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Razao de densidades ("G/"L)

1

0.5

0.2

0.05

0.01

SR = 1

Sr !

uG

uL

0 0.2 0.4 0.6 0.8 1xG

0

0.2

0.4

0.6

0.8

1

!

Razao de densidades ("G/"L)

1

0.5

0.2

0.05

0.01

SR = 1 SR = 1,5

1$A+J#"#$ #" CJ+DE%


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1$A+J#"#$ #" CJ+DE%d +"(5/+$+" +$ '/5&A%$ O +"I(/+$ #"7$5 '$55$5

1)(Y+$5 "' A' 4)7A'",-.

dm = !mAdz= dm

L+ dm

G = 1!!

G( )!L +"G!G"# $%Adz

!m= 1!!

G( )!L +"G!G

1$A+J#"#$ #" CJ+DE%


38/59

1$A+J#"#$ #" CJ+DE%8" 8%n Ce

!G =

1

1+1! x

G

xG

!G

!L

1

!m

=

xG

!G

+

1! xG

!L

,(&F)e


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Y$F*BJ#"#$+ %$F"Gg"


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Y$F*BJ#"#$+ %$F"Gg"

Y$F*BJ#"#$ #$ $+B*%%$a"C$AD*

r $ +/B"%"(E$ "(&%" 4"7)1/+$+"5 !"#$!%&

g)&" XA" ) 1)(1"/&) +" "51)%%"-$'"(&) 5: B$Z 5"(Y+) () 2'>/&) +$54"7)1/+$+"5 'O+/$5 () "5#$E) \C!^@

g$ /(&"%B$1" "(&%" +A$5 B$5"5P )A =A(&) $ A'$ #$%"+" 5:7/+$P $ 1)(Y(A/+$+"

+" 4"7)1/+$+"5 7)1$/5 /(5&$(&2("$5 O -$%$(Y+$ +"4/+) u$EF) 4/51)5$ \1)(+/EF) +" (F)U+"57/Z$'"(&)^@

ur ! u

G "u

L

Y$F*BJ#"#$+ %$F"Gg"


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Y$F*BJ#"#$+ %$F"Gg"

'"mR* #$ $+B*%%$a"C$AD*

Sr !

uG

uL

Y$F*BJ#"#$+ %$F"Gg"


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Y$F*BJ#"#$+ %$F"Gg"

Y$F*BJ#"#$ #$ #$%Jg" b#%Jq g$F*BJDhd

ukj = u

k! j

N)'$ 1)') %"B"%c(1/$ $ 4"7)1/+$+" +) 1"(&%) +" 4)7A'" +$ '/5&A%$

Y$F*BJ#"#$+ %$F"Gg"


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Y$F*BJ#"#$+ %$F"Gg"

:FEW* #$ #$%Jg" b#%Jq UEWd

r $ 4"7)1/+$+" +" +"%/4$ 5A#"%I1/$7P )A 5"=$P ) QAR) 4)7A'O&%/1)5A#"%I1/$7 +" A' 1)'#)("(&" 1)' %"7$EF) $ A'$ 5A#"%v1/" XA"

5" ')4" 1)' ) 1"(&%) +" 4)7A'" +$ '/5&A%$@

jGL

= !G u

G! j( )

jLG

= !L u

L! j( ) = 1!!G( ) uL! j( )

jLG

= !jGL

\L%)#%/"+$+" +) QAR) +" +"%/4$^

Y$F*BJ#"#$+ %$F"Gg"


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Y$F*BJ#"#$+ %$F"Gg"

Y$F*BJ#"#$ #$ #JHE+R* #" H"+$ o

ukm

= uk!

G

!m

= uk! u

m

N)'$ 1)') %"B"%c(1/$ $ 4"7)1/+$+" +) 1"(&%) +" '$55$ +$ '/5&A%$


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P"#%]$+ #$

7+B*"C$AD*X`EJ#*

1$\AJQR


46/59

Q

L$+%J"5 +" "51)$'"(&) 5F) +"I(/+)5 #)% )"F"AQ*+ #$ H*%Q"+ 7)1$/5() /(&"%/)% " "(&%" $5 H"+$+

L$%$ A'$ +$+$ $1"7"%$EF) +$ -%$4/+$+"P &$/5 B)%E$5 +"#"(+"' +$a$*C$D%J" \+/2'"&%)P %A-)5/+$+"P /(17/($EF)^P

T%*T%J$#"#$+ #* $+B*"C$AD*\LP NP Z/P 4$ZJ"5^ " #*+ UEJ#*+ \wP xP y^

3'$ D%"A+JQR*"(&%" #$+%J"5 )1)%%" XA$(+) ) %"-/'" 4/-"(&" 5" &)%($ JA+DIg$

3'$ A*g" D*T*F*aJ" #"+ JAD$%H"B$+ O "5&$>"7"1/+$P )(+" +/B"%"(&"5 '"1$(/5')#$55$' $ +/&$% ) $`EJFX)%J* #$ H*%Q"+

/E)*+ g$%GB"


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d7&$5 B%$EJ"5 +" -H5e #$+%J"5 +"

"51)$'"(&) "' I7'"e 8SE%A $5AEF"%

0 $+B*"C$AD* "AEF"% O ) '$/5 1)'A' "'$#7/1$EJ"5 /(+A5&%/$/5 \$7&) 1)"I1/"(&" +"

&%$(5B"%c(1/$ +" 1$7)%^

8A#"%v1/" +) I7'" 7WXA/+) O 1$%$1&"%/Z$+$#"7$ #%"5"(E$ +" *A#"+P $5 XA$/5 5F) B)(&"5

#$ a*D"+ #$ FX`EJ#* +"4/+) u $EF)1/5$7.$(&" +) -H5

Escoamento ascendente

(Collier and Thome, 1994)

