POS

SPE 25474

Society 01 Petroleum Engineers

Predicting Liquid Re-Entrainment In Horizontal SeparatorsJ.C. Viles, Paraqon Engineering Services Inc.

SPE Member

Copyright 1993. Society of Petroleum Engineers. Inc.

This paper was prepared for presentation at the Production Operations Symposium held in Oklahoma City. OK. U.S.A .. March 21-23. 1993.

This paper was selected for presentation by an SPE Program Comminee followir.g review of information contained in an abstract submitted by the author(s). Contents of the paper.as presented. have not been reviewed by the Society of Petroleum Engineers and are subject to correction by the author(s). The material, as presented. does not necessanty reflectany position of the Society of Petroleum Engineers. its oHicers, or members. Papers presented at SPE meetings are subject to publication review by Editorial Committees of the Societyof Petroleum Engineers. Permission to copy is restricted to an abstract of not more than 300 warns. Illustrations may not be copied. The abstract should contain conspicuous acknow1edgmentof where and by whom the paper is presented. Write Librarian. SPE. P.D. Box 833836. Richardson. TX 75083-3836. U.S.A. Telex. 163245 SPEUT.

ABSTRACT

The design procedure for horizontal separator sizing resultsin a range of configurations of vessel diameter and lengththat will perform adequate gas-liquid separation. The actualdiameter chosen depends on a trade-off between smaller,more economic diameters, and the larger diameters neededto prevent re-entrainment of previously separated liquiddroplets that can break away from the gas-liquid interface.The lower diameter limit has been previously determined bydesign guidelines based on the slenderness ratio of thevessel. This article presents a procedure for determining thelower diameter limit and for calculating the maximum gascapacity of a horizontal separator based on liquid re-entrainment. The method is based on correlations forpredicting the onset of liquid re-entrainment developedpreviously by Ishii and GroImes. The procedure uses knownand predicted liquid and gas properties and may be used inconjunction with normal design procedures for moreeconomic horizontal separator designs.

INTRODUCTION

Entrainment refers to liquid droplets breaking away from agas-liquid interface to become suspended in the gas phase.The term re-entrainment is used in horizontal separatordesign because it is generally assumed that droplets havesettled to the liquid phase and are then removed back to thegas phase.

Re-entrainment of liquids is caused by high gas velocities.Momentum transfer from the gas to the liquid and itsassociated pressure variations on the gas-liquid interface

cause disturbances in the two-phase boundary. Thesedisturbances manifest themselves as waves and ripples. Gasto liquid momentum transfer to the disturbed interface ismore efficient than to a smooth surface, and this allowsdroplets to be broken away from the liquid phase.

Re-entrainment must be avoided in horizontal separatorsbecause it is the reverse of the gas-liquid separation desired.In practical terms, this necessity imposes an upper limit onthe allowed gas velocity across the liquid surface within the.separator, putting a lower limit on the cross-sectional areawithin the vessel for gas flow. The vessel design is therebylimited by a combination of minimum vessel diameter andmaximum liquid level since these determine the cross-sectional area. Previously, rules of thumb, such as amaximum slenderness ratio of 4 to 5, have been used indesign to avoid re-entrainment.'

This article presents a procedure for predicting when re-entrainment is possible based on previously developedcorrelations and discusses modifications to design proceduresto produce more economic horizontal separator designs.

RE-ENTRAINMENT THEORY

Re-entrainment is a physical phenomenon of two-phasestratified fluid flow. The onset of re-entrainment occurs atthe boundary of the stratified wavy and annular mist two-phase flow regimes at relatively high gas-to-liquid velocities,as shown in Figure 1.2 Re-entrainment is caused by rapidmomentum transfer from the gas to the liquid. For purposesof this article, only the onset of re-entrainment must be

591

r

SPE 25474 JOHN C. VILES

The Ishii and Grolmes equations appear in the Appendixpredicted, since no amount of re-entrainment can be allowedin a horizontal separator.

