PRESSURE DROP AND PHASE FRACTION
IN OIL-WATER-AIR VERTICAL PIPE FLOW
by
ARTHUR R. SHEAN
S.B., United States Military Academy
(1969)
SUBMITTED IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE
DEGREE OF
MASTER OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
.lf.lay
1976)
...'-;"r.7-. .. -.-Signature
of
Author
ep4rtment
/ • --
of Mechanical Engineering, May 7, 1976
Certified by
Thesis Supervisor
7/r
Accepted by . . . . . . . . .
Chairman, Department Committee on Graduate Students
ARCHIVES
JUL
9
1976
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2
PRESSURE DROP AND PHASE FRACTION
IN OIL-WATER-AIR VERTICAL PIPE FLOW
by
ARTHUR R. SHEAN
Submitted to the Department of Mechanical Engineering
on May 7, 1976 in partial fulfillment of the requirements for the Degree of Master of Science.
ABSTRACT
The upward flow of oil-water-air and oil-water mixtures in a
.75 inch I.D. tube is investigated. Flow pattern, volume fraction, and
pressure loss data is presented for mixture velocities from 4 to 20 ft/
sec and oil in liquid volume fraction from 0 to 1.0.
The drift flux method of Zuber and Findley is successfully extended from two phase flow to three phase flow in order to predict the
air void while a new correlation method is presented to estimate the In
Situ oil phase volume fraction. In addition, the oil-water flow regimemap of Govier is extended to three phase flow in order to predict the
transition between liquid flow regimes.
Finally several friction pressure loss prediction methods from two
phase flow are modified to three phase flow and compared to actual data.
As a result, a scheme of several methods is recommended for use in preparing three phase flow pressure loss estimates.
Thesis Supervisor:
Title:
Peter Griffith
Professor of Mechanical Engineering
3
ACKNOWLEDGEMENTS
I would like to express my appreciation to my wife for her
patience, understanding and endurance, without which this work may never
have been completed.
Further I thank my parents who originally implanted
the seed of my academic curiosity which Professor Peter Griffith guided
during this work.
Finally, I thank the technicians of the Engineering
Projects Laboratory for their assistance in my experimental effort.
4
TABLE OF CONTENTS
Page
TITLE PAGE
1
ABSTRACT
2
ACKNOWLEDGEMENTS
3
TABLE OF CONTENTS
4
LIST OF TABLES
6
LIST OF FIGURES
7
LIST OF SYMBOLS
10
CHAPTER I:
12
INTRODUCTION
CHAPTER II:
TEST APPARATUS
CHAPTER III:
CHAPTER IV:
EXPERIMENTAL PROCEDURE
CHAPTER V:
SUMMARY OF DATA
CHAPTER VI:
RESULTS AND DISCUSSION
CHAPTER VII:
CONCLUSIONS
SUGGESTIONS FOR FURTHER WORK
REFERENCES
16
20
23
24
77
79
80
APPENDICES
A.
FOREMAN AND WOODS DATA
82
B.
GOVIER'S DATA AND ANALYSIS OF PROPERTY
84
EFFECTS ON TWO PHASE FRICTION PRESSURE LOSS
C.
FLOW REGIME VISUAL OBSERVATIONS
D.
DERIVATION OF QUASI - ANNULAR FLOW
PRESSURE DROP METHOD
96
101
5
Page
E.
FLUID CHARACTERISTICS
105
F.
SAMPLE CALCULATIONS
106
G.
DATA LISTING
110
6
LIST OF TABLES
Page
PREDICTED Fo VERSUS ACTUAL Fo:
TWO PHASE FLOW
45
PREDICTED Fo VERSUS ACTUAL Fo:
THREE PHASE FLOW
66
PRESSURE LOSS METHOD COMPARISON:
THREE PHASE FLOW
68
NUJOL AND WATER CONTACT ANGLES
75
FOREMAN AND WOODS VOID DATA
82
FOREMAN AND WOODS DATA REDUCTION
83
GOVIER TWO PHASE DATA
85
85
7
LIST OF FIGURES
Page
DIAGRAM OF THE APPARATUS
17
INSETS TO DIAGRAM OF THE APPARATUS
18
CONTACT ANGLE TANK
22
THREE PHASE VOID FRACTION ZUBER-FINDLEY PLOTS
26
THREE PHASE VOID FRACTION VELOCITY AND CONCENTRATION
31
DISTRIBUTION PLOTS
THREE PHASE VOID FRACTION OIL - WATER VELOCITY DIFFERENCE
33
PICTURE OF AIR SLUG
34
TEMPERATURE EFFECT ON THE OIL-WATER VELOCITY DIFFERENCE
35
Fo .5
TEMPERATURE EFFECT ON THE OIL - WATER VELOCITY DIFFERENCE
36
Fo .8
INSITU OIL PHASE VOLUME FRACTION VERSUS Fo:
OIL-WATER VELOCITY DIFFERENCE:
TOTAL PRESSURE LOSS:
TWO PHASE FLOW
TWO PHASE FLOW
TWO PHASE FLOW
FRICTION PRESSURE LOSS:
39
41
TWO PHASE FLOW
42
GOVIER'S FLOW REGIME MAP
43
GOVIER'S 20.1 cp OIL TOTAL PRESSURE DROP:
ZUBER-FINDLEY PLOTS VARYING Fo:
38
TWO PHASE FLOW
THREE PHASE FLOW
CONSOLIDATED ZUBER-FINDLEY PLOTS:
THREE PHASE FLOW
44
48
49
AIR VOID, PREDICTED VERSUS ACTUAL:
FOREMAN AND WOODS
52
AIR VOID, PREDICTED VERSUS ACTUAL:
THREE PHASE VOID DATA
53
8
IN SITU OIL PHASE VOLUME FRACTION/IN SITU FLUID PHASE
VOLUME FRACTION VERSUS Fo
INSITU OIL PHASE VOLUME FRACTION, PREDICTED VERSUS ACTUAL:
Page
54
56-
THREE PHASE VOID DATA
INSITU OIL PHASE VOLUME FRACTION, PREDICTED VERSUS ACTUAL:
57
FOREMAN AND WOODS
OIL-WATER VELOCITY DIFFERENCE VERSUS MIXTURE VELOCITY
59
OIL-WATER VELOCITY DIFFERENCE VERSUS Fo
60
FRICTION PRESSURE LOSS VERSUS Fo:
61
TOTAL PRESSURE LOSS VERSUS Fo:
THREE PHASE FLOW
THREE PHASE FLOW
IDEALIZED SLUG FLOW
64
GRAVITY PRESSURE LOSS, PREDICTED AND ACTUAL:
12 FT/SEC
FRICTION PRESSURE LOSS, PREDICTED AND ACTUAL:
12 FT/SEC
CONTACT ANGLE DEFINITION
TOTAL PRESSURE LOSS, PREDICTED AND ACTUAL:
62
71
72
74
12 FT/SEC
FRICTION PRESSURE LOSS, DIAMETER VARIED, 2 FT/SEC:
75
89
TWO PHASE FLOW
FRICTION PRESSURE LOSS, DIAMETER VARIED, 3 FT/SEC:
90
TWO PHASE FLOW
FRICTION PRESSURE LOSS, VISCOSITY VARIED, 2 FT/SEC:
91
TWO PHASE FLOW
FRICTION PRESSURE LOSS, VISCOSITY VARIED, 3 FT/SEC:
92
TWO PHASE FLOW
FRICTION PRESSURE LOSS, MIXTURE VELOCITY VARIED, 150 cp:
TWO PHASE FLOW
93
9
FRICTION PRESSURE LOSS, MIXTURE VELOCITY VARIED, 20.1 cp:
Page
94
TWO PHASE FLOW
FRICTION PRESSURE LOSS, MIXTURE VELOCITY VARIED, .936 cp:
95
TWO PHASE FLOW
TYPICAL FRICTION PRESSURE LOSS CURVE
97
FLOW REGIME DIAGRAM
98
FLOW REGIME DIAGRAM
98
FLOW REGIME DIAGRAM
100
FLOW REGIME DIAGRAM
100
SLUG - ANNULAR FLOW DIAGRAM
101
LINEAR INTERPOLATION OF THE FACTOR K
104
10
NOMENCLATURE
SYMBOL
Definition
A
Cross sectional area of tube
D
Diameter of tube
F
Introduced fluid in liquid volometric fraction
i.e. F
= QO/Qf = B/O
f
f
Friction factor
G
Mass flux
go
Gravitational constant
j
Average volumetric flux density,
L
Length of tube
p
Pressure
Ap
Pressure difference
Q
Volumetric flow rate introduced into the tube
R
Radius of tube
Re
Reynolds number
S
Phase velocity difference
V
Specific Volume
Vw
Superficial velocity (/A.)
v
Velocity
v
Weighted mean velocity, i.e. v
W
Mass flow rate
x
Mass gas quality
a
.e. = Q/A
= Q-/a A.
a
a
11
Definition
Symbol
ca
Insitu volumetric phase fraction
Volumetric flow concentration introduced
into the tube, i.e.
p
Density
iP
Viscosity
0
Contact angle
¢2
Friction multiplier
Subscripts
a
Air
b
Bubble
c
Critical
f
Fluid
F
Friction
g
Gas
m
Mixture
o
Oil
t
Total
w
Water
p
Density
o = Qo/Qt
12
CHAPTER
I
INTRODUCTION
Three phase flows are being encountered in the petroleum industry
more and more often.
