the interaction between a two slotted plate flow …
TRANSCRIPT
THE INTERACTION BETWEEN A TWO SLOTTED PLATE FLOW METER
UNDER ONE, TWO, OR THREE COMPONENT FLOW CONDITIONS
A Thesis
by
SANG HYUN PARK
Submitted to the Office of Graduate Studies of Texas A&M University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
December 2004
Major Subject: Mechanical Engineering
THE INTERACTION BETWEEN A TWO SLOTTED PLATE FLOW METER
UNDER ONE, TWO, OR THREE COMPONENT FLOW CONDITIONS
A Thesis
by
SANG HYUN PARK
Submitted to Texas A&M University in partial fulfillment of the requirements
for the degree of
MASTER OF SCIENCE
Approved as to style and content by:
Gerald L. Morrison
(Chair of Committee)
Je C. Han (Member)
Yassin A. Hassan (Member)
Dennis L. O’Neal (Head of Department)
December 2004
Major Subject: Mechanical Engineering
iii
ABSTRACT
The Interaction Between a Two Slotted Plate Flow Meter
Under One, Two, or Three Component Flow Conditions. (December 2004)
Sang Hyun Park, B.S., Yonsei University, Republic of Korea
Chair of Advisory Committee: Dr. Gerald L. Morrison
In previous work on the slotted flow meter, repeatibility and reproducibility were
studied under different flow conditions and different configurations. In accordance with
previous work, the effects of the distance between the slotted plate were identified as an
area requring further investigation. The preset 5D distance is expanded to the 10D distance.
The flow coefficient KY, the pressure drop, and the uncertainty analysis is conducted.
There were definite deference in the results between the 5D distance and the 10D distance
in many aspects. As a base line, the flow coefficient KY showed 0.8% ~ 2% difference
between the 5D and the 10D distance case. Depending upon the upstream flow conditions,
the reproducibility of the slotted flow meter was affected. The pressure drop increased as
the upstream Reynolds number increased. The result from the analysis of the water cut
meter showed that there are definite relationships between the parameteres of the water cut
meter and the parameters of the flow.
iv
DEDICATION
To my mother and father for supporting my study and my life.
To Young Ran Kim for loving me and trusting in me.
To my colleagues for making me not forget the reason I am here.
To my grunt brother, Sang June Park.
v
ACKNOWLEDGMENTS
The author expresses the greatest gratitude to Dr. G. L. Morrison for being his
mentor, taking care of him, and not being disappointed in him. The author would like to
thank Dr. J. C Han and Dr. Y. Hassan for their support. The author appreciates the great
support and encouragement of Sara Anne Sparks, Dr. Justo Hernandez Ruiz, and Vasanth
Muralidharan. The author expresses thanks to Jung Won Cho for being his long distance
supporter.
vi
TABLE OF CONTENTS
Page
ABSTRACT .......................................................................................................................iii
ACKNOWLEDGMENTS...................................................................................................v
TABLE OF CONTENTS ...................................................................................................vi
LIST OF FIGURES..........................................................................................................viii
LIST OF TABLES ...........................................................................................................xvi
NOMENCLATURE ........................................................................................................xvii
I. INTRODUCTION............................................................................................................1
1.1. The history of the slotted plate flow meter...........................................................1
1.2. The objectives.......................................................................................................3
II. THEORIES .....................................................................................................................5
2.1. Equations for data reduction.................................................................................5
2.2. The flow pattern map..........................................................................................10
2.3. Uncertainty analysis ...........................................................................................11
III. EXPERIMENTAL ......................................................................................................14
3.1. Apparatus............................................................................................................14
3.2. Pressure measurement ........................................................................................18
3.3. Temperature measurement .................................................................................19
3.4. Mass flow rate measurement ..............................................................................20
3.5. The water cut meter ............................................................................................22
3.6. Data sampling.....................................................................................................23
3.7. Procedures ..........................................................................................................23
IV. RESULTS AND DISCUSSION .................................................................................27
4.1. The comparison between 5D and 10D cases ......................................................28
4.2. The flow pattern map..........................................................................................35
4.3. The pressure drop-the permanent head loss .......................................................39
4.4. The water cut meter analysis ..............................................................................40
4.5. The uncertainty analysis .....................................................................................43
vii
Page V. SUMMARY AND CONCLUSIONS...........................................................................51
VI. RECOMMENDATIONS ............................................................................................52
REFERENCES ..................................................................................................................53
APPENDIX A ...................................................................................................................55
APPENDIX B..................................................................................................................161
VITA................................................................................................................................168
viii
LIST OF FIGURES
Page
Figure 1 Beta=0.430 plate................................................................................................55
Figure 2 Beta=0.467 plate................................................................................................56
Figure 3 Schematic diagram of the test facility ...............................................................57
Figure 4 Detail diagram of the test section ......................................................................57
Figure 5 Data acquisition systems and flow control system............................................58
Figure 6 Schematic diagram of PID control ....................................................................59
Figure 7 Test rig setting for 10D distance .......................................................................59
Figure 8 Test rig setting for 5D distance .........................................................................60
Figure 9 Schematic block diagram of water cut sensor ...................................................60
Figure 10 Power law curve fit equation for calibration coefficient divided by Euler number for 9040 data points..............................................................................61
Figure 11 Sketch of flow pattern (Baker, 1954 [16]).........................................................62
Figure 12 Flow pattern map for stratified flow and annular flow (Kadambi, 1982 [12])..62
Figure 13 Plot of flow coefficient KY of the β=430 plate versus DP/P for air-only flow....................................................................................................................63
Figure 14 Plot of flow coefficient KY of the β=430 plate versus Reynolds number for air-only flow ......................................................................................................64
Figure 15 Plot of flow coefficient KY of β=467 plate versus dP/P for air-only flow .......65
Figure 16 Plot of flow coefficient KY of β=467 plate versus Reynolds number for air-only flow............................................................................................................66
Figure 17 Plot of the difference between the KY of the β=430 plate for the 5D distance and the 10D distance vs. upstream Reynolds number.........................67
ix
Figure 18 Plot of the difference between the KY of the β=467 plate for the 5D distance and the 10D distance vs. upstream Reynolds number.........................68
Figure 19 3D plot of KY of β=430 plate vs. Reynolds number and dP/P for 5D distance case ......................................................................................................69
Figure 20 3D plot of KY of β=467 plate vs. Reynolds number and dP/P for 5D distance case ......................................................................................................70
Figure 21 3D plot of KY of β=430 plate vs. Reynolds number and dP/P for 10D distance case ......................................................................................................71
Figure 22 3D plot of KY of β=467 plate vs. Reynolds number and dP/P for 10D distance case ......................................................................................................72
Figure 23 Plot of flow coefficient KY β=430 plate versus GVF for water and air flow...73
Figure 24 Plot of flow coefficient KY β=430 plate versus dP/P for water and air flow ...74
Figure 25 Plot of flow coefficient KY β=430 plate versus quality for water and air flow....................................................................................................................75
Figure 26 Plot of flow coefficient KY β=430 plate versus Reynolds number for water and air flow........................................................................................................76
Figure 27 3D plot of KY of the β=430 plate vs. dP/P and quality under water and air flow condition....................................................................................................77
Figure 28 Plot of flow coefficient KY β=467 plate versus GVF for water and air flow...78
Figure 29 Plot of flow coefficient KY β=467 plate versus dP/P for water and air flow ...79
Figure 30 Plot of flow coefficient KY β=467 plate versus quality for water and air flow....................................................................................................................80
Figure 31 Plot of flow coefficient KY β=467 plate versus Reynolds number for water and air flow........................................................................................................81
Figure 32 3D plot of KY of β=467 plate vs. dP/P and quality under water and air flow condition ............................................................................................................82
Figure 33 Plot of flow coefficient KY of β=430 plate versus GVF for oil and air flow ...83
Figure 34 Plot of flow coefficient KY of β=430 plate versus dP/P for oil and air flow....84
Page
x
Figure 35 Plot of flow coefficient KY of β=430 plate versus quality for oil and air flow....................................................................................................................85
Figure 36 Plot of flow coefficient KY of β= 430 plate versus Reynolds number for oil and air flow........................................................................................................86
Figure 37 3D plot of KY of β=430 plate vs. dP/P and quality under oil and air flow condition ............................................................................................................87
Figure 38 Plot of flow coefficient KY of β= 467 plate versus GVF for oil and air flow ..88
Figure 39 Plot of flow coefficient KY of β= 467 plate versus dP/P for oil and air flow...89
Figure 40 Plot of flow coefficient KY of β= 467 plate versus quality for oil and air flow....................................................................................................................90
Figure 41 Plot of flow coefficient KY of β= 467 plate versus Reynolds number for oil and air flow........................................................................................................91
Figure 42 Plot of KY of β=467 plate vs. dP/P and quality under oil and air flow condition ............................................................................................................92
Figure 43 Plot of flow coefficient KY of β= 430 plate versus GVF for water, oil and air flow...............................................................................................................93
Figure 44 Plot of flow coefficient KY of β= 430 plate versus dP/P for water, oil and air flow...............................................................................................................94
Figure 45 Plot of flow coefficient KY of β= 430 plate versus quality for water, oil and air flow...............................................................................................................95
Figure 46 Plot of flow coefficient KY of β= 430 plate versus Reynolds number for water, oil and air flow........................................................................................96
Figure 47 Plot of flow coefficient KY of β= 467 plate versus GVF for water, oil and air flow...............................................................................................................97
Figure 48 Plot of flow coefficient KY of β= 467 plate versus dP/P for water, oil and air flow...............................................................................................................98
Figure 49 Plot of flow coefficient KY of β= 467 plate versus quality for water, oil and air flow...............................................................................................................99
Page
xi
Figure 50 Plot of flow coefficient KY of β= 467 plate versus Reynolds number for water, oil and air flow......................................................................................100
Figure 51 Plot of flow coefficient of β= 430 plate vs. dP/P for water and air flow (stratified flow)................................................................................................101
Figure 52 Plot of flow coefficient of β= 430 plate vs. Reynolds number for water and air flow (stratified flow) ..................................................................................102
Figure 53 Plot of flow coefficient of β= 430 plate vs. quality for water and air flow (stratified flow)................................................................................................103
Figure 54 Plot of flow coefficient of β= 430 plate vs. dP/P for water and air flow (annular flow) ..................................................................................................104
Figure 55 Plot of flow coefficient of β=430 plate vs. Reynolds number for water and air flow (annular flow).....................................................................................105
Figure 56 Plot of flow coefficient of β= 430 plate vs. quality for water and air flow (annular flow) ..................................................................................................106
Figure 57 Plot of flow coefficient of β=467 plate vs. dP/P for water and air flow (stratified flow)................................................................................................107
Figure 58 Plot of flow coefficient of β=467plate vs. Reynolds number for water and air flow(stratified flow) ...................................................................................108
Figure 59 Plot of flow coefficient of β=467 plate vs. quality for water and air flow (stratified flow)................................................................................................109
Figure 60 Plot of KY of β=430 plate vs. dP/P and quality under water and air flow condition (stratified flow)................................................................................110
Figure 61 Plot of flow coefficient of β=467 plate vs. dP/P for water and air flow (annular flow) ..................................................................................................111
Figure 62 Plot of flow coefficient of β=467 plate vs. Reynolds number for water and air flow (annular flow).....................................................................................112
Figure 63 Plot of flow coefficient of β=467 plate vs. quality for water and air flow (annular flow) ..................................................................................................113
Page
xii
Figure 64 Plot of flow coefficient of β=430 plate vs. dP/P for oil and air flow (stratified flow)................................................................................................114
Figure 65 Plot of flow coefficient of β=430 plate vs. Reynolds number for oil and air flow (stratified flow)........................................................................................115
Figure 66 Plot of flow coefficient of β=430 quality for oil and air flow (stratified flow) ................................................................................................................116
Figure 67 Plot of flow coefficient of β=430 plate vs. dP/P for oil and air flow (annular flow) ................................................................................................................117
Figure 68 Plot of flow coefficient of β=430 plate vs. Reynolds number for oil and air flow (annular flow)..........................................................................................118
Figure 69 Plot of flow coefficient of β=430 plate vs. quality for oil and air flow (annular flow) ..................................................................................................119
Figure 70 Plot of flow coefficient of β=467 plate vs. dP/P for oil and air flow (stratified flow)................................................................................................120
Figure 71 Plot of flow coefficient of β=467 plate vs. Reynolds number for oil and air flow (stratified flow)........................................................................................121
Figure 72 Plot of flow coefficient of β= 467 plate vs. quality for oil and air flow (stratified flow)................................................................................................122
Figure 73 Plot of flow coefficient of β=467 plate vs. dP/P for oil and air flow (annular flow) ................................................................................................................123
Figure 74 Plot of flow coefficient of β=467 plate vs. Reynolds number for oil and air flow (annular flow)..........................................................................................124
Figure 75 Plot of flow coefficient of β=467 plate vs. quality for oil and air flow (annular flow) ..................................................................................................125
Figure 76 Plot of the permanent pressure loss P∆ vs. Reynolds number for air-only flow condition..................................................................................................126
Figure 77 Plot of the permanent pressure loss P∆ vs. Reynolds number for water/air flow condition..................................................................................................127
Page
xiii
Figure 78 Plot of the permanent pressure loss P∆ vs. Reynolds number for water and air flow condition under the upstream condition of stratified flow and annular flow.....................................................................................................128
Figure 79 Plot of the permanent pressure loss P∆ vs. Reynolds number for oil/air flow condition ..........................................................................................................129
Figure 80 Plot of the permanent pressure loss P∆ vs. Reynolds number for water/oil/air flow condition .............................................................................130
Figure 81 Contour plot of quality vs. superficial velocity and delay time for water and air flow.............................................................................................................131
Figure 82 Contour plot of quality vs. superficial velocity and rise time for water and air flow.............................................................................................................131
Figure 83 Contour plot of quality vs. superficial velocity and delay time for oil and air flow..................................................................................................................132
Figure 84 Contour plot of quality vs. superficial velocity and rise time for oil and air flow..................................................................................................................132
Figure 85 Plot of uncertainty of KY of β=430 plate vs. dP/P for air-only flow ..............133
Figure 86 Plot of uncertainty of KY of β=467 plate vs. dP/P for air-only flow ..............134
Figure 87 Plot of uncertainty of KY of β=430 plate vs. dP/P for water and air flow......135
Figure 88 Plot of uncertainty of KY of β=467 plate vs. dP/P for water and air flow......136
Figure 89 Plot of uncertainty of KY of β=430 plate vs. quality for water and air flow ..137
Figure 90 Plot of uncertainty of KY of β=467 plate vs. quality for water and air flow ..138
Figure 91 Plot of uncertainty of KY of β=430 plate vs. dP/P for oil and air flow ..........139
Figure 92 Plot of uncertainty of KY of β=467 plate vs. dP/P for oil and air flow ..........140
Figure 93 Plot of uncertainty of KY of β=430 plate vs. quality for oil and air flow.......141
Figure 94 Plot of uncertainty of KY of β=467 plate vs. quality for oil and air flow.......142
Figure 95 Plot of uncertainty of KY of β=430 plate vs. dP/P for water, oil, and air flow..................................................................................................................143
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xiv
Figure 96 Plot of uncertainty of KY of β=467 plate vs. dP/P for water, oil, and air flow..................................................................................................................144
Figure 97 Plot of uncertainty of KY of β=430 plate vs. quality for water, oil, and air flow..................................................................................................................145
Figure 98 Plot of uncertainty of KY of β=467 plate vs. quality for water, oil, and air flow..................................................................................................................146
Figure 99 Plot of the normalized uncertainty of KY of β=430 plate vs. dP/P for air-only flow..........................................................................................................147
Figure 100 Plot of the normalized uncertainty of KY of β=467 plate vs. dP/P for air-only flow..........................................................................................................148
Figure 101 Plot of the normalized uncertainty of KY of β=430 plate vs. dP/P for water and air flow.....................................................................................................149
Figure 102 Plot of the normalized uncertainty of KY of β=430 plate vs. quality for water and air flow...........................................................................................150
Figure 103 Plot of the normalized uncertainty of KY of β=467 plate vs. dP/P for water and air flow.....................................................................................................151
Figure 104 Plot of the normalized uncertainty of KY of β=467 plate vs. quality for water and air flow...........................................................................................152
Figure 105 Plot of the normalized uncertainty of KY of β=430 plate vs. dP/P for oil and air flow............................................................................................................153
Figure 106 Plot of the normalized uncertainty of KY of β=430 plate vs. quality for oil and air flow.....................................................................................................154
Figure 107 Plot of the normalized uncertainty of KY of β=467 plate vs. dP/P for oil and air flow............................................................................................................155
Figure 108 Plot of the normalized uncertainty of KY of β=467 plate vs. quality for oil and air flow.....................................................................................................156
Figure 109 Plot of the normalized uncertainty of KY of β=430 plate vs. dP/P for water, oil, and air flow...............................................................................................157
Page
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Figure 110 Plot of the normalized uncertainty of KY of β=430 plate vs. quality for water, oil, and air flow....................................................................................158
Figure 111 Plot of the normalized uncertainty of KY of β=467 plate vs. dP/P for water, oil, and air flow...............................................................................................159
Figure 112 Plot of the normalized uncertainty of KY of β=467 plate vs. quality for water, oil, and air flow....................................................................................160
Page
xvi
LIST OF TABLES
Page
TABLE 1 Single phase test points ...................................................................................161
TABLE 2 Two phase flow test points (water and air) .....................................................162
TABLE 3 Two phase test points (oil and air) ..................................................................163
TABLE 4 Three phase flow test points (water, oil, and air) ............................................165
TABLE 5 Curve fit functions for the water cut meter .....................................................166
xvii
NOMENCLATURE
A Cross sectional aera
D Diameter
KY Flow coefficient
m& Mass flow rate
P Absolute pressure
P∆ Differential pressure
Q& Volumetric flow rate
R Gas constant of standard air (286.9 )/ KkgJ ⋅
T Temperature
V Velocity
Vs Superficial Velocity
X Quality
x Axial distance
Y Expansion factor
α Gas volume fraction (GVF)
β Beta ratio
µ Viscosity
ρ Density
ω Uncertainty
xviii
Subscripts:
air Air component
actual Actual value acquired from the experiment
gas Gas phase
liquid Liquid phase
mix Mixture
pipe Property pertaining to pipe
P∆ Property Pertaining to differential pressure
slot Of the slot of the slotted plate flow meter
Th Theoretical value
β Property pertaining to Beta ratio
1
I. INTRODUCTION
1.1. The history of the slotted plate flow meter
The traditional way of metering natural gas from an off shore platform is that, for
each subsea satellite well, the mixture of gas, oil, and water is extracted and the subsea
manifold gathers the output from the satellite wells. Then, by using a seperator, each phase
(component) of the mixture is separated and metered individually via single-phase
measurement technics. This way of metering natural gas and monitoring of each well is
expensive and does not provide enough accuracy to effectively monitor each well. Hence,
the multiphase metering device is needed. Although there are no multiphase flow meters
which are accurate enough over a wide range of operating conditions, these multiphase
meters can be used in individual well testing and allocation measurement.
