Int. J. Multiphase Flow, Vol. 1, pp. 537-553. Pergamon Press, 1974. Printed in Great Britain.

A F L O W P A T T E R N MAP F O R G A S - - L I Q U I D F L O W IN H O R I Z O N T A L
PIPES

J.M. MANDHANE, G.A. GREGORY and K. AZIZ

Department of Chemical Engineering, The University of Calgary, Calgary, Alberta (Canada)
(Received November 29, 1973)

Summary

Various flow pattern maps for two-phase gas--liquid flow in horizontal pipes are tested
against the 5935 flow pattern observations presently contained in the UC Multiphase Pipe
Flow Data Bank.
A new flow regime correlation representing an extension of the work done by Gorier
and Aziz [3] is presented and is shown to be in better agreement with the data than the
other correlations tested. A computer program for this correlation is included.
It is also shown that there is no significant improvement obtained by including the
effects of the physical properties of the fluids using any of the physical property parameters
which have been proposed so far.

Introduction

N u m e r o u s studies [1, 2, 3] have s h o w n t h a t n o single t h e o r y o r c o r r e l a t i o n

can satisfactorily p r e d i c t t h e pressure gradient or liquid h o l d - u p over all
possible f l o w regimes e n c o u n t e r e d in t w o - p h a s e gas--liquid flow in pipes.
A l t h o u g h empirical c o r r e l a t i o n m e t h o d s are still w i d e l y used, t h e r e is a
growing t r e n d t o w a r d t h e use and d e v e l o p m e n t o f m e c h a n i s t i c m o d e l s [3, 16,
17]. In e i t h e r case it is i m p o r t a n t f r o m t h e designer's p o i n t o f view to be able
to p r e d i c t a c c u r a t e l y w h a t f l o w p a t t e r n will o c c u r f o r given i n p u t f l o w rates,
pipe size, and fluid properties. O n l y t h e n can t h e p r o p e r f l o w m o d e l be
selected. M a n y m e t h o d s have b e e n p r e s e n t e d in t h e l i t e r a t u r e for this p u r p o s e ,
usually in t h e f o r m o f t w o - d i m e n s i o n a l m a p s in which t h e locations o f t h e
b o u n d a r i e s b e t w e e n flow p a t t e r n regions are based o n empirical observations.
M a n y o f these m a p s result f r o m d a t a covering a r a t h e r limited range o f fluid
p r o p e r t i e s and pipe diameters. C o n s e q u e n t l y , large discrepancies are o f t e n
observed b e t w e e n a p r e d i c t e d f l o w regime and t h a t a c t u a l l y o b s e r v e d in a
s u b s e q u e n t test.
In this s t u d y , s o m e c o m m o n l y used m a p s are t e s t e d critically against d a t a
r e p r e s e n t i n g a v e r y wide range o f c o n d i t i o n s , in m o s t cases involving t e n t o
t w e n t y times t h e n u m b e r o f observations w h i c h w e r e originally used to
f o r m u l a t e t h e map'. T h e s e t e s t d a t a are c o m b i n e d in a c o m p r e h e n s i v e d a t a

537
bank which will be discussed later in this paper. The terms used here to
designate the various flow patterns (e.g. stratified, slug, etc.) are consistent
with the definitions used by Govier and Aziz [3]. As a consequence of the
evaluation, a modified map is proposed which is simple to use and which is
in overall better agreement with almost six thousand data points than any of
the existing maps.

Previous work

Various flow pattern maps which have appeared in the literature are briefly
discussed below in chronological order.
Bergelin and Gazley [4] suggested one of the first flow pattern maps. Their
diagram, based on the air--water system in a 1-in. pipe, uses the liquid and
gas mass flow rates, M L and MG, as the coordinates. Johnson and Abou-Sabe
[5] proposed a flow pattern map which is very similar to that of Bergelin and
Gazley and is based on air--water data in 0.87-in. pipe.
Alves [6] suggested a map based on data for air--water and air--oil mixtures
in a 1-in. pipe utilizing the superficial liquid and gas velocities, VSL and VSG,
as the coordinates. He was able to represent both of the systems on a single
map.
Baker [7 ] proposed a flow pattern map based on the data of Jenkins [8],
Gazley [9], Alves [6], and Kosterin [10]. Most of these data are for the air--
water system. Baker plotted G/X versus LX$/G, which, for the air--water
system, is equivalent to gas mass velocity, G, versus ratio of liquid to gas
velocity, L/G. Here, X and ~ are fluid property correction factors and are
defined as:

x = L\O.~ \ ~ J (1)

and

a PL
In eqns.(1) and (2), PG and PL have the units (lb./fC), PL has units of
(centipoise) and o is expressed in (dyne/cm).
White and Huntington [11 ] proposed a flow pattern map based on their
data obtained in 1-, 11/~-, and 2-in. pipes with gas--oil, air--oil and air--water
systems. They used liquid and gas mass velocities, L and G, as the coordinates.
Hoogendoorn [12] used the mixture velocity, VM, and the input gas
volume fraction, CG, as coordinates as first proposed by Kosterin [10] in a
flow pattern map which is based on several air--oil and a i r - w a t e r systems.
Hoogendoorn observed modest effects due to pipe diameter and liquid prop-
erties at liquid viscosity less than 50 cP. The coordinate system t h e y used