The emphasis on greater production has forced the
exploitation of marginal oil wells, and forced the use of secondary recovery schemes.
Two methods currently in use to achieve these goals
are, oil field flooding and gas lift wells.
Oil field flooding intro-
duces water into the oil field in an effort to maintain natural liquid
levels.
The result is an oil-water mixture is taken out of the pipe.
If, in addition, natural gas is present, which is not uncommon, a three
phase flow appears in the well tubing.
Gas lift wells on the other
hand inject gas into the well to help lift the natural oil-water mixture to the surface.
encountered.
Again a three phase flow of oil, water and gas is
Despite the frequency of appearance of the three phase
flow, designers lack a complete knowledge of the flow, hence cannot
properly design pipe sizes, production levels, pumping efforts, or optimal flow conditions.
dict phase fractions,
The major inadequacies are the inability to prethe density pressure losses, effective viscosi-
ties and friction pressure loss.
Therefore, there is a need for an in-
vestigation of three phase flow.
The lack of knowledge on three phase flows stems mainly from the
extremely limited number of published works on the subject.
M. Rasin
Tek1 in 1961, Galyomov and Karpushin 2 in 1971 and Bacharov, Andriasov
13
and Sakharov 3 in 1972 have published papers on the subject three phase
performed some work at M.I.T. and furnished
Foreman and Woods
flows.
an unpublished paper in 1975.
Conversely two phase flow, from which this work draws heavily has
been intensely investigated.
6
Govier, Sullivan and Wood
Orkiszewski
work.
9
,
The works of Govier, Radford and Dunn
, Zuber-Findley
and Singh and Griffith
10
7
, Griffith and Wallis
8
,
in particular were used in this
In addition, the correlations of Martinelli11
and McAdams
were employed during comparison calculations.
M. Rasin Tek
in his work considered the two fluids as a single
liquid with multiphase mixture properties.
With this assumption he
provided a correlation of oil well data which supplied satisfactory
pressure loss predictions.
His assumption, however, overlooked the
various flow configurations encountered by the various phases.
Hence,
no insight into the true nature of the flows was gained from his work.
The Russian researchers
'3 examined the effects on the effective vis-
cosity in horizontal pipes caused by the variation of liquid fraction,
gas content, and turbulence of the flow.
Their work did not provide a
correlation, but did find that the three phase flows did vary significantly from two phase flows.
Even more important they recorded the
variation in effective viscosity of the fluid as a function of liquid
fraction (this method is similar to the work of Govier on oil-water
flows).
Their works are significant in that they recognized all three
14
phases effect the nature of the flow.
Foreman and Woods
continued
the separated phase investigation by applying the work of Zuber and
Findley to the gas phase of the flow.
Their limited data indicated
that the gas phase could be handled separately from the liquids.
They,
however, did not approach the question of pressure drop.
The approach of this current work is to attack the three phase
flow first as a gas liquid two phase flow as suggested by Tek, then to
examine the two fluids using a variation of the liquid fraction as suggested by the Russian investigators and Govier.
In the two phase approxi-
mation the Zuber-Findley Drift Flux model will be applied as did Foreman
and Woods.
To execute this approach, experimentation was conducted in a vertical .75" ID plexiglass tube using a mineral oil, water and air mixture
system.
The mineral oil was chosen because its density was less than
that of water and its viscosity was much greater than water (see Appendix E) .
These differences allowed for easier differentiation of the
individual fluid effects on the flow.
The separation was further en-
hanced by the fact the oil, because of its large viscosity, remained in
laminar flow throughout the experiment.
ducted in three parts:
The experimentation was con-
First three phase void fraction data was ob-
tained to verify the Foreman-Woods conclusion that the gas could be
treated by the drift Flux method; then two phase oil water data was obtained and combined with Goviers
data (Appendix B) to determine the
15
variation effects of various parameters on the flow characteristics,
and finally three phase void and pressure drop data was obtained over a
variety of mixture velocities to provide a correlation for the In Situ
Oil Volume Phase Fraction and to check pressure drop predictions.
16
CHAPTER II
TEST APPARATUS
The three phase flow of mineral oil (Nujol), water and air was developed in a 282" by .75" ID vertical tube (Fig. 1).
were drawn by pumps from a separator tank (Inset
flowrator tubes into the vertical tubes.
gate valves.
The oil and water
C to Fig. 1) through
The rates were adjusted by
The air flow was provided by a shop air system and was
likewise metered by a flowrator and pressure gauge.
The connection to
the tube (Inset A to Fig. 1) started the air in the center of the vertical tube.
All observations and measurements were taken approximately
200 L/D up the tube to allow for full developement of the flow.
The test section consisted of a piece of plexiglass tubing which
was separated from the remaining vertical tube by a pair of quick acting valves.
ously.
These valves were linked together and operated simultane-
The section between the valves was 80.25" long.
tubing had two purposes.
observation.
The plexiglass
First, the clear tubing allowed for visual
In some cases, especially in three phase flows, 35mm
camera photographs were necessary to freeze the action for close observation.
In order to differentiate between the fluids, red dye was
added to the water.
white when worked.
The Nujol although clear at rest, became milky
Both effects accentuated observation.
The second
purpose of the plexiglass was to measure the void and fluid fractions.
When the quick acting valves were closed, the mixture settled out into
17
1 Di.ram
i
of the Apparatus.
C copper pipe
P plexiglass pipe
I
ik.
R rubber tube
C)
-I
O oil
i
A air
WI water
iM meter
ST settling tank
CM
LD
PT pressure
00
tap
R
I
1
Li
t C
Lo
fI/
!
18
i'id. 2 Insets to Diagram of th- Apparatus.
T
:"'0
Inset
I
Inset
A
Inset
C
B
19
its component parts.
then be measured.
The volume averaged void and fluid fractions could
Also located between the quick closing valves were
two pressure tapes 74.25 inches apart.
These were used in measuring
the pressure drop.
After departing the test section, the mixture traveled an additional 65 L/D up to an air separator and then back down to the fluid
separator.
The additional length beyond the test section was to avoid
any end effects.
A thermometer was inserted into the side of the fluid
separator so that the temperature of the recycled fluids could be recorded.
In measuring the pressure drop across the test section, two sets
of equipment were used.
For the two phase Nujol and water data, the
water filled pressure tubes were fed from the pressure taps to a differential pressure gauge which read in inches of water.
A cross-over
system (Inset B to Fig. 1) was needed because the water head was overtaken by friction losses under certain flow conditions causing negative
meter readings.
The pressure gauge system was sufficiently accurate
because the pressure deviations across an oil bubble were relatively
small.
The three phase flow however had large pressure deviations over
the air bubbles.
disappointing.
Attempts to dampen out this effect fluidically were
Therefore, Statham pressure transducers and an R.C.
circuit were utilized to dampen out the transient fluctuations in pressure.
This system provided adequate average pressure data.
20
CHAPTER
III
EXPERIMENTAL
A.
PROCEDURES
Three Phase Void Fraction Data:
During this
test the void fraction was measured for a variety of
oil in liquid volume fractions and varying mixture velocities.
In a
particular series of runs, the oil-in fluid volume fraction was fixed and
readings of the void were taken at 10% increments of the maximum air
flow.
The air variation provided the mixture velocity variation.
particular run the specific procedure was as follows:
In a
The oil and water
flow rates were calculated to produce the appropriate fluid volume
fraction and be within the capacity of the apparatus.
then established within the tube.
These flows were
The air flow was then adjusted to the
appropriate increment of maximum flow.
When the flow rates had stabili-
zed, the air metering pressure, flow rates and separator tank temperature
were read and recorded.
Then the flow was visually observed and photo-
graphs, if appropriate, were taken.
After observation the quick acting
valves were closed and the mixture was allowed to separate.
The void
and fluid fractions were recorded using a ruler which was fastened to
the tube supports.
data recorded.
