Holdup in two-phase, gas-liquid flow—II

HOLDUP

IN TWO-PHASE,

GAS-LIQUID

EXPERIMENTAL VAN THANH NGUYEN Department of Chemical and Matermls Engmeermg,

FLOW-II

RESULTS and P Umversity

L

SPEDDING of Auckland, Auckland, New Zealand

(Received 13 June 1976, accepted 29 December 1976) Abstract-Expernnenti data are reported for au-water two-phase flow ma condmt mchned at angles from vertxally upwards to vertxally downwards The results are presented m terms of a new development m the theory of two-phase flow The holdup data fall mto three regunes two of wluch (for slug flow and droplet or annular flow)

follow a relation of the form suggested by earher workers The thud holdup regme ldentied. m the mam apphes to downward and separated flow structures ldentlfied

A general map IS presented whxh allows these particular rewmes to be

calculated from experimental data This 1s not situation 111the case of the general equation,

EXPERIMENTAL

Holdup, pressure drop and flow pattern data are presented for two-phase au-water flow m a 4 55 cm I d , 6 m long perspex pipe at angles from vertically upwards to vertically downwards [I] The test rig 1s shown schematitally m Fig 1 for vertical downwards flow Air flow rates of up to 500 kg/hr and water flow rates of up to 6000 kg/hr could be accommodated m the test apparatus The air and water were metered and then mixed m an annular mixing sectlon fitted with a by-pass which operated when the holdup valves were m the closed position In the annular mixing section water was fed peripherally through a plezometer rmg mto the an stream emerging from a calmmg section Except for vetically downward flow, the an and water mixture emerging from the apparatus was separated m a cyclone which was so arranged as to avoid back pressure waves bemg passed back through the test section The whole test section was held rlsdly to a supportmg frame so as to ehmmate any movement of the test section The experunental procedure was to set the pipe angle and the liquid flow rate and to vary the gas rate from muumum to the possible maximum The holdup was measured by mechanically lsolatmg the test section using two synchromously operatmg gate valves and subsequently measurmg the volume of water held between the valves An electrical cucult was used to ensure that the valves were triggered and acted slmultaneoudy Angles of mclmatlon from the horizontal examined were +90 00,70 00,45 00,ZO 75,2 75,0, -6 17, -20 00, -44 75, -67 75, -90 00 METHOD

OF

DATA

-vVT=C*~T+B

m which CES Vol

32 No

all variables 9--c

are known

x.,

-

(2)

(3)

where

c+ =c* B+=B

A

1 - x,,Ixqo 1-

x&L 1

1 - x,,/xqc /[

1 - x.,/&i

1

(4)

(5)

so that the unknowns C’ and B’ can be determined from experimental data by plottmg vJ& agamst v, Zuber and Flndlay[2] suggested after exammatlon of alternative forms, that the best method of data presentation was a plot between vJ& and 9, This IS not necessardy the case as shown by an exammation of the accuracy m predIction of holdup when eqn (1) 1s used for the calculation of gas holdup The effect on the calculation of hqmd holdup of an error m the predicted value of gas holdup can be found from eqn (6)

FRESZNTATION

either

xq,

-

z=C+vr+B+

Part I of this work it was shown that m many sltuatlons the all-gas region does not exist and the holdup equation reduces to the simple form slmllar to that suggested by Zuber and Fmdlay[2],

C*Vr+B

-

a0

where xq, and x.~ remam unknown Whde eqn (1) 1s solved easily for C* and B rf data pomts are sufficiently numerous, the problem remams as to how to determme the all-gas condltlons under which it applies smce It 1s lmposslble to observe visually when the all-gas reson A1 becomes zero Apparently, there 1s no way to resolve this question at present so the method used m this work IS to rearrange eqn (2) thus

In

g=

x,0

the

(1) or can

be

The error m the calculated 1015

value of &

always has the

1016

VAN THANH NGUYEN and P

L

SPEDDING

to manometer

TEST

Fig

1

Schematic

diagrams of the

opposite sign to the error m & and increases with mcreasmg 2~ values when & < 0 5 the error m the calculation of & IS acceptable, but when RL > 0 5 the error m l% Increases rapldly and approaches infinity as & tends to unity When &. IS predicted first, the error m & which IS calculated from i% follows m exactly the same way These remarks are m agreement with the findings of Dukler et al [3] One method of overcommg this ddliculty IS to predict the holdup ratio mstead of the rndlvldual holdup values of either phase Defining R * = %.I&