538
results, however, in the crowding of important wave and annular-mist patterns
into a very small area on the map.
Govier and Omer [13] presented a map based on their data for a i r - w a t e r
system in a 1.026-in. pipe. The liquid and gas mass velocities, L and G, were
used as the coordinates.
Scott [14] modified Baker's [7] diagram b y making use of the more
recent data of H o o g e n d o o r n [12], and Gorier and Omer [13]. The modified
diagram does not have clearcut transition boundaries but instead shows
relatively wide bands depicting regions of transition from one flow pattern
to another.
Eaton e t al. [15] obtained extensive data on natural gas--water, natural
gas--crude oil, and natural gas--distillate systems in 2- and 4-inch pipes. They
correlated the flow pattern observations on a map using as coordinates, a two-
phase Reynolds number,
MMEL 2
Retp - (3)
Dla M
and a two-phase Weber number,

F PLVSL p G $2 (1 - E L ) w 1
Wetp = D [ ¢rELw + o J (4)

where
laM = laLEL + la G ( 1 - E L ) (5)
and
YsL Ysr
S - (6)
1 - EL EL

Note that the in situ liquid volume fraction, EL, must be known in order to
use the Eaton et al. map. Moreover,their definitions of flow patterns are
somewhat different from those commonly found in the literature which
results in apparent subdivisions of the usually defined regions. The data bank
which is discussed shortly contains the Eaton et al. data, but the flow pattern
observations have been interpreted accordingto the commonly accepted
definitions.
AI-Sheikh et al. [1] have taken an entirely different approach to develop
a method to predict flow pattern. Their correlation is based on the AGA--
API Two-Phase Flow Data Bank referred to by Dukler et al. [2]. They use a
total of 4475 data points and produce a complex correlation which requires
a set of twelve figures on ten different coordinate systems. They did not
attempt to define lines of separation between different flow patterns but
have tried to enclose all of the data belongingto a particular pattern into a

539
closed region. It must be recognized that this effectively assumes all of the
flow pattern observations are completely reliable. A sequential procedure is
required to predict the flow pattern. Because the boundaries of their regions
are highly irregular, this m e t h o d is not readily suited for a computer oriented
study.
Govier and Aziz [3] have presented a revised version of the Govier and
Omer [13] flow pattern map. The revision is based on, in addition to the
Govier and Omer data, the data of Baker [7] and Hoogendoorn [ 1 2 ] , and
others. The coordinate system for this revised diagram is also different from
that originally used by Govier and Omer in that the superficial liquid and gas
velocities, VSL and VSG, are used, as originally suggested by Alves [6].
Govier and Aziz also suggest that with suitable modification to the coordi-
nates, the revised Govier and Omer map can be used with other than the air--
water system. Specifically, these authors recommend that fluid property
parameters, defined as
( lj3
X = Y (7)

1/4

(8)

be used to multiply the actual superficial fluid velocities as follows,

VSG = X VSG (9)

VSL = V VSL (10)

In eqns. (7) and (8), PL and PG are expressed in (lb./ft3), and o has units (dyne/
cm). VSL and VSG are then used in the normal way with the revised Gorier
and Omer map. This is referred to as the revised Govier and Omer map with
physical property parameters. The quantities VSL and VSG thus represent
"effective" superficial velocities for all systems except air--water; for the a i r -
water system, they are the actual superficial velocities.

Two-phase flow data bank

The AGA--API Two-Phase Flow Data Bank as referred to by Dukler et al.

[2] was the first available major compilation of data for two-phase flows in
horizontal, vertical and inclined pipes. In 1970, a copy of this data bank was
acquired b y the present authors in the form of a magnetic tape. It then con-
mined the equivalent of a b o u t 22,000 computer cards representing some
10,000 data points. These data had all been extracted from the literature
available prior to 1962, and had been subjected to consistency tests and
other culling procedures.

540
 In formulating the present study, it was anticipated t h a t this data bank
would be used extensively and it was evident t h a t repeated reading of the
magnetic tape would be a major cost factor in any computer study. Conse-
quently, the various formats specified for the data were carefully examined
to determine whether or not it was possible to compress the tape w i t h o u t
sacrificing any significant information.
It turned out that a reduction of almost 50% in the cost of reading the
complete magnetic tape could be achieved w i t h o u t the loss of any significant
information. Furthermore, the elimination of one card per data point has
significantly reduced the work involved in adding new data to the tape.
The authors have updated the bank with research results published since
1962. Thus, over 4000 additional data points, mostly for horizontal flow,
have been added, bringing the present total to over 14,000 points in all. It is
intended that new data should continue to be included in the UC Multiphase
Pipe Flow Data Bank as they are published or otherwise made available.

