Air-Oil Slug Flow In an Upward-Inclined Pipe - I: Slug Velocity, Holdup And Pressure Gradient
Authors: Mattar L. , Gregory G.A. 
Published: March 2010

Abstract
Experiments were performed with the co-current flow of two-phase "mixtures of air and a light oil in a transparent 1-inch-diameter" pipe at angles of inclination varying from 0 to 10 degrees above the horizontal. Visual observation and numerical data were obtained for in-situ liquid 'Volume fractions, slug velocities, bubble rise velocity in stagnant oil and pressure drop. These data were used to generate expressions for Vb the slug translational velocity, and EL, the -in-situ liquid volume fraction, and to develop a pressure gradient prediction scheme. A new and reliable method for measuring Vb is described, based on the simultaneous 'recording of traces from two capacitance-type volume fraction sensors.

Introduction
WITH CROSS-COUNTRY PIPELINES and oil and gas field gathering lines, purely horizontal orientations are rare. Most of the grades encountered are relatively shallow, however and the pipe is inclined only slightly to the horizontal. For example, in a pipeline test section studied by Flanigan(1), the steepest angle was 8 ? degrees from the horizontal.
In downhill sections, a two-phase (gas and liquid) mixture will usually adopt the stratified flow configuration whereas in uphill sections the slug flow 1'egime predominates. The in-situ liquid volume fractions and pressure drop characteristics of these two flow patterns are quite different. The most important consequence of this, from an economic point of view, is that, unlike single-phase liquid flow, the hydrostatic component of the pressure drop in the uphill section of the pipeline is not recovered in the following downhill portion. Thus, considering only the net change in elevation between the inlet and outlet of the pipeline in calculating a hydrostatic head term for a pressure-drop prediction is not valid.
In the prediction of over-all pressure losses for two-phase flow in cross-country pipelines, the hydrostatic head component in the pressure-drop equations is usually the major contributor to the total pressure loss. This term depe.nds directly on the mixture density, which in turn depends on the in-situ liquid volume fraction or holdup, With the constant need for improvement in pipeline design techniques and prediction methods, there has been an increase in the development and use of mechanistic models. These models are generally more amenable to extrapolation and variation in fluid properties than the earlier and generally less reliable correlation methods. Testing these mechanistic models over a wide range of conditions is often hampered by a lack of reliable data regarding in-situ liquid volume fractions, slug velocities and pressure gradient for a variety of flow rate ranges. The presentation of some new data and a modified pressure-drop calculation for two-phase slug flow in an uphill pipe are the subjects of this paper.

Previous Work
Two-phase flow in horizontal and vertical pipes has been studied extensively, as evidenced in, for example. the recent book by Govier and Aziz(2). This is not the case for such flows in inclined pipes. Very few studies have been published; most are briefly summarized in the following paragraphs.
Flanigan(l) suggested that the total pressure drop consists of two principal contributions: