Kokal e Stanislav 1987.pdf

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Chemcal E,s neering Science, Vol. 44, No. 3, pp. 66S679, 1989. @XS-2549/89 $3.00+0.00Printed inGreat Britain. 0 1989 Per&mnon Press plc

AN EXPERIMENTAL STUDY OF TWO-PHASE FLOW INSLIGHTLY INCLINED PIPES-I. FLOW PATTERNSS. L. KOKAL

andJ . F. STANISLAV

University of Calgary, Calgary, Alberta, Canada T2N lN4(Received 10 December 1987; acceptedfor publi cation 1 August 1988)

Abstract-A series of oil-air two-phase flow experiments were conducted with a 25 m long acrylic pipeinstalled on au inclinable trestle. Three different pipe diameters 25.8, 51.2 and 76.3 mm) at seven angles0, + 1, f 5 and f 9) were studied. The fluids used were air and a light oil of 858 kg/m3 density and 7 mPa sviscosity at an average temperature of 23C and pressure of 230-350 kPa. The data include Bow patternobservations and their transitions over a wide range of flow conditions. These data have been analyzed totest existing semi-theoretical models, and new improved models have been proposed.INTRODUCTION

During co-current gas-liquid flow in pipes; a variety offlow patterns can exist depending on the flow rates,fluid properties and system parameters. Thegas-liquid flow behavior can change significantly fromone flow pattern to another. Consequently, an under-standing of any two-phase flow problem requires theknowledge of the flow pattern. The flow patterndetermination is also the first step for developing two-phase flow models to predict liquid holdup and press-ure drop.Classification of flow patterns is somewhat arbi-trary and depends to a large extent on the interpret-ation by individual researchers. Generally there is agradual change of flow patterns with the flow ratesrather than abrupt changes from one flow pattern tothe other. Within the transitional zones, the flowbehavior exhibits characteristics of the flow patternson both sides of the transition. Since flow patterndetermination is mostly based on visual observations,there is an element of subjectivity involved in de-lineating the individual flow regimes.Most of the available flow pattern maps are eitherfor horizontal or vertical pipes with very limited workreported for inclined pipes. The common procedurehas been to use the correlations developed for verticalpipes in off-vertical pipes and horizontal maps forpipes with small angles of inclination. This can giverise to large errors since some transitions are verysensitive to the angle of inclination.Gould et al. (1974) studied flow patterns in a pipeinclined at +45 as well as in horizontal and verticalpositions. They plotted their results using liquid andgas velocity numbers as proposed by Duns and Ros1963). They defined three flow regimes corresponding

to bubble liquid continuous), intermittent both

+ Present address: Petroleum Recovery Institute, 35 12 33rdStreet N.W., Calgary, Alberta, Canada T2L 2A6. Authorto whom correspondence should be addressed.

phases continuous) and annular (gas phase continu-ous). Mukherjee (1979) reported flow pattern maps forthe entire range of pipe inclinations. Empirical corre-lations were proposed for the flow pattern transitionboundaries. A similar approach was taken bySpedding and Nguyen (1980) who determined flowpattern maps for air-water data in a 4%mm pipe aangles both uphill and downhill.Weisman and Kang (1981) reported data forair-water and air-glycerol systems in slightly inclinedpipes and a one-component (Freon) system for higherangles. Empirical equations were formulated for altransitions. Experiments were also conducted inhorizontal and slightly inclined pipes with anair-water system by Barnea et al. (1980).A physical model for flow pattern transitions ininclined pipes was recently proposed by Barnea et al(1982) (downward inclined pipes) and Barnea et al(1985) (upward inclined pipes). These models are extensions of the previously developed models by Taiteland Dukler (1976) for horizontal and slightly inclinedpipes and Taitel et al. (1980) for vertical upward flow.They compared the air-water experimental data withtheir model predictions. Recently Barnea (1986, 1987proposed models to cover the entire range of pipeinclinations.

Crawford et al. (1985) collected data for flow pat-terns in downward inclined pipes using liquid refrigerant and its vapor. They extended the correlationsdeveloped for horizontal and upward flow byWeisman et al. (1979) and Weisman and Kang (1981)An excellent summary of the work on flow patterns igiven by Barnea and Taitel (1986) which lists 12references.

EXPERIMENTALThe experimental setup consisted of a 25 m longpipeline which was installed on an inclinable trestleand could be set at + 10 from the horizontal. The tessection was constructed from lengths of smooth trans


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666 S. L. KOKAL and J. F. STANISLAVparent cast acrylic pipe flanged together at intervalswith allowance made for static pressure taps andcapacitance type volume sensors. The pipeline isequipped with sfveral Validyne variable reluctancetype differential pressure transducers and seven vol-ume sensors. A detailed description of the apparatus isgiven by Kokal (1987).

FLOW PATTERN DESCRIPTIONSWhen gas-liquid mixtures flow in pipes, the twophases can distribute in a number of regimes de-pending on the gas-liquid spatial distribution. Theflow is often chaotic and difficult to describe. Thedefinitions of flow patterns have not been standard-ized and thus different researchers recognize differenttypes of flow regimes (Taitel and Dukler, 1976, Barneaer al . , 1980; Spedding and Nguyen, 1980).In this study all flow patterns were detected withvolume sensor signature traces (Kokal, 1987). Thismethod is considered objective and allows for correctidentification of the flow pattern. The flow patternmap has been divided into three basic flow regions: the

gas-dominated, intermittent and liquid-dominatedflows.Gus - dum inu t ed J r ows

S t ra t zBed . In this flow regime the liquid moves atthe bottom of the pipe with the gas moving at the topwithout any intermixing between the two phases. Atlow gas and liquid velocities, the interface is smoothand the flow regime is called stratified smooth (SS).With an increase in the gas flow rate, the interfacebecomes wavy in nature and the flow regime is termedstratified wavy (SW). The interface has a rough ap-pearance due to the occurrence of small waves andripples on the liquid surface. Often, small bubbles areseen on the liquid surface as well. With an increase ofthe gas flow rate the liquid layer starts to climb thepipe wall and the interface becomes rougher. Thesmall waves which move on the liquid surface areunsteady in nature; they appear in groups, move for ashort distance and disappear. Eventually, at higher gasflow rates, the stratified flow pattern changes to theproto-slug and annular flow regimes.