Scope of this study

For use in this study, all of the data for horizontal flow in which an
observed flow pattern was recorded were separated from the main tape. This
a m o u n t e d to a total of 5,935 individual observations which can be used for
testing purposes. The wide range of values for physical properties and flow
parameters encompassed by these data is indicated in Table 1.

TABLE 1

Range of parameter values for data used in this study

Inside pipe diameter (D) 0.5--6.5 in.
Liquid phase density (PL) 44.0--63.0 lb./ft ~
Gas phase density (PG) 0.05--3.15 lb./ft 3
Liquid phase viscosity (PL) 0.30-90.0 centipoise
Gas phase viscosity (PG) 0.010--0.022 centipoise
Surface tension (o) 24.0--103.0 dynes/cm
Superficial liquid velocity (Vs b ) 0.003--24.0 ft./s
Superficial gas velocity ( VSG ) 0.14--560 ft./s

A subset of the above data that is of interest, especially for comparing

flow pattern maps, contains only those data relating to the air--water system.
These air--water data were selected on the basis of the physical property
constraints indicated in Table 2. The ranges are specified in order to account
for pressure and temperature difference in the various studies represented.
On this basis, a total of 1178 points were found for the air--water system.
In constructing his flow pattern map, Baker [7] used data from a number
of studies, including those of Bergelin and Gazley [4] and Alves [6]. Since
the Baker correlation is very widely used in the petroleum industry, it is of

541
TABLE 2

Range of parameter values used as criteria for air--water system

Liquid phase density (PL) 60.0--65.0 lb./ft 3
Gas phase density (PG) 0.065--0.090 lb./ft 3
Liquid phase viscosity (PL) 0.75--1.1 centipoise
Gas phase viscosity (PG) 0.017--0.02 centipoise
Surface tension (a) 69.0--73.0 dyne/cm

particular interest to test this method against all of the 5,935 observations.
The flow pattern maps presented by Hoogendoorn [12] and Govier and
Aziz [3] have both resulted from extensive data, representing a reasonably
wide range of parameter values. Consequently, both were selected to be
thoroughly investigated in this study.
Since the map of Eaton e t al. [15] requires knowledge of the in situ hold-
up, and furthermore, since the definitions these authors use for flow patterns
are not consistent with those found elsewhere throughout the literature, their
correlation was not included in the present comparison.
Scott's [ 14] modification of Baker's correlation is not treated separately,
since it is very similar to the original Baker diagram except for his use of
transition regions between flow patterns.
The diagram presented by White and Huntington [11] is limited to low
liquid velocities and is not promising as an overall prediction device. It is
therefore not included in this study.
As discussed above, the observations of Bergelin and Gazley [4] and Alves
[6] have essentially been included in the consideration of Baker's flow pattern
map. For this reason, the individual diagrams presented by those authors are
not considered here.
The map of Johnson and Abou-Sabe [5] is based on data covering a very
limited range; it was not included in this study.
Finally, due to its unwieldy nature, the correlation procedure of A1-Sheikh
e t al. [1] is also excluded.

Evaluation of existing flow pattern maps

The various diagrams under study were written into the computer program
in terms of the original coordinate systems used by the authors. Two parame-
ters, defined below, were calculated to facilitate comparisons.
/ N u m b e r of points correctly predicted \
to lie in flow regime i
ai = I,.v_________~/Numbe~-nf~nint--~whi~w~r-~observ~--~d
~__v X 100 (11)
m flow regime i

542
Thus, a i represents the percentage success of a given flow pattern map with
respect to a particular flow regime.
Total number of observations
correctly predicted to lie in

/3 . .
their respective flow regimes
. . . .
Total number of observations
} × 100 (12)

/3 is thus the overall percentage success of a given flow pattern map.

Results of the comparison based on the air--water data are shown in Table 3.
It should be noted that in Table 3 the bubble and elongated bubble (some-
times referred to as plug) flow regimes are grouped together as simply bubble
flow. Also no distinction is drawn between annular and annular-mist flow.
The region designated in this study as dispersed bubble is sometimes also
referred to in the literature as froth flow.

TABLE 3

Comparison of flow pattern maps using air--water data

Flow Number Values of

pattern of
observations Baker Hoogendoorn Revised
Govier--Omer

Bubble 12 58.4 91.6 58.4

Stratified 229 72.1 89.1 52.8
Wave 162 9.9 64.2 43.2
Slug 453 49.0 57.8 73.7
Annular-mist 320 97.5 94.1 95.0
Dispersed bubble 2 0.0 0.0 0.0

Total 1178

/3 61.3 74.9 71.0

The results of the comparison of flow pattern maps for all 5,935 observa-
tions are shown in Table 4.
It is interesting to note that while the fluid property corrections defined
by eqns. (7) and (8) were expected to improve the reliability of the revised
Govier and Omer map, in fact the reverse is true for most of the flow regimes.
It is also interesting to note the total failure of all of these maps to predict
the dispersed bubble flow regime. In fact, there is some evidence that the data
(at least the observation regarding flow pattern) are partly at fault. When all
5,935 points are plotted on VSL , VSG coordinates, a substantial number of
the observations designated as."dispersed b u b b l e " are seen to lie in the region
of high gas rate and low liquid rates where one would normally expect annular-