= Z&/(1 - &)

= (1 - &>/&

(7)

then the errors are A&J&

= (AR*/R*)

A&&

- [AR*/(l

+ R*)]

= - AR */( 1 + R *)

(8)

(9)

It 1s evident that the error fractions of l& and & always have a smaller magnitude than that of R * Also the error m l% has the same sign as that of R* wlule the error 111& has the oppos& sign Therefore holdup data were presented usmg the holdup ratio R* rather than the mdlvldual phase holdup m order to obtam a higher degree

test ng showmg dlmensmns

SECTION

III metres

of accuracy To facilitate this, eqn (3) 1s rearranged to give the form suggested by Govler et al [5] R*

=

R,/&

=

(C++EJ~+(c+-Z

1)

WI

and a plot of R* agamst ~SL/~SS, will provide a more accurate basis for presentation of the experlmental data Indeed a detailed exammatlon of the alternative methods of graphlcal presentation of data show that the method suggested by Zuber and Fmdlay[2] as being the best means of plottmg data, namely a plot of ~SSG/& against v,, generally confines the non-linear section of the holdup curve (referred to as holdup regime III m this work) to such a small region that it can be ignored This IS not the case with the method of presentation suggested here, namely a plot of R * against ~SLI~SG where the non-linear region 1s presented adequately As IS dlscussed below this reson of non-hnearhty is of importance particularly for horizontal and downward flows and consequently cannot properly be ignored RF..SULTS

Generally the results gave three types of characteristic curves as illustrated m Fig 2 The data were too extensive to present here m detail so where they were found to

Holdup III two-phase,

Fig 2 Characteristic curves of the holdup ratio agamst the flow rate ratlo for constant hquld flow rates exhlblt a straight hne relation of the slmphfied form of eqn (1) then the intercepts and slopes were determmed These are presented m Figs 3 to 7 The results for the non-linear portion of the holdup data for characterlstlc curves of Type two 111the reaon III where value of C’ and B+ cannot readtly be calculated, are held by the authors and can be supphed on request In comparing the curves of one pipe mclmatlon with those of another pipe mclmatlon, It was found that the curves for horizontal flow possessed characterlstlcs found m both upward and downward flows Therefore the complete data for horizontal flow are presented m graphlcal form m Fig 3 as dlustratlve of the general trends which were found for the whole data DJSCUSSION OF RESULTS

A detailed exammatlon of the results showed that under slmllar experimental condltlons the results were m general

gas-hqmd flow-II

1017

agreement with data reported for horlzontal[2, 4-91 and vertical flow [IO-141 Dukler et al [3] have outlmed the dltficulties to be expected when comparmg results of dlfferent workers in this way and the gutdmg principles set out by them also were used in this instance Figure 2 shows three dtierent holdup regimes mto which the results fall, designated holdup regimes I. II and III The hnear portion of the curve at high holdup ratios IS termed holdup regime I, wl-ule the lmear portion of the curve at low holdup and flow rate ratios 1s termed holdup regime II, and what 1s essentmlly the non-lmear potion of the curve is termed holdup regune III It can be seen from an exammatlon of the curves m Fig 3 that for low hquld flow rates the curves are predommantly in the holdup regime III As the hquld flow rate 1s increased the holdup regune II and the holdup regime I appear while holdup regime III reduces steadlly until It vamshes at very high liquid flow rates For the conditions employed m this work the holdup regune III IS dominant m all the downward flows Figure 2 also shows three types of characterlstlc curves which were obtamed Type I curve only appears m homontal and downward flows The curve shows a hmltmg holdup ratio which 1s approached as the gas rate tends to zero The limit represents a situation no other than what 1s termed the “free surface channel flow” condltlon Detads of this regon of holdup regune III m which curves of Type I appear wfi be presented elsewhere [ 151, but suffice to say here that when the gas flow rate tends to zero for relatively low liquid flow rates m the honzontal and downward posltlon a separated strattfied flow results Type 2 appears m some horuontal and downward flows but only at high liquid flow rates As the liquid flow rate 1s mcreased the extent of the