A n n u l a r . Annular flow occurs at high gas flow ratesand borders with the proto-slug and SW flow regimes.The liquid forms a thin film around the pipe wall.When the gas flow rate is relatively low, most of thisliquid travels along the bottom of the pipe with a veryrough surface. This type of flow is called annular wall(AW) flow. At even higher gas flow rates, some of theliquid breaks off from the film and forms a dispersedmist within the gas phase.Intermittent flowThe intermittent flow regime was observed mostfrequently and was given special attention. It is thedominant flow regime in horizontal and upward in-clined pipes and occurs to a limited extent in down-ward flow. It consists of liquid slugs and large gas

bubbles which are normally much longer than onepipe diameter. The liquid slugs move at an averagefrequency with slug and bubble lengths varying in astochastic manner. The intermittent flow regime hasbeen divided into four distinct regimes depending onthe gas holdup in the liquid slug.E longa t ed bubb l e (EB ) . The EB flow pattern is alimiting case of intermittent flow with the liquid slugs

free of entrained bubbles as shown in Fig. 1. The gasbubble is generally streamlined with a nose and a tailThe flow of the liquid beneath the bubble is similar tostratified smooth two-phase flow while the flow in theliquid slug is essentially laminar. The tail of the bubblesometimes breaks off from the main body of thebubble and is subsequently picked up by the nextbubble.E l onga t ed bu bb le w i th d i spe rsed bubb l es (EDB ) . Asthe mixture velocity is increased, dispersed bubblesstart to appear at the leading edge of the slug. Theappearance of dispersed bubbles in the slug is associ-ated with the transition of the liquid in the slug fromlaminar to turbulent flow. The nose of the slug be-comes a short turbulent mixing zone where the dis-persed bubbles are generated.Slug (SL). SL flow is a continuation of the EDB flowregime with gas holdup in the liquid slug greater than10%. The transition from EDB flow to SL flow occurswhen Egs= 10%. This condition was generally foundto correspond with V,,, = 1.5-2.4 m/s for all three pipesizes. The turbulence level in the slug increases and theliquid layer beneath the gas bubble exhibits aninterface similar to SW flow with small dispersedbubbles. The slug and bubble lengths were found tovary in a stochastic manner. Similar behavior was alsoobserved for the slug frequency.Slug f r o t h (SLF ) . The liquid in the slug and thefilm becomes very frothy due to the turbulence andintermixing. This regime was observed at high gas andiiquid flow rates and borders with the DBF Bowregime. The liquid in the slug has similar character-istics to the froth flow regime. The transition from SLflow to SLF flow takes place at V,,, ~4-5 m/s with

E ,%30%.L i q u i d - d om i n a t e d j l ow s

In this region the liquid is the dominant phase withgas dispersed in it.Di spersed bubb l e (DB) . The gas phase is dispcrscd assmall discrete bubbles in a continuous liquid phase. Atrelatively low gas rates these bubbles are located nearthe top of the pipe due to buoyancy but at higher gasrates the bubbles are dispersed more uniformly. Thebubble size varies from a few millimeters to a fewcentimeters in diameter.Di spersed f ro th (DBF ) . This regime is observed athigh gas and liquid flow rates and the intermixing is so


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Two-phase flow in slightly inclined pipe-1 667

6

14I51617

NAME ABBREVSINGLE PHASE GAS SPHG)SINGLE PHASE LIQUIDELONGATED BUBBLEELONGATED BU66L EDISPERSED BUBBLES

SPHLIEB)

IND EDB) 1SLUG FLOW INTERMITTENTSLISLUG ANDFROTH FLOW SLF)PROTO -SLUG FLOW P S) -IPROTO -SLUG ANDFROTH FLOW PSFI I

TRLINSITIONSWAVE FLOODINGDOWN HILL FLOW ONLY ) WF) JDISPERSED BUBBLE DB) 1DISPERSED BUBBLE

IDISPERSED

AND FROTH DBF) BUBBLEDISPERSED BUBBLE TO OB-I)INTERMITTENT TRANSITION -IANNULAR WALL Awl 1ANNULAR MIST ROUGH ANNULARLAYER OF UOUID ALSO AM)COVERS ENTIRE PIPE WALL)STRATIFIED SMOOTHSTRATIFIED SMOOTH TOINTERMITTENT TRANSITION * - ) STRATIFIEDANDSTRATIFIEDSTRATIFIED WAVY TRANSITIONSSTRATIFIED WAVY TOINTERMITTENT TRANSITION

Fig. I. Flow regime descriptions.

high that it is impossible to detect which is thedispersed phase. The flow becomes frothy in nature(Fig. 1). This flow regime is associated with highpressure drops and is also referred to as churn flow bymany observers.Transi t ions

Strat i f ied- in term it tent S-Z) transi t i on. The tran-sition from stratified to intermittent flow was difficultto locate in the 26 mm diameter pipe for horizontalflow. In this transition region extremely long bubblesare sometimes observed which are characterized bylengths several times the pipeline length. The liquidlevel rises until a solitary slug is formed and passesthrough the pipe and sweeps part of the liquid out;then the whole cycle is repeated. It was observed thatthe transition could be shifted by changing the liquidlevel in the separator relative to the pipe centerline.The stratified flow could be extended by keeping theliquid level in the separator below the pipe and theintermittent flow could be extended by increasing itover the pipe centerline.For horizontal flow the gas-liquid mixer at the inletof the pipe also had some effect on the transitionboundary. In the initial stages of the study, the phases

were mixed and transported to the inlet through a 5 mlong flexible hose. This increased the intermittent flowregion possibly due to the slugs existing in the hosewhich persisted along the entire length of the pipeline.Later, the gas-liquid mixer was replaced with the oneshown in Fig. 2 which allowed mixing of the twophases immediately upstream of the pipe section. Withthe new mixer the stratification of the phases wasenhanced.The horizontal S-l transition was also sensitive toslight deviations of the angle from the horizontal.These deviations could be due to flow induced vibra-tions, resetting of the trestle after calibration of thevolume sensors (E, = 1) or the accuracy involved in themeasurement of the angle itself ( + 0.03 ). It was there-fore difficult to locate the S-I transition precisely. Ininclined pipe flow, this transition was not affected byas many factors as for the horizontal case. In upwardinclined pipes, stratified flow was observed to a verylimited extent.A ney regime so far not reported in the literaturewas observed near the S-I transition and was denotedas wave flooding (WF). This flow regime was observedonly for downhill flow and was characterized bytransient liquid blockages or slugs which could remain