543
TABLE 4

Comparison of flow pattern maps using all available data

Flow Number of Values of

pattern observations
Baker Hoogendoorn Revised Revised Govier--
Govier--Omer Omer with
physical property
parameters

Bubble 758 20.4 64.6 32.4 23.3

Stratified 397 54.7 80.9 51.6 46.3
Wave 783 16.0 41.5 17.5 16.5
Slug 2020 24.0 58.7 63.4 58.6
Annular-
mist 1746 84.7 90.5 91.0 93.2
Dispersed
bubble 231 2.2 0.0 0.0 0.0

Total 5935

41.5 65.7 58.3 55.6

mist flow to predominate. In any case, this flow pat t ern designation represents
less th an 4% o f t he total data and its i m por t ance will not be overstated here.
All o f the maps do very well with respect to the annular-mist flow regime,
whereas w i t h o u t e x c e p t i o n t h e y t end to predict wave flow very poorly. For
all maps, there is evidence t h a t t he b o u n d a r y between dispersed bubble and
slug flow is located at a liquid flow rate t hat is t o o low. F r o m the calculated
values o f ~, it is appar e nt that the map presented by H o o g e n d o o r n [12] is
substantially mor e reliable than that of Baker [7], which has been used
extensively, b o t h in literature and in industrial design calculations.

Proposed flow pattern map

Following th e examination of the flow p a t t e r n maps from the literature,

it appeared that certain improvements could be made.
In th e interests of simplicity, it was decided t o generate a basic flow pattern
map based on air--water data, and t hen a t t e m p t t o apply physical p r o p e r t y
corrections. While this is certainly n o t a new approach, previous workers have
n ot had access to t he a m o u n t of data that were available for this study.
In all the previous a t t e m p t s to apply physical p r o p e r t y corrections t o a
base diagram, the axes o f the diagram were modified. This approach shifts
t h e flow regime boundaries for non-air--water data in only one direction.
A n o t h e r approach, which has n o t been used so far, is t o shift specific transi-
tion boundaries according to some scheme. This is equivalent to assuming

544
that the effect of changes in a particular physical property may be different
for different ranges of the flow rates of the t w o phases.
Another major decision involves the selection of the coordinate axes. There
does not seem to be any reason to use c o m p l e x and difficult-to-calculate
parameters when it is apparent from the Govier and Aziz studies that the
superficial phase velocities represent reasonable discrimination criteria. The
choice was thus made to base the diagram on a log--log plot using VSL and
VSG as the coordinate axes.
The proposed flow pattern map is shown in Fig. 1. The transition bound-
aries indicated were located primarily on the basis of a log VSL v s . log VSG
plot of the 1 1 7 8 flow pattern observations for the air--water system. However,
where a reasonably distinct transition line was not obvious, reference was
made to a second similar plot containing all 5,935 flow pattern observations
from the data bank. Unfortunately, neither of these t w o data plots can be
reduced in size with sufficient clarity to be included here. Coordinates for
the transition boundaries shown in Fig. 1 are given in Table 5.
It is of interest to examine the relationship between the boundaries of the
map proposed in this study and those of the other maps which have been
discussed. In Fig. 2, the Baker, Hoogendoorn and revised Govier--Omer maps
have been superimposed on the map shown in Fig. 1. In order to translate
the Baker and Hoogendoorn maps to the log VsL--log VSG axes, the physical
20.0

I0.0

B U B B L E, :~;:~:::
0 ELONGATED SLUG
LU
BUBBLE FLOW FLOW
I.-
1.1_

:>~l.c
>:
t--
0 ANNULAR,
0
,.,J
Ld ANNULAR MIST
Q FLOW

_1
-J 0.1 STRATIFIED FLOW

u.
hi

if)

0.01 ......
0.1 1.0 I0.0 I00.0 500.0
SUPERFICtAL GAS VELOClTY,VsG,FT/SEC

Fig. 1. Proposed flow pattern map.

545
TABLE 5

Coordinates for transition boundaries of proposed flow pattern map*

Transition VSG VSL Physical property

boundary (ft./s) (ft./s) correction -- multiply
equation of transition
boundary by

Stratified to 0.1 0.5

elongated bubble 5.0 0.5 1.0/Y

Wave to slug 7.5 0.3 Y

40.0 0.3

Elongated bubble and 0.1 14.0

Y
slug to dispersed bubble 230.0 14.0

Stratified and 35.0 0.01

elongated bubble to 14.0 0.1
wave and slug 10.5 0.2
X
2.5 1.15
2.5 4.8
3.25 14.0

Wave and slug to 70.0 0.01

annular-mist 60.0 0.1
38.0 0.3
40.0 0.56 X
50.0 1.0
100.0 2.5
230.0 14.0

Dispersed bubble 230.0 14.0 X

to annular-mist 269.0 30.0

*To be plotted on log--log scale.

properties of the air--water system and a 1-in_diameter pipe were assumed.