Each run was repeated at least three times and the
This repetition was essential because the inconsistency
of the churn turbulent flow and the length of the slugs-within the test
section gave different results on any single run.
in other tests which included air flow.
This was found true
21
Normally the air flow was initiated at low volume rates and increased.
With frequency of run, however, the separator tank temperature
would rise due to friction loss and pump work.
affected the viscosity of both fluids.
This temperature change
In order to avoid any data bias
at the higher air flows, the progression was occasionally reversed.
In
later tests, each series of runs was completed prior to any repetition
so that temperatures for a series would be more uniform.
B.
Two Phase Liquid Flows:
During this test the total volume flow rate was held constant while
the oil volume fraction was varied from zero to one.
As before, the
flows were calculated to provide the appropriate fraction and within
the apparatus capacity.
and allowed to stabilize.
The flows were then introduced into the tube
The flows, separator tank temperature, and
pressure drop across the test section were recorded.
observed and the void data read and recorded as above.
The flow was then
Various mixture
velocities were obtained by varying the total volume flow rates.
each run was repeated three times.
was completed prior to any repeats.
Again
Except as noted above, each series
This repetition was unnecessary in
this test because the fluctuations were less without air flow.
C.
Three Phase Pressure Loss and Void Tests:
In this test the fluid volume flow rate was held constant while
the oil in liquid volume fraction was varied from zero to one.
Air was
introduced in varying amounts to obtain various mixture velocities.
22
Each series of runs was characterized by a different mixture velocity.
The same procedure as the two phase oil water test above was utilized except air flow and metering pressure were recorded.
Also the pressure at
the top and bottom of the test section were recorded rather than the
difference.
D.
Contact Angle Measurements:
A glass fish tank was filled with red dye water and Nujol and allowed to settle.
A flat plate of test material was introduced so that its
midpoint was at the fluid interface.
Observing the edge of the plate it
was tilted until the fluid interface adjacent to the plate became parallel
to the remainder of the interface (Fig. 3).
At this point, the angle
between the plate and interface was the contact angle for the fluids
and material.
A photograph was taken to record this angle.
ment was repeated for several materials.
Figure
3
This measure-
23
CHAPTER IV
See Appendix G:
Data Listing
24
CHAPTER V
RESULTS AND DISCUSSION
A.
Three Phase Void Fraction Test
Zuber and Findley predicted that in a two phase flow the gas velocity plotted as a straight line with the following equation:
va = C
v
(5.1)
+Vaj
where vaj is the bubble rise velocity.
For turbulent slug flow in a
vertical tube the suggested valves of Co varied between 1.0 and 1.5 while
the vaj is of the order of .5 ft./sec..
All of the current tests were
within this slug flow range and did indeed plot as straight lines.
Fig-
ures 4a through 4e show the following quantities plotted versus the mixture velocity:
a
w
_
o
= Qa
aA
a
(5.2)
=
Q
a A
(5.3)
QA
(5.4)
aA
The Co for all air velocity curves ranged between 1.19 and 1.32 with .j
between .4 and .6 ft./sec..
The variation in Co showed no dependence on
the oil in liquid volume fraction (Fo) or the velocity of the mixture or
fluid components.
Such close results indicate that the assumptions of
25
Tek and the conclusion of Foreman and Woods, that the air can be separately handled from the liquid, is reasonable.
In addition, the methods
of Zuber-Findley can be extended to three phase flow to perform this
function.
Figure 4a through 4e show another interesting result.
of Vw and v , except for the Fo = .50 plot, cross.
All the plots
Likewise, the data
of Foreman and Woods when similarly plotted show the same occurance.
Zuber and Findley in their work ascribed a higher velocity to the air
which was flowing in the center of the tube.
This was based on assumed
velocity and concentration profiles such as Fig. 5a.
this concentration profile.
Fig. 7 illustrates
The fluid with higher concentration on the
outside moved at a lower average velocity than that of the air at the
center with a higher velocity profile.
Similarly if the oil water con-
centration profile is divided as in Fig. 5b, then the average value of
v
would be greater than v .
If the two fluid concentration profiles are
reversed, then the bulk of the oil would be on the outside of the tube
where the velocity profile is the lowest.
velocity would be lower.
Therefore the average oil
Conversly the bulk of the water would be more
toward the center of the tube and the average water velocity would be
higher.
The result is a reversal of the oil water velocity difference.
Comparison of observation with data verify this correspondence between
the switching of position and velocity difference reversal.
When the
velocity reversal occurs, the fluid color changes from red to white indicating an increase in oil concentration next to the wall.
A further
26
Figure 4a.
Three Phase Void Fraction Zuber- Findley
Plot.
20
15
4,,0
o
m0 10
N
aN,
5
Qt/A ft/sec
0
27
Figure 4b. Three Phase Vid Fraction Zuber-Findley
Plot.
30
Qa w 1.32 Qt
A
COaA
+
'5
25
I
20
r
15
0
' 5a
o
0
x
o
fO
X
/
.
J0
~
/6
X
il
X
0
5
x6
O
8'
A."
.1
5
Qt/A
ft/sec
/
/
28
Figure 4c.
Three Phase Void Fraction
Plot.
Zuber-Findley
3v
25
20
a
105
5
10
Qt/A
15
ft/sec
20
29
Figure
d. Three Phase Void Fraction
Plot.
pi le
20
0
10
5
Qt/A ft/sec
Zuber-Findley
30
Figure 4e. Three Phase Void Fraction Zuber-Findley
Plot.
v
!
9(
o
/
x
5
.A
WI
Qt/ A ft/sec
31
Figure 5.
Three Phase Void Fraction Velocity and
Concentration Distribution Plots.
U
U m
Oca
Oca ave.
A.
I
I
I-O a
Oca ave.
II
I%-
-
w
O a ave.
O o
OCa ave.
B.
FIG. 5.
32
demonstration of this switching can be seen in Figure 6, where the oil
water velocity difference (Sow) is plotted against the mixture velocity.
As the curves cross the zero line, the oil and water switch positions
with relation to the wall.
The location of the switching appears to be
independent of the mixture velocity, however the .5 Fo curve indicates
that the switch occurs only above a certain Fo.
Later the boundry will
be shown to be the Fo for the transition from oil bubbles in water to
water bubbles in oil.
In addition to the oil water velocity change, a temperature effect
was observed.
During the experiment the temperature was not controlled
but recorded.
Figures 8 and 9 show the result of temperature deviations
for Fo's of .5 and .8.
A lower temperature indicated a higher velocity
difference except at higher velocity were the difference reversed.
possible explanation is as follows:
A
At lower velocities the flows are
in the slug regime and the oil travels in bubbles within the water.
If
the bubbles were smaller, the distribution of oil would be better with a
subsequent smaller Sow.
diameter
Rohsenow and Choi
13
give an estimate of bubble
as:
Db = CO
2g a
(5.5)
gAp
where C is a constant and 0 is the contact angle and a function of the
surface tension.
Although p and a decrease with higher temperature, a
falls off more rapidly.
Hence a higher temperature indicates a smaller
bubble diameter with a lower expected velocity difference.
At higher
33
Figure 6.
Three Phase Void Fraction Oil- Water
Velocity Difference.
a0
rn
0
LO
II
I
oe9/
AO
I
I
"I
FIO
35
Figure 8. Temperature Effect on the OIl- Water
Velocity Differences FO
.5
0
(v
o
%
'.4
U
0
#4
0
0
-4
vIN
A
0
q-
,
C0
I
so
De
.
I
9^j
AOS
CI
eE
36
Figure 9. Temperature Effect on the Oil-Water
Velocity Differences Fo=.8.
U
4
it
14
CO
0
0
-4
N
so
0
ur
o
0
ao
#
-4
Cvl
N4 09/;
IUhS
NC
f
-I.-
37
velocities the flow approaches an annular flow in which viscosities play
a greater role.
Viscosity again falls off with increasing temperature.
Thus, lower temperature indicates a higher viscosity which retards the
fluid flows reducing the Sow.
In both cases illustrated, the tempera-
ture effect did not change the shape of the curves, just the relative
locations.
B.
Also, the effect on the air data was minimal.
Two Phase Void Fraction and Pressure Drop Test
In the past, researchers have been successful in applying two phase
information to three phase flow problems.
For example, Zuber and Find-
ley's approach worked well in part A while the Russian researchers employed the plotting technique of Govier .
Therefore, it seems logical
to assume that two phase oil water information may be instrumental in
separating the oil water portion of a three phase flow.
appears to be true.
This in fact
The flow characteristics of the two phase flow turn
out to be very similar to those of three phase flow and because of this,
predictions of In Situ Phase Volume Fraction, critical oil in liquid
volume fraction, and effective viscosity can be made from modified two
phase flow information.
