase flow in pipes. In the present paper, different interfacial friction factor correlations were used to predict the liquid holdup and pressure gradients. The comparison of predictions with experimental observations shows that most existing correlations for the interfacial friction factor can lead to large deviations from measurements and that the standard method underestimates the liquid phase wall friction factors. New correlations for both the liquid phase wall friction factor and the interfacial friction factor were developed based on large amounts of available experimental data. The resulting correlations were used to predict liquid holdup and pressure gradient for different experiments. Considerable improvement in predictions was observed.

Introduction
Gas-liquid flow in pipes is of practical importance in petroleum, chemical, nuclear and geothermal industries, and has been the subject of intensive research for dozens of years. Theoretical analyses and experiments have been conducted to predict key factors, such as pressure drop, liquid holdup, gas-liquid interfacial area, heat and mass transfer and temperature distribution.
In general, gas-liquid two-phase flow is much more complicated than single phase flow, due primarily to the existence of a phase interface and the spatial distribution of the phases. Some consequences of the complex nature of gas-liquid pipe flow are:–Pressure drop in transmission lines increases significantly even with the presence of very small quantities of condensate. Significant energy loss occurs as a result of acceleration and transportation of the liquid which wets the pipe wall and creates waves at the gas-liquid interface. The liquid film reduces the area of the pipe and increases the effective roughness.–Whereas in hilly terrain the pressure loss because of gravity head on the uphill side of a pipe would be recovered on the downhill side for single phase flow, this is often not the case for gas-liquid two-phase flow.–In hilly terrains and in submerged river crossings, energy is lost in lifting the liquid over natural obstacles. If the pressure is insufficient to overcome the obstacle, there may be flooding of the pipe, thus further reducing the area accessible for gas flow and therefore creating an even larger pressure drop.–In single phase flow, pressure drop decreases as pipe diameter increases, but this is not necessarily so in gas-liquid flow. Under certain conditions, pressure drop exhibits a minimum with pipe diameter.
Due to the complex nature of gas-liquid two-phase flow, the problem was first approached through empirical or engineering methods. This approach is based on empirical or semi-empirical relations and has dominated practical design procedures. It leads to correlations that should be extrapolated with caution outside the range of parameters investigated in the experimental work. Most of the available correlations deal with air-water or steam-water systems, their reliability for other systems of industrial importance is questionable.
Recently the trend has shifted towards the modeling approach, or mechanistic models. This approach is based on the fundamentals of multiphase flow and fluid dynamics. The fundamental postulate in this kind of approach is the existence of flow patterns or flow regimes and it has greatly contributed to the basic understanding of the nature of gas-liquid two-phase flow. P. 285