It is p e r h a p s n o t surprising t o see t h a t t h e p r o p o s e d m a p is essentially an
" a v e r a g e " o f t h e o t h e r three.
O n e m i g h t a r g u e o n p h y s i c a l g r o u n d s t h a t t h e r e s h o u l d n o t be an a p p a r e n t
d i s c o n t i n u i t y in t h e superficial liquid v e l o c i t y as i n d i c a t e d b e t w e e n t h e
e l o n g a t e d b u b b l e to s t r a t i f i e d f l o w t r a n s i t i o n line a n d t h e slug to w a v e f l o w
t r a n s i t i o n line. While this m i g h t be t r u e f o r a single specific s y s t e m , it m u s t
be r e m e m b e r e d t h a t (a) t h e t r a n s i t i o n b o u n d a r i e s s h o u l d m o r e c o r r e c t l y be
v i e w e d as t r a n s i t i o n regions, a n d (b) t h e d i a g r a m p r e s e n t e d r e p r e s e n t s an
average c o m p r o m i s e over a w i d e v a r i e t y o f c o m b i n a t i o n s o f p h y s i c a l p r o p e r t i e s
and pipe diameters.
T h e r e did n o t a p p e a r t o b e a n y d i r e c t p r o c e d u r e f o r devising t h e p h y s i c a l
p r o p e r t y p a r a m e t e r s . As a first step, t h e a i r - - w a t e r d a t a w e r e s o r t e d a c c o r d i n g

546
 20.0

DB DB DB ~ ~ ~'
I0.0 I ~ - -
EB
. _
" ~ _ _
s_
~ ~ /
/
\ //
t,iJ
P_.
h

I "~

>-" 1,0
p-
\ k• /
' /!
0 EB

w
> ST
(3
0
_1
_1

E. 0.1
o:
LIJ
n
(/) -~ - HOOGENDOORN (1959) \
- GOVIER 8, OMER (Revised)(1972)
-~wx,~ NEW MAP (1973) ~t

0.01
0.1 1.0 IO.O I00.0 500.0
SUPERFICIAL GAS VELOCITY, VSG , F T / S E C

Fig. 2. Comparison of proposed flow pattern map with others used in this study.
EB Bubble, elongated bubble flow; ST Stratified flow; W Wave flow; S Slug flow;
AM Annular, annular-mist flow; DB Dispersed bubble flow.

to pipe diameter t o investigate any possible effect of this variable. Although

the resulting groups of data were t o o small to permit firm conclusions t o be
drawn, there was no observable diameter effect for pipe diameters greater
t h an one inch. Any effect which actually does exist is masked by being
included in th e calculation o f the superficial velocities.
As a starting poi nt t he physical p r o p e r t y factors defined by eqns. (7) and
(8) were used. All of t h e possible directional effects were evaluated for t he
various flow p at t er n boundaries. Various pert urbat i ons on the e x p o n e n t s used
in th e p ar amete r definitions were then tried and finally, a viscosity effect was
added. Th e final f o r m of the physical p r o p e r t y parameters is expressed as
follows:

- (13)
X' = 0.0808 62.4 o

547
 7 2 . 4 ) 0.25

w h e r e PG and PL are expressed in lb./ft 3, PL and PG are expressed in

centipoise, and o has units o f d y n e / c m . T h e s e factors are applied t o the
flow p a t t e r n b o u n d a r i e s r a t h e r t h a n to t h e axes o f the map. T h e transition
b o u n d a r y can be d e f i n e d using the c o o r d i n a t e s specified in Table 5, in t h e
form,
VSL = ~(VsG ) (15)
T o c o r r e c t for physical p r o p e r t i e s , t h e right h a n d side o f eqn. (15) is multi-
plied b y the a p p r o p r i a t e f a c t o r as specified in t h e last c o l u m n o f T a b l e 5.
T h e p r o p o s e d map, and t h e physical p r o p e r t y c o r r e c t i o n p r o c e d u r e were
t h e n c o m p a r e d with the observations f r o m t h e d a t a bank, with the results
s h o w n in Table 6.
It is s o m e w h a t surprising to n o t e the relatively small e f f e c t of t h e physical
p r o p e r t y p a r a m e t e r s . In m o s t c i r c u m s t a n c e s one is o b v i o u s l y justified in
ignoring t h e m altogether. C o m p a r i n g Table 6 with Tables 3 and 4, it can be
n o t e d t h a t t h e p r o p o s e d m a p is in substantially b e t t e r a g r e e m e n t w i t h the
a i r - - w a t e r d a t a t h a n a n y o f the o t h e r s tested, and it is in slightly b e t t e r agree-
m e n t with the overall data. While o t h e r f o r m s o f physical p r o p e r t y factors
c o u l d c e r t a i n l y have b e e n chosen, it is d o u b t f u l if a n y criteria can b e deter-
m i n e d which will s h o w a significantly greater success level, y e t still retain t h e
TABLE 6