Isbii and Gr olmcs.':' have proposed correlations forpredicting the minimum velocity required for re-entrainmentof liquid into gas for eo-current flow. The equations arebased on i.nterpretation of experimental data taken fromseveral gas-liquid systems, including water or oil andnitrogen or helium. The correlations use the Reynolds filmnumber and an interfacial viscosity number to characterizethe two-phase flow. These are defined as:

(1)ilL

and

(2)[ (_0_)0.5]0.5PL 0

g hp

The Reynolds film number, Re., is a measure of theturbulence of the liquid phase, and it indicates whichmechanism of re-entrainment is most likely for the flowconditions considered.

Ishii and Grolmes proposed three distinct mechanisms forre-entrainment. For Reynoids film numbers less than 160,a wave undercut mechanism was proposed whereby gasimpinges 'on the gas-liquid interface, undercutting it andbreaking displaced liquid away from the interface. At higherReynolds film numbers, roll wave shear becomes thedominant mechanism, where the tops of waves are shearedoff by high relative velocities between gas and liquid.Reynolds film numbers above 1635 indicate a highlyturbulent condition dominated by interfacial properties. AsReynolds number increases, the liquid surface becomes morerough, and the importance of Re! diminishes asymptotically.These mechanisms occur in three flow regimes, referred toas low Reynolds number « 160), transition (160-1635), andrough turbulent (> 1635). Re-entrainment is more likely athigh Reynolds film numbers.

The interfacial viscosity number, N~, is a measure of theresiliency of the liquid surface under turbulent conditions.In physical terms, it is the ratio of viscous forces induced inthe liquid by flow to the surface tension maintaining the gas-liquid interface. Re-entrainment becomes more likely withhigher interfacial viscosity numbers. The tendency of liquidsto re-entrain increases appreciably as NI' exceeds 1/15.

2

APPLICATION

Design of horizontal separators allows for some flexibility inchoosing a combination of length and diameter to performthe separation required. The design constraints for liquidand gas capacity are;'

Gas Capacity Constraint:

OG T Z (1 - 13) [r21~Dl0.5d Lerr ~ 420 ----=--

P (1 - a) lhp dm

(3)

Liquids Capacity Constraint:

t 00 + t Owd2 ra rw

Lerr 2 ---:--:---- 1,4 a(4)

Seam-to-seam vessel length may be estimated fromequations appearing in the Appendix.

Only one constraint will govern for a given design. Eachconstraint imposes a limit on either diameter or effectivelength, but not both, The design engineer is free to selectone variable, usually the diameter, thus fixing the othervariable, For a given diameter, the design is said to be gasdominated if Equation 3 controls the design and liquidsdominated if Equation 4 controls.

For gas dominated separator designs, smaller diameters(requiring longer lengths) tend to be less costly due tosmaller wall ·thicknesses required. Smaller diameters,however, leave less area for gas flow, resulting in highervelocities and potential re-entrainment problems, Thus,there is an optimum vessel diameter that minimizes cost butdoes not support re-entrainment The correlations of ISMand Grolmes can be modified to predict re-entrainment inhorizontal separators, allowing the best design to be found.

First, the correlations must be rearranged to give themaximum gas velocity explicitly. These modified re- _entrainment criteria are presented in Table I.

Next, the equations must be integrated into the designprocedure. The hydraulic diameter and surface tension mustbe evaluated so that the Reynolds film number andinterfacial viscosity number can be computed,

592

3 PREDICTING LIQUID RE-ENTRAINMENT IN HORIZONTAL SEPARATORS SPE 25474

The general hydraulic diameter for a duct is defined as fourtimes the hydraulic radius, which is the cross-sectional areafor liquid flow divided by the wetted perimeter. Therefore:

(5)

The area for liquid flow is given by:

(6)

where a is the fraction of total vessel area used for liquidflow and is given by:

a =2.cos-1 (1-28) - ~ (1 -2~ )(~ _~2)0.5

1! 1!

