State of the Art in Multiphase Flow
Authors: Brill J.P. , Arirachakaran S.J. 
Published: December 2007

Introduction
The technology of multiphase flow in pipes has undergone significant changes in the past decade; many of these occurred after Brill's 1987 article. In this paper, we briefly trace the chronology of multiphase-flow technology.

The Empirical Period
Multiphase-flow technology began in the petroleum industry around 1950. Most early investigators used data obtained from laboratory test facilities, but some used field data. These data usually included volumetric gas and liquid flow rates. physical properties of each phase, pipe diameter and inclination angle, and pressures at the pipe inlet and outlet. In some cases, flow pattern was observed and liquid holdup was measured with quick-closing ball valves. Fluids were treated as homogeneous mixtures. Gas and liquid phases, however, were permitted to travel at different velocities, with slippage effects being accounted for through empirical liquid-holdup correlations. Empirical flow pattern maps, often based on dimensionless groups, were used. Steady-state pressure-gradient equations were developed on the basis of pressure-gradient equations were developed on the basis of principles of conservation of momentum and mass applied to the principles of conservation of momentum and mass applied to the homogeneous mixtures. Frictional pressure losses relied on single-phase flow equations, resulting in extensive use of mixture Reynolds numbers. Some investigators also used an empirical multiplicative factor to represent the increased friction resulting from a second phase. In the 1970's, the petroleum industry began to adopt some basic physical mechanisms, already in use in other industries, to predict flow patterns and gas-bubble-rise velocities in liquid predict flow patterns and gas-bubble-rise velocities in liquid columns. Two classic papers on multiphase flow in horizontal pipes clearly show that mechanistic models for slug flow and pipes clearly show that mechanistic models for slug flow and flow-pattern prediction were already available.

The Awakening Years
Empirical correlations for predicting the pressure gradient, coupled with the introduction of the PC in the early 1980's, dramatically improved the practical tools available to petroleum engineers. Techniques for numerically integrating the pressure gradient from one end of a pipe to the other were well understood, and virtually every major producing company had a computer program that predicted the pressure drop or flow rates for wells and pipelines. Procedures for connecting wells to reservoirs through pipelines. Procedures for connecting wells to reservoirs through simple inflow performance relationships abounded, and the true concept of nodal or production system analysis was born. Unfortunately, many problems with the available methods were quickly recognized. Empirical flow-pattern maps were inadequate. Flow-pattern transitions, previously thought to depend mostly on flow rates (or superficial velocities), were found to be very sensitive to other parameters, especially inclination angle. An empirical liquid-holdup correlation for each flow pattern was equally inadequate, and the assumption of a homogeneous mixture was oversimplified. It became clear that, no matter how many data were gathered from laboratory test facilities or carefully tested field installations, the accuracy of the predictions could not improve without the introduction of more basic physical mechanisms. Fortunately, progress in this area had already been made by the nuclear industry. Although the fluids used for these studies (steam and water) were trivial in comparison with those encountered in the petroleum industry, the methods used to formulate conservation equations were much more advanced.

The Modeling Period
The modeling period began in the 1980's, when the petroleum industry faced challenges that required a much better understanding of multiphase-flow technology. The increased cost of arctic and offshore developments justified increased spending, and millions of dollars were invested in multiphase flow through research consortia in the U.S., Norway, France, and the U.K. Investigators recognized that improved understanding of multiphase flow in pipes required a combined experimental and theoretical approach.
JPT
P. 538