The traditional standard orifice meter shows quite decent accuracy only at the single
gas phase flow and the accuracy is very sensitive to the upstream flow condition. The gas
well contains many contaminations in the natural gas such as sand, water, etc. Thus the
standard orifice flow meter can not be effectively used in the offshore gas production
facility. In the beginning development of the slotted orifice flow meter, the first concept
was devised by Dr. Kenneth Hall and Dr. James Holste from the Department of Chemical
Engineering at Texas A&M University. At that stage, the slotted orifice flow meter was
used as a proportional flow splitter. Later, the slotted meter was evaluated as a flow
conditioner, then as a flow meter. In Dr. G.L. Morrison et al.’s work the slotted flow meter
was proven to reduce the pressure drop across the plate significantly compared to the
This thesis follows the style and format of the Journal of Turbomachinery.
2
orifice flow meter and to accommodate faster pressure recovery.[1,2]
The numerical analysis of the flow field and an experimental evaluation of the
slotted flow meter were performed by Morrison et al.[3] In their work, various proto types
of the slotted meter were analyzed as a flow conditioner. The numerical analysis of the
turbulence intensity and the mean axial velocity of the single phase flow were acquired for
the tube bundle and the slotted plate through 0D to 15D region. For the 1/8" thick uniform
porosity plate, which is comparable to the slotted plate flow meter, behaves similarly to the
19 tube bundle. However, the initial turbulence level is larger (12% compared to 6%) with
both showing a steady decrease to lower levels (4% and 2%) by X/D=13.5.
The slotted flow meter works as flow conditioner such as a conventional tube
bundle, and the performance as a flow conditioner was proven to exceed that of
conventional conditioner [4]. In Brewer’s works, he studied the location for differential
pressure taps. He used flange taps and 2.5D pressure taps for measureing differential
pressure. In this experiment, he showed that the accuracy in reading of pressure and
temperature for calculating the flow coefficient KY were not effected by the distance of
pressure tap from the slotted plate flow meter.[5] Thus, by using the same flow metering
facility for the standard orifice flow meter which uses flange pressure taps for measuring
differential pressure, the slotted plate can be used as ‘drop-in’ substitute for the standard
orifice flow meter.
The effects of the presence of liquid in the gas flow were studied by Dr. G.L.
Morrison et al.[6,7]. In their study, the slotted flow meter was proven to respond to two
phase flow in a predictable manner, which showed the relationship between the quality of
the mixture and pressure difference on the slotted flow meter and the response of the slotted
3
meter to the decreasing quality. Morrison et al suggested a universal calibration for the
slotted flow meter under various situations using only the Euler number (Eu) and the ratio
of β =AA
slot
pipe
The calibration curve of the slotted meter’s flow coefficient KY versus
Euler number was obtained by Flores[8] regardless of β value and flow condition (the type
of the pipe, the substances of the mixture, and etc.). In her works, she found that there is
one curve for relationship between KY, Eu number, and β . Moreover these results were
confirmed by showing that 9040 data points were fell onto a single curve. This curve is
shown in Figure 10.
In previous studies, the β =0.430 plate and β =0.467 plate (Figure 1 and Figure 2,
respectively) were suggested to be used as densitometer and volumetric flow meter,
respectively, or the flow conditioner and the mass flow meter, when these two plates are
used at the same time. The distance between these plates were also suggested as 5D in 2 in.
pipe test. In 5D distance they showed that the slotted flow meter showed great repeatability
and reproducibility. Recent studies at CEESI in high pressure, high Reynolds number
suggest the slot jets are not completely dissipating before encountering the downstream
plate. This indicates that 5D separation may be inadequate at high Reynolds numbers.
1.2. The objectives
The effects of the distance between two plates in series upon various factors which
are needed to aid the analysis of performance of slotted plate will be studied. Previous work
utilized a distance of 5D between two plates under the air, air/water, air/oil, and
air/water/oil flows. The analysis of data from the 0.467 plate showed some scattering in
4
discharge coefficient plot compared to that of the 0.430 plate which was installed 5D
upstream. Although the 0.467 plate has showed great repeatability, this scattering pattern in
the discharge coefficient induces suspicion that the first plate imposes certain effects on the
performance of the second plate. The scattering in discharge coefficient were also repeated
in other tests on the slotted flow meter. In this work, the distance between plates will be
increased to 10D and any change in discharge coefficient and the pressure recovery under
the single, two, and three phase flow will be analyzed. Also, a previously suggested flow
pattern map will be used in categorizing and comparison of scattering of data. To do so,
visual recording of flow under various conditions will also be referenced. The readings
from a water cut meter located downstream of the slotted plates will be compared to the
quality of the fluid obtained from the mass flow meter readings. Finally an uncertainty
analysis for two cases (5D and 10D case) will be performed.
5
II. THEORIES
2.1. Equations for data reduction
The flow facility used independently measures the flow rate of the gas and the
flowrate/density of the liquid. The two streams are then combined in the slotted meter run.
2.1.1. Mass flow rate of the air
Two different turbine flow meters are used simultaneously to measure the
volumetric flow rate &Q of the air. Then, from the perfect gas equation for dry air, the
density of the air is calculated
ρairair
air
PRT
= (1)
The equation (1) uses temperature and pressure measured between the two turbine flow
meter.
In this work, the compensation for density changes in turbine flow meter were
considered and using the volumetric flow rate and density of the air, the actual volumetric
flow rate is calculated.
&&
&. .
ab c
Q
actual =+ −ρ1 5 1 5
(2)
where a,b, and c are the empirical constants obtained from sonic nozzle calibrations of each
turbine flow meter.
The mass flow rate is given by:
& &m Qgas gas gas= ρ (3)
6
2.1.2. Quality
By the definition, the quality indicates the ratio of the mass flow rate of the gas
phase to the mass flow rate of the mixture (e.g. gas+liquid).
Xm
m mgas
gas liquid=
+
&
& & (4)
when the liquid mass flow rate is measured using Coriolis meters.
2.1.3. Mixture density
The mixture density can be calculated by using following eauation.
ρρ
ρρ
mixgas
gas
liquidX X
=+ −( )1
(5)
where the liquid density is measured by the Coriolis meters.
2.1.4. Mixture viscosity
The viscosity of the mixture is hard to calculated correctly, thus most previous
workers used a guess–based equation. Among the equations, the equation of Isbin et al. is
recommended, which has the same form as the equation for mixture density. [9]
µµ
µµ
mixgas
gas
liquidX X
=+ −( )1
(6)
where the gas and liquid viscosities are based upon the thermodynamic properties.
2.1.5. β ratio
The conventional definition of β ratio is the ratio of the diameter of the single
orifice hole to the diameter of the pipe. Although this definition is normally used for the
standard orifice flow meter, the slotted flow meter also uses this definition for geometric
7
property. Since the slotted flow meter has several holes instead of one concentric hole, the
β ratio is defined as
β =AA
slots
pipe. (7)
2.1.6. Superficial velocity
The superficial velocity is used for defining the flow pattern.
The superficial velocity of the gas phase is the velocity if the gas in the two-phase flow is
flowing along in single phase flow in the pipe.
Vsm
Agasgas
gas pipe
=&
ρ (8)
The superficial velocity of the liquid phase is the velocity if the liquid in the two-
phase flow is flowing along in single phase flow in the pipe.
Vsm
Aliqliq
liq pipe=
&
ρ (9)
2.1.7. Gas volume fraction
The gas volume fraction (GVF) is the time-averaged fraction of the pipe volume
which is occupied by the gas phase. In this work, the GVF is calculated by using the
volumetric flow rate of each phase at each location of interest. The volumetric flow rate of
the gas phase at certain position is
&&
qm
gasgas
gas=ρ
. (10)
Then the volumetric flow rate of the mixture at the same position as the gas phase is
&& &
qm m
mixgas liquid
mix=
+
ρ. (11)
8
The GVF is
α =&
&
gas
mix
. (12)
2.1.8. Flow coefficient, KY
The evaluation of the performance of the slotted plate is accomplished by
monitoring the flow coefficient KY. The assumptions used in calculating flow coeficient
are
· Steady state flow
· Incompressible flow ( ρ ρ ρslot pipe= = )
· No friction due to the small thickness of the slotted plate
· Uniform flow at the slots and right before the plate
· Horizontal orientation of the plate
Bernoulli’s equation for the above assumption is
P V P Vslot
slot
slot pipe
pipe
pipe
ρ ρ+ = +
2 2
2 2. (13)
and the continuity equation is
ρ ρslot slot slot pipe pipe pipeA V A V= . (14)
Using equations (13) and (14), one can calculate the velocity at the slot.
VP P
AA
slotpipe slot
slot
slot
=−
−
2
1 2
( )
( )ρ (15)
The theoretical mass flow in the pipe is
9
&m A
AA
Pthslots
slots
pipe
=
−⎛
⎝⎜
⎞
⎠⎟1
22
ρ∆ , where ∆P P Ppipe slot= − . (16)
However the empirical coefficient C is introduced since there is a decrepancy
between the real mass flow rate and theoretical mass flow. Hence the actual mass flow rate
is
& &m Cmactual th= . (17)
Plus, using the β ratio in equation (7), one obtains the real mass flow from the
following calculation.
&m CA
Pactualslot=−1
24β
ρ∆ . (18)
Also ( )A A Dslot pipe pipe= =β β π2 2 24 . (19)
The incompressibility assumption is somewhat invalid if the fluid of the interest is a
compressible gas. For this reason the expansion factor Y is introduced to equation (18).
Finally the actual mass flow rate can be calculated by following equation.
( )&m CY
DPactual
pipe=
−
π β
βρ
2
44 12 ∆ . (20)
In this work, the coefficient C and the β ratio are combined to make the flow
coefficient K.
KC
=−1 4β
(21)
The flow coefficient K and the expansion factor Y are combined and the equation
for KY is by
10
( )KY
m
D Pactual
pipe
=&
π β ρ4
21
2 ∆. (22)
Using the mass flow rate of the mixture of the gas phase and the liquid phase and
the mixture density, one obtains the KY value for the 2 phase flow.
( )KY
m
D Pmixactual mix
pipe mix
=& ,
π β ρ4
21
2 ∆ (23)
2.2. The flow pattern map
Extensive work has been performed to verify the mechanism which produces a
certain flow pattern for a certain flow condition. Hoogendoorn, Spedding and Nguyen,
Mandhane et al, Scott, and the first researcher on this field, Kosterin, suggested different
flow pattern maps using different parameters [10] . In their works, however, disagreements
were found on every flow pattern map. These problems were caused by different flow
conditions which each of the researchers were using and the subjective definition of the
flow pattern witnessed via a transparent pipe. This causes most of the problems and one can
easily say that,so far, there is no perfect flow pattern model for universal application.
Futhermore, these discrepencies were found mostly for the transition region.
In this study, two selected flow pattern models will be applied to the previous
experiments on the flow pattern analysis obtained in this facility for this particular flow
meter. Brewer and Sparks performed flow visualizations of the slotted flow meter.[5,11]
They used clear acrylic pipe with a slotted flow meter made of clear polycarbonate.
They investigated various flow conditions including two phase flow (air-water and air-oil).
11
In this work, the flow pattern maps of Kadambi [12] will be utilized. In his work, he
verified his maps with a series of experiments performed in 2-inch pipe which is the same
size pipe used in this work. This way the error caused by scaling the pipe size will be
eliminated. After watching flow visualization videos of Sparks and Brewer, only two kinds
of flow patterns were found-stratified with wavy flow or annular-mist flow. In Kadambi’s
work, these flow patterns were predicted via Figure 12. The transition between straified and
annular flow occurs over the curve shown in Figure 12. The flow patterns for this
experiment will be acquired by analyzing the flow visualization videos recorded by Brewer
and Sparks.[5, 11]
2.3. Uncertainty analysis
The series of uncertainty analyses were performed on the flow coefficient KY, and
those uncertainties were graphed versus many properties which shows the flow condition
(e.g. differential pressure, gas volume fraction, etc.). In this work, the uncertainty analysis
of Kline and McClintock was used [13] . Since the purpose of this uncertainty analysis is to
compare the effect of the distance between the plates upon the uncertainty, under the same
apparatus, the instrument’s uncertainty in the individual sensors will be ingnored. In other
word, since the same experimental device were used in both the 10D case and 5D case, the
bias errors which were brought by the sensors in measurement for the 5D and the 10D
distance case were assumed same. Also it was found that the uncertainty in the differential
pressure measurement was far larger than the instrument’s uncertainty which is maximum
0.224% of the full span. Therefore the instrument’s uncertainty is nigligible in this work.