(7)

where fi is the fractional liquid height within the vessel. Thewetted perimeter is given by:

(8)

For the most common case of a half-full separator, .thehydraulic diameter equals the vessel inside diameter.

Gas velocity, as a function of vessel diameter and fractionfull, is given by:

(9)

While liquid (oil) velocity is given by

V = 00o 15387AL

(10)

If it is not known from experimental data, the surfacetension may be calculated by a variety of methods." Oneuseful correlation? is:

o =0.0022 [42.4 -0.D47(T - 460) -0.267 CAPI) J e -{)OOO7P (11)

In three phase applications, only surface liquid (oil) and gasproperties are used in the above equations. The wettedperimeter is based on total fluids, and liquid velocity is basedon the surface (oil) phase.

Once the Reynolds film number and film viscosity numbershave been evaluated, the appropriate equation can be

selected from Table I to calculate the maximum permissiblegas velocity relative to the oil phase. Comparison of thisvalue with the actual velocities calculated in equations 9 and10 indicates if re-entrainment is possible.

DETERMINATION OF MINIMUM VESSEL DIAMETER

Two strategies may be employed concurrently to optimize ahorizontal separator design to minimize cost. In equations3 and 4, the engineer has a choice of vessel diameter. Sincesmaller diameter separators of the same capacity aretypically less costly, the first strategy is to use the minimumdiameter that will not support re-entrainment.

The minimum diameter cannot be solved for explicitly dueto its influence on Re, and the series of equations thatdepend on it. Solution requires an iterative procedure. Aninside diameter is assumed and then (Vr)max and the actualgas velocity relative to the oil phase are calculated andcompared. New diameters are tried until (Vr)max equals therelative gas velocity, V r.

Figure 2 illustrates the design constraints for a high pressure,gas dominated design as the vessel diameter is varied. Thisdesign is liquid dominated for diameters less than 35 inchesand gas dominated for larger diameters. Acceptable designs,based on equations 3 and 4, lie above both the gas andliquids design lines. Vessel weight, calculated fromestimating equations presented in the Appendix, is alsoplotted.

Since vessel cost correlates closely to vessel weight, it is clearthat the most economic designs lie to the left on the graph.When solved for minimum diameter, the equations predictre-entrainment in any designs with diameters less than 42inches in this example. This coincides with a slendernessratio of 4. Therefore, the optimum acceptable design forthis case has standard dimensions close to, but greater than,42 inches inside diameter and 13 ft. seam-to-seam length.

DETERMINATION OF MAXIMUM LIQUID HEIGHT

The second approach to optimized design is to adjust the'liquid height in the vessel. Depending on the requirementsfor gas and liquid capacity, the liquid level can be increasedor decreased to bring the required gas and liquid seam-to-seam lengths into closer agreement. As in the case above,an explicit solution is not possible, and a trial and errorprocedure must be-used to find the maximum liquid height.An assumption for the vessel diameter is required,

Figure 3 plots the design constraints for a liquids dominated

593

SPE 25474 JOHN C. VILES 4

design as the fractional liquids height is varied. Theequations presented here predict re-entrainment possible atliquid heights above 72% full, even though gas capacity(Equation 3) is not the governing design constraint for thisliquid level.

In theory, both liquid height and vessel diameter must beoptimized concurrently. This involves a trial and errorprocedure in which different vessel diameters and liquidheights are tried until the lowest cost standard size vessel ischosen. The most economic liquid level should be that atwhich the required -gas and liquid vessel lengths are equal.However, considerations for vessel surge capacity, clearancesfor vessel internals, and room for instrumentation, oftendictate that other combinations of diameter and length beselected.