Comparison of proposed flow pattern map with available data

Air--water data All data

Flow Number Values of 0~ Number Values of 0~ Values of

pattern of for proposed of for proposed for proposed
observations base diagram observations base diagram base diagram
with physical
property
parameters

Bubble 12 83.3 758 50.5 64.5

Stratified 229 78.6 397 72.5 73.0
Wave 162 71.6 783 50.2 55.2
Slug 453 79.7 2020 71.4 73.9
Annular-
mist 320 92.8 1746 84.8 76.9
Dispersed
bubble 2 0.0 231 0.0 0.0

Total 1178 5~35

/3 81.8 67.2 68.2

548
desirable simplicity of a single two-dimensional map. It must also be remem-
bered t h a t assigning a flow regime label to a given flow condi t i on is not an
exact p r o c e d u r e and is based on a visual interpretation. It is thus a subjective
j u d g e m e n t on the part o f the investigator, which is particularly true when t he
flow is in a transition be t w een t w o or m o r e flow regimes.
As a final check for possible diameter ef fect on flow pattern, t he 5,935
observations were divided into t hr e e diameter ranges and values of ~ and
were d e t e r m i n e d as before. The results are shown in Table 7. Clearly, the

TABLE7

Effect of pipe diameter on agreement of data with proposed flow pattern map

Flow pattern D < 2.000" 2.000" < D < 4.000" D t> 4.000"

Number of a Number of a Number of

observations observations observations

Bubble 422 69.7 166 46.4 170 69.4

Stratified 162 74.1 163 73.0 72 70.8
Wave 585 63.2 102 52.0 96 10.4
Slug 1431 70.9 265 79.6 324 82.4
Annular-mist 1512 80.1 224 59.4 10 0.0
Dispersed bubble 94 0.0 75 0.0 62 0.0

Total 4206 (70.9%) 995 (16.8%) 734 (12.3%)

71.6 59.6 60.8

proposed map tends to be m o r e successful with data from small diameter

pipes (less th an 2 inches). This is n o t t o o surprising considering t hat approxi-
mately 70% of t he flow pat t er n observations in the data bank are in this
category. However, t he overall success level o f a b o u t 60% for the larger
diameters still compares favorably with the overall success levels o f the ot her
maps for all the data (see Table 4). The proposed map has a significant
advantage over t he o t h e r maps when only the "larger t han 4 i n c h " data are
considered. In this case, the p-value of 60.8 for t he proposed map compares
with 15.0 for Baker, 55.6 for H o o g e n d o o r n , and 45.5 for the revised Govier--
O mer map. F u r t h e r m o r e , in the larger diameter ranges, t he proposed map is
very successful (about 80%) in t h e i m p o r t a n t slug flow kegime. It is clear,
however, t h a t m or e flow pat t er n observations f r o m large diameter systems are
required for a t h o r o u g h investigation of diameter effects.
A F o r t r a n c o m p u t e r program, based on the proposed map (including the
physical p r o p e r t y factors), is given in the Appendix. This program can be
used to predict flow patterns resulting f r o m given input flow rates, fluid
properties and pipe diameter for gas--liquid flow in horizontal pipes.

549
Conclusions

The c o m m o n l y used flow pattern maps have been compared using

extensive data which cover a wide range of physical properties and flow
parameters. The diagram presented by Hoogendoorn [12] is shown to be the
most reliable of those selected from the literature to be tested.
A new flow pattern map, representing an extension of the work of Govier
and Aziz [3], is presented which is in substantially better agreement with
air--water data than any other, and is slightly better than the Hoogendoorn
diagram for all available data. Because of its simplicity, it is well suited to
either c o m p u t e r or hand calculations.
The effect of pipe diameter appears to be adequately taken into account
by using the superficial velocities, VSL and VSG, as the coordinate axes.
At the present time, no method exists for including the effect of the
physical properties of the fluids which yields a significant improvement in
flow pattern prediction. It is concluded that errors in the positions of the
transition boundaries on a VSL vs. VSG diagram almost eliminated whatever
physical property effects which may exist.
The designation of existing observations in the two-phase flow data bank
as "dispersed b u b b l e " should be considered suspect at the present time. As
more data become available for this flow regime, a decision can be made
regarding the validity of that allocation.

Acknowledgements

One of us (JMM) is grateful for the financial support received in the form
of a Province of Alberta Graduate Fellowship. Financial support for this
study has also been received from the National Research Council of Canada
and The Petroleum Aid to Education Fund. The technical assistance of Mrs.
M. Fogarasi has been much appreciated. Finally we wish to thank Dr. G.W.
Govier for his helpful suggestions and comments on the results of this study.