Figures 10 and 11 show the essential void fraction information of
an oil-water mixture.
The In Situ oil phase volume fraction and velocity
difference show a marked crossover where the two liquids exchange places
on the wall.
During this test the switching became much more visible
because the mixture velcoities were much lower than three phase flows.
38
Figure 10.
In Situ Oil Phase Volume Fraction Versus
Fo , Two Phase Flow.
o
I
I
El
0
00
V.
4-1%-
0 fQ
O
O
'.Qofinox00
cO
C%-
%O
%
n
04
C
.w
39
Figure
Oil-Water Velocity Differences
11.
Two Phase
Flow.
0
'S
N%
Nop
0
0
%0
1
·
. ,,--
.
r
.
mtN
I;
I
I
Ii
I
I
II II
I
I1
54
l
u
-
000
00
I 11I i
i
I
* Ox
UIN
S
r-
%O
V%
4-
-4
l
M
os/;j
-4
MOS
i
I
I
cN
I
m
I
4
I
I
%0
I
40
In both bases the switching appeared dependent upon the oil in liquid
volume fraction.
In Figure 10 the curves approach the straight homo-
geneous line (o)
with increasing mixture velocity.
curve appeared to be the limit from which a
The two ft/sec
approached
o
.
Also the
void defect from that of the homogeneousline is in the fluid away from
the wall, i.e. in oil when water is on the wall.
This fact further re-
inforces our assumed velocity and concentration profile of Figure 5.
The examination of the pressure drop curves (figures 12 and 13)
shows further consequences of the oil-water position switching.
In both
cases a very sharp jump in pressure occurs at an Fo corresponding to that
where the fluids exchange places at the wall.
Before and after the
switching, the friction pressure curves are relatively constant at values
close to that of the individual fluids flowing alone in the tube.
The
coupling of the levels and the identity of the fluid next to the wall
suggests that the effective viscosity of the fluid mixture is that of
the fluid flowing next to the wall.
This is not unreasonable since most
friction losses in a viscous fluid flow occur near the wall where the
fluid is slowed down to match the no slip condition.
Again the picture
Another observation from Figure 12
in Fig. 5b seems more plausible.
and 13 is that the total pressure loss curve has the same shape as the
The only difference being the level.
friction pressure curve alone.
This indicates that the friction pressure loss causes the major deviation in the total pressure loss.
In order to clarify the dependence of the friction pressure loss on
41
Figure 12. Total Pressure Loss, Two Phase Flow.
0
1-4
C-
0
0I
caJ
I
I
00q )(
I
I
I
I
I
I
I
4
00
('4
vlsd
X
W4
Iav
42
Figure 13. Friction Pressure Loss: Two Phase Flow.
O
C
0
0
c)
Nt
W
O
UIo
fn
CN
O
N
-4
-4
-Tsd
I'
j
dV
43
Figure 14. Govier's Flow Regime ap.
A-
Extension
5
0
I
4O
k
-4
>
Water Drop
in Oil
.q4
4o
fm
$4
PI
.1
.,
Oil in Liquid Volume Fraction (F0 )
-,_
44
k'igure 15. Goviers
20.1 cp Oil Total Pressure Drops
Two Phase Flow.
-
-4
-
1
/Jo
W ..
4
t-
xv
14A
d
M
-4
A
45
TABLE
1.
Fa Versus Actual F n, Two Phase Flow
Predicted
4&
440 d
*
*
O-
4)
04
a
NI
o
o
0
*
*
a
o4
A A
A
J
Ii
t
V
V
a
n
c t
.
.
C4
4
o
.
F
4 0
Ca
0 00
0
0O
O
* A0
4r
0
O
BS
O
V
0
0Cv
0 0 00
0
0
00
C)
d
4)
4.
_,
>
0
P'4
:4
UV1 V
*'~ *
0o
o
0
0'
O
O
O
as
*
O
0o
o
d
C
O
O
a4'
ad
N.
lB
Is ,~
46
various flow parameters, the above data was plotted with that of Govier
in Appendix B.
cosity.
1.
The parameters were diameter, mixture velocity and vis-
The results were as follows:
The location of the switching was independent of the diameter
while the effect on the level decreased with higher mixture velocities.
2.
The velocity had a marked effect on the level, but relatively
little effect on the switching location.
3.
The viscosity of the oil affected the level only after the shift
but did not affect the switch location.
From the above investigation it has become apparent that the single
most important item in dividing the oil from the water is determining
the location of the shift from water to oil on the wall also that this
location appears to be based on a critical oil in liquid volume fraction.
addressed the problem
Govier in his work with Sullivan and Wood
by creating a regime map (Figure 14) based upon Regime observations and
the fluctuations of the total pressure curves (Figure 15).
Govier
stated that this map was relatively insensitive to a change in the oil
viscosity except that the froth lines (points a, b and c, Figure 15)
In this investigation
merge in the data for high viscosities (150 cp).
a similar absence of separate points is observed.
The map became valu-
able because it successfully located the critical oil in liquid volume
fraction for the current test to within the accuracy of this data (±.05,
see Table 1).
The implications of this are that for two phase flow one
can predict when the a
0
will be above or below
0
and the viscosity of
47
which fluid can be used as the effective fluid viscosity.
The most im-
portant point, however, is that these results will be extended to three
phase flow in the next section.
C.
Three Phase Flow Void Fraction and Pressure Drop Test
The results of this final test draw together all the information
of the previous two tests and provide acceptable prediction methods for
gas void, liquid phase Volume Fraction, critical oil in liquid volume
fraction (Fo), and effective viscosity in a three phase flow.
results will be presented in three parts.
2.
and prediction method.
1.
These
Void fraction results
Pressure drop results and 3.
Pressure drop
prediction methods and comparison.
1.
In part A, the results indicated that the plot-
Void Fraction:
ting method of Zuber and Findley successfully correlated the air void
data.
Likewise in this test the same method was successful.
Figure 16
shows the individual air void curves for each of the oil in liquid volume fractions (Fo) tested.
The distribution of these lines except for
.95 and 1.0 show no systematic arrangement.
the distribution is independent of Fo.
This fact indicates that
Because of this, a single aver-
aged curve may likewise be independent of Fo.
dated curves are shown in Fig. 17.
In fact, the two consoli-
From these curves the following
equations may be derived:
o<Fo<.9
- -
+ .4 ft/sec
a = 1.28 m
v
(5.6)
48
Three
Zuber-Findley Plots Varying F
Phase Flow.
Figure 16.
40
F-
a.
b.
35
30
C.
d.
e.
f.
o 25
g.
h.
420
l2
15
10
0
5
10
'm ft/sec
15
20
49
Figure 17. Consolidated Zuber-Findley Plotss Three
Phase Flow.
I
aO
0
431
H
%rN
c'J
0
Oa
B/
4
0
!
ft.'
50
.9 < F
< 1.0
-o -
v
a = 1.794 m + .384 ft/sec
(5.7)
The fact that two equations are achieved is reassuring because for
Fo >.9 the oil dominates the flow and as was mentioned earlier, the oil
was in laminar flow throughout these experiments.
For laminar flow sev-
eral authors 8,12 suggest that the Zuber-Findley constant may range up
to 1.7 for two phase laminar flows.
Hence when the oil is on the wall of
the tube a value of 1.794 as in Eq. 5.7 is reasonable.
Likewise, 1.28
for turbulent slug flow is akin to the values suggested by Govier and
Aziz and Griffith for similar two phase flows.
The above equations may
be rearranged to obtain the following prediction method for the air void
fraction.
0 < Fo < .9
a
=
Va
(5.8)
1.28 i
m
o<-1.0 a =
.9 < F
+ .4
Va
1.794
(5.9)
m + 3.85
In all three phase cases examined in this experiment, the bubble rise
velocity was small with respect to the mixture velocity and may be neglected without loss of accuracy.
When the bubble rise velocity is neg-
lected, the following equations for air void are obtained:
0 < F
< .9
a
a
(5.10)
1.28 QT
,9 < Fo < 1.0
aa =
Qa
1.794
(5.11)
QT
51
As a result of this simplification the only information necessary for
field calculation of the air void is the oil, water and air volume flow
rates.
It should be noted that equations 5.7, 5.9 and 5.11 are valid
only when the Reynolds number based on the mixture velocity and the oil
viscosity indicate the flow is laminar.
These equations are compared
against the data obtained in Part A and that of Foreman and Woods (Fig.
18 and 19).
In both cases these equations give excellent results.
The
comparison with Foreman and Woods is especially interesting because their
data is based on kerosene which has a significantly lower viscosity than
Nujol.