GENERAL CONSIDERATIONS

General treatment of re-entrainment potential is difficult dueto the dependency of Re, on individual vessel geometries. Ifonly rough turbulent (Re, > 1635) re-entrainment isconsidered, and oil velocity is assumed to be negligiblecompared to gas velocity, however, dependency on vesselgeometry disappears, and a more general analysis can be .performed. Conservative velocity limits versus operatingpressure and API gravity of liquids are plotted in Figure 4 .Re-entrainment tendency is over predicted since horizontalseparators do not always operate in the rough turbulentliquid regime and oil velocities are not zero. Required oilproperties are correlated to °API, surface tension is based onEquation 11, and viscosity comes from reference 1.

From the graph, it can be seen that less gas velocity ispermissible at higher pressures because of higher gasdensities and reduced liquid surface tension.

The critical velocity is 2-20 ft/s for most light crudeapplications at ambient temperatures. Critical velocitydecreases for heavier crudes, particularly where NI' > 1/15.The higher viscosity of heavy crude oils interferes withoil/water separation, however, so these crudes are processedat higher temperatures where Figure 4 does not apply.

By utilizing the rough turbulent liquid re-entrainmentcorrelations, in conjunction with the gas capacity constraint(Equation 3), one can determine the generalized maximumslenderness ratio allowed for a wide range of gas capacities.Results are plotted in Figure 5.

It is clear that the re-entrainment correlation treated herefollows the slenderness ratio rule of thumb for crude oils of

30° API gravity and lighter in high pressure applications.Lower pressures can allow more slender, and therefore moreeconomical, designs to be used. It is obvious again thatheavier crudcs are more susceptible to re-entrainment,particularly when the film viscosity number exceeds 1/15(0.0667). Due to their higher viscosity, these heavy crudesare more likely to exhibit low Reynolds number behavior,indicating that wave undercutting is a likely re-entrainmentmechanism for them. In addition to re-entrainment of liquidinto gas, gas is trapped in the liquid phase by this method.Thus, "foaming" of heavy crudes observed in some horizontalseparators can actually be caused by re-entrainment effectsrather than an inherent problem of the crude type.

Most separators designed for heavy crude applications aresized on liquids capacity constraints. Gas velocity for suchdesigns is usually low. For this reason, re-entrainment is notas common a problem for separators in heavy crude serviceas Figure 5 would suggest.

CONCLUSIONS

The correlations presented here provide a means forpredicting when re-entrainment can occur in horizontalseparators, and they can be used directly for economicalseparator design. The techniques discussed here confirm thegeneral guidelines on slenderness ratio that are usually usedin horizontal separator sizing.

The following guidelines apply to re-entrainment prediction:

1) Re-entrainment should be considered in highpressure separators sized on gas-capacityconstraints. A maximum slenderness ratio of 4 to5 for half-full horizontal vessels applies to this case.Higher slenderness ratios are possible at pressuresless than 1000 psia.

2) Re-entrainment becomes more likely at higheroperating pressures. This tendency is a result ofincreased gas density and reduced gas-liquid surfacetension. Higher pressures may require less slenderdesigns.

3) Re-entrainment IS more likely as oil viscosityincreases. As a result, re-entrainment is muchmore likely for heavier crudes, especially below ~API. Higher operating temperatures reduce thetendency for re-entrainment in horizontal separatorsby reducing the viscosity of the crude oil.

594

5

NOMENCLATURE

PREDICTING LIQUID RE-ENTRAlNMENT IN HORIZONTAL SEPARATORS SPE 25474

a Vessel fraction full based on liquid areaAPT gravity at 600 FVessel area for liquid flowVessel fraction full based on liquid heightDroplet drag coefficient for gravity settingVessel inside diameter, in.Vessel inside diameter, ft.Liquids hydraulic diameter, It.Droplet maximum diameter removed,micronsacceleration of gravity, 32.2 ft/S2Vessel effective length for separation, ft.Vessel seam to seam length, ft.Dynamic liquid viscosity, Ibm/ft-sInterfacial viscosity number, dimensionlessAbsolute pressure, psiaVessel wetted perimeter, ft.Liquid flow rate, BPDGas flow rate, MMSCFDReynolds film number, dimensionlessDensity, lbm/fr'Density difference between liquid and gas,lbm/fr'Surface tension between liquid and gas,lbm/s'Vessel wall thickness, in.Absolute temperature, ORLiquid residence time, min.Velocity, ft/sGas velocity relative to liquid, ft/sVessel estimated weight, Ibs.Gas compressibility factor

gLet!