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668 S. L. KOKAL and J. F. STANISLAV260 mm I 260 mm I 220 mm

25.8 mm. 51.2 mm 51.2 mm ACRYLICOR 76.3 mm ACRYLIC PIPEPIPE SECTION

PIPE

Fig. 2. Gas-liquid inlet mixer.stationary for some time before draining off. Details ofthis flow regime are shown in Fig. 3. WF was observedat low gas and medium liquid velocities. It was foundto be unstable and exhibited a hysteresis phenom-enon. It was prominent in the 26mm pipe and was notobserved at all in the 76-mm pipe.

Strati ed-annular (S-A) and intermittent-annular(Z-A) transitions. These transitions take place at highgas flow rates (V,, > 2-3 m/s). The transition regionconstitutes a wide band and consists of proto-slug flow(PS) at low liquid velocities and proto-slug froth flow(PSF) at higher liquid flow rates. These flow regimesare characterized by unsteady waves which are unableto bridge the pipe due to the insufficient supply ofliquid. The waves move in a jerky manner at velocitieslower than that of the gas. The PS and PSF regimesshow characteristics of stratified, intermittent andannular flow regimes.

I ntermi ttent-dispersed bubble (I -DB) transition. Thetransition between the intermittent and DB flow

regimes was observed at high liquid flow rates. Thetwo different inlet mixers mentioned earlier affectedthe location of the I-DB transition boundary in the26- and 51-mm pipes. This boundary also representsthe limit for intermittent flow for which the slugtranslational velocity could not be measured using thevolume sensor signature traces.

FLOW PATTERN DETECTIONThe flow patterns described above were determinedvisually and by using the volume sensor traces. Theuse of visual observation for determining flow patternshas the disadvantage of being subjective and can leadto differences in the interpretation of flow patterns.The development of a simple quantitative means forthe determination of flow patterns was therefore con-sidered desirable.The volume sensors described in the Appendix wereused for a quantitative identification of the flowpatterns. The traces from the volume sensors wererecorded using a Hewlett-Packard strip chart re-corder. Each flow pattern had a characteristic trace

_O~SPERSED BUBBLES

OIL DRAINAGE

AIR BUBBLE

STRATIFIED WAVY FLOWFig. 3. Wave flooding phenomena in downhill flow.


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and some typical traces are shown in Fig. 4 for hori-zontal flow.Two-phase flow in slightly inclined pipes-I 66

by the stochastic semi-slugs moving on the liquidsurface. The amplitude of the traces decrease and foannular flow these fluctuations become even smalleand random in nature [Fig. 4(f) and (g)].Intermittent flow had the most distinctive trace[Fig. 4(a)-(d)]. For low gas flow rates, the EB flowregime was observed with liquid slugs free of entrainedgas bubbles. A typical trace for the EB flow regime isshown in Fig. 4(a). It can be seen that the peak voltage(corresponding to liquid slugs) coincides with the V,,,(100% liquid) mark. EDB flow is characterized by the

presence of dispersed bubbles in the liquid slug. Atrace for the EDB flow regime is shown in Fig. 4(b)and the voltage peaks do not quite reach the V,,,mark due to the gas holdup in the slug. For SL flowthe response is similar [Fig. 4(c)] except that the gasholdup in the slug is generally greater than 10%.

The traces for DB flow are shown in Fig. 4(h) and(i)The fluctuations for DB flow (low V,) are random inature with small amplitudes and high frequency buthe average voltage is higher due to the higher averageliquid holdup. This distinguishes the DB flow from PSwhere the fluctuations might be similar but occur at lower average voltage. In DBF (high V+J, the fluctuations are random with higher amplitudes and lowefrequencies.

PS and PSF make up the wide transition betweenthe intermittent and annular flows and some typicaltraces are shown in Fig. 4(d) and (e). These are marked

The SS flow [Fig. 4(j)] shows no fluctuations anthe trace is a straight line. The SW flow [Fig. 4(k)] iobserved at higher gas flow rates and is characterizedby the small amplitudes of the traces. As the gas rate iincreased further, the frequency of the fluctuations

Fig. 4. Flow regimes from volume sensor traces.


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670 S.L. KOKAL and J. F. STANISLAVincrease. The distinction between the AW [Fig. 4 f)]and SW [Fig. 4 k)] flow regimes was difficult to makewith the volume sensor traces. For this reason visualobservations were used to distinguish between theseflow patterns. In AW flow the liquid climbs the pipewall whereas in SW flow the waves are on the liquidsurface.The criteria set above were used to detect flowpatterns and the results were compared with visualobservations. The agreement was found to be good.The final flow pattern maps were based on visualobservations and by using the volume sensor traces.