-

-j

P-

v-

HORIZONTAL AIR-

1

2

3

4

QG

5

(

to

000

FLOW WATER

6

crn3/ set

1

Fig 3 Holdup regimes for horlzonti flow for various hqmd flow rates

7

s

9

1018

VAN THANH NGUYEN and P

HOLDUP

REGIME

L SPEDDING

I

1 5

C*

1 cl

__ UL PL0

QL I f-ID

1

Fe 4 Correlatron for the dlstnbuuon coefficient C* for holdup regune I

HOLDUP

REGIME

I

0 0 --------

l%g 5 Correlation for the nuhal function B for holdup regune I non-hear type III holdup regime decreased Type 3 curve 1s found only 111certain horizontal and upward flows Visual observation allowed several general comments to be made about the holdup regmes 111relation to the flow patterns occurrmg 111the pipe There IS an absence of an all-gas region m the holdup regimes I and II However, the converse is not true as condltlons where an all gas

region was not observed also occurred m holdup regune III In all these cases where an all gas region does not occur the slmphfied eqn (1) apphes Flow patterns m the holdup regme I always have the gas phase m the form of bubbles gvmg a flow wluch 1s termed m the hterature bubble-, plug-, slug-, or froth-flows Flow patterns m the holdup regime II always have the hqurd phase m the form

Holdup m two-phase, gas-hquzd flow-II r

I IO

,

I

, ,I,,,,

HOLDUP

I

1

REGIME

11,111,

I

I

I,1111,

II

I

III

I

105

C*

1 00

Fig 6 Correlatton for the d=tnbution coe5clent

C* for holdup regme II

67 5-

4-

HOLDUP

REGIME

II

3-

2-

l9-

s765-

4-

3-

2-

Rg 7 Correlation for the m&al functron B for holdup reguue II of droplets with or without hquld film on the pipe wall These patterns have been classdied m the hterature as droplet-, mist-, mist-annular-, or annular-flows Flow patterns m the holdup regune III are mostly of the type

havmg separated structure but sometlmes they Include also those fiow patterns observed m other holdup regunes A least square regression techmque was used to calculate values for C* and B 111the re@ons where the

VAN THANH NGUYEN and P

1020

slmpldied eqn (1) applied, I e for the holdup regimes I and II with the characteristic curves type 2 and 3 Data mdlcate that C* and Z3 exhibit a correlation with pipe mclmation and hquld flow rate The data therefore were corrected for interdependence arising from the type of least square regression technique which was used and the resulting prediction curves are presented m Figs 4-7 The mittal function and hqmd flow rate used m Figs 4-7 were made dimensionless by using the parameters suggested by Dumltrescu[16], Solovlev et al [17] and others B’ = Bv(gD)

(11) W)

It can be seen from Fig 5 that the magnitude of B’ m horizontal flow and m upward flow at small angles of mclmatlon decreases to a negative value at high liquid flow rates The negative value of B’ can be explained by an exammatlon of the flow structure m the holdup remme I m question as illustrated m Fig 8 For this holdup regime the gas 1s flowing in the form of bubbles Due to the existence of a velocity profile m the liquid stream, the gas bubble IS forced into a rotational motion m addltlon to the translational motion m the mean flow direction The rotation motion 1s induced by a torque made up by the shear force m the duectlon opposite to that of the mean flow at the pipe wall and the shear force m the flow dlrectlon exerted by the hquld The rotational motion of the bubble would conceivably mcrease with mcreasmg liquid flow rate unti it reached a pomt where the bubble velocity actually IS smaller than the mean time-average velocity flr3 surroundmg the bubble The net result IS that p’ land vi- wdl always have the same sign, I e (13) and this will cause B to be negative There are obvious trends of the parameters C* and B agamst angle of mchnatlon which can be drawn from Figs 5-7 but It IS felt that It would be unwise to try and attempt a general correlation against the angle of m&nation until more data are available particularly for the angles close to the horizontal The correlation of holdup with angle of mclmatlon suggested by Beggs[19] could not be substantmted The apparatus used by Beggs m wluch upward and downward pipes were interconnected