Thus the comparison of uncertainties calculated by using Kline and McClintock’s method
12
bewtween two cases will be the comparison of the ramdom errors and unsteadiness of each
case.
The calculation of the uncertainty utilizes the following equation
wRv
wRv
wRv
wRn
n= + +( ) ( ) ( )∂∂
∂∂
∂∂1
12
22
2 2L (24)
where wR =uncertainty of the dependent variable.
R =the dependent variable
v n nn ( )= 1L =the independent variables
In this work, the independent variables for the calculation of the flow coefficient
KY are the pipe diameter DPipe , the beta ratioβ , the density of the mixture fluidρmix , the
mass flow rate of the mixture fluid &mmix , and the differential pressure ∆P . The uncertainty
equation for the flow coefficient KY is
wKY
Dw
KYw
KYw
KYm
wKY
PwKY
pipeD
mix mixm Ppipe mix mix
= + + + +( ) ( ) ( ) (&
) ( )&
∂∂
∂∂β
∂∂ρ
∂∂
∂∂β ρ
2 2 2 2 2
∆ ∆ . (25)
The individual derivatives in equation (25) are as follows:
∂∂ πβ ρ
KYD
mD Ppipe
mix
pipe mix
=−8
22 3
&
∆ (26)
∂∂β πβ ρKY m
D Pmix
pipe mix
=−8
23 2
&
∆ (27)
( )∂∂ρ πβ ρ
KY m P
D Pmix
mix
pipe mix
=−4
22 23
2
& ∆
∆ (28)
∂∂ πβ ρ
KYm D Pmix pipe mix&
=4
22 2 ∆ (29)
13
( )∂∂
ρ
πβ ρ
KYP
m
D Pmix mix
pipe mix∆ ∆
=−4
22 23
2
& (30)
The uncertainties of the independent variables are calculated by using the same
equation (25) except for the wDPipe. wDPipe
is the uncertainty in measuring the inner diameter
of the pipe. With the conventional vernier calipers, this uncertainty is set to ±0 001. in.
Flores[8] had performed the uncertainty analysis on her experiment, however, here in this
work, the thermodynamic properties are not of interest because it is assumed that there is no
phase change. Thus the calculation of the uncertainty of the gas density and liquid density
upstream of the plates are not calculated in the same way that Flores had used. The
uncertainty of the density of the gas is calculated by using perfect gas equation (1) and, for
the liquid density, the standard deviation from the densitometer in the Coriolis meter for the
liquid phase is used.
The normalized uncertainty,
PwC
C= × 100 (31)
where wC =uncertainty of the variable of the interset and C = the variable of the interest,
will be used to compare the results between the 5D and 10D distance case.
14
III. EXPERIMENTAL
3.1. Apparatus
The test facility in the Turbomachinery Laboratory was used. The test configuration
for the 5D-distance setting and the 10D-distance setting are basically same except for the
distance between plates. However, in this test, a water cut metering device from E.S.I.
(Environmental Sensor Incorporated) was added to the test facility. The schemetic diagram
of the facility for both cases are shown in Figure 7 and Figure 8, respectively. In this
section, the equipments and sensory devices will be described and listed.
3.1.1. Test rig
The 430 plate has a beta ratio of 0.430 and 467 plate has a 0.467 beta ratio. These
plates are made of 1/8 inch-thick stainless steel. The dimensions of both plates are show in
Figure 1 and Figure 2. These plates are placed between pipe spools which all have the same
dimensions. Each spool has length of 5D, is made of schedule stainless steel, and for the
spool which comes before or after slotted plate, pressure taps are present on the flanges at
1/2D from each end of the spool for measuring differential pressure (Figure 8).
Brewer showed that the position of the pressure taps for the measuring differential
pressure does not affect the accuracy of the calculation of the flow coefficient KY. The
venturi meter is placed inside the last two consecutive spools. This venturi meter is used for
calculating volume flow rate and velocity at the inlet of the watercut meter. There are
pressure taps upstream and at the throat of the venturi meter for measuring differential
pressure.
15
3.1.2. Data acquisition
The Data Acquisition System (DAS) includes an IBM PC (1), A/D converter, 4-
20mA current to 0-10V voltage converter, signal conditioner (DRN-FP model from the
Omega company) for converting the frequency output of the turbine meter to voltage output,
and IBM PC (2) for recording digital data from the Honeywell pressure transducers. Since
the type of the data stream from the Honeywell transducers are different than the other
signals from the sensory devices, a interpreter is needed to send the pressure data to IBM
PC(1). This job was performed by IBM PC(2) and the data was sent to IBM PC(1) via a
router. IBM PC (2) is used to collect the output data from the digital Honeywell transducers
(pressure and temperature) and write a row of data to the computer hard drive which consist
of those outputs. This row of data is read from the IBM PC (1) via direct LAN
communication (NetBIOS packet communication). The optimum condition for data
acquisition is for all the equipment to work at the same time. However, since this
experiment only involves steady state conditions followed by recording of the mean value
of each variables, the syncronyzation is not monitored. This equipment’s setup is shown in
Figure 5. IBM PC (1) is used to monitor output from every other sensory device via a
Labview program.
3.1.3. Control of flow of the fluids
Valve controllers are basically voltage potentiometers. The voltage output from the
potentiometer is converted into 4-20mA signal and sent to the valve and the shop air
pressurized with 14.7psi opens and closes the Masoneilan valve. Each potentiometer
controls one Masoneilan electro-pneumatic valve. Once the test point is determined, the
16
operator uses the potentiometers for setting the air mass flow rate, liquid mass flow rate,
and the line pressure.
A PID controller is used to achieve stable liquid flow rate. Due to the characteristics
of the plunger pump and the effect of the backpressure at the pump, the readings from the
Coriolis flow meter is not constant, even if the flow control valve is set to a certain position.
This controller reads the Coriolis flow meter’s output and sends a continuous DC voltage
output to the electro-pneumatic valve using preset P, I, and D values to diminish the
fluctuation on the Coriolis flow meter’s reading.
P,I, and D value settings were performed by watching the liquid flow rate while
changing P, I, and D values. As a setup procedure for P, I, and D controller, the arbitrary
liquid flow rate is set and the voltage output from the Coriolis meter is sent to the PID
controller and, by changing P, I, and D values, one will find optimum values which will
generate constant liquid flow rate. The schematic diagram for this control system is shown
in Figure 6.
3.1.4. Single phase flow
For test using only air, two oil-free Ingersoll-Rand air compressors supply air at
about 105 psig from a compressor facility outside to the laboratory facility through a 4 inch
pipe. The reason why the two compressors are used is that a single compressor can not
compress enough air for the required mass flow rate.
Once the air enters the laboratory facility, it is directed through a 2 inch rubber hose.
The air is then administered into a 2 inch stainless pipe which is connected to the test
facility. Between the test facility and the intake of air flow, there is a Masoneilan valve for
controlling volumetric flow rate of air going into the facility and 2 turbine meters in series
17
for measuring volumetric flow rate of the air. The test facility includes a series of stainless
spools which are the same dimension. In this test, 6 spools are used and the slotted plates
are place in designated points. The configuration of the test facility is shown in Figure 3
and Figure 4. After the 0.467 plate there is a venturi meter present upstream of the watercut
meter. This watercut meter was used throughout the test with the 10D-distance
configuration even for this single phase flow test.
3.1.5. Two phase flow
For the test using water-air two phase flow, the potable water line inside the Turbo
machinery Laboratory which has line pressure of 100psig was used. Although this facility
has a plunger pump which is capable of sending fluid with pressures of 1500psig, for a
stable supply of water, the facet water line was used, which will produce a more constant
liquid flow rate.
The water supply line includes two Coriolis mass flow meters, an electro-pneumatic
valve for control of mass flow rate, two needle valves for fine control of mass flow rate, a
magnetic flow meter for measuring volumetric flow rate of the water and a spool in the
meter run where the fluid is injected. Through the fluid injection spool, the water is injected
into the facility and sent through the six spools then exits to a reservoir tank outside the
building.
For the oil-air two-phase flow, SAE30 oil was used. The oil is caught in the
stainless tank outside the building and by using a plunger pump, the oil is sent to the test
facility through the same route as the water flow. The mass flow rate of oil is measured by
the same two Coriolis meters. In order to prevent contamination of the oil with water
already in the facility, oil was circulated in the facility and re-circulated for 1 hour. The
18
water stratified below the oil in the catch tank was drained. After that procedure the air-oil
two phase flow test was performed.
3.1.6. Three phase flow
The oil, water, and air were used for the three phase flow test. First, the oil and
water were poured into the stainless tank outside the building and mixed by the propeller
type mixer which is installed in the stainless tank.
From the experience from previous three phase flow test, the mixture of oil and
water will be a milky fluid which has higher viscosity and density between oil and water.
The plunger pump was used to pump the mixture to the facility.
3.2. Pressure measurement
Four pressure transducers are used. Two are from Honeywell Company and they are
digitally operating transducers. These transducers use a diaphragm to measure pressures
like conventional pressure transducers, but the digital processor inside the transducer
produces the digitized pressure reading so that no calibration is required except for zeroing.
These transducers are more sensitive to low differential pressure than the SMART 3051
pressure transducers from Rosemount Company which were used in previous studies. Thus
it is expected that these pressure transducers will produce more accurate differential
pressure readings, which will contribute to reducing the uncertainty in the KY calcuation.
According to the specifications of the Rosemount transducers, the pressure difference
should be above 1% of its full span. Because the relationship between pressure difference
and the voltage output below 1% of full span is different than that at the pressure range
above 1% of its full span. For example, among the Rosemount pressure transducers, the 18
19
psi (50 inches of water) span was the smallest range available at the laboratory. For this
transducer, the minimum pressure difference recordable is 0.018 psi (0.5 inches of water).
While the minimum pressure difference for the SMV 3000 Honeywell transducer is
0.003609 psi (0.1 inches of water). This means that this experiment can study lower
pressure difference with more accuracy in low pressure difference.
These two transducers are used to measure the differential pressure and absolute
pressure upstream of the each plate (Figure 4). One single variable digital output transducer
is used for measuring pressure difference produced by the venturi flow meter. One
analogue output pressure transducer is used to measure the air pressure at the turbine flow
meter.
3.3. Temperature measurement
Three T-type thermocouples are used for measuring air and mixture temperature.
The first thermocouple is placed between the Quantumn and Daniel gas turbine meters. It is
used to calculate the density of the air, so that one can calculate the mass flow rate of the air.
The second thermocouple is placed in the middle of the first spool connected to the front
face of the 430 plate. The third thermocouple is placed similarly to the second
thermocouple from the 467 plate (Figure 4). The second and third thermocouples measure
the temperature upstream of each plate to acquire the density of air or the mixture.
20
3.4. Mass flow rate measurement
3.4.1. Liquid flow rate
For the water and air two phase flow test, the magnetic flow meter is used for
measuring volumetric flow rate. Then the mass flow rate is calculated simply multiplying
the density of water which is already known (0.997805 g cm3 ).
Two Coriolis meters were used for measuring the mass flow rate of oil or water/oil
mixture. One is capable of handling 2 - 40 lbm/min with fluid densities from 0 - 5 g/cm3,
and the other one is for the flow rate of 0.1 - 3.30 lbm/min with the same density
measurement capability. These meters can also measure the density of the fluid. Since these
meters use analog voltage output, calibration is required. The flow rate calibration is
performed using a timer, a digital scale, and a bucket. This method can introduce a
significant amount of human error during the process, however multiple data points were
acquired and a linear calibration line drawn. Assuming that there is a perfect linear
relationship between flow rate and voltage output, the bad data points which are thought to
be originated from the human error and contribute making the R-Square correlation value
drop below 1 were discarded. After all, 10 data points were acquired making the R-Square
correlation value 1, the process was repeated for other Coriolis meter. The 2-point
calibration was used for the calibration of each Coriolis meter’s densitometer. The analog
voltage output is read while the meter is fully filled with standard SAE30 Oil then repeated
for pure water. The densities of these fluids are already known (SAE30 Oil:
0.888046 g cm3 , pure water: 0.997805 g cm3 ). The known densities for oil and water and
the voltage output make the density calibration line.
21
3.4.2. Air mass flow
The two turbine meters used for measuring the volumetric air flow rate are placed
upstream of the meter run. These are manufactured by Quantumn Company and Daniel
Company. The Quantumn turbine meter is capable of measuring 5 to 250 ACFM (actual
cubic feet per min) and Daniel meter has 10 to 100 ACFM capability. However, while
calibrating the Quantumn meter, the reading was found to be very unstable and inaccurate
in the range of 0 to 10 ACFM. To correct the inaccuracy in that range, the Daniel meter was
used concurrently and the outputs from both turbine meters were compared.
The calibration of these turbine meters were performed by utilizing a series of sonic
nozzles. The discharge coefficient and diameter of these nozzles were calibrated by a
certified facility (CEESI). When the velocity at the throat of the nozzle reaches Mach 1 and
chokes, by knowing the temperature and abolute pressure upstream of the nozzle, one can
compute the air mass flow rate or volumetric flow rate. The turbine meter is placed
upstream of the bank of the nozzles. The output voltage from the turbine meter is recorded
while the real volumetric flow rate from the turbine meter is also recorded. By generating a
linear relationship between the output voltage and the real volumetric flow rate, the
calibration curve (line) is acquired. Then the air density at the turbine meter is multiplied by
the volumetric flow rate from the turbine meter to obtain the air mass flow rate.
The instrument’s uncertainty of the turbine flow meter was calculated. The mass
flow rate acquired from the turbine flow meter and that from the sonic nozzle were
compared. The Quantumn turbine meter showed the uncertainty of 1.6% and Daniel turbine
meter showed 1.45%.
22
3.5. The water cut meter
The water cut meter from E.S.I. Company is used for metering the volumetric water
content level inside a water/oil flow. In this work, by placing this watercut meter
downsteam of the flow conditioner such as β =0.467 plate, one can achieve a homogenized
flow and the volumetric water content can be measured via above theory of operation of the
watercut meter. The effects of air in the meter will be investigated.
The electronic circuit inside the meter generates a stream of high-speed voltage
pulses and launches them into the coaxial transmission line sensor. Water flows through the
coaxial transmission line sensor which has a concentric pipe shape (Figure 9). The signal
generated from the eletric circuit passes through the coaxial sensor and returns to the
electric circuit. The electric circuit measures each round trip transit time of the 60,000,000
pulses a second. Then the averaged transit time of the 60,000,000 measurement is used to
calculate the volumetric water content inside the watercut meter. The transit time through
the coaxial transmission line sensor depends in part on the volumetric water content of the
fluid flow. With this relationship and a correction for the salinities of the fluid, the water
cut meter generates a digitized signal for the volumetric water content level within the fluid.
This signal is composed of 3 parts, the delay time caused by the presence of a fluid in the
sensing area, the time lag on the received sing-around pulse, and the calculated percent
water cut.