L••jl

Nil

PPLoOGReIp

6p

a

t

Tt,VV,WZ

Subscripts

LGoW

Liquid (surface) phaseGas phaseOilWater

ACKNO~EDGEMENTS

The Author wishes to express his appreciation to ParagonEngineering Services Incorporated for assistance inpublishing this article. Special thanks go to Mary E. Thro,Kenneth E. Arnold, and John E. Van Meter for theircriticism and editorial assistance.

595

REFERENCES1. Arnold, K. and Stcwart, M., Surface Production

Operations, Gulf Publishing Company, Houston(1986), pp. 65,104-114,135-138.

2. Griffith, P., "Multiphase Flow in Pipes", JPT,(March 1984), pp. 363-367.

3. Ishii, M. and Grolmes, M. A., "Inception Criteriafor Droplet Entrainment In Two-Phase ConcurrentFilm Flow," AlChE Journal (Mar. 1975), Vel. 21,No. 2, pp. 308-318.

4. Ishii, M. and Kaichiro, M. "Droplet entrainmentcorrelation in annular two-phase flow," Int. J. HeatMass Transfer (1989), Vol 32, No. 10, pp. 1835-18460

50 Perry Ro Ho, and Green, Do w., Edso Perry'sChemical Engineers' Handbook. Sixth Edition.McGraw Hill, New York (1984), Set. 3, pp 288-2890

60 Baker, 00, and SwerdJoff, Wo, "Finding SurfaceTension of Hydrocarbon Liquids", Oil and GasJournal, Jan 2, 1956, p. 1250

70 One-Dimensional Two-Phase Flow. McGraw Hill,New York (1969) ppo 320, 345-351, 376-391.

SPE 25474 JOHN C. VILES

APPENDIX Vessel wall thickness in inches (based on 17500 psi allOWf.lstress) is calculated as:

Additional EquationsThe Ishii and Gr olmes'' Inception Criteria are as follows: Pd

t = -:::3~5000=-+-:::-0.-;;-8-;::;-P (A-8)

For the low Reynolds number regime (Re, < 160),Vessel weight in pounds is then estimated to be:

(A-I)W=1O.7IdL t+

d2tJ" 12

(A-9)

For the transition regime (160 .s. Re, .s. 1635),

if N~~ 1 (A-2)15

if N >~ (A-3)~ 15

For the rough turbulent regime (Re, > 1635):

JlLVr [PG105

2 N:.sa PL

1if N~~

15(AA)

[ 105

11 V P~ ~ >0.1146

a PL

J·f N 1>-~ 15

(A-5)

Entrainment is possible if the appropriate equation issatisfied.

The minimum vessel seam-to-seam length was estimatedfrom the vessel effective length by the following equations:

If Leeris based on the gas capacity constraint (Equation 3)then:

La = the larger of [ ~ Leeror Leer+0] (A-6)

If Leeris based on the liquid capacity constraint (Equation 4)then:

L••= the larger of [ ~ Leeror Let!+2.5] (A-7)

596

III!