Equilbrio hidrodinmico:taxas idnticas de entranhamento e deposio

/E)*+ g$%GB"


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Slug Churn Annular

z51/7$EJ"5 +$ B$5" 7WXA/+$ 5F)1$%$1&"%W5Y1$5 +)5 #$+%J"5 6FEa" 8SE%A

(Watson e Hewitt, 1999)

/E)*+ g$%GB"


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Slug flow Churn flow

9"T"+ #$ '$aJC


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T a

Hewitt-Roberts map

:%*AD$J%"+"(&%" %"-/'"5 +" "51)$'"(&) 5F)/+"(YI1$+$5 1)' %"7$EF) " UEW*+ HI+JB*+ \($

'$/)%/$ +)5 '$#$5^

d5 B%)(&"/%$5 5F) +"&"%'/($+$5 #)% '"/) +"JA+T$QR* gJ+E"F )A &O1(/1$5 #$ #$D$BQR*

\5"(5)%"5P %$/)U{ "&1@^

d5 B%)(&"/%$5 5F) "T%*WJC"#"+@ !"4/+) $)(|'"%) +" B$&)%"5 /(QA"(1/$(+) 1$+$&%$(5/EF)P O #%$Y1$'"(&" JCT*++Xg$F

1)%%"7$1/)($% &)+$5 "7$5 "' A' -%HI1) G!@

/E)*+ g$%GB"


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8A>="Y4/+$+" ($ +"&"%'/($EF) "17$55/I1$EF) +)5 #$+%J"5 +"

"51)$'"(&)

(Govier e Aziz, 1972)

0.1 1.0 10 100

Superficial Gas Velocity, jG, ft/sec.

SuperficialWaterVelocity,

jL

,ft/sec.

10

1.0

0.1

FLOW DIRECTION

ANNULARMIST

(WaterDispersed)

O P Q R

H I J K L

A B C D E F GBU

BBLE

(AirD

ispers

ed)

SLUG

(AirD

ispers

ed) FR

OTH

(Both

Phas

es

Disp

ersed)

M N

/E)*+ S*%Jm*AD"


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Horizontal Flow

(Collier and Thome, 1994)

d $7&)5 f&A7)5P #%"4$7"1"'e7+D%"G\B"#*P 6=r"gh " 5AEF"%

5 a%"gJ#"#$ O A' #$%2'"&%) /'#)%&$(&"e5/'"&%/$ 1)' %"7$EF) u 7/(.$ +" 1"(&%)

5%%"+D$ +" -)&$5 #)+" &$'>O' 5"% /'#)%&$(&""' #$+%J"5 AR*="AEF"%$+

(Badie et al., 2001, IJMF 27, 1259-69)

A-WULSfixed

UGS

A-OU

GSfixed

ULS

/E)*+ S*%Jm*AD"


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(a) Bubbly

(b) Dispersed Bubbly

(c) Plug/Elongated Bubble

(d) Annular/Dispersed


54/59

`)("5 \CllG^e

8"

+"4"%H .$4"% "5&%$YI1$EF)@

L

um

>

D

vd

/E)*+ S*%Jm*AD"


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WavyAnnular

Slug

Plug

Stratified Bubbly

Froth

Dispersed

0.1

0.2

0.51.0

2.0

5.0

10

20

50

10 20 50 100 1,000 5,000 20,000

G(1 x)(kg/m 2.s)

Gx/

(kg/m2.s

)

Baker map

/E)*+ S*%Jm*AD"


56/59

S T

NO

P

Q R

L M

FG I

J

BA

H

C D

K

E

DISPERSED BUBBLE

FLOWDIRECTION E

LONG

ATED

BUBB

LE

ANNULARMIST

SLUG

WAVEST

RATI

FIED

(Sm

ooth

Inte

rface

)

20

10

2.0

1.0

0.2

0.1

.02001010.11.0

Superficial Gas Velocity, jG , ft/sec

SuperficialWaterVelocity,

jL

,ft/sec

STRA

TIFI

E

D

(Rip

ply

Inte

rface

)

(Govier e Aziz, 1972)

(J)FJ*a%"\


57/59

B.J. Azzopardi. Gas-Liquid Flow. Begell House Inc., NY, 2006.

C. E. Brennen. Fundamentals of Multiphase Flow. Cambridge University Press, 2005.

J.G. Collier and J.R. Thome. Convective Boiling and Condensation. Oxford University Press, Oxford, UK, thirdedition, 1994.

C.T. Crowe. Multiphase Flow Handbook, CRC - Taylor and Francis, 2006.

S. M. Ghiaasiaan. Two-Phase Flow, Boiling and Condensation in Conventional and Miniature Systems. CambridgeUniversity Press, 2007.

F.W. Govier, K. Aziz. The Flow of Complex Mixtures in Pipes. R. E. Krieger Ed., Malabar, FL, 1972.

G.F. Hewitt. Measurement of two-phase flow parameters. Academic Press, London, UK, 1978.

E. S. Rosa. Escoamento Multifsico Isotrmico, Bookman, 2012

O. Shoham. Mechanistic Modeling of Gas-Liquid Two-Phase Flow in Pipes. Society of Petroleum Engineers, 2006.

G.B. Wallis. One Dimensional Two-Phase Flow. McGraw-Hill, New York, 1969.

P0>0 >")


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7C$%aJAa /$BSA*F*aJ$+ JA 8**FJAa "A# /S$%C*TSh

:F*%J"AkT*FJ+K (%"mJF bNL*sOt6 uv*Ns


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jader barbosa jem2012

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