At first this meter was expected to yield the actual watercut level, but the watercut
meter produces an error message when gas is present. Nonetheless, all the digital data from
the watercut meter were recorded. The first two digitized data (transit time and the time lag)
are thought to be useful in analyzing flow characteristics. Although it was unable to
23
determine the direct watercut level from the waretcut meter, there seems to be a
relationship among the transit time, time lag, quality of the flow, and velocity of the flow.
This relationship will be discussed later in the results and discussion chapter.
3.6. Data sampling
The Data Acquisition System (DAS) includes an IBM PC (1), A/D converter, 4-
20mA current to 0-10V converter, signal conditioner (DRN-FP) for frequency output of the
turbine meter, and IBM PC (2) for recording a row of data from the Honeywell transducers.
IBM PC (1) is used to monitor output from every sensory device via Labview program
from National Instrument company. IBM PC (2) is used to collect the output data from the
digital Honeywell transducers (pressure and temperature) and to write a row of data to the
computer hard drive which consist of those outputs. This row of data is then read from the
IBM PC (1) via direct LAN communication (NetBIOS packet communication).
3.7. Procedures
The Labview program directly reads all analog data which is converted into digital
data via the A/D board in IBM PC (1). In the Labview program, the sampling was , at first,
done at the rate of 1 sample/second to synchronize all the data from IBM PC(1) to the
output of watercut meter, since the watercut meter was thought to generate new digital
output about once per second. However, due to the time requirement for averaging and
validating data in the water cut meter, the water cut meter does not generate its output data
exactly once per second, rather ranging from 1 data output per 0.90 second to 1.10second.
This caused a problem in synchronizing IBM PC(1) to the watercut meter. The solution was
24
to decrease sampling the rate to 0.92 second and for Labview program to check any error in
synchronization. Labview program records data on the output file only when there is no
error in synchronization. The processing of data from the Honeywell’s digital transducers
was accomplished through the IBM PC (2). This procedure doesn’t require any
synchronization since the data taken from Honeywell transducers are stored in a temporary
file on IBM PC (2). IBM PC (1) only needs to read that file whenever it is required.
The volumetric flow rate of air is measured from the two turbine flow meters. These
flow meters generate analog data in Hz. The DRN-FP device from OMEGA Engineering
company converts this frequency signal to DC voltage data, which is recorded by an A/D
board in IBM PC(1). Thermocouple data are directly recorded by the A/D board which also
processes a cold junction compensation circuit. The test points includes test under single
phase flow (air only), two phase flow (air-water, air-oil), and three phase flow (air-oil-
water).
3.7.1. Single phase flow test
The 430 plate and 467 plate are installed with a distance between them of 10 D. The
data points for this test have the same operating conditions as the test with 5 D distance
performed by Vasanth [14] and Ruiz [15]. The volumetric flow rate of air is changed while
maintaining the pressure upstream of the 0.430 plate.
The upper limits of volumetric air flow rate depend on the capability of the
compressor and upstream pressure. In this test, only two out of three compressors were
used due to the massive vibration on the air supply line when using all three compressors.
With the above settings, the Labview program commences sampling at the rate of 1 sample
per 0.92 second. The number of the total samples is 1600. First 800 samples are averaged
25
and the standard deviation is calculated then a second 800 samples are averaged and again
the standard deviation is calculated. Then first and second averages and standard deviations
are averaged. In the output file the averaged average, standard deviation, and error between
first and second standard deviation are recorded. Thus the total sampling time for 1 data
point will be 1600 seconds (27 minutes).
3.7.2. Two phase flow test
3.7.2.1. Water and air
In this test, the water and the air stream is joined inside the stainless spool. The
mass flow rate of water is maintained at the certain flow rate by using the PID controller.
Then the quality of the mixture fluid is altered by changing the volumetric air flow rate.
The data points for water and air two phase flow condition are shown in Table 1. Due to the
unstable mass flow rate of water at the low flow rate, quality near %0 was not achieved.
3.7.2.2. Oil and air
Oil has a higher viscosity compared to that of water, which causes the pressure drop
in the oil supply line to be large. As a result, the mass flow rate of oil is far lower than that
of water. Achieving a low quality (below %60) was not possible in this facility.
Furthermore, due to the unstable pump pressure of the plunger pump, a large number of
data points are required. By doing so, the risk of wrong judgments from the one data point
which represents unknown data region are thought to be diminished. The data points for oil
and air two phase flow condition are shown in Table 2.
3.7.3. Three phase flow test
In the three phase procedure, an oil and water mixture is injected into the air stream
in the test facility. By using a mixer inside the stainless tank overnight, a homogeneous
26
mixture with a density of 0.95g/cm3 is obtained. The characteristics of the resultant mixture
(viscosity, density, and etc.) will be different than that of oil or water. The viscosity of the
water/oil mixture was too large for the plunger pump used in this work to supply the fluid
with enough flow rate to the facility. As a result, the quality in this test could not go
below %50. The data points for three phase flow test are shown in Table 3.
27
IV. RESULTS AND DISCUSSION
In this section the comparison of the results between the β =430 plate and β =467
plate will be discussed. First the flow coefficient KY for the 5D case and 10D case will be
plotted versus a series of independent parameters, such as differential pressure, quality, and
upstream Reynolds number on one graph. How well data from the 5D and 10D cases
coincide with each other in this graph will show how much reproducibility the slotted plates
posses. If any irregularities are found, further investigations will be conducted, i.e. by
looking at the plots seperately for different flow patterns upstream of the β =430 plate.
Ruiz [15] has shown that the type of the liquid affects the performance of the slotted plate
and one can not force one universal equation on the relationship between KY and various
properties when dealing with different types of liquid. For this reason, when considering
the water-oil-air flow test, only the part of the 5D and 10D distance data which has the
same liquid density will be compared.
The water cut meter’s data will be analyzed. The digitized outputs from the water
cut meter, the transit time and the lag time will be considered independent parameters
which will be used in plotting the various properties of the flow such as quality, volumetric
flow rate of the gas, and so on. However, due to the high level of gas content, the water cut
meter produces on error message instead of the water cut value. Since the analysis of water
cut is unable to be conducted, the other outputs-transit time and lag time-will be analyzed.
In the final section, the uncertainty of the meter will be discussed. The uncertainty of the
flow coefficient KY is plotted versus differential pressure and the quality. Plus, the
normalized uncertainty of flow coefficient KY is calculated using following equation.
28
$ (%)wwKYKY
KY= × 100 (32)
The uncertainty is presented versus the differential pressure and the quality since the
uncertainty is most sensitive to the uncertainty in the differential pressure and mixture
density. Since the mixture density is a function of quality, as the quality is selected as an
independent parameter instead of the mixture density.
4.1. The comparison between 5D and 10D cases
4.1.1. Air-only flow condition
In Figures 13 and 15, the flow coefficient KY is plotted versus dP/P (differential
pressure divided by the absolute pressure measured upstream of the slotted plate) for
β =430 and β =467 plate, respectively for the 5D distance and 10D distance seperation.
For the air-only case, one can see that there is linear relationship between KY and dP/P.
The descending trends are due to the effects of compressibility. However, between dP/P of
0 and 0.025, the KY of β =430 plate flattens out while that of β =467 plate doesn’t. At low
dP/P, for β =467 plate, the linear relationship seems to be lost: for both 5D and 10D
distance case, scatter is found at low dP/P. Although it was expected that there would be a
good reproducibility for the β =430 plate and β =467 plate, as dP/P value becomes larger,
there is a noticible off-set. It is assumed that, for each plate, the small debris stuck in the
slot obstructs the flow causing different test condition. In fact, while changing the distance
from 5D to 10D, small debris were found in a number of slots. For β =467 plate, the scatter
is found over the entire dP/P range for 5D distance case while the scatter is smaller as dP/P
value increases the for the 10D distance case. For the reason for the difference of the flow
29
coefficient KY of the β =467 plate (Figure 18), many hypotheses were made. In Vasanth’s
work [14], it was found that, for the same differential pressure and the same line pressure
the slotted plate meter, possessed a higher flow coefficient KY if it is installed upstream of
another slotted plate. It was thought that the same effects is exerted on the slotted plate
which is downstream of another plate. However the largest percentage difference in the
flow coefficient of the slotted plate flow meter in this experiment was almost 2% which is
smaller than the uncertainty in the measurement which will be studied in a later section.
In Figures 14 and 16, KY is plotted versus upstream Reynolds number. In these
plots, the compressibility effects are shown, which is the wide variation on a given
Reynolds number. On the 3 dimensional graph of KY versus dP/P and Reynolds number,
the flow coefficient KY versus dP/P and Reynolds number make one smooth curve (Figure
19 through Figure 22).
It is found that the flow coefficient KY for the 5D distance case is systemically
higher than that for the 10D distance case. For the slotted plate downstream of another
slotted plate, the difference of the flow coefficient for the downstream plate between the 5D
distance case and the 10D distance case is larger than that for the upstream slotted plate. In
Figure 17, the difference between the flow coefficients of the β =430 plate for the 5D
distance and the 10D distance is shown in percentage value for the β =430 plate. In Figure
18, the same plot is shown for the β =467 plate. The difference of the flow coefficient of
the slotted plate meter in this work shows the maximum value of 0.8% for the β =430 plate
and 2.0% for the β =467 plate. It is assumed that the difference shown in Figure 17 for
30
β =430 plate could be caused by the difference in the ambient pressure for each case and
the slight difference in the installation of the β =430 plate for the 10D distance case.
4.1.2. Water and air flow condition
In Figure 23 and Figure 28 the flow coefficient KY is plotted versus gas volume
fraction (GVF). As shown in the figures, the GVF is almost 1.0 which indicates that the
volume of the gas phase is much larger than that of the liquid phase. Although the KY
value changes with very small changes of GVF, one can observe good reproducibility by
looking at the KY values which are collapsing into the one plot for both β =430 plate
(Figure 23) and β =467 plate (Figure 28). The flow coefficient KY steadily decreases as
the GVF value increase. This is a unique trend of the water-air flow condition compared to
that of oil-air which will be shown in next section.
In Figure 24 and Figure 29, for β =430 plate and β =467 plate, respectively, the
KY value is plotted versus normalized differential pressure, dP/P. These plot shows that,
above dP/P value of 0.05, there is good reproducibility between 5D case and 10D case. The
higher KY values shown at the low dP/P value region in the plot are where the Reynolds
numbers are less than 100,000 (Figure 26). The β =467 plate’s trends in Figure 29 shows
that both 5D and 10D case follows the same fashion as that of β =430: the wide variation
of flow coefficient at low dP/P. As dP/P value approaches to 0, the KY values diverge for
β =430 plate and β =467 plate. In fact, on a 2-D plot of the flow coefficient versus quality,
the diverging part in Figure 24 and Figure 29 correspond to the top edge part shown in
Figure 25 and Figure 30, respectively. It seems that there is large difference between 5D
distance and 10D distance case. However, if the 3 dimensional plot of KY versus dP/P and
31
quality is made (Figure 27 and Figure 32), two plots for both 5D and 10D distance case
collaps onto each other. From these relationships between KY, dP/P, and quality, one can
predict the KY value by knowing dP/P and quality of the flow.
In Figure 26 and Figure 31, the flow coefficient KY is plotted versus upstream
Reynolds number for β =430 plate and β =467 plate, respectively. In Figure 31 the flow
coefficient KY for the β =467 plate of the 10D distance case varies over a wider range at a
given Reynolds number than that for the β =430 plate of the 10D distance case (Figure 26).
While the flow coefficient KY for the β =430 plate and β =467 plate of the 5D distance
have a similar range of variation. It is supposed that these results may support the studies
from CEESI which have shown that, at high Reynolds numbers, the slot jets from the
upstream plate are not completely dissipating and have an effect on the β =467 plate.
4.1.3. Oil and air flow condition
In Figure 33 the flow coefficient KY for the β =430 plate continually decreases as
the GVF increases up to around GVF=0.998 . Then, above GVF=0.998, the flow
coefficient KY increases as the GVF increases. In Figure 38], the trends for the β =467
plate are different than that of β =430 plate. The flow coefficient values converge up to
around 0.998, then again the KY values increase as the GVF increases. In Figure 35 and
Figure 40, for β =430 plate and β =467 plate, the flow coeffficient KY decreases then
increases with the turning point at quality of 0.8 and 0.7, respectively. An interesting fact is
that the slotted plate acts totally different under oil-air flow conditions than under water-air
flow condition. Although the 5D distance data doesn’t cover the same range of values of
quality as 10D distance does, the data of 5D distance and 10 distance together produce one
32
consistent trend. This once again shows good reproducibility of the slotted plate flow meter.
This good reproducibility can be seen in Figure 34 and Figure 39. The data for the 5D
distance case and the 10D distance case together produce one trend. In fact, when the 3D
plot of KY versus dP/P and quality is shown (Figure 37 and Figure 42), the 5D distance
data and 10D distance data make one valley-shaped graph. However, the flow coefficient of
the β =430 plate make one 3-dimensional curve which has totally different shape than that
of β =467 plate. The flow coefficient of β =430 plate has a turning point: a change from
decreasing KY values to increasing of KY at a quality of 0.75. The plot of the flow
coefficient for β =467 plate versus quality shows that the value of KY (Figure 40) keeps
converging up to the point where quality is 0.70, then KY diverges up to where quality is
1.00. Interesting facts are seen in Figure 36 and Figure 41. In Figure 36 the flow coefficient
of β =430 plate is plotted versus upstream Reynolds number. It seems that for the 5D
distance, data steadily decrease. However the KY value for the 10D distance stays at a
certain range of value of KY as the Reynolds number increases. The flow coefficient KY
and Reynolds number for the 5D distance case and the 10D distance case produce an L-
shaped plot where the decreasing KY values stops at about Re=150000. The flat portion of
the plot of KY versus Reynolds number is where the GVF value is above 0.995. In other
words, as the GVF appoaches to 1.000, one or more parameters are needed to verify the
relationship between KY and Re. In Figure 41], the KY values for the β =467 plate for the
5D distance case keep increasing up to Re=200000, then the KY values decrease from that
point to Re=500000. However, again the KY values make flat portion throughout the entire
33
range of Reynolds number (from Re=200000 to Re=500000). This flat portion starts where
the GVF value is 0.998.
4.1.4. Water, oil and air flow condition
Unfortunately, when the data reduction for 10D distance test was done, it was found
that the liquid density was fluctuating with large amplitude. At first the liquid density was
0.952 g cm3 , and kept falling down to 0.933 g cm3 . Since there was no water added to the
liquid reservoir, it was assumed that there was evaporation of water or the oil-water mixture
was becomes stratified inside the reservoir tank. As a result, only part of the data were used
in this work. The liquid densities between 0.933 g cm3 and 0.940 g cm3 were used
because, in this range, the largest number of data for 5D distance case and 10D distance
case can be found. After all the data reduction, the number of data points were more or less
20 for both the 5D distance data and the 10D distance data, which is much smaller than that
of air-only, water-air flow, or oil-air flow. This is because, in addition to the contribution of
the variation of the liquid density, the facility used in this work would not work properly at
low quality due to the high viscosity of the water-oil mixture. The liquid supply unit which
is composed of reservoir tank, plunger pump, Coriolis flow meter, Masoneilan valve, and
supply line was not capable of pumping the high viscosity liquid at a high mass flow rate.
Although it is difficult to recognize the trends or the characteristics in the data due to the
small number of data points, the previous results from the oil-air flow case and the water-
air flow case were conferred and observations were made.
In Figure 43, the flow coefficient KY for the β =430 plate is plotted versus GVF.