Nomenclature

cG volume fraction of gas in the input mixture

D pipe diameter (L)
EL in situ liquid volume fraction
G mass velocity of the gas phase (M/L 2T)
L mass velocity of the liquid phase (M/L 2T)
MG mass flow rate of the gas phase (M/T)
ML mass flow of the liquid phase (M/T)
MM (ML + MG ), the total mass flow rate (M/T)
S slip velocity (L/T)
VSG superficial gas velocity (L/T)
VSL superficial liquid velocity (L/T)

550
VM (VsL + VSG ), the mixture velocity, (L/T)
percent success in predicting a particular flow pattern, defined
by eqn. (11)
percent success in overall predictions for a particular map,
defined by eqn. (12)
k Baker's fluid property correction factor, defined by eqn. (1)
PG viscosity of the gas phase at operating conditions (M/LT)
PL viscosity of the liquid phase at operating conditions (M/LT)
PM mixture viscosity (M/LT)
PG density of the gas phase at operating conditions (M/L 3)
PL density of the liquid phase at operating conditions (M/L 3)
O interfacial tension (F/L)
Baker's fluid property correction factor, defined by eqn. (2)

References

1 J.N. AI-Sheikh, D.E. Saunders and R.S. Brodkey, Can. J. Chem. Eng., 48 (1970) 21.
2 A.E. Dukler, M. Wicks and R.G. Cleveland, AIChE J., 10 (1964) 44.
3 G.W. Govier and K. Aziz, The Flow of Complex Mixtures in Pipes, Van Nostrand-
Reinhold, N e w York, 1972, p.503.
40.P. Bergelinand C. Gazley, Proc. Heat Transfer and Fluid Mechanics Inst.,May 1949,
p.5.
5 H.A. Johnson and A.H. Abou-Sabe, Trans. A.S.M.E., 74 (1952) 977.
6 G.E. Alves, Chem. Eng. Progr., 50 (1954) 449.
7 0 . Baker, Oil and Gas J., 53 (1954) 185.
8 R. Jenkins, M.S. Thesis, Univ. of Delaware, 1947.
9 C. Gazley, Ph.D. Thesis, Univ. of Delaware, 1949.
10 S.I.Kosterin, Izv. Akad. Nauk. S.S.S.R., Otd. Tekh. Nauk., No. 12, 1949, pp.1824.
11 P.D. White and R.L. Huntington, The Petrol.Eng., 27 (9) (1955) D40.
12 C.J. Hoogendoorn, Chem. Eng. Sci.,9 (1959) 205.
13 G.W. Gorier and M.M. Omer, Can. J. Chem. Eng., 40 (1962) 93.
14 D.S. Scott, in Advances in Chemical Engineering, Vol. 4, Academic Press,N e w York,
1963, p. 200.
15 B.A. Eaton, D.E. Andrews, C.R. Knowles, I.H. Silberbergand K.E. Brown, J. Petrol.
Technol., 19 (1967) 815.
16 M.G. Hubbard and A.E. Dukler, paper presented at 65th Nat. Mtg. of A.I.Ch.E., Tampa,
Fla.,May 1968.
17 S.S. Agrawal, G.A. Gregory and G.W. Gorier, Can. J. Chem. Eng., 51 (1973) 280.

551
APPENDIX

COMPUTER PROGRAM LISTING F O R P R O P O S E D FLOW PATTERN CORRELATION

PROGRAM REGION(INPUT,OUTPUT)

THIS PROGRAM CALCULATES THE FLOW PATTERN REGION FOR ANY TWO
COMPONENTS FLOWING COCURRENTLY IN A PIPE, ACCORDING TO FLOW
PATTERN HAP OF MANDHANE, GREGORY, AND AZIZ.

INPUT DATA
VSL=SUPERFICIAL LIQUID VELOCITY, FT/SEC
VSG=SUPERFICIAL GAS VELOCITY, FT/SEC
OE~ISL=~ENSITY OF LIQUID, LQM/CU.FT,
DENSG=DENSITY OF GAq, LBM/CU.FT.
AMUL=VISCOSITY OF LIQUID, CENTIPOISE
AMUG=VISCOSITY OF GAS, CENT:POISE
SIG~A=INTERFACIAL TENSION, OYNES/CM.