L

SPEDDING

undoubtedly led to an interaction which affected the data obtamed Ln fauness to Beggs, it should be noted that some weak correlation between holdup ratio against flow ratio at constant hquld flow rate could be discerned in this work particularly when the correlation was attempted Anomalies m the wlthm the same holdup regime correlation are notlceable only near the horizontal and vertical posltlons while at other angles of mchna0on, the holdup IS observed to alter very little with angle and increase wrth flow ratio at constant liquid flow rate It 1s important to note the extent of the non-linear holdup regime III region Previous workers have so arranged the data that this Important region IS Ignored by and large and have used a relation slmrlar to eqn (1) Such a course of actlon 1s mlsleadmg and to be more correct a relation of type presented m eqn (3) should be used It should be noted that eqn (3) ts not necessarily linear but It depends on the area of the conduit occupied by the all gas region The correlations given m Figs 5-7 cannot be used to predict holdup unless the hmlts of their apphcatlon are estabhshed At first R* and PsJv,, were used as plottmg variables m an endeavour to map the holdup regimes but the results were not satisfactory The best separation of the holdup reames was obtained using a plot v&‘(gD) against QL/Qc as shown m Fig 9 Usmg this map rt IS possible to establish the holdup regime type which wrll be encountered for any p~cular set of flow parameters under the condltlons operating m this work If the holdup falls m either of the regimes I or II, the data from Figs 4-7 can be used to calculate the holdup using eqn (1) The mean deviation of any calculated value was found to be -0 15% If the map in Fig 9 indicates that the holdup falls mto regnne III the data from Fig 3 for the horizontal condltlon, or more extensive data[l9] for other angles of mchnation, can be applied to give the holdup values An exammatlon of Figs 4 and 6 indicated that for vertical upward and downward flow the values obtained for the dlstnbutlon coefficients C* and Co varied wlthm the limits predicted by the theoretical development m the first part of this work ([20] see Table 3) Furthermore, the wide vmation m the values of C* and Co that were predicted for horizontal and inclined flows were obtained expenmentally The m&d functions B’ and B detailed m Figs 5 and 7 varied m a comphcated manner as predicted by theory

Holdup regrmo I

Fig 8 Shearmg effect on a small gas bubble at lugh liquid rate

Fig 9

Holdup regune map for honzontal to upward flow of au water m a 4 55 cm I d plastic pipe

Holdup m two-phase, CONCLUSION

Data are provided on the holdup of air and water m a 4 55 cm I d pipe mchned at angles of 90 00,70 OO,45 00, 2075, 275, 0, -6 17, -7000, -44 75, -67 75, -9000 degrees from the horizontal It was possible to develop a general map which predlcted, for any particular set of flow rates, any one of three types or regunes of holdup which ~111occur The holdup_ regunes were Identied, two of which enabled the holdup to be predzted by use of a simple

equation

of the type

F=C*vT+B 0

(1)

and tabulated values of C* and B The third regme be fitted to the theoretical equation I?*=

could

[c++~]$+(c+-I)

but requued the use determine the holdup

of

extensive

data

(10)

m order

to

1021

gas-hquld flow-11

E31Dukler A. E . WI& HI Move and Cleveland A Z Chem E&g 1 1964 10(l) 38, 4.4

R

G .

[43 Govler G W and Omer M M , Cnn J Chem Engng 1%2 40

[S] E&hart R W and Martmelh R C C E P 1949 45 39 [6] Hughmark G A, Chem Engng SCI ‘1%5 20 1007 [7] Eaton B A , Andrews D E , Knowles C R , Sdberberg I H and Brown K E , J Pet Tech 1%7 19(6) 815 [8] Greskovlch E J and Shner A L , A I Chem Engng J 1971 17(5) 1214 [91 Stepanek J B and Kasturl G, Chem Engng Scr 1972 27 1881 [lOI Govler G W , Radford B A and Dunn 3 S C , Can 3 Chem Engng 1957 35(8) 58 [Ill Govler G W and Short W L , Can J Chem Engng 1958 36(8) 195 Cl21 Brown R A S , Sulhvan G A and Govler G W , Can J Chem Engng 1960 38 62 1131 Hughmark G A and Pressburg B S , A Z Chem Engng J 1%1 7(4) 677 Ueda T , Bull Jupan Sot EC/I Engng 1%7 10 (42), 989 1000 Speddmg P L and Nguyen V T . to bc Dubhshed [ii Gmltre&u D T, Z Angew J&h Me.& 1943 23(3) I39 [I71 Solov’ev A V , Preobrazhensku E I and Semenov P A, Znt Chem Engng 1%7 7(l) 59 WI Bergs H D , Ph D Dissertation, Umverslty of Tulsa 1972 [I91 Speddmg P L and Nguyen V T , Lkpt Engng 122 LJluv Auckland 1976

REFERENCES

[l] Nguyen V T , Ph D Thesis, Umverslty of Auckland 1975 [2] Zuhcr N and Fmdlay J A, Tmns A S M E 1965 87 (C) 453

WI Nguyen V T and Speddmg P L , Chem Engng Scl 1977 32 1003