As seen in the Oil-Air flow case, the flow coefficient KY decreases then increases with
34
increasing GVF. There is a turning point at GVF=0.9985 which is almost same as that for
the Oil-Air flow case. In Figure 47, for the β =467 plate, there is a pivot point at about
GVF=0.999, which is higher than that for the β =430 plate’s result (GVF=0.9985).
In Figure 44 and Figure 48, the flow coefficient KY is plotted versus dP/P. There is
no clearly discernable pattern, however it can be seen that the data for three phase flow
follows the general data trends of the oil-air flow condition. In Figure 44, the KY values
converge to one value as the dP/P value increases as was shown in Figure 34 for the oil and
air mixture. It is an interesting fact that both the β =430 plate and β =467 plate, under
three phase flow condition, have a similar trend as that for the oil and air flow conditions.
In Figure 45, the plot of flow coeffieicnt KY versus quality makes a ‘V’ shape as
the quality increases. This was previously observed for the oil-air flow condition. However,
in Figure 39, the flow coefficient KY plot changes very little as the quality increases
compared to that of the β =467 plate’s result shown in Figure 39 for the oil and air flow.
Also, the overall KY values are lower than for any other flow condition. The reason for this
small change in KY is hypothesized to be due to the high viscosity of the oil-water mixture.
The air flow is not afffected by the liquid phase flow. Because such a ‘sticky’ liquid phase
doesn’t consume the energy of the gas phase flow since there is not enough energy in the
gas phase to achieve atomization of liquid phase flow.
In Figure 46 and 50, the flow coefficient KY is plotted versus upstream Reynolds
number. Unfortunately, due to small number of samples, the pattern or the characteristics
are hard to identify any relationship between these figures and the figures for the oil-air
flow or the water-air flow condition.
35
4.2. The flow pattern map
A study of the video recordings of Brewer [5] and Sparks [11] show that the flow
patterns upstream of the β =430 plate were either stratified flow or annular flow. Although
the recognition of the stratified flow and the annular flow could be very subjective, there
existed definite flow patterns of stratified and annular flow and the sketchs for each flow
pattern from the Baker (1954)’s work [16] (Figure 11) were used to set the objective point
of view.
The stratified flow and annular flow regime exist next to each other in flow pattern
map of Kadambi (Figure 12). This flow pattern map was scanned and digitized to enable it
to be plotted with data from this study. Although the map of Kadambi is not a universal
flow pattern map, the verification of his theory was performed in a 2-inch pipe which is the
same pipe size as the one used in this experiment. Plus, the video recording of Sparks and
the flow pattern matched with the predicted flow pattern upstream of β =430 plate from the
Kadambi’s map. From this verification, the flow patterns of each data point in this
experiment can be predicted with high confidence. In Kadambi’s flow pattern map, the
parameters which are required to predict the flow pattern are the superficial velocity of the
gas phase and the liquid phase. These parameters can be calculated from the reading of the
necessary properties and the flow pattern upstream of β =430 plate can be predicted by
using the Kadambi’s map. However, the study of the video recording showed that the flow
pattern after the β =430 plate was always annular-mist flow generated by the first slotted
plate. This shows that the multi phase flow will be homogenized. This means that the flow
pattern prediction can not be used for any other region beyond the β =430 plate because of
36
the homogenization and atomization process which occurred in the slotted plate flow meter.
This was already predicted from the fact that the slotted plate will act as an atomizer for the
liquid phase, the prediction of flow pattern for the simple pipe flow will not work. Plus the
categorizing of the flow pattern for the region of any other region than the upstream of the
β =430 plate will not be necessary since, from the above facts, the flow pattern for the
region beyond the β =430 will be only annular-mist flow. Thus the effect of distance
between the plates will be considered for the different flow pattern upstream of the β =430
plate under water-air flow and oil-air flow conditions. By performing this analysis, the need
for another flow conditioner located upstream of β =430 plate will be discussed.
Unfortunately, as stated the previous section, the number of data points for the water, oil,
and air flow condition is too low to conduct this analysis. The flow pattern analysis for this
will not be performed for the water, oil, and air flow condition.
4.2.1. Water and air flow condition
The plot of flow coefficient KY versus dP/P of the β =430 plate, Figure 24, is
divided into two plots-Figure 51 and Figure 54. Each plot is for the upstream condition of
stratified and annular flow, respectively. It seems that the upstream condition doesn’t affect
the reproducibility under water and air flow condition. Figure 53 and Figure 56 show the
plot of KY versus quality for the two different upstream conditions. These data show that,
for both stratified and annular flow, the flow coefficient KY varies in the same range at the
a given quality no matter what upstream condition is involved. The relationship between
the flow coefficient KY and Reynolds number under different upstream conditions for the
β =430 plate and the β =467 plate (Figure 52, Figure 55, Figure 58, and Figure 62) doesn’t
37
show any irregularity on reproducibility under different upstream condition or distance
between the plates. Furthermore, at a given quality for the upstream condition of stratified
flow, the Reynolds number dependence was smaller than that for the upstream condition of
annular flow.
Figure 29, the plot of flow coefficient KY versus dP/P for the β =467 plate is
divided into Figure 57 and Figure 61 to investigate the effects of upstream flow condition.
In Figure 57, there are some discrepancies between the 5D distance case and the 10D
distance case below dP/P value of 0.1. This low dP/P region corresponds to the top edge
portion of Figure 59 - the plot of KY versus quality. These discrepancies are more apperent
when the 3-D plot of KY is generated (Figure 60). It is assumed that the reason for this
disagreement is either the revival of stratified flow after the β =430 plate or the lack of
homonization of water and air mixture at the β =430 plate under straitified flow condition.
4.2.2. Oil and air flow condition
In Figure 64 and Figure 65, for the β =430 plate, there are differences in the
relationship between KY and dP/P or KY and Reynolds number for the 5D distance case
and the 10D distance case. However these differences are caused by the difference in the
data flow condition. The data point for the 5D distance case covers dP/P value up to 0.06
while the 10D distance case covers up to 0.16 and each case covers a different region of
quality value (Figure 66). However, where the 5D distance data and the 10D distance data
are overlapping, the flow coefficient KY for the 5D distance seems to possess wider
variation of the KY values compared to the KY value of 10D distance case.
38
Figure 67 through Figure 69 show good reproducibility between the 5D case and the
10D case for the β =430 plate under the upstream condition of annular flow. In the limited
region in Figure 67, where the 5D distance case data and the 10D distance case are
overlapping, good reproducibility is revealed. As predicted, when the upstream condition is
more homogenious, well mixed mixture, the slotted plate shows better reproducibility.
As discussed above, for the upstream condition of stratified flow, the flow
coefficient calculation is somewhat vague because the flow coefficient KY for the 5D
distance case and the 10D distance case show different trends. For further detailed analysis,
experiments which have more overlapping data points than this work for the 5D distance
case and the 10D distance case under the upstream condition of straitfied flow are needed.
Additionally, a series of tests which are conducted with an additional flow conditioner (i.e.
tube bundles) upstream of β =430 plate could be utilized to compare the flow coefficient
KY calculation under the upstream condition of annular flow.
In Figure 70 through Figure 72, the flow coefficient KY of β =467 plate for the
upstream condition of stratified flow is plotted. While the flow coefficient KY of β =430
plate for the 10D distance does not follow the trend of the 5D distance case, that of β =467
plate for the 10D distance follows the trends for the 5D distance case. For the annular flow
condition (Figure 73 through Figure 75), the Reynolds number dependence is far less than
that for the upstream condition of stratified flowAs Brewer suggested in his work, this
Reynolds number dependence could be resulted from the slotted plate meter located
upstream of the β =467 plate. He found that the upstream slotted plate has less Reynolds
number dependence than that at the downsteam location does. However, under the
39
upstream condition of annular flow, the upstream plate shows larger Reynolds number
dependence. When considering the annular flow condition as a resultant flow from another
flow conditioner upstream of β =430 plate, there seems that a certain effect from the
upstream slotted plate exists.
4.3. The pressure drop-the permanent head loss
The pressure drop in the 2-inch pipe between the two slotted plate flow meters is
studied. The pressure drop is calculated as a overall pressure drop ( P∆ ) between two
slotted plates. Lockhart and Martinelli also studied and tried to set up an empirical
relationship between a pressure drop parameter (α ) and the Lockhart-Martinelli number
(X). However, the later studies showed that the relationship which was set by Lockhart and
Martinelli is valid only under very limited conditions.[13] Other than that, on each
application, the pressure drop should be studied with its own empirical relationship. Since
applying the expansive work such as that of Lockhart and Martinelli or other workers is out
of the scope of this study, only the pressure drop in terms of Reynolds number will be
analyzed.
In Figure 76, P∆ is plotted versus upstream Reynolds number for the air-only flow
condition. As shown in this plot, the 5D distance case has almost same degree of the
pressure drop as 10D distance case. As Reynolds number increases the pressure drop
increases, which is the same fact for the other flow conditions.
In Figure 77, P∆ is plotted versus Reynolds number for water and air flow
condition. The pressure drop for the 5D distance case is slightly higher than that for the
10D distance. It is interesting that, for Renolds numbers below 300,000 for the 10D
40
distance case of water and air flow condition, there are some points that have negative
pressure drop: the pressure upstream of the β =467 plate is higher than that of the β =430
plate. It is thought that this is due to the low Reynolds number effect and the flow pattern
upstream of the β =430 plate. As shown in Figure 78], most of negative pressure drop
points are residing in the stratificed upstream flow condition.
In Figure 79, P∆ is plotted versus Reynolds number for the oil and air flow
condition. Again in this plot, the pressure drop for the 5D distance case is high than that for
the 10D distance case, and the difference increases as the upstream Reynolds number
increases.
In Figure 80, the plot of P∆ versus Reynold number under the water, oil, and air
condition, the same facts (higher pressure drop for the 5D distance case and Reynolds
number dependence) can be found. It is assumed that this higer pressure drop for the 5D
distance case is due to the interaction between the small jets from the slots of the upstream
slotted plate meter and the relatively well developed flow downstream of the first plate. As
the upstream Reynolds number increases, the range of the effect of the jets from the slots
increases, which cause the region of the interaction downstream of the plate to be expanded.
This interaction could consume the total head and result in more permanent pressure head
loss.
4.4. The water cut meter analysis
The water cut meter calculates the water cut value in percentage unit. For instance,
if the volume fraction in the fluid is 50%, the water cut meter will indicate 50.00 as a
digitized output. The output could be as low as -0.5% and as high as 109.9%. A output of
41
the water cut meter of 110.0% is error message that indicates a condition which the water
cut meter can not calculate the water cut value due to a significant amount of entrained gas
bubbles. Of all test point, the water cut meter was used only in the 10D distance case and
the water cut meter generated a %110.0 message above a quality of %30. In the 10D
distance case, to achieve %30 quality, the air mass flow rate was too low to acquire
accurate air mass flow rate readings. According to the theory of operation of the water cut
meter, as the water cut level increases the delay time increases and the water cut is
calculated by using both delay time and rise time. It was found that the delay time ranges
from 300 picosecond to 1700 picosecond and the rise time is more or less 200 picosecond
from the other experiment that has valid output values from the water cut meter. However,
the delay time and rise time acquired in this work were all below 200 picosecond. Hence,
all of the data points, the water cut values acquired were %110.0. However, the water cut
meter-transit time (delay time) and lag time (rise time) were recorded and a series of plots
made relating quality to superficial velocity , transit time, and lag time. The superficial
velocity upstream of the watercut meter is that rate at which the gas bubbles flow through
the water cut meter. It is thought to be a crucial factor for the water cut meter to sense the
level of water content.
4.4.1. Water and air flow condition
In Figure 81 through Figure 83, contours of predicted quality and actual quality
versus superficial velocity and delay time. The actual quality shown in these plots are from
the actual quality measurement, and they are shown in small diamond shape dots filled with
color which represents quality. These plots are showing how the predicted quality is close
to the actual quality measured in this work. The predicted quality is claculated by utilizing a
42
3-dimensional curve fitting program and, among the suggested curve fit functions, the
function which the R-square correaltion value is nearest to 1 was selected. Also,
considering the fact that the delay time ranges up to 1700 pico second, the selection of
curve fit function was performed to cover the 0 to 1700 pico second delay time range. The
curve fit function selected in this work is shown in Table 5. In Figure 81, the contour plot
of quality for water and air flow condition, shows that there is a solid relationship between
quality, superficial velocity, and delay time. In this plot, the quality approaches to 1.0 far
before the delay time reaches 1700 pico second. Plus, when the superficial velocity is above
15 m/s, as the delay time increases, the rate of decrease of qulaity becomes to high, so that,
far before the delay time reaches 1700 picosecond range, the quality approaches 0.00. In
Figure 82, the contour plot of quality for water and air flow condition versus rise time and
superficial velocity is shown. Before the rise time reaches 200 picosecond level the quality
already reached 1.00 and. Then, although this is not shown in this plot, after the this peak of
quality, as the rise time increases the quality dereases. This means that the valid rise time is
located above this peak. Due to these problems the water cut meter could not sense the
level of water cut. The high flow rate of gas phase through the waer cut meter sensor
caused the delay time and the rise time to be too low for the water cut meter to calculate the
accurate water cut level.
4.4.2. Oil and air flow condition
In Figure 83, the contour plot of the predicted quality versus superficial velocity and
delay time for the oil and air flow condition is presented. This plot shows the delay time
range is lower than that for the water and air flow condition. Since the mixture of oil and air
does not contain any water, the water cut meter’s speed of signal is high and the delay time
43
in this case is too low for the water cut meter to calculate the accurate water cut level. In
Figure 84, the contour plot of the predicted quality versus superficial velocity and rise time
is presented. Since the rise time is dependent upon the salinity of the fluid, judging from the
almost same rise time range as that of the water and air case, the salinity in the fluid isn’t
different from that of the water and air case. This is already anticipated in that the water
that was used is fresh water and the oil is not supposed to contain any salt. However it is
also found that there is a solid relationship between the quality, superficial velocity and rise
time.
4.5. The uncertainty analysis
In this section the uncertainty analysis is performed. As stated above, this work will
compare the performance of the slotted plate flow meter under different conditions by
comparing the uncertainties which only use the standard deviation not the accuracies of
individual sensors. This means that the uncertainty of the metering facility and the
measurement of all the parameters which are needed for calculating the flow coefficient
KY will be calculated and the uncertainty of the slotted meter itself will not be carried out
in this section. The uncertainty of the parameters of the metering facility which are
identical for the 5D distance and 10D distance case are mostly not taken into account in the
calculation of the uncertainty.
According to the specification of the magnetic flow meter, the accuracy of the flow
meter is ±0.5% of the full span and this was taken into account in calculating the
uncertainty of the flow coefficient only for the water and air flow condition for the 10D
distance case. Other than that case, the instrument’s uncertainty of the Corioilis flow meter
44
was neglected since the same Corioilis meters were used. The normalized uncertainty of the
measurement calculated by using only standard deviation of the differential pressure is
found to be maximum 6% throughout the experiment. The accuracy of the differential
pressure transducer was 0.224% which was calculated by using following equation
according to the operation manual of Honeywell transducer.
%1001.0%2.02
2 •⎟⎟⎠
⎞⎜⎜⎝
⎛+=
OinHSpanOinHAccuracy (33)
The zero stability errors of the pressure transducers are not considered since the
same pressure transducers are used in both experiment and the zeroing of each pressure
dransducers is performed once for all. The uncertainty of the T-type thermocouple is 1K
(1.8F ) which is larger than the maximum value of the uncertainty in the measurement of
the temperature (0.749K). However the uncertianty of the thermocouple is also exclued
from the calculation of the uncertainty in this work since the two cases use the same
thermocouple. As stated in the previous section, the instrument’s uncertainty of the turbine
flow meter is 1.45%.