In an effort to separate the two fluid Volume Fractions, the
method of plotting the Insitu oil phase volume fraction versus the oil
in liquid volume fraction of Part B may be employed.
However, this
method must be modified to isolate the fluids from the gas.
The Insitu
oil phase volume fraction must be divided by the liquid phase Volume
Fraction and the oil in liquid volume fraction (Fo) is defined as B°/Bf.
In-this way Figure 20 may be obtained.
This curve has a striking resemb-
lance to Figure 10 for oil and water alone.
In fact, both ordinates
reduce to those of Figure 10 when the air flow is zero.
The most im-
portant point of both curve is that they both cross the homogeneous
line as the fluids exchange places near the wall.
In Figure 10 the
curves show dependence on the mixture velocity while Figure 20 does not.
The difference is that the mixture velocity in the two phase is obtained
by varying the fluid mass flow rate while in the three phase flows the
fluid mass flow rate was constant.
The air flow was varied instead.
52
Figure 18. Air Void, Predicted Versus Actuals Foreman
and Woods.
l-
I
Irq
4.
a
'V
6
I
I
*o
o
0o
.
D
N
0o
poopqPJd
.)
0
94
53
Figure 19. Air Void, Predicted Versus Actuals Three
Phase Void Data.
cO
'0
%O
U
Cd
c:
6-p
'-4
'O
cm
·
pe!opa.d
m
weO
q-4
54
Figure 20. In Situ Oil Phase Volume Fraction/ In Situ
Fluid Phase Velume Fraction Versus F .
0
0
.
0
Pk
III
0
co
*3
*O
4c0
*
c
C
'0O,4,o,)Oo
O
55
Therefore, the results appear to be dependent on the fluid mass flow
rate and oil in liquid volume fraction (Fo) only.
In this test then,
because the mass flow rate is constant, a single equation for the curve
may be obtained.
a
o
where
This equation is:
=1.037 af(Fo)
1.536
(5.12)
f
f
=
l-a
(5.13)
a
As a consequence of this equation, and that for the air void, we can now
estimate the Insitu water phase Volume fraction as follows:
l-(a +ac)
a=
w
or for
a
0 < F
-o
(5.14)
o
< .9
-
1.536
a
= .9 64 -a f(Fo)
(5.15)
Again the data of Part A and Foreman and Woods are compared with the
new correlation (Figures 21 and 22).
The Part A data show good results
while that of Foreman and Woods show a systematic deviation.
When the
latter data is plotted in Figure 20, it plots closer to the homogeneous
line.
From Figure 10 this indicates that the Foreman-Woods data has a
higher fluid mass flow rate and, in fact, it is 50% higher.
kerosene has a much lower viscosity than that of Nujol.
Also, the
This differ-
ence allows for more turbulent flow with greater mixing of the two fluids.
The mixing flattens the concentration curves of Figure 5b, and reduces
the fluid velocity difference.
Finally, the reduced velocity difference
56
Figure 21. In Situ Oil PhaeeVolumeFraction, Predicted
Versus Actuals Three Phase Void Data.
0
cO C-
. .
o
o~
. ..
PK a· xo'nO
XO
S
WA
O
o
P.4
0
K
4J
.
0
a
N,
,<'
<
O
\9ss
0
.
a
0
0
D,.
u1%
4
cM
pwoppeaJd 0)
Ce
0
57
Figure 22. In Situ Oil Phase VolumeFraction, Predicted
Versus Actual* Foreman and Woods.
.5
.4
+ .3
~4
o.2
.1
-
.
58
implies a slower oil velocity and a larger in situ oil phase volume
fraction.
As a result, the predicted values of Eq. 5.12 are less, and
the values should fall below the diagonal in Fig. 22 as they do.
Some
of the fluid mass flow rates of Part A also differ from those of Part
C.
The step near a
0
actual of .3 is a junction between several runs
with different fluid mass flow rates.
Again, those below the diagonal
generally had higher flow rates than did Part C. It should be noted
that these correlations for void fractions are only estimates and adjustments may be necessary to insure the total of all three Volume Fractions is one.
This is especially true at the higher values of the oil
in liquid volume fraction (Fo).
To complete the void fraction results the oil water velocity difference is shown plotted versus Fo and mixture velocity in Figures 2
24.
and
From these curves we may observe the switch point is again strongly
dependent upon Fo while the mixture velocity weakly influences the location of the crossing.
Later it will be shown that the superficial
water velocity, is the actual cause of this weak dependence.
Figure 24 is very similar to Figure 6 for two phase flow.
Finally,
Therefore,
the characteristic shape of the velocity difference curves appear relatively independent of the gas volume flow rate.
2.
Pressure Drop
Figures 25 and 26 summarize the pressure drop data obtained from
this test.
In Figure 25 the friction pressure loss curves show a marked
dependence on the mixture velocity for their level while the shape of
59
Figure 24. Oil-Water Velocity Difference Versus
Mixture Velocity.
10
5
In 0
-5
60
Figure 23. Oil-Water Velocity Difference Versus Fo .
10
5
0
0
0
.0
En
F0
-5
61
Figure 25. Friction Pressure Loss Versus Fo s Three
Phase Flow.
2.5
2.0
1.5
so
Cv
I0
1.0
.5
0
.25
..5
Fo
.50
.75
Lo
62
Figure 26. Total Pressure Loss Versus FThree
Phase Flow
O
.
-4
0
0
0
.
[
0
o
Pk
0
0
0
0
Cd
Band ! v
O
J1
.-4
63
the curves appears to be independent.
Also, the shape appears to be very
similar to Govier's oil water curves in Appendix B.
Because of this
similarity, and the fact the variance in mixture velocity is a function
of air flow only, the shape can be assumed to be a characteristic of the
fluid flow only.
As with Figure 13, the friction pressure drop is re-
latively uniform up to the critical Fo for transition to water bubble
flow.
As a result, for estimate purposes, the viscosity of the water
may be used as the mixture viscosity up to the critical Fo.
The nega-
tive pressure losses shown in Figure 25 may be attributed to the counterflow experienced as a slug of air passes through the tube.
comments on this effect in his book.
of such a flow over a slug.
Collier
Figure 27 gives an idealized view
As can be seen, the shear over the bubble
can balance the loss over the fluid slug and givea positive time averaged shear stress and a negative friction pressure loss.
The total pressure drop is unaffected by the mixture velocity.
As
the air flow increases, the gravity pressure loss decreases, but the
resulting increase in mixture velocity increases the friction pressure
loss.
Figure 26 indicates that these two effects balance one another
under the test flow conditions.
The shape of this curve resembles that
of Govier's 20.1 cp oil-water curve, Figure 15, especially the critical
points a,b and c.
This indicates that the air flow apparently lowered
the effective viscosity of the oil as experienced by the water.
This
similarity of the total pressure curves suggests that we may use Govier's
map to predict the critical oil in liquid volume fraction.
With some
64
Figure 27.
Idealized Slug Flow
-f
SHEAR
65
modification this appears to be true.
These modifications are:
The
boundary between the oil slugs and froth must be extended as in Figure
14, and the superficial water velocity is redefined as flowing through
the liquid Phase Volume Fraction as follows:
v
W
=
qw
(5.16)
afA
Because all three critical points appear in the three phase total presTable 2 shows a summary of the
sure curve, all three will be predicted.
modified Govier map applied to the current data.
The results are very
good considering the accuracy of the data.
3.
Pressure Loss Prediction Methods, Comparison and Discussion
Based on the foregoing information and data, several known methods
for predicting two phase friction pressure loss may be applied to the
three phase flow.
Homogeneous
These are the Singh-Griffith1 0 method, McAdams -
method and Lochart-Martinelli
correlation.
The first
two are based on assumptions of the flow regime while the latter is
basically imperical.
In addition, an annular flow method suggested by
Griffith is applied at the higher oil-in-liquid volume fractions.
derivation is shown in Appendix D.
A
The method used by Singh-Griffith
to estimate the gravity pressure loss is also used herein.
these methods several modifications are necessary.
In applying
As was discussed
earlier, the viscosity of the mixture is assumed to be that of water up
to an Fo of .9 and that of Nujol from there to 1.0.
In the Singh-
66
Table 2. Predicted
Fo Versus Actual Fo,
Three Phase. Flow
4/sec Pa
aa
4
-25-50
.75
8
.25
.25
bp
C
ba
Pba
.75-80
.80
.85
c
a
.90
.75-.80 .80
.85-.90 .85
.75-.80
.75
.80
12
.25
16
0-.25
.25
.75-.80
.75
.80-.85 .85
20
.25
.25
.75-.80
.75
.85-.90 .85
p predicted
a actual
a,b,and c keyed from figure 15.
