A Study of Two-Phase Flow in Inclined Pipes
Authors: Beggs D.H. , Brill J.P. 
Published: December 2007

Gas-liquid flow in inclined pipes was investigated to determine the erect of pipe inclination angle on liquid holdup and pressure loss. Correlations for liquid holdup and friction factor were developed for predicting pressure gradients for two-phase flow in pipes at all angles for many flow pressure gradients for two-phase flow in pipes at all angles for many flow conditions.

Introduction
The prediction of pressure drop and liquid holdup occurring during two-phase gas-liquid flow in pipes is of particular interest to the petroleum, chemical, and nuclear industries. In the nuclear industry, two-phase flow occurs in reactor cooling equipment, and liquid holdup greatly affects heat transfer. Two-phase flow occurs frequently in chemical processing, and the design of processing equipment and piping systems requites knowledge of pressure drop, liquid holdup, and often flow pattern. In the petroleum industry, two-phase flow occurs in pipelines and in oil and gas wells. More than one-half the natural gas gathered in the U. S. flows in two-phase flowlines. Most gas-producing wells produce some liquid and most oil wells produce some gas. As the natural reservoir energy is depleted, many wells are equipped with artificial-lift systems such as gas lift. To design these systems, a method of predicting two-phase-flow pressure gradients is required. pressure gradients is required. Although extensive research in two-phase flow has been conducted during the last 25 years, most of this research has concentrated on either horizontal or vertical flow. Several good correlations exist for predicting pressure drop and liquid holdup in either predicting pressure drop and liquid holdup in either horizontal or vertical flow, but these correlations have not been successful when applied to inclined flow. Many gathering lines and long-distance pipelines pass through areas of hilly terrain. This presents no problem in single-phase flow because the potential energy problem in single-phase flow because the potential energy lost going uphill is regained in the downhill section. This is not the case for two-phase flow, because the liquid holdup, and thus the mixture density, are usually much lower in downhill flow. For this reason, pressure recovery in the downhill sections is usually pressure recovery in the downhill sections is usually neglected in the design of two-phase pipelines. The number of directional or inclined wans is increasing as the search for petroleum moves into previously unexplored areas. In offshore drilling, previously unexplored areas. In offshore drilling, several directional wells are usually drilled from one platform for economic reasons. Deviations of 35 deg. to platform for economic reasons. Deviations of 35 deg. to 45 deg. from the vertical are common. In the permafrost areas of Alaska and Canada, the cost of drilling-rig foundations and the difficulty of transportation require that several wells be directionally drilled from one location. Existing vertical-flow correlations frequently fail to predict pressure gradients in these wells within acceptable limits. Gathering lines from offshore wells usually are laid along the sea floor that slopes up to the shore. The elevation pressure gradient in a pipeline with a very small upward inclination from horizontal can be much greater than the frictional pressure gradient. Therefore, in order to predict pressure drop, the liquid holdup must be accurately predicted. The ability to predict liquid holdup also is essential for designing field processing equipment, such as gas-liquid separators.
JPT
P. 607