Flores showed that the uncertainty of the flow coefficient KY is most sensitive to
the uncertainty in the caculation of the beta ratio. [8] Although the same slotted plate
meters are used, the calculations of the uncertainty of the beta ratio are included in this
work to compensate the propagation of the uncertainty of the beta ratio. The uncertainty in
the measurement of the beta ratio was 0.004145.
The procedures and results of the calculation of the individual slotted plate flow
meter are shown in the works of Brewer [5] and Flores [8]. The Figure 85] through Figure
45
98] are showing the calculated uncertainty, and the Figure 99] through Figure 112] are
showing the normalized uncertainty.
4.5.1. The uncertainty of the flow coefficient for the β =430 plate
4.5.1.1. Air only flow case
In Figure 85, the uncertainties of the flow coefficietn KY for the 5D and 10D
distance cases for β =430 plate are presented. In this plot, one can see that the uncertainty
for the 5D case has a little bit higher uncertainty than that of 10D case. This difference is
small , but the normalized uncertainty for the 5D distance case (Figure 99]) shows some of
large difference regardless of dP/P value, while the normailzed uncertainty for the 10D
distance remains below 2% for the same range of dP/P value.
4.5.1.2. Water and air flow case
In Figure 87, the trends in the relationship between the uncertainty of the flow
coefficient and differential pressure for β =430 plate show that as the differential pressure
increases the uncertainty decreases. This is due to the differential pressure decreasing the
uncertainty in the measurement of differential pressure as it increases. However, it is
expected that, if the Rosemount 3051 pressure transducers were used, the overall
uncertainty will be higher than that for the Honeywell transducers.
The overall uncetainties are higher than that of air only flow case. This is due to the
added uncertainty from the liquid mass flow rate which has to be taken into account in
calculating the uncertainty of the flow coefficient. Plus the minimum normalized
uncertainty is as low as 2% for the 5D and 10D distance cases, which is the highest
uncertainty from the air only flow case.
46
Although it will be explained later in this section, the uncertainties of KY for the
10D distance case at low dP/P value is relatively higher than those of 5D distance case no
matter what kind of fluid is present. The first and second greatest contributor to the
calculation of KY are the uncertainty in measuring the β ratio of the slotted plate and the
mixture density [8]. Since the same slotted plates are used in the 5D distance test and the
10D distance test, the contribution of the uncertainty of the measurement of β ratio to the
calculation of the uncertainty of the flow coefficient is the same for both case. Thus the
uncertainty in the calculation of the mixture density is thought to be the one that contributes
most in making difference in the uncertainty of the flow coefficient KY between two cases.
It can be seen in Figure 89 that, for the same quality, the difference in the uncertainty can
be seen clearly. The magnetic flow meter is found to have a relatively more unstable than
the Coriolis mass flow meter in that the standard deviation from the magnetic flow meter is
much higher than that of the Coriolis flow meter and the accuracy stated in the manual is
higher than that of the Coriolis meter. This fact can be clearly seen when compared with
oil/air or oil/water/air flow condition where the Coriolis meter is used for the measurement
of mass flow rate of liquid. In the oil/air or the oil/water/air flow condition, the normailzed
uncertainties are about the same for both cases. However, it was not supposed that the
magnetic flow meter is at fault. Because the magnetic flow meter can measure only
volumetric flow rate and the mass flow rate is later calculated by multiplication of density
of the liquid to the volumetric flow rate. Here the density of the liquid is set to be constant
throughout the 10D distance water/air run, which prevent the mass flow rate calculation
from being corrected by utilizing the correct density that perturbs slightly. The large
sampling time is also blamed for the large uncertainty in calculation of quality or mixture
47
density. Because the calculation of the quality requires many stages of the calculation of
properties, the uncertainties from the other properties are concertrated in the calculation of
the quality and the large sampling time makes the standard deviation of the data large. In
fact, the standard deviation of the data at those irregular points which show large difference
in Figure 89 were rather higher than other data points. Furthermore, the differential
pressure measurements were found to be largely unstable at low dP/P values. Since the
measurement of low dP requires certain amount of sampling time during which the reading
is stable, the total sampling time which is much larger than this proper sampling time make
the standard deviation of measurement of dP large, which means the large sampling time
induced unecessary noise in the recording of the data. The normalized uncertainty of the
flow coefficient KY shown in Figure 101 and Figure 103 also show the same trends as the
plots of the uncertainty of the flow coefficient. Figure 102 and Figure 104 show the
normalized uncertainty for the 5D distance case it is a function of only a quality, while that
for the 10D distance case still shows a dispersed trends which is due to the large standard
deviation.
4.5.1.3. Oil and air flow case
In Figure 91, the uncertainty decreases as the differential pressure increases.
However, the overall uncertainty for both the 5D distance case and the 10D distance case is
lower than that for the water and air flow case. The interesting feature observed in Figure
93] is the two plots of uncertainty versus quality for the 5D and the 10D case collaps onto
one curve.
As quality increases the uncertainty decreases and, above a quality of %80, this
trend stops and the normalized unceratinty stays at 0.014. It is supposed that this occurs,
48
above a quality of %80 due to the hold-up of oil inside pipe being so small that the
characteristcs of two phase flow disappears and the flows is similar to that of air only flow.
In Figure 105 and Figure 106, the normalized uncertainty of the flow coefficient versus
dP/P and quality are shown. It seems that the normalized uncertainty is affected only by
quality since the plot of the uncertainty versus qulaity is one single curve. However the
normalized uncertainty for the 10D distance case is also higher than that for the 5D distance
case for a given quality.
4.5.1.4. Water, oil, and air flow case
In Figure 95, the uncertainty of the 10D case stays at constant level while the
normalized uncertainty of the 5D case decreases as the differential presssure keeps
increasing slightly. In Figure 97, it seems that the uncertainty follows the same trends as
that of oil and air flow condition. In Figure 110, the normalized uncertainty versus quality
plot shows that, again, the same trends as that of oil and air flow condition: the normailzed
uncertainty is a function of only a quality. The normailzed uncertainties for the 5D and the
10D case of the β =430 plate are the same at a given quality.
4.5.2. The uncertainty of the flow coefficient of β =467
4.5.2.1. Air only flow case
In Figure 86, the plot of uncertainty of the flow coefficient KY versus dP/P is made.
The normalized uncertainty of the β =467 plate is below 2.0%. The interesting fact is that
the trend of the uncertainty follows that of the flow coefficient KY. However the reason
why the uncertainty at the high dP/P is low is that the pressure transducers sense the
pressure difference with less accuracy when the pressure difference is small. In Figure 100,
49
it is shown that the normalized uncertainties for the 5D and the 10D distance case are
almost the same.
4.5.2.2. Water and air flow case
In Figure 88, the plot of the uncertainty of the flow coefficient KY versus dP/P is
shown. The uncertainty of the 10D distance case is much higher than that of the 5D
distance case compared to the results of the β =430 plate. This is partly due to the standard
deviation of the differential pressure measurement of the 10D distance case being almost 10
times higher than that of the 5D distance case. It is supposed that the higher standard
deviation of the differential pressure measurement is caused by the large sampling time.
Furthermore, since the magnetic flow meter was used only for the water and air flow
condition, it is supposed that the higher uncertainty than that of Coriolis mass flow meter
which was used in the 5D distance case will be a contributing factor. In Figure 90, the
relationship between the uncertainty and the quality is shown. Although the uncertainty of
the 10D distance case is much higher than that of the 5D distance case, some of the points
follow the trends of the 5D distance. Due to this high uncertainty, the calculation of the
uncertainty of the flow coefficient could have lower confidence, however the large number
of samples could diminish the noise in the calculation of the mean value of each parameter.
In Figure 103 and Figure 104, the normalized uncertainty shows the same trends as the
uncertainty plots (Figure 88 and Figure 90).
4.5.2.3. Oil and air flow case
In the oil and air flow condition, the Coriolis mass flow meter was used to measure
the oil flow rate. As a result, the overall uncertainty of the 10D distance case was very
similar to that of 5D distance. In Figure 92, as the uncertainties of the β =430 plate, as the
50
dP/P value increases the uncertainty of the 5D case decreases, while that of the 10D
distacnce case seems to stay at a constant value. An interesting fact is that the uncetainty of
the β =467 plate is lower than that of the β =430 plate. Plus, while the plot of the flow
coefficient KY for the β =467 plate seems to have more scatter than the β =430 plate,
actually the calculation of those flow coefficients were performed with lower uncertainty.
In Figure 108, the normalized uncertainty of the flow coefficient for both the 5D and the
10D distance case make one curve while the same plot of the β =430 plate shows that the
normalized uncertainty for the 10D case is higher than that for the 5D distance case.
4.5.2.4. Water, oil, and air flow case
In Figure 96, the plot of uncertainty versus dP/P for the β =467 plate is shown.
Although there are not many data points, there are trends which are very similar to that of
the β =430 plate. Furthermore, the overall uncertainty is at same level as the β =430 plate.
In Figure 98, the uncertainty versus quality for the β =467 plate is shown. The same trend
for the β =430 plate where the uncertainty decreases as the qulaity increases can be seen in
this plot. Also, the plot of the normailzed uncertainty versus quality shows the same trends
as that of β =467 plate under the oil and air flow condition. In Figure 111 and Figure 112,
the normalized uncertainty versus dP/P and quality, respectively, also shows sole
dependence of the normalized uncertainty upon quality.
51
V. SUMMARY AND CONCLUSIONS
The effects of the distance between two slotted plates were analyzed in many
aspects. The flow coefficient of the β =430 plate and the β =467 plate seems to be
independent to the distance between plates. In the air-only flow condition, the slotted plate
flow meter showed an off-set between the 5D and the 10D distance cases and the
differences were a maximum of 0.8% and 2.0% range for β =430 plate and β =467 plate,
respectively. For other flow conditions (water-air, oil-air, and water-oil-air), the 5D
distance case and the 10D distance case showed fair reproducibility even though the
scatters which original reason for this study were present for the 5D and the 10D distance
case. However, further investigation using the flow pattern map showed that the
reproducibility was affected by the upstream condition (stratified or annular flow).
The slotted plate showed best reproducibility under oil and air flow conditions. This was
due to low standard deviation in the recorded data and predictable results in the unceratinty
analysis.
The negative pressure drop which was shown in section 3, chapter IV was a
phenomenon which was very hard to explain. However, for every flow conditions, the
permanent pressure drop for the 5D distance case was higher than that for the 10D distance
case.
The water cut meter is a useful device for comparing the performance of the slotted
plate flow meter. However, most of the flow conditions did not meet the condition which
the meter requires. To prevent the “110.0%” error message, the experiment should be
conducted under low quality (below 0.3).
52
VI. RECOMMENDATIONS
In this work the data for the 5D distance case and the 10D distance case were not
quiet coincident. This kept the comparison from being perfromed under more detailed
anaylysis. This was caused by different conductors performing the experiment with
different points of view.
The flow pattern map for the water and air flow condition works well. However, for
the oil-air or the water-oil-air flow condition, further validation of the flow pattern map is
required. Although the density and the viscosity effects on the flow pattern map were
included in the flow pattern map according to Kadambi, no experimental substantiation was
provided. Flow visualization for the flow conditions other than water-air flow is required.
In this experiment, only one type of the configuration for the slotted plate (upstream plate:
β =430 plate, downstream plate: β =467 plate) was used. However, investigation of the
effects of β =430 plate or β =430 plate to the downstream plate at various distances will
clarify the doubt that the effects of the distance which were shown in this work could also
be due to the β =430 plate being upstream of β =467 plate.
In three phase flow condition, because the density of the fluid which were used in
the 5D distance case and 10D distance case were not matched in every data points, the
investigation of the effects was hard to perform. To prevent this problem, the density of the
fluid should be monitored at the end of each data acquisition process.
If the water cut meter were capable of operating at high quality, the detailed information on
the flow condition could be acquired. On other hand, for the low quality experiment, the
water cut meter will be a very useful device.
53
REFERENCES
[1] Morrison, G.L., Hall, K.R., Holste, J.C., De Otte, Jr, R.E., Macek, M.L., Ihfe, L.M.,
1994, “Slotted Orifice Flow Meter,” AIChE J. 40(10), pp. 1757-1760.
[2] Morrison, G.L., Hall, K.R., Holste, J.C., DeOtte Jr, R.E., Macek, M.L., Ihfe, L.M.,
Terracina, D.P., 1994, “Comparison of orifice and slotted plate flowmeters,” Flow
Meas. Instrum., 5(2), pp71-77.
[3] Morrison, G.L., Hall, K.R., Holste, J.C., Ihfe, L., Gaharan, C., DeOtte, Jr., R.E., 1997,
“Flow development downstream of a standard tube bundle and three different porous
plate flow conditioners,” Flow Meas. Instrum, 81(2), pp 61-76.
[4] Ihfe, L.M., 1994, “Development of slotted orifice flow conditioner,” M.S. Thesis,
Texas A&M University.
[5] Brewer, C.V., 1999, “Evaluation of the slotted orifice plate as a two-phase flow
meter,” M.S. Thesis, Texas A&M University.
[6] Morrison, G.L., Terracina, D., Brewer, C., Hall, K.R., 2001, “Response of a slotted
orifice flowmeter to an air/water mixture,” Flow Meas. Instrum., 12, pp. 175-180.
[7] Morrison, G.L., Hall, K.R., Brewer, C., Flores, A, 2002, “Universal slotted orifice
flow meter flow coefficient equation for single and two phase flow,” 5th Int. Flow
Symp. (Revised).
[8] Flores, A. E., 2000, “Response evaluation of a slotted orifice plate flow meter using
horizontal two phase flow,” M.S. Thesis, Texas A&M University.
[9] P.B. Whalley, 1996, Two-phase Flow and Heat Transfer, Oxford Science Publications,
New York.
54
[10] Hoogendoorn, C. J., 1959, “Gas-liquid flow in horizontal pipes,” Chemical
Engineering Science, 9, pp. 205-217.
[11] Sparks, S., 2004, “Two phase mixing comparison, oil contamination comparison and
manufacturing accuracy effect on calibration of slotted orifice meter,” M.S. Thesis,
Texas A&M University.
[12] Kadambi, V., 1982, “Stability of annular flow in horizontal tubes,” Int. J. Multiphase
Flow, 8(4), pp.311-328.
[13] Kline, S.J., McClintock, F.A., 1953, “Describing uncertainties in simple-sample
experiments,” Mechanical Engineering 1, pp. 3-10.
[14] Vasanth, M., 2003, “Response of a slotted plate flow meter to horizontal two-phase
flow,” M.S. Thesis, Texas A&M University.
[15] Ruiz, J.H., 2004, “Low differential pressure and multiphase flow measurements by
means of differential pressure devices,” Ph.D. dissertation , Texas A&M University.
[16] Baker, O., 1954, “Simultaneous flow of oil and gas,” The Oil and Gas Journal, 53, pp.
185-195.