.85
67
Griffith method, the in situ water phase volume fraction alone must be
used up to an Fo of .5.
Then the total in situ fluid volume fraction is
used for the remainder.
The reason being that the oil bubbles do not
interfere with the water counter-flow until that point.
Finally, in
order to truly test these methods and not the void prediction technique,
the actual measured in situ Volume fractions were used where necessary.
Table 3 summarizes the results obtained from these methods, while Figures 28 and 29 show a comparison between the actual values of the gravity and friction pressure losses against estimated values.
As can be
seen, the gravity pressure loss estimates are very good, however the
friction pressure loss estimates vary in success.
The inconsistency of the various friction pressure loss prediction
methods
is the result
is varied.
of the variety
of flow regimes
encountered
Appendix C, outlines these regimes in detail.
as Fo
As a result,
the Singh-Griffith method fails in the slug and quasi annular areas and
the Annular method fails in slug and froth flow.
The Lockhart-Martin-
elli method applies only where its data base applies.
Consequently,
no method alone adequately predicts the friction pressure loss.
Instead,
a combination of methods must be employed.
The above data suggests the following assortment of methods be used
to achieve acceptible pressure loss predictions.
For gravity pressure
loss the Singh-Griffith methods are recommended:
a.
O<F0 oil slug-froth boundary and Fo=.9.
O--
The Singh-Griffith
68
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71
Figure 28.
Gravity Pressure Loss, Predicted and Actualt
12 ft/see.
O
f
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72
Figure 29. Friction Pressure Loss, Pr®dicted and Actuals
12 ft/sec
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73
method.
In this region the flow is predominately slug flow which this
method is based upon.
b.
Water froth boundary <Fo<
The McAdams-Homogeneous method.
oil froth-water bubble boundary:
In this region the fluid is in a froth
state and the oil and water are mixed fairly uniformly.
of the air slugs is somewhat broken up.
Also, the form
This method does not follow the
actual values well, however, the average values match.
c.
F >.9:
0
The Quasi Annular Flow method.
In this region the slugs
of air become exceedingly long while the velocity of the oil on the
wall reverses to an upward velocity, characteristic of annular flow.
However, oil slugs are still present.
The resulting values follow the
actual pressure losses rather well.
When the estimates for the gravity and friction pressure losses are
combined, acceptible estimates of the total pressure are obtained.
Table
3 for all test values and Figure 31 for a mixture velocity of 12 ft./sec.
show the comparison of actual to estimated values of total pressure loss.
Although the individual pressures vary, the average deviation for the
12 ft//sec. case is .016 psi.
Finally it should be noted that at low
velocities the negative friction pressure loss discussed earlier causes
the estimated values of total pressure to be consistently high.
D.
Contact Angle Data
The results of the contact angle test are shown in Table 4.
materials except glass were preferentially wetted by the oil.
All
This in-
dicates that the oil would be expected next to the tube.where the contact
74
TABLE 4.
NuJol and WaterContact Angles
Material
Contact Angle
Plexiglass
1.5
Glass
154o
Copper
17.5
Aluminum
130
Cold rolled steel
28.50
Galvanized sheet metal
340
OIL
WATER
SURFACE
Figure 30. Contact Angle Definition.
75
FiEure 31. Total Pressure Loss, Predicted and Actuals
12 ft/sec.
o
4
I
I
I
I
Il
0
IIY-
I
I
I
I
la
u0
+
+2
I
a w
< wt~
I
I
I
I
I
I
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I
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o
v\
0
0
I sd
0
76
angle influence predominates.
This, however, as indicated earlier is in
opposition to the effects of density.
In the case of glass, however,
we can expect the water to remain next to the wall totally.
This is be-
cause the contact angle and density effect are reinforcing.
The metals tested are those normally used in commercial piping.
The
contact angles of these metals are similar to those of plexiglass.
Therefore, the trends and data obtained herein may be transferred, while
those of tests in glass tubes should be employed only after the effect
of contact angle has been proven negligible.
Finally, these contact
angle measurements are static tests and the dynamic contact angles may
vary.
77
CHAPTER VI
CONCLUSIONS
A.
GENERAL
1.
The gas void fraction for a three phase slug flow may be deter-
mined by treating the two liquid phases as a single phase and using the
Zuber Findley Plot.
2.
The individual In Situ Liquid Phase Volume fractions can be
correlated through knowledge of the gas void fraction, oil-in-liquid
volume fraction and the liquid mass flow rates.
3.
See equation 5.12.
The relative velocities of the two liquids and the friction
pressure loss depend on which fluid dominates the flow next to the wall.
4.
The transition from water on the wall to oil on the wall depends
on the relative liquid flows only.
5.
Two phase oil-water flow is the limiting case of a three phase
air-oil-water flow with negligible air flow.
6.
A combination of pressure drop prediction methods based on flow
regime is necessary to adequately predict the pressure losses of a three
phase flow.
B.
SPECIFIC
1.
The transition from water on the wall to oil on the wall is in-
dependent of the gas flow rate and may be predicted using a flow.regime
map based on pressure deviations with the superficial water velocity as
78
a parameter.
2.
In preparing engineering estimates of the friction pressure loss
the viscosity of water may be used as the effective fluid viscosity up
to the transition from liquid froth flow to oil dominated liquid flow.
After which the viscosity of the oil may be used.
3.
A flow regime map based on two phase oil-water flow may be used
successfully to predict three phase flow liquid regime transitions.
4.
The contact angles observed in these flow experiments are simi-
lar to those expected in actual applications.
79
CHAPTER VII
SUGGESTIONS FOR FURTHER WORK
The following further work is suggested:
A.
The current work was performed at near atmospheric conditions.
Hence, further testing should be performed at elevated pressures.
B.
The mass flow rates for these tests did not vary substantially.
Therefore, work with larger flow rates should be'examined in order to
determine the influence on the In Situ Oil phase Volume Fraction prediction correlation.
C.
At the transition from water froth to oil froth at an F
of
o
about .85, the friction pressure loss abruptly rose then fell.
The
hypothysis that this pressure jump is caused by the shearing of oil
bubbles between the wall and the air slugs should be verified'or dismissed.
D.
Further work should be done to verify and refine the Govier
flow regime map for three phase flow.
E.
Finally a method of dealing with the negative friction pressure
loss effect should be investigated.
80
REFERENCES
1.
Rasin Tek, M., "Multiphase Flow of Water, Oil and Natural Gas
Through Vertical Flow Strings", Journal of Petroleum Technology,
pp. 1029-1036, October, 1961.
2.
Galyamov, M. N. and Karpushin, N. L., "Change in the Viscosity of
the Liquid Phase During The Movement of Gas-Water-Oil Mixtures
in Pipelines", Transport i khranenie nefti i nefteproduktov,
no. 2, pp.14-16, 1971.
3.
Bocharov, A. N., Andriasov, R. S. and Sakharov, V. A., "Investigation of the Motion of Gas-Water-Oil Mixtures in Horizontal
Pipes", Neftepromyslovoe delo, no. 6, pp. 27-30, 1972.
4.
Foreman, F. J. and Woods, P. H., "Void Fraction Calculations for
Three Phase Flow in a Vertical Pipe", Project Report Course 2.673,
M.I.T., 1975.
5.
Govier, G. W., Radford, B. A. and Dunn J.S.C., "The Upwards Flow of
Air-Water Mixtures", The Canadian Journal of Chemical Engineering,
pp. 58-70, August, 1957.
6.
Govier, G. W., Sullivan, G. A. and Wood, R. K. "The Upward Flow of
Oil-Water Mixtures", The Canadian Journal of Chemical Engineering,
pp. 67-75, April, 1961.
7.
Zuber, N. and Findlay, J. A., "Average Volumetric Concentration in
Two-Phase Flow Systems", Journal of Heat Transfer, pp. 453-468,
November, 1965.
81
8.
Griffith, P. and Wallis, G. B., "Two Phase Slug Flow", Journal of
Heat Transfer, Trans. ASME, p. 307, August, 1961.
9.
Orkiszewski, J., "Predicting Two-Phase Pressure Drops in Vertical
Pipe", Journal of Petroleum Technology, pp. 829-838, June, 1967.
10.
Singh, G. and Griffith, P., "Determination of the Pressure Drop
Optimum Pipe Size for a Two-Phase Slug Flow in an Inclined Pipe",
ASME Paper No. 70-Pet-15.
11.
Collier, J. G., "Convective Boiling and Condensation", McGraw-Hill,
1972.
12.
Govier, G. W. and Aziz, K., "The Flow of Complex Mixtures in Pipes",
Van Nostrand Reinhold Company, 1972.