MODELING FLOW PAlTERN TRANSITIONSS-I transitionTaitel and Dukler 1976) proposed an analysis ofthe transition from stratified to intermittent flow. Theanalysis is based on the condition of equilibriumstratified flow (Fig. 5). A momentum balance on eachphase yields

- A, g - tlS, + ziSi - plA,g sin p = 0 (1)

-A,g-r,S,-riSi--p,A,gsin/3=0 (2)where zl, 2, and zi are the liquid, gas and interfacialstresses, respectively. S, and S, are the tube perimetersin contact with the liquid and the gas phases, respect-ively, while Si is the interfacial perimeter. j? is con-sidered positive for upward flow. Eliminating thepressure gradient dP/dx from eqs 1) and 2) gives

The shear stresses are evaluated as follows: 51hv:

2

(6)where I+ and vg are the in situ velocities, andS, and fe,the friction factors, are functions of the liquid and gas

Reynolds numbers:

The equivalent diameters D, and D, for the liquid andgas phases are defined asD,2

I

D,= 4A,S,+Si

(9(10

The friction factors are calculated by using the equa-tion of Chen (1979):i= -4.010g 5.0452E-_Jf 3.70550 Re

A simplified equation for the friction factor is alsogiven by Chen 1984). The equations were transformedto dimensionless form using the reference quantities: Dfor length, 0 for area, and V,, and V,, for the liquidand gas velocities. Denoting the dimensionless variables by -, eq. 3) becomes

where X is the Lockhart-Martinelli parameter:

and Y is defined as(14

The parameter X can be easily calculated from thliquid and gas flow rates, fluid properties and tubdiameter. The parameter Y represents a ratio o

Fig. 5. Stratified flow in pipes.


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Two-phase flow in slightly inclined pipes-1 6gravity and pressure forces. In the above equations,& andand f,, are the single-phase liquid and gas frictionfactors based on the superficial velocities. The dA,/dS;, = Jl -(21;, - 1)2. (25interfacial friction factor, J, is calculated using theEllis and Gay (1959) correlation: The variables in eq. (23) are the superficial gas velocitand the liquid level I .

fi= L3Re,-0.57. (15) The S-I transition is thus determined by threThe basic difference between the approach taken dimensionless groups, X, Y and F r . For fixed Y, thhere and that of Taitel and Dukler (1976) is the way transition is defined by X and Fr only. Thus, for

the friction factors are calculated. In this study, eq. (11)given superficial gas velocity, eqs (12) and (23) ar

was used for calculating the gas and liquid friction solved simultaneously for V,, and 5,.factors, and eq. (15) for the interfacial friction factor. The transition boundary calculated in terms of VTaitel and Dukler (1976) assumed that fi =fe and Vs ses plotted in Figs 7-9 for the different angleAll dimensionless quantities are functions of and pipe sizes.h, = h J D as follows: I - DB t r a n s i t i o n;I,=0.25[n-cos- (2h,-1)+(23;,-l)Jl-(2h,-1)2] For horizontal and slightly inclined pipe flow

(16) Taitel and Dukler (1976) suggested that the transition;1,=0.25[cos- (2X,- 1) -(2h,- l)Jl-(2h,- l) ] from intermittent to DB flow regime takes placwhen the turbulence in the liquid overcomes th(17) buoyant forces. A slightly different approach is con

S,=7r-coS-1(2ht-l)S,=cos-1(2h,-l)si = Jl - (2T;, 1)2--&=A/A,--Q = A/A,

(18)(19)(20)(21)w

The three variables in eq. (12) are the liquid level, I&,and the parameters X and Y [eqs (13) and (14)]. If Xand Y are specified, eq. (12) can be solved for A,.Based on the Kelvin-Helmholtz stability theory,Taitel and Dukler (1976) proposed a criterion fortransition from stratified to intermittent flow regimeand is given by

Fr=(l -%I[_ d;,dA,] (23)where F r is a modified Froude number given by

112 v,,J l cos P (24)

sidered here.A fully DB flow is shown in Fig. 6. Two dominanforces act on the bubble: a buoyant force which tendto lift the bubble to the upper part of the pipe and turbulent force which tends to disperse it in the liquidIt is assumed that these two forces are approximatelyequal for the transition from intermittent to DB flowThe turbulent forces acting on the bubble are estmated from Levich (1962):

where v s the radial velocity fluctuation which can bestimated using the friction velocity u,:A0 112(py = u* = I -2 (27

wheref, is the liquid phase friction factor. The buoyanforces acting on the bubble are(2

BUBBLES

Fig. 6. Dispersed bubble flow.


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672 S. L. KOKAL and J. F. STANISLAVAt the transition

F,>F, (29)substituting of eqs (26)(28) into eq. (29) yields

v < 8 (PI-Ppg)g=JsB1 I l/2_____ .fi db (30)PI

For liquids of low viscosity a simple equation devel-oped by Davidson and Schuler (1960) for the stablebubble diameter, d,, is

= I.,,,(% I&) 1 29-S/?. (31)Substituting eq. (3 l), with I+ = VJE , and g = 9.8 1 m/sinto eq. (30) gives

1112go23vo.4w . 32)

The validity of eq. (31) is limited to bubble formationin a stagnant pool of liquid. At the I-DB transitionthe bubbles are generally confined to the upper part ofthe tube especially at low gas rates. This means thatthe buoyancy force is higher than the turbulent disper-sive forces. For these reasons, and to obtain a good fit,the coefficient 4.56&i in eq. (32) was replaced with acoefficient of 0.8 and the inequality removed. The finaltransition criterion becomes

l/ZDo.8 V0.4JB 1 - (33)Equation (33) represents a criterion for the transitionfrom the intermittent to the DB flow regime.I A transitionAs described in the previous section, the liquidholdup in the slug decreases as the gas superficialvelocity is increased in the intermittent flow regime. Astable slug is maintained when there is sufficient liquidin the film ahead to sustain it. When there is insuf-ficient liquid, the slug becomes an unsteady wavewhich is swept around the wall resulting in PS andPSF. These flows make up a wide transitional regionbetween the intermittent and annular flow regimes.The PS is also classified by many as wavy annular flowand it has characteristics of both intermittent andannular flow.The average liquid holdup, E,, is typically around0.25 at this transition which is the limiting value forstable slug flow. It is suggested that for liquid holdupsless than this value, the transition to wavy annularflow takes place.Based on bubble rise theory and experimental re-sults, numerous authors (Armand, 1946; Griffith andWallis, 1961; Nicklin et al., 1962; Hughmark, 1965;Zuber and Findlay, 1965; Bonnecaze et al., 1971;Dukler and Hubbard, 1975; Spedding and Chen, 1984,1986; Hasan and Kabir, 1986) have proposed anexpression for gas holdup in horizontal as well as

inchned pipes:E+ b

where V , is the bubble rise velocity given by Zuber andFindlay (1965) and others:v*=c,v,+ v, (35)

where C, is the flow distribution parameter and I ,, sthe drift velocity or terminal rise velocity. The value ofC, is taken as 1.2 based on theoretical as well asexperimental results (Zuber and Findlay, 1965; Wallis,1969). Hasan and Kabir (1986) have also shown thatthis value is independent of the angle of inclination(except for stagnant liquid).On the other hand, the drift velocity, V,,, is affectedby the angle inclination and depends on the Eotvosnumber, Eo[gD (p, - pg)/e], and the inverse viscositynumber, NfCD3s(pr- P,P~/PJ PM-ski, 1966;Wallis, 1969).The effect of the inclination on the drift velocity isgiven by Hasan and Kabir (1986) as