55
APPENDIX A
Figure 1 Beta=0.430 plate
56
Figure 2 Beta=0.467 plate
57
MasoneilanValve
MasoneilanValve
Needle Valve
Ingersol Air Compressors
PlungerPump
ReservoirFor Liquid(Open Top)
Check Valve
Ball Valve
CoriolisMass Flow Meter
CoriolisMass Flow Meter
T
Thermocouple
FI
Turbine Flow Meter
Mixing Junction
TEST SECTION
Figure 3 Schematic diagram of the test facility
MasoneilanValve
Venturi
Beta=0.430 PlateBeta=0.467 Plate
WatercutMeter
To Reservoir
P
HoneywellPressure
Transducer
T
Thermocouple
T
Thermocouple
P
HoneywellPressure
Transducer
P
HoneywellPressure
Transducer
From the mixing junction
Figure 4 Detail diagram of the test section
58
IBM PC(2)
OPERATOR
P
Honeywell Pressure
Transducers
F
Coriolis MassFlow Meter
T
Thermocouples
FI
Turbine Flow Meters
Electro-pneumaticMasoneilan Valves
For Air Mass Flow Control
IBM PC(1)A/D Converter
Router
SignalConditioner
Potentiometer
Electro-pneumaticMasoneilan Valves
For Liquid Mass Flow Control
PID Controller
Figure 5 Data acquisition systems and flow control system
59
PID Controller
Signal
?
MasoneilanValve
Liquid Flow CoriolisMass Flow
Meter
Figure 6 Schematic diagram of PID control
Figure 7 Test rig setting for 10D distance
β =0.430 Plateβ =0.467 PlateThe water cut meter
5D Length Spool
Flow
Venturi (inside the 2 spools)
60
Figure 8 Test rig setting for 5D distance
Coaxial TransmissionLine Sensor
TransmittedPulse
EletronicCircuit
ReceivedPulse
StandardCoaxial Cables
Fluid Flow
Figure 9 Schematic block diagram of water cut sensor
Flow
Flange Pressure Tap
1/2D Pressure Tap Venturi
(inside the 2 spools)
61
Figure 10 Power law curve fit equation for calibration coefficient divided by Euler
number for 9040 data points
62
Figure 11 Sketch of flow pattern (Baker, 1954 [16])
1 10 100 1000Superficial Velocity ofGas Phase (m/s)
0.01
0.1
1
10
Sup
erfic
ial V
eloc
ity o
fLi
quid
Pha
se (m
/s)
Stratified Flow With Wavy Flow
Annular Flowor Annular Mist Flow
Figure 12 Flow pattern map for stratified flow and annular flow (Kadambi, 1982 [12])
63
0 0.1 0.2 0.3 0.4dP/P
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
Figure 13 Plot of flow coefficient KY of the β =430 plate versus DP/P for air-only
flow
64
100000 200000 300000 400000 500000Reynolds Number
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 14 Plot of flow coefficient KY of the β =430 plate versus Reynolds number for
air-only flow
65
0 0.1 0.2 0.3 0.4dP/P
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
Figure 15 Plot of flow coefficient KY of β =467 plate versus dP/P for air-only flow
66
100000 200000 300000 400000 500000Reynolds Number
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
5D Distance
10D Distance
Figure 16 Plot of flow coefficient KY of β =467 plate versus Reynolds number for air-
only flow
67
100000 200000 300000 400000 500000Reynolds Number
0
0.2
0.4
0.6
0.8
Per
cent
Diff
eren
ce (%
)
Figure 17 Plot of the difference between the KY of the β =430 plate for the 5D
distance and the 10D distance vs. upstream Reynolds number
68
100000 200000 300000 400000 500000Reynolds Number
0
0.4
0.8
1.2
1.6
2
2.4
Per
cent
Diff
eren
ce (%
)
Figure 18 Plot of the difference between the KY of the β =467 plate for the 5D
distance and the 10D distance vs. upstream Reynolds number
69
0 .72
50.
7 50 .
775
0.8
0.82
5Fl
owC
oeffi
cie n
t,K
Y
0
0.05
0.1
0.15
0.2dP/P
200000
300000
400000
500000
Reynolds Number
0.840.830.820.820.810.800.800.790.780.770.770.760.750.750.74
Figure 19 3D plot of KY of β=430 plate vs. Reynolds number and dP/P for 5D
distance case
70
0.65
0.7
0.75
0.8
0.85
Flow
Coe
ffici
ent,
KY
0
0.1
0.2
0.3dP/P
200000
300000
400000
500000
600000
Reynolds Number
0.860.850.830.820.810.790.780.770.750.740.720.710.700.680.67
Figure 20 3D plot of KY of β=467 plate vs. Reynolds number and dP/P for 5D
distance case
71
0.75
0.8
Flow
Coe
ffici
ent,
KY
0
0.05
0.1
0.15
0.2
dP/P
150000
200000
250000
300000
350000
400000
450000
Reynolds Number
0.830.830.820.810.800.800.790.780.780.770.760.750.750.740.73
Figure 21 3D plot of KY of β=430 plate vs. Reynolds number and dP/P for 10D
distance case
72
0.65
0.7
0.75
0.8
0.85
Flow
Coe
ffici
ent,
KY
0
0.1
0.2
0.3
dP/P
200000
300000
400000
Reynolds Number
0.860.850.830.820.810.790.780.770.750.740.720.710.700.680.67
Figure 22 3D plot of KY of β=467 plate vs. Reynolds number and dP/P for 10D
distance case
73
0.98 0.985 0.99 0.995 1Gas Volume Fraction
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y
10D Distance
5D Distance
Figure 23 Plot of flow coefficient KY β =430 plate versus GVF for water and air flow
74
0 0.05 0.1 0.15 0.2 0.25dP/P
0.6
0.8
1
1.2
1.4
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 24 Plot of flow coefficient KY β =430 plate versus dP/P for water and air flow
75
0.2 0.4 0.6 0.8 1Quality
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 25 Plot of flow coefficient KY β =430 plate versus quality for water and air
flow
76
0 200000 400000 600000Reynolds Number
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 26 Plot of flow coefficient KY β =430 plate versus Reynolds number for water
and air flow
77
Figure 27 3D plot of KY of the β=430 plate vs. dP/P and quality under water and air
flow condition
78
0.98 0.985 0.99 0.995 1Gas Volume Fraction
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, KY
10D Distance
5D Distance
Figure 28 Plot of flow coefficient KY β =467 plate versus GVF for water and air flow
79
0 0.1 0.2 0.3 0.4dP/P
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 29 Plot of flow coefficient KY β =467 plate versus dP/P for water and air flow
80
0 0.2 0.4 0.6 0.8 1Quality
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y
10D Distance
5D Distance
Figure 30 Plot of flow coefficient KY β =467 plate versus quality for water and air
flow
81
0 200000 400000 600000Reynolds Number
0.6
0.8
1
1.2
Flow
Coe
ffici
ent,
KY10D Distance
5D Distance
Figure 31 Plot of flow coefficient KY β =467 plate versus Reynolds number for water
and air flow
82
0.8
1
1.2
FlowC
o efficie nt.KY
0
0.1
0.2
0.3
dP/P
0.3 0.4 0.5 0.6 0.7 0.8 0.9Quality
0.860.850.830.820.810.790.780.770.750.740.720.710.700.680.67
5D Distance10D Distance
Figure 32 3D plot of KY of β=467 plate vs. dP/P and quality under water and air flow
condition
83
0.988 0.992 0.996 1Gas Volume Fraction
0.5
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 33 Plot of flow coefficient KY of β =430 plate versus GVF for oil and air flow
84
0 0.05 0.1 0.15 0.2 0.25dP/P
0.5
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
Figure 34 Plot of flow coefficient KY of β =430 plate versus dP/P for oil and air flow
85
0.4 0.6 0.8 1Quality
0.5
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 35 Plot of flow coefficient KY of β =430 plate versus quality for oil and air
flow
86
0 200000 400000 600000Reynolds Number
0.5
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 36 Plot of flow coefficient KY of β = 430 plate versus Reynolds number for oil
and air flow
87
0.65
0.7
0.75
0.8
0.85
F low
Co e
ffic i
e nt,
KY
0
0.05
0.1
0.15
0.2
dP/P
0.40.5
0.60.7
0.80.9
1
Quality
0.860.840.830.810.800.780.760.750.730.720.700.690.670.650.64
5D Distance10D Distance
Figure 37 3D plot of KY of β=430 plate vs. dP/P and quality under oil and air flow
condition
88
0.988 0.992 0.996 1Gas Volume Fraction
0.5
0.6
0.7
0.8
Flow
Coe
ffici
ent,
KY10D Distance
5D Distance
Figure 38 Plot of flow coefficient KY of β = 467 plate versus GVF for oil and air flow
89
0 0.1 0.2 0.3dP/P
0.5
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 39 Plot of flow coefficient KY of β = 467 plate versus dP/P for oil and air flow
90
0.4 0.6 0.8 1Quality
0.5
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 40 Plot of flow coefficient KY of β = 467 plate versus quality for oil and air
flow
91
0 200000 400000 600000Reynolds Number
0.5
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 41 Plot of flow coefficient KY of β = 467 plate versus Reynolds number for oil
and air flow
92
0.6
0.65
0.7 FlowC
oefficien t,KY
00.1
0.2
dP/P
0.5
0.75
1
Quality
0.730.720.710.700.690.680.670.650.640.630.620.610.600.590.58
5D Distance10D Distance
Figure 42 Plot of KY of β=467 plate vs. dP/P and quality under oil and air flow
condition
93
0.997 0.998 0.999 1 1.001Gas Volume Fraction
0.45
0.5
0.55
0.6
0.65
0.7
Flow
Coe
ffici
ent,
KY
10D distance
5D distance
Figure 43 Plot of flow coefficient KY of β = 430 plate versus GVF for water, oil and
air flow
94
0 0.05 0.1 0.15 0.2 0.25dP/P
0.4
0.5
0.6
0.7
0.8
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 44 Plot of flow coefficient KY of β = 430 plate versus dP/P for water, oil and
air flow
95
0.4 0.6 0.8 1Quality
0.4
0.5
0.6
0.7
0.8
Flow
Coe
ffici
ent,
KY10D Distance
5D Distance
Figure 45 Plot of flow coefficient KY of β = 430 plate versus quality for water, oil and
air flow
96
0 100000 200000 300000 400000 500000Reynolds Number
0.4
0.5
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY10D Distance
5D Distance
Figure 46 Plot of flow coefficient KY of β = 430 plate versus Reynolds number for
water, oil and air flow
97
0.997 0.998 0.999 1 1.001Gas Volume Fraction
0.4
0.5
0.6
0.7
0.8
Flow
Coe
ffici
ent,
KY10D Distance
5D Distance
Figure 47 Plot of flow coefficient KY of β = 467 plate versus GVF for water, oil and
air flow
98
0 0.1 0.2 0.3dP/P
0.4
0.5
0.6
0.7
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 48 Plot of flow coefficient KY of β = 467 plate versus dP/P for water, oil and
air flow
99
0.4 0.6 0.8 1Quality
0.4
0.5
0.6
0.7
0.8
0.9
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 49 Plot of flow coefficient KY of β = 467 plate versus quality for water, oil and
air flow
100
0 100000 200000 300000 400000Reynolds Number
0.4
0.5
0.6
0.7
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 50 Plot of flow coefficient KY of β = 467 plate versus Reynolds number for
water, oil and air flow
101
0 0.05 0.1 0.15 0.2 0.25dP/P
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 51 Plot of flow coefficient of β = 430 plate vs. dP/P for water and air flow
(stratified flow)
102
0 200000 400000 600000Reynolds Number
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 52 Plot of flow coefficient of β = 430 plate vs. Reynolds number for water and
air flow (stratified flow)
103
0.2 0.4 0.6 0.8 1Quality
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 53 Plot of flow coefficient of β = 430 plate vs. quality for water and air flow
(stratified flow)
104
0 0.1 0.2 0.3 0.4dP/P
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 54 Plot of flow coefficient of β = 430 plate vs. dP/P for water and air flow
(annular flow)
105
0 200000 400000 600000Reynolds Number
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 55 Plot of flow coefficient of β =430 plate vs. Reynolds number for water and
air flow (annular flow)
106
0.2 0.4 0.6 0.8 1Quality
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 56 Plot of flow coefficient of β = 430 plate vs. quality for water and air flow
(annular flow)
107
0 0.1 0.2 0.3 0.4dP/P
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 57 Plot of flow coefficient of β =467 plate vs. dP/P for water and air flow
(stratified flow)
108
0 200000 400000 600000Reynolds Number
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 58 Plot of flow coefficient of β =467plate vs. Reynolds number for water and
air flow(stratified flow)
109
0.2 0.4 0.6 0.8 1Quality
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 59 Plot of flow coefficient of β =467 plate vs. quality for water and air flow
(stratified flow)
110
0.7
0.8
0.9
1
1.1
1.2
Flow
Co e
ffic i
ent ,
KY
0.250.5
0.75
Quality
0
0.1
0.2
0.3
dP/P
1.161.121.091.051.020.980.950.910.880.850.810.780.740.710.67
10D Distance5D Distsance
Figure 60 Plot of KY of β=430 plate vs. dP/P and quality under water and air flow
condition (stratified flow)
111
0 0.05 0.1 0.15 0.2 0.25dP/P
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 61 Plot of flow coefficient of β =467 plate vs. dP/P for water and air flow (annular flow)
112
0 200000 400000 600000Reynolds Number
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 62 Plot of flow coefficient of β =467 plate vs. Reynolds number for water and
air flow (annular flow)
113
0.2 0.4 0.6 0.8 1Quality
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y10D Distance
5D Distance
Figure 63 Plot of flow coefficient of β =467 plate vs. quality for water and air flow
(annular flow)
114
0 0.04 0.08 0.12 0.16 0.2dP/P
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 64 Plot of flow coefficient of β =430 plate vs. dP/P for oil and air flow
(stratified flow)
115
0 100000 200000 300000 400000 500000Reynolds Number
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 65 Plot of flow coefficient of β =430 plate vs. Reynolds number for oil and air
flow (stratified flow)
116
0.2 0.4 0.6 0.8 1Quality
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 66 Plot of flow coefficient of β =430 quality for oil and air flow (stratified
flow)
117
0 0.1 0.2 0.3dP/P
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 67 Plot of flow coefficient of β =430 plate vs. dP/P for oil and air flow (annular