13.
Rohsenow, W. M. and Choi, H. Y., "Heat, Mass, and Momentum Transfer",
Prentice-Hall, 1961.
82
APPENDIX A:
Foreman and Woods Data:
TABLE A-1
Void Fraction Data
9Q0
(GPM)
Q
(GPM)
Qa
(GPM)
ho
(in.)
hw
(in.)
ha
(in.)
Pla
(psi)
P2a
(psi)
3.5
3.5
2.07
31.75
32.5
16.75
20.0
13.5
3.5
3.5
4.14
27.25
27.25
26.75
20.8
13.8
3.5
3.5
6.21
26.0
25.0
30.0
21-.75
14.75
3.5
3.5
8.28
22.25
23.25
35.5
23.0
16.0
3.5
3.5
10.35
22.75
22.0
36.25
27.0
20.0
3.5
3.5
12.42
22.75
21.5
37.0
27.0
20.0
3.5
3.5
14.49
19.0
21.75
40.0
27.5
20.5
3.5
3.5
16.56
19.0
20.75
41.0
28.0
21.0
3.5
3.5
18.63
19.0
20.25
42.0
29.0
22.0
3.5
3.5
20.70
17.25
18.5
45.75
30.0
23.0
1.0
4.0
2.07
12.5
47.25
21.0
18.0
11.0
1.0
4.0
4.14
10.25
40.75
30.0
17.0
10.0
1.0
4.0
6.21
9.5
35.5
36.25
17.5
10.5
1.0
4.0
8.28
8.0
29.5
43.75
18.0
11.0
1.0
4.0
10.35
7.0
28.0
45.0
19.0
12.0
1.0
4.0
12.42
5.0
28.0
47.0
19.0
12.0
1.0
4.0
14.49
4.0
24.0
49.0
20.0
13.0
1.0
4.0
16.56
3.0
22.0
51.0
21.0
14.0
1.0
4.0
18.63
4.5
23.0
52.5
21.0
14.0
1.0
4.0
20.70
2.5
25.0
56.5
22.0
15.0
83
TABLE A-2
Three-Phase Flow Data Reduction
Qo
QW
Qa
a
a
Q
IA/Aa
Q/A
(ft /sec)
(ft /sec)
(ft /sec)
(in/in)
(ft/sec)
(ft/sec)
.0022
.0089
.00443
.26
5.554
5.062
.0022
.0089
.00886
.37
7.805
6.506
.0022
.0089
.0133
.4475
9.687
7.953
.0022
.0089
.0177
.54
10.684
9.387
.0022
.0089
.0221
.55
13.097
10.82
.0022
.0089
.0266
.58
14.95
12.3
.0022
.0089
.031
.605
16.7
13.72
.0022
.0089
.0354
.629
18.34
15.156
.0022
.0089
.0399
.648
20.07
16.62
.0022
.0089
.0443
.6975
20.7
18.06
.0078
.0078
.00443
.2068
6.98
6.53
.0078
.0078
.00886
.33
8.75
7.973
.0078
.0078
.0133
.37
11.72
9.42
.0078
.0078
.0177
.438
13.2
10.85
.0078
.0078
.0221
.4475
16.1
12.3
.0078
.0078
.0226
.4568
18.98
13.76
.0078
.0078
.031
.494
20.45
15.2
.0078
.0078
.0354
.506
22.8
16.62
.0078
.0078
.0399
.52
25.0
18.09
.0078
.0078
.0443
.565
25.56
19.52
84
APPENDIX B:
Analysis of Parametric Effects on Two Phase Friction
Pressure Loss.
The data obtained in the two phase portion of this experimentation
can be combined with the constant velocity data obtained from Govier,
Sullivan and Wood (Table B-i) to ascertain the influences on the friction pressure loss of the diameter, viscosity of the fluid, and the mixture velocity.
to B7.
The results of this comparison are shown in Figures B1
From these figures we may conclude the following:
1.
A variation in the diameter of the tube shows no definite in-
fluence on the pressure loss, however the location of the transition
from water on the wall to oil is not influenced.
2.
Figs. B1 and B2.
The viscosity of the oil influenced the level of pressure loss
after the transition.
As a result we see clearly where the viscosity
of the water is important and where the oil predominates.
Also, the
oil viscosity did not influence the location of the transition F
Figs. B3 and B4.
3.
Finally the mixture velocity influences the level of the pres-
sure loss, but again the transition F
B5 to B7.
is relatively independent.
Figs.
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89
Figure
B1.
Friction Pressure Loss, Diameter Varied,
2 ft/sec
Two Phase Flow.
7
5
0
A
.1
rM
0,
qH
:5
N
4
3
05
%4
1.039 I.D.
.01
.01
.005
.0
Fo
90
Figure B2.
Friction Pressure Loss, Diameter Varied,
3 ft/sec Two Phase Flow.
1.0
.5
I
I
I
I
0
p
I
4.,
:5
I
I
I
I
I
I
0
*3
N
I
II
II
I
4
0
+X
%4
.1
4
I
'1
.05
, - oD
.20
.80
F0
.0
w
91
Figure B3. Friction Pressure Loss, Viscosity Varied,
2 ft/sect
Two Phase Flow.
4.A
I- 0
IVIJ
C5
0
9-'
0o
: .05
Pi
at.
.01
.20
.40
.60
Fo
.80
1.0
92
Figure B4.
Friction Pressure Loss, Viscosity Varied,
3 ft/sect
Two Phase Flow.
I.U
4
d\
.5
L,= .936 cp
FL = 20.1 cp
3 = 15
cp
0
o+0
or04)3
494
.1
4-3
f4"I$4
.o5
FL'
WATER
.O01
.20
.
Fo
_
)To
93
Figure B5.
Friction Pressure Loss, Mixture Velocity
Varied,
150 cpa Two Phase Flow.
1.0
.5
4)
0
4m
04)
4,
4-
94
.1
.05
.01
0
Fo
94
Figure B6. Friction Pressure Loss, Mixture Velocity
Varied, 20.1 cps Two Phase Flow.
1.0
.5
I.
1 ft/sec
3.
4.
5.
3 ft/sec
4 ft/sec
5 ft/sec
2.
2 ft/sec
III
0
o
0
I
0
5
CM
0
I%
03:
.1
%-4
0
.1
-1
I
4-3
44
I
.05
I
I
I
I
I
I
2
--
.01
I
- - -- I
.20
.80
F0
0
95
Figure
B7.
Friction Pressure Loss, Mixture Velocity
Varied, .936 cps Two Phase Flow.
.12
1.
2,.
3.
1 ft/s ec
2 ft/sec
3 ft/sec
4.
4 ft/sec
5.
5 ft/sec
.10
0
P
go
,,
-
.08
..
0
0
4-4
3 .06
,,1
-
,,
I
0
16114
.04
'-.
2.
.02
0
.0
FO
96
APPENDIX C:
Flow Regime Visual Observations.
Figure C1 shows a typical friction pressure loss curve disected into four main flow regime areas.
The variation of this curve is keyed to
Govier's flow regime map (Fig. 14) and can be explained as follows:
A.
O<F <a:
In this region the water predominates the fluid flow
and can be characterized as a typical slug flow.
typical view of the tube.
Figure C2 shows a
In region A the fluid is in counter flow a-
round the air slugs while in region B the fluid flows at a rate commensurate with that of the air slugs.
water in small bubbles.
The oil is distributed throughout the
At higher velocities the negative shear around
the air slugs is small compared to that in the liquid slugs.
As does
Singh and Griffith the negative shear can be assumed to be neglected in
most cases.
When the oil in liquid volume fraction is increased from O,
the size of the liquid slugs decreases and the counterflow area thickens.
This causes a decrease in the friction pressure loss.
This decrease
continues until the regime change at a.
B.
froth.
a<F <b:
At the transition a, the liquid flow changes to a
The water still predominates the flow (Fig. C3) next to the wall,
but the oil bubbles in the water slug area begin to coalesce into oil
slugs.
The area A is still in counterflow, however in area B the water
flow around the oil slugs in cocurrent.
Hence the effective length of
the water slugs begins to increase and the friction loss increases.
As
the water in the fluid slug is completely replaced by oil, the layer of
97
Figure
C1,.
Typical Friction Pressure Loss Curve.
I
E-4A
3HQ
xJ
zL_
O
IS-4
i4o
I
_
0
k
E4
0
o~
,,,,,,,,,,,0
-
A,
'
o
-
-·IL
·I
·-
-
-
c
rM
:
4
V)
vsd
jdV
_
_
_
_
_
_
_
_
_
98
Figure C2 & C).
·
i.
.
Flow Regime Diagram.