V,,=VJ~~(l+sir~/?)i.~ (36)where Vds is the drift velocity in a pipe with aninclination of B. For the range of angles considered inthis study, the effect of inclination is small and there-fore V,, was used for all angles. Moreover, the values ofVd is small and hence the effect of its variation withinclination angle is negligible.Wallis (1969) shows that for Nf> 300 and Eo> 100the drift velocity is given by

v,=o.345 [oD(p:;p3 I . (37)The minimum values of Eo and Nfwere calculated tobe 180 and 1600, respectively, for the fluids use in thisstudy. With E,=0.25, eqs (34), (35) and (37) give thenecessary criterion for the transition from intermittentto annular flow regime:

I ,= 10.36V,,+ C, (38)where

C, ~2.98 [ gD ;lp,)] . (39)Equation (38) locates the I-A boundary approxi-mately since the transition between intermittent andwavy annular flow is a gradual one and it is difficult todistinguish between a highly aerated slug and wavyannular flow (proto-slug) with roll waves.EB -EDB transitionEB flow is a limiting case of SL with the liquid slugfree of any dispersed bubbles. A method for estimatingthe liquid holdup in the slug was recently proposed byBarnea and Brauner (1985). They suggested that thegas is dispersed in the liquid slug in the form ofdispersed bubbles.


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Two-phase flow in slightly inclined pipes-1 67The gas holdup in the slug can be estimated from abalance between the turbulent dispersive forces andbuoyant coalescence forces. These forces also deter-mine the location of the I-DB transition. When co-alescence forces are high, the small dispersed bubblesagglomerate into elongated bubbIes with aeratedslugs. On the other hand, high turbulent forces willcause transition to dispersed bubble flow. At the I-DBtransition, the two forces are equal.A point on the I-DB transition is represented bycertain values of V,, and I +,. The gas holdup at thispoint can be estimated by using eq. (34). This is themaximum holdup that the liquid slug can accommo-date as dispersed bubbles at a given turbulence levelwhich depends on the mixture velocity V,,, = V, + VW).Starting at this point on the I-DB transition andincreasing Vss, while keeping V,,,constant, will cause atransition to the intermittent flow regime. The vel-ocity of the liquid in the slug, V,, is equal to themixture velocity based on continuity requirements.

Therefore, for a given mixture velocity, the turbulentforces within the slug are the same as in the DB flow atthe I-DB transition. Consequently the slug will sus-tain the same gas holdup as it does at the I-DBboundary with a mixture velocity V,,, which can beeasily calculated using eq. (34).The EB-EDB transition can be predicted for thelimiting case when E,,+ 1 which corresponds to E,+ 1or E,-+O at the I-DB boundary. Barnea and Brauner(1985) used the criterion for the I-DB transition

10.1

0.01 .+-c-y__>..- xXx*.**. xxx.+.* 1x1 I.I f f xx ,...E:+* ... . . + ...** + . ..n.B= - ~* ~0.01 0.1 1 lo x30

proposed by Taitel and Dukler (1976) and calculatedthe gas holdup E,) using the no-slip flow condition atthe transition In this work the I-DB transition waspredicted using eq. (33) and the gas holdup wascalculated using eq. (34). To estimate the EB-EDBtransition, a point is located on the I-DB transitionfor E,,-+O using eqs (33) and (34). Theoretically thiswill correspond to a value of Vs, = 0 but the transitionswere calculated for a small value of V,, =O.OOl m/E, x 0 .00 1 ).EDB-SL t r a n s i t i o n .In the EDB flow regime the gas holdup in the slug(E& is greater than zero but less than 0.1. TheEDB-SL transition is predicted in a similar manner asthe EEEDB transition with E,=O.l at the I-DBtransition using eqs (33) and (34).

RESULTSThe experimental data and theoretical results areplotted on flow pattern maps using superficial gas and

liquid velocities as coordinates. Figures 7-9 presentthe results for the three pipe diameters at differentinclinations. The solid curves represent theoreticalresults while the dotted curves are the experimentallydetermined boundaries. The points represent experi-mental data. The predictions of Taitel and Dukler(1976) model using the rough pipe friction factor(Taitel, 1977) are also shown on these maps.

Fig. 7. Flow pattern map for 25.8-mm pipe.


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674 S. L. KOKAL and J . F. STANISLAV

0.0 0 01 0.1 1 10 luox) ___---____ w-i x x. . .. ._* . . . x= *. .__> 0.1m. ._.: t; .:. . 1aA \+r , . -.._.. :*i ; ;aol 8= +I ___--__-I* ,. . ..--Ii .. .+.m. :. . . . ,.:.11. ; * : ;. .:.. . 1 : 1 :. .:.P= Oi i :0.01 0.1 1 x) loo ____-_-;; ,x x * 1++ xx .. * *:? :=I 4lIrTi. . . .:.1.1 * ;. .:.. . . i * ] j. .:*@= $).: :0 01 0.1 1 lo 100.01 0.1 1 R loolo

* 12p 0.1

0.01 0.0 0.1 1 10 I33

Fig. 8. Flow pattern map for 51.2-mm pipe.