flow)
118
0 200000 400000 600000Reynolds Number
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 68 Plot of flow coefficient of β =430 plate vs. Reynolds number for oil and air
flow (annular flow)
119
0.2 0.4 0.6 0.8 1Quality
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 69 Plot of flow coefficient of β =430 plate vs. quality for oil and air flow
(annular flow)
120
0 0.05 0.1 0.15 0.2 0.25dP/P
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 70 Plot of flow coefficient of β =467 plate vs. dP/P for oil and air flow
(stratified flow)
121
0 100000 200000 300000 400000 500000Reynolds Number
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 71 Plot of flow coefficient of β =467 plate vs. Reynolds number for oil and air
flow (stratified flow)
122
0.2 0.4 0.6 0.8 1Quality
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 72 Plot of flow coefficient of β = 467 plate vs. quality for oil and air flow
(stratified flow)
123
0 0.1 0.2 0.3dP/P
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 73 Plot of flow coefficient of β =467 plate vs. dP/P for oil and air flow (annular
flow)
124
0 200000 400000 600000Reynolds Number
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 74 Plot of flow coefficient of β =467 plate vs. Reynolds number for oil and air
flow (annular flow)
125
0.2 0.4 0.6 0.8 1Quality
0.5
0.6
0.7
0.8
0.9
1
Flow
Coe
ffici
ent,
KY
10D Distance
5D Distance
Figure 75 Plot of flow coefficient of β =467 plate vs. quality for oil and air flow
(annular flow)
126
0 200000 400000 600000Reynolds Number
0
4
8
12
16
Pre
ssur
e D
rop-
P (p
si)
10D Distance
5D Distance
Figure 76 Plot of the permanent pressure loss P∆ vs. Reynolds number for air-only
flow condition
127
0 200000 400000 600000Reynolds Number
0
10
20
30
Pre
ssur
e D
rop-
P (p
si)
10D Distance
5D Distance
Figure 77 Plot of the permanent pressure loss P∆ vs. Reynolds number for water/air
flow condition
128
0 200000 400000 600000Reynolds Number
0
10
20
30
Pre
ssur
e D
rop-
P (p
si)
Stratified-10D
Annular-10D
Figure 78 Plot of the permanent pressure loss P∆ vs. Reynolds number for water and
air flow condition under the upstream condition of stratified flow and annular flow
129
0 200000 400000 600000Reynolds Number
0
4
8
12
16
20
Pre
ssur
e D
rop-
P (p
si)
10D Distance
5D Distance
Figure 79 Plot of the permanent pressure loss P∆ vs. Reynolds number for oil/air flow
condition
130
0 200000 400000 600000Reynolds Number
0
4
8
12
16
20
Pre
ssur
e D
rop-
P (p
si)
10D Distance
5D Distance
Figure 80 Plot of the permanent pressure loss P∆ vs. Reynolds number for
water/oil/air flow condition
131
Delay Time (pico second)
Sup
erfic
ialV
eloc
ity(m
/s)
60 80 100 120 140
10
20
30
40
1.000.940.880.820.760.700.640.590.530.470.410.350.290.230.17
Quality
Figure 81 Contour plot of quality vs. superficial velocity and delay time for water and
air flow
Rise Time (pico second)
Sup
erfic
ialV
eloc
ity(m
/s)
110 120 130 140
10
15
20
25
30
35
40
1.000.950.890.840.790.730.680.620.570.520.460.410.360.300.25
Quality
Figure 82 Contour plot of quality vs. superficial velocity and rise time for water and air
flow
132
Delay Time (pico second)
Sup
erfic
ialv
eloc
ity(m
/s)
40 50 60 70 805
10
15
20
1.000.980.940.930.900.870.860.830.800.790.760.720.710.690.650.640.610.580.570.540.510.500.470.43
Quality
Figure 83 Contour plot of quality vs. superficial velocity and delay time for oil and air
flow
Rise Time (pico second)
Sup
erfic
ialv
eloc
ity(m
/s)
110 120 130 140 1505
10
15
20
25
0.990.960.940.910.890.860.840.810.790.760.740.710.690.660.64
Quality
Figure 84 Contour plot of quality vs. superficial velocity and rise time for oil and air
flow
133
0 0.05 0.1 0.15 0.2 0.25dP/P
0.014
0.015
0.016
Unc
erta
inty
, wKY
10D Distance
5D Distance
Figure 85 Plot of uncertainty of KY of β =430 plate vs. dP/P for air-only flow
134
0 0.1 0.2 0.3 0.4dP/P
0.012
0.014
0.016
Unc
erta
inty
, wKY
10D Distance
5D Distance
Figure 86 Plot of uncertainty of KY of β =467 plate vs. dP/P for air-only flow
135
0 0.05 0.1 0.15 0.2 0.25dP/P
0.01
0.02
0.03
0.04
0.05
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 87 Plot of uncertainty of KY of β =430 plate vs. dP/P for water and air flow
136
0 0.1 0.2 0.3dP/P
0.04
0.08
0.12
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 88 Plot of uncertainty of KY of β =467 plate vs. dP/P for water and air flow
137
0.2 0.4 0.6 0.8 1Quality
0.01
0.02
0.03
0.04
0.05
0.06
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 89 Plot of uncertainty of KY of β =430 plate vs. quality for water and air flow
138
0 0.2 0.4 0.6 0.8 1Quality
0.4
0.6
0.8
1
1.2Fl
ow C
oeffi
cien
t, K
Y
10D Distance
5D Distance
Figure 90 Plot of uncertainty of KY of β =467 plate vs. quality for water and air flow
139
0 0.05 0.1 0.15 0.2 0.25dP/P
0
0.01
0.02
0.03
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 91 Plot of uncertainty of KY of β =430 plate vs. dP/P for oil and air flow
140
0 0.1 0.2 0.3dP/P
0
0.01
0.02
0.03
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 92 Plot of uncertainty of KY of β =467 plate vs. dP/P for oil and air flow
141
0.4 0.6 0.8 1Quality
0
0.01
0.02
0.03
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 93 Plot of uncertainty of KY of β =430 plate vs. quality for oil and air flow
142
0.4 0.6 0.8 1Quality
0
0.01
0.02
0.03
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 94 Plot of uncertainty of KY of β =467 plate vs. quality for oil and air flow
143
0 0.1 0.2 0.3dP/P
0
0.01
0.02
0.03
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 95 Plot of uncertainty of KY of β =430 plate vs. dP/P for water, oil, and air
flow
144
0 0.1 0.2 0.3dP/P
0
0.01
0.02
0.03
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 96 Plot of uncertainty of KY of β =467 plate vs. dP/P for water, oil, and air
flow
145
0.4 0.6 0.8 1Quality
0
0.01
0.02
0.03
Unc
erta
inty
, wK
Y10D Distance
5D Distance
Figure 97 Plot of uncertainty of KY of β =430 plate vs. quality for water, oil, and air
flow
146
0.4 0.6 0.8 1Quality
0
0.01
0.02
0.03
Unc
erta
inty
, wKY
10D Distance
5D Distance
Figure 98 Plot of uncertainty of KY of β =467 plate vs. quality for water, oil, and air
flow
147
0 0.05 0.1 0.15 0.2 0.25dP/P
0
0.01
0.02
0.03
Nor
mal
ized
Unc
erta
inty
, wK
Y/K
Y10D Distance
5D Distance
Figure 99 Plot of the normalized uncertainty of KY of β =430 plate vs. dP/P for air-
only flow
148
0 0.1 0.2 0.3 0.4dP/P
0.0183
0.0184
0.0185
0.0186
Nor
mal
ized
Unc
erta
inty
, wK
Y/K
Y10D Distance
5D Distance
Figure 100 Plot of the normalized uncertainty of KY of β =467 plate vs. dP/P for air-
only flow
149
0 0.05 0.1 0.15 0.2 0.25dP/P
0.01
0.02
0.03
0.04
0.05
Nor
mal
ized
Unc
erta
inty
, wK
Y/K
Y10D Distance
5D Distance
Figure 101 Plot of the normalized uncertainty of KY of β =430 plate vs. dP/P for water
and air flow
150
0.2 0.4 0.6 0.8 1Quality
0.01
0.02
0.03
0.04
0.05
0.06
Nor
mal
ized
Unc
erta
inty
, wK
Y/K
Y10D Distance
5D Distance
Figure 102 Plot of the normalized uncertainty of KY of β =430 plate vs. quality for
water and air flow
151
0 0.1 0.2 0.3dP/P
0.04
0.08
0.12
0.16
Nor
mal
ized
Unc
erta
inty
, wK
Y/K
Y10D Distance
5D Distance
Figure 103 Plot of the normalized uncertainty of KY of β =467 plate vs. dP/P for water
and air flow
152
0.2 0.4 0.6 0.8 1Quality
0.04
0.08
0.12
0.16
Nor
mal
ized
Unc
erta
inty
, wK
Y/K
Y5D Distance
10D Distance
Figure 104 Plot of the normalized uncertainty of KY of β =467 plate vs. quality for
water and air flow
153
0 0.05 0.1 0.15 0.2 0.25dP/P
0.016
0.02
0.024
0.028
0.032
Nor
mal
ized
Unc
erta
inty
, wK
Y/KY
10D Distance
5D Distance
Figure 105 Plot of the normalized uncertainty of KY of β =430 plate vs. dP/P for oil
and air flow
154
0.4 0.6 0.8 1Quality
0
0.01
0.02
0.03
Nor
mal
ized
Unc
erta
inty
, wK
Y/K
Y10D Distance
5D Distance
Figure 106 Plot of the normalized uncertainty of KY of β =430 plate vs. quality for oil
and air flow
155
0 0.1 0.2 0.3dP/P
0
0.01
0.02
0.03
Nor
mal
ized
Unc
erta
inty
, wK
Y/K
Y
10D Distance
5D Distance
Figure 107 Plot of the normalized uncertainty of KY of β =467 plate vs. dP/P for oil
and air flow
156
0.4 0.6 0.8 1Quality
0
0.01
0.02
0.03
Nor
mal
ized
Unc
erta
inty
, wK
Y/KY
10D Distance
5D Distance
Figure 108 Plot of the normalized uncertainty of KY of β =467 plate vs. quality for oil
and air flow
157
0 0.1 0.2 0.3dP/P
0
0.01
0.02
0.03
Nor
mal
ized
Unc
erta
inty
, wK
Y/KY
10D Distance
5D Distance
Figure 109 Plot of the normalized uncertainty of KY of β =430 plate vs. dP/P for water,
oil, and air flow
158
0.4 0.6 0.8 1Quality
0
0.01
0.02
0.03
Nor
mal
ized
Unc
erta
inty
, wK
Y/K
Y10D Distance
5D Distance
Figure 110 Plot of the normalized uncertainty of KY of β =430 plate vs. quality for
water, oil, and air flow
159
0 0.1 0.2 0.3dP/P
0
0.01
0.02
0.03
Nor
mal
ized
Unc
erta
inty
, wKY
/KY
10D Distance
5D Distance
Figure 111 Plot of the normalized uncertainty of KY of β =467 plate vs. dP/P for water,
oil, and air flow
160
0.4 0.6 0.8 1Quality
0
0.01
0.02
0.03
Nor
mal
ized
Unc
erta
inty
, wKY
/KY
10D Distance
5D Distance
Figure 112 Plot of the normalized uncertainty of KY of β =467 plate vs. quality for
water, oil, and air flow
161
APPENDIX B
TABLE 1 Single phase test points Upstream Pressure (psi) Volumetric Air Flow Rate ( min/3ft )
80 80, 70, 60, 50, 40, 30, 20
60 80, 70, 60, 50, 40, 30, 20
40 60, 50, 40, 30, 20
30 45, 40, 30, 20
20 35, 30, 20
162
TABLE 2 Two phase flow test points (water and air) Quality(%) Upstream Pressure (psi) Volumetric Air Flow Rate ( min/3ft )
80 60, 50, 40, 30, 20
60 60, 50, 40, 30, 20 50
40 40, 30, 20
80 80, 70, 60, 50, 40, 30, 20
60 80, 70, 60, 50, 40, 30, 20
40 70, 60, 50, 40, 30, 20 57
30 45, 40, 30, 20
80 80, 70, 60, 50, 40, 30, 20
60 67, 60, 50, 40, 30, 20 70
40 50, 40, 30, 20
80 80, 70, 60, 50, 40, 30, 20
60 70, 60, 50, 40, 30, 20 80
40 53, 40, 30, 20
80 80, 70, 60, 50, 40, 30, 20
60 70, 60, 50, 40, 30, 20 90
40 55, 50, 40, 30, 20
163
TABLE 3 Two phase test points (oil and air) Quality(%) Upstream Pressure (psi) Volumetric Air Flow Rate ( min/3ft )
80 50, 40, 30, 20
70 60, 50, 40, 30, 20
60 50, 40, 30, 20
50 40, 30, 20
40 37, 30, 20
30 27, 20
60
20 20
80 70, 60, 50, 40, 30, 20
70 60, 50, 40, 30, 20
60 53, 50, 40, 30, 20
50 40, 30, 20
40 40, 30, 20
30 30, 20
70
20 25, 20
80 70, 60, 50, 40, 30, 20
70 60, 50, 40, 30
60 60, 50, 40, 30, 20
50 50, 40, 30, 20
40 40, 30, 20
30 30
80
20 20
80 80, 70, 60, 50, 40, 30, 20
70 70, 60, 50, 40, 30
60 60, 50, 40, 30, 20
50 50, 40, 30, 20
40 40, 30, 20
30 30, 20
90
20 20
164
Quality(%) Upstream Pressure (psi) Volumetric Air Flow Rate ( min/3ft )
80 80, 70, 60, 50, 40, 30, 20
70 80, 70, 60, 50, 40, 30
60 70, 60, 50, 40, 30, 20
50 60, 50, 40, 30, 20
40 40
95
30 40
TABLE 3 Continued
165
TABLE 4 Three phase flow test points (water, oil, and air) Quality(%) Upstream Pressure (psi) Volumetric Air Flow Rate ( min/3ft )
50 20 20
40 30, 20
30 27, 20 60
20 20
60 50, 40, 30, 20
50 40, 30, 20
40 30, 20 70
30 20
80 70, 60, 50, 40, 30, 20
70 60, 50, 40, 30
60 50, 40, 30, 20
50 40, 30, 20
40 40, 30, 20
30 30, 20
80
20 20
80 70, 60, 50, 40
70 60, 50, 40, 30
60 50, 40, 30
50 40, 30, 20
40 40, 30, 20
30 28, 20
90
20 20
166
TABLE 5 Curve fit functions for the water cut meter
Flow
Condition Equation
4325432 )y(lnj)y(lni)y(lnhylngfxexdxcxbxaz ++++++++=
(x=Risetime, y=Superficial Velocity, z=Quality)
a=-3043.58773 b=120.0802616
c=-1.88811718 d=0.014794584
e=-5.7765e-05 f=8.99185e-08
g=-1.69089933 h=1.351852288
Water and
Air
i=-0.45449208 j=0.051522869
54325432
yk
yj
yi
yh
ygfxexdxcxbxaz ++++++++++=
(x=Delaytime, y=Superficial Velocity, z=Quality)
a=2.82295566 b=-0.12869866
c=0.003624454 d=-4.8687e-05
e=2.98988e-07 f=-6.826e-10
g=-24.9577745 h=798.4796342
i=-8987.71923 j=44209.85323
Water and
Air
k=-80307.0121
167
Flow
Condition Equation
4325432 jyiyhygyfxexdxcxbxaz +++++++++=
(x=Risetime, y=Superficial Velocity, z=Quality)
a=-817.999233 b=31.29597108
c=-0.47576922 d=0.003593564
e=-1.3483e-05 f=2.01054e-08
g=0.052038191 h=-0.00673208
Oil and Air
i=0.000313309 j=-4.7577e-06
54325432 kyjyiyhygyfxexdxcxbxaz ++++++++++=
(x=Delaytime, y=Superficial Velocity, z=Quality)
a=3.60526125 b=-0.18194679
c=0.005664081 d=-8.5955e-05
e=6.19823e-07 f=-1.7122e-09
g=-0.10874772 h=0.018247324
i=-0.0014671 j=5.35436e-05
Oil and Air
k=-7.1618e-07
TABLE 5 Continued
168
VITA
Sang Hyun Park is the son of Kil Yong Park and Eun Hee Cho. He was born on
Febuary 10, 1977 in Seoul, Republic of Korea. He has a brother, Sang June. He graduated
from Hwa Gok High School in 1995. In 1999, he received his Bachelor of Science degree
in mechanical engineering from Yonsei University, Republic of Korea. He served two years
and two months in the army of joint forces of the Republic of Korea and the United States
of America between 1999 and 2001 and was dismissed with the rank of Sergeant. He
worked 8 months at the Korea Aerospace Research Institute as research assistant in 2002.
He enrolled in the Master of Science program in mechanical engineering at Texas A&M
University in 2002. His permanent mailing adress is 117-807 Daewoo Apt. Hwa Gok 3
Dong Kang Seo Ku Seoul, Republic of Korea.