Predicting Liquid Re-Entrainment in Horizontal Separators
Authors: Viles J.C. 
Published: December 2007

Summary
The design procedure for horizontal-separator sizing results in a range of configurations of vessel diameter and length that will perform adequate-liquid separation. The actual diameter chosen depends on a trade-off between smaller, more economic diameters and the larger diameters needed to preventre-entrainment of previously separated liquid droplets that can break away from the gas/liquid interface. The lower diameter limit has been determined previously by design guidelines based on the slenderness ratio of the vessel. This article presents a procedure for determining the lower diameter limit and calculating the maximum gas capacity of a horizontal separator on the basis of liquid re-entrainment. The method is based on correlations for predicting the onset of liquid re-entrainment developed by Ishii and Grolmes. The procedure uses known and predicted liquid and gas properties and may be used in conjunction with normal design procedures for more economic horizontal-separator designs.

Introduction
Entrainment refers to liquid droplets breaking away from a gas/liquid interface to become suspended in the gas phase. The term re-entrainment is used in horizontal-separator design because it generally is assumed that droplets have settled to the liquid phase and then are returned to the gas phase.
Liquid re-entrainment is caused by high gas velocities. Momentum transfer from the gas to the liquid and associated pressure variations on the gas/liquid interface cause disturbances in the two-phase boundary. These disturbances manifest themselves as waves and ripples. Gas-to-liquid momentum transfer to a disturbed interface is more efficient than to a smooth surface, which allows droplets to break away from the liquid phase.
Re-entrainment must be avoided in horizontal separators because it is the reverse of the gas/liquid separation desired. This necessity imposes an upperlimit on the gas velocity allowed across the liquid surface in the gravity settling section of the separator, which places a lower limit in the vessel on the cross-sectional area for gas flow. Vessel design therefore is limited by a combination of minimum vessel diameter and maximum liquid level because these determine the cross-sectional area. Previously, such rules of thumb as a maximum slenderness ratio of 4:5 have been used to avoid re-entrainment.1
This article presents a procedure for predicting when re-entrainment is possible on the basis of previously developed correlations and discusses modifications to design procedures to produce more economical horizontal-separator designs.

Re-Entrainment Theory
Re-entrainment is a physical phenomenon of two-phase stratified fluid flow. The onset of re-entrainment occurs at the boundary of the stratified wavy and annular mist two-phase flow regimes at relatively high gas/liquid velocities, as Fig. 12 shows. Re-entrainment is caused by rapid momentum transfer from gas to liquid. For the purposes of this article, only the onset of re-entrainment must be predicted because no amount of re-entrainment can be allowed in a horizontal separator.
Ishii and Grolmes3 and Ishii and Kaichiro4 proposed correlations for predicting the minimum velocity required for re-entrainment of liquid into gas for concurrent flow. The equations (see Appendix) are based on interpretation of experimental data taken from several gas/liquid systems, including water or oil and nitrogen or helium. The correlations use the Reynolds film number and an interfacial viscosity number to characterize the two-phase flow. These are defined asEquation 1and Equation 2
N Ref is a measure of the turbulence of the liquidphase and indicates which mechanism of re-entrainment is most likely for the flow conditions considered.
Ishii and Grolmes3 proposed three distinct mechanisms forre-entrainment. For NRef&lt;160, a wave undercut mechanism was proposed where gas impinges on the gas/liquid interface, undercutting it and breaking displaced liquid away from the interface. Athigher NRef, roll wave shear, where the tops of waves are sheared off by high relative velocities between gas and liquid, becomes the dominant mechanism. NRef&gt;1,635 indicates a highly turbulent condition dominated by interfacial properties. AsNRef increases, the liquid surface becomes rougher, and the importance of NRef diminishes asymptotically. These mechanisms occur in three flow regimes, called low Reynolds number(&lt;160), transition (160 to 1,635), and rough turbulent (&gt;1,635).Re-entrainment is more likely at high NRef.
N μ is a measure of the resiliency of the liquid surface under turbulent conditions. In physical terms, it is the ratio of viscous forces induced in the liquid by flow to the surface tension maintaining the gas/liquid interface. Re-entrainment becomes more likely with higherNμ. The tendency of liquids to re-entrain increases appreciably as Nμ exceeds 1/15.