0 0 0.0 0.1 1 lo loolo ___---_---rrti Ii.rri ,lI?icl.; ..i7*. .:7 -:::; .; i 73=1- L0.01 0.1 1 lo lo0

___---__---rttri: II :. ..*. I1%. ..*+i .I.a. *; . t. ...+- . . I..*.,. F . . ;P >m 0.1B=ts. :I, :I

0.01 oat 0.1 1 l0 loo 0.0 0.1 1 lo 100D

2 >m 0.1Fig. 9. Flow pattern map for 76.3-mm pipe.


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Two-phase flow in slightly inclined pipes-1 675Ho r i z o n t a lThe horizontal flow patterns are shown in Figs 7-9for the three pipe sizes. The S-I transition was foundto be very sensitive to slight deviations of the anglefrom the horizontal. A number of factors affect thistransition as discussed earlier. Since the accuracy inthe pipe inclination was limited to +0.03 , threecurves were plotted for the horizontal S-I transition at+ 0.03, 0 and - 0.03 .

The I-A transition [eq. (38)] predictions comparewell with the experimental results. This transition islocated at higher gas velocities-for the larger diameterpipes due to the effect of diameter on the drift or risevelocity [eq. (37)]. The I-A transition is valid outsidethe range of stable stratified flow. The transition fromintermittent to annular flow is a gradual one as theflow exhibits various flow regime characteristics in thetransition region.The I-DB transition [eq. (33)] shows a good agree-ment with the experimental transition. It should benoted that the validity of eq. (31) is limited to gasbubbles rising in a stagnant pool of liquid and themovement of the continuous phase has some effect onthe bubble size. Also for high gas holdups, the bubblescoalesce and are not uniform in size. Nevertheless, thecriterion [eq. (3311 predicts the transition rather well.This boundary is shifted to higher liquid velocities forthe larger pipe sizes which was confirmed experi-mentally. Only limited data points could be taken forthis transition in the 51-mm pipe and no data pointswere taken for the 76-mm pipe due to the oil pumpcapacity.The theoretical EB-EDB transition is also shown inFigs 7-9 using the criterion given in the previoussection. This transition i s obtained for slugs free ofdispersed bubbles and corresponds to a constant valueof V,,, for E,,+O. The EDB-SL transition is alsoshown for a constant value of V,,, at EgS=O.l. Thepredictions compare very well with the experimentaldata.The results of the Taitel and Dukler (1976) modelare also presented for comparison with the experi-mental data. The predictions for the S-I and I-Atransitions show a good agreement with the data.Equation (38) reduces to the criterion proposed byTaitel and Dukler for the horizontal case. The Taiteland Dukler theory overpredicts the I-DB transition interms of the superficial liquid velocity. This has alsobeen confirmed by Barnea et al. (1980). Taitel andDukler did not differentiate between the EB, EDB orSL flow regimes and considered them as theintermittent flow regime.The effect of pipe diameter on the different tran-sitions is shown in Fig. 10 for the horizontal case. Thecurves represent theoretical predictions. The S-I tran-sition is quite sensitive to the pipe diameter and the STflow region expands with the pipe size. The I-DBtransition is also affected by the pipe diameter and islocated at higher liquid velocities for the large pipes.This is because a higher turbulence level is required toproduce DB flow in the larger pipe diameters. The I-A

Fig. 10. Effect of pipe diameter on transition boundaries in ahorizontal pipe.transition is relatively insensitive to the pipe size. Thishas also been confirmed by Taitel and Dukler (1976)and Spedding and Chen (1981).E fSec t o f i n c l i n a t i o nThe uphill-flow regimes were found to be similar tothe horizontal-flow regimes except that very limitedstratified flow was observed for uphill flows. Thedownhill-flow regimes on the other hand were foundto be very different and more complex. The majordifference was the substantial expansion of the strati-fied flow region between the horizontal and - 1 . Thestratified region further expanded with an increase inthe angle but the expansion was less rapid than thatbetween the horizontal and - 1 . This is clearly seen inFig. 11. For downward stratified flow the surface of

Above ines I-NT3elow lines STRATIF IEDPipe Diameter = 25.8 -

0.01 a.1Superficial gas Lcity 100V p/sFig. 11. Effect of pipe inclination on stratified-intermittenttransition.


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676 S. L. KOKAL and J. F. STANISLAVthe liquid was never smooth and became progressivelymore wavy in nature as the S-I transition was ap-proached. The intermittent region shrunk in size as theangle of inclination was increased in downhill flow.The S-I boundary was most sensitive to the incli-nation angle. In downward flow the liquid movesfaster with low holdups due to gravity and thereforetransition to intermittent flow takes place at highergas and liquid flow rates. On the other hand, upwardinchnations cause the liquid to move slower withhigher liquid holdups and prevents stratification.Figure 11 shows the effect of inclination on the I-Stransition for the 26-mm pipe.The flow pattern results are shown in Figs 7-9for the various inclination angles. The agreementbetween theory and experimental data is very good.The I-S transition in downhill flow is correctlypredicted by the criterion given by eq. (23). As noted,this transition is very sensitive to pipe inclination. TheI-DB and I-A transitions are relatively insensitive tothe angle of inclination. The inclination angle willhave some effect on the I-A transition because thebubble rise velocity, V,,, depends on the angle ofinclination. For the angles considered in this study,however, this effect is negligible. On the other hand,the I-A and I-DB transitions are sensitive to the pipediameter.The Taitel and Dukler theory predicts the I-Sboundary well, but the I-DB and I-A transitionspredictions are not satisfactory. For the I-A tran-

sition, the Taitel and Dukler theory shows a significant effect on the pipe inclination especially for uphilflow which was not observed experimentally. Similadisagreement with experimental data was reported bBarnea et a l . (1980). The present theory predicts thitransition very well.To test the validity of the model equations with datfrom other sources, the data of Shoham (1982) werselected and the results are plotted in Fig. 12. There ia slight improvement over the Taitel and Dukler(1976) results for the S-I and I-DB transitions. ThI-A transition is not very well predicted by the newmodels. The reason for this is the way annular flow idistinguished by Shoham (1982). The PS and PSF flowregimes have been included in the.annular flow regimewhile Shoham (1982) presumably has included these ithe intermittent flow regime. To distinguish betweenthe annular and intermittent flow regimes by a singlcurve on a V,, vs V,, plot is rather ambiguous becausthe transition between these two flow regimes occurover a wide range of gas and liquid flow rates.