100 FORMAT(7FIO.5)
lOl FORMAT(IOX,SPREDICTED FLOW PATTERN: ELONGATED BUBBLES)
103 FORMAT(IOX,SPREDICTED FLOW PATTERN: STRATIFIED#)
I05 FORMAT(IOX,#PREDICTED FLOW PATTERN: WAVE#)
I0l FOPMAT(IOX,~PPEDICTED FLOW PATTERN: SLUGS)
I09 FOR~AT(]OX,#RREDICTED FLOW PATTERN: ANNULAR MISTS)
lit FOQ~AT(IOX,~PPEDICTED FLOW PATTERN: DISPERSED RURHLES)
112 FORMAT( IOX,~SUPERFICIALLIQUID VELOCITY,FT/SEC = #~FIO,sIIOX~
I#SIJPERFICIAt GA~ VELOCITY,FT/SFC = #,FIO.5/IOX,~DENSITY oF LIOU
~ID,LBM/CU,FT. = ~FIO.S/]OX,#OENSITY OF GAS,LBM/CU.FT.
3 = #,FIO.S/IOX,#VlSCOSITY or LIOUID,CENTIPOISE = #,FIO.S/
410X,SVISCOSITY OF GAS,CENT:POISE = #,FIO.5/]OX,#INTERFACIAL
5 TENSION,DYNES/CM. - ~,FIO.S/IOXt#X! CORRECTION
6 = ~ , F I O . S / I O X , # Y I CORRECTION = s,
7FlO.5//)
113 FORMAT(IHI,qx,#CALCULATIONS ACCORDING TO FLOW PATTERN MAP OFS/
IIqX~#MANDHANE, GREGORY~ AND AZIZS)
PRINT 1 1 3
READ IO0~VSL,VSG,DENSL,OENSG,AMUL,AMUG,SIGMA
XI=((DENSG/O.OGO8)**O.333)*((DENSL*?2.4/(62,4*SIGMA))**O.25)*
I((AMUG/O.OI~)**O.2)
YI=((DENSL*72.4/(62.4*SIGMA))**O.25)*((AMUL/I.O)**O.2)
PRINT II2,VSL,VSG,OENSL,DENSG,AMUL,AMUG,SIGMA,XI,YI
IF(VSL.LT.14.0*YI)GO TO I I ~
I F ( V S G . L E . ( 2 3 0 . O * ( ( V S L / I 4 . 0 ) * * O . 2 0 6 } * X I ) ) G OTO 150
GO TO 1 ~ 8
114 IF(VSL.LE,O,I )GO TO 1 2 2
IF(VSL,LE.O.2 )GO TO 120
IF(V~L.LE.I,15)GO TO 1 1 8
I F ( V S L . L E . 4 . 8 )GO TO 116
YI34~:P,S*(VSL/4.R)**0.248
GO TO 1 2 6
116 Y1345=2,5
GO TO 1 2 6
118 Y I 3 4 5 z l O , S * ( V S L / O . 2 ) e * ( - 0 . 8 1 6 )
GO TO 1 2 6
120 Y I 3 ~ S = I ~ . O * ( V S L / O . I ) * * ( - O , 4 1 5 )
GO TO 1 2 6
122 YI345=I4,0*(VSL/O°I)**(.O.368)

552
126 IF(VSL.LEeO.I )GO TO 136
IF(VSL.LE.O.3 )GO TO 13~
IF(VSL.LE.,O.56)GO TO 132
IF(VSLoLE.I,O )GO TO 130
IF(VSL.LE,2°5 )GO TO 128
Y456=IOO°O~(VSL/2°5)~O.463
GO TO 138
128 Y 4 5 6 = 5 0 . O * ( V S L / I o O ) ~ 0 , 7 5 6
GO TO 138
130 Y 4 5 6 = 4 0 . O ~ ( V S L / O o 5 6 ) * ~ O , 3 8 5
GO TO 138
132 Y 4 5 6 = 3 8 , O ° ( V S L / O , 3 ) ~ * O * 0 8 1 3
GO TO 138
134 Y 4 S G = 6 0 ° O * ( V S L / O . I ) ~ ( - O , 4 1 5 )
GO TO 138
136 Y 4 S G = T O o O ~ ( V S L / O ° O I ) g * ( - O . 0 6 7 5 )
X38 Y4S=O.3~YI
Y3I=O,5/Y1
YI345=YI345~Xl
Y4S,6:Y456*Xl
IF(VSG.LE.YI34S°AND.VSL.GEoY31)~ TO 140
IF(VSGoLE°YI34S.AND.VSL.LE°Y31)~ TO 142
IF(VSG.GE.YI34S.AND,VSG,LE.Y456,ANDoVSL*GT*Y45)GO TO 146
IF(VSG.GE.YI345.AND,VSG,LE.Y456,AND.VSL.LE.Y45)GO TO 144
GO TO I~8
140 PRINT 101
GO TO lS2
142 PRINT |03
GO TO 152
144 PRINT 105
GO TO 152
146 PRINT 107
GO TO 152
148 PRINT 109
GO TO 1.52
150 PRINT 111
152 STOP
END

TYPICAL OUTPUT LISTING

CALCULATIONS ACCORDING TO FLOW PATTERN MAP OF

MANDHANE, GREGORY, AND AZIZ
SUPERFICIAL LIQUID VELOCITY,FT/SEC = 1,00000
SUPERFICIAL GAS VELOCITY,FT/SEC = I0.00000
DENSITY OF LIQUID.LBM/CU.FT. = 55.00000
DENSITY OF GAS,L~M/CU.FT. o0~000
VISCOSITY OF LIQUID,CENTIPOISE = SoO0000
VISCOSITY OF GAS,CFNTIPOISE = .01000
INTERFACIAL IENSION,DYNES/CMo = 65,00000
Xl CORRECTION = .70027
YI CORRECTION I.37339

PREDICTED FLOW PATTERN: SLUG

553