0
-
.
A
.
AIR
with
Oil
es
o,·0
,~.U_~
,.
..'
5
oAIR~~~~·
a..
,
..
AI
SCI
I
Ct
S
6
-Water
Continuous
So
.6
oJ
i·~~~~~
i:'i~~~~~~~~~q
;r with
X Oil
)les
!
·
Fig. C2.
Fig. C3.
99
water on the tube wall becomes thinner and thinner until at the transition b the layer is too thin to contain any oil bubbles, and the bubbles
are sheared between the wall and the air slugs.
When this occurs the
friction loss makes a sharp upward jump until the oil bubbles are forced
out of the water layer.
C.
b<Fo<c:
The pressure jump is point b on Figure C1.
At b the flow changes from water dominated froth to oil
froth and the water is considered to be bubbles of water in oil.
The
exception is that a thin layer of water still persists on the wall of
the tube.
However, this layer is too thin to contain any oil bubbles.
The laminar nature of the oil flow dampens the turbulence of the water
and air and transition to pure slug flow is quickly achieved.
At point
c, full slug flow is achieved and the water is finally replaced by oil
on the wall.
When this occurs the counterflow friction loss dominated
now by the viscosity of the oil, decreases.
This dip can be seen at
point c in Figure C1.
D.
c<Fol.O:
In this region the flow transitions from pure slug
flow to a quasi annular flow.
As Fo increases, the counterflow velocity
region (A in Fig. C5) reverses to co-current and increases in thickness
while that of the slug region (B) decreases in size.
After this reversal
the combination of the oil viscosity and the increased upward velocity
cause a sharp rise in the pressure losses.
Figure C1.
Again, this is apparent in
100
Figure C4 & C5. Flow Regime Diagram.
Bubbles
-A
Film
-
Fig. C4.
Fig. C5.
B
101
Derivation of Annular Flow Pressure Drop
APPENDIX D:
Melthod.
I
Annular flow is characterized by a continuous
i
AIR
column of gas and a continuous annulus of fluid
in co-current flow (A in Fig. D1) while slug flow
I
1
is characterized by counter fluid flow over the
gas slugs and co-current flow in the fluid slugs
A
A
I
However, in the transition
(B in Fig. D1).
-
I
both co-current annulus and slug fluid flows
occur simultaneously.
Therefore the basis of
can be modeled as a basic annular flow with a
decreased annular fluid velocity.
The decrease
accounts for the remaining fluid slugs.
I
i
I
B
B
this method is the assumption that transition flow
--
I1
I I
a
A
I
lI1
FLUID
In addition,
in calculating the friction pressure loss the
C>
FIG. D1
modified annular velocity of the fluid in the annulus
is assumed to be the velocity of the fluid flowing alone in the entire
tube.
From annular flow the fluid velocity is as follows:
-
vf
A.
= Q
f
(D 1)
Aaf
This can then be modified for the Quasi-annular flow by a constant K,
which is less than one.
Vf
Af
Af
(D 2)
102
Based on this the following pressure loss analysis is derived:
= KQfDPf
AafPfg o
Re
(D 3)
Due to the high viscosity of the Nujol, the oil flow was laminar
Hence the laminar friction factor equation
throughout the experiment.
is used.
f = 16
(D 4)
= 16AfPfgo
Ref
KQfDpf
The shear stress is then:
T
=
(D 5)
= 8fKQf
fpv
AafD
2go
and the friction pressure loss is:
APf = 4
=
D
32K pfQf
D
ADZaf
(D 6)
which is a constant (K) times the loss associated with a complete annular flow.
In calculating the total friction pressure loss of the flow, we
must recognize the transitional nature of the flow.
lar and slug flows contribute to the loss.
That is, both annu-
Therefore, we can assume
that the total loss due to friction will be a portion of a full annular
flow superimposed over the slug losses.
friction pressure loss is as follows:
We may then say that the total
103
Apf
=
K
ffannular + (1-K)APf
annular
slug
(D 7)
The annular flow portion is calculated as in equation D 6 while the slug
flow portion can be assumed to be that at Fo equal to zero where slug
flow predominates.
Finally, the weighting factor K must be determined.
In the flow
investigated the quasi annular flow appeared only above the froth critical oil in liquid volume fraction.
In this case approximately .85.
so, the flow was nearly annular at Fo equal to one.
Al-
If, based on this,
we assign a value of .9 to K at Fo equal to one, we may linearly interpolate the values of K as shown in Fig. D 2.
The values for the total friction pressure loss derived from the
above analysis are shown in Table 3 of the main text and show very close
results.
104
Figure D 2.
Linear Interpolation
of the Factor K.
.9
.6
.3
0
F
0
105
APPENDIXE.
OIL(
Physical
Data.
NUJOL)
p
= .0015
p
= 55.5 lbm/ ft 3
lb sec/ ft2 at
100 F
WATER
Al= .000015 lb sec/ft
p
= 62. 4
bm/ ft
2
at 100 F
3
AIR
L = 3.9x10
p
7
lb sec/ ft
.075 bm/ ft 3
2
at
100 F
106
APPENDIX F. Sample Calculations.
A.
Example of Slug Flows
1. Datas Qw = .282 CFM, Qo=.094 CFM, Qa= 1.82 CFM,
D= .75
inches,& L74.25
inches.
2. Void Fractions
Qw+ qo
F°
O
BwS
= .865
(y= 1. 28'Q'
Eq. 5.12
oco
1.0370c
.25
1.82
_
Qa
Eq. 5.10
.282+.094
0
1. 28( 1.82+. 282+. 094)
F1 '
53 6 =
1.037(1-.65)(.25)1 '
= .04
Eq. 5.14
-ccw= 1(Oca+OCo)= 1-(.65+.04)=
.31
3. Pressure Loss
Po 0+ Pa a)
Ap 4(Pw
o+
32.2x74.25
32.2x12x144 (55.5(.04)+62.4(.31)+.65(.075))
=.93 psi/ length
and Vw'=
f
From Fig.14 for F.25
the flow regime is slug.
-A
4.38 ft/sec
Therefore we use the Singh-
Griffith method for the friction loss.
Re=
'Vm Pf
D
/4f
= 58,544.
f= .0051
2 L fPflrmCw
fTotal Preure=
=
.58
psi/ length
51 p/lng
Total Pressure Loss - 1.51 psi/length
536
107
B. Example of Froth Flows
1.
Data
Qw = .076 CFM, Qo = .30
1.82
CFM,& Qa
CFM.
2. Void Fractions
Same as method in A-2.
Oc = .63
OCw = .10
Oo= .27
3.
Pressure Losss
Same as method in A-3.
APp = .91 psi/ length
Qo
F
°
.80
OQ+ Qw
Qw
Vw=
.-
1,11 ft/sec
=
Ocf A
From fig. 14 the flow regime is froth.
Therefore we
use the homogeneous method.
Velocity of the fluid flowing in the tube alones
fo
Os
Re =
Qf
= 2.04 ft/sec
9387
f= .008
Quality(X)s
X=
PaQa
Paa+ Pf Qf
-
.006
108
AP f
-
AP
-
-
gm
o
[I+X
pLLPa]
p ]
[
.41 psi/ length
C. Example of Quasi-Annular Flows
1. Data, Qw= .019
2. Voids
Q
.36 CFM, & Qa= 1.82 CFM.
Same Method as A2 except
eq. 5.11 was
used instead of eq. 5.10.
Oca ,.46
O w= .02
OXC'
.52
3.Pressure Loss
Same method as A-3.
APp = 1.30 psi/length
Fo = .95
w=n 5.16 ft/sec
From fig.14 the flow regime is the water drop in oil
regime.
Therefore the quasi-annular flow method is
used.
From eq. D 6
APM
Af
annular
From the Singh-Griffith
From fig. D 2 K
.6
32L4/ Q.
A D
ethod APfn
pOf
a
psi/
.712 psi/L
From eq.
109
D 71
Pf tot
=
KAPf ann+ (1-K)APf slug
APf tot= .6(2.0) +.4(.712)= 1.48 psi/length
The total pressure loss iss
APt
=
1.30 + 1.48
2.78 psi/ length
110
APPENDIX G:
Data Listing
The following code was used to designate the various runs:
A 80- 10- 3
a
a.
b
c
d
Test Disignation.
A.
Three Phase Void Fraction Test
B.
Two Phase Oil-Water Pressure Void Test
C.
Three Phase Pressure and Void Test
D.
Contact Angle Test
b.
Introduced oil in liquid volume fraction (Fo)
c.
Percent of maximum input air flow for test
A and the mixture velocity for test B and C.
d.
Identification number of individual run.
0z
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1-4
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