CONCLUSIONSUnique experimental data have been collected fothe flow patterns and their transitions over a widrange of gas and liquid flow rates. The data on flowpatterns were compared with the Taitel and Dukler(1976) flow pattern map. While this theory predictsthe S-1 transition correctly, it fails to predict the othe

Fig. 12. Flow pattern map for 25mm pipe with data of Shoham 1982).


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Two-phase flow in slightly inclined pipes-1 67boundaries satisfactorily. Improved models were de-veloped for these transitions. v, average translational velocity of the slug andbubble, m/sThe flow regimes were found to be very sensitive tothe inclination angle. The major effect of inclinationwas observed for the S-I transition. For the horizontalpipe, even a small deviation (_tO.O3 ) could signifi-cantly affect the location of this transition. Uphill-flowregimes were predominantly intermittent while down-ward flow was dominated by stratified flow. The I-Aand I-DB transitions were relatively insensitive to theinclination angle. Pipe diameter had a distinct effecton all transition boundaries. The gas-liquid inletmixer can affect the location of the transition bound-aries. Entrance effects were observed for some range ofgas and liquid flow rates. The models developed forthe flow regime transitions (S-I, I-DB and I-A)predict the boundaries correctly for the entire range offlow variables, pipe diameter and system variables.

NOTATIONcross-sectional area of the pipe, m2cross-sectional area of pipe for gas, mzcross-sectional area of pipe for liquid, mzfilm distribution parameterconstant for eq. (38) defined by eq. (39)bubble diameter in DB flow [eq. (31)-J, mpipe diameter, mequivalent diameter for gas phase [eq. (lo)], mequivalent diameter for liquid phase [eq. (911,maverage in situ gas fraction in pipeaverage in situ gas fraction in the slugaverage in s i t u liquid fraction in the pipeaverage in situ liquid fraction in the sluggas phase friction factor based on Ree [eq. (S)]interfacial frictio? factor [eq. (15)]liquid friction factor based on Re, [eq. (7)]gas phase friction factor based on superficialvelocityliquid phase friction factor based on superficialvelocitymodified Froude number [eq. (24)]buoyant forces in DB flow [eq. (28)], Nturbulent forces in DB flow [eq. (26)], Nacceleration due to gravity, m/s2liquid depth in pipe, mgas phase Reynolds number [eq. S)]liquid phase Reynolds number [eq. 7)]gas wetted perimeter with pipe waI1[eq. 19)]. minterface wetted perimeter between gas andliquid [eq. 20)], mliquid wetted perimeter with pipe wall, mfriction velocity [eq. 27)], m/sin situ gas velocity = VJE , m/sin situ liquid velocity = VJE,), m/sradial velocity fluctuation [eq. 27)], m/sbubble rise velocity [eq. 35)], m/sdrift velocity [eq. 37)], m/sdrift velocity [eq. 3611, m/ssuperficial gas velocity, m/ssuperficial liquid velocity, m/s

V 1,,,, volume sensor voltage corresponding to singlephase liquid flow, V

X Lockhart-Martinelli parameter [eq. 13)]parameter [eq. 14))angle of inclination, o

=r

pipe roughness, mfilm geometry parameter, ogas viscosity, Pa sliquid viscosity, Pa sgas density, kg/m3liquid density, kg/m3gas shear at pipe wall, N/m2interfacial shear stress between gas and liquidN/m2liquid shear stress at pipe wall [eq. (4)], N/m2

REFERENCESArmand, A. A., 1946, The resistance uring he movementotwo-phase ystems n horizontalpipes.Zzv.V.T.Z. 1, 1623.Bamea, D., 1986, Transition from annular flow and fromdispersed bubble flow-unified models for the whole range

of pipe inclinations Znt. J. Multi phase Fl ow 12, 733-744.Bamea, D., 1987, A unified mode1 for predicting flow-patterntransitions for the whole range of DiDe inclinations. Znt. JMulti phase Fl ow 13, 1-12. - - -Bamea D. and Brauner N.. 1985.Holdup of liquid slug itwo phase intermittent Row. Znt. J. M + e Fl ow-11,43-49.Bamea, D., Shoham, 0. and Taitel Y., 1980, Flow patterntransitions for gas-liquid flow in horizontal and inclinepipes: comparison of experimental data with theory. Znt. JMulti phase Fl ow 6, 217-225.Bamea. D., Shoham, 0. and Taitel Y.. 1982, Flow patterntransition for downward inclined two phase flow: horizontal to vertical. Chem. Engng Sci. 37, 735-740.Bamea, D., Shoham, 0. and Taitel Y., 1985, Gas liquid flowin inclined tubes; flow pattern transitions for upward flowChem. Enmo Sci. 40, 131-136.Bamea, D. a -Taitel Y:, 1986, Flow pattern transition in twophase gas-liquid flows, in Encyclopedia of Fl uid Mechanics(Edited by N. Cheremisinoff), Vol. 3, pp. 403-474.Bonnecaze, R. H., Erskine, W. and Greskovich E. .I., 197Holdup and pressure drop for two-phase slug Row iinclined pipeline. A.1.Ch.E. .Z. 17, 1109-I 113.Chen, J. i -J., 1984, A simple explicit formula for thestimation of pipe friction factor. Proc. Znstn civ. Engr sPart 2, Technical Note 400, 77, 49-55.Chen, N. H., 1979, An explicitequation or friction factor ipipe. Znd. Engng Chem. Fundam. l 296-297.Crawford, T. J., Weinberger, C. B. and Weisman, J., 198Two-phase flow patterns and void fractions in downwardflow, Part.1: steady state flow patterns. Znt. J. MultiphaseFlow 11, 61-782.Davidson, J. F. and Schuler, 0. G., 1960, Bubble formation aan orifice in an inviscid liquid. Trans. Znstn them. Engrs 38335342.Dukler, A. E. and Hubbard, M. G., 1975, A model fogas-liquid slug flow in horizontal and near horizontatubes. Ind. Engng Chem. Fundam. 14,337-347.Duns, H., Jr. and Ros, N. C. J .,1963, Vertical flow of gas anliquid mixtures from boreholes, in Proceedings of the 6thWor ld Petroleum Congress, Section 2, Paper 22, FrankfurtEllis, S. R. M. and Gay, B., 1959,The parallel flow of two fluistreams: interfacial shear and fluid-fluid interactionTrans. Instn them. Engrs 37,206.Gould, T. L., Tek, M. R. and Kaltz, D. L., 1974, Two-phaseflow through vertical inclined or curved pipe. J. PetroTechnol. 26, 914-926.