TABLE I

RE-ENTRAINMENT CRITERIA FOR MAXIMUM GAS VELOCITY

Eg. RCr NI' (Vr)mu

A. < 160 --- .1.5-"-[-'-']"' Re,<'III Pr;

[]"' ,B. 160s Rc,s 1635 s 0.0667 11.78~ 2 N~8Rer-1III PG

[r 'o Pl -1C. 160s Rers 1635 > 0.0667 1.35- - Re,

III PG

D. > 1635 s 0.0667_~-[-'-' 1\~III PGJ

E. > 1635 >0.0667 0.1146 -"-[-'-'rIII PG

597

Horizontal Two-Phase Flow Regime Map

10 o,spers&d Bu~e -1- -I

I

EIOrlQated BvooIe SIUQ

1 - -

Int9fTT'11nerrt

U) 100::::>.oo<l>>U::Jer

:::::i<U:g 0.1<l>Q::J

Cl) 0.010.1 1000

Slr;n;~.ao Smooth

1 10 100Superficial Gas Velocity, fVs

Adapted from: P. Griffith. "Multi phase Flow in Pipes", JPT, March 1984, pp. 363-367

Figure 1. General multiphase flow regime map. Line positions depend on fluids and conditions.

Horizontal Separator Design LimitsHalf-Full Vessel Diameter Optimization

.30 -r-------------...,..17000--

- - j -

I~ Entrainmen~1 No Entrainment .•.

~--~--~---+--~---~--~500055

..c-g>25<l>-l

- -l-4d8000

~ 20enQ)

>~15Q)

Cl)o-10EC'OQ)

Cl)5

25

100 MMSCFD (0_65 SG, 140 micron removal)5,000 BOPD (40 APt. 2 min. retention)80 deg F. 1000 psia

DesignTransition

14000 _x:.QlQ)

11 000 ~COEXo'-QQ-c

liquids

Gas

30 35 40 45 50Inside Diameter, in.

en.0

Figure 2. Design constraints on vessel diameter for a gas-dominated horizontal separator.

598

75 I-------;:::::::;;~==:::~====~5000050 MMSCFD (0.65 SG. 140 micron removal)_......:65 U 'd 50.000 BOPD (30 API. 3 min. retention)

~ - - qUI S . - - - - 80 dag F. 250 psia66 in. 1.0..r::'0>55

cQ)

-J 45ECO

~ 35o~ 25COQ)

Cl) 15

Horizontal Separator Design LimitsLiquid Height Optimization

Cf)

45000 D.•....r::0>Q)

40000~2coE-x

35000 ~«

Figure 3. Design constraints on liquid height for a liquids-dominated horizontal separator.

I. ~ - - - - - - - - - -

Vessel Weight

----~- ~__~__;...;,._..•...._ -._..-_.0.------ "'7'- - - - - -Gas -

~No Entrainment 1Entrainment ~

~ 10LL>..•...'g 1CD>Cf)CO

CJ 0.1

0.0120

50.4r----+----+----+----~·~_~~-430000

0.90.5 0.6 0.7 0.8Fractional Liquid Height

Critical Re-entrainment Gas Velocity(Based on zero velocity turbulent oil)

1001r=======~-----------------'l80cIogF.O.65~G" I

L_---------SOpsia

60

r ..:~~:...:.~~;;;....;::=:::::::2SOpsia - -.l.C===_-------SOO psia:-:=-_---:::=====1000 psia~C==::"_------1500 psia

25 30 35 40 45 50API Gravity of Crude Oil

55

Figure 4. Maximum gas velocity based on conservative liquid phase assumptions.

599

o-.....~ 10~C"?-'<:t 8o--~ 6enenID 4cL-G.)

-g 2IDo:

Critical Slenderness Ratio

12Gas Cap.cty eon.hinod •••• FIAHorizor<aI ~""Size Bewd on 1.w mc:ron ct'op6cItr~eo dog F. 0 65 GrM!y Go. 50 psia

60

Figure 5. Maximum slenderness ratio based on conservative liquid phase assumptions.

250 psia

500 psia

__ ~ 1000 psia=-_--- 1500 psia .

':-;1'=0.0667 .

o~~~~~~~~--~~~20 25 5545 5030 35 40

API Gravity of Crude Oil (In Turbulent Flow)

600

,-