Prologue

Chapter 2 gives considerable attention to slug flow because of its central role in understanding the configuration of the phases in horizontal and inclined pipes. Several criteria have been identified to define the boundaries of this regime: (1) viscous large-wavelength instability of a stratified flow; (2) Kelvin–Helmholtz instability of a stratified flow; (3) stability of a slug; (4) coalescence of large-amplitude waves. Bontozoglou & Hanratty (1990) suggested that a sub-critical non-linear Kelvin–Helmholtz instability could be an effective mechanism in pipes with very large diameters, but this analysis has not been tested. A consideration of the stability of a slug emerges as being particularly important. It explains the initiation of slugs for very viscous liquids, for high-density gases, for gas velocities where wave coalescence is important and for the evolution of pseudo-slugs into slugs. Chapter 2 (Section 2.2.5) outlines an analysis of slug stability which points out the importance of understanding the rate at which slugs shed liquid. Section 9.2 continues this discussion by developing a relation for Qsh and for the critical height of the liquid layer needed to support a stable slug. Section 9.3 develops a tentative model for horizontal slug flow. Section 9.4 considers the frequency of slugging.

Necessary conditions for the existence of slugs

Figure 9.1 presents simplified sketches of the front and the tail of a slug in a pipeline. The front has a velocity cF; the back has a velocity cB. The stratified liquid layer in front of the slug has a velocity and area designated by uL1, AL1. The mean velocity of the liquid in the slug is uL3. The slug is usually aerated; the mean volume fraction of gas in the slug is designated by α. The gas at station 1 is moving from left to right at a velocity uG1. The assumption is made that the velocity fields can be approximated as being uniform.