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678 S. L. KOKAL and J . F. STANISLAVGri ffith, P. and Wallis, G. B., 1961, Two-phase slug flow. J. Wallis, G. B., 1969, One Dimensional Two Phase Fl ow.Heat Transfer 83, 307-320. McGraw-Hil l, New York.Hasan, A. R. and Kabir, C. S., 1986, Predicting multiphaseflow behavior in a deviated .well . SPE paper 15449 pre-sented at the 61st Annual Technical Meeting, NewOrleans, LA.

Weisman, J ., Duncan, D., Gibson, J . and Crawford, T., 1979Effect of fluid properties and pipe diameter on two-phaseflow pattern in horizontal lines. I nt. J. Multi phase Fl ow 5437-462.Hughmark, G. A., 1965, Holdup and heat transfer in horizon-tal slug gas-liquid flow. Chem. Engng Sci. 20, 1007-1010.Kokal, S. L., 1987, An experimental study of two phase flowin inclined pipes. Ph.D. Thesis, University of Calgary,Calgary.

Levich, V. G., 1962, Physiochemical Hydrodynamics.Prentice-Hall, Englewood Cli ff, NJ .Mukherjee, H., 1979, An experimental study of inclined two-phase flow. Ph.D. Dissertation, University of Tulsa, Tulsa,OK.

Weisman, J . and Kang, S. Y., 1981, Flow pattern transition invertical and upwardly inclined lines. Int. J. MultiphaseFl ow 7, 271-291.Zuber, N. and Findlay, J . A., 1965, Average volumetricconcentration in two-phase flow systems. .r. Heat Transfer87, 453-468.Zukoski, E. E., 1966, Influence of viscosity, surface tensionand inclination angle on motion of long bubbles in closedtubes. J. Fl uid Mech. 25, 821-837.

Nicklin, D. J ., Wilkes, J . 0. and Davidson, J . F., 1962, Two-phase flow in vertical tubes Trans. Instn them. Engrs 40,6149.Shoham. O., 1982, Flow pattern transition and character-ization in gas-liquid two phase flow in inclined pipes.Ph.D. Thesis, Tel-Aviv University, Tel-Aviv.Spedding, P. L. and Chen, J . J . J ., 1981, A simplified methodof determining flow pattern transition of two phase flow ina horizontal pipe. Int. J. Multi phase Fl ow 7, 729-731.Spedding P. L. and Chen, J . J . J ., 1984, Holdup in two-phaseflow. Int. J. Mu lti phase Fl ow 10, 07-339.Spedding, P. L. and Chen, J . J . J ., 1986, Holdup in multiphaseflow, in Encyclopedia of Fluid Mechanics Edited by N.Cheremisinoff), Vol. 3, Chap. 18, pp. 493-531.Spedding, P. L. and Nguyen, V. T.. 1980, Regime maps forair-water two-phase flow. Chem. Engng Sci. 35, 779-793.Taitel, Y., Barnea, D. and Dukler, A. E., 1980. Modeling flowpattern transitions for steady upward gas-liquid flow invertical tubes. A.I.Ch.E. J. 26, 345-354.Taitel, Y. and Dukler, A. E., 1976, A model for prediction offlow regime in horizontal and near horizontal gas-liquidRow. A.1.Ch.E. J. 22, 47-55.

APPENDTX: CAPACITANCE VOLUME SENSORSThe in situ liquid fraction or holdup was measured using capacitance type volume sensor originally designed andfabricated by Gregory and Mattar 1973) and used success-fully by Agrawal l971) and Singh 1982) for air-oil studies. Asimilar device was also used successfully by Mukherjee1979).A continuous measurement of the liquid holdup can bemade with the volume sensors by making use of the two

different dielectric constants of air and oil . The sensorbehaves as a parallel-plate capacitor for which the capaci-tance varies linearly with the dielectric of the material flowingthrough the sensor volume and follows a simple relationship:C=aK, At)

where C =capacitance of the volume sensor, K, = dielectricconstant of the mixture flowing through the sensor, anda = proportionality constant device-dependent).The mixture dielectric constant, K,, is the sum of thevolumetric fraction weighted dielectric constants of the fluid

Table Al. Volume sensor dimensions

fipc Flange Sensor Total Electrode NumberID OD length length Pitch width ofd D I L P W spirals25.8 100 146 171 70 10 251.2 133 177 216 154 25 176.3 164 192 227 168 47 1

+ All dimensions in mm.

Fig. Al. Capacitance volume sensor details.


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Two-phase flow in slightly inclined pipes--I 67phases inside the pipe and is given by insensitive to the distribution of the two phases within th

K, = E,K, +(l - E,)K, (AZ) sensor volume. The design also resulted in a convenientlinear calibration curve. Due to the temperature dependencewhere K, and K, are the dielectric constants for the liquid of the dielectric constants, a small temperature correction and gas phases, respectively. required if the experiments are conducted at a temperatureThe volume sensors consist of a shielded pair of helical different from the calibration temperature. Since the expericapacitor plates wrapped around the outside of the acrylic ments were performed inside the building, the temperaturepipe wall. A typical volume sensor is shown in Fig. Al. The fluctuations were small. The pertinent design details for thhelical plate design was chosen because it was found to be volume sensors are given by Gregory and Mattar (1973).

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